Development Of Preferred Orientation Research Articles

Unravelling the development of preferred crystallographic orientation in dual-phase amorphous/nanocrystalline Zr-V thin films

Dual-phase amorphous/nanocrystalline alloys have been proven to present enhanced properties compared to their amorphous or nanocrystalline single-phase counterparts. These dual-phase materials are typically composed of nanocrystalline cores embedded in an amorphous matrix. In contrast, a new kind of dual-phase metallic films has recently been reported in which cone-shaped crystalline regions evolve as a result of competitive growth between the amorphous and crystalline phases with increasing film thickness. Here, we demonstrate that, unlike typical dual-phase alloys, Zr-V thin films exhibiting crystalline/amorphous competitive growth develop a preferred crystallographic orientation upon growth. Relying on pole figure observations, we uncover the development of a preferred orientation of the (110) crystallographic planes in the growth direction of the film with increasing film thickness. High-resolution transmission electron microscopy analysis reveals that the crystalline regions are formed by nano-branches which grow (110)-oriented. Based on this result, together with scanning and transmission electron microscopy observations, we associate the development of the thickness-dependent preferred orientation to the impingement between cone-shaped crystalline regions. This process triggers a selective growth mechanism that favors the selection of nano-branches growing near the direction of film growth. Our results and analyses provide a step forward in understanding the growth kinetics of dual-phase alloys presenting complex microstructures.

Microstructure and mechanical properties of Cr films with different orientations before and after plasma nitriding

In this paper, the Cr films with preferred orientation evolution from (110) to (200) were deposited on the surface of austenitic stainless steel. These films were driven by a pulsed bias with different duty cycles from 20% to 80%, followed by a postnitriding process for 1 h using a hot wire plasma-enhanced magnetron sputtering system. XRD result showed Cr film had a body-centered cubic lattice structure, and the orientation transformed from (110) to (200) with the increase in the duty cycle. SEM and EDS measurements revealed that Cr film structured with columnar crystals could contribute to the continuous diffusion of nitrogen into austenite lattice. N atoms tended to diffuse along the (200) orientation of Cr films than the close-packed (110) orientation. As a result, the best wear resistance and adhesion strength were obtained when Cr film deposited at 80% duty cycle was nitrided, and the wear volume decreased by 95.7% compared with that before nitriding.

Deformation and Transformation Textures in the NaMgF3 Neighborite—Post-Perovskite System

The D″ region of the lower mantle, which lies just above the core–mantle boundary, is distinct from the bulk of the lower mantle in that it exhibits complex seismic heterogeneity and seismic anisotropy. Seismic anisotropy in this region is likely to be largely due to the deformation-induced texture (crystallographic preferred orientation) development of the constituent mineral phases. Thus, seismic anisotropy can provide a marker for deformation processes occurring in this dynamic region of the Earth. Post-perovskite-structured (Mg,Fe)SiO3 is believed to be the dominant mineral phase in many regions of the D”. As such, understanding deformation mechanisms and texture development in post-perovskite is important for the interpretation of observed seismic anisotropy. Here, we report on high-pressure diamond anvil cell deformation experiments on NaMgF3 neighborite (perovskite structure) and post-perovskite. During deformation, neighborite develops a 100 texture, as has been previously observed, both in NaMgF3 and MgSiO3 perovskite. Upon transformation to the post-perovskite phase, an initial texture of {130} at high angles to compression is observed, indicating that the {100} planes of perovskite become the ~{130} planes of post-perovskite. Further compression results in the development of a shoulder towards (001) in the inverse pole figure. Plasticity modeling using the elasto-viscoplastic self-consistent code shows this texture evolution to be most consistent with deformation on (001)[100] with some contribution of glide on (100)[010] and (001)<110> in NaMgF3 post-perovskite. The transformation and deformation mechanisms observed in this study in the NaMgF3 system are consistent with the behavior generally observed in other perovskite–post-perovskite systems, including the MgSiO3 system. This shows that NaMgF3 is a good analog for the mantle bridgmanite and MgSiO3 post-perovskite.

