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During casting residual stresses are developed due to the solidification and cooling. In this work the robustness of residual stresses in casted brake discs with respect to variations in four parameters is evaluated. The parameters are Young’s modulus, yield strength and hardening, time of breaking the mould and the thickness of the brake disc. The robustness analysis is performed by Monte Carlo simulations of metamodels which are surrogates to a finite element model. Quadratic response surfaces and Kriging approximations are considered. Those are based on finite element analyses defined by a Latin hypercube sampled design of experiments. In the finite element analyses an un-coupled approach is utilized where a thermal analysis generates a temperature history of the solidification and cooling. Then follows a structural analysis which is driven by the temperature history. After casting the machining of the brake disc is analyzed by gradually removing elements in the finite element model. The results show that the variation in the studied parameters yield large variation in residual stresses. The thickness of the brake disc is the parameter that has largest influence to the variation in residual stresses. Furthermore, the level of the residual stresses are in general high and might influence the fatigue life of the brake disc.

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In this work the robustness of residual stresses in finite element simulations with respect to deviations in mechanical parameters in castings is evaluated. Young’s modulus, the thermal expansion coefficient and the hardening are the studied parameters. A 2D finite element model of a stress lattice is used. The robustness is evaluated by comparing purely finite element based Monte Carlo simulations and Monte Carlo simulations based on linear and quadratic response surfaces. Young’s modulus, the thermal expansion coefficient and the hardening are assumed to be normal distributed with a standard deviation that is 10% of their nominal value at different temperatures. In this work an improved process window is also suggested to show the robustness graphically. By using this window it is concluded that least robustness is obtained for high hardening values in combination to deviations in Young’s modulus and the thermal expansion coefficient. It is also concluded that quadratic response surface based Monte Carlo simulations substitute finite element based Monte Carlo simulations satisfactory. Furthermore, the standard deviation of the responses are evaluated analytically by using the Gauss formula, and are compared to results from Monte Carlo simulations. The analytical solutions are accurate as long as the Gauss formula is not utilized close to a stationary point.