Combination Of Slip Systems Research Articles

Development of the new fast approach for calculation of texture evolution during hot deformation of aluminum alloys

In recent years a lot of models for calculation of texture evolution during hot deformation have been proposed. The main deficit of these models its speed which is not enough for using them directly in hot rolling mills control systems. That is why new more simple and faster algorithms of texture calculation are crucial. In this work a new method for predicting changes in orientation of FCC crystals during deformation was proposed, based on representing deformation as slide along slip systems of certain crystal selected by minimization of plastic power. The method was developed for flat (plane strain) deformation, i.e. for sheet rolling.Any deformation work with conservation of volume may be represented as five vector components which can be derived from any of the 12 slip systems of FCC crystal. This means that any arbitrary deformation of crystals can be presented as linear combination of five linearly independent vectors corresponding to the slip systems of a crystal. Here are altogether 384 linear independent combinations of vectors corresponding to 12 slip systems are possible and, straight forward calculation of plastic deformation power can be done fast enough by using modern computers. Therefore, in the proposed new method all possible combination of slip systems are realized and selected to find the optimum.The advantage of this approach as compared to linear programming method consist in that even complicated laws of deformation hardening can be included. Any non-linear dependence of the slip systems critical stress on deformation and deformation rate may be introduced as well as the influence of interacting slip systems. The Full constraint method was used here, but with minor modification any relaxed constraint model is also applicable.

Influence of slip system combination models on crystal plasticity finite element simulation of NiTi shape memory alloy undergoing uniaxial compression

The influence of various slip system combination models on crystal plasticity finite element simulation of NiTi shape memory alloy subjected to uniaxial compression deformation is investigated according to three combinations of slip systems, including combination of {010}〈100〉 and {110}〈111〉 slip modes, combination of {110}〈100〉 and {110}〈111〉 slip modes and combination of {110}〈100〉, {010}〈100〉 and {110}〈111〉 slip modes, which consist of 18, 18 and 24 slip systems, respectively. By means of simulating mechanical response, strain distribution, stress distribution and Schmid factor, it can be found that in terms of simulation accuracy, combination of {110}〈100〉 and {110}〈111〉 slip modes is in good agreement with combination of {110}〈100〉, {010}〈100〉 and {110}〈111〉 slip modes. The contribution of {110}〈100〉 slip mode to plastic strain is primary in plastic deformation of NiTi shape memory alloy, whereas {010}〈100〉 slip mode, which makes small contribution to plastic deformation, can be regarded as the unfavorable slip mode. In the case of large plastic strain, the {010}〈100〉 slip mode contributes to the formation of (001) [01¯0] texture component, while {110}〈100〉 and {110}〈111〉 slip modes facilitate the formation of γ-fibre (〈111〉) texture.

A dislocation density-based single crystal constitutive equation

Single crystal constitutive equations based on dislocation density (SCCE-D) were developed from Orowan’s strengthening equation and simple geometric relationships of the operating slip systems. The flow resistance on a slip plane was computed using the Burger’s vector, line direction, and density of the dislocations on all other slip planes, with no adjustable parameters. That is, the latent/self-hardening matrix was determined by the crystallography of the slip systems alone. The multiplication of dislocations on each slip system incorporated standard 3-parameter dislocation density evolution equations applied to each slip system independently; this is the only phenomenological aspect of the SCCE-D model. In contrast, the most widely used single crystal constitutive equations for texture analysis (SCCE-T) feature 4 or more adjustable parameters that are usually back-fit from a polycrystal flow curve. In order to compare the accuracy of the two approaches to reproduce single crystal behavior, tensile tests of single crystals oriented for single slip were simulated using crystal plasticity finite element modeling. Best-fit parameters (3 for SCCE-D, 4 for SCCE-T) were determined using either multiple or single slip stress–strain curves for copper and iron from the literature. Both approaches reproduced the data used for fitting accurately. Tensile tests of copper and iron single crystals oriented to favor the remaining combinations of slip systems were then simulated using each model (i.e. multiple slip cases for equations fit to single slip, and vice versa). In spite of fewer fit parameters, the SCCE-D predicted the flow stresses with a standard deviation of 14 MPa, less than one half that for the SCCE-T conventional equations: 31 MPa. Polycrystalline texture simulations were conducted to compare predictions of the two models. The predicted polycrystal flow curves differed considerably, but the differences in texture evolution were insensitive to the type of constitutive equations. The SCCE-D method provides an improved representation of single-crystal plastic response with fewer adjustable parameters, better accuracy, and better predictivity than the constitutive equations most widely used for texture analysis (SCCE-T).