Deformation microstructures of low- and high-strain epidote-blueschist (Ryukyu arc, Japan): Implications for subduction interface rheology

We present field and microstructural data from an exhumed subduction complex in the Ryukyu arc, Japan, where epidote-blueschist, Triassic, Tomuru metamorphic rocks with block-in-matrix structure crop out. With the aim to constrain epidote-blueschist rheology, we investigate fabric development and infer deformation mechanisms of blocks and matrix through microstructural analyses on the main fabric-forming minerals: glaucophane, epidote and albite. The blocks have a poorly developed, discontinuous foliation. In contrast, the matrix has a well-developed, continuous foliation. Glaucophane is the principal foliation-forming phase, arranged in interconnected layers that surround epidote and albite, which suggests that glaucophane controls epidote-blueschist rheology. Deformation mechanisms inferred from petrographic and electron backscatter diffraction (EBSD) analysis are similar in blocks and matrix, with glaucophane deformed by diffusion creep accompanied by reaction-driven creep, albite by diffusion creep, and epidote by brittle fracture and incipient dislocation creep, based on degrees of internal misorientations, lattice preferred orientation (LPO) development and grain size. During deformation, shear stress must have been relatively low, which is implied by the predominance of diffusion and reaction creep as the dominant deformation mechanisms, and by the small viscosity contrast between blocks and matrix, reflected by their similarity in dominant deformation mechanism.

A key role for diffusion creep in eclogites: Omphacite deformation in the Zermatt-Saas unit, Italian Alps

Eclogites commonly form from subducted oceanic crust and as such carry key information on subduction zone rheology. Using a combination of microanalytical techniques on deformed eclogites from the Zermatt-Saas unit of the Italian Alps, we explore the mechanisms which resulted in both an omphacite shape and lattice preferred orientation. Omphacite defines both foliation and lineation in these rocks and displays a strong S-type lattice preferred orientation. Scarcity of microstructures associated with dislocation creep combined with observed sharp asymmetrical chemical zonation in foliated grains suggest diffusion creep plays an important role in the development of omphacite lattice preferred orientation in these eclogites. Modelling of the pressure-temperature conditions possible for observed mineralogy and mineral geochemistry, and textural relationships between omphacite and retrogressive minerals, place the action of diffusion creep, at the latest, by the onset of retrogression of these Zermatt-Saas eclogites. We propose a model of eclogite deformation that occurred initially via small amounts of dislocation creep which moved quickly into a dominant diffusion creep field, particularly as exhumation/retrogression of these eclogite rocks began. This result suggests that diffusion creep can dominate eclogite deformation at high P-T conditions in subduction zones.

The evolution of preferred orientation and morphology of AlN films under various sputtering parameters

Wurtzite aluminum nitride (AlN) films with (100) and (002) preferred orientations are obtained on Si (100) wafers by radio frequency magnetron sputtering. The effects of target to substrate distance (TSD), RF power, deposition pressure and substrate temperature on crystal orientation and morphology of AlN films are analyzed. It is demonstrated that the TSD is the key factor affecting the preferred orientation of AlN films. The preferred orientation transforms from (002) to (100) with the increase of TSD. Further increase of substrate temperature and RF power causes the coexistence of (002) and (100) orientation. The evolution of orientation is explained by the change in kinetic energy of sputtered particles. The correlation between the crystal orientation and the surface morphology is investigated.

Melt Network Reorientation and Crystallographic Preferred Orientation Development in Sheared Partially Molten Rocks

AbstractWe investigated the co‐evolution of melt, shape, and crystallographic preferred orientations (MPOs, SPOs, and CPOs) in experimentally deformed partially molten rocks, from which we calculated the influence of MPO and CPO on seismic anisotropy. Olivine‐basalt aggregates containing 2 to 4 wt% melt were deformed in general shear at a temperature of 1,250°C under a confining pressure of 300 MPa at shear stresses of τ ≤ 175 MPa to shear strains of γ ≤ 2.3. Grain‐scale melt pockets developed a MPO parallel to the loading direction by γ < 0.4. At higher strains, the grain‐scale MPO remained parallel to the loading direction, while incipient sample‐scale melt bands formed at ∼20° to the grain‐scale MPO. An initial SPO and CPO were induced during sample preparation, with [100] and [001] axes girdled perpendicular to the long axis of the starting material. At the highest explored strain, a strong SPO was established subperpendicular to the loading direction, and the [100] axes of the CPO clustered nearly parallel to the shear plane. Our results demonstrate that grain‐scale and sample‐scale alignments of melt pockets are distinct. Furthermore, the melt and the solid microstructures evolve on different timescales: in planetary bodies, changes in the stress field will drive a relatively fast reorientation of the melt network and a relatively slow realignment of the crystallographic axes. Rapid changes to seismic anisotropy in a deforming partially molten aggregate are thus caused by MPO rather than CPO.

Supplementary information for Melt network reorientation and crystallographic preferred orientation development in sheared partially molten rocks

Supplementary information for Melt network reorientation and crystallographic preferred orientation development in sheared partially molten rocks

Rolling-sliding contact fatigue failure and associated evolutions of microstructure, crystallographic orientation and residual stress of AISI 9310 gear steel

In the present study, rolling-sliding contact fatigue (RSCF) failures of AISI 9310 gear steel were analyzed systematically, in terms of characterizing the fatigue life, evolution of microstructure and crystallographic orientation, and variation of microhardness and residual stress distributions. The RSCF experiments were conducted using a twin rollers fatigue test rig. The RSCF life of AISI 9310 steel roller decreased continuously with increasing the maximum Hertzian contact pressure, however, it could be effectively improved by additional shot peening process owing to the enhanced microhardness and compressive residual stress near the roller surface. The main fatigue damage characteristics near the roller surface were consisted of inclined cracks, micropitting, spallation and plastic deformation. Although the compressive residual stress was reduced by RSCF, there was an obvious increase in the microhardness which should be attributed to the refined microstructure, increased dislocation density as well as phase transformation from retained austenite to martensite. In addition, the accumulated plastic strain during RSCF resulted into development of several preferred crystallographic orientations corresponding to ideal shear texture components of body-centered cubic (BCC) materials that has been seldom reported.

Preferred Orientation Evolution of Hole Transport Materials for High Emitting Dipole Orientation Ratio of the Emitting Material

AbstractControl of the molecular orientation is an effective approach to enhance the performance of organic light‐emitting diodes. This study examines the molecular dipole orientation of hole transport materials depending on the deposition step and the consecutive effect on the transition dipole orientation of the emitting dopant. In contrast to other reference materials, 4,4′,4′′‐tris(carbazole‐9‐yl)triphenylamine (TCTA) shows a preferred orientation only in the continuously deposited films that is dependent on the film thickness. The horizontal dipole orientation ratio of the emitting dopant deposited on the TCTA is improved by the alignment of TCTA molecules. The power efficiency of the device produced from the above materials is increased from 28.9 to 34.4 lm W−1owing to the dual enhancement of the hole mobility of TCTA and the horizontal dipole orientation ratio of the emitting dopant. The molecular orientation of the charge transport layer contributes to charge transport in the layer and the molecular orientation of the adjacent emitting layer.

Crystallographic preferred orientation (CPO) patterns in uniaxially compressed deuterated ice: quantitative analysis of historical data

AbstractStrain, temperature and strain rate are crucial factors governing the development of crystallographic preferred orientations (CPO) in ice. To better understand how CPO patterns change in response to these variables, we performed quantitative analyses on neutron diffraction data between 2010 and 2019, collected in situ during uniaxial compression experiments on deuterium ice. At strains >10% and temperatures <−10°C, thec-axis pattern switches from a single maximum (‘cluster’) to small circle (‘cone’), both oriented parallel to shortening. The diameter and mean width of the cone pattern decrease as strain and/or strain rate increases. Prismatic axis (aandm) patterns are characterised by great circles parallel to the pole figure margin and may be distinguishable from the patterns in ice deformed under simple shear. While strain has the main influence on the degree of preferred orientation (or CPO ‘strength’), both temperature and strain rate have minor influences, which limits the extent to which CPOs can be used to measure strain. As cluster patterns can be observed in thec-axes of ice deformed under both pure and simple shear settings, this may complicate interpretations of flow geometry in terrestrial ice unless the prismatic axis patterns are also considered.

