• Transactions of Materials Processing
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• v.26 no.5
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• pp.286-292
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• 2017

Magnesium alloy shows strong anisotropy and asymmetric behavior in tension and compression curve, especially at room temperature. These characteristics limit the application of finite element method (FEM) which is based on conventional continuum mechanics. To accurately predict the material behavior of magnesium alloy at microstructural level, a methodology of fully coupled multiscale simulation is presented and a crystal plasticity model as a constitutive equation in the simulation of metal forming process is introduced in this study. The existing constitutive equation for rigid plastic FEM is modified to accommodate deviatoric stress component and its derivatives with respect to strain rate components. Viscoplastic self-consistent (VPSC) polycrystal model was selected as a constitutive model because it was regarded as the most robust model compared to Taylor model or Sachs model. Stiffness matrix and load vector were derived based on the new approach and implemented into $DEFORM^{TM}-3D$ via a user subroutine handling stiffness matrix at an elemental level. The application to extrusion and rolling process of pure magnesium is presented in this study to assess the validity of the proposed multiscale process.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2004.08a
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• pp.72-82
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• 2004

The deformation mechanism of hexagonal close-packed materials is quite complicate including slips and twins. A deformation mechanism, which accounts for both slip and twinning, was investigated for polycrystalline hop materials. The model was developed in a finite element polycrystal model formulated with initial strain method where the stiffness matrix in FEM is based on the elastic modulus. We predicted numerically the texture of Mg alloy(AZ31B) sheet by using FEM based on crystal plasticity theory. Also, we introduced the recrystallized texture employed the maximum energy release theory after rolling. From the numerical study, it was clarified that the shrink twin could not be the main mechanism for shortening of c-axis, because the lattice rotation due to twin rejects fur c-axis to become parallel to ND(normal direction of plate). It was showed that the deformation texture with the pyramidal slip gives the ring type pole figure having hole in the center.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2001.10a
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• pp.309-312
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• 2001

FEM simulating system of the cross-rolling texture formation offers a systematic and efficient way of exploring the relationship between the process variables and the state of plastic anisotropy of sheet product. Cross-rolled sheets possess higher average plastic strain ratios and lower planer anisotropy than those of the straight-rolled sheets. The employed model is a finite-element polycrystal model which each element used in FEM is assumed to be a crystal having different orientation by Takahashi. Texture development, deformation textures due to cross-rolling are predicted for face-centered cubic sheet metal. Crystal orientations are assigned on the basis of the pole figures obtained by X-ray diffraction. Development of anisotropy during cross rolling of an fcc sheet material is predicted theoretically with respected to flow stress and R-value in tensile test.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2000.10a
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• pp.70-73
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• 2000

A finite element analysis model is suggested for analysis of forming process of milli structure whose size is from a few hundreds ${\mu}m$ to a few mm. In this paper, finite element formulation which assemble crystal plasticity theory considering texture development with damage mechanics is developed, since orientation development and growth of micro voids became the primary factors for deformation aspects in large deformation of milli structure. Applying to, extremely, extrusion process of single crystal and extrusion/drawing process of polycrystal milli-size bar, extrusion force, preferred orientation, and damage evolution are examined to understand the characteristics of deformation of milii-size bar.

• Korean Journal of Metals and Materials
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• v.46 no.3
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• pp.135-143
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• 2008

The inhomogeneous texture through the thickness direction can be developed during hot rolling deformation in aluminum alloy. In this study, the inhomogeneous texture evolution through the thickness direction during hot rolling deformation in Al-5 wt%Mg alloy produced by a new strip casting technology was measured experimentally. Macrotexture measurement was conducted using X-ray diffractometer. A finite element analysis with ABAQUS/StandardTM and rate sensitive polycrystal model were used to predict the evolution of hot rolling texture. The experimental results of Al-5 wt%Mg alloy were compared with calculated results. The shear texture components tend to be increased at the surface region of the hot-rolled specimen. It is found that triclinic sample symmetry is more accurate assumption for texture analysis and simulation in the surface region of hot-rolled aluminum alloy.

