Explicit Analysis of Sheet Metal Forming Processes Using Solid-Shell Elements

To simulate sheet metal forming processes precisely, an in-house dynamic explicit code was developed to apply a new solid-shell element to sheet metal forming analyses, with a corotational coordinate system utilized to simplify the nonlinearity and to integrate the element with anisotropic constitutive laws. The enhancing parameter of the solid-shell element, implemented to circumvent the volumetric and thickness locking phenomena, was condensed into an explicit form. To avoid the rank deficiency, a modified physical stabilization involving the B-bar method and reconstruction of transverse shear components was adopted. For computational efficiency of the solid-shell element in numerical applications, an adaptive mesh subdivision scheme was developed, with element geometry and contact condition taken as subdivision criteria. To accurately capture the anisotropic behavior of sheet metals, material models with three different anisotropic yield functions were incorporated. Several numerical examples were carried out to validate the accuracy of the proposed element and the efficiency of the adaptive mesh subdivision.

On the Use of Homogeneous Polynomial Yield Functions in Sheet Metal Forming Analysis

Sheet metal forming techniques are a major class of stamping and manufacturing processes of numerous parts such as doors, hoods, and fenders in the automotive and related supplier industries. Due to series of rolling processes employed in the sheet production phase, automotive sheet metals, typically, exhibit a significant variation in the mechanical properties especially in strength and an accurate description of their so-called plastic anisotropy and deformation behaviors are essential in the stamping process and methods engineering studies. One key gradient of any engineering plasticity modeling is to use an anisotropic yield criterion to be employed in an industrial content. In literature, several orthotropic yield functions have been proposed for these objectives and usually contain complex and nonlinear formulations leading to several difficulties in obtaining positive and convex functions. In recent years, homogenous polynomial type yield functions have taken a special attention due to their simple, flexible, and generalizable structure. Furthermore, the calculation of their first and second derivatives are quite straightforward, and this provides an important advantage in the implementation of these models into a finite element (FE) software. Therefore, this study focuses on the plasticity descriptions of homogeneous second, fourth and sixth order polynomials and the FE implementation of these yield functions. Finally, their performance in FE simulation of sheet metal cup drawing processes are presented in detail.

A Virtual Laboratory Based on Full-Field Crystal Plasticity Simulation to Characterize the Multiscale Mechanical Properties of AHSS

In this work, we proposed a virtual laboratory based on full-field crystal plasticity simulation to track plastic anisotropy and to calibrate yield functions for multi-phase metals. The virtual laboratory, minimally, only requires easily accessible EBSD data for constructing the high-resolved microstructural representative volume element and macroscopic flow stress data for identifying the micromechanical parameters of constituent phases. An inverse simulation method based on global optimization scheme was developed for parameters identification, and a nonlinear least-squares method was employed to calibrate the yield functions. Various mechanical tests of an advanced high strengthening steel (DP980) sheet under different loading conditions were conducted to validate the virtual laboratory. Three well-known yield functions, the quadratic Hill48, Yld91, and Yld2004-18p, were selected as the validation benchmarks. All the studied functions, calibrated by numerous stress points under arbitrary loading conditions, successfully captured both the deformation and strength anisotropies. Furthermore, the full-field CP modeling well correlates the microscopic deformation mechanism and plastic heterogeneity to the macro-mechanical behavior of the sheet. The proposed virtual laboratory, which is readily extended with physically based CP model, could be a versatile tool to explore and predict the mechanical property and plastic anisotropy of advanced multi-phase metals.

Inverse Identification for the Balanced Biaxial Yield Stress of AA5182-O Alloy Sheet

Advanced yield functions, such as Yld2004, could describe the elastic boundary of materials better than the traditional. However the balanced biaxial yield stress σb which is essential to determine the parameters of advanced yield functions is hard to measure using frequently used test equipment. This work presented an inverse method to calibrate σb of AA5182-O alloy sheet based on the Erichsen test. The maximum punch force (MPF) measured from this test was used for the inverse identification. A modification coefficient was used to drop down the simulation MPF from shell element, as the application of shell element result in higher simulation punch force. Then the relationship between σb and MPF was established based on the plane stress Yld2004. With this relationship and the real measured MPF, σb could be inversely identified. Additionally, a hydraulic bulge test was performed to verify the accuracy of this inversely obtained σb.