Topology optimization method for PBF-LB components with consideration of manufacturing-related residual stresses

To slow down global warming, it is necessary to reduce CO2 emissions. Lightweight construction can contribute to this by minimizing the weight of moving masses, which leads to less energy consumption and eventually less CO2 emissions. Topology optimization can be used to obtain a design proposal for weight-reduced components. This often results in complex designs that are difficult to produce using conventional manufacturing processes. Additive manufacturing, such as laser powder bed fusion (PBFLB), by contrast, is very suitable as it offers a high degree of design freedom due to the layered build-up. However, high temperature gradients during production in PBF-LB result in high residual stresses in the finished component, which must be considered during the topology optimization. Therefore, a topology optimization method is developed that can iteratively consider the residual stresses.
To be able to map the residual stresses in each iteration of the topology optimization, initially X-ray diffraction was used to measure the planar stress state of PBF-LB components both on the surface and in depth. A general residual stress function was derived that can be used to approximate a stress tensor for each point within PBF-LB components, depending on the surface geometry, orientation and distance from the surface.
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Within the density-based topology optimization, an interruption takes place in each iteration after the density distribution is calculated by the optimizer. Depending on the density, a smoothed surface is generated that reflects the geometry of the current design proposal. The distance and orientation of each finite element (FE) inside the smoothed surface to the nearest surface element on the smoothed surface is determined. Subsequently, a stress tensor for each FE is obtained by calculating the residual stress function and by scaling dependent on their densities. In the last step of the interruption, the residual stress tensors of each FE are stored in an initial stress distribution before the actual load case step.
The objective function of the topology optimization is to maximize the stiffness for a given volume reduction. Since the method is also intended to find designs in which there is no critical overlapping of residual stresses and tensile stresses caused by the load case, a maximum stress criterion is considered.
The developed method is applied to PBF-LB components in blasted and non-blasted condition which show a different residual stress behavior near the components surface. Improved designs could be obtained for non-blasted PBF-LB components.