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

Metals ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 1013 ◽  
Author(s):  
Armin Abedini ◽  
Cliff Butcher ◽  
Michael Worswick

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.

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Guoqiang Wang ◽  
Xiaolei Qian ◽  
Xuefei Li ◽  
Haijing Hou ◽  
Yi Liu ◽  
...  

Effect of anisotropy in compression is studied on hot rolling of AZ31 magnesium alloy with a three-dimensional constitutive model based on the quadratic Hill48 yield criterion and nonassociated flow rule (non-AFR). The constitutive model is characterized by compressive tests of AZ31 billets since plastic deformations of materials are mostly caused by compression during rolling processes. The characterized plasticity model is implemented into ABAQUS/Explicit as a user-defined material subroutine (VUMAT) based on semi-implicit backward Euler's method. The subroutine is employed to simulate square-bar rolling processes. The simulation results are compared with rolled specimens and those predicted by the von Mises and the Hill48 yield function under AFR. Moreover, strip rolling is also simulated for AZ31 with the Hill48 yield function under non-AFR. The strip rolling simulation demonstrates that the lateral spread generated by the non-AFR model is in good agreement with experimental data. These comparisons between simulation and experiments validate that the proposed Hill48 yield function under non-AFR provides satisfactory description of plastic deformation behavior in hot rolling for AZ31 alloys in case that the anisotropic parameters in the Hill48 yield function and the non-associated flow rule are calibrated by the compressive experimental results.


Author(s):  
Lin Wang ◽  
Qiao-Yun Qin ◽  
Fan Zhang ◽  
Cheng-Wen Tan

Abstract Magnesium alloy is very attractive in many industrial applications due to its low density. The structure-property relationships of the magnesium alloy under quasi-static loading have been extensively investigated. However, the dynamic behavior, particularly the mechanism of high-rate plastic deformation, of the magnesium alloy requires more in-depth investigations. In this paper, the effect of aging treatment on the quasi-static and dynamic properties of a typical rare earth Mg-Gd-Y magnesium alloy is investigated. In particular, the plastic deformation mechanism under dynamic compression loading is discussed. Split Hopkinson Pressure Bar (SHPB) was used to carry out dynamic compression tests with controllable plastic deformation by using stopper rings. The experimental results demonstrate that both static and dynamic properties of the Mg-Gd-Y alloy vary under various aging treatment conditions (under-aged, peak-aged and over-aged conditions), due to two different kinds of second phases: remnant micro size phase from solid solution treatment and nano precipitation from aging treatment. The results of microstructure characterization and statistic analysis of the metallographic phase are presented. The area fraction of the twinned grains increases due to aging treatment and dynamic loading. The main plastic deformation mechanism of the rare earth Mg-Gd-Y magnesium alloy is possibly dislocation slip, rather than twinning for the conventional AZ31 magnesium alloy under high strain rate loading.


2021 ◽  
Author(s):  
Jingyu Liang ◽  
Dechun Lu ◽  
Xiuli Du ◽  
Wei Wu ◽  
Chao Ma

A non-orthogonal elastoplastic constitutive model for sand with dilatancy is presented in the characteristic stress space. Dilatancy of sand is represented by the direction of plastic flow, which can be directly determined by applying the non-orthogonal plastic flow rule to an improved elliptic yield function. A new hardening parameter is developed to describe the contractive and dilative volume change during the shear process, which is co-ordinated with the non-orthogonal plastic flow direction. The combination of the non-orthogonal plastic flow rule and the proposed hardening parameter renders the proposed model with the ability to reasonably describe the stress-strain relationship of sand with dilatancy. The model performance is evaluated by comparing with the experimental data of sand under triaxial stress conditions.


Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 136
Author(s):  
Shize Xiao ◽  
Xiaohui Cheng ◽  
Zhou Yang

This paper establishes a non-equilibrium thermodynamic constitutive model that can predict the undrained shear behavior of saturated sand. Starting from the basic laws of thermodynamics, the model does not require the classical concepts in elasto-plastic models, such as the yield function, the flow rule, and the hardening rule. It is also different from the existing thermodynamic constitutive models in soil mechanics literatures. The model does not use a complex nonlinear elastic potential as usually and introduces a coupling energy dissipative mechanism between the viscosity and elasticity relaxation, which is essential in granular materials. Then this model was used to simulate the undrained shear test of Toyoura sand. The model can predict the critical state, dilatancy-contraction and hardening-softening characteristics of sand during undrained triaxial shearing.


2010 ◽  
Vol 654-656 ◽  
pp. 580-585 ◽  
Author(s):  
Karl Ulrich Kainer ◽  
Joachim Wendt ◽  
Kerstin Hantzsche ◽  
Jan Bohlen ◽  
Sang Bong Yi ◽  
...  

