Texture and anisotropy in the mechanical properties of titanium alloys caused by the mechanism of plastic deformation

Texture formation during sheet stamping and die forging of α titanium alloys is studied, and the effect of texture and the mechanism of plastic deformation on the strength of internal-pressure spherical vessels is considered. It is shown that, apart from texture, the anisotropy of the strength properties of the α alloys, which is estimated from the difference in the uniaxial-and biaxial-loading strengths, also depends on the chemical composition of the alloy. In the textureless state, the strength of the spherical vessels is higher than the uniaxial strengths of the VT5-1kt, PT3V, and PT3Vkt alloys by 4, 16, and 38%, respectively. This effect is found to be caused by the difference in the relative values of the critical shear stresses for operating slip and twinning systems. The high ductility of the PT3Vkt alloy is related to the fact that it has a ratio of critical shear stresses in the operating slip and twinning systems such that the material is virtually isotropic with respect to tensile loads. This specific feature minimizes the effect of the incompatibility of deformation in grains with different orientations during tension, which is the main cause of the fracture of titanium alloys. The results obtained are used to propose a quantitative criterion to estimate the technological ductility in order to design new titanium alloys.     

The relation of incompatibility and dislocation motion to plastic deformation

The elementary theory of dislocation motion is based on three concepts, namely: that plastic strain rate is proportional to dislocation velocity; that dislocations multiply in proportion to strain; and that dislocation velocity is a function of stress. The first two of these concepts are shown to be included in the more general theory of continuously distributed dislocations, as direct consequences of the incompatibility equation.     

The plastic anisotropy of an Al-Li-Cu-Zr alloy extrusion in unidirectional deformation

The plastic anisotropy resulting from the initial deformation microstructure and various aging treatments applied to several regions of an AA2090 near-net-shape extrusion has been investigated. Yield behavior was measured by uniaxial compression in multiple orientations of each region. Two models of the plastic anisotropy were generated: the Taylor/Bishop-Hill model, based on crystallographic texture, and the plastic inclusion model, developed by Hosford and Zeisloft,^[5] which incorporates anisotropic-precipitate effects. In overaged conditions, the Taylor/Bishop-Hill model adequately describes the observed plastic anisotropy. As the strengthening increment due to second-phase particles increases, there is a concurrent increase in the magnitude of the precipitate contribution to anisotropy. This anisotropy can not be accurately predicted solely by crystallographic texture. By incorporation of terms describing the precipitate anisotropy, the plastic inclusion model correctly predicts the yield strength variation in all regions tested. Examination of the fundamental interaction between matrix and precipitation strengthening reveals that there is a stronger basis for taking the critical resolved shear stress (CRSS) of the precipitates as a constant, rather than their effective yield strength. This consideration provides a more consistent and accurate form of the plastic inclusion model.     

Hall-petch relation and the localization of plastic deformation in aluminum

The plastic deformation macrolocalization parameters are compared to the Hall-Petch relation parameters for the flow stress in polycrystalline aluminum specimens with a grain size of 8 × 10⁻³−5 mm. Two branches in the dependence of the localized plastic deformation autowave length on the grain size and two versions of Hall-Petch hardening are found in this grain size range. The boundary between the versions of the dependences corresponds to d _b = 0.1 mm for both cases. The correspondence between localized plastic flow patterns and the Hall-Petch relation is studied.     

Precipitate-induced plastic anisotropy: Explicit solutions of the plastic anisotropy due to plate-shaped precipitates

In some aluminum alloys, the observed plastic anisotropy cannot be explained solely by the measured Taylor factor variation. Qualitatively, it has been suggested that this difference results from a secondary effect due to plate-shaped precipitates. Models addressing the effect of plastically-deforming and elastically-deforming precipitates have been previously proposed. In the present article, explicit solutions of the anisotropic strengthening increment are presented for the case of plate-shaped precipitates. These solutions allow a quantitative consideration of the effect of precipitates on different habit planes and of the effect due to stress aging. Generally, in fcc materials, precipitates on {100} habit planes are predicted to minimize the anisotropy due to texture; precipitates on {111} habit planes are predicted to accentuate the anisotropy due to texture; and precipitates on other habit planes are predicted to produce a minor effect resulting from an averaging over a greater number of crystallographcally equivalent habit planes. Stress aging to alter the relative orientation distribution of a single precipitate type is predicted to produce only slight changes in the plastic anisotropy. Larger effects on the yield variation will be observed when stress aging alters the relative volume fractions of two precipitate types on different habit planes.     

