Monday, May 5, 2014

HOW LITHICS REALLY WORK


SOLLBERGER'S HOUSE IN DALLAS




HOW LITHIC STONE REALLY
              REACTS TO FLAKING FORCES  

 
A LOST ESSAY BY:

                                                                   J. B. SOLLBERGER



 

                                                          ABSTRACT

 

          This report describes the distortions of lithic stone from the instant of first force contact externally to internally that produce designed fracture and abortions.  Fracture propagation is traced in-continuum from surface deformation and internal particle compression through the events of  1)  The bowl of compression.  2)  The fracture ring crack.  3)  The cone or part of the cone.  4)  The cone flare regression to complete the bulbar aspect.  5)  The six facets formation of a common flake.  6) 

  The forces that guide a fracture front.  7)  The mechanics of fracture abortion.

 

 

                                                        INTRODUCTION

 

          As an amateur archeologist's since the late 1920's I have studied fracture in brittle elastic stone from empirical evidence.  Since the Crabtree years of 1966 onward, I have practiced the art of replicating chipping stone tools.  On reading J. D. Speth (1972), his reply to me was that we did not speak the same language.  Faulkners (1972) dissertation convinced me that our stone must be studied as being a particulate solid – not on the large scale of grain size.  Moffat (1981) made a conclusion that archaeologists must develop their own fracture theory based on the physical sciences because the engineering world did not address archaeological fracture problem.  My text was so guided in development.

 

          Cotterell and Kamminga (1987) should reflect the state of the art on fracture studies in lithic stone.  However, I cannot without serious omissions, find a continuum of their instigations, propagations, and termination, from which they describe THE FORMATION OF FLAKES.  My text should be read not as criticism, but as an attempt to fill some of their omissions on the basis of how my empirical evidence has been developed and tested over a half of a century.

 

          In text, I have argued that Cotterell and Kamminga have badly miss-used their Hertzian fracture concept.  That modern replicators of stone age tools do not reproduce “text book” cones.  I have presented new insights on stone distortions by flaking forces that relate directly to fracture morphology that others have ignored.  On the basis that our stone is elastic, some examples are; Endenters form various shapes of a bowl of compression.   The rim of a bowl of compression locates the ring crack of fracture inception.  A force of secondary compression, set up by bending, influences fracture trajectory and feature formation.


          Cotterell and Kamminga (1988) list sixty nine references.  My question is:  How many of those texts are instructive to archeologists?  Should we mathematically calculate the amount and type of force, the fracture velocity, there stones chipability etc., for each of the perhaps 1000 flakes that may be required to reproduce a fine Eden type point?  Must we consider also Rayleigh force waves when no one understands them to have a functional value in fracture?  How meaningful to archeologists are cantlever beam tests, sawed stone blocks slotted with sawed grooves, clamped to steel tables, compressed to fracture by hydraulics or steel screws.  Does every engineer need to tell us that fracture to instigate, must first find a surface flaw? 

 

          Recent high magnification photographs show our stone to be crowded with flaws and rods and visiculations filled with water to about two percent of the mass weight that can be thermally eliminated.  Must we believe Cotterell and Kamminga (ibid) that only the bipolar flake types are compression force fractures when no archeologist can make chipped stone tools without applying compression to load a flaking platform?

 

          Archeologists - all, have waited and depended on the engineering world to provide us our fracture knowledge.  So, we have an abundance of knowledge that does not apply to our research.  Personally, I am in debt to industrial fracture research.  My test is an effort to separate the chaff from the wheat; to eliminate the extraneous.  To describe the act of fracture from instigation to whatever termination under stone age conditions and to base all topics on empirical evidence.  My story must begin with cone fractures because all flakes by both man and natural forces start as cones or cone parts.  Please note that I did not say – Hertzian Cone fracture.

 

 

                                                          LITHIC STONE

          Our stone is a silica mineral solid whose chemistry and properties has been described by others.  Shepherd (1972) is an excellent reference.  In order to perform precise fractures, the variously named flints, cherts, volcanics, etc, must be free of foreign imperfections and be isotropic in fracture.  Isotropic, means it can be fractured in any direction from a suitable flaking platform.  Above all, true or not, our stone must be considered to be a particulate solid.  A particle must be seen as being smaller than a grain in size and the whole must be uniformly bonded to the same strength.  In the real world, that will not always be true.

 

          Others have determined that various stone types may range from 50 to 500 times stronger in compression than in tension.   The greater strength in compression over tension is the property that makes possible, controlled fracture reduction of a mass into a preconceived form of product.

 

          Fracture instigates in practical terms, only across a surface where a tensional stress has increased to exceed the stones elastic strength.  Fracture propagates below that surface as tension extends deeper into the stone and increases to exceed the critical level of particle layers in-depth.  Therefore, fracture extends over a period of time and as we will see later, its velocity is subject to increases and decreases according to volume changes just beyond the fracture front.

 

 

                                                         

                                     THE BOWL OF COMPRESSION

 

          Cotterell and Kamminga (1987: Figure 4) do not recognize a bowl of compression in THE FORMATION OF FLAKES.   In their discussion and illustrations, they show no deformation of either the percusser tool nor the spot loaded in the mass.  A bowl of compression was reported by Sollberger (1981:  13-15).  The bowl of compression (bc) is important to fracture studies.  It is particularly important to fracture interpretations even though its presence in form is limited by the withdrawing of flaking force.  The bc does a number of things.  It determines the radius of the ring crack of instigation for cones and flakes.  The bc diameter to its rim at the instant of ring crack inception in relation to its depth at that instant, determines the diffuseness or saliency of the bulb of force fracture formation on flakes and blades.  Other factors may also apply.

 

          On the reality of the bowl of compression:  It is common language among flintknappers to say:  The ring crack opens just outside of the diameter of force contact.  Turner, et al (1967) state:  “the fracture ring crack circle opens in a field of tension at a 12-20% greater diameter than the diameter of force contact”.  Those references must certainly refer to a bowl of compression, forms differently according to flaking platform configuration and location.

 

                  

                                     HERTZIAN CONES AND NON HERTZIAN

 

          Hertzian cones were named after Hertz (1896).  Cotterell and Kamminga (1987) still maintain that cone flare angles are about 136 degrees and Hertzian cones represent the initiation phase or proximal ends of conchoidal flakes.  I argue here that the term Hertzian is wrongly used because that term to be correct must conform to the rigid specifications for Hertzian cone fracture which are found in Speth, (1972) and Faulkner (1972).  One must deviate from vertical to the spot loaded, from well inside of the outer free mass face, and add an outer force component to the Hertzian line of applied force, in order to form the force blub of flakes and blades. 

Non Hertzian cones are the ones made by natural forces and by stone age man over the past million years.  They do not flare as greatly as Hertzian cone fractures nor is their maximum fracture depth possible limited to about three times the radius of force contact.  Hertzian loading and the depth of produced face tend to be much straighter than the marked convexity on the bulbar length of conchoidal flakes.  That length convexity on common cones is the direct result of the outward force cracking open the negative cone cavity of the mass which is a prior fact to be accomplished for converting cones to conchoidal fractures.

 

I assert here that the mechanics of conchoidal fracture are so different from flakes and blades that they should be considered to be only one form of flaking.

 

          With hammer stones, pointed Brandon type English blade making hammers, and various weights of steel sledge hammers I have made dozens and dozens of cone fractures into masses of flints and chert and retrieved them for accurate measuring.  The maximum flare angle that can be made in thick stone is not as great as 136 degrees nor 140 degrees as cited by Moffat (1981:201).  It is only 120 degrees and smaller.  Return now to Cotterell and Kamminga (ibid: 685) where they cite the cone fracture diameter to be “about one and a half times that of the ring crack”.  In the real world of stone knapping as we shall see, that citation is wrong.  Please refer to Figure 1 herein. 

 

          Other problems in our literature regarding cone fractures in the real world of execution are, that no one reports the common occurrence of biangular faces on both cones and flakes.  Archeologists do not recognize that cone flare angle can be regulated to form between about 67 degrees and 120 degrees by predetermining the diameter and depth of the bowl of compression by the size and hardness of force contact from the percusser tool.  It is not recognized that cones in flakes are not Hertzian but are common asymmetrical cones of many divergent forms which will be discussed following what I term the text book form drawn as Figure 1.A.  On Figure 1, letters dfc represent the diameter of force contact.  Letters mdp represent maximum depth possible.  Flare angles are noted in numerals.  A, is drawn deeper that text book specifications while 3 and C, are drawn to scale.

 

          Cone Figure 1.3, has a flare angle of 113 degrees which is a significant 22 degrees below the conventional 136 degrees.  The flare angle of cone C, is 67 degrees which is 68 degrees below the angle that everyone quotes everyone else as being correct for Hertzian cones.  The ring crack diameter of C is 1.0 mm.  The depth of fracture if 9.0 mm, which is six times the maximum text book depth for Hertzian fracture.  Cone 3, has a ring crack diameter of 10 mm and a vertical depth of 23.5 mm.  It had greater depth which I lost in retrieving it from the mass.  However, the text book formula of depth being limited to about one and a half times the diameter of force contact is clearly wrong.  The length of the face between the platform surface and the far edge of retrieval from the mass is 43.0 mm which is 28.0 mm in excess of 1 ½ contact diameter. 

 

In discussion on Hertzian loading, I find that the smallest cone flare angle can be made only with an iron hammer that has been filed to a sharp point.  The largest flare angles result from ten pound three inch diameter sledge hammers.  Archeologists should be interested in the cones produced by past and present stone workers made by hammer stones of the real world.  They will then find that a vast majority of cone fractures have flare angles between 120 degrees and 80 degrees. 

 

 

                             CONES BY NATURAL FORCES

 

Natural forces have made cones and flakes by uncountable millions.  The attributes of those cones are identical to man-made cones.  No one can distinguish between percussion and pressure cones.  Figure 2 is a typical example.  The mass was found on a river gravel bar.  My first strike for a flake blank caused the old water stained fracture to pop off and expose the upper part of a cone made by natural forces.  Its ring crack diameter is 10.0 mm.  The cone flare angle is 80 degrees.  The exposed depth is 8.0 but the crack extends deeper.  The only conclusion possible is that the text book specifications for 136 degree cone flare angles is incorrect.

 

Let’s pause briefly from presenting fracture data from nature and modern flint workers.  I have shown you that the text book specifications for Hertzian cone fractures cannot be replicated by natural forces or todays flint workers.  My question is:  Am I the only one between Hertz (1896) and Cotterell and Kamminga (1897) to make and measure cone fractures?  If others have done so, where are their reports?

 

Our stone has long been described as being a brittle elastic solid.  Our percussers and pressure flaking tools have long been described as being endentars.  Why then, when such flaking tools instigate the fractures in full 360 degree circles, am I the only one to report that a bowl of compression, is endented into the stone surface?  Past fracture reports all say that ring crack arcs or circles instigate in a major surface flaw just outside of the spot of force contact.  Why not say that surface flaws are always plentiful and that the rim of the bowl of compression is the line where tension first exceeds the stones elastic strength?

