Influence of f.c.c. rolling textures on biaxial sheet stretching

The behaviour of sheet metals initially having f.c.c. rolling textures is simulated under biaxial stretching conditions. A rate-sensitive crystal plasticity model together with the full-constraint Taylor theory is used. Closed-form analytical solutions for the stress states, slip distributions and lattice spins are obtained for the ideal orientations of f.c.c. rolling textures. The three-dimensional lattice rotation fields at these ideal orientations, and their evolution paths in Euler space, are predicted for various biaxial stretching ratios. Similar simulations are also carried out for polycrystalline textures. It is shown that, for a copper-type initial texture (the β-fibre) and a strain ratio ϱ < 0.5, the corresponding biaxial-stretching texture will not be much different from the initial texture. However, for ϱ > 0.5 the β-fibre deteriorates and the α-fibre increases relatively quickly. If the initial texture is the R-recrystallization texture (cube + S₁), the main component of the simulated biaxial-stretching textures is the fibre near β for ϱ < 0.5, but the α-fibre for ϱ > 0.5. The simulated equibiaxial-stretching texture is an agreement with the published measured textures for aluminum sheets.     

Overview no. 76: Mechanism of deformation and development of rolling textures in polycrystalline f.c.c. metals—II. Simulation and interpretation of experiments on the basis of Taylor-type theories

Simulations of f.c.c. rolling textures based on homogeneous slip under conditions of full and relaxed constraints (Taylor-type theories) are presented. The characteristic peak and fibre components found in the resultant ODFs for the various relaxed shear possibilities are analysed in great detail and compared with the experimentally observed textures in Al and the CuZn alloys given in Part I. Special attention has been paid to the questions of stability and metastability of different orientations, the position of the fibres in orientation space, the influence of initial textures, the pathways that individual orientations take together with their rates of rotation along and their arrival rates at the fibres. Finally the topological distribution of grains in connection with the compatibility problem of the different stable orientations caused by relaxed shears is discussed.     

Prediction of transformation textures in steels

Both discrete and continuous mathematical formalisms are employed to simulate texture evolution during the γ-to-α transformation in steels. Five f.c.c. NiCo alloys with different stacking fault energies (SFE's) were previously cold rolled to four reductions (40, 70, 90 and 95%) and their textures characterized by the orientation distribution function (ODF) method. The corresponding b.c.c. transformation textures are calculated from these experimental textures according to three different orientation relationships. The ODF's derived from the Bain relation are much sharper than the ones deduced from the Kurdjumov-Sachs (KS) or the Nishiyama-Wassermann (NW) relations, although the general trends of the three families of textures are similar. Ferrite textures determined on controlled rolled steels, heavily deformed in the unrecrystallized γ region, agree reasonably well with the b.c.c. textures calculated, according to the KS relationship, from the NiCo alloy with similar SFE. The two major ferrite components, namely the {332} 〈113〉 and {113} 〈110〉, are shown to originate from the three main orientations of cold rolled f.c.c. material, i.e. the {112} 〈111〉 (Cu), {110} 〈112〉 (Bs) and {123} 〈634〉 (S). Such ferrite formation from heavily deformed austenite follows the KS relationship without any variant selection. By contrast, the texture of martensite produced from deformed austenite involves significant amounts of selection.     

Effect of hot rolling on the dendritic texture of directionally solidified steel ingots

Directionally solidified ingots of three commercial steels—AISI 1010, Fe-3.4 pct Si, and Type 430 stainless steel—were hot-rolled at 1850°F in order to study the effect of hot deformation on the as-cast dendritic texture. The strong dendritic (100) orientation of both the Fe?Si and Type 430 alloys was completely destroyed by the heavy reductions typical of the commercial hot rolling of ingots. The primary effect of hot rolling is to eliminate the texture present in the ingot, and to create certain new textures. These new textures are in every case weak. For example, the AISI 1010 steel, which had very little of the dendritic <100> orientation in the ingot stage, has a combination of two weak textures after hot rolling: (100) [011] and (110) [110]. Likewise, with the other two materials, which had a strong dendritic <100> orientation in the ingot stage, hot rolling resulted in weak textures: (110) [001] with a rotation of this orientation of ±45 deg about the [001] rolling direction, followed by (110) [001] rotated ±35 deg about the [110] in the transverse direction.     

