Abstract
The identification of the post-necking strain hardening behavior of metal sheet is important for finite element analysis procedures of sheet metal forming process. The inverse modeling method is a practical way to determine the hardening curve to large strains. This study is thus focused on the evaluation of the inverse modeling method using a novel material performance test. In this article, hot uniaxial tensile test of a commercially pure titanium sheet with rectangular section was first conducted. Utilizing the raw data from the tensile test, the post-necking hardening behavior of the material is determined by a FE-based inverse modeling procedure. Then the inverse method is compared with some classical hardening models. In order to further evaluate the applicability of the inverse method, biaxial tensile test at elevated temperatures was performed using a special designed cruciform specimen. The cruciform specimen could guarantee that the maximum equi-biaxial deformation occurs in the center section. By using the inverse modeling procedure, the hardening curves under biaxial stress state are able to be extracted. Finally the stress-strain curves obtained from the two experiments are compared and analysis studies are provided.
Highlights
Nowadays the Finite Element Analysis (FEA) is used widely in the design stage of sheet metal forming operations with the aim of reducing the number of trial steps, controlling dimension accuracy and obtaining high-quality sheet forming products [1] and is almost indispensable in the manufacturing industries
The stress and strain values of the uniaxial tensile test can be obtained by using an extensometer that measures the elongation of a certain gauge length but the calculated stress value is accurate on the assumption that the test specimen is subjected to homogeneous state of uniaxial loading, which means that the stress-strain relationship identified by standard uniaxial tensile test is valid only before the so-called diffuse necking
It is obvious that the predicted post-necking hardening curve greatly depends on the choice of phenomenological constitutive models and one model that is best fitted to a certain material may not suits for another [6]
Summary
Nowadays the Finite Element Analysis (FEA) is used widely in the design stage of sheet metal forming operations with the aim of reducing the number of trial steps, controlling dimension accuracy and obtaining high-quality sheet forming products [1] and is almost indispensable in the manufacturing industries. A new optical-numerical measurement techniques, i.e., the Digital Image Correlation (DIC) method, is used widely for obtaining full-field information for both in-plane displacements and strains of the test specimen and has been applied by many researchers for determining the post-necking hardening curve of uniaxial test [12,13], Scheider et al [14] investigated the necking phenomenon based on finite element analysis with the help of DIC technique and proposed a new post-necking model which has a higher accuracy than Zhang’s [9] model Another effort to identify the post-necking stress-strain curve of uniaxial tensile test is concentrated on the inverse modeling procedures.
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