Strain rate sensitivity (SRS) is an important material property that governs the rate dependent mechanical behaviors associated with deformation rate changes, creep, stress relaxation, formability, ...etc. The variety of activated deformation mechanisms of magnesium alloys under different loading paths, e.g. tension vs. compression, implies that SRS of magnesium alloys obviously depends on loading paths, and each deformation mechanism has its own SRS. However, a single SRS scheme is commonly employed in numerical modeling to describe the rate dependent behaviors of magnesium alloys, which disregards the distinction of SRSs among different deformation mechanisms. The implementation of the constitutive model that works for a wide range of values of SRSs has been a challenge to crystal plasticity modeling for metals with multiple deformation mechanisms like magnesium. Especially, very small values of SRS, corresponding to low rate-sensitivity, generally lead to high nonlinearity involved in the governing equations, and then computational failure. In this paper, the elasto-viscoplastic self-consistent (EVPSC) crystal plasticity model is improved to enhance its numerical robustness for very small SRS values. Taking advantage of this improvement, different SRSs for various deformation mechanisms are employed to investigate the strain rate dependent behaviors of magnesium alloys at room temperature. First, the SRSs for various deformation mechanisms are determined based on the compressive stress relaxation tests on an AZ31 alloy plate; secondly, the obtained SRSs are applied to interpret internal elastic strain evolution of the same magnesium alloy under in-plane compression; finally, the determined SRSs are applied to investigate the deformation of another AZ31 alloy under various deformation paths and strain rates. The present work is the first effort on studying effects of strain rate-sensitivity on mechanical behavior of Mg alloys under wide range of applied strain rates by using an improved self-consistent polycrystal plasticity model. Good agreement between the experiments and simulations reveals the importance and necessity of using different SRSs for the deformation mechanisms involved. The rate dependent behaviors of magnesium alloys can be better described by using multiple SRSs associated to each operative deformation mechanism.
•Numerical stability of EVPSC model when treating multiple/small SRSs is enhanced.•Rate sensitivity of Mg alloys can be better described by using multiple SRSs.•SRSs are obtained for basal, prismatic, pyramidal slip and extension twinning.•Compact slip systems corresponds to low SRS; twinning is rate insensitive.•The SRSs are validated by internal elastic strain and a rate related experiment.
In order to investigate the evolution of deformation mechanisms of AZ31B Mg alloy sheet and their correlation with material property development under intermediate temperatures, systematic ...experimental examination and in-depth crystal plasticity analysis on the material are performed. The mechanical responses of AZ31B Mg alloy sheet are measured under uniaxial tension and compression along RD (rolling direction), TD (transverse direction) and ND (normal direction) directions and over the temperature range 100 ∼ 300°C. The evolution of anisotropy (r-value), texture, and microstructure with respect to temperature and strain are examined. Two uncommon deformation behaviors in AZ31 sheet deformation are observed in the experiments for the first time. Firstly, the slope of r-value versus strain curve in RD compression at lower temperature changes from a positive to a negative one when temperature rises to 200°C and 300°C. Secondly, micro-bands are formed during RD compression at 200°C, in contrast to uniform equiaxed dynamic recrystallization (DRX) grains in RD tension and ND compression. The evolution of deformation mechanisms in the uniaxial tension/compression deformation is analyzed with the visco-plastic self-consistent (VPSC) model that takes the variation of r-value into account. The correlation between the experimental observations and deformation modes evolution is probed. It is found that the negative slope of activity ratio of prismatic to basal slip is highly consistent with the change in r-value with strain during uniaxial compression at 200°C. The different rotation ‘room’ caused by basal slip in uniaxial compression at 200°C, together with the restriction of grain boundary, leads to higher misorientation evolution rate in loading direction than in the other directions, and then results in the formation of micro-bands.
•Systematic deformation tests of AZ31B sheet are performed in RD/TD/ND directions, from 100 °C to 300 °C.•A negative trend of r-value with increasing strain is observed in RD compression at 200 °C and 300 °C.•Formation of special micro-bands is found during RD compression at 200 °C.•Crystal plasticity simulation is performed considering the evolution of r-value.•The correlations between deformation modes and r-value, texture and micro-bands are thoroughly investigated.