Commercial magnesium alloys such as AZ31 exhibit strong crystallographic textures during massive deformation such as rolling. A randomisation of the texture, however, was found in alloys with rare earth (RE) elements in solid solution. This paper describes the development of microstructure and texture during rolling of the Al-free RE-containing wrought magnesium alloy ZEK100 during hot rolling. This alloy develops a strong texture with a pronounced component towards the transverse direction (TD) of the sheets. This TD component forms already after the first rolling pass, persists through all following passes and is further enhanced by subsequent heat treatment. These results are contrasted with results from a study on texture development of binary RE containing Mg-alloys, which show that the presence of RE elements alone is not responsible for the tilt of basal planes towards the TD. There is, however, a threshold concentration at which the texture begins to weaken.


2019 ◽  
Vol 122 ◽  
pp. 285-318 ◽  
Author(s):  
Saadi A. Habib ◽  
Jeffrey T. Lloyd ◽  
Christopher S. Meredith ◽  
Akhtar S. Khan ◽  
Scott E. Schoenfeld

2014 ◽  
Vol 937 ◽  
pp. 178-181 ◽  
Author(s):  
Quan An Li ◽  
Wen Chuang Liu ◽  
Xiao Jie Song

Magnesium alloys as the emerging commercial metal structure material have excellent specific properties, low density, and stability, which are more and more vital for researchers. This paper reviews the behavior of rare earth in magnesium alloy and the way to enhance the elevated temperature properties of Mg-RE alloys. The current Mg-RE alloys are summarized. The future development direction is pointed.


Author(s):  
Lin Wang ◽  
Qiao-Yun Qin ◽  
Fan Zhang ◽  
Cheng-Wen Tan

AbstractMagnesium alloy is very attractive in many industrial applications due to its low density. The structure-property relationships of the magnesium alloy under quasi-static loading have been extensively investigated. However, the dynamic behavior, particularly the mechanism of high-rate plastic deformation, of the magnesium alloy requires more in-depth investigations. In this paper, the effect of aging treatment on the quasi-static and dynamic properties of a typical rare earth Mg-Gd-Y magnesium alloy is investigated. In particular, the plastic deformation mechanism under dynamic compression loading is discussed. Split Hopkinson Pressure Bar (SHPB) was used to carry out dynamic compression tests with controllable plastic deformation by using stopper rings. The experimental results demonstrate that both static and dynamic properties of the Mg-Gd-Y alloy vary under various aging treatment conditions (under-aged, peak-aged and over-aged conditions), due to two different kinds of second phases: remnant micro size phase from solid solution treatment and nano precipitation from aging treatment. The results of microstructure characterization and statistic analysis of the metallographic phase are presented. The area fraction of the twinned grains increases due to aging treatment and dynamic loading. The main plastic deformation mechanism of the rare earth Mg-Gd-Y magnesium alloy is possibly dislocation slip, rather than twinning for the conventional AZ31 magnesium alloy under high strain rate loading.


Materials ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 6681
Author(s):  
Yanfei Chen ◽  
Zhengqiang Zhu ◽  
Jixue Zhou ◽  
Huasheng Lai

Since the commercial applications of rare earth magnesium alloys are increasing gradually, there are considerable advantages to developing lower cost and higher performance magnesium alloys with high abundance rare earth (RE) elements. However, the alloying order of a matrix magnesium alloy is completely changed with the addition of RE elements. Therefore, further study of the strengthening mechanism of Ce element in magnesium alloys is required. In this work, the thermodynamic stability of the possible second phases in a Mg-Al-Mn-Ce multicomponent magnesium alloy were analyzed, based on first-principle calculations, and the precipitation sequence of the key RE phases was deduced as a consequence. Combined with Scanning Electron Microscope (SEM), X-ray Diffractometer (XRD), Energy Dispersive Spectrometer (EDS), and other experimental methods, it was investigated whether the preferentially precipitated second phases were the nucleation core of primary α-Mg. The complex alloying problem and strengthening mechanism in a multi-elemental magnesium alloy system were simplified with the aid of electronegativity theory. The results showed that the preferentially precipitated Al11Ce3 and Al10Ce2Mn7 phases could not be the nucleation core of primary α-Mg, and the grain refinement mechanism was such that the second phases at the grain boundary prevented the growth of magnesium grains. Moreover, the tensile test results showed that the reinforced structure, in which the Al-Ce phase was mixed with Mg-Al phase, was beneficial for improving the mechanical properties of magnesium alloys, at both ambient temperature and high temperature.


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