Evidence for basal 〈 a〉-slip in Zircaloy-2 at room temperature from polycrystalline modeling

Polycrystalline modeling has been used to interpret the evolution of lattice strain and texture in zirconium based alloys. Challenges in matching model and experimental results have mainly arisen from an insufficient knowledge of intrinsic deformation mechanisms (slip and twinning). Specifically, there is little concrete evidence that basal 〈 a〉-slip occurs during room-temperature deformation or whether pyramidal 〈 a〉-slip is an alternate mechanism. Also, the critical resolved shear stresses (CRSSs) for slip and twinning systems relevant to polycrystals are not well established. We have developed an understanding of the contribution of basal 〈 a〉-slip to deformation by applying an elasto-plastic self-consistent model to an extensive experimental database, obtained by neutron diffraction measurements on textured Zircaloy-2. By considering a variety of slip system combinations, the roles of each slip system in lattice strain development were investigated. Parameters for the model were obtained by best fitting to a large experimental database, including both macroscopic data (flow curves and Lankford coefficients) and microscopic internal strain data. Based on optimized agreement between model and experimental data we conclude that there is evidence that basal slip does occur, while the effects which might be attributed to pyramidal 〈 a〉-slip can be represented by the influence of other combinations of slip systems. We propose reasonable ranges of initial CRSSs for each slip system, which should benefit the modeling of similar materials (e.g. Zircaloy-4).

Petrofabric-derived seismic properties of a mylonitic quartz simple shear zone: implications for seismic reflection profiling

Abstract The link between petrofabric (LPO) and seismic properties of an amphibolite-facies quartzo-feldspathic shear zone is explored using SEM/EBSD. The shear-zone LPO develops by a combination of slip systems and dauphine twinning, with a -maximum parallel to lineation ( X ) and c -maximum normal to mylonitic foliation ( XY ). The LPO are used to predict elastic parameters, from which the three-dimensional seismic properties of different shear-zone regions are derived. Results suggest that LPO evolution is reflected in the seismic properties but the precise impact is not simple. In general, the P-wave velocity ( V P ) minimum is parallel to the a -axis maximum; the direction of maximum shear-wave splitting ( AV S ) is parallel to mylonitic foliation; and the V P maximum and AV S minimum are parallel to the c -axis maximum. The seismic anisotropy predicted is significant and increases from shear zone wallrock to mature mylonite. The P-wave anisotropy ranges from 11 to 13%, fast and slow shear waves’ anisotropies range from 6 to 15% and the magnitude of shear-wave splitting ranges from 9 to 16%. Nevertheless, such anisotropy requires a considerable thickness of rock with this LPO before it becomes seismically visible (i.e. 100s of m for local earthquakes; 10s of m for controlled source experiments). However, reflections and mode conversions provide much better resolution, particularly across tectonic boundaries. The low symmetry and strong anisotropy due to the LPO suggest that multi-azimuth wide-angle reflection data may be useful in the determination of the deformation characteristics of deep shear zones.

