Crack length correction and root rotation angle in a sandwich single cantilever beam (SCB) fracture specimen

Abstract

Crack root rotation is a measure of deviation from clamped boundary conditions of region in front of the crack tip. The root rotation depends on the shear force and bending moment acting at the crack tip. Such rotation significantly affects the compliance and energy-release rate. Crack root rotation analysis of Single Cantilever Beam (SCB) sandwich specimens is presented here. Closed-form solutions for the root rotation angle obtained from the foundation analysis are compared to finite element analysis (FEA) predictions. The derived expressions closely match for a range of sandwich configurations. An expression for the energy-release rate, derived from the foundation analysis was found to agree with FEA predictions over a large range of face-to-core modulus ratios. Energy-release rate and mode mixity phase angle increased with decreasing crack length due to the transverse shear effects. At longer crack lengths, both energy-release rate and phase angle reached a value independent of crack length. The foundation model is used to derive a simple expression for the offset crack length for the SCB sandwich fracture test. It is shown that the obtained formulation agrees closely well with both numerical and experimental values. In addition, SCB fracture tests performed using an in-house built translatable rig showed close relation to both analytical and numerical compliance results.