 

               

                                              BI-ANGULAR CONES

 

          I have search archeological literature for the phenomenon of bi-angular cone fractures (Figure 4) and have found neither illustrations nor discussions for these common artifacts.  Figure 4, A-3, are prehistoric Indian made flakes.  A, has a bi-angular cone whereas 3 has a 340 degree ring crack below which is a normal, non-Hertzian cone.  Figure 4, A is from a Bell County, Texas site.  Flake B, is from a site near Uvalde, Texas.  For flake A as I found it, the remaining flaking platform surface is marked with pencil lines.  The ring crack diameter is 1.2 mm.  The upper cone-half flares to 84 degrees.  The lower cone half forms an apex angle of 30 degrees.  That is the lower face lacks only 30 degrees from being a true cylinder.  The eye can clearly see its fracture extending down into the flake mass.   The angle of applied force is estimated to be 45 degrees from the platform surface.  The measure of cone fracture depth is 28 mm.   

 

          Figure 4, -B, has a 340 degree ring crack.  The cone flare angle is 88 degrees.  Cone depth at maximum flare is 12.0 mm.  The ring crack diameter is 3.75 mm.  The angle of the applied force was not vertical to the platform surface but nearly so because the ring crack lacks 25 degrees being a full circle.  Flake B is 129 mm long by 73 mm wide by 26 thick.

 

          Figure 5 is a bi-angular cone in top view A, and profile B.  I made this cone with an English type of iron blade making hammer whose tip was filed to a point.   His five pound hammer was delivered with all of my arm strength.  The core mass was then flaked away from the cone as shown.  The ring crack diameter is 2.0 mm.  The upper cone flare is 79 degrees, to a depth of 19 mm.  That initial flare angle reduced drastically and continued as a cone fracture an additional 26.7 mm before decaying in the mass.  Using Speth (1972) as referenced by Cotterell and Kamminga (1987), the maximum depth attainable should be 1 ½ times the ring crack diameter which is 3.0 mm.  Instead, the cone fracture is 47.2 mm deep.  Question:  Am I the only archeologist who has ever made cones and exposed them for measuring?

 

 

             THE WHY OF BI-ANGULAR OR TWO FACED CONES

 

          Under Hertzian loading specifications single faced cones are fractured but only when the mass outside of the spot loaded is sufficient to provide uniform symmetrical force transfer into the mass.  For example, a hemispherical mass with the North Pole being the spot loaded by compression.  The convex-convex surface provides a fairly constant resistance volume to the flaring expansion of cone fracture propagation but only to a certain depth.  At the depth the fractures front is opposed by a suddenly greater resistance of mass distortion outside of the fracture front.  That greater outside volume has a greater resistance to being distorted, which causes the cone fracture to reduce its flare angle quickly to a lesser angle as I illustrate on Figures 4 and 5.

 

 

  

 

  

 

            ON PUNCHING OUT A CONE FREE OF THE MASS

 

On reading Speth (1972) or Faulkner (1972), we read that cone fractures cannot penetrate a thick mass deeper than about three times the radius of force contact but, many refer to cones punched out of thin sheet or plate glass.  On thick glass or stone, it is said that at a certain depth the primary cone ceases to propagate regardless of the amount of load or flaking force addition.  I can find no reference to cite which provides the mechanics for why cones can be punched out of thin plate but not thick.   I offer the following:  Hook’s Law of continuum distortion applies:  At the on-set of force loading the spot area of force contact deflates that spot into a shallow bowl which I have named the bowl-of-compression.  The bowl of compression has a rim where it joins the flat surface.  Prior to the instant of fracture, the particles of the mass below the lower face of the bowl of compression will be stressed in compression to a dished bottom and cone form not defined by fracture.  The intensity of distortion on these particles varies according to the various depth of the bowl of compression below the pre-stressed surface. 

 

When the bowl depth places its rim in critical tension, fracture forms the ring crack face.  The ring crack face depth is limited by the flare of particle compression below in its path of propagation.   The fracture then turns outward to define in fracture, the pre-established cone in compression.  The cone fracture will continue in propagation as long as the force maintains a critical value of compression below the circle of the fracture front.  As the freed height of the cone lengthens, the cone diameter between the bowl of compression and the fracture front expands under Hook’s Law.  That diameter increase around the fracture front will press the cone volume against the mass volume thereby closing the crack faces together to prevent any further fracture unless the bottom of the cone of compression has began to distort the under face (surface) outward.  If that happens, it will open the crack faces and allow the cone to be pushed out clear of the mass.  When a mass thickness is such that its lower face cannot be bulged outward by the hemispherical central front of an approaching cone of compression, that thickness does provide a maximum debth for cone fracture penetration.  That limitation is certainly not the text book statement.

 

My data on Hertzian loading and cone fracture proves that our text books are wrong for archeological studies on Stone Age fracture.  You cannot produce cone fractures to the metrics of text book specifications.  You cannot produce small radium ring cracks with larger radius tool contacts.  My concept of, bowl-of-compression, is proven by the cone fracture metrics given.

 

 

 

 

                  HOW AND WHY FLAKES DIFFER FROM CONES

 

Cone fractures develop their major amount of critical tension from the mass side around the fracture front.  Cone volumes are force distorted downward only, within their negative fractured cavities.  Cones become flakes when starting at the ring crack faces, the mass cavity is opened by new fractures.  The continuum of these mechanical events are described from Figure 6.

 

Figure 6 illustrates a typical, common flake.  Note the following:  The angle of applied force is directed towards the lower middle of the mass dorsal face.  The bowl-of-compression, its rim, and deflation below the pre-stressed position, all indicate that the flaking load is in-place.  The profile shows fracture accomplished, down to just below line BC which is bulbar formation completed.  Line MBE, marks the maximum depth of bulbar expansion which is the cone fracture feature.  Note that the cone crack dies before reaching the dorsal face.  It dies because the triangle of mass above the cone fracture was too thin and weak in that small volume (too close to outer free face).

 

The ventral face view shows that a common flake develops six facial facets not including the transition face that surrounds the bulbar protrusion.  Starting at the bottom of the ring crack face, only the cone face is fractured down to short of line MBE.  That length allows the angled applied force to start an added distortion to that freed Length – outwards.  The outward distortion provides two lines of critical tension to open two new fractures.  These two progress from the ring crack face outwards toward establishing the upper width of a flake.  They each also propagate downward and outward as a transitional curve from the cone face.  Faces 3 and 3, are tear fractures because they are above and outside of the cone of compression.  As the flakes lateral edges lengthen downward, the outward directed force begins to widen the fracture crack.  That force distortion starts shifting tension development from the mass side of the cone fracture front, to greatest on the cone side.  That shift is completed along line MBE which technically, ends the cone fracture aspect.  The cone fracture ceases to increase its flare radius and starts Figure 6: face 5 as bulbar flare reduction.  Fracture advance down face 5 plus the lengthening of faces 3 and 3 down the flakes lateral margins, opens the fracture races between the mass and the flake at line BC.  Line 3C marks the end of bulbar regression as well as being the arced line where fractures 3 and 3 join the start of face 4.  The joining of faces 3 and 3 with face 5 places all three for the first time into a single united fracture front cross the full width of the flake which further widens the crack faces.  That widening stops all bulbar regression and transitions the thinning of the flake from a dorsal direction to downward as the dashed trajectory shown on edge-view of Figure 6.  Face 6, the dashed projection, can take one of several different trajectories by manipulation the direction of critical tension formation below the crack front to be into the flake or into the mass.  The details are as follows.

 

 

                     ON THE ACT AND PROPOGATION OF FRACTURE

 

From Figure 5 the mechanics of the first five stages of flake facial formation have been described.  Bulbar regression was completed to start face 6.  On Figure 7, face 6 fracture has been arrested in propagation in order to detail the mass distortions that are the act of fracture along the continuous fracture front from margin to margin of the flake.  The following conditions are in-place in continuum:  The flake volume if fully charged in compression down to letters NN which indicate neutral stress in the mass and flake.  The three pronged arrow-C, represent the greatest advance of the compression front (force wave).  Note that compression is spreading into the mass directly below the fracture trajectory.  Note that the angle of applied force on the flaking platform is widening the fracture gap.  That widening the bending which forms Secondary Compression – SC, on the flakes dorsal face (See Sollberger 1986:101-105).  Note that the mass is stress free – N, down to just above the fracture front because the passage of fracture has relieved the upper mass of stress.  Now, note the circle drawn half in the mass and half in the flake.  This circle is the fracture process zone that follows the advance of the compression front.

 

The stresses in the process zone are as follows.  On the mass side, the particles being split are distorting downward because of the flaking load on the platform.  They are resisting outward tensional pull inward and upwards in the mass.  As they split, tension is release inward and upward of the mass face.

 

Looking now at the process zone in the flake, the three pronged arrow shows compression invading the mass below the fracture crack front.  The particles are being stressed downward and dorsally by the outward tensional pull of opening the crack front in continuum of fracture propagation.  The mass side of a fracture front is constantly being stress-relieved by fracture propagation while the flake side at and below, is constantly being charged in compression.

 

 

                                 ON GUIDING A FRACTURE

 

Cotterell and Kamminga (1987:694) tell us that the fracture time interval is measured in milliseconds.  That it is impossible for a person to manipulate the indenter in such a short time.  They and others have largely looked at externals such as applied force angles and outer core face geometry.  In this report, my focus is on the internal stress developments and their effects on the fracture front.  I have described how cone flare can be regulated within reasonable tolerances.  How force bulb formations expand and regress in fracture radius.  That typical flakes have six discrete facial formations that are defined from inside the core to outside.  The act-of-fracture has been detailed.  Therein, I said that compression below a fracture front was constantly invading the mass from just below the approaching fracture front.  Controlling that invasion (Figure 7) starting at line BC – Figure 6, can produce the following results.

 

When the freed length is minimally widening the fracture gap crack front, critical tension develops primarily in the mass at and below the crack front which produces concave flake length.  When freed length is moderately widening the crack front, more tension is shifted to the flake side at and below the crack front to produce a straight fracture trajectory.

 

When the freed length acts as an outward pulling lever across the crack front, still more critical tension shifts to the flake side which guides the flake length convex.  For full length ventral face convexity, I refer you back to Figure 3, conchoidal flake formations.

 

          The angle of exterior applied force is not the whole story.  The leverage action on freed length of a flake at the crack front is the prime mover for fracture trajectory.   Core rotation and deflection changes the angle of applied force within the fracture time interval.  Flintknappers compensate for trajectory control by varying the degree of rotation and deflection with differing holding and support systems.  The action within the process zone is significantly altered by whether or not the flake is bending or buckling between the applied load and the fracture front.  See Sollberger 1985 and 1986.

 

          I turn now to some specific flake types or categories.

 

 

                                                  CONCHOIDAL FLAKES

 

          Before fracture analysis by archeologists, flints were described as being stones that broke with a conchoidal fracture. Conchoidal fractures means being in the shape of one face of a mussel or clam shell.  Cotterell and Kamminga (1987:675) say, “despite popular belief, flakes are not all of the conchoidal variety”.   Those authors describe a “bending flake” as being not conchoidal because “they have no force-bulb formation.”  Their use of the term conchoidal includes specialized cores and flakes such as polyhedral core blades.  On some of those blades the entire bulbar formation covers less than one twentieth part of the whole face.  Most mussel and clam shells have a totally “bulbar” surface.   So, a fuller description of the mechanics of conchoidal flaking seems to be in order.

 

          Figure 3 illustrates two examples of true conchoidal flakes.  Conchoidl fractures used as tools, are also called fan scrapers, ulu knives, squaw knives, and side-struck flakes.  The in-common attributes are that they are struck from flat faced thick edged tabular cores with largely little or no platform preparation.  Therefore, their dorsal faces are likely, cortex covered.  Their width is generally greater than length (Figure 3) because the wide straight junction of the platform face to the core face minimize and delays the outward opening of the fracture crack below the upper surface. Consequently, the bulbar form frees much wider and deeper before bulbar regression can start.  (Please review Figure 6: line MBE, and the shifting of major tension from the mass to the flake side of the fracture front).

