Various degrees of rolling reductions account for diverse recrystallization mechanisms and thus different microstructural and texture features. The development of deformation and recrystallization textures is discussed based on experimental data and results of finite element and crystal plasticity simulations. A recrystallization model is presented that incorporates the microstructural heterogeneities and changes in local stored energy. The experimental observations and results of crystal plasticity calculations testify that orientation selection during recrystallization is controlled by low stored energy nucleation which is incorporated in the recrystallization model. Results of texture simulations show that the evolution of {100} and {011} components is related to a particle stimulated nucleation mechanism

Decroos, Koen

Kestens, Leo

Petrov, Roumen

Sidor, Jurij

Ghent University Academic Bibliography

MODELING THE RECRYSTALLIZATION TEXTURES IN PARTICLE CONTAINING Al ALLOYS AFTER VARIOUS ROLLING REDUCTIONSJurij J. Sidor1, Roumen H. Petrov 1,2, Koen Decroos3, Leo A.I. Kestens1,21Gent University, Department of Materials Science and Engineering, Technologiepark 903, B-9052 Gent, Belgium;23Catholic University of Leuven, Faculty of Engineering, Department of Metallurgy and MaterialsDelft University of Technologies, Department of 3ME, Mekelweg 2, 2600 GA Delft, the Netherlands.Engineering , 3001 Heverlee (Leuven), Belgium.Keywords: Recrystallization, Deformation, PSN, Strain heterogeneity.AbstractVarious degrees of rolling reductions account for diverse recrystallization mechanisms and thus different microstructural and texture features. The development of deformation and recrystallization textures is discussed based on experimental data and results of finite element and crystal plasticity simulations. A recrystallization model is presented that incorporates the microstructural heterogeneities and changes in local stored energy. The experimental observations and results of crystal plasticity calculations testify that orientation selection during recrystallization is controlled by low stored energy nucleation which is incorporated in the recrystallization model. Results of texture simulations show that the evolution of {100}<130>and {011}<233> components is related to a particle stimulated nucleation mechanism.1. IntroductionThe microstructure and texture evolution in deformed and recrystallized materials is strongly affected by the material’s chemistry and rolling conditions. The chemical composition of the material controls the formation of large non-deformable particles while the strain magnitude and the friction conditions affect the deformation flow around the hard inclusions and deformation flow across the thickness, respectively. In FCC materials with a low volume fraction of non-deformable constituents, the rolling texture is dominated by a ȕ-fiber [1] which represents a continuous tube of orientations that connects the Copper orientation ({112}<111>) through the S orientation ({123}<634>) to the Brass orientation (B-{011}<211>) in Euler space. Duringannealing, the rolling texture conventionally transforms to a texture that is dominated by the Cube ({100}<001>) and Goss ({110}<001>) components. The presence of large constituent particles produces strain heterogeneities during cold rolling which causes specific texture development during recrystallization [1]. The current contribution aims to clarify the effect of microstructural heterogeneities involved in severe rolling reductions on the development of recrystallization (RX) texture based on both finite element modeling and results of crystalplasticity calculations.2. Experimental and Computational MethodsThe material used in the current study is conventionally cast Al-2.8Mg-0.21Mn-0.14Si aluminum alloy from 5xxx series. The as-cast block was subjected to different cold rolling reduction levelswhich have led to three materials of different microstructural features, designated as A, B and C. In the current case, the as-cast block was cold rolled to various final thicknesses without13th International Conference on Aluminum Alloys (ICAA13) Edited by: Hasso Weiland, Anthony D. Rollett, William A. Cassada TMS (The Minerals, Metals & Materials Society), 2012 299homogenization heat treatment with the aim to preserve a minimum level of fine precipitates and thus to reveal the effect of large non-deformable particles on the evolution of recrystallization texture. The investigated materials were rolled on a laboratory rolling mill from a block with an initial thickness of 26.5 mm. The materials A, B and C were subjected to the following thickness reductions: ~88 %, ~96% and 98% corresponding to von Mises strain of 2.4, 3.7 and 4.5,respectively. The final annealing of all rolled samples was performed in a salt bath at 550°C for ~12 seconds.The cold rolling textures were determined by measuring X-ray pole figures in the conventional back reflection mode. From a set of {111}, {200}, {220}, {311} pole figures the orientation distribution function (ODF) was calculated using the conventional series expansion method. The through-thickness texture was calculated by integrating all the sub-layer textures into one average ODF. The through-thickness textures of the annealed specimens were measured by means of the EBSD technique. The textures were calculated by the harmonic series expansion method assuming orthorhombic sample symmetry and by superimposing a Gaussian peak for each individual orientation with a spread of 7° around the exact orientation. To the purpose of obtaining a reliable comparison between deformation and recrystallization textures, both XRD and EBSD orientation data were post-processed with the MTM-FHM software [2]. In order to investigate a strain field around non-deformable constituent particles the finite element modeling (FEM) was performed using the ANSYS® software. In the FE calculations, a particle containing aluminum matrix was subjected to plane strain compression deformation (PSC). The annealing textures were computed by recrystallization model [3] which combines both oriented nucleation and oriented growth mechanisms of recrystallization. 