Shape optimization of the X0-specimen: theory, numerical simulation and experimental verification
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ORIGINAL PAPER
Shape optimization of the X0-specimen: theory, numerical simulation and experimental verification Jan Liedmann1
· Steffen Gerke2 · Franz-Joseph Barthold1 · Michael Brünig2
Received: 12 May 2020 / Accepted: 4 August 2020 © The Author(s) 2020
Abstract The paper deals with the gradient based shape optimization of the biaxial X0-specimen, which has been introduced and examined in various papers, under producibility restrictions and the related experimental verification. The original, engineering based design of the X0-specimen has been applied successfully to different loading conditions persisting the question if relevant stress states could be reached by optimizing the geometry. Specimens with the initial as well as with the two load case dependent optimized geometries have been fabricated of the aluminum alloy sheets (AlSi1MgMn; EN AW 6082-T6) and tested. The strain fields in critical regions of the specimens have been recorded by digital image correlation technique. In addition, scanning electron microscope analysis of the fracture surfaces clearly indicate the stress state dependent damage processes. Consequently, the presented gradient based optimization technique facilitated significant improvements to study the damage and fracture processes in a more purposeful way. Keywords Optimal specimens · Variational sensitivity analysis · Shape optimization · Biaxial experiments · Damage · Stress state dependence
1 Introduction Ductile sheet metals are of outstanding relevance in many engineering applications and consequently, the need to improve the lightweight design, to decrease the energy consumption and to increase the cost efficiency is evident and thus, the utilization factor of these materials has to be augmented. This leads to the demand to characterize the material behavior within the inelastic domain properly and to avoid early localization of irreversible strains as well as damage and fracture within structural components. The connected material failure processes strongly depend on the stress state: In tension dominated regions nucleation, growth and coalescence of micro-voids prevail, whereas shear stress states facilitate micro-shear-cracks. To analyze this behav-
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Jan Liedmann [email protected] Steffen Gerke [email protected]
1
TU Dortmund University, August-Schmidt-Straße 8, 44227 Dortmund, Germany
2
Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85579 Neubiberg, Germany
ior, experiments with carefully designed specimens covering a wide range of relevant stress states have to be performed. Standard specimens are frequently designed to generate one pre-defined stress state within the region of interest whereas only one loading condition can be applied. Recent developments in this field indicate the request to develop new geometries for in-plane sheet metal testing in a representative range of loading conditions. In this context, the stress is frequently characterized by the stress intensity, the stress triaxiality and the Lode parameter which can be
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