Experimental observations indicate that pre-deformation can influence the mechanical properties of magnesium alloys. However, inconsistent or even contradictory conclusions have been drawn mainly due ...to the difficulty of isolating an individual influencing factor from those playing interactive roles in an experiment. Therefore, a systematical study in terms of crystal plasticity modeling is performed to evaluate the effect of pre-deformation (pre-rolling and pre-compression) in the current work. The subsequent tensile response of the magnesium alloy AZ31B sheet along the transverse direction and the rolling direction after pre-deformation is simulated. It is found that both pre-rolling and pre-compression can either enhance or deteriorate the mechanical properties of the AZ31B sheet. If annealing is applied, the pre-deformed microstructure is retained and the mechanical properties are generally enhanced. Pre-compression with ~ 3% strain and annealing are able to enhance the overall mechanical properties of a rolled Mg alloy sheet the most. Based on the modeling results, the properties of magnesium alloys can be affected differently with different pre-straining paths, different loading directions, with annealing or without. These findings help us understand the inconsistency in different experimental studies and also reveal the role of pre-deformation and the accompanying influencing factors on the properties of magnesium alloys.
A series of electron backscattered diffraction (EBSD) experiments is carried out to explore nucleation features in the continuous dynamic recrystallization (CDRX) of AZ31 Mg alloy sheets at 200 °C. ...The CDRX mechanism that misorientation accumulated from the core area to grain boundary leads to nucleation of dynamic recrystallization grains around parent grains can be identified for the present fine-grained AZ31B Mg alloy rolling sheet. A crystal plasticity approach for DRX simulation is extended to simulate the hot deformation and CDRX of the AZ31B magnesium alloy sheets. The experimental results of uniaxial tension along rolling direction (RD) and compression tests along RD and normal direction of the AZ31B sheets at 200 °C are numerically investigated by the current model in terms of mechanical behaviors, grains’ rotation, textures orientation and grain size evolution. The VPSC-DRX model that considers multiple slip systems and indirectly incorporates the misorientation can reproduce well the stress-strain curves, r-values, grain size change and texture evolution. The introduction of DRX will change the slip mode activities at 200 °C. The VPSC-DRX model can better predict the texture evolution compared to the simulation results regardless of DRX effects.
A straightforward approach integrating a visco-plastic self-consistent (VPSC) model with a phenomenological dynamic recrystallization (DRX) criterion is proposed for coupling simulation of hot ...deformation and accompanying DRX. The phenomenological DRX nucleation and growth criteria are embedded into VPSC through a dislocation density based hardening model. The approach is validated and demonstrated by simulating compression of polycrystal copper at various conditions. The key characteristics of DRX during hot deformation of copper, in terms of mechanical response and microstructure evolution, are well reproduced and illustrated with the VPSC-DDRX coupling simulation approach. Furthermore, a series of numerical studies on the hot deformation behaviors corresponding to different loading paths and initial textures are carried out to explore their effects on dynamic recrystallization and further demonstrate the capability of the proposed method. The innovation of current work is establishing a relatively simple crystal plasticity based DRX simulation method that incorporates crystal information, deformation modes and grain population, and realizes integrated computation of deformation, texture and DRX process.
•A polycrystalline plasticity based DRX simulation method is developed.•Plastic deformation, DRX process and texture evolution can be simulated simultaneously.•Hot deformation of copper is numerically investigated by the developed method.
Hot forming often has to be resorted when processing metals with limited room-temperature formability, such as aluminum, magnesium, etc. The temperature rise induced by plastic work, especially under ...high strain rates, can exert significant effect on mechanical response as well as dynamic recrystallization of deformed metals. In the present work, a polycrystal plasticity based thermo-mechanical-dynamic recrystallization (DRX) coupled approach is established by implementing thermo-mechanical effect in a VPSC-DRX model where a grain nucleation and growth model is implemented into the VPSC framework. The modeling parameters associated with various slip modes, temperatures and strain rates are calibrated by isothermal compression experiments, and then evolution functions of hardening and DRX related parameters with respect to temperature and strain rate are established. The integrated computation of plastic deformation, texture, grain size and temperature update in hot deformation of metals can be achieved. The proposed method is verified and then applied to simulate hot extrusion processes of magnesium alloy bars at three different ram speeds. The influences of ram speed on development of deformation texture and grain size are analyzed. The temperature rise due to plastic work enhances stress softening and stimulates grain growth, makes the macro/micro responses of materials no longer monotonically varied with strain rate.
