The Relative Sensitivity of Formability to Anisotropy

This work compares the relative importance of material anisotropy in sheet forming as compared to other material and process variables. The comparison is made quantitative by the use of normalized dependencies of depth to failure (forming limit is reached) on various measures of anisotropy, as well as strain and rate sensitivity, friition, and tooling. Comparisons are made for a variety of forming processes examined previously in the literature as well as two examples of complex stampin s in this work. 7 The examples rover a range from near y pure draw to nearly pure stretch situations, and show that for materials following a quadratic yield criterion, anisotropy is among the most sensitive parameters influencing formability. For materials following higher-exponent yield criteria, the dependency is milder but is still of the order of most other process parameters. However, depending on the particular forming operation, it is shown that in some cases anisotropy may be gnored, whereas in others its mnsideration is crucial to a good quality analysis. fINTRODUCTION AND MOTIVATION This work was motivated in part by the findings ‘“ of one of the authors in a previous work [1 but in la e k? part flavored by timely discussions at the UMISHE T 96 and as documented in those proceedings [21. The large quantity of information assembled in the Limiting Dome Height (LDH) benchmark has allowed the question to be credibly raised as to the relative (quantitative) importance of anisotropy as compared to other sensitivities in sheet forming processes. Since a sensitivity stud [ was petformect b entrants m the DH Simulation BenJmJ?&l)ml NUMISHEET 96, the key aspects of the conclusions of this work had their origins in an examination of that data. However, since SB-1 involved the LDH test, which is predominantly stretch in nature, it was felt that any attempt to be even moderately thorough in examining relative sensitivities should include a variety of forming operations. To that end, quantitative statements are developed below regarding what is important during the following forming operations: LDR (Limiting Draw Ratio) [3], predominantly a draw situation: LD~Jt&~iting Dome Height) [2], a predominantly stretch T onical “Cupping [4-6], where inhibition of wrinkli demands a stretch/draw balance: T aring during Cupping [7,8], another process where draw is the main mode: Blank shape optimization for a rectangular box [1,9], a stretch/draw situation: Blank shape for a cylindrical cup [1], a draw dominated situatiin: Hydroforming of a Yish”-shaped rover plate [10], a stretch/draw operation: Closed-die stamping of an ‘&ircraft door frame [11], predominantly stretch with some draw component. The rtinent information about these processes r is reviewe below and summarized in a form that reveals where each material and process parameter is most relevant. Included in these is the means of characterizi~ the anisotropy; this may be viewed in a hypothetical way regard Y which of several yield surfaces is chosen nufnefica/yto re resent the material, P or alternately in terms of the rea ism to which each criterion captures a given sheet material’s measured pro rties. The various criterion chosen as extensions r tot e isotropic Von Mises include the 1948 Hill [12, also i called H48 or “a=2” in this work, the 1979 New Hi , form c1 #4 13], also referred to as NH4 or “a<2 in this work, an the 1979 Hosford [14], also called H79 or “a=8 in this work. Since that criteriin is numerically similar to the one proposed by Barlat and Lian in 1989 [15], the latter will be included in the “a=8 nomenclature in this work. Forms of these criterion have been implemented into versions of W-DYNA3D at LLNL [1], and into LSDYNA3D and LS-NIKE3D at LSTC[16,1 ~. The quadratic 1948 Hill yield surface takes the form —7. F(cTb– ac)z+ G(C7C–CJJ2+H(CYC-C*)2+D CT= R+l . ..(1) Eqn. (1) relates the effective stress to the three normal components of Cauchy stress, with the term O containing the shear stress terms: D= 2Ldk + 2Mdw + 2Ndd (2) x The values for the constants in Eqns. (1) and (2) can be expressed in terms of the in-plane strain ratios R=Ro, Q=RAs, and P=RSUJand S=R/P, with the following additional relations needed: