Scale effects in necking

Abstract

Geometrically similar specimens spanning a scale range of 100:1 are tested quasi-statically to failure. Images of neck development are acquired using optical means for large specimens, and in-situ scanning electron microscope testing for small specimens, to examine the dependence of neck geometry on a broad range of specimen sizes. Size effects typically arise when the smallest specimen dimension is on the order of a microstructural length (e.g. grain size, dislocation mean free path, etc.), or in the presence of significant plastic strain gradients, which increase the density of geometrically necessary dislocations. This study was carried out for the purpose of investigating scale dependence in models used for predicting dynamic deformation and damage to very high strains for ballistic impact applications, such as the Goldthorpe path-dependent failure model, which includes temperature and strain-rate dependence but does not account for specimen size or a dependence on microstructural lengths. Although the experiments show that neck geometry does not exhibit a clear dependence on specimen size across the range of length scales tested, the statistical variation due to microstructural variations was found to increase monotonically with decreasing size, becoming significant for the smallest (0.35 mm diameter) size, allowing a limit to be identified for reliable model calibration.