Modelling the evolution of geometrically necessary boundaries at large plastic strains

In polycrystals undergoing large plastic strains, the strain compatibility between adjacent misoriented areas is usually ensured by the activation of different slip system combinations leading to localised orientation gradients. The latter are accommodated by GNBs, or Geometrically Necessary Boundaries, of increasing misorientation. A new model is developed for the evolution of a GNB between two crystallites under multiple slip conditions. This model takes the crystal plasticity of each cell block into account (using a Taylor–Bishop–Hill approach) and leads to a dynamic accommodation of the boundary disorientation on the basis of dislocation arrays. In particular the optimal dislocation configuration of the GNBs is obtained by minimising the sub-boundary energy within the range of conditions imposed by the slip system kinematics. Applied to the case of plane strain compression of fcc crystals, the model shows that the GNB dislocation lattice is very sensitive to the initial grain orientations, stable texture components like Brass {110}〈112〉 or S {123}〈634〉 leading to the lowest dislocation densities. The strain path and the relative positions of the misorientation axis and boundary plane normal also have an influence on the final dislocation structure, albeit to a smaller extent.

Grain orientation dependence of microstructure in aluminium deformed in tension

The evolution of deformation microstructure in medium to high stacking fault energy fcc metals has been described in terms of a general framework of grain subdivision involving the formation of rotates volume elements for all deformation modes. The rotated volume elements are ordinary dislocation cells and cell blocks, where a cell block contains a group of cells. The cell blocks are bounded by dislocation boundaries accommodating the lattice misorientations between neighboring cell blocks that deform with different slip system combinations and/or by different strains or strain amplitudes. An important aspect of the deformation structure development is the pronounced dependence on the crystal orientation. This has been shown by the formation of different types of deformation microstructures, for which the dislocation boundaries formed during deformation are characterized by their different morphology, spacing, crystallographic orientation and misorientation angle, in single crystals of different orientations deformed in tension and in rolling. Studies of polycrystal behavior are much less extensive but an orientation effect has been observed on a macroscopic scale in specimen deformed in rolling and on a microscopic scale in specimens deformed in tension and in rolling. The previous studies have shown a need for a more precise characterization of the effectmore » of grain orientation on the microstructural evolution of polycrystalline metals. Such a characterization, if successful, could lead to prediction of the evolution of the deformation microstructure in order to establish quantitative correlation between microstructure, crystallographic texture and properties of polycrystals. The present study only concerns the microstructure, which has been characterized in pure polycrystalline aluminium deformed in tension at room temperature.« less

Experimental deformation of fine‐grained anhydrite: Evidence for dislocation and diffusion creep

Deformation experiments on two fine‐grained anhydrite aggregates have revealed two high‐temperature flow regimes: (1) twinning and dislocation creep at high stresses (σ), and (2) diffusion creep accompanied by grain boundary sliding at low stresses. Each regime is characterized by a power law constitutive equation, diagnostic microstructures, and crystallographic preferred orientations (CPO). Experiments were performed at 400°–800°C, strain rates of 10−3–10−6 s−1, and confining pressures of 150–300 MPa on natural (d = 30 μm) and synthetic (d = 12 μm) anhydrites. The data for both anhydrites, corrected for grain size (d), are combined into a single composite flow law. The anhydrites show strain hardening for σ > 150 MPa and steady state flow for σ ≤ 150 MPa. Regime 1 is characterized by a flow law with a stress exponent (n) = 5. The deformation microstructures are indicative of twinning and dislocation creep: twins, undulatory extinction, grain flattening, serrate grain and twin boundaries, high dislocation densities, and newly recrystallized strain‐free grains. Recrystallization occurs by grain and twin boundary migration and subgrain rotation. The CPO reflects twinning at low strains and a combination of slip systems at high strains. In regime 2 the rheology is indicative of diffusion creep with n = 1. There is very little microstructural evidence of the bulk deformation. Grains are equant and have very low dislocation densities, and grain boundaries are smooth and gently curved. Split cylinder experiments reveal significant grain boundary relief attributed to grain boundary sliding. The CPO within this regime is random. The rheology and microstructures of regime 2 strongly suggest that diffusion creep accompanied by grain boundary sliding is the dominant deformation mechanism.

