Notch-sensitivity of non-linear materials

Abstract

The relationships between breaking stress, σB, and crack length, a, and between breaking strain, eB, and a have been calculated for materials whose stress-strain behaviour is approximated by σ=ke n. The results take the form σB∝ (a) −m and eB∝ (a) −p, where m=n/(n+1) and p=1/(n+1). For n=1 (the linear case), m=p=1/2. For n>1, m>1/2>p and for n 1, σB drops off very rapidly with increasing defect size, whereas eB is far less dependent on a. These may be appropriate properties for a material where the degree of extension, rather than the peak loads encountered, is critical to its in vivo performance. For materials where n<1, breaking stress is far less sensitive to crack length than fracture strain, which may be more appropriate properties for applications in which applied stress, but not strain, is critical.