On the modeling of large ratcheting strains and anisotropy in pearlitic steel

Sammanfattning: Thermodynamically consistent constitutive material models for describing the large strain response of polycrystalline metals are proposed. Emphasis is put on the multiaxial ratcheting under cyclic loading and the evolution of anisotropy in pearlitic steel. For cyclic loading, the experimentally observed large ratcheting strains is modelled by the classical Armstrong-Frederick type of evolution with several back-stresses. In addition, with the purpose to mimic a multiaxial ratcheting rate, a dependence on the Hessian of the yield function is suggested. Furthermore, the model parameters are identified against different sets of experimental data for pearlitic steel. Next, two different models for the evolution of deformation induced anisotropy at large strains are proposed. The first model is inspired by recent material modeling for applications in biomechanics. In the second model, the reorientation of the pearlitic grains under large deformations is homogenized analytically to the macroscopic length scale. The use of a Hill type of yield criterion on the macroscopic length scale is motivated from the homogenization. In order to increase computational efficiency, an adaptive time-stepping algorithm is proposed for solving boundary value problems under cyclic loading conditions with a large amount of load cycles. The algorithm is based on large time increments that span several loading cycles and is less computationally demanding as compared to standard time incrementation. Finally, the performance of the models is illustrated by numerical examples. In particular, the models are used to predict the long term deformations of a railway turnout when it is subjected to repeated loading.