• Korean Journal of Materials Research
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• v.25 no.2
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• pp.81-89
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• 2015

A strain-gradient crystal plasticity constitutive model was developed in order to predict the Hall-Petch behavior of a Ni-base polycrystalline superalloy. The constitutive model involves statistically stored dislocation and geometrically necessary dislocation densities, which were incorporated into the Bailey-Hirsch type flow stress equation with six strength interaction coefficients. A strain-gradient term (called slip-system lattice incompatibility) developed by Acharya was used to calculate the geometrically necessary dislocation density. The description of Kocks-Argon-Ashby type thermally activated strain rate was also used to represent the shear rate of an individual slip system. The constitutive model was implemented in a user material subroutine for crystal plasticity finite element method simulations. The grain size dependence of the flow stress (viz., the Hall-Petch behavior) was predicted for a Ni-base polycrystalline superalloy NIMONIC PE16. Simulation results showed that the present constitutive model fairly reasonably predicts 0.2%-offset yield stresses in a limited range of the grain size.

• Journal of the Korean Society for Precision Engineering
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• v.29 no.8
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• pp.818-823
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• 2012

In order to predict necking behaviour of aluminium sheets, a crystal plasticity model is introduced in the finite element analysis of tensile test. Due to the computational limits of time and memory, only a small part of tensile specimen is subjected to the analysis. Grains having different orientations are subjected to numerical tensile tests and each grain is discretized by many elements. In order to predict the sudden drop of load carrying capacity after necking, a well-known Cockcroft-Latham damage model is introduced. The mismatch of grain orientation causes stress concentration at several points and damage is evolved at these points. This phenomenon is similar to void nucleation. In the same way, void growth and void coalescence behaviours are well predicted in the analysis. For the comparison of prediction capability of necking, same model is subjected to finite element analysis using uniform material properties of polycrystal with and without damage. As a result, it is shown that the crystal plasticity model can be used in prediction of necking and fracture behavior of materials accurately.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.485-488
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• 2005

Most metals are polycrystalline material whose deformation is dominated by the slip system. During the deformation process, orientation of slip systems is rearranged with preferred orientations, leading to deformation-induced crystallographic texture which is called deformation texture. Depending on the texture development, the property of material can be changed. The rate-independent crystal plasticity which is based on the Schmid law as a yield function causes a non-uniqueness in the choice of active slip systems. In this work, to avoid the slip system ambiguity problem, rate-independent crystal plasticity model based on the smooth yield surface with rounded-off corners is adopted. In order to simulate the polycrystalline material under plastic deformation, we employ the Taylor model of polycrystal behavior that all the grains are assumed to be subjected to the macroscopic velocity gradient. Rigid-plastic finite element program based on this rate-independent crystal plasticity is developed to predict the grain-level deformation behavior of FCC metals during metal forming processes. In the finite element calculation, one integration point is considered as a crystalline aggregate which has a number of crystals. Macroscopic behavior of material can be deduced from the behavior of aggregates. As applications, the extrusion processes are simulated and the changes of mechanical properties are predicted.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2006.05a
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• pp.349-352
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• 2006

The plastic deformation of polycrystalline materials is induced by changes of the microstructure when the loading is beyond the critical state of stress. Constitutive models for the crystal plasticity have the common objective which relates microscopic single crystals in the crystallographic texture to the macroscopic continuum point. In this paper, a new consistent tangent stiffness for the anisotropic elasto-viscoplastic analysis of polycrystalline deformation is developed, which can be used in the finite element analysis for the slip-dominated large deformation of polycrystalline materials. In order to calculate the consistent tangent stiffness, the state function is defined based on the consistency condition between the elastic and plastic stress. The rate of shearing increment($\Delta{\gamma}^{\alpha}$) is calculated with satisfying the consistency condition. The consistency condition becomes zero when the trial resolved shear stress($\tau^{{\alpha}^*}$) becomes resolved shear stress($\tau^{\alpha}$) at every step. Iterative method is utilized to calculate the rate of shearing increment based on the implicit backward Euler method. The consistent tangent stiffness can be formulated by differentiating the rate of shearing increment with total strain increment after the instant rate of shearing increment converges. The proposed tangent stiffness is applied to the ABAQUS/Standard by implementing in the ABAQUS/UMAT.