An elasto-plastic constitutive model for evolving asymmetric/anisotropic hardening behavior of AZ31B and ZEK100 magnesium alloy sheets considering monotonic and reverse loading paths

Muhammad, Waqas; Mohammadi, Mohsen; Kang, Jidong; Mishra, Raja K.; Inal, Kaan

doi:10.1016/j.ijplas.2015.03.004

Cited by 100 publications

(39 citation statements)

References 51 publications

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“…The weaker texture of ZE10 reduces strain hardening, resulting in a hardening rate similar to the one found during uniaxial tension. Recent results by Muhammad et al (2015) obtained from AZ31 and a similar material to ZE10 (ZEK100) support this response.…”

Section: Summary -Concluding Remarksmentioning

confidence: 74%

“…Recently, some contributions treat the micromechanical mechanisms of dislocation glide, twinning and detwinning during reverse loading by separate constitutive components, e.g. (Li et al, 2010;Kim et al, 2013;Mohr et al, 2013;Muhammad et al, 2015). In the following, a similar approach is chosen.…”

Section: Constitutive Equationsmentioning

confidence: 99%

“…This is different from the approach commonly applied, where the difference between the corresponding stress potential function and the experimental data for elementary tests (uniaxial, biaxial, plane strain) at certain deformation stages is minimised. By following the latter approach, Muhammad et al (2015) state that the anisotropy coefficients "evolve rapidly with accumulated plastic strain and tend to reach an almost constant value with continuing plastic deformation". It appears reasonable to use the "saturated" values to describe the plastic deformation, tolerating a certain inaccuracy at small strains.…”

Section: Summary -Concluding Remarksmentioning

confidence: 99%

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Mechanism-based modelling of plastic deformation in magnesium alloys

Steglich

Tian

Besson

2016

European Journal of Mechanics - A/Solids

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International audienceThe plastic deformation of two different rolled magnesium sheets (AZ31 and ZE10) under quasi-static tensile and compressive loading conditions at room temperature is studied. Beside glide by dislocation motion, deformation twinning leads to evolving flow stress asymmetry and evolving plastic anisotropy in these alloys. These mechanisms cause a significant change in the shape of the yield surface with accumulated plastic deformation which cannot be described by traditional hardening concepts. A phenomenological plasticity model in which the primary deformation mechanisms, slip and (extension) twinning, are treated separately is developed here and incorporated in the finite element framework. Deformations caused by these mechanisms are modelled by a symmetric and an asymmetric plastic potential, respectively. The hardening functions are coupled to account for the latent hardening. The necessary input for model parameter calibration is provided by mechanical tests along different orientations of the rolled sheets. Tensile tests of notched samples and shear tests are furthermore incorporated in the parameter optimisation strategy, which is based on minimising the difference between experimental behaviour and FE prediction over the entire deformation range up to failure. The model accounts for the characteristic tension-compression asymmetry and the evolution of strain anisotropy. Both, the convex-up and the concave-down shaped stress–strain response are predicted. The computational model is exemplified by studying the evolution of the plastic multipliers during a shear test. It is shown that despite its phenomenological character, the model predicts the dominant deformation mechanism present at monotonous loading of the magnesium sheets investigated

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Section: Summary -Concluding Remarksmentioning

confidence: 74%

Section: Constitutive Equationsmentioning

confidence: 99%

Section: Summary -Concluding Remarksmentioning

confidence: 99%

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Mechanism-based modelling of plastic deformation in magnesium alloys

Steglich

Tian

Besson

2016

European Journal of Mechanics - A/Solids

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“…Also, it is emphasized that in the most published studies mentioned above, the CPB06 yield function was reduced to 2-D stress states with shell elements (e.g., [11,21,48]), whereas the current implementation accounts for a general 3-D stress state. Shell elements are not suitable for the evaluation of local fields after the onset of necking while solids elements can provide more accurate predictions of localized deformation and through-thickness gradients of stress and strain fields.…”

Section: Implementation Into a Finite Element Codementioning

confidence: 99%

“…To consider evolving anisotropy, Plunkett et al [17] proposed a piece-wise linear interpolation of the CPB06 yield function calibrated at different levels of plastic deformation. Similar approaches were adopted in Reference [11,[18][19][20][21] for magnesium alloys and in Reference [22][23][24][25] for titanium alloys. It should be noted that evolving plastic anisotropy and distortional hardening in hcp alloys occurs even during monotonic proportional loading.…”

Section: Introductionmentioning

confidence: 99%

Application of an Evolving Non-Associative Anisotropic-Asymmetric Plasticity Model for a Rare-Earth Magnesium Alloy

Abedini

Butcher

Worswick

2018

Metals

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Magnesium sheet metal alloys have a hexagonal close packed (hcp) crystal structure that leads to severe evolving anisotropy and tension-compression asymmetry as a result of the activation of different deformation mechanisms (slip and twinning) that are extremely challenging to model numerically. The low density of magnesium alloys and their high specific strength relative to steel and aluminum alloys make them promising candidates for automotive light-weighting but standard phenomenological plasticity models cannot adequately capture the complex plastic response of these materials. In this study, the constitutive plastic behavior of a rare-earth magnesium alloy sheet, ZEK100 (O-temper), was considered at room temperature, under quasi-static conditions. The CPB06 yield criterion for hcp materials was employed along with a non-associative flow rule in which the yield function and plastic potential were calibrated for a range of plastic deformation levels to account for evolving anisotropy under proportional loading. The non-associative flow rule has not previously been applied to magnesium alloys which require the use of flexible constitutive models to capture the severe anisotropy and its evolution with plastic deformation. The non-associative flow rule can provide the required flexibility by decoupling the yield function and plastic potential. For the associative flow rule, such flexibility can only be achieved by multiple linear transformations of the stress tensor resulting in expensive models for calibration and simulations. The constitutive model was implemented as a user material subroutine (UMAT) within the commercial finite element software, LS-DYNA, for general 3-D stress states along with an interpolation technique to consider the evolution of anisotropy based upon the plastic work. To evaluate the accuracy of the implemented model, predictions of a single-element model were compared with the experimental results in terms of flow stresses and plastic flow directions under various proportional loading conditions and along different test directions. Finally, to assess the predictive capabilities of the model, full-scale simulations of coupon-level formability experiments were performed and compared with experimental results in terms of far-field load-displacement and local strain paths. Using these experiments, the constitutive model was evaluated across the full range of representative stress states for sheet metal forming operations. It was shown that the predictions of the model were in very good agreement with experimental data.

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