The relation between preferred orientation and the Lankford parameter r of plastic anisotropy

Calculation of the r-value of plastic anisotropy from experimentally determined texture data on the basis of the Taylor theory with different assumptions about the glide systems. Experimental determination of the r-value at different angles to the rolling direction in a steel RSt 14. Comparison of the experimental results with the theory on the basis of texture and cell formation.     

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

We present in this work a visco-plastic self-consistent (VPSC) anisotropic approach for modeling the plastic deformation of polycrystals, together with a thorough discussion of the assumptions involved and the range of application of such approach. We use the VPSC model for predicting texture development during rolling and axisymmetric deformation of Zirconium alloys, and to calculate the yield locus and the Lankford coefficient of rolled Zircaloy sheet. We compare our results with experimental data and find that they are in good agreement with the available experimental evidence. We also compare the VPSC predictions with the ones of a Full Constraints approach and observe that they differ both quantitatively and qualitatively: according with the predictions of the VPSC scheme, deformation is accommodated mostly by the soft systems, the twinning activity is much lower, and fewer systems are active, in average, per grain. These results are a consequence of having accounted for the grain interaction with its surroundings, which is a crucial aspect when modeling plastically anisotropic materials.     

The deformation of polycrystalline zirconium

The deformation of polycrystalline zirconium has been examined in terms of the power-law and the thermally activated rate equation approach to deformation. It is shown that the thermal component of the flow stress is independent of strain and that the athermal component is the main contributor to work hardening. The deformation behavior is in general agreement with Fleischer’s force-distance diagram for tetragonal defect-dislocation interaction. Electron microscopy however, showed that the majority of slip activity occurred on the prism planes and interstitials in octahedral positions do not interact strongly with dislocations on the prism planes. It is therefore suggested that deformation is controlled by solute atoms interacting with the dislocation core and that this interaction has a force-distance relationship equivalent to that suggested by Fleischer.     

Measurement and prediction of plastic anisotropy in deep-drawing steels

R-values and yield stresses were measured as a function of inclination with respect to the rolling direction on 15 steels selected from four basic types [high-strength low-alloy (HSLA), Al-killed drawing quality (AKDQ), interstitial-free (IF), and rimmed]. Orientation distribution functions (ODF’s) were also determined for these steels, using both X-ray and neutron diffraction techniques. The series expansion method was employed for predicting the plastic anisotropy of the rolled sheets. Comparison with the experimental measurements indicates that the “pancake” relaxed constraint model is a more accurate predictor of behavior than the Taylor, Sachs-Kochendörfer, or two other relaxed constraint models. The best quantitative agreement is obtained when the critical resolved shear stress (CRSS) ratio for glide on the {112} (111) and {110} (111) slip systems (t₁₁₂/t₁₁₀) is 0.95. A “lath” relaxed constraint model (with ?₂₃ relaxed), associated with the same CRSS ratio, leads to good results for steels with elongated microstructures.     

Elastic and plastic anisotropy in sheets of cubic metals

Methods are described for the calculation of the elastic and plastic properties of textured polycrystalline metals. The calculations involve the crystallite orientation distribution function derived from X-ray texture data together with data which describe the single crystal behavior. Subsequently, it is shown how a knowledge of the elastic properties can be used to make an analytical prediction of the plastic properties. In making this prediction use is made of the fact that for cubic metals both the elastic and plastic properties are influenced predominantly through the zeroth and fourth order coefficients of the crystallite distribution function. The methods are illustrated by application to the analysis of the data of Stickels and Mould. The statistical correlation they observed is shown to have a justifiable analytical basis.     

