Shuhui Li

Forming Limits of a Sheet Metal After Continuous-Bending-Under-Tension Loading

Forming limit diagrams (FLD) have been widely used as a powerful tool for predicting sheet metal forming failure in the industry. The common assumption for forming limits is that the deformation is limited to in-plane loading and through-thickness bending effects are negligible. In practical sheet metal applications, however, a sheet metal blank normally undergoes a combination of stretching, bending, and unbending, so the deformation is invariably three-dimensional. To understand the localized necking phenomenon under this condition, a new extended Marciniak–Kuczynski (M–K) model is proposed in this paper, which combines the FLD theoretical model with finite element analysis to predict the forming limits after a sheet metal undergoes under continuous-bending-under-tension (CBT) loading. In this hybrid approach, a finite element model is constructed to simulate the CBT process. The deformation variables after the sheet metal reaches steady state are then extracted from the simulation. They are carried over as the initial condition of the extended M–K analysis for forming limit predictions. The obtained results from proposed model are compared with experimental data from Yoshida et al. (2005, “Fracture Limits of Sheet Metals Under Stretch Bending,” Int. J. Mech. Sci., 47(12), pp. 1885–1986) under plane strain deformation mode and the Hutchinson and Neales (1978(a), “Sheet Necking—II: Time-Independent Behavior,” Mech. Sheet Metal Forming, pp. 127–150) M–K model under in-plane deformation assumption. Several cases are studied, and the results under the CBT loading condition show that the forming limits of post-die-entry material largely depends on the strain, stress, and hardening distributions through the thickness direction. Reduced forming limits are observed for small die radius case. Furthermore, the proposed M–K analysis provides a new understanding of the FLD after this complex bending-unbending-stretching loading condition, which also can be used to evaluate the real process design of sheet metal stamping, especially when the ratio of die entry radii to the metal thickness becomes small.

Analytic solution for interlaminar stresses in a multilaminated cylindrical shell under thermal and mechanical loads

Abstract An analytical method is presented for the problem of interlaminar stresses in a cross-ply multilaminated cylindrical shell subject to thermal loading and radial pressure with various end boundary conditions. The interlaminar stresses are determined exactly by using the method of separation of variables in three-dimensional theory of anisotropic elasticity. The results obtained can not only be used as a reference for approximate theories, but are also valuable for application in the design of composite structures.

Ductile Fracture Initiation of Anisotropic Metal Sheets

The objective of this research is to investigate the influence of material plastic anisotropy on ductile fracture in the strain space under the assumption of plane stress state for sheet metals. For convenient application, a simple expression is formulated by the method of total strain theory under the assumption of proportional loading. The Hill 1948 quadratic anisotropic yield model and isotropic hardening flow rule are adopted to describe the plastic response of the material. The Mohr-Coulomb model is revisited to describe the ductile fracture in the stress space. Besides, the fracture locus for DP590 in different loading directions is obtained by experiments. Four different types of tensile test specimens, including classical dog bone, flat with cutouts, flat with center holes and pure shear, are performed to fracture. All these specimens are prepared with their longitudinal axis inclined with the angle of 0°, 45°, and 90° to the rolling direction, respectively. A 3D digital image correlation system is used in this study to measure the anisotropy parameter r0, r45, r90 and the equivalent strains to fracture for all the tests. The results show that the material plastic anisotropy has a remarkable influence on the fracture locus in the strain space and can be predicted accurately by the simple expression proposed in this study.

Failure Investigation for QP Steel Sheets under uniaxial and Equal-Biaxial Tension Conditions

The Quenching and Partitioning (QP) steel sheet is new generation material to induce phase transformation for plasticity in forming vehicle parts. The phase transformation is strongly stress state dependent behavior in experiments, which should affect the failure timing and limit strain in forming processes. In this paper, Nakajima test with QP980 and DP1000 steel sheets under equal-biaxial loading condition is performed for failure behavior. X-ray diffraction (XRD) is adopted to obtain the volume fraction of retained austenite (fA). Digital Image Correlation (DIC) is used to record the surface strain field and its evolution during equal-biaxial tension deformation. The same level Dual Phase (DP) steel is also employed for the purpose of comparison. The results show that phase transformation in QP steel gives small impact on failure strain under equal biaxial tension condition which is contradicted with our understanding. It suggests that failure behavior under uniaxial tension of QP980 is strongly phase transformation dependent. But it shows almost independent under equal biaxial tension condition.

A Grain Structure Model based on Voronoi polygon of Non- oriented Electrical Steel in Blanking Process

World-wide there is a trend to develop higher permeability grades, thin thickness and coarse grain of non-oriented electrical steels, a core function material of motors. Blanking is the most popular technique for producing the motor laminations. However, the deformation of material is significantly influenced by grain size. In this paper, Voronoi polygon is used for generate the random microstructures of the studied non-oriented electrical steel. Finite Element (FE) model considering grain size is thus established to analysis the blanking process. The material behaviour of grains is derived from the widely accepted surface layer model. Compared to the conventional model without considering the grain size, the novel model shows good matching with the experimental results.

Prediction of the Volume Fraction of Retained Austenite in Sheet Metal Forming for Trip Steels

The dependence of the transformation rate on the multiaxial stress state corresponding to different loading paths is investigated. To achieve different loading paths, single shear uniaxial tension, plane strain and equi-biaxial stretching tests have been carried out for BTR380 steel. On Based of the experimental results, the influence of the stress state on stability of retained austenite is analyzed and an equation of transformation kinetics is developed to predict stress triaxiality-dependence strain-induced transformation. In sheet metal forming, the material undergoes complicated deformation. The prediction of the volume fraction of retained austenite during forming process is essential to estimate the contribution of the TRIP effect to improving formability. To this aim, the volume fraction of retained austenite in the part’s different regions has been calculated using the proposed transformation kinetics equation introduced into finite element method. The calculated results were successfully compared with the experimental data measured in deep drawing experiments.Copyright