Deformation banding and copper-type rolling textures

It is shown by a crystallographic etching technique applicable to copper that deformation banding is an important deformation mode in f.c.c. metals and alloys. In a cold rolled coarse grain copper, deformation banding forms in a three dimensional manner dividing the grain on average into over 600 regions of different orientations. The influence of this important, but long ignored deformation mode, is studied by incorporating it into the Taylor model. The predicted textures from the new model are better than those from other existing models in mainly two respects. Firstly, the DB model predicts the co-existence of the three major f.c.c. rolling texture components, namely {123}〈634〉 or S component, >112>〈111〉 or C and >110>〈112〉 or {f}B{/f}. The existing models are deficient in that they predict either C and S or B, but not their co-existence. The second point is that textures predicted by the existing models are always too sharp compared to the experimental textures. The DB model predicts texture peaks with larger spread and hence more realistic texture sharpness. Another feature of the model is that only two independent slip systems, instead of five, are required to accomodate the imposed shape change, which agrees with experimental observation.     

Deformation textures of AA8011 aluminum alloy sheets severely deformed by accumulative roll bonding

A fully annealed AA8011 aluminum alloy sheet containing a number of large particles (∼5 μm) was severely deformed up to an equivalent strain of 12 by an accumulative roll-bonding (ARB) process. The texture evolution during the ARB process was clarified, along with the microstructure. The ARB-processed aluminum alloy sheets had a different texture distribution through the sheet thickness, due to the high friction between the roll and the material during the ARB process. The shear textures composed of {001} 〈110〉 and {111} 〈110〉 orientations developed at the sheet surface, while the rolling textures, including Cu {112} 〈111〉 and Dillamore {4,4,11} 〈11,11,8〉 orientations, developed at the sheet center. The textural change from a shear texture to a rolling texture at the sheet center during the ARB process contributed to an increase in the fraction of high-angle boundaries. Also, a large number of second-phase particles in the AA8011 alloy sheets weakened the texture. Up to the medium strain range (below ɛ=6.4), relatively weak textures developed, due to the inhomogeneous deformation around the second-phase particles; after the strain of 6.4, strong rolling-texture components, such as the Dillamore and Cu orientations, developed. This remarkable textural change can be explained by the reprecipitation of fine particles in grain interiors.     

Textures and plastic anisotropy in γ-TiAl

A polycrystalline alloy of composition Ti-36 wt % Al consisting mainly (about 95 vol. %) of γ-TiAl has been deformed in compression at 450°C as well as in rolling at 1040°C. The textures of the deformed specimens were measured and analyzed in terms of orientation distribution functions (ODFs). The textures after hot rolling show a cube-like component (100) [010] with an alignment of the c-axis with the transverse direction. A comparison of measured compression textures with those simulated on the basis of the Taylor theory of polycrystal deformation leads to the following conclusions. Both the “easy” {111} 〈110〉 and “hard” {111} 〈101〉-slip modes of deformation occur in γ-TiAl at 450°C. The critical resolved shear stresses (CRSSs) for these two slip modes differ by a factor of less than 2, the CRSS for {111}〈110〉-slip being higher than that for {111}〈101〉-slip. The rolled specimens show a pronounced plastic anisotropy, which can only be explained on the basis of microstructural considerations.     

