scispace - formally typeset
Journal ArticleDOI

A variable strain hardening model for anisotropic sheet metals

16 May 2012-Journal of Strain Analysis for Engineering Design (SAGE Publications)-Vol. 47, Iss: 5, pp 289-296
Abstract: A phenomenological approach is proposed to model the influence of texture-induced anisotropy in the variation of strain hardening characteristics of a sheet material The variation of uniaxial strain hardening exponent with rolling direction is modelled using existing anisotropic yield criteria assuming power law strain hardening behaviour The model is extended to the biaxial region to predict the effective strain hardening exponent with the assumption of constant plastic work The prediction of both uniaxial and biaxial strain hardening is compared with the experimental data available in the literature It is observed that a variable strain hardening exponent provided greater accuracy of numerical prediction than the existing isotropic model The accuracy of the proposed model is dependent on the yield criteria and the flow rule used for the modelling
Citations
More filters


References
More filters

Journal ArticleDOI
Abstract: A theory is suggested which describes, on a macroscopic scale, the yielding and plastic flow of an anisotropic metal. The type of anisotropy considered is that resulting from preferred orientation. A yield criterion is postulated on general grounds which is similar in form to the Huber-Mises criterion for isotropic metals, but which contains six parameters specifying the state of anisotropy. By using von Mises' concept (1928) of a plastic potential, associated relations are then found between the stress and strain-increment tensors. The theory is applied to experiments of Korber & Hoff (1928) on the necking under uniaxial tension of thin strips cut from rolled sheet. It is shown, in full agreement with experimental data, that there are generally two, equally possible, necking directions whose orientation depends on the angle between the strip axis and the rolling direction. As a second example, pure torsion of a thin-walled cylinder is analyzed. With increasing twist anisotropy is developed. In accordance with recent observations by Swift (1947), the theory predicts changes in length of the cylinder. The theory is also applied to determine the earing positions in cups deep-drawn from rolled sheet.

3,097 citations


"A variable strain hardening model f..." refers background or methods or result in this paper

  • ...The Hill48 criterion for plane stress condition is given as 2f sij =F syy 2 +G sxxð Þ2 +H sxx syy 2 +2Nt2xy =1 ð1Þ where F, G, H and N are material constants....

    [...]

  • ...In the case of the transverse direction, the predictions of both Hill48 and Barlat89 were similar (for yield stress and n) and hence the error function for both the criteria yielded the same value....

    [...]

  • ...The anisotropic effect on the variation of n is demonstrated using Hill (referred to as Hill48) and Barlat and Lian (referred to as Barlat89) criteria....

    [...]

  • ...It is observed that the error function for variation of yield stress using the Hill48 criterion is close to unity along the diagonal (u=45) and hence is more accurate than the prediction by Barlat89 criterion....

    [...]

  • ...Barlat89 criterion is used for the prediction, as Kuwabara et al. concluded that the Hosford yield criterion (Barlat89 is a generalization of Hosford criterion) fits the experimental data better than the Hill48 criterion....

    [...]


Journal ArticleDOI
Abstract: The process of the loss of stability is analysed for sheet metal subjected to biaxial tension when the ratio of the principal stresses 0.5 ⩽ σ 2 /σ 1 ⩽ 1 . The loss of stability manifests itself by a groove running in a direction perpendicular to the larger principal stress. In this groove local strains begin to concentrate gradually. In the initial stage of the process the deepening of the groove is associated with a gradually fading strain in the regions adjacent to the groove. This fading strain attains a certain limiting value e∗. This paper contains both experimental results and a theoretical analysis of the process of the generation of the groove based on anisotropic plasticity theory. The system of equations derived was solved numerically with the aid of a computer, which enabled the limiting strain of the sheet metal to be determined as a function of the following properties of the material: (i) Initial inhomogeneity of the sheet metal, (ii) exponent of the strain-hardening function, (iii) coefficient of normal anisotropy, (iv) initial plastic strain, (v) strain at which the fracture occurs. The results are discussed and the properties are described that influence the drawability of sheet metal used in the stretch-forming process.

1,705 citations


"A variable strain hardening model f..." refers background in this paper

  • ...However, it is proven that irrespective of the initial strain ratio, the failure of sheet metals is preceded by plane strain mode deformation.(35) Hence the proposed model is not suitable to predict the yield locus shape close to necking....

    [...]


Journal ArticleDOI
Abstract: A yield function that describes the behavior of orthortropic sheets ,metals exhibiting planar anisotropy and subjected to plane stress conditions is proposed. It is shown to give a reasonable approximation to plastic potentials calculated with the Taylor/Bishop and Hill theory of polycrystalline plasticity for plane stress states. Therefore, this formulation should be particulary useful to study, at a low degree of complexity, the influence of polycrystalline textures on the forming performances of metal sheets. In part II, this yield function will be used to study the influence of the yield surface shape on failure behavior of sheet metals.

992 citations


Journal ArticleDOI
Abstract: A large number of polycrystalline materials, both manmade and natural, display preferred orientation of crystallites. Such alignment has a profound effect on anisotropy of physical properties. Preferred orientation or texture forms during growth or deformation and is modified during recrystallization or phase transformations and theories exist to predict its origin. Different methods are applied to characterize orientation patterns and determine the orientation distribution, most of them relying on diffraction. Conventionally x-ray polefigure goniometers are used. More recently single orientation measurements are performed with electron microscopes, both SEM and TEM. For special applications, particularly texture analysis at non-ambient conditions, neutron diffraction and synchrotron x-rays have distinct advantages. The review emphasizes such new possibilities. A second section surveys important texture types in a variety of materials with emphasis on technologically important systems and in rocks that contribute to anisotropy in the earth. In the former group are metals, structural ceramics and thin films. Seismic anisotropy is present in the crust (mainly due to phyllosilicate alignment), the upper mantle (olivine), the lower mantle (perovskite and magnesiowuestite) and the inner core (e-iron) and due to alignment by plastic deformation. There is new interest in the texturing of biological materials such as bones and shells. Preferred orientation is not restricted to inorganic substances but is also present in polymers that are not discussed in this review.

496 citations


"A variable strain hardening model f..." refers methods in this paper

  • ...The anisotropy due to the texture effect can be quantified experimentally using X-ray Pole figure analysis and other techniques.(4,5) The influence of anisotropy on the yield strength (initiation of plastic deformation) can be modelled directly from experimental data....

    [...]


Journal ArticleDOI
Abstract: Deformation by 〈111〉-pencil glide has been analyzed by an upper-bound model which combines a least-shear analysis and Piehler's maximum virtual work analysis. The least-shear analysis gives exact solutions if three 〈111〉 slip systems are active, while the maximum work analysis provides solutions for the case of four active slip systems. Independent checks are used to determine which solution method is appropriate. Computer calculations using this model have been made to determine; (1) the orientation dependence of the Taylor factor for axisymmetric deformation; (2) the yield loci for textured materials having [100], [110] and [111] sheet metals and rotational symmetry; (3) the isotropic yield locus for randomly oriented materials; and (4) flow stresses along critical loading paths for various assumed textures with rotational symmetry. The latter calculations indicate that anisotropic yield loci of textured bcc metals with rotational symmetry are much better approximated by σ x a + σ y a + R¦σ x − σ y ¦ a = (R + 1)Y a where R is the strain ratio and Y is the tensile yield strength with an exponent a = 6 rather than with a = 2 as postulated by Hill. It is not known how well upper-bound calculations like these represent actual yielding behavior.

340 citations


Performance
Metrics
No. of citations received by the Paper in previous years
YearCitations
19941