Right-hand Side Of Forming Limit Diagram Research Articles

Influence of thickness reduction on forming limits of mild steel DC01

The Forming Limit Diagram (FLD) is an essential tool to assess sheet metal formability in sheet metal deep drawing. In FLDs/FLC (Forming Limit Curve) is representation of material formability limits at which material is not able to withstand higher deformation. In this work, different methodologies for FLC determination of mild steel DC01 are investigated. The Nakajima test is a well-known experiment for FLC determination but, however, contact conditions that can appear in the form of either friction or pressure may perturb the results. The former may cause the need for repetitions for different widths by altering the necking location, whereas the latter may be responsible for overestimation of the material formability. Another method for FLC determination without those effects is to use the cruciform specimen test under biaxial loading conditions. As the first step, Necking has to be induced at the center of cruciform specimen by thickness reduction or groove. Therefore, in this work, the cruciform geometry under biaxial loading is optimized using FEM through the comparative analysis. The goal of simulation was to induce the necking just in the thinner gauge, not adjacent zone. Thereupon, different loads on biaxial machine’s axes can provide different strain paths at the thinner gauge of the optimized specimen. After reviewing of various researches in connection with thickness reduction effect on sheet metal deformation, it was found that thickness reduction might not influence the material formability during uniaxial and plane strain tensions, but it was observed that there is gradual decrease of limit strains with decreasing the thickness for equi-biaxial tension.Manufacturing process like milling, cause small defects on material surface and local instability takes place at lower level of deformation. Besides, it was found that existence of through thickness normal stress leads to higher value of FLC. Deformation during Nakajima and cruciform experiments were captured by Digital Image Correlation (DIC) system. The execution and evaluation of those experiments are explained in detail and Time Dependent Method (TDM) was applied to detect the beginning time of instability. Experimental strain paths are compared with consideration of strain rates and, as it was expected, FLC from cruciform specimen is lower than Nakajima one, especially on the right hand side of FLD. The remarkable difference can be attributed to defects in the material and existence of through-thickness normal stress, which leads to overestimation of the material formability during Nakajima experiment.

A Study of Improving the Formability of the Commercial Pure Titanium Foils

Abstract In order to obtain the optimum forming process for commercial pure titanium grade 2 foils, a series of tensile tests and micro scale limited dome height (µ-LDH) tests at four temperatures, and meso scale limited dome height tests (meso-LDH) with three punch speeds were conducted on the as-received foils with a thickness of 75 µm. The effects of temperature, geometry, and high-velocity impact were investigated to understand their influences on the formability of the foils. It has been found in the tensile tests that the formability can be improved by elevating temperatures; this has been validated by the µ-LDH tests. Based on forming limit diagrams (FLDs) of the meso-LDH specimens, the high-velocity impact forming process results in not only much better formability but also more uniform thickness distributions than the quasi-static. By analyzing the fractographical scanning electron microscope (SEM) pictures of the meso-LDH specimens, it has been proven that the formability of the foils by using high-velocity impact process is superior to the conventional process. Furthermore, high-velocity impact causes forming limit curve (FLC) to shift in the upper right direction on the right-hand side of FLD. Therefore, it is suggested forming the foils by using high-velocity impact forming process at the elevated temperature for obtaining a better formability and more uniform thickness distribution. It is also recommended to make the radius of the LDH hemisphere punch close to the smallest feature of the designed products for obtaining more accurate FLCs.

A theoretical and experimental study on forming limit diagram for a seamed tube hydroforming

The purpose of this work is to establish the forming limit diagram (FLD) for a seamed tube hydroforming. A new theoretical model is developed to predict the FLD for a seamed tube hydroforming. Based on this theoretical model, the FLD for a seamed tube made of QSTE340 sheet metal is calculated by using the Hosford yield criterion. Some forming limit experiments are performed. A classical free hydroforming tool set is used for obtaining the left hand side forming limit strains, and a novel hydroforming tool set is designed for the right hand side of FLD. The novel device required the simultaneous application of lateral compression force and internal pressure to control the material flow under tension–tension strain states. Furthermore, the suitable loading paths for the left hand side of FLD by theoretical formulas and for the right hand side of FLD by finite element (FE) simulations are calculated. Finally, a comparison between the theoretical results and experimental data is performed. The theoretical predicting results show good agreement with the experimental results.

An Investigation Into the Prediction of Forming Limit Diagrams for Normal Anisotropic Material Based on Bifurcation Analysis

In this paper, formula derivation for bifurcation analysis based on a constitutive model including Hill 48 yield criterion with normal anisotropy of a pointed vertex on subsequent yield loci to predict the entire forming limit diagram (FLD) is carried out. Proportional loading, total deformation theory of plasticity, and power law relation are assumed. Predicted limit strains for Hill’s zero and minimum extension of localized neck orientation is derived. The dominancy of zero extension and minimum extension on the left-hand side of FLDs for different work hardening components and r-values are investigated in detail. An implicit four order rational function equation for major strain, which preferred that the orientation of neck correspond to minimum value of limit strain, is found by a developed optimization method. Optimized predicted limit strains for typical work hardening components and different r-values are obtained and discussed. Limit strains vary directly on the left and reversely on the right-hand side of FLD when r-value increases. Comparison between the predicted and experimental results exhibits a better agreement compared with those from the isotropic material. In addition, on the left-hand side, the resulted prediction limit strains represent a full dependency to assumed yield criterion. A comparison between the current work and Chow et al. results are performed and discussed in detail.

Forming Limit Analysis of Sheet Metals Based on a Generalized Deformation Theory

This paper presents the development of a generalized method to predict forming limits of sheet metals. The vertex theory, which was developed by Sto¨ren and Rice (1975) and recently simplified by Zhu, Weinmann and Chandra (2001), is employed in the analysis to characterize the localized necking (or localized bifurcation) mechanism in elastoplastic materials. The plastic anisotropy of materials is considered. A generalized deformation theory of plasticity is proposed. The theory considers Hosford’s high-order yield criterion (1979), Hill’s quadratic yield criterion and the von Mises yield criterion. For the von Mises yield criterion, the generalized deformation theory reduces to the conventional deformation theory of plasticity, i.e., the J2-theory. Under proportional loading condition, the direction of localized band is known to vary with the loading path at the negative strain ratio region or the left hand side (LHS) of forming limit diagrams (FLDs). On the other hand, the localized band is assumed to be always perpendicular to the major strain at the positive strain ratio region or the right hand side (RHS) of FLDs. Analytical expressions for critical tangential modulus are derived for both LHS and RHS of FLDs. For a given strain hardening rule, the limit strains can be calculated and consequently the FLD is determined. Especially, when assuming power-law strain hardening, the limit strains can be explicitly given on both sides of FLD. Whatever form of a yield criterion is adopted, the LHS of the FLD always coincides with that given by Hill’s zero-extension criterion. However, at the RHS of FLD, the forming limit depends largely on the order of a chosen yield function. Typically, a higher order yield function leads to a lower limit strain. The theoretical result of this study is compared with those reported by earlier researchers for Al 2028 and Al 6111-T4 (Grafand Hosford, 1993; Chow et al., 1997).