The analysis of deformation size effects using multiple gauge length extensometry and the essential work of rupture concept

Size dependence of the load–displacement and stress–strain curves is a phenomenon widely reported in the literature and readily observed in experiments. The present paper introduces two developments in the analysis of ductile rupture, one in the area of experimental technique and interpretation, and one in the area of numerical modelling. Firstly, the new experimental technique is described of multiple gauge length optical extensometry (laser scanning) that provides a uniquely powerful means of collecting the data needed for the study of size effects, from a single tensile test on a ductile specimen. The interpretation procedures are presented based on the considerations about the nature of deformation and energy expenditure within different material volumes in a tensile specimen. Consequently, the property of the specimen can be defined and identified that relates to the energy consumption per unit cross-sectional area required to rupture the specimen entirely (the essential work of rupture). Another energetic measure is also obtained from the test that relates to the plastic work dissipation per unit volume in pre-peak deformed material. Secondly, the observed size effects and specific energy determination procedures are discussed in the context of non-local coupled plasticity-damage modelling. Conventional local numerical models of inelastic deformation fail to predict the sequence of deformation responses observed in the tensile test, namely, uniform deformation followed by strain localisation, necking and rupture. It is shown here that coupled non-local damage-plasticity modelling is capable of capturing the hardening–softening and global–local plasticity transitions, and hence the trends observed in ductile fracture. The predictions of the coupled non-local damage-plasticity modelling for different deformation regimes are shown to agree qualitatively with the experimentally observed behaviour. The two aspects of the proposed approach, experimental and modelling, are presented here together since they are intimately linked at the fundamental level. The implications of the proposed approach are discussed for the deformation analysis of plastically deforming and damageable materials and structures at various scales, from macroscopic to miniature.