Preferred orientation of calcium silicate hydrate and its implication to concrete creep

Calcium silicate hydrate (C–S–H) is the primary binding phase of cement-based and alkali-activated materials. The preferred orientation of C–S–H under non-hydrostatic pressure (e.g., uniaxial/biaxial load) is overlooked yet crucial in understanding concrete's multiscale mechanical performance. Here, we unveil the texture formation of C–S–H under compressive deviatoric stress, S, from 0 to ∼200 MPa, using high-pressure X-ray diffraction. Texture initiated at S < 12 MPa: the c-axis (normal to the basal plane) of C–S–H nanocrystallites preferentially re-oriented towards the direction of the principal compressive stress. Below S ∼100 MPa, the preferred orientation intensified through translation and rotation of C–S–H nanocrystallites; above ∼100 MPa, the texture stopped growing then weakened, suggesting internal transformations of C–S–H nanocrystallites. The time-dependence of the preferred orientation development is unveiled by the texture weakening after full unloading. The findings implicate that concrete creep under service loads is contributed by the intergranular preferential re-orientation of C–S–H nanocrystallites, not interlayer sliding or silicate chain breakage.

On the Implementation and Usability of Crystal Preferred Orientation Evolution in Geodynamic Modeling

AbstractFlow in the Earth's mantle causes the preferred orientation of crystals called lattice/crystal preferred orientation (LPO or CPO). This preferred orientation is one of the main reasons why seismic anisotropy is observed. Seismic anisotropy observations could therefore be used to constrain the mantle flow in geodynamic models through tracking CPO evolution, and computing the resulting elastic tensor and the anisotropy predicted at the surface. Even though there are many types of CPO models, only a few studies include CPO calculations due to the complexity and computational cost. Here, we implemented an extended version of the CPO model D‐Rex into the open‐source community geodynamics code ASPECT. We show that the implementation is correct, how to use it, and that it is feasible and important to use in large 3D models. We also show that it is important to calculate CPO, especially for models focusing on plate boundary of smaller scale flow because the resulting fast axis directions can greatly deviate from the flow direction. The added infrastructure will also allow for future enhancement, testing, and even replacement of the CPO model.

Microstructural Shift due to Post‐Deformation Annealing in the Upper Mantle

AbstractSyntectonic microstructural evolution is a well‐known phenomenon in the mantle and lower crust associated with two main processes: grain size reduction through dynamic recrystallization and development of crystallographic preferred orientation (CPO). However, the effects of annealing via static recrystallization on grain size and CPO have been largely overlooked. We investigated mantle annealing by analyzing a suite of kimberlite‐hosted garnet peridotite xenoliths from the Wyoming Craton. We focus on five xenoliths that show microstructures reflecting different degrees of recrystallization, with annealed grains characterized by distinctive faceted boundaries crosscutting surrounding, nonfaceted matrix grains. These textures are indicative of discontinuous static recrystallization (DiSRX). Electron backscatter diffraction analysis further demonstrates a ∼10°–20° misorientation between DiSRXed grains and the matrix grains, resulting in an overall weaker CPO. These characteristics are remarkably similar to microstructures observed in samples that were annealed after deformation in the laboratory. Measurements of the thermal conditions and water contents associated with the last equilibration of the xenoliths suggests that high homologous temperatures (T/Tm &gt; 0.9) are necessary to induce DiSRX. We postulate that annealing through DiSRX occurs under high temperatures after a short episode of intense deformation (years to hundreds of years) with timescales for annealing estimated as weeks to years, significantly slower than the timescale of hours expected for a kimberlitic magma ascent. We conclude that microstructural transformation due to DiSRX will occur during transient heating events associated with mantle upwelling, plumes, and lithospheric thinning.

Preferentially oriented Ag-TiO2 nanotube array film: An efficient visible-light-driven photocatalyst

Ag-TiO2 nanotube array films with the preferential orientation of crystals were fabricated on ITO glass by magnetron sputtering and anodization. Comprehensive characterization was performed to ascertain the composition and microstructure characteristics of thin films. The photocatalytic activities were evaluated through the reduction of hexavalent chromium (Cr2O72− (Cr (VI)) as a model compound under visible light irradiation. XRD and XPS studies reveal the development of preferred orientation along [001] in anatase TiO2 nanotubes by adjusting the Ag content during magnetron sputtering. Such unusual behavior is attributed to the minimization of anatase (001) surface energy assisted by Ag. The Ag-TiO2 nanotube arrays having preferred crystal orientation exhibit superior separation/transfer of photo-induced charges. Furthermore, the Ag-TiO2 nanotube arrays show improved absorption of visible light due to the SPR effect induced by Ag and the formation of heterojunction between the TNAs and Ag2O. TNA-3Ag exhibits the highest photocatalytic activities by removing 99.1 % Cr (VI) in 90 min under visible light illumination.

