Double-Cantilever Cleavage Mode of Crack Propagation

Abstract

The quantitative cleavage method for determining specific surface energies of solids is subject to several possible sources of error. Some of these are investigated analytically in this study, and a general expression for the surface energy is derived from beam theory for a linearly elasticmaterial. The exact equation of motion for the propagating crack is derived but not solved. Errors associated with each term of the general expression are assessed. The ratio of shear to bending strain energy is small if the initial crack length is long compared with the specimen depth. The term arising from strains in the specimen past the tip of the crack is not developed, but is estimated; and a procedure is outlined for determining this term experimentally. Comparison of simple beam theory with more exact elasticity theory shows that in the main spans the difference is small because it involves only the shear strain energy. Also, restriction of anticlastic curvature near the crack tip is unimportant if the initial crack length is long compared with the specimen width. Elasticanisotropy is unimportant when shear can be neglected, provided the appropriate modulus is used. For nonlinear elasticmaterial, as the crack propagates a small amount, the work increment is either zero or double the strain energy increment. A surface energy expression is developed in terms of Timoshenko's ``reduced modulus,'' and upper and lower bounds are fixed. For plastic materials the analysis is based on pseudoinstantaneous plastic response. Justification of this assumption is difficult to defend or deny. Therefore, an important conclusion is that whenever possible specimens should be designed to remain grossly within the elastic limit of the material. Superposition of large axial forces is a potential source of large errors in surface energy determinations, and possible eccentricities in the application of such forces makes even the sign of these errors difficult to determine. Hence, this method for stabilizing the crack plane is not recommended.