Effect of grain structure and strain rate on dynamic recrystallization and deformation behavior: A phase field-crystal plasticity model

https://doi.org/10.1016/j.commatsci.2020.109707Get rights and content

Abstract

In this work, we combined phase field method and crystal plasticity to study the effects of initial grain structures, recrystallized grain orientation, and strain rates on dynamic recrystallization and deformation behavior under stress states typical of the Shear Assisted Processing and Extrusion (ShAPE) process. The geometrically necessary dislocation density was used as the nucleation criterion for recrystallization, and the minimization of the deformation energy drove the growth of the recrystallized grains. With the set of material properties and model parameters, the simulation results demonstrate that (1) a polycrystalline structure with the texture observed in ShAPE process has the lowest yield stress under the ShAPE stress conditions, (2) the recrystallized grains with the texture observed in ShAPE process largely soften the materials, and (3) higher shear strain rate or rotation speed results in larger magnitude of material softening.

Introduction

Shear Assisted Processing and Extrusion (ShAPE) is a novel, patented, direct extrusion process [1], [2], [3]. The extrusion apparatus includes a shear tool that applies rotational and axial shear forces to plasticize the billet material. The plasticized material is extruded through a die along the length of the inner bore of the shear tool, which produces hollow or solid extrusion structures. Compared with conventional direct extrusion, ShAPE has the following advantages: (1) the ram force required is more than ten times lower than that required by conventional direct extrusion for a similar size tubing, and (2) friction heat is the only process heat generated at the billet/die interface; it softens the local material. These advantages make ShAPE likely to reduce costs and a good candidate for scale-up for industry. The microstructural evolution under ShAPE involves deformation-induced dynamic recrystallization (DRX), which is associated with new grain nucleation, grain growth, and texture formation that release stress and/or deformation energy. Experimental results for aluminum alloy 6061 (AA6061) [4] indicate that the ShAPE process parameters, including axial extrusion force, extrusion rate, rotation speed, and temperature, could dramatically affect the microstructure development and material properties and performance of the extruded structures. Therefore, understanding the microstructure evolution under ShAPE may provide a basis for optimizing ShAPE process parameters to achieve desired microstructures and properties.

Extensive experimental and theoretical investigations of grain nucleation and growth during DRX have been done. Three different dynamic recrystallization mechanisms have been proposed [5]. They are discontinuous dynamic recrystallization (DDRX), continuous dynamic recrystallization (CDRX), and geometric dynamic recrystallization (GDRX). DDRX refers in general to a process that has clear nucleation and growth stages, which usually first occur at triple junctions and the original grain boundaries. CDRX occurs in materials with high stacking fault energy as a result of efficient dynamic recovery: new cell or subgrain structures with low-angle grain boundaries (LAGBs) are formed during deformation, and the LAGBs progressively evolve into high angle grain boundaries (HAGBs) at larger deformations [6]. For GDRX, the deformed grains become elongated and the grain boundaries become serrated where they are contact with LAGBs belonging to subgrains. When grain thickness is below1–2 sub-grain size as deformation increases, the points of the serrations touch, and equiaxed grains with HAGBs formed. Substantial grain refinement is thus obtained through grain elongation and thinning [5]. Although the nucleation mechanisms of recrystallization such as the formation of sub-boundary misorientation new grains are still unclear at atomistic level, it is commonly accepted that for the three DRX processes the new grains all form as a result of an increase in sub-boundary misorientation which is associated with continuous dislocation accumulation, and development of dislocation networks, twin structures, and/or serrated boundaries driven by deformation [7], [8], [9], [10], [11], [12], [13], [14].

