Energy Release Rate Formulations for Non-conventional Fracture Test Geometries

Abstract

Non-conventional fracture test geometries such as single cantilever bending, clamped beam bending and clamped wire bending have been developed over the years to suit the needs of micro- and nano-scale testing. The same geometries can also be used at the macro-scale if testing standards are well established. Development of length scale compatible geometries helps the materials engineer to seamlessly extract material properties across multiple length scales. This article proposes the crack driving force (or energy release rate G) criteria for the above three geometries. These geometries have found widespread use at the micro-scale and can be adapted to the macro-scale. Use of a global energy-based criterion instead of the local stress-based criteria (stress intensity factor K) has its own advantages, especially in multi-phase materials and interface-dominated structures which display an R-curve. Aspects of crack stability even under load control arising because of the geometric factors, especially the beam or wire aspect ratio, are discussed in this context. Validation of the compliance approach is carried out by comparing it to the J-integral extracted directly for a linear elastic material using extended finite element modeling and also using the analytical formulation for a double-cantilever beam specimen. Experimental evidence of the validity of the solutions in determining the fracture energy of a linear elastic brittle material, PMMA, as a homogeneous model system is shown.