 

          Conchoidal flakes are an intermediate form between cones and designed flakes.  Those such as Figure 3 are to be avoided because they ruin the process of core preparation for flake blanks and or bifacing.  The expression that flints break with a conchoidal fracture is grossly over used.   I have followed wheel ditching machines for miles spewing out soft limestone conchoidal flakes at the rate of several hundred per minute.  Regarding Figure 3 your eye should tell you that the greater than 90 degree hinged terminations formed because the compression value beyond the fracture front dropped too low.  That the fracture type change from compression-led to fracture-in-bending.  The extreme length width convexity tells you that early on, fracture supporting tension was shifted from the mass side to the flake side in the fracture process zone.  The undulation ripples starting above maximum cone flare tell you that the fracture velocity was too low relative to a decelerating compression front.  Probably, all of the above was enhanced by core rotation because of the lack of sufficient anvil support.

 

          Figure 3, upper, the biangular formation.  The angle of applied force was directed to obtain greatly longer fracture.  The core mass was light in weight relative to the weight and velocity of the percusser.  The cone face was being defined by fracture but the core mass quite suddenly was deflected and rotated.  The result being a sudden shift of compression propagation from in to the mass to away from the mass.  The result was bulbar regression became an angle.

 

 

          BENDING TYPE FRACTURE VERSUS COMPRESSION-LED FRACTURE

 

          Cotterell and Kamminga (1897: 675; 689-690; figure 4 and Figure 12) describe a new flake type which they term the Bending Type.  Their description is that bending type flakes are not “Hertzian” because they have no bulbar formation.  They describe a classic bending type as being “waisted” in fracture initiation.  In their words the recognition of bending flakes is long overdue.  Their Figure 12 ideal includes a long flake length with cross-sections so their discussion is not limited to an initiation stage.  Their error in naming bending flakes is confusion between what is bending, and what is particle volume distortions by a load of flaking force.  Their over-all error is the miss-use of Hertzian loading specifications by combining cone fractures and flake fractures into one and the same thing.  I have already provided the mechanics for their separation. 

 

          First, fracture-in-bending, requires that both the upper and under face of a nucleus start bending concomitantly.  Bending places the inside of the bow in compression while placing the outer convex surface in tension until fracture inception occurs (Sollberger 1981:1986).   The line of fracture will be essentially a straight line along the crest of the bend.  The authors (ibid) inception line is a uniform radius formed by a non-Hertzian bowl of compression the rim of which is greatly more remote from the diameter of force contact than Hertzian loading. 

 

Explanation:         

 

          To be Hertzian, the load must be vertical to the surface well inside of any outer free face.  The loaded spot is punched down to form a rim around the spot.  There is no surface particle compression outside of the bowl rim.  When the rim surface exceeds the stones elastic strength, the result is a 360 degree Hertzian fracture face of inception.  Violation of Hertzian is to load a spot near an outer free surface so that a symmetrical cone of compression cannot form.  Then, whether or not the angle of applied force is vertical, directed inward or outwards of the platform surface only a part cone can be fracture defined.  Violation of Hertzian loading to on-the-edge, or closely behind-the-edge, commonly distorts the nucleus in compression outside of the spot of force contact a considerable distance across a platform surface.  That distance to inception increases as bowl-of-compression distortion as long as the wedge of nucleus distortion between the platform surface and the outer face of the internal undefined by fracture cone of compression are in distortion as a unit.  When the surface distortion arc radius stabilizes and ceases to increase, that extended bowl rim builds to a critical tension for ring crack fracture inception.  That face depth continues until it is turned by is joining the outer face of the internal primary force cone of compression flare.

 

          Please refer back to Figure 7; Line MBE which describes cone flare and bulbar regression.  When a deep lipped face of inception intersects the cone flare above line MBE, both cone fracture flare and bulbar regression are defined on deeply lipped flakes.  When the face of instigation meets the cone of compression below line MBE, only bulbar regression is defined by fracture.  That intersection is always above Figure 7; line BC.

 

          My photographs are honest, not idealized.  Figure 8; top row, are heavily lipped above clearly defined cone flare and bulbar regression.  Note that upper right is also “waisted”.  Figure 8; lower row all have bulbar regression thinning as just above Figure 7; line BC.

 

          The idealized flake drawn by Cotterell and Kamminga (1987; Figure 12) is a compression-led fracture on which the initiation crack face meets the inner cone of compression flare volume between my Figure 7; lines MBE and BC.  Therefore, only the lower part of bulbar regression is defined by fracture.  Those authors (ibid) say no blub was formed because they do not understand bulbar conversion mechanics in the continuum of fracture propagation.

 

          Lipped flakes most commonly form because the striking force contacts thin edges such as in bifacing.  Billets are most commonly used to prevent crushing those thin edges.  The edge indentation takes the form of a new moon (a crescent).  Both the upper and under faces are distorted locally.  The rim of that bowl of compression can be 10 mm. beyond the line of force contact.  Fracture instigation opens a deep arced face.   When that lipped face reaches the outer face of the internal cone of compression, the fracture is turned to be compression-led as described under flake length.  Fracture-in-bending always propagates towards the nearest outer free face of a mass.  It would be a mistake to adopt a, ending type flake, into archeological fracture mechanics.

 

 

                                        HINGE FRACTURES

 

          Cotterell and Kamminga (1987:705) write “more needs to be known about the mechanics of hinge fracture”.  Within the mechanics of fracture as presented herein, there is little to be learned about hinge fractures that is not known.  A hinge fracture is a 90 degree or more fracture turn from an established fracture trajectory towards the nearest outer free face of the mass being flaked.  Flintknappers commonly produce flake terminations where the hinge rolls a full 180 degrees (Figure 9).  Hinge terminations are intentional of some blade cores.  They are also by intent in producing flat faced bifaces where the individual flakes are called diving flakes.

 

          All hinges develop because the particle compression value just beyond the fracture front is suddenly dropped below the value needed to maintain the original fracture trajectory.  With practice a Flintknapper can produce hinges at will.  The mechanics are as follows.

 

          Hold a core by hand to allow some rotation and deflection by the compresser hammer strike.  Make the strike just strong enough for the fracture to reach the desired length.  Then, core deflection stops the original trajectory.   Core rotation hinges the angle of applied force to be drastically outward.  With the core now unloading itself of compression, the fracture type changes from compression-led, to fracture-in-bending to form the 90 degree roll towards the near outer surface.  As the fracture approaches the free surface, the bend by the outward flaking force sets up a stronger Secondary Compression (Sollberger 1986) which forms a second turn downward in order for the hinge to be freed from the mass.

 

          The 180 degree rolled hinge differs in that the flaking tool maintains a too low particle compression in the flake long enough to allow a stronger secondary compression to develop and the flaking tool still has a minor downward compression in the flake as the fracture crack opens from outward bending of the flake.  That combination of forces causes the first 90 degree roll to turn upward and become a 180 degree roll.  The height of the upward turn is limited by the width of the crack opened by outward bending of the flakes freed length.  When the flaking tool force closes that space, the fracture becomes a pure form of fracture-in-bending.  The final termination thru the dorsal face of the mass being the same as the 90 degree hinge roll.

 

          In flake and blade making, a prior hinge causes all flakes following to hinge also.  That is because the first hinge adds thickness to later ones at that length to increase their particle volume.  That added volume requires more time to reach a compression value to lead the following fracture but the striking force cannot wait.  It continues to bend the freed length away from the mass which forms another hinge as described above.

 

          Hinges also form when the percusser bounces up and off of the flaking platform.  That loss of force unloads the compression below the fracture front which stops the primary fracture.  The bounced hammer holds the flake bend in-place long enough for the hinge to form.  Great numbers of hinges are formed when the flake, blade or fluting channel flake buckle breaks between the flaking tool and the compression-front.

 

          Diving flakes, called also, super biface thinning flakes, have hinged terminations. 

They can change a biface cross section from convex convex, to concave concave.  That is the perimeter edges can be thicker than the central face.  The mechanics are, start the fracture from a small flaking platform where the flake will widen and thicken as it lengthens use a light horn billet with just enough force to carry the fracture to or slightly beyond the biface mid width.  The increasing particle volume over length reduces the compression value at that length to stop the primary fracture.  The outward element of primary force converts the freed length into a lever to produce the hinge roll.  Secondary compression (Sollberger 1986) in the dorsal face determines the final fracture form to termination.

 

          In this reply to Cotterell and Kamminga (ibid: 705), there is no relationship in hinge fractures to flaking tool types.  The flakes lineal edges can be feathered, thick or mixed.   The hinge roll width (not particle can start from either flat or convex ventral faces.  Figure 3 herein clearly shows a fully convex flake in width and length terminated by hinge fracture.  Figure 9 illustrates a rectangular flat faced core with a hinged flake removed from its negative cavity.  There is nothing of significance unknown about the mechanics of hinge fractures.

 

 

                 THE MECHANICS OF UNDULATION FRACTURE

 

          The Formation of Flakes cannot be fully detailed on the mechanics of applied force on the basis of inception, propagation, and terminations, as Cotterell and Kamminga (l987) have done.  The continuum of compression advance thru those three stages is three dimensional and fracture feature formations must be related to nucleus support types, nucleus other free face geometry, as well as acceleration and decelerations of the fracture front.

 

          There are two principle varieties of undulations that result from two causes.  The common variety is Figure 10: A.  The unrecognized variety is Figure 10: B.

 

Figure 10: A variety is the result of fracture velocity loss caused by an increased particle volume on the dorsal face surface such as a high ridge left by a bifacing flake removal.  The force conditions are:  The applied force compressed the flaking platform to start the compression propagation into the stone.  The following fracture inception opened a deep lipped face below which a diffuse bulbar formation opened.  The compression front at 40 mm length slowed its propagation in order to fill the volume added by the dorsal face ridge.  The decelerating compression front required a time interval to regain its value while filling the added volume.  In doing so, compression also invaded the core mass which required that the closely following fracture width to turn into the mass and free the flake to the bottom of the undulation valley.  Meanwhile, the compression front had accelerated because it had reached the reduced volume beyond the thick ridge.  That acceleration of compression front allowed the outward applied force to increase the leverage on the flake length to pull the fracture out of the valley because the outward bending of the flake length from the flaking platform was not decelerated as was the compression front. 

 

          With the flaking load, the rate of compression, and following tension, all resynchronized together, the fracture continued to the preform tip.  I will add that had the resynchronization not occurred in time, the undulation would have divided the preform by outrepasse, reverse hinge, or overshot fracture all of which are the same thing.

 

          Figure 10: B-left, illustrates a negative flake scar which is free of compression rings and undulations.  I made the preform face free of humps, flat spots, and prominent bifacing flake scar ridges.  Also, the fracture length propagation was compatible to the rate of outward leverage by the fluting tool.  I commonly produce such flutes on both faces when the preform is perfectly contoured.

 

          Figure 10: B right, illustrates an undulation for which the mechanics has not been recognized or described.  You can see that its valley cut thru the right lateral margin so that the flake contains a part of the opposite face of the preform.  Figure 10:  B undulation is a very severe form of a very common occurrence on long flute flakes, blades, and common flakes.  This variety can be identified on the basis of their close proximity to just below bulbar regression where the first five fracture facets are united into a common fracture front.