Material process modeling is a powerful tool for investigating mechanical response in heterogeneous materials undergoing microstructure and mechanical property evolution during material fabrication and operation [15], [16]. Mesoscale mechanical models such as crystal plasticity (CP) have been equipped with physics-based constitutive theories [17], [18], [19], [20], [21] and efficient numerical schemes [22], [23], [24], [25]. Different microstructure models, such as phase field (PF), Potts, and cellular automaton, have been developed to study deformation-induced microstructure evolution processes such as dislocation dynamics [26], twinning and de-twinning [27], static recrystallization [28], [29], and dynamic recrystallization [30]. Takaki et al. integrated the phenomenological Kocks-Mecking model of dislocation evolution [31], [32] or the CP finite element (CP-FE) [29] into PF models to study dynamic recrystallization. Popova et al. [33] simulated texture formation during DRX in magnesium by coupling CP-FE with probabilistic cellular automata. PF models integrating crystal plasticity were developed to study the effect of boundary migration and grain boundary sliding on plastic deformation, grain growth and recrystallization in the presence of a varying deformation field [34], [35], [36]. Chen et al. [28] developed a fast Fourier transform (FFT)-based computational approach integrating the PF method and CP to model recrystallization of plastically deformed polycrystals in three dimensions. Zhao et al. [30] provided an integrated modeling scheme in which the mechanical response was fully coupled with the underlying microstructure evolution by employing FFT-CP and PF. Very recently, Ask et al. developed a recrystallization model by coupling the Kobayashi-Warren-Carter (KWC) phase field model with Cosserat crystal plasticity[37]. The model naturally used grain orientations as field variables and incorporated the evolution of grain orientation, dislocation density, and recrystallization grains. Admal et al. have extended the KWC phase field model by using five independent field variables to describe a general grain boundary[38].

Considering that inhomogeneous structures such as grain morphology and distributed second phase particles play an important role in the evolution of subgrain defect structures (e.g., dislocation networks, multiple slip bands, grain boundary bulging, and/or twinned structures), such subgrain defect structures are potential nucleation sites of recrystallized grains [8], [14], [39], [40], [41]. DRX models must account for inhomogeneous structures. The advantages of the PF approach of (1) using non-boundary-tracking field descriptions of microstructures and (2) naturally dealing with multi-physics coupling under the framework of the first and second laws of thermodynamics have made PF a powerful, robust tool for modeling and predicting microstructure evolution in materials processes [42], [43], [44], [45], [46], [47], [48]. In this work, we employ a PF-CP model to study the effect of initial grain structures, recrystallized grain orientations, and strain rates on dynamic recrystallization and deformation behavior under stress states typical during ShAPE. We used dislocation-density–based CP theory [28], [30] to describe the evolution of stresses and dislocation density in a polycrystalline structure under deformation. Geometrically necessary dislocation (GND) density is used as the nucleation criterion for recrystallization, and grain growth is driven by minimizing the distorted energy.

The paper is organized as follows: the PF model of dynamic recrystallization and the involved CP and stored deformation energy calculation are described in Section 2. The ShAPE process and experimentally observed microstructures of AA6061after the ShAPE process are briefed in Section 3. The material modeled is pure aluminum. The model parameters and the effects of initial grain structures, recrystallization parameters, and strain rates on dislocation structure evolution, DRX, and mechanical properties will be presented in Section 4. Section 5 summarizes the work.

Section snippets

Phase field model of grain growth

Nucleation and growth of recrystallized grains are thought to be driven by minimizing the local distorted energy or the dislocation density. Experiments also show that recrystallized grains contain low dislocation density [49]. This implies that small recrystallized grains have different mechanical behavior from that of the original large grains. To distinguish the different mechanical properties, our PF model employs two sets of order parameters, ηdef,i and ηrex,i, (i=1,, Ng) to describe the

Experimental observation of microstructure evolution under ShAPE

The extrusion apparatus for the ShAPE process includes a shear tool that applies a rotational shear force and an axial extrusion force to plasticize the billet material. The plasticized material is extruded through a die along the inner bore of the rotating shear tool, which can produce hollow or solid extrusion structures. Fig. 1(a) schematically shows the structure of the ShAPE equipment. The red lines denote the interface region between the billet materials and die where friction heat is

Crystal plasticity model parameters

Pure aluminum is taken as our model material in this work. Aluminum has face centered cubic (FCC) crystals. It has 12 slip systems with slip plane 111 and Burgers vector <1 1 0〉 . The elastic constants are listed in Table 1 where Cmn is the Voigt notation for tensor cijkl. The other parameters used in our CP model are also found in the table, and τ0sx=τ00s+0tτ̇0sdt, τ̇0s=Hs=1Nγ̇sx.

