• Title/Summary/Keyword: work softening

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Characteristics of solutions in softening plasticity and path criterion

  • Chen, G.;Baker, G.
    • Structural Engineering and Mechanics
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    • v.16 no.2
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    • pp.141-152
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    • 2003
  • Characteristics of solutions of softening plasticity are discussed in this article. The localized and non-localized solutions are obtained for a three-bar truss and their stability is evaluated with the aid of the second-order work. Beyond the bifurcation point, the single stable loading path splits into several post-bifurcation paths and the second-order work exhibits several competing minima. Among the multiple post-bifurcation equilibrium states, the localized solutions correspond to the minimum points of the second-order work, while the non-localized solutions correspond to the saddles and local maximum points. To determine the real post-bifurcation path, it is proposed that the structure should follow the path corresponding to the absolute minimum point of the second-order work. The proposal is further proved equivalent to Bazant's path criterion derived on a thermodynamics basis.

Work Softening Behavior of Zn-15%Al alloy (Zn-15%Al 합금의 가공연화 거동)

  • Jun, Joong-Hwan;Seong, Ki-Duk;Kim, Jeong-Min;Kim, Ki-Tae;Jung, Woon-Jae
    • Journal of the Korean Society for Heat Treatment
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    • v.18 no.1
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    • pp.18-23
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    • 2005
  • Effect of cold rolling on microstructural changes has been investigated for a Zn-15%Al alloy to elucidate the reason for its work softening behavior. Fully annealed microstructure of the Zn-15%Al alloy is characterized by ${\eta}$ grains and (${\eta}+{\alpha}$) lamellar colonies, where ${\eta}$ and ${\alpha}$ are Zn-rich HCP and Al-rich FCC phases, respectively. The hardness decreases continuously with increasing cold rolling degree, exhibiting work softening behavior. It is revealed that during the cold rolling, (${\eta}+{\alpha}$) lamellar colonies gradually change into equiaxed ${\eta}$ and ${\alpha}$ grains due to dynamic recrystallization at room temperature, while pre-existing ${\eta}$ grains are only deformed without recrystallization. Furthermore, cold rolling causes the precipitation of dissolved Al solutes in ${\eta}$ grains. In view of these results, change of (${\eta}+{\alpha}$) phases from lamellar to equiaxed morphology, which results in structural softness and increase in equiaxed ${\eta}/{\alpha}$ grain boundaries with higher mobility, and deterioration of solution hardening by precipitation of Al solutes from ${\eta}$ grains, are thought to contribute to the work softening of Zn-15%Al alloy.

Effect of C/Ti Atom Ratio on the Deformation Behavior of TiCχ Grown by FZ Method at High Temperature

  • Shin, Soon-Gi
    • Korean Journal of Materials Research
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    • v.23 no.7
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    • pp.373-378
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    • 2013
  • In order to clarify the effect of C/Ti atom ratios(${\chi}$) on the deformation behavior of $TiC_{\chi}$ at high temperature, single crystals having a wide range of ${\chi}$, from 0.56 to 0.96, were deformed by compression test in a temperature range of 1183~2273 K and in a strain rate range of $1.9{\times}10^{-4}{\sim}5.9{\times}10^{-3}s^{-1}$. Before testing, $TiC_{\chi}$ single crystals were grown by the FZ method in a He atmosphere of 0.3MPa. The concentrations of combined carbon were determined by chemical analysis and the lattice parameters by the X-ray powder diffraction technique. It was found that the high temperature deformation behavior observed is the ${\chi}$-less dependent type, including the work softening phenomenon, the critical resolved shear stress, the transition temperature where the deformation mechanism changes, the stress exponent of strain rate and activation energy for deformation. The shape of stress-strain curves of $TiC_{0.96}$, $TiC_{0.85}$ and $TiC_{0.56}$ is seen to be less dependent on ${\chi}$, the work hardening rate after the softening is slightly higher in $TiC_{0.96}$ than in $TiC_{0.85}$ and $TiC_{0.56}$. As ${\chi}$ decreases the work softening becomes less evident and the transition temperature where the work softening disappears, shifts to a lower temperature. The ${\tau}_c$ decreases monotonously with decreasing ${\chi}$ in a range of ${\chi}$ from 0.86 to 0.96. The transition temperature where the deformation mechanism changes shifts to a lower temperature as ${\chi}$ decreases. The activation energy for deformation in the low temperature region also decreased monotonously as ${\chi}$ decreased. The deformation in this temperature region is thought to be governed by the Peierls mechanism.