Malleability and plastic anisotropy of iridium and copper

Room-temperature plane-strain compression tests were performed on iridium and copper single crystals with (110) [110] and (110) [001] orientations that represent contrasting flow strengths. Both copper and iridium show plastic anisotropy in agreement with flow theories. At a given shear strain, the shear strengths of copper and iridium are proportional to the elastic shear modulusG calculated for the fcc slip system. The ability of fcc metals to be cleaved appears to be associated with small values of the quotientK/G, whereK is the elastic bulk modulus. It is concluded that the brittleness of iridium is probably inherent. Formerly with Department of Physical Metallurgy Science of Materials of the University of Birmingham, Birmingham, England     

Diffusion-induced stresses and plastic deformation

Thin-sheet (<0.2 mm thick in the direction of diffusion) Au/Ag couples undergo plastic deformation bending during interdiffusion at 750 and 850°; the Ag-rich side forms the concave surface of a deformed couple. This bending is caused primarily by diffusion-induced stress and can be prevented by either mechanical constraint during diffusion or mass constraint of the couple (thicker in the diffusion direction). Because the atomic radii of gold and silver are essentially equal, the stresses cannot arise from lattice parameter gradients. Rather, they are produced by processes (such as dislocation climb) associated with the annihilation and generation of vacancies which accommodate mass displacements within the diffusion zone. These nonconservative processes produce volume changes and corresponding stresses in the diffusion zone which are opposed in the transverse direction (normal to diffusion flow) by the elastic mass constraint of the outlying (especially nondiffused) regions of the couple, thereby creating transverse bending stresses across the couple. A simplified stress analysis indicates that when mass constraint is sufficiently small, the couple undergoes bending primarily by low-stress creep, the transverse stress in the outer fiber of a bent couple being approximately 1 MPa (150 psi). A much smaller, secondary contributor to bending is mass which is displaced in a directional normal to the diffusion flux, but this bend-producing mass displacement accounts for <1 pct of the total mass displaced by the operation of vacancy sinks and sources in the diffusion zone. Therefore, even in the thinnest, bending couples, nearly all (>99 pct) of the mass displacement is parallel to diffusion and this causes substantial marker shifting in all the (bending and nonbending) couples. This strong preference for mass displacement to occur parallel (rather than normal) to diffusion is consistent with both minimal mass constraint and the operation of vacancy sinks and sources in regions of maximum (vacancy) chemical stress. Formerly Graduate Student, Departmentof Metallurgical Engineering, Ohio State University, Columbus, OH43210     

Theory of plastic and viscous deformation

A theory of inelastic deformation, previously applied to 304 stainless steel with good quantitative agreement,² is used to study a variety of materials which differ in the degree to which dislocation motion is resisted by viscous drag forces. In the theory, mobile dislocations are injected into the material by the rising stress, move over a mean free path to create strain, and are trapped. The velocity of motion, determined by the magnitude of an effective stress relative to the viscous drag, determines the mean lifetime of mobile dislocations and thereby, in part, the mobile density. An attractive feature of the theory is its simplicity. There are only three significant physical constants, two which characterize the dislocation velocity and one, taken in this case to be material independent, which determines the strain-hardening coefficient. The calculations have been done to simulate a variety of tests done in a soft tensile machine, in which the principal control is exerted over the rate of stress increase. The results show diversetransient strain rate behavior, determined by the magnitude of the drag forces, but a commonsteady state strain rate, controlled by strain hardening. Soft materials with low viscous drag, such as copper, exhibit brief transients on change of stress rate, whereas in hard materials with high drag, such as iron-3.5 pct silicon, the transients are very long. These transients include the onset of yielding at the start of a strain-stress test, low temperature creep, and the strain rate response to a brief pulse of high stress rate. Thus for example, hard materials show long loading transients (slow approach to steady state), extensive low temperature creep, and no evident ‘rapid’ strain during a high rate stress pulse. For soft materials the converse results obtain. These differences and others distinguish, respectively, viscous and plastic deformation behavior.     

Theory and practice of plastic deformation

The first scientific-technical conference “Theory and Practice of Plastic Deformation — 96” was held on October 8–10, 1996 at the Moscow State Institute of Steel and Alloys (MSISA). The conference was devoted to the memory of Petr Ivanovich Polukhin, whose name is linked with an important stage in the growth of the Institute. Polukhin was in large part responsible for establishing the Institute as a leader among the metallurgical institutions of the country and making it an authority on the world level. Moscow Institute of Steel and Alloys. Translated from Metallurg, No, 1, pp. 32–34, January, 1997.     