Using these material parameters, we simulated cases of both uniaxial tension and shear under pressure with three

Conclusions

A PF model of dynamic recrystallization has been developed by integrating CP theory and dislocation density evolution. With the model, the effect of grain orientation, recrystallization criteria, and strain rate on recrystallization and deformation behavior were simulated. The results indicate that (1) a polycrystalline structure with the texture produced by the ShAPE process has the lowest yield stress under the stress state imposed by ShAPE; (2) recrystallized grains with the texture observed

CRediT authorship contribution statement

Yulan Li: Conceptualization, Methodology, Investigation, Data curation, Visualization, Writing - original draft, Writing - review & editing. Shenyang Hu: Conceptualization, Methodology, Formal analysis, Writing - original draft, Writing - review & editing. Erin Barker: Conceptualization, Funding acquisition, Project administration, Writing - review & editing. Nicole Overman: Conceptualization, Data curation, Visualization, Writing - review & editing. Scott Whalen: Conceptualization, Data

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors would like to acknowledge the financial support of the Laboratory Directed Research and Development initiative at Pacific Northwest National Laboratory, which is operated by Battelle for the U.S. Department of Energy under Contract DE-AC05-76RL01830.

References (66)

  • A. Ma et al.

    A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations

    Acta Mater.

    (2006)
  • H. Gao et al.

    Geometrically necessary dislocation and size-dependent plasticity

    Scr. Mater.

    (2003)
  • I.J. Beyerlein et al.

    A dislocation-based constitutive law for pure Zr including temperature effects

    Int. J. Plast.

    (2008)
  • R.A. Lebensohn et al.

    A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys

    Acta Metall. Mater.

    (1993)
  • S.R. Niezgoda et al.

    Stochastic modeling of twin nucleation in polycrystals: An application in hexagonal close-packed metals

    Int. J. Plast.

    (2014)
  • R.A. Lebensohn et al.

    An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials

    Int. J. Plast.

    (2012)
  • P. Eisenlohr et al.

    A spectral method solution to crystal elasto-viscoplasticity at finite strains

    Int. J. Plast.

    (2013)
  • S.Y. Hu et al.

    Simulations of stress-induced twinning and de-twinning: A phase field model

    Acta Mater

    (2010)
  • L. Chen et al.

    An integrated fast Fourier transform-based phase-field and crystal plasticity approach to model recrystallization of three dimensional polycrystals

    Comput. Methods Appl. Mech. Eng.

    (2015)
  • T. Takaki et al.

    Static recrystallization simulations starting from predicted deformation microstructure by coupling multi-phase-field method and finite element method based on crystal plasticity

    Int. J. Mech. Sci.

    (2010)
  • P.Y. Zhao et al.

    An integrated full-field model of concurrent plastic deformation and microstructure evolution: Application to 3D simulation of dynamic recrystallization in polycrystalline copper

    Int. J. Plast.

    (2016)
  • H. Mecking et al.

    Kinetics of flow and strain-hardening

    Acta Metall. Mater.

    (1981)
  • E. Popova et al.

    Coupled crystal plasticity - Probabilistic cellular automata approach to model dynamic recrystallization in magnesium alloys

    Int. J. Plast.

    (2015)
  • L. Zhao et al.

    On the plastic driving force of grain boundary migration: A fully coupled phase field and crystal plasticity model

    Comp Mater Sci

    (2017)
  • T.L. Cheng et al.

    Diffuse interface approach to modeling crystal plasticity with accommodation of grain boundary sliding

    Int J Plasticity

    (2019)
  • A. Ask et al.

    A Cosserat crystal plasticity and phase field theory for grain boundary migration

    J. Mech. Phys. Solids

    (2018)
  • N.C. Admal et al.

    A three-dimensional misorientation axis- and inclination-dependent Kobayashi–Warren–Carter grain boundary model

    J. Mech. Phys. Solids

    (2019)
  • A.M. Wusatowska-Sarnek et al.

    Nucleation and microtexture development under dynamic recrystallization of copper

    Mater. Sci. Eng., A

    (2002)
  • N. Moelans et al.

    An introduction to phase-field modeling of microstructure evolution

    Calphad-Comput. Coupling Ph. Diagrams Thermochem.

    (2008)
  • Y.L. Li et al.

    A review: applications of the phase field method in predicting microstructure and property evolution of irradiated nuclear materials, npj

    Computational Materials

    (2017)
  • M. Asta et al.

    Solidification microstructures and solid-state parallels: Recent developments, future directions

    Acta Mater.

    (2009)
  • S.M. Allen et al.

    Microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening

    Acta Metall. Mater.

    (1979)
  • A. Ma et al.

    A constitutive model for fcc single crystals based on dislocation densities and its application to uniaxial compression of aluminium single crystals

    Acta Mater

    (2004)
  • Cited by (0)

    View full text