 

          The cause for this undulation is that the force load on the flaking platform lacked a sufficient outward leverage on the then-freed-length to shift a sufficient amount of tension from the core side to the flake side of the fracture process zone.  However, length propagation into the valley increased the mechanical advantage of freed length to pull the undulation back up to the flakes designed thickness.   All forms of undulation are the early stage of outrepasse.   Outrepasse occurs when the major tensional development remains in the mass side or a fracture front.

 

 

   PLUNGING FRACTURE ARREST FOLLOWED by a FINIAL EXTENSTION

 

          Cotterell and Kamminga (1987: 701) tell us that plunging fracture is caused by the end of the core.  No mechanical explanation is provided other than reference to Crabtree.  Not true.  Students of fluted projectile points often term plunging, a reverse hinge fracture.  Such frequently occur in the proximal end of a preform.  Plunging is a long radius outrepasse.  It is the result of a strong compression front spreading into the mass below the fracture front as a result of insufficient outward leverage by the reed length of the flake.  Plunging can be arrested to become an undulation (Figure 10), or it can be turned downward as per Figure 11.

 

          Figure 11 illustrates a full length unbroken channel scar on which the plunging turn turned again short of the rear face.  The channel flake (left) has a deep lipped ring crack, a very low bulbar profile.  The flake certainly was not by fracture-in-bending.  The channel flake did not shorten the original preform length.  Impossible?

 

          Well, such are not uncommon to me.  When the preform is clamped vertical to an immovable integral to the clamp tip support board (Sollberger, 1985) many abortions are prevented.

 

          Tip support prevented the inward turn from being completed through the rear face.  Tip support prevented distal end bending rearward by the flaking force and the out-leverage of the flake length.  Lineal edge clamping provided for no rotation or deflection of the core place.  The lever force, forty to one, took the advantage that flints may be fifty to five hundred times stronger in compression than in tension.  That’s saying that both ends of the core had elevated strength at the instant of fracture inception; then when the fracture made its turn towards the rear face. That face was strong enough to allow the outward leverage by the now longer flake length, to shift critical tension over to the flake side of the fracture process zone.  From that shifting, the fracture continued and intersected the ground preform tip.   From Figure 11, you can see that the distal end of the flake is 5.5 mm thick and the distal end of the core piece is only 2.0 mm thick.  The plunge turn started 23 mm above the distal end.

 

          Those who relate any anvil support to bipolar fracture consider Figure 11.  The prepared platform was the same size as the tip resting on the tip support board.  Both ends were loaded in compression equally and simultaneously.  So why does fracture always instigate proximally?  The answer is that the volume lateral to and behind the flaking platform were outside of the cone flare of compression deflation.  The more acute angled tip end was completely inside of the cone flare distally, therefore no surface for a critical tension to develop.  So, the entire preform volume was loaded between the two cones.  The full length fracture had to invade partical compession full length.  Review – Figure 7.

 

                                                                

                                                          FINIALS

 

          Cotterell and Kamminga (1987: 701-705, Figure 4) describe finials as fractures that have turned away from the initiation face to create a thin and often fragile extension to the flake ending.  They describe these endings in terms of inflexed (down), reflexed (up-turn), and pseudo bifurcation.   Lenoir (l975) called them languette or tongue fractures.   Faulkner (19847: 328) called simple bending terminations hang nails.  Sollberger (1985: 101-1405) described the mechanics for finial extensions.   More can be said on the mechanics of finials that Cotterell and Kamminga provide.

 

          Their term pseudo bifurcation, means false branching.  Contrary to authors (ibid: Figure 4), fracture in bending makes at times, true branching’s that free whole unbroken pieces as per Sollberger (l986:  Figure 3).  Finials do not necessarily form at flake endings as described above.  They occur as most all snap breaks and hinged forms (Sollberger 1986:  Fires 1-2-3).  Those long thin extensions are not confined to flake endings.  For example, see one on the nucleus herein Figure 11: right.

 

          Drawings are teaching aids and should be technically correct.  The authors (ibid: Figure 4) step fracture (a) cannot start its dorsal turn from the very end of the primary fracture as a square turn.  It must be a rolling hinge.  Its final end must also roll because of secondary compression.  Step (b) must also terminate as a roll because of SC.

 

 

 

 

                                                  DISCUSSION

 

          Most fractures are completed in less than a millisecond over time.  So, how can one be sure about such things as, bowl of compression?  Be practical.  Use a synthetic sponge.  Lay it on a table.  Use a pencil as an indenter.  Push in slowly and release slowly from all surfaces corners and edges.  You can observe and analyze all shape deformations.  Compression will flatten the round holes.  Tension will elongate the holes towards the stress source.  Simple bends will do the same but on opposite faces of the bend.

 

          To check outward displacement of a freed length being responsible for force bulb conversion, take a half round length of paper, cardboard, sheet metal or pipe.  Secure one end.  Apply a down and out force to the free end.  When the bending displacement starts, you can see the radius of the bend increase towards flat across.  As the bend increases on pipe for example, the compression in the outside of the bend changes into tensile stress which thins that wall thickness.  Conversely, the inside wall thickness becomes thicker.  The originally round shape becomes a wide oval between the inner and outer faces.  Pipes or solids, it makes no difference.  Your micrometer will prove it.  Such simple demonstrations prove the force of secondary compression, the shifting of compression from the mass side to the flake side of a fracture front and, the redistribution of flaking compression from cones to bulbs, to flake lateral flatness.

 

 

          My text has been accumulative.  Refer backwards and forward.

 

 

 

                           TERMINOLOGY

 

 

Bowl of Compression,  bc, is the surface distortion made by flaking force contact.

 

Rim of the bowl of compression, is the arc or circle crest at the instant of fracture inception.

 

Secondary compression, is the particle volume placed in compression by bending.

 

Flake, is a piece that is usually wider than thick that has a bulbar formation in whole or in part at the proximal end.

 

Shatter refers to multiple flakes, broken pieces, etc. without force bulbs.

 

Compression-led fracture, includes all flake types.

 

Fracture process zone, is the layer(s) of particles being fractured.  The crack-front propagation zone.

 

Outward leverage is a fracture directional control in the process zone.

 

Fracture crack front is the layer of particles next to be fractured.

 

Cone fracture, is in the shape of a cone.

 

Force bulb, is a fracture form on which the upper one part ceases its outward flare to a reducing radius at the on-set of outward distortion of the then-freed length.

 

Tear fracture(s), are the faces outside of the flare angle of effective particle compression of force bulb formations.

 

Bending fractures, are the result of concomitant bending of both faces of  nucleus or flake to a critical tension.  The fracture propagates towards the nearest opposite face.

 

Fracture, is the formation of two faces within a solid as a progression below a surface.

 

 

                                                      LIST OF FIGURES

 

 

Figure 1    Hertzian, versus Stone Age cones

 

Figure 2    A cone made by natural forces

 

Figure 3    Conchoidal flakes

 

Figure 4    Two prehistoric Indian flakes – Compare cone types

 

Figure 5    Two views of a biangular one

 

Figure 6    The six fracture faces of a common flake

 

Figure 7    Mechanics of fracture:  Act of & Trajectory

 

Figure 8    Lipped, versus bending flake mechanics

 

Figure 9    Hinge fractures.


Figure 10 Undulations, two categories

 

Figure 11 Plunging fracture, arrested

 

 

 

 

                 HOW LITHIC STONE REALLY REACTS TO FLAKING FORCES  

 

                                                                   J. B. SOLLBERGER

 

                                                          ABSTRACT

 

          This report describes the distortions of lithic stone from the instant of first force contact externally to internally that produce designed fracture and abortions.  Fracture propagation is traced in-continuum from surface deformation and internal particle compression through the events of  1)  The bowl of compression.  2)  The fracture ring crack.  3)  The cone or part of the cone.  4)  The cone flare regression to complete the bulbar aspect.  5)  The six facets formation of a common flake.  6) 

  The forces that guide a fracture front.  7)  The mechanics of fracture abortion.

 

 

                                                        INTRODUCTION

 

          As an amateur archeologist's since the late 1920's I have studied fracture in brittle elastic stone from empirical evidence.  Since the Crabtree years of 1966 onward, I have practiced the art of replicating chipping stone tools.  On reading J. D. Speth (1972), his reply to me was that we did not speak the same language.  Faulkners (1972) dissertation convinced me that our stone must be studied as being a particulate solid – not on the large scale of grain size.  Moffat (1981) made a conclusion that archaeologists must develop their own fracture theory based on the physical sciences because the engineering world did not address archaeological fracture problem.  My text was so guided in development.

 

          Cotterell and Kamminga (1987) should reflect the state of the art on fracture studies in lithic stone.  However, I cannot without serious omissions, find a continuum of their instigations, propagations, and termination, from which they describe THE FORMATION OF FLAKES.  My text should be read not as criticism, but as an attempt to fill some of their omissions on the basis of how my empirical evidence has been developed and tested over a half of a century.

 

          In text, I have argued that Cotterell and Kamminga have badly miss-used their Hertzian fracture concept.  That modern replicators of stone age tools do not reproduce “text book” cones.  I have presented new insights on stone distortions by flaking forces that relate directly to fracture morphology that others have ignored.  On the basis that our stone is elastic, some examples are; Endenters form various shapes of a bowl of compression.   The rim of a bowl of compression locates the ring crack of fracture inception.  A force of secondary compression, set up by bending, influences fracture trajectory and feature formation.


          Cotterell and Kamminga (1988) list sixty nine references.  My question is:  How many of those texts are instructive to archeologists?  Should we mathematically calculate the amount and type of force, the fracture velocity, there stones chipability etc., for each of the perhaps 1000 flakes that may be required to reproduce a fine Eden type point?  Must we consider also Rayleigh force waves when no one understands them to have a functional value in fracture?  How meaningful to archeologists are cantlever beam tests, sawed stone blocks slotted with sawed grooves, clamped to steel tables, compressed to fracture by hydraulics or steel screws.  Does every engineer need to tell us that fracture to instigate, must first find a surface flaw? 

 

          Recent high magnification photographs show our stone to be crowded with flaws and rods and visiculations filled with water to about two percent of the mass weight that can be thermally eliminated.  Must we believe Cotterell and Kamminga (ibid) that only the bipolar flake types are compression force fractures when no archeologist can make chipped stone tools without applying compression to load a flaking platform?

 

          Archeologists - all, have waited and depended on the engineering world to provide us our fracture knowledge.  So, we have an abundance of knowledge that does not apply to our research.  Personally, I am in debt to industrial fracture research.  My test is an effort to separate the chaff from the wheat; to eliminate the extraneous.  To describe the act of fracture from instigation to whatever termination under stone age conditions and to base all topics on empirical evidence.  My story must begin with cone fractures because all flakes by both man and natural forces start as cones or cone parts.  Please note that I did not say – Hertzian Cone fracture.

 

 

                                                          LITHIC STONE

          Our stone is a silica mineral solid whose chemistry and properties has been described by others.  Shepherd (1972) is an excellent reference.  In order to perform precise fractures, the variously named flints, cherts, volcanics, etc, must be free of foreign imperfections and be isotropic in fracture.  Isotropic, means it can be fractured in any direction from a suitable flaking platform.  Above all, true or not, our stone must be considered to be a particulate solid.  A particle must be seen as being smaller than a grain in size and the whole must be uniformly bonded to the same strength.  In the real world, that will not always be true.

 

          Others have determined that various stone types may range from 50 to 500 times stronger in compression than in tension.   The greater strength in compression over tension is the property that makes possible, controlled fracture reduction of a mass into a preconceived form of product.