The variation of plastic anisotropy during straining

The relationship between length and width strain during a tensile test has been studied in detail for a wide range of low carbon steels. The data have been analyzed in terms of the conventionalr-value,r _e, the instantaneous r-value, r_i, and a linear regressionr-value,r _r. r_r is derived from a linear regression between width strain and length strain, as first suggested by Liu, using data obtained between yield and uniform elongation.r _r was found to be the most suitable method of characterizing the average anisotropic behavior, because its value is unaffected by the presence or absence of inhomogeneous yielding. There are reproducible variations of width strain from linear behavior which are not due to experimental error. These causer _e to vary with strain. No systematic increase or decrease ofr _e with strain was observed, in contrast to previous reports in the literature.     

The plastic deformation of TiAl

The deformation substructure of TiAl (Llo type ordered lattice) tested in compression, and the factors determining it were investigated. Two types of dislocations take part in the plas-tic deformation, namely a/2 [110] and a/2 [Oil]. The latter type will disorder the Llo super-lattice and therefore would be expected to move in pairs as superdislocations. Some obser-vations are essentially in agreement with the predictions, however the large proportion and morphology of a/2 [O1l] dislocations observed was unexpected. Twins of the [112] (111) type play an important role in the deformation of the alloy, and the early stages of their formation have been recorded. Finally, equi-Schmid factor lines have been constructed in an attempt to evaluate the importance of the sense of the applied stress on the deformation capability of the alloy. Formerly visiting Scientist at the Aerospace Research Laboratories     

Estimation of plastic deformation in the technologies of bulk cold deformation

A technique for determining the degree of reduction upon forming by cold bulk shaping has been proposed. The technique is based on a comparison of the measurement data on the hardness of a cold-worked metal with that of the same metal subjected to a compression test at a certain strain intensity. The technique has been tested in technological operations of reduction and thread rolling.     

Inhomogeneity of plastic flow in constrained deformation

Crystals of copper, Cu+6 wt pct Al, and Ag+4 wt pct Sn were compressed along [111] with flow restricted to [ \(\bar 1\bar 12\) ]. After deformation, four differently oriented regions were observed. Their origin is explained by the instability of the (111)[ \(\bar 1\bar 12\) ] orientation which can rotate to either (112) \(\bar 1\bar 11\) or (110)[001] during the imposed shape change. The direction of rotation is determined by which of two initially equally favored pairs of slip systems operate. Surface friction produces shear stresses which favor one pair over the other (depending on the sign of the shear stress) and thus one of the final orientations. Since the sign of the frictional stress varies systematically with position in the deforming crystal, a systematic variation of orientation results. Another orientation (001)[110] has also been observed to behave similarly. During rolling, the frictional forces drawing the crystal into the roll gap are also expected to lead to the division of the crystal into two misoriented regions. The predictions are generalized to include bcc metals of ( \(\bar 1\bar 12\) )[111] and (110)[001] orientations. Previously reported observations of rolled crystals of FeNi₃, Fe-3.5 pct Si, and Fe-2 pct Al are in accord with the present analysis.     

Modeling of the plastic anisotropy of textured sheet

An alternative is proposed to the classical crystallographic and continuum techniques for representation of polycrystal anisotropy. It involves the use of continuum yield criteria to reproduce the yielding behavior of a collection of disoriented grains displaying typical experimental spreads. It is shown that the anisotropic properties pertaining to single ideal orientations are readily assessed. Yield surfaces as well as strain rateR(θ) and yield stressσ(θ)/σ(0) ratios are calculated for polycrystalline materials displaying several texture components. The Taylor, Sachs, and Kochendörfer grain interaction models are used for this purpose, the last of which leads to the fastest computations because it permits the texture/plastic properties relationship to be described analytically. Such methods are particularly well suited to FEM and CAD-CAM calculations. The predictions obtained from the present analysis are compared to experimental observations reported in the literature.