Experimental and computational study of fracturing in an anisotropic brittle solid

Abstract

For isotropic materials, stress-and energy-based fracture criteria lead to fairly similar results. Theoretical studies show that the crack-path predictions made by these criteria are not identical in the presence of strong material anisotropy. Therefore, experiments are performed to ascertain which criterion may apply to anisotropic materials. Notched specimens made from sapphire, a microscopically homogeneous and brittle solid, are used for the experiments. An attempt is made to locate the notch on different crystallographic planes and thus to examine the fracture path along different cleavage planes. The experimental observations are compared with the numerical results of the maximum tensile stress and the maximum energy-release rate criteria. It is observed that most of the notched specimens are fractured where the tensile stress is maximum, whereas the energy criterion fails to predict the fracture path of most of the specimens. For the tensile-stress Žn.fracture criterion, a dimensionless parameter, A s 2p R s r g E , is introduced, where s and E , respectively, ' ' 0 n n a n n n n n n Ž are the tensile stress and Young's modulus in the direction normal to the cleavage plane specified by the angle a the . fracture surface energy of this plane is g and R is a characteristic length, e.g. the notch radius. Five out of six notched a 0 specimens which were tested, fractured at the point and along a cleavage plane where A Žn. is maximum. This parameter takes into account the effects of the surface energy of the corresponding cleavage plane, as well as the strength of the atomic bonds in the direction normal to the cleavage plane. It is suggested that for a specimen with a pre-existing crack, the Žc. maximum value of the parameter, A s K r g E , should be used as the measure of the fracturing condition, where ' nn a n n K is the hoop stress intensity factor in the direction normal to the cleavage plane. For the notched sapphire specimens, nn Laue-diffraction analysis, along with the considerations of the geometry of the unit cell of sapphire, shows that the weakest Ä 4 Ä 4 family of cleavage planes, 1012 and 1010 , are the fractured planes. q

The effect of anisotropy on the deformation and fracture of sapphire wafers subjected to thermal shocks

“…Moreover, single crystal materials have a discrete number of cleavage planes and do not always fracture in the direction of the highest tensile stress, but rather in the direction where a high tensile stress acts on a weak cleavage plane. This was supported experimentally [26] and the results on notched A-plane sapphire specimens showed that the energy criterion fails to predict the fracture path of most of the specimens. A dimensionless parameter A was introduced to measure the onset of crack initiation.…”

“…Reports on γ λ of different cleavage planes in single crystal sapphire [26] show that the strongest plane is the basal c-plane (0 0 0 1) having γ λ > 40 J/m 2 , and the weakest family of planes is {1 0 1 2} having γ λ = 6 J/m 2 . The other families of cleavage planes are stronger: {11 2 6} with γ λ = 24.2 J/m 2 and {1 01 0} with γ λ = 7.3 J/m 2 .…”

“…1) and c = 12.991Å is the crystal dimension along the optical c-axis. Table 1 also lists the surface energy γ λ [26] and the critical fracture toughness K Ic on all cleavage planes.…”

Lattice dynamics of a mist-chemical vapor deposition-grown corundum-like Ga2O3 single crystal

“…The lowest surface energies are found for the f10 10g and f 1012g planes. 24 The orientation of the lateral surface in our sample was determined to be ð10 10Þ by means of XRD measurements. Figure 3 shows the polarized Raman spectra obtained from the ð10 10Þ lateral face.…”

Phase‐field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy

“…While most theoretical and computational studies have focused on elastic anisotropy [1][2][3], the anisotropy of the fracture toughness influences more strongly the crack propagation of a wide variety of materials including single crystals [4][5][6], extruded polymers [7], geological materials [8,9], including sedimentary [10] and granitic rocks [11], or apple flesh [12]. The issue of brittle crack propagation in materials with anisotropic surface energy deeply interrogates our understanding of fracture and is receiving increasing attention from a variety of points of view, such as molecular dynamics [13], continuum mechanics [14,15], phase-field modeling [16,17], and experiments [7,18]. Here, by exploiting the analogy with crystal growth, we develop and implement numerically a phase-field model for brittle fracture of materials with strongly anisotropic surface energy and interpret our numerical results in the light of recent theories and experiments.…”