Geometrically necessary boundaries and incidental dislocation boundaries formed during cold deformation

The evolution of microstructure during plastic deformation has recently been described in terms of grain subdivision involving the formation of rotated volume elements. These elements are ordinary dislocation cells and cell blocks where a cell block contains from one to several cells. The cell blocks are bounded by dislocation boundaries which accommodate the lattice misorientation between neighboring cell blocks which deform with different slip system combinations and/or by different amount of shear. The boundaries which accommodate these lattice misorientations are called geometrically necessary boundaries or GNBs. The ordinary cells are also bounded by dislocation boundaries which, however, form as a result of statistical trapping of glide dislocations supplemented by unpredicted dislocations. These boundaries have been called incidental dislocation boundaries of IDBs. The formation and characteristics of the two types of boundaries was discussed and it was suggested that: (i) the misorientation across GNBs should typically be much larger than across IDBs and should rise faster with increasing strain, and (ii) the influence on the flow stress should be different for the two types of boundaries. The present study was initiated to examine the validity of the first suggestion by characterizing the deformation structure in terms of boundary type and bymore » analyzing the boundaries by measuring their spacing and their angular misorientation as a function of the plastic strain. Pure aluminum rolled at room temperature has been used by way of example.« less

Overview no. 96 evolution of f.c.c. deformation structures in polyslip

The microstructural evolution during polyslip in f.c.c. metals in investigated by the examples of Al, Ni, NiCo alloys and an AlMg alloy, deformed at room temperature either by rolling or by torsion. The principles governing this evolution appears to be the following: (a) There are differences in the number and selection of simultaneously acting slip systems among neighboring volume elements of individual grains. In any one volume element (called a cell block), the number of slip systems falls short of that required for homogeneous (Taylor) deformation, but groups of neighboring cell blocks fulfil the Taylor criterion collectively. (b) The dislocations are trapped into low-energy dislocation structures in which neigboring dislocations mutually screen their stresses. The microstructural evolution at small strains progresses by the subdivision of grains into cell blocks delineated by dislocation boundaries. These boundaries accomodate the lattice misorientations, which result from glide on different slip system combinations in neighbouring cell blocks. The cell blocks are subdivided into ordinary cells and both cell blocks and cells shrink with increasing strain. All observations appear to be in good accord with the theoretical interpretation. However, some problems remain to be solved quantitatively.

Geometrically necessary, incidental and subgrain boundaries

During the deformation of polycrystals, the grains break up into domains within which the selection of operative slip systems differs. The domains then subdivide into “cell blocks”. Locally, each group of cell blocks comes near to fulfilling the Taylor criterion when taken collectively, but the number of active glide systems in any one cell block is fewer than predicted. The boundaries between cell blocks and/or domains accommodate the lattice misorientations which result from glide on the different slip system combinations. They are therefore named “geometrically necessary bpundaries”. They, like all boundaries capable of accommodating variable lattice misorientations, are composed of dislocations. Microscopically, such boundaries appear as “dense dislocation walls” and “microbands”. Geometrically necessary boundaries are distinguished from ordinary dislocation cell boundaries by the absence of a change of glide systems across the latter. In materials deforming with a cell structure, ordinary dislocation cell boundaries as well as traditional “deformation bands” arise from the mutual trapping of dislocations into low-energy configurations. Such cell boundaries or walls are therefore named “incidental dislocation boundaries”. The misorientation across incidental boundaries is typically much smaller than for geometrically necessary boundaries. A further distinction is their respective on the flow stress. The average spacing of dislocation cell walls is inverse proportional to the flow stress whereas geometrically necessary boundaries obey the Hall-Petch relationship. Since they tend to occur more frequently the incidental boundaries typically control the flow stress. At increasing strain the angles between dislocation cells increase and different slip system combinations can operate in neighbouring cells. Cell walls are then no longer incidental boundaries but geometrically necessary boundaries. Such boundaries are termed “subgrain boundaries”.