 

          Fracture instigates in practical terms, only across a surface where a tensional stress has increased to exceed the stones elastic strength.  Fracture propagates below that surface as tension extends deeper into the stone and increases to exceed the critical level of particle layers in-depth.  Therefore, fracture extends over a period of time and as we will see later, its velocity is subject to increases and decreases according to volume changes just beyond the fracture front.

 

 

                                                         

                                     THE BOWL OF COMPRESSION

 

          Cotterell and Kamminga (1987: Figure 4) do not recognize a bowl of compression in THE FORMATION OF FLAKES.   In their discussion and illustrations, they show no deformation of either the percusser tool nor the spot loaded in the mass.  A bowl of compression was reported by Sollberger (1981:  13-15).  The bowl of compression (bc) is important to fracture studies.  It is particularly important to fracture interpretations even though its presence in form is limited by the withdrawing of flaking force.  The bc does a number of things.  It determines the radius of the ring crack of instigation for cones and flakes.  The bc diameter to its rim at the instant of ring crack inception in relation to its depth at that instant, determines the diffuseness or saliency of the bulb of force fracture formation on flakes and blades.  Other factors may also apply.

 

          On the reality of the bowl of compression:  It is common language among flintknappers to say:  The ring crack opens just outside of the diameter of force contact.  Turner, et al (1967) state:  “the fracture ring crack circle opens in a field of tension at a 12-20% greater diameter than the diameter of force contact”.  Those references must certainly refer to a bowl of compression, forms differently according to flaking platform configuration and location.

 

                  

                                     HERTZIAN CONES AND NON HERTZIAN

 

          Hertzian cones were named after Hertz (1896).  Cotterell and Kamminga (1987) still maintain that cone flare angles are about 136 degrees and Hertzian cones represent the initiation phase or proximal ends of conchoidal flakes.  I argue here that the term Hertzian is wrongly used because that term to be correct must conform to the rigid specifications for Hertzian cone fracture which are found in Speth, (1972) and Faulkner (1972).  One must deviate from vertical to the spot loaded, from well inside of the outer free mass face, and add an outer force component to the Hertzian line of applied force, in order to form the force blub of flakes and blades. 

Non Hertzian cones are the ones made by natural forces and by stone age man over the past million years.  They do not flare as greatly as Hertzian cone fractures nor is their maximum fracture depth possible limited to about three times the radius of force contact.  Hertzian loading and the depth of produced face tend to be much straighter than the marked convexity on the bulbar length of conchoidal flakes.  That length convexity on common cones is the direct result of the outward force cracking open the negative cone cavity of the mass which is a prior fact to be accomplished for converting cones to conchoidal fractures.

 

I assert here that the mechanics of conchoidal fracture are so different from flakes and blades that they should be considered to be only one form of flaking.

 

          With hammer stones, pointed Brandon type English blade making hammers, and various weights of steel sledge hammers I have made dozens and dozens of cone fractures into masses of flints and chert and retrieved them for accurate measuring.  The maximum flare angle that can be made in thick stone is not as great as 136 degrees nor 140 degrees as cited by Moffat (1981:201).  It is only 120 degrees and smaller.  Return now to Cotterell and Kamminga (ibid: 685) where they cite the cone fracture diameter to be “about one and a half times that of the ring crack”.  In the real world of stone knapping as we shall see, that citation is wrong.  Please refer to Figure 1 herein. 

 

          Other problems in our literature regarding cone fractures in the real world of execution are, that no one reports the common occurrence of biangular faces on both cones and flakes.  Archeologists do not recognize that cone flare angle can be regulated to form between about 67 degrees and 120 degrees by predetermining the diameter and depth of the bowl of compression by the size and hardness of force contact from the percusser tool.  It is not recognized that cones in flakes are not Hertzian but are common asymmetrical cones of many divergent forms which will be discussed following what I term the text book form drawn as Figure 1.A.  On Figure 1, letters dfc represent the diameter of force contact.  Letters mdp represent maximum depth possible.  Flare angles are noted in numerals.  A, is drawn deeper that text book specifications while 3 and C, are drawn to scale.

 

          Cone Figure 1.3, has a flare angle of 113 degrees which is a significant 22 degrees below the conventional 136 degrees.  The flare angle of cone C, is 67 degrees which is 68 degrees below the angle that everyone quotes everyone else as being correct for Hertzian cones.  The ring crack diameter of C is 1.0 mm.  The depth of fracture if 9.0 mm, which is six times the maximum text book depth for Hertzian fracture.  Cone 3, has a ring crack diameter of 10 mm and a vertical depth of 23.5 mm.  It had greater depth which I lost in retrieving it from the mass.  However, the text book formula of depth being limited to about one and a half times the diameter of force contact is clearly wrong.  The length of the face between the platform surface and the far edge of retrieval from the mass is 43.0 mm which is 28.0 mm in excess of 1 ½ contact diameter. 

 

In discussion on Hertzian loading, I find that the smallest cone flare angle can be made only with an iron hammer that has been filed to a sharp point.  The largest flare angles result from ten pound three inch diameter sledge hammers.  Archeologists should be interested in the cones produced by past and present stone workers made by hammer stones of the real world.  They will then find that a vast majority of cone fractures have flare angles between 120 degrees and 80 degrees. 

 

 

                             CONES BY NATURAL FORCES

 

Natural forces have made cones and flakes by uncountable millions.  The attributes of those cones are identical to man-made cones.  No one can distinguish between percussion and pressure cones.  Figure 2 is a typical example.  The mass was found on a river gravel bar.  My first strike for a flake blank caused the old water stained fracture to pop off and expose the upper part of a cone made by natural forces.  Its ring crack diameter is 10.0 mm.  The cone flare angle is 80 degrees.  The exposed depth is 8.0 but the crack extends deeper.  The only conclusion possible is that the text book specifications for 136 degree cone flare angles is incorrect.

 

Let’s pause briefly from presenting fracture data from nature and modern flint workers.  I have shown you that the text book specifications for Hertzian cone fractures cannot be replicated by natural forces or todays flint workers.  My question is:  Am I the only one between Hertz (1896) and Cotterell and Kamminga (1897) to make and measure cone fractures?  If others have done so, where are their reports?

 

Our stone has long been described as being a brittle elastic solid.  Our percussers and pressure flaking tools have long been described as being endentars.  Why then, when such flaking tools instigate the fractures in full 360 degree circles, am I the only one to report that a bowl of compression, is endented into the stone surface?  Past fracture reports all say that ring crack arcs or circles instigate in a major surface flaw just outside of the spot of force contact.  Why not say that surface flaws are always plentiful and that the rim of the bowl of compression is the line where tension first exceeds the stones elastic strength?

 

               

                                              BI-ANGULAR CONES

 

          I have search archeological literature for the phenomenon of bi-angular cone fractures (Figure 4) and have found neither illustrations nor discussions for these common artifacts.  Figure 4, A-3, are prehistoric Indian made flakes.  A, has a bi-angular cone whereas 3 has a 340 degree ring crack below which is a normal, non-Hertzian cone.  Figure 4, A is from a Bell County, Texas site.  Flake B, is from a site near Uvalde, Texas.  For flake A as I found it, the remaining flaking platform surface is marked with pencil lines.  The ring crack diameter is 1.2 mm.  The upper cone-half flares to 84 degrees.  The lower cone half forms an apex angle of 30 degrees.  That is the lower face lacks only 30 degrees from being a true cylinder.  The eye can clearly see its fracture extending down into the flake mass.   The angle of applied force is estimated to be 45 degrees from the platform surface.  The measure of cone fracture depth is 28 mm.   

 

          Figure 4, -B, has a 340 degree ring crack.  The cone flare angle is 88 degrees.  Cone depth at maximum flare is 12.0 mm.  The ring crack diameter is 3.75 mm.  The angle of the applied force was not vertical to the platform surface but nearly so because the ring crack lacks 25 degrees being a full circle.  Flake B is 129 mm long by 73 mm wide by 26 thick.

 

          Figure 5 is a bi-angular cone in top view A, and profile B.  I made this cone with an English type of iron blade making hammer whose tip was filed to a point.   His five pound hammer was delivered with all of my arm strength.  The core mass was then flaked away from the cone as shown.  The ring crack diameter is 2.0 mm.  The upper cone flare is 79 degrees, to a depth of 19 mm.  That initial flare angle reduced drastically and continued as a cone fracture an additional 26.7 mm before decaying in the mass.  Using Speth (1972) as referenced by Cotterell and Kamminga (1987), the maximum depth attainable should be 1 ½ times the ring crack diameter which is 3.0 mm.  Instead, the cone fracture is 47.2 mm deep.  Question:  Am I the only archeologist who has ever made cones and exposed them for measuring?

 

 

             THE WHY OF BI-ANGULAR OR TWO FACED CONES

 

          Under Hertzian loading specifications single faced cones are fractured but only when the mass outside of the spot loaded is sufficient to provide uniform symmetrical force transfer into the mass.  For example, a hemispherical mass with the North Pole being the spot loaded by compression.  The convex-convex surface provides a fairly constant resistance volume to the flaring expansion of cone fracture propagation but only to a certain depth.  At the depth the fractures front is opposed by a suddenly greater resistance of mass distortion outside of the fracture front.  That greater outside volume has a greater resistance to being distorted, which causes the cone fracture to reduce its flare angle quickly to a lesser angle as I illustrate on Figures 4 and 5.

 

 

  

 

  

 

            ON PUNCHING OUT A CONE FREE OF THE MASS

 

On reading Speth (1972) or Faulkner (1972), we read that cone fractures cannot penetrate a thick mass deeper than about three times the radius of force contact but, many refer to cones punched out of thin sheet or plate glass.  On thick glass or stone, it is said that at a certain depth the primary cone ceases to propagate regardless of the amount of load or flaking force addition.  I can find no reference to cite which provides the mechanics for why cones can be punched out of thin plate but not thick.   I offer the following:  Hook’s Law of continuum distortion applies:  At the on-set of force loading the spot area of force contact deflates that spot into a shallow bowl which I have named the bowl-of-compression.  The bowl of compression has a rim where it joins the flat surface.  Prior to the instant of fracture, the particles of the mass below the lower face of the bowl of compression will be stressed in compression to a dished bottom and cone form not defined by fracture.  The intensity of distortion on these particles varies according to the various depth of the bowl of compression below the pre-stressed surface. 

 

When the bowl depth places its rim in critical tension, fracture forms the ring crack face.  The ring crack face depth is limited by the flare of particle compression below in its path of propagation.   The fracture then turns outward to define in fracture, the pre-established cone in compression.  The cone fracture will continue in propagation as long as the force maintains a critical value of compression below the circle of the fracture front.  As the freed height of the cone lengthens, the cone diameter between the bowl of compression and the fracture front expands under Hook’s Law.  That diameter increase around the fracture front will press the cone volume against the mass volume thereby closing the crack faces together to prevent any further fracture unless the bottom of the cone of compression has began to distort the under face (surface) outward.  If that happens, it will open the crack faces and allow the cone to be pushed out clear of the mass.  When a mass thickness is such that its lower face cannot be bulged outward by the hemispherical central front of an approaching cone of compression, that thickness does provide a maximum debth for cone fracture penetration.  That limitation is certainly not the text book statement.

 

My data on Hertzian loading and cone fracture proves that our text books are wrong for archeological studies on Stone Age fracture.  You cannot produce cone fractures to the metrics of text book specifications.  You cannot produce small radium ring cracks with larger radius tool contacts.  My concept of, bowl-of-compression, is proven by the cone fracture metrics given.

