The Haensel damage model correlates lifetime of a component until crack initiation to the dissipated and stored energy in the material during cyclic loading. The crack initiation is influenced by mean stresses. The Haensel damage model considers the mean stress effect by including compressive and tensile stresses in calculations of elastic strain energy during cyclic loading conditions. The goal of the paper is to extend the above model to predict crack propagation under large cyclic plasticity and non-proportional loading conditions. After voids initiation onset of necking, voids growth and linking takes place among them. During this process a mesocrack is created. This stage of fracture involves the same amount of released energy for new crack surface creation as dissipated energy for mesocrack initiation. The amount of dissipated and stored energy is related to the process zone size and to the number of cycles. Ilyushin’s postulate is used to calculate the amount of dissipated energy. In order to consider a contribution of tensile stresses only during loading to crack propagation, tensile/compressive split is performed for the stress tensor. One of the key drivers of this paper is to provide a straightforward engineering approach, which does not require explicit modelling of cracks. The proposed mathematical approach accounts for redistribution of stresses, strains and energy during crack propagation. This allows to approximate the observed effect of distribution of dissipated energy on the front of a crack tip. The developed approach is validated through FE (Finite Element) simulations of the Dowling and Begley experiment. The Haensel lifetime prediction of Dowling’s experiment is in good agreement with the experimental data and the explicit FE results. Finally, the proposed mathematical approach simplifies significantly the engineering effort for Nonlinear Fracture Mechanics lifetime prediction by avoiding the requirement to simulate real crack propagation using node base release methods, XFEM or remeshing procedures.
In situ monitoring of dislocation, twinning, and detwinning modes in an extruded magnesium alloy under cyclic loading conditions