3. Results and Discussions3.1 Constituent ParticlesFig. 1 reveals a distribution of constituent particles in the as-cast and deformed materials. It is evident that the coarse-grained as-cast structure comprises irregularly shaped coarse constituent particles located on the grain boundaries (Fig. 1a). The high deformation levels involved in the cold rolling changes the initial distribution of constituent particles. After 98% thickness reduction (Fig. 1b), the primary non-deformable phases tend to fragment and assume an aligned arrangement along the rolling direction (RD). In rolling, an average distance between the particles along the normal direction (ND) is reduced with an increase of thickness reduction.3.2 Texture EvolutionThe evolution of deformation texture depends on both the processing parameters as well as material’s chemistry. The chemical composition of the material controls the formation of the large non-deformable particles while the processing parameter conditions affect the volume fraction of particles, particle size and deformation flow across the thickness and around the hard inclusions. Despite the fact that the investigated materials contain a large amount of non-deformable constituents, the evolved deformation textures resemble the conventional rolling ones. Since the cold rolling process was performed under well lubricated condition, the initially isotropic material with almost random texture (Fig. 2a) has transformed to a strongly textured one (Figs 2b-d) with the components characteristic for plane strain compression deformation, i.e E-fibre texture. The variety of rolling reductions produces deformation textures identicalqualitatively while the intensity of the evolved textures enhances with the rolling reduction.The recrystallization ODFs after various rolling reductions are revealed in Figs. 4 b-d. Despite the fact that the deformation textures are identical qualitatively, the evolved recrystallization textures reveal essential qualitative differences. In conventional thermo-mechanical processing chain, the rolling E-fibre transforms to the T and D fibres with maxima on the Cube 300({001}<100>), Goss ({011}<100>) and P ({011}<233>) orientation [1, 3] while in the current case a non-conventional types of recrystallization textures are observed, i.e. a ~20° rotated cube orientation (CH) mixed with weak P, Goss and bended J-fibre components. (see Fig.3). It appears that an increase of rolling reduction gives rise to texture rotation along the T-fibre. Fig. 3 20 Pm100 PmFig. 1. Distribution of constituent particles: a) as-cast material; b) after 98% thickness reduction.(a) (b)Fig. 2. Texture evolution during the rolling process (<111> pole figures): a) as-cast texture; b) material A, 88% reduction; c) material B, 96% reduction; d) material C, 98% reduction. E-fibre(a) (b) (c) (d)Fig. 3. Recrystallization textures evolved after various rolling reductions (M2=45° ODF section): a) main orientation and fibres in M2=45° ODF section; b) material A; c) material B; d) material C.(a) (b) (c) (d)301shows that Cube orientation tends to split up and intensifies at {100}<130>component after sever thickness reductions (c.f. Figs.3 c and d).3.3 Strain heterogeneities in particle containing alloysIn conventional rolling practice, the deformation flow across a thickness of material depends on roll diameters, thickness reduction and friction conditions. While rolling a material, the sub-surface region is subjected to a combination of simple shear and plane strain compression whereas the bulk of the material is majorly deformed by the PSC. Neglecting the shear strain which is mainly concentrated within a thin layer, the rolling process under well lubricated condition could be approximated by a plane strain compression mode of deformation on a macroscopic scale. In the particle containing materials, there is an issue of how the macroscopic strain is translated to the microscopic level in the vicinity of a non-deformable particle. The presence of large constituent particles produces strain heterogeneities that give rise to strain localization as it is shown in Fig. 4. Depending on the particle shape, the deformation flow in their vicinity could be approximated by a complex strain velocity gradient field Lij:11 12 1322 233300 0L L LL L LLª º« » « »« »¬ ¼(1)Finite element calculations (Fig. 4a) of the strain field around a single non-deformable particle provide evidence for the presence of extension along RD in the vicinity of point 1(L13|L12|L23|0; L11 /11+L22+L33=0) and also RD-ND shear (L13 /11|L22|L33|0) in the vicinity of point 2. The strain velocity gradient tensor gradually changes with distance along RD, ND and TD. In a multi-particle-matrix system (Fig. 4b), the strain fields around single particles overlap leading to more extensive highly strained domains. These highly strained fields (HSF) are characterized by a complex strain velocity gradient fields with dominating extension strain mode (L11+L22+L33=0) whereas the ratios among Lij components are different in various points. For instance, the characteristic strain velocity fields in the vicinity of points 1 and 2 (see Fig.4b) reveal the following extension modes: (L11/L22/L33|0.7/0.3/-1) and (L11/L22/L33|1/-0.3/-0.7), respectively. It is evident that the mentioned strain modes strongly deviate from the PSC strain mode associated with rolling and lead to the unconventional texture evolution during annealing.1212HSFFig. 4. Von Mises strain distribution in the vicinity of hard non-deformable inclusions: a) single particle case, 50% thickness reduction; b) multi particle case, 25% thickness reduction. The materials were subjected to plane strain compression deformation.