Cold deformation microstructures

AbstractThe evolution of the cold deformation microstructure is described for medium to high stacking fault energy, single phase fcc metals. Macroscopic strain accommodation for polycrystalline metals is considered, and it is suggested that grains subdivide during deformation on a smaller and smaller scale, and that each volume element is characterised by an individual combination of slip systems. A number of microstructural observations (especially of aluminium, nickel, and copper) are described, and dislocation arrangements are discussed on the basis of the general principle that they are low energy dislocation structures. It is shown that the microstructural evolution is quite similar in polycrystalline metals and in single crystals deforming by multislip, and ways in which metallurgical parameters such as stacking fault energy and grain size can affect the microstructure are examined. The general principle of grain subdivision during cold deformation is discussed with reference to the microstructural ...

Cold deformation microstructures

The evolution of the cold deformation microstructure is described for medium to high stacking fault energy, single phase fcc metals. Macroscopic strain accommodation for polycrystalline metals is considered, and it is suggested that grains subdivide during deformation on a smaller and smaller scale, and that each volume element is characterised by an individual combination of slip systems. A number of microstructural observations (especially of aluminium, nickel, and copper) are described, and dislocation arrangements are discussed on the basis of the general principle that they are low energy dislocation structures. It is shown that the microstructural evolution is quite similar in polycrystalline metals and in single crystals deforming by multislip, and ways in which metallurgical parameters such as stacking fault energy and grain size can affect the microstructure are examined. The general principle of grain subdivision during cold deformation is discussed with reference to the microstructural observations.MST/1290

Slip geometry in partially constrained deformation

The deviations from ideal plane-strain conditions in rolling and in channel deformation are such as to decrease the number of prescribed strain components on deforming single crystals or grains in polycrystals from five to three. As a consequence, only three slip systems are necessary to satisfy the boundary conditions. A method is proposed to derive the combination of slip systems that fulfills both the boundary conditions and the yield conditions for any particular crystal orientation. Once this slip system combination is known, the magnitude of the free shears as well as the resulting orientation change follow from kinematics. These results are generally unambiguous, whereas a requirement of five independent systems does not have a unique solution in f.c.c. materials. Texture development under partially constrained deformation should therefore be primarily prescribed by crystal geometry; physical differences between materials enter only after symmetric orientations have been reached, and only in the absence of geometric orientation stability. A new discussion is given of the distinction between orientation changes (which determine texture development) and classical rigid-body rotations. Results for some special orientations in f.c.c. metals are in accord with experimental observations.

A general kinematical analysis of double slip

G eneral kinematic solutions for double slip in fcc and bcc crystals are presented which are free from constitutive assumptions: that is, the analysis does not presuppose equal amounts of slipping on equallystressed slip systems, in contrast to the standard solutions (wherein Taylor hardening is implicitly assumed). The axis rotations and limiting positions on a stereographic projection are illustrated for several different slip-system combinations, initial axis positions (none on a symmetry line), and proportional slip ratios in both fcc and bcc crystals. It is suggested that the solutions have particular application to the experimental study of double slip in the tensile test of prestrained crystals.

The stacking fault energy dependence of the mechanisms of deformation in Fcc metals

The influence of stacking fault energy on the choice of deformation mechanisms is considered. Experimental evidence is reviewed to distinguish between the possible mechanisms and a limited analysis of crystal rotations is performed. It is shown that twinning, pencil glide, and the more usual octahedral slip are all mechanisms which could be operative under different conditions of stacking fault energy or temperature but that even if only octahedral slip occurs stacking fault energy may affect slip rotations by influencing the choice of operative slip systems. Using the simplifying assumption that deformation is homogeneous, and applying Bishop and Hill’s maximum work principle to derive possible combinations of slip systems, a set of criteria are developed to indicate the influence of stacking fault energy on the choice from among the available slip systems, and hence on slip rotations. An empirical method of relating stacking fault energy to texture is outlined and the experimental results obtained by this method are compared with results obtained by other methods. are compared with results obtained by other methods.