Rolling and recrystallization textures in directionally solidified aluminium

From directionally solidified aluminium with a 〈100〉 fibre texture specimens of different orientations were cut and the textures after rolling (95% reduction) and recrystallization were determined. The results are discussed on the basis of the current concepts on deformation and recrystallization in single and polycrystalline materials. Due to the strong influence of the different starting textures, characteristic differences in the rolling textures are obtained. For the first time, a case is reported for which an experimental rolling texture is completely explicable in terms of the Taylor theory under full constraints condition. Further, the recrystallization textures, although appearing more uniform, exhibit clear differences which yield new evidence with respect to the mechanisms of formation of the cube texture. It shows that in the present case for obtaining a pronounced cube texture, both the conditions of oriented growth (in the sense of 40° 〈111〉 rotations) and oriented nucleation (in the sense of properly oriented transition bands) must occur.     

Effect of rolling temperature on the deformation and recrystallization textures of warm-rolled steels

Warm-rolling trials were carried out on three interstitial-free (IF) steels (stabilized with either niobium or titanium), an extralow-carbon (ELC) steel, and an experimental low-carbon chromium (LC Cr) material at temperatures between 440 °C and 850 °C. The influence of rolling temperature on their as-rolled microstructures and deformation and recrystallization textures was investigated. Also, the effect of coiling simulation and degree of rolling reduction on the r values of some of these materials was examined. In-grain shear bands were evident in all as-rolled microstructures, but their sensitivity to deformation temperature varied between steels. Shear bands of moderate intensity were formed in the IF steels across all temperatures. In the ELC material, intense shear bands were formed at low rolling temperatures, but at higher temperatures, this intensity was drastically reduced. The development of shear bands at the higher rolling temperatures was significantly enhanced by alloying with chromium. The deformation textures produced were typical of rolled ferrite materials. The intensity of this texture increased markedly with temperature for the ELC grade. Conversely, the intensity of the recrystallization texture decreased with increasing temperature. The addition of chromium was found to strengthen the {111} component and, hence, the formability. The sharpness of both the deformation and recrystallization textures of the IF steels was relatively unaffected by rolling temperature. These differences are attributed to the intensity and frequency of shear-band formation and the dynamic strain-aging (DSA) behaviors of the various materials.     

The effect of textures and grain shape on the shear band formation in rolled F.C.C. metals

In rolled f.c.c. metals, the commonly observed textures are {110}〈001〉, {110}〈112〉, and {112}〈111〉. A theoretical Taylor factor calculation was made to give the influence of these three textures on plastic deformation. The combined effect of textures and grain shape on the shear band formation and fracture in rolled f.c.c. metals were discussed and compared with experimental results. It is concluded that among the three textures studied, the Goss {110}〈001〉 textured grains in rolled f.c.c. metals are easier deformed than the others, which gives an explanation of the form of shear bands usually observed in rolled f.c.c. metals.     

Comparison between simulated and experimental transformation textures in a Nb microalloyed steel

Samples of a Nb microalloyed steel were control rolled and finished (i) at 1020°C (in the γ recrystallization range) and (ii) at 870°C (in the γ no-recrystallization range). The textures of these materials were compared with b.c.c. transformation textures derived analytically from (i) annealed and (ii) cold rolled samples of an f.c.c. Ni30Co alloy. For this purpose, the Kurdjumov-Sachs relationship was assumed, together with the absence of variant selection. The ferrite texture of the experimental steel finish rolled in the γ recrystallization range is sharper than the corresponding simulated texture, the major components of both being {100}〈011〉 and {110}〈110〉. The texture of the experimental steel finish rolled in the γ no-recrystallization range is again sharper than the corresponding simulated texture, both containing {113}〈110〉, {332}〈113〉 and {100}〈011〉 as the major components. The detailed textural features of the steel finished at 1020°C can be explained by allowing for some variant selection, together with selective growth of the {100}〈011〉 oriented α grains during transformation. A combination of selective α grain growth and variant selection is again required to explain the detailed texture of the steel sample finished at 870°C.     

