This Hertzian cone is made from a chert nodule from the Barkly Tableland in the Northern Territory, Australia. The Hertzian cone was created in the recent past by a rock collector using a steel hammer.
The cone in this model was made on Barkly Tableland chert from the Northern Territory, Australia. It was made in the recent past when the chert nodule was struck near the middle of one face with a steel hammer by a rock collector assaying the stone’s interior colour and patterns. Stone fracture occurs in microseconds, and two phases can be inferred from this object. In the first instant, during the initial contact with the hammer, the Hertzian cone was formed. As the energy increased and the full force of the hammer was delivered onto the top of the cone, the stone was compressed and transferred this energy through to the bottom of the cobble, punching it through and fracturing the surrounding material. The latter phenomenon is poorly understood as most fracture mechanics and ballistic studies induce cones in ca. 5 mm thick plate glass and the ‘punch-through’ phenomenon is rarely observed.
See the annotations for technological details about this stone tool.
Small star fractures are a familiar form of damage to glass windows and windscreens, often caused by stones kicked up by passing vehicles or lawnmowers. A close look at this damage shows that the star fractures are cone-shaped, with the apex on the struck side opening up to a much larger diameter on the opposite side. Sometimes the cone pops out entirely, leaving a cone-shaped hole with a small perforation. This type of fracture is known as a Hertzian cone. The wave-front physics of Hertzian cone formation were described in in 1881-1882 by the physicist Heinrich Hertz, famous for proving the existence of electromagnetic waves.
Hertzian cones are most clearly expressed when a blow is delivered straight onto the surface of the stone or glass, well-away from the edge. The area within the contact surface is depressed until the material fails and a crack starts. The crack follows the boundary of the molecules compressed under the indentor. This boundary is cone-shaped with the sides flaring outward at ca. 136º to the direction of force. If there is no ‘free’ face to reflect back the forces controlling the crack—that is, if the blow is away from the edges of the stone—the cone will continue to grow until it runs out of energy and stalls. The cone geometry created by the forces delivered in stone-flaking is relatively consistent, but forensic studies of Hertzian cones created by bullets demonstrate that high-velocity impacts result in more steeply-angled cones.
The amount of force required to for a cone to grow increases exponentially with depth, and on thick materials the force is quickly used up and the crack stops: the cone is embedded as an unseparated cone-shaped crack. Nature often does this when siliceous stones tumble in riverbeds or beaches—bouncing off other stones—and this creates ‘incipient cone cortex’, a type of ‘neocortex’. However, if the blow is struck near the edge of the stone, the radiating force quickly encounters the stone’s outside or ‘free’ face; this causes the crack to change shape to run down the free face. The reconfiguration of the crack from cone-shaped to relatively flat results in what archaeologists call the ‘bulb of percussion’ or ‘bulb of force’ on the ventral surface of the flake. This is how fractures in stone-flaking are initiated ‘conchoidally’ (bending and wedging initiations are quite different from conchoidal initiations).
On thin, fine-grained material like window glass, not much force is required to punch the Hertzian cone right through, creating a hole. The hole of a perfectly-formed cone is usually very small on the struck side of the glass: this is the diameter of the surface area that was depressed by the indentor. The thicker the glass, the larger the hole on the reverse side, because the boundary expands ever-outward at 136º. A cone can form in safety glass, like a windscreen, but a hole is not created and the cone-shaped crack remains embedded, refracting the light. This is because a plastic layer is embedded in the glass and the fracture ends there.
The direction and shape of a conchoidal crack in stone toolmaking is determined by the orientation of the Hertzian cone within the stone. This, in turn, is determined by the location near the core edge where the blow was landed, combined with the orientation of the blow. It is important to realise, however, that the Hertzian cone proper on a stone flake is usually tiny—about three times longer than the radius of the contact circle, or less than ca. 3 mm long in the majority of cases. Unless the material is very fine-grained, it is difficult to discern the outline of the Hertzian cone on a stone flake. It is also incorrect to say that the bulb of percussion is the same thing as a Hertzian cone; although bulb formation is related to the Hertzian cone, they are different things. Fully-formed Hertzian cones are sometimes encountered on ancient quarry sites where heavy percussion was used to initially break up the rock. They are relatively rare, however, since stoneworkers usually applied even the heaviest of blows close to the edge of the stone. They are more common in rocks broken-up with steel hammers by modern lapidary enthusiasts and geologists, who tend to strike samples near the middle to induce fracture.
Hertzian cones were sometimes deliberately made by traditional stoneworkers to create perforations in stone objects. Recall that the crack initiates at the boundary of the area depressed by the indentor. The resulting hole on the face struck by the indentor is precisely the diameter of the depressed area. Depending on the size of the indentor, the hole might be as small as 1 mm diameter (although the cone flares out to a larger diameter on the opposite side). The trick is landing the blow precisely where it is needed and with enough force to punch out the cone without snapping the stone in half through bending stress. A common approach was to drill or peck part-way or most of the way through the stone from one side, place a punch inside the hole, and strike the punch, popping the cone out the opposite side. A team led by the famous archaeologist and flintknapper Jacques Tixier documented this technique applied by bead-makers at Larsa, Iraq, ca. 1000-3000 BP. A similar technique was used by Aztecs to produce tiny holes in eraillure flakes: a small depression was drilled into the middle of one face, and the hole was punched through with an exceptionally small punch, such as a sliver of bone or a cactus needle. Perforated objects called ‘eccentrics’ were made by the Mayans and Aztecs of Mesoamerica. Their manufacture involved perforating the bifacial blank—perhaps using a variant of the Hertzian cone technique, although there is no direct evidence of this—then enlarging and shaping the margins of the hole by pressure or indirect percussion.
Recent gunflint-makers in Brandon, England, perforated flint flakes to make bracelets and rings to sell to visitors. The hole was initially made by a Hertzian cone and then the inside of the hole was enlarged. The Brandon hole-making technique involved first sectioning a flint nodule to prepare a relatively flat surface. The centre of this surface was given a hard rap with a steel hammer, embedding a Hertzian cone crack into the stone. A flake was next struck so it propagated down this face and travelled around the pre-existing Hertzian cone crack. If the flake came away without breaking, it left the cone stuck to the core face, and the flake had a perforation on its dorsal face. If the flake dove below the limits of the embedded cone, the cone came away with the flake, but it could be punched out afterward by striking at the top of the embedded cone. Modern ‘evil eye’ (nazar boncuğu) glass amulets from Turkey are sometimes perforated using a Hertzian cone technique. The depression on one face is made by the pontil-rod when the glass is still molten. The depression penetrates about half the ornament’s thickness. After the glass cools and hardens, the opposite face is punched through, blowing out a Hertzian cone. The perforations in slate roofing tiles were also made using a Hertzian cone technique, by striking the surface with a pointed hammer. This left a small hole on the struck face and punched out a much larger area from the opposite face. Although the grain in slate prevented the formation of a classic Hertzian cone, the results were analogous. The slate was then flipped over for nailing to the roof purlins—the blown-out concavity acted as a countersink for the nail so that the overlapping slate did not come into contact with the underlying nail’s head.