Numerical approach to the evaluation of forming limit curves for zircaloy-4 sheet
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The forming limit strains (FLSs) of zircaloy-4 sheets are studied. After having obtained the true stress–strain curve of zircaloy-4 using the weighted-average method, limit dome height (LDH) tests are performed to establish experimental FLSs. We summarize related theoretical forming limit curves (FLC) and discuss their limitations. Two finite element (FE) models are established for determining FLSs; an LDH test FE model for the negative minor strain sector, and a biaxial tensile FE model for the positive minor strain sector. The numerical FLSs are found to agree well with experimental data. Since the numerical FLC gives the strain at the onset of local thinning (whereas the experimental FLC provides the strain between local necking and ductile fracture), resulting FE FLS values are slightly lower than the experimental ones so that results can be regarded as conservative. Our FE approach substitutes the expensive and time-demanding experimental LDH tests.
I. INTRODUCTION
Formability describes the capability of a sheet metal to undergo plastic deformation to get desired shape without defects. Keeler1 and Goodwin2 suggested the forming limit curve (FLC) where the critical major strain (e1) is plotted against the corresponding minor strain (e2). The corresponding diagram is called forming limit diagram (FLD). The FLC provides the forming limit strains (FLSs) for all possible combinations of major/minor strains. If a major/minor strain pair lies below the FLC, local necking or fracture is supposed not to occur. The FLD is also used in stamping or die tryout and serves to analyze the origin of forming errors and to handle forming difficulties. For instance, it indicates that fracture probability becomes higher when the strain mode approaches plane strain. For a material in plane strain, the forming process may be changed to drawing or stretching by varying die shape or lubrication, thereby increasing formability. By comparing the FLS with major/minor strains occurring in a forming process, we can predict the regions of possible fracture or instability. Recently, finite element (FE) analysis and theoretical models have been combined to predict FLSs. 3–15 If accurate FLCs can be obtained by numerical analysis, costs for die tryout to find the optimum shape can be reduced. Since the strain-based FLC is sensitive to prestrain path, 16 formability prediction is difficult with an FLC obtained by single deformation path. Contributing Editor: Yang-T. Cheng a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2015.293 J. Mater. Res., Vol. 30, No. 21, Nov 13, 2015
If path-independence of the forming limit stress curve (FLSC) can be established, then the formability will be predicted accurately using a combination of the FLSC and FE analysis. 17 However, there has been no experimental validation for the FLSC, because it is difficult to determine the exact stress state in a sheet material experimentally. Therefore, despite the usefulness, FLSC is not widespread. In spite of limitations in its applic
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