 

 

 

 

                  HOW AND WHY FLAKES DIFFER FROM CONES

 

Cone fractures develop their major amount of critical tension from the mass side around the fracture front.  Cone volumes are force distorted downward only, within their negative fractured cavities.  Cones become flakes when starting at the ring crack faces, the mass cavity is opened by new fractures.  The continuum of these mechanical events are described from Figure 6.

 

Figure 6 illustrates a typical, common flake.  Note the following:  The angle of applied force is directed towards the lower middle of the mass dorsal face.  The bowl-of-compression, its rim, and deflation below the pre-stressed position, all indicate that the flaking load is in-place.  The profile shows fracture accomplished, down to just below line BC which is bulbar formation completed.  Line MBE, marks the maximum depth of bulbar expansion which is the cone fracture feature.  Note that the cone crack dies before reaching the dorsal face.  It dies because the triangle of mass above the cone fracture was too thin and weak in that small volume (too close to outer free face).

 

The ventral face view shows that a common flake develops six facial facets not including the transition face that surrounds the bulbar protrusion.  Starting at the bottom of the ring crack face, only the cone face is fractured down to short of line MBE.  That length allows the angled applied force to start an added distortion to that freed Length – outwards.  The outward distortion provides two lines of critical tension to open two new fractures.  These two progress from the ring crack face outwards toward establishing the upper width of a flake.  They each also propagate downward and outward as a transitional curve from the cone face.  Faces 3 and 3, are tear fractures because they are above and outside of the cone of compression.  As the flakes lateral edges lengthen downward, the outward directed force begins to widen the fracture crack.  That force distortion starts shifting tension development from the mass side of the cone fracture front, to greatest on the cone side.  That shift is completed along line MBE which technically, ends the cone fracture aspect.  The cone fracture ceases to increase its flare radius and starts Figure 6: face 5 as bulbar flare reduction.  Fracture advance down face 5 plus the lengthening of faces 3 and 3 down the flakes lateral margins, opens the fracture races between the mass and the flake at line BC.  Line 3C marks the end of bulbar regression as well as being the arced line where fractures 3 and 3 join the start of face 4.  The joining of faces 3 and 3 with face 5 places all three for the first time into a single united fracture front cross the full width of the flake which further widens the crack faces.  That widening stops all bulbar regression and transitions the thinning of the flake from a dorsal direction to downward as the dashed trajectory shown on edge-view of Figure 6.  Face 6, the dashed projection, can take one of several different trajectories by manipulation the direction of critical tension formation below the crack front to be into the flake or into the mass.  The details are as follows.

 

 

                     ON THE ACT AND PROPOGATION OF FRACTURE

 

From Figure 5 the mechanics of the first five stages of flake facial formation have been described.  Bulbar regression was completed to start face 6.  On Figure 7, face 6 fracture has been arrested in propagation in order to detail the mass distortions that are the act of fracture along the continuous fracture front from margin to margin of the flake.  The following conditions are in-place in continuum:  The flake volume if fully charged in compression down to letters NN which indicate neutral stress in the mass and flake.  The three pronged arrow-C, represent the greatest advance of the compression front (force wave).  Note that compression is spreading into the mass directly below the fracture trajectory.  Note that the angle of applied force on the flaking platform is widening the fracture gap.  That widening the bending which forms Secondary Compression – SC, on the flakes dorsal face (See Sollberger 1986:101-105).  Note that the mass is stress free – N, down to just above the fracture front because the passage of fracture has relieved the upper mass of stress.  Now, note the circle drawn half in the mass and half in the flake.  This circle is the fracture process zone that follows the advance of the compression front.

 

The stresses in the process zone are as follows.  On the mass side, the particles being split are distorting downward because of the flaking load on the platform.  They are resisting outward tensional pull inward and upwards in the mass.  As they split, tension is release inward and upward of the mass face.

 

Looking now at the process zone in the flake, the three pronged arrow shows compression invading the mass below the fracture crack front.  The particles are being stressed downward and dorsally by the outward tensional pull of opening the crack front in continuum of fracture propagation.  The mass side of a fracture front is constantly being stress-relieved by fracture propagation while the flake side at and below, is constantly being charged in compression.

 

 

                                 ON GUIDING A FRACTURE

 

Cotterell and Kamminga (1987:694) tell us that the fracture time interval is measured in milliseconds.  That it is impossible for a person to manipulate the indenter in such a short time.  They and others have largely looked at externals such as applied force angles and outer core face geometry.  In this report, my focus is on the internal stress developments and their effects on the fracture front.  I have described how cone flare can be regulated within reasonable tolerances.  How force bulb formations expand and regress in fracture radius.  That typical flakes have six discrete facial formations that are defined from inside the core to outside.  The act-of-fracture has been detailed.  Therein, I said that compression below a fracture front was constantly invading the mass from just below the approaching fracture front.  Controlling that invasion (Figure 7) starting at line BC – Figure 6, can produce the following results.

 

When the freed length is minimally widening the fracture gap crack front, critical tension develops primarily in the mass at and below the crack front which produces concave flake length.  When freed length is moderately widening the crack front, more tension is shifted to the flake side at and below the crack front to produce a straight fracture trajectory.

 

When the freed length acts as an outward pulling lever across the crack front, still more critical tension shifts to the flake side which guides the flake length convex.  For full length ventral face convexity, I refer you back to Figure 3, conchoidal flake formations.

 

          The angle of exterior applied force is not the whole story.  The leverage action on freed length of a flake at the crack front is the prime mover for fracture trajectory.   Core rotation and deflection changes the angle of applied force within the fracture time interval.  Flintknappers compensate for trajectory control by varying the degree of rotation and deflection with differing holding and support systems.  The action within the process zone is significantly altered by whether or not the flake is bending or buckling between the applied load and the fracture front.  See Sollberger 1985 and 1986.

 

          I turn now to some specific flake types or categories.

 

 

                                                  CONCHOIDAL FLAKES

 

          Before fracture analysis by archeologists, flints were described as being stones that broke with a conchoidal fracture. Conchoidal fractures means being in the shape of one face of a mussel or clam shell.  Cotterell and Kamminga (1987:675) say, “despite popular belief, flakes are not all of the conchoidal variety”.   Those authors describe a “bending flake” as being not conchoidal because “they have no force-bulb formation.”  Their use of the term conchoidal includes specialized cores and flakes such as polyhedral core blades.  On some of those blades the entire bulbar formation covers less than one twentieth part of the whole face.  Most mussel and clam shells have a totally “bulbar” surface.   So, a fuller description of the mechanics of conchoidal flaking seems to be in order.

 

          Figure 3 illustrates two examples of true conchoidal flakes.  Conchoidl fractures used as tools, are also called fan scrapers, ulu knives, squaw knives, and side-struck flakes.  The in-common attributes are that they are struck from flat faced thick edged tabular cores with largely little or no platform preparation.  Therefore, their dorsal faces are likely, cortex covered.  Their width is generally greater than length (Figure 3) because the wide straight junction of the platform face to the core face minimize and delays the outward opening of the fracture crack below the upper surface. Consequently, the bulbar form frees much wider and deeper before bulbar regression can start.  (Please review Figure 6: line MBE, and the shifting of major tension from the mass to the flake side of the fracture front).

 

          Conchoidal flakes are an intermediate form between cones and designed flakes.  Those such as Figure 3 are to be avoided because they ruin the process of core preparation for flake blanks and or bifacing.  The expression that flints break with a conchoidal fracture is grossly over used.   I have followed wheel ditching machines for miles spewing out soft limestone conchoidal flakes at the rate of several hundred per minute.  Regarding Figure 3 your eye should tell you that the greater than 90 degree hinged terminations formed because the compression value beyond the fracture front dropped too low.  That the fracture type change from compression-led to fracture-in-bending.  The extreme length width convexity tells you that early on, fracture supporting tension was shifted from the mass side to the flake side in the fracture process zone.  The undulation ripples starting above maximum cone flare tell you that the fracture velocity was too low relative to a decelerating compression front.  Probably, all of the above was enhanced by core rotation because of the lack of sufficient anvil support.

 

          Figure 3, upper, the biangular formation.  The angle of applied force was directed to obtain greatly longer fracture.  The core mass was light in weight relative to the weight and velocity of the percusser.  The cone face was being defined by fracture but the core mass quite suddenly was deflected and rotated.  The result being a sudden shift of compression propagation from in to the mass to away from the mass.  The result was bulbar regression became an angle.

 

 

          BENDING TYPE FRACTURE VERSUS COMPRESSION-LED FRACTURE

 

          Cotterell and Kamminga (1897: 675; 689-690; figure 4 and Figure 12) describe a new flake type which they term the Bending Type.  Their description is that bending type flakes are not “Hertzian” because they have no bulbar formation.  They describe a classic bending type as being “waisted” in fracture initiation.  In their words the recognition of bending flakes is long overdue.  Their Figure 12 ideal includes a long flake length with cross-sections so their discussion is not limited to an initiation stage.  Their error in naming bending flakes is confusion between what is bending, and what is particle volume distortions by a load of flaking force.  Their over-all error is the miss-use of Hertzian loading specifications by combining cone fractures and flake fractures into one and the same thing.  I have already provided the mechanics for their separation. 

 

          First, fracture-in-bending, requires that both the upper and under face of a nucleus start bending concomitantly.  Bending places the inside of the bow in compression while placing the outer convex surface in tension until fracture inception occurs (Sollberger 1981:1986).   The line of fracture will be essentially a straight line along the crest of the bend.  The authors (ibid) inception line is a uniform radius formed by a non-Hertzian bowl of compression the rim of which is greatly more remote from the diameter of force contact than Hertzian loading. 

 

Explanation:         

 

          To be Hertzian, the load must be vertical to the surface well inside of any outer free face.  The loaded spot is punched down to form a rim around the spot.  There is no surface particle compression outside of the bowl rim.  When the rim surface exceeds the stones elastic strength, the result is a 360 degree Hertzian fracture face of inception.  Violation of Hertzian is to load a spot near an outer free surface so that a symmetrical cone of compression cannot form.  Then, whether or not the angle of applied force is vertical, directed inward or outwards of the platform surface only a part cone can be fracture defined.  Violation of Hertzian loading to on-the-edge, or closely behind-the-edge, commonly distorts the nucleus in compression outside of the spot of force contact a considerable distance across a platform surface.  That distance to inception increases as bowl-of-compression distortion as long as the wedge of nucleus distortion between the platform surface and the outer face of the internal undefined by fracture cone of compression are in distortion as a unit.  When the surface distortion arc radius stabilizes and ceases to increase, that extended bowl rim builds to a critical tension for ring crack fracture inception.  That face depth continues until it is turned by is joining the outer face of the internal primary force cone of compression flare.

 

          Please refer back to Figure 7; Line MBE which describes cone flare and bulbar regression.  When a deep lipped face of inception intersects the cone flare above line MBE, both cone fracture flare and bulbar regression are defined on deeply lipped flakes.  When the face of instigation meets the cone of compression below line MBE, only bulbar regression is defined by fracture.  That intersection is always above Figure 7; line BC.

 

          My photographs are honest, not idealized.  Figure 8; top row, are heavily lipped above clearly defined cone flare and bulbar regression.  Note that upper right is also “waisted”.  Figure 8; lower row all have bulbar regression thinning as just above Figure 7; line BC.