Texture simulation for hot rolling of aluminium by use of a Taylor model considering grain interactions

The hot rolling textures of aluminium are simulated by means of a Taylor type model which takes into consideration dislocation slip on 111〈110〉 and 110〈110〉 glide systems and the interaction of grains. For the investigation of the stability of the cube component during hot rolling various ratios of the corresponding critical resolved shear stresses τ¹¹⁰/τ¹¹¹ are applied. Whereas the orientation densities and the positions of the β-fibre components 112〈111〉 and 123〈634〉 are not substantially influenced by slip on 110〈110〉 glide systems the cube component is developed at the expense of the 110〈112〉 orientation when the yield surface for 110 slip is within that for 111 slip.     

Electron microscopical investigations on the precipitation of various h.c.p. phases in an Al-6.8 at.% Zn alloy

In an Al-6.8 at.% Zn alloy aged at T = 120°C the precipitation of h.c.p. phases was studied by high-resolution electron microscopy and high voltage electron microscopy. The shapes of the respective precipitates, the hexagonal lattice parameters as well as the orientation relationship between the h.c.p. precipitates and the f.c.c. matrix were determined. Information was mainly gained from the spacings and orientations of lattice fringes and, occasionally, from the Moiré patterns. Three h.c.p. phases were found, two of which are characterized by the same lattice parameters but have different orientation relationships to the f.c.c. matrix crystal.     

Structural bonding contributions and the elastic response of b.c.c. and f.c.c. crystals

The anisotropic elastic response of body centered cubic (b.c.c.) and face centered cubic (f.c.c.) crystals is reviewed within the framework of general elasticity and particular model dependent relations. It is found that important trends in the observed behavior of specific groups of crystals can be reproduced by models that include only structural contributions to crystal binding. In fact, a very simple model, consisting of only nearest and next nearest neighbor interactions, reproduces the salient behavior, including the algebraic signs of Poisson's ratio and the orderings of the shear moduli, Young's moduli, and Poisson's ratios associated with major crystallographic symmetries. The analysis provides insight into the differences between the b.c.c. transition metals and the b.c.c. alkali metals.     

A dislocation-based model for variant selection during the γ-to-α′ transformation

A phase transformation model is described for variant selection during the austenite-to-martensite transformation. The model depends entirely on the presence of glide dislocations in the deformed austenite. The direct correlation between the 24 slip systems of the Bishop and Hill (B-H) crystal plasticity model and the 24 〈112〉 rotation axes of the Kurdjumov-Sachs (K-S) orientation relationship is employed. Two selection criteria, based on slip activity and permissible dislocation reactions, govern the variants that are chosen to represent the final transformation texture. The development of the model via analysis of the experimental results of Liu and Bunge is described. The model is applied to the four distinct strain paths: (1) plane strain rolling, (2) axisymmetric extension, (3) axisymmetric compression, and (4) simple shear. Experimental deformation and transformation textures were produced for comparison purposes via appropriate deformation and quenching procedures. In each case, the transformation texture predicted using the dislocation reaction model is in excellent agreement with the experimental findings.     

The orientation dependence of grain boundary motion and the formation of recrystallization textures

Abstract

The theoretical models of grain boundary motion are reviewed and compared with the experimental data on the orientation dependence of this motion. The extent that the experimental data on recrystallization textures (mainly of f.c.c. metals) can be interpreted by the orientation dependence of grain boundary motion is discussed.

Résumé

L'auteur passe en revue les modèles théoriques de migration des joints de grains et les compare aux résultats expérimentaux relatifs à l'influence de l'orientation sur cette migration. Il discute jusqu'à quel point les résultats expérimentaux relatifs aux textures de recristallisation (surtout pour les métaux c.f.c.) peuvent être interprétés en fonction de la désorientation des joints de grains.     

