Modeling single crystals: time integration, tangent operators, sensitivity analysis and shape optimization

In this paper, a comprehensive overview of the numerical analysis of single crystalline materials at high temperatures is presented, including implicit higher order time integration, consistent linearization and respective sensitivity analysis. Both a phenomenological and a crystallographic model are employed to simulate the mechanical isothermal behavior of the nickel-based superalloy CMSX-4 at 950°C in a finite element environment. A shape optimization methodology for testing specimen design based on extensive finite element computations is presented. The sensitivity analysis according to the chosen time integration scheme is performed leading to an algorithm for simultaneous analysis and design (SAND). Examples for the shape optimization of a cruciform specimen for biaxial tensile experiments at high temperatures are given and discussed in detail.