 

          The idealized flake drawn by Cotterell and Kamminga (1987; Figure 12) is a compression-led fracture on which the initiation crack face meets the inner cone of compression flare volume between my Figure 7; lines MBE and BC.  Therefore, only the lower part of bulbar regression is defined by fracture.  Those authors (ibid) say no blub was formed because they do not understand bulbar conversion mechanics in the continuum of fracture propagation.

 

          Lipped flakes most commonly form because the striking force contacts thin edges such as in bifacing.  Billets are most commonly used to prevent crushing those thin edges.  The edge indentation takes the form of a new moon (a crescent).  Both the upper and under faces are distorted locally.  The rim of that bowl of compression can be 10 mm. beyond the line of force contact.  Fracture instigation opens a deep arced face.   When that lipped face reaches the outer face of the internal cone of compression, the fracture is turned to be compression-led as described under flake length.  Fracture-in-bending always propagates towards the nearest outer free face of a mass.  It would be a mistake to adopt a, ending type flake, into archeological fracture mechanics.

 

 

                                        HINGE FRACTURES

 

          Cotterell and Kamminga (1987:705) write “more needs to be known about the mechanics of hinge fracture”.  Within the mechanics of fracture as presented herein, there is little to be learned about hinge fractures that is not known.  A hinge fracture is a 90 degree or more fracture turn from an established fracture trajectory towards the nearest outer free face of the mass being flaked.  Flintknappers commonly produce flake terminations where the hinge rolls a full 180 degrees (Figure 9).  Hinge terminations are intentional of some blade cores.  They are also by intent in producing flat faced bifaces where the individual flakes are called diving flakes.

 

          All hinges develop because the particle compression value just beyond the fracture front is suddenly dropped below the value needed to maintain the original fracture trajectory.  With practice a Flintknapper can produce hinges at will.  The mechanics are as follows.

 

          Hold a core by hand to allow some rotation and deflection by the compresser hammer strike.  Make the strike just strong enough for the fracture to reach the desired length.  Then, core deflection stops the original trajectory.   Core rotation hinges the angle of applied force to be drastically outward.  With the core now unloading itself of compression, the fracture type changes from compression-led, to fracture-in-bending to form the 90 degree roll towards the near outer surface.  As the fracture approaches the free surface, the bend by the outward flaking force sets up a stronger Secondary Compression (Sollberger 1986) which forms a second turn downward in order for the hinge to be freed from the mass.

 

          The 180 degree rolled hinge differs in that the flaking tool maintains a too low particle compression in the flake long enough to allow a stronger secondary compression to develop and the flaking tool still has a minor downward compression in the flake as the fracture crack opens from outward bending of the flake.  That combination of forces causes the first 90 degree roll to turn upward and become a 180 degree roll.  The height of the upward turn is limited by the width of the crack opened by outward bending of the flakes freed length.  When the flaking tool force closes that space, the fracture becomes a pure form of fracture-in-bending.  The final termination thru the dorsal face of the mass being the same as the 90 degree hinge roll.

 

          In flake and blade making, a prior hinge causes all flakes following to hinge also.  That is because the first hinge adds thickness to later ones at that length to increase their particle volume.  That added volume requires more time to reach a compression value to lead the following fracture but the striking force cannot wait.  It continues to bend the freed length away from the mass which forms another hinge as described above.

 

          Hinges also form when the percusser bounces up and off of the flaking platform.  That loss of force unloads the compression below the fracture front which stops the primary fracture.  The bounced hammer holds the flake bend in-place long enough for the hinge to form.  Great numbers of hinges are formed when the flake, blade or fluting channel flake buckle breaks between the flaking tool and the compression-front.

 

          Diving flakes, called also, super biface thinning flakes, have hinged terminations. 

They can change a biface cross section from convex convex, to concave concave.  That is the perimeter edges can be thicker than the central face.  The mechanics are, start the fracture from a small flaking platform where the flake will widen and thicken as it lengthens use a light horn billet with just enough force to carry the fracture to or slightly beyond the biface mid width.  The increasing particle volume over length reduces the compression value at that length to stop the primary fracture.  The outward element of primary force converts the freed length into a lever to produce the hinge roll.  Secondary compression (Sollberger 1986) in the dorsal face determines the final fracture form to termination.

 

          In this reply to Cotterell and Kamminga (ibid: 705), there is no relationship in hinge fractures to flaking tool types.  The flakes lineal edges can be feathered, thick or mixed.   The hinge roll width (not particle can start from either flat or convex ventral faces.  Figure 3 herein clearly shows a fully convex flake in width and length terminated by hinge fracture.  Figure 9 illustrates a rectangular flat faced core with a hinged flake removed from its negative cavity.  There is nothing of significance unknown about the mechanics of hinge fractures.

 

 

                 THE MECHANICS OF UNDULATION FRACTURE

 

          The Formation of Flakes cannot be fully detailed on the mechanics of applied force on the basis of inception, propagation, and terminations, as Cotterell and Kamminga (l987) have done.  The continuum of compression advance thru those three stages is three dimensional and fracture feature formations must be related to nucleus support types, nucleus other free face geometry, as well as acceleration and decelerations of the fracture front.

 

          There are two principle varieties of undulations that result from two causes.  The common variety is Figure 10: A.  The unrecognized variety is Figure 10: B.

 

Figure 10: A variety is the result of fracture velocity loss caused by an increased particle volume on the dorsal face surface such as a high ridge left by a bifacing flake removal.  The force conditions are:  The applied force compressed the flaking platform to start the compression propagation into the stone.  The following fracture inception opened a deep lipped face below which a diffuse bulbar formation opened.  The compression front at 40 mm length slowed its propagation in order to fill the volume added by the dorsal face ridge.  The decelerating compression front required a time interval to regain its value while filling the added volume.  In doing so, compression also invaded the core mass which required that the closely following fracture width to turn into the mass and free the flake to the bottom of the undulation valley.  Meanwhile, the compression front had accelerated because it had reached the reduced volume beyond the thick ridge.  That acceleration of compression front allowed the outward applied force to increase the leverage on the flake length to pull the fracture out of the valley because the outward bending of the flake length from the flaking platform was not decelerated as was the compression front. 

 

          With the flaking load, the rate of compression, and following tension, all resynchronized together, the fracture continued to the preform tip.  I will add that had the resynchronization not occurred in time, the undulation would have divided the preform by outrepasse, reverse hinge, or overshot fracture all of which are the same thing.

 

          Figure 10: B-left, illustrates a negative flake scar which is free of compression rings and undulations.  I made the preform face free of humps, flat spots, and prominent bifacing flake scar ridges.  Also, the fracture length propagation was compatible to the rate of outward leverage by the fluting tool.  I commonly produce such flutes on both faces when the preform is perfectly contoured.

 

          Figure 10: B right, illustrates an undulation for which the mechanics has not been recognized or described.  You can see that its valley cut thru the right lateral margin so that the flake contains a part of the opposite face of the preform.  Figure 10:  B undulation is a very severe form of a very common occurrence on long flute flakes, blades, and common flakes.  This variety can be identified on the basis of their close proximity to just below bulbar regression where the first five fracture facets are united into a common fracture front.

 

          The cause for this undulation is that the force load on the flaking platform lacked a sufficient outward leverage on the then-freed-length to shift a sufficient amount of tension from the core side to the flake side of the fracture process zone.  However, length propagation into the valley increased the mechanical advantage of freed length to pull the undulation back up to the flakes designed thickness.   All forms of undulation are the early stage of outrepasse.   Outrepasse occurs when the major tensional development remains in the mass side or a fracture front.

 

 

   PLUNGING FRACTURE ARREST FOLLOWED by a FINIAL EXTENSTION

 

          Cotterell and Kamminga (1987: 701) tell us that plunging fracture is caused by the end of the core.  No mechanical explanation is provided other than reference to Crabtree.  Not true.  Students of fluted projectile points often term plunging, a reverse hinge fracture.  Such frequently occur in the proximal end of a preform.  Plunging is a long radius outrepasse.  It is the result of a strong compression front spreading into the mass below the fracture front as a result of insufficient outward leverage by the reed length of the flake.  Plunging can be arrested to become an undulation (Figure 10), or it can be turned downward as per Figure 11.

 

          Figure 11 illustrates a full length unbroken channel scar on which the plunging turn turned again short of the rear face.  The channel flake (left) has a deep lipped ring crack, a very low bulbar profile.  The flake certainly was not by fracture-in-bending.  The channel flake did not shorten the original preform length.  Impossible?

 

          Well, such are not uncommon to me.  When the preform is clamped vertical to an immovable integral to the clamp tip support board (Sollberger, 1985) many abortions are prevented.

 

          Tip support prevented the inward turn from being completed through the rear face.  Tip support prevented distal end bending rearward by the flaking force and the out-leverage of the flake length.  Lineal edge clamping provided for no rotation or deflection of the core place.  The lever force, forty to one, took the advantage that flints may be fifty to five hundred times stronger in compression than in tension.  That’s saying that both ends of the core had elevated strength at the instant of fracture inception; then when the fracture made its turn towards the rear face. That face was strong enough to allow the outward leverage by the now longer flake length, to shift critical tension over to the flake side of the fracture process zone.  From that shifting, the fracture continued and intersected the ground preform tip.   From Figure 11, you can see that the distal end of the flake is 5.5 mm thick and the distal end of the core piece is only 2.0 mm thick.  The plunge turn started 23 mm above the distal end.

 

          Those who relate any anvil support to bipolar fracture consider Figure 11.  The prepared platform was the same size as the tip resting on the tip support board.  Both ends were loaded in compression equally and simultaneously.  So why does fracture always instigate proximally?  The answer is that the volume lateral to and behind the flaking platform were outside of the cone flare of compression deflation.  The more acute angled tip end was completely inside of the cone flare distally, therefore no surface for a critical tension to develop.  So, the entire preform volume was loaded between the two cones.  The full length fracture had to invade partical compession full length.  Review – Figure 7.

 

                                                                

                                                          FINIALS

 

          Cotterell and Kamminga (1987: 701-705, Figure 4) describe finials as fractures that have turned away from the initiation face to create a thin and often fragile extension to the flake ending.  They describe these endings in terms of inflexed (down), reflexed (up-turn), and pseudo bifurcation.   Lenoir (l975) called them languette or tongue fractures.   Faulkner (19847: 328) called simple bending terminations hang nails.  Sollberger (1985: 101-1405) described the mechanics for finial extensions.   More can be said on the mechanics of finials that Cotterell and Kamminga provide.

 

          Their term pseudo bifurcation, means false branching.  Contrary to authors (ibid: Figure 4), fracture in bending makes at times, true branching’s that free whole unbroken pieces as per Sollberger (l986:  Figure 3).  Finials do not necessarily form at flake endings as described above.  They occur as most all snap breaks and hinged forms (Sollberger 1986:  Fires 1-2-3).  Those long thin extensions are not confined to flake endings.  For example, see one on the nucleus herein Figure 11: right.

 

          Drawings are teaching aids and should be technically correct.  The authors (ibid: Figure 4) step fracture (a) cannot start its dorsal turn from the very end of the primary fracture as a square turn.  It must be a rolling hinge.  Its final end must also roll because of secondary compression.  Step (b) must also terminate as a roll because of SC.

 

 

 

 

                                                  DISCUSSION

 

          Most fractures are completed in less than a millisecond over time.  So, how can one be sure about such things as, bowl of compression?  Be practical.  Use a synthetic sponge.  Lay it on a table.  Use a pencil as an indenter.  Push in slowly and release slowly from all surfaces corners and edges.  You can observe and analyze all shape deformations.  Compression will flatten the round holes.  Tension will elongate the holes towards the stress source.  Simple bends will do the same but on opposite faces of the bend.