Localized failure in damage dynamics

  • Do, Xuan Nam;Ibrahimbegovic, Adnan;Brancherie, Delphine
    • Coupled systems mechanics
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    • v.4 no.3
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    • pp.211-235
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    • 2015
  • In this work we present a one-dimensional damage model capable of representing the dynamic fracture for elastodamage bar with combined hardening in fracture process zone - FPZ and softening with embedded strong discontinuities. This model is compared with another one we recently introduced (Do et al. 2015) and it shows a good agreement between two models. Namely, it is indicated that strain-softening leads to a sensitivity of results on the mesh discretization. Strain tends to localization in a single element which is the smallest possible area in the finite element simulations. The strain-softening element in the middle of the bar undergoes intense deformation. Strain increases with increasing mesh refinement. Strain in elements outside the strain-softening element gradually decreases to zero.

Material model optimization for dynamic recrystallization of Mg alloy under elevated forming temperature (마그네슘 합금의 온간 동적재결정 구성방정식 최적화)

  • Cho, Yooney;Yoon, Jonghun
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.18 no.6
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    • pp.263-268
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    • 2017
  • A hot forming process is required for Mg alloys to enhance the formability and plastic workability due to the insufficient formability at room temperature. Mg alloy undergoes dynamic recrystallization (DRX) during the hot working process, which is a restoration or softening mechanism that reduces the dislocation density and releases the accumulated energy to facilitate plastic deformation. The flow stress curve shows three stages of complicated strain hardening and softening phenomena. As the strain increases, the stress also increases due to work hardening, and it abruptly decreases work softening by dynamic recrystallization. It then maintains a steady-state region due to the equilibrium between the work hardening and softening. In this paper, an efficient optimization process is proposed for the material model of the dynamic recrystallization to improve the accuracy of the flow curve. A total of 18 variables of the constitutive equation of AZ80 alloy were systematically optimized at an elevated forming temperature($300^{\circ}C$) with various strain rates(0.001, 0.1, 1, 10/sec). The proposed method was validated by applying it to the constitutive equation of AZ61 alloy.

Prediction on Flow Stress Curves and Microstructure of 304 Stainless Steel (304 스테인리스강이 고온 유동응력곡선과 미세 조직의 예측)

  • 한형기;유연철;김성일
    • Transactions of Materials Processing
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    • v.9 no.1
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    • pp.72-79
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    • 2000
  • Dynamic recrystallization (DRX), which may occur during hot deformation, is important for the microsturctural evolution of 304 stainless steel. Especially, the current interest in modelling hot rolling demands quantitative relationships among the thermomechanical process variables, such as strain, temperature, strain rate, and etc. Thus, this paper individually presents the relationships for flow stress and volume fraction of DRX as a function of processing variables using torsion tests. The hot torsion tests of 304 stainless steel were performed at the temperature range of 900~110$0^{\circ}C$ and the strain rate range of 5x10-2~5s-1 to study the high temperature softening behavior. For the exact prediction of flow stress, the equation was divided into two regions, the work hardening (WH) and dynamic recovery (DRV) region and the DRX region. Especially, The flow stress of DRX region could be expressed by using the volume fraction of DRX (XDRX). Since XDRX was consisted of the critical strain($\varepsilon$c) for initiation of dynamic recrystallization (DRX) and the strain for maximum softening rate ($\varepsilon$*), that were related with the evolution of microstructure. The calculated results predicted the flow stress and the microstructure of the alloy at any deformation conditions well.