Effect of austenite pancaking on texture formation in a plain carbon and A Nb microalloyed steel

The way in which texture development is affected by austenite pancaking was studied in a plain carbon and a niobium steel. Three processing parameters (austenitizing temperature, finish rolling temperature and amount of reduction) were varied, and their influence on the state of the austenite was analyzed. It was found that the presence of niobium, which leads to pancaking of the austenite when low finishing temperatures are employed, strengthened the transformation products produced from the copper, brass, S and Goss orientations in the austenite. Larger reductions resulted in sharper textures, especially in the microalloyed steel. The effect of austenitizing temperature was not particularly strong. Several f.c.c. ideal orientations were transformed according to the Kurdjumov-Sachs relationship, and the b.c.c. products resulting from this analysis are compared with the experimental results. When recrystallized austenite transforms, it is shown that the cube component transforms preferentially into the {001}<110> rotated cube orientation, with lower than expected intensities displayed by the Goss and rotated Goss components. Similar trends are observed with respect to the four main deformation components; these tendencies are interpreted in terms of variant selection and selective growth.     

Near-threshold fatigue crack growth behavior of 2195 aluminum-lithium-alloy—prediction of crack propagation direction and influence of stress ratio

Tensile properties and fatigue crack propagation behavior of a 2195-T8 Al-Li alloy were investigated at different stress ratios, with particular emphasis on their dependence on specimen orientation. Specimens with orientations of 0, 15, 30, 45, and 90 deg to the rolling direction were tested. The alloy contained a strong brass-type texture and a profuse distribution of platelike precipitates of T ₁ (Al₂CuLi) phase on {111} matrix planes. Both tensile strength and fatigue thresholds were found to be strongly dependent on the specimen orientation, with the lowest values observed along the direction at 45 deg to the rolling direction. The effect of stress ratio on fatigue threshold could generally be explained by a modified crack closure concept. The growth of fatigue crack in this alloy was found to exhibit a significant crystallographic cracking and especially macroscopic crack deflection. The specimens oriented in the L-T + 45 deg had the smallest deflection angle, while the specimens in the L-T and T-L orientations exhibited a large deflection angle. The dependence of the fatigue threshold on the specimen orientation could be rationalized by considering an equivalent fatigue threshold calculated from both mode I and mode II values due to the crack deflection. A four-step approach on the basis of Schmid’s law combined with specific crystallographic textures is proposed to predict the fatigue crack deflection angle. Good agreement between the theoretical prediction and experimental results was observed.     

Crystallographic textures in rolled and annealed Fe-Ga and Fe-Al alloys

The feasibility of obtaining [001] preferred texture in polycrystalline Fe₈₅Ga₁₅ and Fe₈₅Al₁₅ magnetostrictive alloys containing 1 mol pct NbC using a low-cost conventional thermomechanical processing approach is shown in this work. Thermomechanical processing conditions examined consisted of a sequence of hot rolling, two-stage warm rolling at 400 °C with intermediate anneal at 900 °C and texture anneal in the temperature range of 900 °C to 1300 °C for time periods up to 24 hours. Textures present prior to and after texture annealing were characterized using orientation imaging microscopy in a scanning electron microscope. In the case of Fe₈₅Ga₁₅ alloy with 1 mol pct NbC, the deformation-induced texture after a two-stage warm rolling consists of mixed {100} 〈110〉 and {111} 〈110〉 type partial textures. Texture annealing of the Fe₈₅Ga₁₅ alloy with 1 mol pct NbC at 1150 °C for 2 hours changes the texture to a predominant texture that is close to {001}〈100〉. On increasing the annealing time to 24 hours, the texture shifts toward {110}〈100〉. While texture anneal at both 1150 °C and 1300 °C produces a [001] or near-[001] preferred orientation along the rolling direction in the Fe₈₅Ga₁₅ alloy with 1 mol pct NbC, 1150 °C-24 hour treatment was found to provide the strongest [001] orientation among the conditions examined. Similar trends are observed for the case of Fe₈₅Al₁₅ alloy with 1 mol pct NbC.