Effect of twinning and detwinning on inelastic behavior during unloading in a magnesium alloy sheet

Abstract.Although the initial stress-strain behavior in a tensile test is often characterized as linear elastic up to a yield stress and nonlinear plastic thereafter, the pre-yield transition region is known to exhibit significant curvature and hysteresis. Hundreds of high-precision loading-unloading-loading tensile tests were performed using 26 commercial sheet alloys exhibiting a wide range of strength, ductility and crystal structure. Analysis of the results reveals the following:1. There is no significant linear elastic region; the proportional limit is ~0 MPa when measured with sufficient sensitivity. 2. Each of the hundreds of measured transitional stress-strain curves can be characterized by a single parameter, here called the "modulus reduction rate." The corresponding equation captures ~80% of the observed variation, a factor of 3 to 6 better than a one-parameter linear approximation. 3. Most interestingly, the transitional behavior for all alloys follows a "Universal Law" requiring no fit parameters. The law depends only upon the strength of the material and its Young's modulus, both of which are can be measured by independent tests or adopted from handbooks. The Universal Law captures ~90% of the variation represented by the one-parameter representation and eliminates the need for mechanical testing to implement and apply. The practical and theoretical implications of these results are discussed. The results provide a simple path to significantl y improving applied constitutive models in the transitional regime. The consistency of the effect for such a wide range of metals and suggests that the origin of the behavior lies in the pile-up and relaxation of dislocation arrays.

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“…A twinning and detwinning [11][12][13] mechanism cannot explain experimentally observed nonlinearity in non-HCP structured metals.…”

Section: Discussionmentioning

confidence: 99%

Elastic-plastic transition: A universal law

Chen

Bong

et al. 2016

MATEC Web Conf.

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“…Because a crystal plasticity analysis on unloading processes has scarcely been conducted except for our previous works in a Mg alloy sheet, 24,25) the availability of a crystal plasticity analysis on unloading processes in various materials are not understood yet. Therefore, in the present study, the applicability of a crystal plasticity analysis on unloading processes is also discussed.…”

Section: Crystal Plasticity Finite-element Methodsmentioning

confidence: 99%

“…We also depicted that the nonlinear deformation during unloading in the Mg alloy sheet can be predicted well using a crystal plasticity finiteelement simulation. 24,25) The aforementioned studies exhibited that the nonlinear deformation during unloading is observed in various metal sheets and the nonlinearity during unloading plays an important role in the springback prediction. Recently the nonlinear effects are being taken into account in the constitutive models.…”

Section: Introductionmentioning

confidence: 99%

Non-linear Deformation Behavior during Unloading in Various Metal Sheets

et al. 2015

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The deformation behavior during unloading was examined under uniaxial tension in a mild steel sheet (body-centered cubic metal), an aluminum alloy sheet (face-centered cubic metal), and a magnesium alloy sheet (hexagonal close packed metal). A crystal plasticity finite-element method was also used to investigate the difference in the deformation behavior among on the materials. The nonlinearity during unloading was the largest in the magnesium alloy sheet, and the mild steel sheet showed a larger nonlinearity than the aluminum alloy sheet. On the other hand, the apparent elastic moduli determined from the linear approximation of unloading curves were not always consistent with the characteristics observed in the nonlinearity, and this inconsistency became pronounced as the degree of nonlinearity increased. It was found that the degree of nonlinearity would have a strong correlation with the strain rate sensitivity, suggesting that the apparent elastic modulus was not suitable to model the unloading behavior for materials with high strain rate sensitivity. The crystal plasticity analysis demonstrated that the nonlinearity was much larger in the magnesium alloy sheet than in the other two sheets as observed in the experimental results. The simulation results suggested that one of the reasons that gave rise to the nonlinearity during unloading would be the difference in the critical resolved shear stresses among the slip systems.

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“…The stress-strain curves of Mg alloy sheets are significantly different between tension and compression [21,31,[40][41][42]. Moreover, a sigmoidal curve occurs when a Mg alloy sheet is subjected to compression followed by tension, whereas this curve does not occur under tension followed by compression [20,21,41].…”

Section: Effect Of Twinning Activity On Mechanical Behaviormentioning

confidence: 99%

“…The abovementioned asymmetric work-hardening behaviors arise because of the activities of <101 � 2> twinning and detwinning [20,[40][41][42]. Clearly, the twinning activity plays an important role in the stressstrain curves in Mg alloy sheets.…”

Section: Effect Of Twinning Activity On Mechanical Behaviormentioning

confidence: 99%

Anisotropic deformation behavior under various strain paths in commercially pure titanium Grade 1 and Grade 2 sheets

Hama

Kobuki

et al. 2016

Materials Science and Engineering: A

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In this study, the anisotropic deformation behavior in commercially pure titanium Grade 1 and Grade 2 sheets under various strain paths was examined. A small but sharp stress peak arose during tension following compression in the Grade 1 sheet when loaded in the rolling direction, and the occurrence of a stress peak was retarded when the sheet was subjected to cyclic loading; however, such behavior did not occur in the Grade 2 sheet. Similarly, the work-hardening rate was different between the initial and latter stages of compression following tension. These behaviors did not arise when the sheets were loaded in other directions. The type of active twin mode was different depending on the loading path. When loaded in the rolling direction in both Grade 1 and Grade 2 sheets, <101 � 2> twinning and detwinning were active, respectively, during compression and tension following compression, whereas <112 � 2> twinning and detwinning were active during tension and compression following tension. The twinning activity was much more pronounced in the Grade 1 sheet than in the Grade 2 sheet. The abovementioned stress-strain responses were presumed to result from twinning and detwinning activities as for magnesium alloy sheets.However, we concluded that the effect of twinning activity on the stress-strain curves was much smaller in the titanium sheet than in magnesium alloy sheets.

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Effect of twinning and detwinning on inelastic behavior during unloading in a magnesium alloy sheet

Cited by 75 publications

References 64 publications

Elastic-plastic transition: A universal law

Elastic-plastic transition: A universal law

Non-linear Deformation Behavior during Unloading in Various Metal Sheets

Anisotropic deformation behavior under various strain paths in commercially pure titanium Grade 1 and Grade 2 sheets

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