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.
Highlights
Ductile sheet metals are of outstanding relevance in many engineering applications and the need to improve the lightweight design, to decrease the energy consumption and to increase the cost efficiency is evident and 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
Cf. e.g. [6,45], and the discrete approximations, i.e. the nodal vector of test functions, displacements and displacement variation v, u, δu ∈ Rndof, the nodal design vector and its variation X, δX ∈ Rndv, as well as the vector of variations of global internal variables δhn,h ∈ Rnhv, we find the discrete versions of Eqs. (25), (47), (48) and (49), respectively
Summary
Ductile sheet metals are of outstanding relevance in many engineering applications and the need to improve the lightweight design, to decrease the energy consumption and to increase the cost efficiency is evident and the utilization factor of these materials has to be augmented. 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. To investigate the material behavior and the damage mechanisms in a more satisfactory way in a first cut it is preferable to reach on one hand high stress triaxialities (micro-voids) and on the other hand low stress triaxialities (micro-shearcracks) For this purpose, mathematical optimization techniques can be utilized to modify the shape of specimens in order to gain these preferred stress states in an area of interest.
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