A physically-based constitutive model for metal deformation

Ghosh, A.

doi:10.1016/0001-6160(80)90046-2

Cited by 71 publications

(26 citation statements)

References 22 publications

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“…The varying strain hardening rates in Figures 4(d) through (f) can be interpreted as increased softening due to dynamic recovery as strain rate decreases, permitting more time for concurrent recovery. [31,32] Thus, the result is an indication that hardening rate has positive strain rate dependence due to dynamic recovery. A combination of higher strain hardening rate, a higher rate sensitivity of the strain hardening rate, and a higher rate sensitivity of flow stress (m~0.4 to 0.5) exert stabilizing influence on deformation to enhance uniform and postuniform elongations at 200°C and strain rates of 2 9 10 -4 s -1 and lower.…”

Section: A Enhanced Formabilitymentioning

confidence: 93%

Formability of Ultrafine-Grain Mg Alloy AZ31B at Warm Temperatures

Yang

Ghosh

2008

Metall Mater Trans A

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Warm formability of ultrafine-grain (UFG) AZ31B Mg alloy in the range of 150°C to 311°C is investigated. Refinement of grain size significantly improves the formability primarily through increasing strain rate sensitivity of flow stress and increasing diffuse quasi-stable flow, as compared with the coarse-grain AZ31B alloy. Strain rate sensitivity increases with increasing temperatures, and seems to be connected with dynamic recovery and grain boundary processes. For fine-grain sizes, twinning is inhibited. At 200°C and strain rates below 2 9 10 -4 s -1 , the UFG AZ31B alloy demonstrates a high rate of strain hardening up to a true strain of 0.6, in addition to its high strain rate sensitivity, which is responsible for its enhanced formability. Examination of the microstructure shows that there is competition between dynamic grain growth and grain refinement during deformation at modest warm forming temperatures, the former causing hardening and the latter causing softening. Increasing the test strain rate and starting with larger grain size initiates deformation twinning during forming, and assists in the refinement of the coarser grains followed by recrystallization.

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Section: A Enhanced Formabilitymentioning

confidence: 93%

Formability of Ultrafine-Grain Mg Alloy AZ31B at Warm Temperatures

Yang

Ghosh

2008

Metall Mater Trans A

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“…It is reported that such microplastic strains are the main reason for nonlinear elastic response, the change in Young's modulus, and the difference in Young's modulus with regard to elastic loading and unloading [13]. This phenomenon is explained by the motion of dislocations between obstacles, the release of dislocations from cell walls, and their reaction with other mobile dislocations [14,15], so it seems natural to expect an increase in the stiffness degradation with plastic straining. However, the recovery obviously differs from steel to steel.…”

Section: Study Of the Recovery Effectmentioning

confidence: 99%

The Evolution of Effective Elastic Properties of a Cold Formed Stainless Steel Sheet

2010

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In accordance with the great importance given to the subject of stiffness degradation, in particular with regard to metal forming, this work experimentally investigates the anisotropic elastic properties of plastically prestrained coldrolled sheet metal (stainless steel EN 1.4301, also AISI 304). From the experiments performed, two main conclusions regarding stiffness degradation can be extracted. First, since under specific stretching the intensity of the normalized Young's moduli degradation in both directions remains approximately similar, it may be concluded that the potential initial elastic anisotropy tends to be preserved during loading. Second, as the evidenced stiffness degradation has proved to be strongly correlated with the stretching direction of the sheet metal, it can be concluded that the stiffness evolution in the cold rolled sheet steel is path dependent. These interesting discoveries also provide some answers for modelling the kinetic damage evolution laws in damage mechanics.

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“…This strain would not belong to an extra elastic strain but instead to a microplastic strain (e mp ). As discussed in the introduction, e mp is directly related to the dislocation structure, [19][20][21][22] since this extra strain can be produced by mobile or pinned dislocations, depending on the model. As can be derived from Eq.…”

Section: Inelastic Effects On Loadingmentioning

confidence: 99%

“…Equation (1) shows the calculation of Young's modulus (E), in which the deformation (e) can be divided into elastic (e e ) and plastic or microplastic deformation (e mp ), while s denotes stress. This microplastic deformation results firstly from the short range of motion of mobile dislocations, 19) and secondly from the bowing of the dislocation line between pinning points following models proposed by Mott and Friedel,20,21) and by Granato and Lücke. 22) This extra deformation, which occurs below the internal strength level of the material, is recoverable, and is affected by the dislocation density and the total length of dislocation line that is able to move or bow out.…”

Section: Introductionmentioning

confidence: 98%

Study of the Inelastic Response of TRIP Steels after Plastic Deformation

2005

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A study of the elastic response before and after tensile plastic strain was undertaken for two commercial low-alloyed TRIP steels. These steels, TRIP 700 (C-Mn-Al alloy) and TRIP 800 (C-Mn-Si) are commercial alloys used in sheet metal stamping. The behaviour of the instantaneous tangent modulus (E T ) versus stress during loading and unloading was measured for each degree of prestrain. Loading curves show a decrease in the E T of the deformed samples as compared with the undeformed state. Though at low stresses a highly linear response was measured for both steels, a decrease was obtained for TRIP 700 as strain increased, whereas TRIP 800 remained unchanged. During unloading, a progressive decrease in E T was obtained in all deformed states, with lower chord modulus values as the tensile plastic prestrain increased. The inelastic response observed is attributed mainly to microplastic strain caused by the displacement of mobile dislocations. Thus, the differences between the two TRIP steels studied are related to the microstructure and the different dislocation structures observed in them. A notable consequence of this study is a better accuracy in the prediction of springback passes due to a better understanding of these inelastic effects that stems from going beyond mere use of traditional Young's modulus values.KEY WORDS: TRIP steels; springback; Young's modulus; dislocation structure. This microplastic deformation results firstly from the short range of motion of mobile dislocations, 19) and secondly from the bowing of the dislocation line between pinning points following models proposed by Mott and Friedel,20,21) and by Granato and Lücke. 22) This extra deformation, which occurs below the internal strength level of the material, is recoverable, and is affected by the dislocation density and the total length of dislocation line that is able to move or bow out. Thus, when e mp grows, a decrease in E is expected. The following Eq. (2), proposed by Granato and Lücke,22) summarizes this idea:where b is the magnitude of the Burgers vector, r is the density of the mobile dislocations and x is the average displacement of a dislocation line of length l.As springback appears after tools have been removed, it is the behaviour of Young's modulus 'during unloading' that should be investigated to obtain a more accurate prediction of the recovery from strain after forming. Ghosh et al. 13,23) used uniaxial tensile tests to study strain recovery after plastic prestrain for a type of steel used in sheet metal stamping, and demonstrated the nonlinearity of the unloading part of the stress-strain curve. This "inelastic behaviour" results in an extra deformation that is not predicted by the usual values of Young's modulus, and again is resumed as microplastic strain. This deformation must be accounted for in FEM simulations in order to better predict the final shape of the pieces stamped. The nature of microplastic strain during unloading is mainly associated with the backward movement of the dislocations that pile up during...

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A physically-based constitutive model for metal deformation

Cited by 71 publications

References 22 publications

Formability of Ultrafine-Grain Mg Alloy AZ31B at Warm Temperatures

Formability of Ultrafine-Grain Mg Alloy AZ31B at Warm Temperatures

The Evolution of Effective Elastic Properties of a Cold Formed Stainless Steel Sheet

Study of the Inelastic Response of TRIP Steels after Plastic Deformation

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