Coupled damage variable based on fracture locus: Modelling and calibration

Abstract

A continuum ductile damage and failure model coupled with metal plasticity is presented, with the focus on capturing different failure mechanisms and prediction of the strain localisation. The onset of diffuse necking and local thinning is observed in the early stage of experiment and it is caused by the very low strain hardening capability of the material under study. Uniaxial tensile tests have been performed on notched and shear samples, specifically designed to cover different stress states by varying both the notch radius and orientation with respect to the sample axis. The experiments have revealed strain localisation caused by material softening. The latter is modelled by a coupled damage accumulation rule whose magnitude is dictated by the actual stress state and strain to fracture. Since the numerical model relies on the fracture strain determined by digital image correlation (DIC), which is dependent on the length scale imposed by the resolution of the DIC grid, an experimentally resolved length scale parameter l is introduced by nonlocal regularization of the material flow, based on large-deformation gradient theory. Apart from its common role of ensuring mesh independency, the length scale parameter obtains a new additional role: it makes the fracture locus calibration procedure robust under changes induced by different spatial averaging of the experimental fracture strain. The measured width of the strain localisation equals to the regularization length scale parameter l used in finite element (FE) simulations, thereby ensuring tight correspondence of physical reality and numerical model on the basis of a measurable quantity. As a result, the nonlocal regularization term prevents the strain in the numerical model to localise to a higher extent than experimentally observed. Eventually, the fracture locus has been constructed as a function of stress triaxiality ratio and Lode angle parameter. The FE-modelling methodology is calibrated by force-displacement curves and surface strain profiles prior to failure, obtained by DIC for a subset of sample geometries. The predictive capability of the proposed methodology is demonstrated by computing and comparing FE results to another experimentally characterized sample, not used in calibration procedure, i.e. dog-bone specimen. It undergoes a complicated loading path different from the paths used in the calibration procedure. It has been shown that regularization of strains and metal plasticity model supplemented by a damage variable are indispensable for an overall agreement of experimental and numerical results. The unique numerical model formulation has proven capable of capturing strongly different ductile failure modes, which are experimentally observed and further discussed.