Determination of fracture toughness from the extra penetration produced by indentation-induced pop-in

Abstract

The fracture toughness of small volumes of brittle materials may be investigated by using pyramidal indenters to initiate radial cracks. The length of these cracks, together with indenting load and the hardness to modulus ratio of the material, were combined to calculate the critical stress intensity factor Kc pertinent to fracture toughness. Modulus and hardness may be obtained from the literature or may be measured using nanoindentation techniques. If the material volume is very small, such as single grains in a conglomerate, a reduction of scale may be obtained by reducing the internal face angles of the indenter. This encourages crack initiation at lower loads, but cracks produced at very low loads are short and difficult to measure. Experiments on fused silica and glassy carbon suggested that radial cracks are initiated during loading and that when indenters with sufficiently small angles are used these cracks immediately pop-in, to become fully developed median/radial crack systems. Following pop-in, the rate of penetration of the indenter increases and at higher loads there is an extra increment of penetration over that which would otherwise have occurred. In this study a method is described whereby this extra penetration may be determined. Then for two dissimilar brittle materials, crack length is shown to be correlated with extra penetration leading to a relationship that may possibly avoid the necessity for crack-length measurement.

Effect of Electrochemical Charging on Elastoplastic Properties and Fracture Toughness of LiXCoO2

“…[2] Figure 1 illustrates the parameters used to calculate the fracture toughness of brittle materials from nanoindentation hystereses, according to the pop-in method of Field et al 38 The crack length c was determined according to Equation 3, where E and H were measured as described above for indentations at lower loads, and pop-in depth h m and length h x as defined in Fig. 1 were determined for each indentation according to a Hertzian fitting procedure using a custom Mathematica 7.0 (Wolfram) code:…”

Biomechanics of the Bat Limb Skeleton: Scaling, Material Properties and Mechanics

“…This approach employs a microscopic indenter, typically 1-10 m in diameter, that can be applied to a prepared surface with a small, precisely measured force, in the range of tens to hundreds of millinewtons, to a controlled depth, typically hundreds to thousands of nanometers. The response of the calibrated system can then be used to accurately compute material stiffness, as well as other elastic constants, and, with the proper application, nanoindentation can also be used to assess fracture toughness as well [Li and Bhushan, 2002;Field et al, 2003;Scholz et al, 2004]. This approach is beginning to be applied in bone biology with great success [Erickson et al, 2002;Goodwin and Sharkey, 2002;Hengsberger et al, 2002;Wang et al, 2002] and is ideally suited to assessing mechanical properties of the small, delicate bones of bats.…”

Compliant Yet Brittle Mechanical Behavior of Li2S–P2S5 Lithium‐Ion‐Conducting Solid Electrolyte

“…[19,32,33] However, these LPS solid electrolyte samples did not exhibit detectable displacement excursions associated with radial cracking under our accessible instrumented indentation conditions. Thus, we conducted microindentation with a diamond Vickers probe geometry (LECO LM248AT; Saint Joseph, MI) to apply Newton-scale loads to the material.…”