PQR Model-based Micromechanical Analysis of Hysteresis Loops for Single Crystal Fatigue: Aspects of Multi-Axial Loading, Geometric Effects and Creep

The micromechanical theory of fatigue crack initiation, namely the PQR model with a gating mechanism proposed by Lin (1992), is systematically summarized and further generalized to arbitrary loading conditions which may occur in reality. All possible loading cases and slip mechanisms are considered for a FCC single crystal. The Schmid factors for both primary and secondary slip systems are presented. A 3D boundary element method is adopted to compute the stress influence coefficients for the residual stress field. The hysteresis loops, which are due to a general two phase sequential loading process, i.e., a uni-axial loading followed by a multi-axial loading applied by combined shear and axial loadings, are given to illustrate the fatigue development and demonstrate the proposed methodology. The results show that the two stage loading may increase the magnitudes of intrusion and extrusion. Subsequently the geometry influence for intrusion is studied. The effect of geometry variation caused by intrusion is taken into account through updating the stress influence coefficients as well as the applied resolved stress when intrusion grows. This process is continued until the saturated state of fatigue crack initiation is reached. Comparison of geometry influence on intrusion growth is shown as well. It turns out that the geometric change could become an important factor for the intrusion growth. Finally by replacing the plastic strain with creep strain the present model is easily extended to investigate the steady hysteresis loops for single crystal creep at elevated temperature. The results compare favorably with the available experimental data.