A reduced-order method for parameter identification of a crystal plasticity model considering crystal symmetry

The focus of this paper is to identify the material parameters of a crystal plasticity model for Ni-base single crystal superalloys. To facilitate the stepwise calibration of the multistage flow rules, further decoupling and simplification are implemented without compromising its simulating capability. Reduced-order kinematics in crystal plasticity, which only comprise scalar components instead of their original tensors, are derived by considering the crystal symmetry and uniaxial loading condition. The relationships between components in elastic and plastic deformation gradient are established by explicitly accounting the control quantities, which is overall load in stress-controlled creep tests or displacement of gauge section in strain-controlled experiments, respectively. In addition, their approximate forms are also given by neglecting both elastic changes in volume and section area. A new objective function based on the shortest distance was introduced to correlate data from the simulations and experiments, and an integrated optimization process without finite element computation was developed into a commercial software package. Parameters in the crystal plasticity model are successfully calibrated by the efficient reduced-order method from the experimental data in such a sequence as: elastic, plastic, primary stage and secondary to tertiary stages creep laws. The multistage weak coupling flow rules can significantly reduce the non-uniqueness of the optimal solution under the circumstance of excessive parameters but insufficient experimental data. Finally, the optimized results with the reduced-order method have been validated by the finite element method.