(a) (b)3023.4 Modeling the recrystallization texturesThe evolution of recrystallization texture is modeled with the model [3] the basic idea of which is presented in Fig.5. In the model, an orientation selection is made based on thecrystallographic dependence of the stored energy of plasticstrain. The model assumes orientation selection during both the nucleation and growth stages of recrystallization. A brief overview on the model is given below while a comprehensive description of the model is presented elsewhere [3].In the current RX texture simulation, a growth selection is introduced by attributing enhanced mobility to the nuclei which exhibit a particular orientation relationship with respect to the deformed matrix. In FCC metals a <111>40°boundaries reveal a growth advantage and thus these nuclei represent a growth potential texture FGP(g). In addition to the growth selection, an orientation selection is implemented in the model by applying a nucleation operator Pn(g) on the growth potential texture FGP(g). In this way, from all the orientations with a potential for selective growth FGP(g), only the ones will appear in the RX texture that have nucleated according to a low stored energy nucleation mechanism. The combined effect of nucleation and growth operators on the deformation texture produces the calculated recrystallization texture fR( ) ( ) ( )R n GPf g cP g F g (g):(2)where c is the constant that normalizes the recrystallization texture to unity.The stored energy of plastic deformation in the model is approximated by a constant fraction of the dissipated plastic energy per time unit, i.e. Taylor factor (TF). Assuming a monotonic strain mode, a crystallographically resolved measure of stored energy could be approximated in this way. In the current model, the TFs were calculated with the full constraints Taylor theory whereby only the {111}<110> octahedral slip systems were taken into account. Results of FEM calculations presented in Fig.4 indicate that the energy stored in the material also depends on the strain mode and strain distribution/localization. In a case of particle containing alloy, the strain localization occurs due to the presence of large non-deformable particles whereby the highly strained domains are considered as fertile fields for nucleation of recrystallization. Since the deformed matrix is shaped by various strain modes discussed in paragraph 3.3, the TFs were computed separately for each strain mode, i.e. PSC, simple shear and two types of extension. For each particular strain mode the low stored energy nuclei were selected according to the expression:> @min 1min( )1 for all orientations g fulfilling the condition 0,( )0 for all other orientationsnM g McMP gH­ ½° ° ® ¾° °¯ ¿(3)where the constant c1=0.258 [3] is considered as a model parameter and Mmin is the absolute minimum TF value for a particular strain mode, which is referred to by the superscript H.When growth selection is combined with oriented nucleation, the recrystallization texture is calculated for each considered strain mode and afterwards the weighted average gives a simulated RX texture ( )Rf g :( ) ( ) ( )R n GPf g w P g F gHH ¦ (4)where the weighting factors wH ( 1wH  ¦ ) correspond to the volume fraction of crystals that was deformed according to strain mode H.Fig.5. Schematic representation of the recrystallization model.303In addition to the macroscopic and local strain modes deduced from the FEM calculations, afraction of randomly oriented nuclei were considered in order to improve the results ofsimulation. The textures calculated by equation 4 (Fig.6) reasonably resemble the main features of the corresponding experimental counterparts of Fig.3. The weight fractions wH tuned for the investigated samples (Fig. 6d) indicate that with increase of rolling reduction the nuclei generated by deformation modes different from the macroscopic one (PSC) are majorly responsible for texture evolution during recrystallization. This implies that with increase of rolling reduction the texture resulted from particle stimulated nucleation (PSN) prevails over the bulk texture associated with the macroscopic strain mode. The weight fraction wH of nuclei generated by the PSC and the ones associated with the local strain heterogeneities were calculated from the volume fraction of non-deformable particles as it is explained in detail in ref. [3] whereas the final tuning of the wH values was performed based on the results of FEM calculations and concurrent iteration.ConclusionsAn increase of rolling reduction promotes a PSN texture evolution in particle containing Al alloys. Results of texture simulations show that the local strain heterogeneities in the vicinity of non-deformable constituent particles are responsible for the evolution of unconventional textures such as {100}<130> and {110}<233> components.AcknowledgementsThis research was supported by the FWO-Odysseus Program within the project: Engineering of 3D microstructures in metals: bridging ten length scales of functionality.References[1] F.J. Humphreys, M. Hatherly, “Recrystallization and related annealing phenomena”(Pergamon, Oxford, 2004), 574.[2] P. Van Houtte, “MTM-FHM Software Version”, (MTM-KU, Leuven, 1995), 65.[3] J.J. Sidor, R. H. Petrov, L. A.I. Kestens, “Modeling the crystallographic texture changes in aluminum alloys during recrystallization”, Acta Materialia 59 (2011) 5735–5748.Fig. 6. Calculated recrystallization textures by Eq.4 with the following weight fractions wH: a) material A, wPSC=0.12, wShear=0.265, wExt1=0.235, wExt2=0.31, wRand=0.07; b) material B, wPSC=0.115, wShear=0.25, wExt1=0.21, wExt2=0.35, wRand=0.075; c) material C, wPSC=0.1, wShear=0.23, wExt1=0.18, wExt2=0.4, wRand=0.09; d) dependence of weighting factors wH on the amount of deformation.(a) (b) (c) (d)304

Modeling the recrystallization textures in particle containing al alloys after various rolling reductions

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