 

          To check outward displacement of a freed length being responsible for force bulb conversion, take a half round length of paper, cardboard, sheet metal or pipe.  Secure one end.  Apply a down and out force to the free end.  When the bending displacement starts, you can see the radius of the bend increase towards flat across.  As the bend increases on pipe for example, the compression in the outside of the bend changes into tensile stress which thins that wall thickness.  Conversely, the inside wall thickness becomes thicker.  The originally round shape becomes a wide oval between the inner and outer faces.  Pipes or solids, it makes no difference.  Your micrometer will prove it.  Such simple demonstrations prove the force of secondary compression, the shifting of compression from the mass side to the flake side of a fracture front and, the redistribution of flaking compression from cones to bulbs, to flake lateral flatness.

 

 

          My text has been accumulative.  Refer backwards and forward.

 

 

 

                           TERMINOLOGY

 

 

Bowl of Compression,  bc, is the surface distortion made by flaking force contact.

 

Rim of the bowl of compression, is the arc or circle crest at the instant of fracture inception.

 

Secondary compression, is the particle volume placed in compression by bending.

 

Flake, is a piece that is usually wider than thick that has a bulbar formation in whole or in part at the proximal end.

 

Shatter refers to multiple flakes, broken pieces, etc. without force bulbs.

 

Compression-led fracture, includes all flake types.

 

Fracture process zone, is the layer(s) of particles being fractured.  The crack-front propagation zone.

 

Outward leverage is a fracture directional control in the process zone.

 

Fracture crack front is the layer of particles next to be fractured.

 

Cone fracture, is in the shape of a cone.

 

Force bulb, is a fracture form on which the upper one part ceases its outward flare to a reducing radius at the on-set of outward distortion of the then-freed length.

 

Tear fracture(s), are the faces outside of the flare angle of effective particle compression of force bulb formations.

 

Bending fractures, are the result of concomitant bending of both faces of  nucleus or flake to a critical tension.  The fracture propagates towards the nearest opposite face.

 

Fracture, is the formation of two faces within a solid as a progression below a surface.

 

 

                                                      LIST OF FIGURES

 

 

Figure 1    Hertzian, versus Stone Age cones

 

Figure 2    A cone made by natural forces

 

Figure 3    Conchoidal flakes

 

Figure 4    Two prehistoric Indian flakes – Compare cone types

 

Figure 5    Two views of a biangular one

 

Figure 6    The six fracture faces of a common flake

 

Figure 7    Mechanics of fracture:  Act of & Trajectory

 

Figure 8    Lipped, versus bending flake mechanics

 

Figure 9    Hinge fractures.


Figure 10 Undulations, two categories

 

Figure 11 Plunging fracture, arrested

 

 

 

 
 



Figure 1.  Hertzian cones versus stone age cones.  The diameter of force contact is, dfc.  Maximum fracture depth possible is, mpd.  A, is he standard text book flare angle.   B,C, is the flare angles maximum to minimum, that natural forces and stone workers can produce.   

 


 
 

                                   Figure 2  A cone made by natural forces

 

 

 



 

                       

Figure 3.  Upper, has a biangular bulbar formation.  Lower, a typical conchoidal flake.  Both are non-Hertzian because spot loaded was near an outer free mass face.      

 

 




 

 

 

 


 

 

Figure 4.  Two prehistoric Indian made flakes.  Flake A has a biangular cone.  Flake B was non-Hertzian loaded and has a single faced cone flare.

 

 

 

 


 

Figure 5.  Two views of a biangular cone made with a five pound pointed Brandon, England type blade making hammer.  See TEXT for details.

 

 

 


 

 

Figure 6.  The six discrete fracture faces of a common flake. 

1)      The instigation or lip

2)     Cone flare

3)     3 and 3

4)     Missing in drawing

5)     Bulbar regression

6)     The face below bulbar regression




 

Figure 7.  The mechanics of flake fracture and fracture direction control.  A, the bowl of compression.  B, the process zone in the circle.  N, neutral stress volume. C, particle volume in compression. SC, Secondary compression from outward flake bending.  The three pronged arrow shows the compression front.

 

 

 

 

 


 

Figure 8.  Deeply lipped soft hammer flakes.  Top row has full development of cone expansion and bulbar regression.  Bottom row has instigating faces that intersect bulbar regression above the thickness that starts face 6 of Figure 6.

 

 

 



Figure 9.  A 180 degree hinge fracture negative cavity as seen from the left lateral edge of the nucleus.

 




 

 



 
Figure 10.  The mechanics of undulations.  A, is the common form.  B, right, is ripple undulation free. B, left, the undulation flake took part of the rear face.

 
 

 

 


 

Figure 11.  A plunging fracture arrest short of the rear that continued to the preform ground tip.

                                                        REFERENCES CITED

 

Cotterell, B and  J. Kamminga

          1987  THE FORMATION OF FLAKES, American Antiquity, 52 (4); 675-708

 

 

Crabtree, D. E.

          1966  A stone Worker’s Approach to Analyzing and Replication the Lindenmeier

          Folsom.  TEBIWA 9: 3-59

 

1968  Mesoamerican Polyhedral Cores and Prismatic Blades.  American Antiquity 33: 446-478

 

          1972  An Introduction to Flint Working,  Occasional Papers of the Idaho State

Museum No. 28.  Pocatello

 

 

Faulkner, A.

1972  Mechanical Principles of Flint Working.  Ph.D. Dissertation, Washington State University, Micro Films, Ann Arbor, Michigan

 

1984  Examining Chipped Stone Tools.  Wisconsin Archeologist 65:  507-525

 

 

Hertz, H.

          1896  Hertz’s Miscellaneous Papers, Reprinted MacMillan, London

 

 

Lenoir, M.

          1975  Remarks on Fragments with Languette Fractures.  In Earl Swanson,

          Editor, Lithic Technology; Making and Using Lithic Stone Tools,

          Pp 120-132, Aldine, Chicago.

 

 

Moffat, C.R.

          1981  The Mechanical Basis of Stone Flaking: Problems and Prospects.

          Plains Anthropologists 26 (93) 195-211

 

 

Shepherd, Walter

          1972  FLINT:  Its Origin, Properties and Uses.  FABER AND FABER, 3 Queen

          Square, London

 

Sollberger, J. B.

          1981  A Discussion on Force Bulb Formation and Lipped Flakes. 

          FLINTKNAPPERS EXCHANGE.  4(1)  13-15

 

          1985  A Technique for Folsom fluting, Lithic Technology  14 (1) 41-50

 

          1986  Lithic Fracture Analysis; A Better Way.  Lithic Technology

`        15(3)  101-105

 

 

Turner, D.N., Ph.D. Smith and W. B. Rotsey

          1967 Hertzian Stress Cracks in Beryllia and Glass.  Journal of the

          American Ceramic Society, 50: 594-598

 

This Report was the last works of Sollberger and was given to his good friend Joe Miller of Greenville Texas. This report was a badly damaged Xerox and this modern recreation was reconstructed by Carol Piri and John Piri of Ridgecrest California in September of 2013.   
 
We can all learn from this excellent report.
 
 


Figure 1.  Hertzian cones versus stone age cones.  The diameter of force contact is, dfc.  Maximum fracture depth possible is, mpd.  A, is he standard text book flare angle.   B,C, is the flare angles maximum to minimum, that natural forces and stone workers can produce.   

 


 
 
                                   Figure 2  A cone made by natural forces

 

 

 

 
                       

Figure 3.  Upper, has a biangular bulbar formation.  Lower, a typical conchoidal flake.  Both are non-Hertzian because spot loaded was near an outer free mass face.      

 

 




 

 

 

 


 

 

Figure 4.  Two prehistoric Indian made flakes.  Flake A has a biangular cone.  Flake B was non-Hertzian loaded and has a single faced cone flare.

 

 

 

 


 

Figure 5.  Two views of a biangular cone made with a five pound pointed Brandon, England type blade making hammer.  See TEXT for details.

 
 

 



 

 

Figure 6.  The six discrete fracture faces of a common flake. 

1)      The instigation or lip

2)     Cone flare

3)     3 and 3

4)     Missing in drawing

5)     Bulbar regression

6)     The face below bulbar regression



 

Figure 7.  The mechanics of flake fracture and fracture direction control.  A, the bowl of compression.  B, the process zone in the circle.  N, neutral stress volume. C, particle volume in compression. SC, Secondary compression from outward flake bending.  The three pronged arrow shows the compression front.

 

 

 

 
 


 
Figure 8.  Deeply lipped soft hammer flakes.  Top row has full development of cone expansion and bulbar regression.  Bottom row has instigating faces that intersect bulbar regression above the thickness that starts face 6 of Figure 6.

 

 
 




Figure 9.  A 180 degree hinge fracture negative cavity as seen from the left lateral edge of the nucleus.

 




 

 


 

Figure 10.  The mechanics of undulations.  A, is the common form.  B, right, is ripple undulation free. B, left, the undulation flake took part of the rear face.

 

 

 

 


 

Figure 11.  A plunging fracture arrest short of the rear that continued to the preform ground tip.

                                                        REFERENCES CITED

 

Cotterell, B and  J. Kamminga

          1987  THE FORMATION OF FLAKES, American Antiquity, 52 (4); 675-708

 

 

Crabtree, D. E.

          1966  A stone Worker’s Approach to Analyzing and Replication the Lindenmeier

          Folsom.  TEBIWA 9: 3-59

 

1968  Mesoamerican Polyhedral Cores and Prismatic Blades.  American Antiquity 33: 446-478

 

          1972  An Introduction to Flint Working,  Occasional Papers of the Idaho State

Museum No. 28.  Pocatello

 

 

Faulkner, A.

1972  Mechanical Principles of Flint Working.  Ph.D. Dissertation, Washington State University, Micro Films, Ann Arbor, Michigan

 

1984  Examining Chipped Stone Tools.  Wisconsin Archeologist 65:  507-525

 

 

Hertz, H.

          1896  Hertz’s Miscellaneous Papers, Reprinted MacMillan, London

 

 

Lenoir, M.

          1975  Remarks on Fragments with Languette Fractures.  In Earl Swanson,

          Editor, Lithic Technology; Making and Using Lithic Stone Tools,

          Pp 120-132, Aldine, Chicago.

 

 

Moffat, C.R.

          1981  The Mechanical Basis of Stone Flaking: Problems and Prospects.

          Plains Anthropologists 26 (93) 195-211

 

 

Shepherd, Walter

          1972  FLINT:  Its Origin, Properties and Uses.  FABER AND FABER, 3 Queen

          Square, London

 

Sollberger, J. B.

          1981  A Discussion on Force Bulb Formation and Lipped Flakes. 

          FLINTKNAPPERS EXCHANGE.  4(1)  13-15

 

          1985  A Technique for Folsom fluting, Lithic Technology  14 (1) 41-50

 

          1986  Lithic Fracture Analysis; A Better Way.  Lithic Technology

`        15(3)  101-105

 

 

Turner, D.N., Ph.D. Smith and W. B. Rotsey

          1967 Hertzian Stress Cracks in Beryllia and Glass.  Journal of the

          American Ceramic Society, 50: 594-598

 

This Report was the last works of Sollberger and was given to his good friend Joe Miller of Greenville Texas. This report was a badly damaged Xerox and this modern recreation was reconstructed by Carol Piri and John Piri of Ridgecrest California in September of 2013.   

 

We can all learn from this excellent report.

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