•A thermo-mechanical, polycrystal plasticity and DRX coupled model is proposed.•Thermo-mechanical coupling behaviors of Mg and Al alloys are studied.•Stress, grain size, texture and temperature can be predicted simultaneously.•Deformation induced heat makes macro/micro response not monotonically varied with strain rate.
The effects of cladding layers of rate-sensitive materials on the ductility and fracture strain of compressed rings are numerically investigated by using the finite element method (FEM) and employing ...the Johnson-Cook (J-C) model. The results show that ductility is governed by the behavior of the material that is located at the ring outer wall regardless of the volume fraction of the core and clad materials. However, as the number of layers increases, this influence becomes less noticeable. Moreover, as barreling increases at the outer wall and decreases at the inner wall, fracture strain increases. Furthermore, the effects of ring shape factor and bonding type of clad and core materials are numerically evaluated. The numerical results show that less force per unit volume is required to fracture narrower rings and that using a noise diffusion pattern at the interface of the materials is more suitable to simulate crack propagation in the compressed rings and functionally graded materials (FGMs). Additionally, delamination has a direct relation to layer thickness and can occur even in the presence of perfect bonding conditions owing to differences among the material and fracture parameters of laminated layers.
In plane tension of magnesium alloy sheets is accommodated by prismatic and basal slip, whereas {10−12} twinning is activated when grains are elongated along the axis. The plastic behavior of ...Mg-3Al-1Zn in tension has been investigated using a thick rolled plate with a strong basal texture. Tensile tests were performed along five directions distributed between the normal direction and the transverse direction, allowing various amount of {10–12} twinning, basal, and prismatic slip to take place. The twinning behavior has been investigated using EBSD measurement and EVPSC modeling, and Schmid factor analysis was performed. The observed amount of variants with a Schmid factor of high rank is higher than predicted, emphasizing the necessity of strain accommodation between grains and twins. Compared with compression, even when twinning activity is low, more {10–12} twin variants are predicted in tension. This study confirms extension twinning as a major deformation mechanism in all tensile directions and an efficient way to harden Mg alloys by twin-twin boundaries.
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•EVPSC-TDT simulations of the mechanical behavior in ND-TD plane of a magnesium alloy AZ31 thick rolled plate in tension•{10–12} twinning is activated and investigated in tension along different directions.•{10–11} twinning is also included in the EVPSC-TDT model for the first time.•More {10–12} twin variants of low Schmid factor are observed than predicted.•More {10–12} variants are predicted in tension than in compression.
The deformation mechanisms of a rolled high-purity α-titanium plate under monotonic loading along the rolling direction (RD), transverse direction (TD), and normal direction (ND) are investigated by ...the Elastic Visco-Plastic Self-Consistent (EVPSC) model, which incorporates a Twinning and De-Twinning (TDT) scheme to describe twinning behavior during straining. In the EVPSC-TDT model, plastic deformation is assumed to be accommodated by prismatic, basal and pyramidal
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slip modes as well as the
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extension and
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contraction twin modes. Numerical results based on the EVPSC-TDT model are in good agreement with the corresponding experimental data. The tension–compression asymmetry, anisotropic initial yielding and strain hardening behavior are interpreted in terms of the predicted relative activities of various deformation modes, twin volume fractions and texture evolutions. It is demonstrated that twinning plays an important role in tension–compression asymmetry and plastic anisotropy, which is closely related to the loading direction with respect to crystal orientations in the initial texture. In addition, it can be concluded that the TDT scheme permits better performance in describing twinning-associated deformation behavior for the rolled high-purity α-titanium plate than the Predominant Twin Reorientation (PTR) model even when detwinning is not involved.
Graphical abstract
A MATLAB algorithm was developed to insert cohesive elements at the interfaces between the matrix and precipitates in two dimensional (2D) representative volume elements (RVEs) of metals. The RVEs ...were created using OOF2 and imported into the “Complete ABAQUS Environment” (CAE) interface. These RVEs are based on actual images of the metal at the microscale, where the precipitates have irregular shapes. The RVEs contain precipitates that are dispersed into matrix materials. Commercial finite element (FE) ABAQUS software does not provide the option to automatically generate cohesive elements at the interfaces. The presented algorithm enables the insertion of cohesive elements at the interfaces between the matrix and precipitate in a convenient manner. This algorithm enables the simulation of the fracture process, including initiation at the interfaces and propagation at microscale, for metals that contain precipitates and/or particles. This algorithm extends the simulation capabilities of the FE solver ABAQUS.
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