Identification of material parameters for thin sheets from single biaxial tensile test using a sequential inverse identification strategy

Abstract

An inverse analysis methodology to simultaneously identify the parameters of various anisotropic yield criteria together with isotropic work-hardening models of metal sheets is outlined. This identification makes use of results of the cruciform biaxial test, i.e., the evolution of the force during the test, for the two axes of the sample, and the major and minor strain distributions along both axes, at a given moment during the test. Based on a study of the sensitivity of the constitutive parameters to the biaxial tensile test results, the inverse identification consists on a procedure that sequentially minimises the gap between experimental and numerical results. Each step of the sequence uses a distinct cost function according to the type of results to be minimised, using a gradient-based optimisation algorithm, the LevenbergMarquardt method. The inverse methodology allows for the identification of constitutive parameters of complex constitutive models. This sequential identification strategy is compared to a strategy based on a single cost function, involving all parameters and type of results, which has lower performance.

Inverse Strategies for Identifying the Parameters of Constitutive Laws of Metal Sheets

“…(1) Strategies Using Cruciform Specimens. There has been a steadily growing interest in developing inverse identification strategies supported by the use of the biaxial tensile test of cruciform specimens, coupled with full-field displacement or strain measurements (e.g., [21,[24][25][26][27][28][29]). In general, this test allows (i) strain paths ranging from uniaxial tension (in the arms region of the specimen) to balanced biaxial tension (in the centre section of the specimen), (ii) high strain gradients from the centre region of the specimen to the end of the arms region, and (iii) no contact between surfaces and therefore no friction.…”

“…Prates et al [25,26] designed a cruciform sample and developed two strategies for simultaneously identifying the parameters of the anisotropic yield criteria and isotropic hardening law of sheet metals. Both strategies use the results of the load evolution during the test and of the major and minor principal strains distributions, along the axes of the sample, at a given moment of the test, preceding the maximum load.…”

“…This allowed extending the strategy to more complex constitutive models (yield criteria and isotropic hardening laws). Therefore, a general inverse identification strategy that sequentially uses three distinct cost functions was developed [26]. It resorts to the Levenberg-Marquardt algorithm for sequential optimization of the parameters of the yield criteria and isotropic hardening laws.…”

“…The full-field measurements allow the acquisition of enriched information from mechanical tests, such as displacement and strain fields; 2 Advances in Materials Science and Engineering an overview on this topic can be found in [20]. This allows attenuating the constraints on the geometry and loading conditions of the mechanical tests used for the identification of materials parameters, so that nonhomogeneous stress and strain distributions can be developed in the region of interest (e.g., [21][22][23][24][25][26][27][28][29]). In this sense, the identification of constitutive parameters from nonhomogeneous strain fields and complex loading conditions provides a more reliable description of the material behaviour during real sheet metal forming processes [21].…”

“…Note: 1D: in one direction in the sheet plane; 2D: on the surface of the sheet plane; 3D: three-dimensional. Cruciform specimen geometries proposed in the literature for FEMU strategies: (a) Schmaltz and Willner[24]; (b) Cooreman et al[21]; (c) Prates et al[25,26]; (d) Zhang et al…”