On the mechanics of edge chipping from spherical indentation

Abstract

Edge chipping is a basic failure mode in brittle materials which is dictated by a wealth of material and geometric variables. Here we examine the effect of indenter bluntness on chipping load and chip dimensions. Soda-lime glass and YTZP plates are subject to surface-normal loading near an edge by a W/C ball or a Vickers tool. The ball radius r is varied from 0.2 to 8.7 mm while the indent distance h is varied from several millimeters down to a few microns. Although cone cracks are a common feature under spherical indentation, the chipping event is dominated by median-radial cracks formed under the contact. The fracture behavior is characterized by a "large" indent distance regime where the median cracks progress stably up to chipping and a "small" one where they grow unstably to form a chip once initiated. Closed-form relations for chipping load P F under spherical indentation is developed with the aid of the test data and non-dimensional arguments. While in the "large" distance regime P F is proportional to h 3/2 irrespective of tool bluntness, in the "small" regime P F is proportional to r 1/2 h 3/4 . Interestingly, the chip dimensions are virtually independent of ball radius, varying linearly with h. Beyond relevance to structural integrity, the chipping test facilitates a simple means for determining fracture toughness K C as well as the load needed to initiate median cracks in opaque brittle materials. An attempt is made to extend the static analysis to low-velocity impact. The results show that the damage formed during the fracture process has a major influence on dynamic chipping.

A new perspective of lithic reduction in archaeology: numerically simulating flintknapping with peridynamics

“…However, the results obtained from sharp indenter analyses should still be informative for archaeologists. Blunt indentation has been specifically considered by Chai (2011) and Spelt 2010, 2011)), and will be discussed in Figure 8, the same two crack branches that grow outwards between images (a) and (d) correspond to the growth of the dark shadow in Figure 9, images (a) to (d), as it progressively moves to the left of the image (the free surface). The growth of the dark shadow in Figure 9 illustrates the crack growth in Figure 8 both curving around in a hemispherical form and growing down into the glass sample.…”

“…But, by understanding what causes particular morphological traits to appear on a stone tool, archaeologists would be able to reconstruct how a stone tool was made. As such, there is a desire to understand the physical processes which influence conchoidal fracture in stone (Rezek et al 2016;2011).…”

“…Subsequent edge chipping experiments utilizing blunt indenters (in the form of steel and ceramic balls) by Mohajerani and Spelt (2010) have found that as opposed to sharp indentation, a crack initiates from an asymmetric Hertzian cone crack. In particular, this crack develops at the margin of the contact patch (see Figure 12 and 13 reproduced from Mohajerani and Spelt (2010) and Chai (2011) below). This contrasts with the penny-shaped median cracks produced by sharp indenters, which initiate from the centre of the contact patch (Mohajerani and Spelt 2010).…”

“…This may indicate that an unknown product of certain parameters is potentially varying the observed crack propagation and termination mechanisms between each analysis method. For example, from the available results in edge chipping studies it appears that chips produced by Chai (2011;2017) and Mohajerani and Spelt (2011) are typically no greater in length than 10 mm, whilst the results of Dibble and Rezek (2009) and Rezek et al (2011) indicate the experimental flakes produced are typically of lengths around 10 cm or greater. It is not fully understood what causes this difference to exist, although one notable difference identified was the force required to produce a chip (the chipping load).…”

“…However, it is suspected that the main reason for this difference is the different indentation distance used in each experiment. Chipping load tends to increase with indentation distance (Chai 2011;Mohajerani and Spelt 2010). Finally, the discrepancy in length observed between edge chipping 'chips' and controlled experiment 'flakes' may also be explained if the different experiments used different sized glass cores (it is assumed that archaeological controlled experiments use larger cores given the larger flake length).…”