A polygonal FEM and continuum damage mechanics based framework for stochastic simulation of fatigue life scatter in duplex microstructure titanium alloys

Abstract

The scatter in the fatigue behavior of duplex microstructure titanium alloys occurs due to microstructural randomness. The presence of two phases in titanium alloy microstructure also contributes to the scatter in fatigue life data. In the literature, several mathematical frameworks have been developed to consider the effect of microstructural randomness on the prediction of fatigue scatter. However, no numerical study has been found that considers the effect of presence of two phases on the fatigue life scatter. Thus, in the present work, a mathematical framework based on continuum damage mechanics (CDM) and polygonal finite element method (PFEM) is developed to predict the fatigue life scatter in α+β titanium alloys. In this framework, PFEM is applied to perform the numerical simulations and CDM is used to explain the fatigue behavior of material. In PFEM, the Voronoi tessellation approach is used to generate the idealized microstructure models. The Waschpress shape functions are adopted to compute the shape functions over the arbitrary convex polygonal elements. In CDM, a fatigue damage model is adopted to consider the crack initiation and propagation under the cyclic loading conditions. The advantage of combined CDM-PFEM framework is that the numerical simulation can be performed at relatively coarser mesh which decreases the computational cost and increases the efficiency of the computational model.While predicting the fatigue life, it has been observed that micro cracks may initiate and propagate at several locations inside the microstructure. Thus, to track the nucleation and growth of micro cracks effectively, a machine learning based technique ‘cluster analysis’ is employed in the developed framework. The “cluster analysis” identifies the location and dimensions of the micro and dominant crack patterns in the domain. Furthermore, for an idealized representation of duplex microstructures, both phases of titanium alloy (i.e., primary α and β) are modeled using random distribution function. The effect of different sources of randomness in microstructures i.e., topology of microstructure, grain size, volume fraction of alpha phase, inhomogeneity in elastic modulus and internal voids, on the fatigue life is investigated. Several simulations are performed on the numerically generated microstructures at various loads. The statistical analysis of the predicted fatigue lives data is performed through normal and Weibull distribution fits. The simulation results highlight that the combined CDM-PFEM based framework is simple and an effective tool to predict the fatigue life scatter and can effectively analyze the mean fatigue life in titanium alloys under cyclic loading conditions.