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The Evolution of Dynamically Recrystallized Microstructure for SCM 440 (SCM 440 강재의 동적 재결정 조직 변화에 관한 연구)

  • 한형기;유연철
    • Transactions of Materials Processing
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    • v.10 no.1
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    • pp.35-41
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    • 2001
  • The high temperature deformation behavior of SCM 440 can be characterized by the hot torsion test in the temperature ranges of $900^{\circ}C$~$1100^{\circ}C$ and strain rate ranges of 0.05/sec~5/sec. The aim of this paper is to establish the quantitative equation of the volume fraction of dynamic recrystallization (DRX) as a function of processing variables, such as strain rate ($\varepsilon$), temperature (T), and strain ('$\varepsilon$). During hot deformation, the evolution of microstructure could be analyzed from work hardening rate ($\theta$). For the exact prediction of dynamic softening mechanism the critical strain ($\varepsilon_c$), the strain for maximum softening rate ($\varepsilon^*$ and Avrami' exponent (m') were quantitatively expressed by dimensionless parameter, Z/A, respectively. The transformation-effective strain-temperature curve for DRX could be composed. It was found that the calculated results were agreed with the experimental data for the steel at any deformation conditions.

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FEM Analysis of Blanking of Mild Steel Sheet at Various Punch Speeds (연강 판재의 속도에 따른 블랭킹의 유한요소해석)

  • Song, Shin-Hyung;Choi, Woo Chun
    • Journal of the Korean Society of Manufacturing Technology Engineers
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    • v.25 no.6
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    • pp.458-461
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    • 2016
  • In this study, a finite element analysis for high-speed blanking of mild steel is performed. A thermomechanically coupled simulation model of a blanking process was developed using ABAQUS/Explicit. Through a simulation of the high-speed blanking process of mild steel, the influence of the punch speed, tool edge radius, and work material thickness on the development of the plastic heat and punch load were studied. The results of the study revealed that a higher punch speed caused thermal softening of the work material and decreased the punch load. Decreasing tool edge radius could help reduce the punch load. In addition, the results of the study revealed that the thermal softening effect was more dominant in the blanking of a mild steel sheet with a greater thickness as compared to that in the blanking of a mild steel sheet with a lower thickness.

Evolution of post-peak localized strain field of steel under quasi-static uniaxial tension: Analytical study

  • Altai, Saif L.;Orton, Sarah L.;Chen, Zhen
    • Structural Engineering and Mechanics
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    • v.83 no.4
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    • pp.435-449
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    • 2022
  • Constitutive modeling that could reasonably predict and effectively evaluate the post-peak structural behavior while eliminating the mesh-dependency in numerical simulation remains to be developed for general engineering applications. Based on the previous work, a simple one-dimensional modeling procedure is proposed to predict and evaluate the post-peak response, as characterized by the evolution of localized strain field, of a steel member to monotonically uniaxial tension. The proposed model extends the classic one-dimensional softening with localization model as introduced by (Schreyer and Chen 1986) to account for the localization length, and bifurcation and rupture points. The new findings of this research are as follows. Two types of strain-softening functions (bilinear and nonlinear) are proposed for comparison. The new failure criterion corresponding to the constitutive modeling is formulated based on the engineering strain inside the localization zone at rupture. Furthermore, a new mathematical expression is developed, based on the strain rate inside and outside the localization zone, to describe the displacement field at which bifurcation occurs. The model solutions are compared with the experimental data on four low-carbon cylindrical steel bars of different lengths. For engineering applications, the model solutions are also compared to the experimental data of a cylindrical steel bar system (three steel bars arranged in series). It is shown that the bilinear and nonlinear softening models can predict the energy dissipation in the post-peak regime with an average difference of only 4%.