Grain Structure and Electrical Properties of Transparent Indium Oxide Thin Films Prepared by RF Magnetron Sputtering

Transparent conductive films of indium oxide (In2O3) are deposited on a glass substrate by RF magnetron sputtering and their electrical properties are investigated in relation to their microstructure. Sputtering deposition was carried out with variations of normalized substrate temperature (Ts/Tm where Tm is the melting temperature) and argon partial pressure (PAr). At a very low substrate temperature (Ts/Tm &lt; 0.1), the columnar grains with voided grain boundaries are observed in the In2O3 films, which are attributed to the low surface mobility and atomic shadowing effect. With an increase in the substrate temperature, tight grain boundaries are formed between the growing columnar grains. At high temperature (0.3 &lt; Ts/Tm &lt; 0.5), the grain surface is faceted, which is due to the high surface mobility of the sputtered atoms, and development of preferred orientation with grain growth is promoted. The growing morphology is also dependent on the argon partial pressure. At low PAr deposition, an inclined fibrous grain oriented to the target direction and a smooth surface structure is developed. As the PAr increases, a dome-shaped surface structure and columnar grains normal to the substrate are developed due to the scattering effect of the sputtered atoms. The growing morphology with substrate temperature and argon pressure coincides with the Thornton's Structure Zone Model (SZM). The lowest electrical resistivity (2.1×10-2 Ωcm) is observed in the In2O3 films with tight grain boundaries and faceted grains, which corresponds to zone II region of the SZM.

Experimentally deformed lawsonite at high pressure and high temperature: Implication for low velocity layers in subduction zones

Lawsonite is considered to be one of the most likely hydrous minerals to explain the persistence of seismic low-velocity layers (LVLs) atop subducted slabs to depths of 100–250 km due mainly to the fact that it can persist to these depths, in contrast to other hydrous minerals such as antigorite. However, as it is highly anisotropic and subjected to intense deformation during subduction, further constrains on the development of lawsonite crystal preferred orientation (CPO) at high pressure and temperature are required in order to evaluate its role in slowing seismic waves. We have deformed lawsonite aggregates at 5 GPa and 500–800 °C corresponding to 150 km depth and covering temperatures for both cold and hot subduction zones. In this study, we report a new lawsonite CPO pattern resulting from dislocation creep deformation that has not been previously observed. The [100] axes concentrate into the shear direction and the [010] axes are normal to the shear plane, respectively (we refer to this as “type-1” CPO). Such CPO is consistent with our transmission electron microscope (TEM) observations identifying (010)[100] as a dominant dislocation slip-system. The seismic properties resulting from this CPO show the fast P-wave direction to be parallel to the shear direction, and the slow P-wave direction and maximum S-wave anisotropy normal to the shear plane. We performed calculation of omphacite-lawsonite aggregates using our experimental data and varied both the lawsonite contents and the slab dipping angle. Our results show that a reasonable amount of lawsonite can explain Vs reduction in the LVLs, but cannot explain the Vp reduction. However, the presence of lawsonite would induce a rotation of the fast S-wave polarization toward the trench direction as the S-wave anisotropy increases or decreases according to the lawsonite proportion, its CPO strength and the slab dipping angle. We believe that our calculation can now be used for investigation of lawsonite effect in various subductions zones.

Recrystallization processes, microstructure and crystallographic preferred orientation evolution in polycrystalline ice during high-temperature simple shear

Abstract. Torsion experiments were performed in polycrystalline ice at high temperature (0.97 Tm) to reproduce the simple shear kinematics that are believed to dominate in ice streams and at the base of fast-flowing glaciers. As clearly documented more than 30 years ago, under simple shear ice develops a two-maxima c axis crystallographic preferred orientation (CPO), which evolves rapidly into a single cluster CPO with a c axis perpendicular to the shear plane. Dynamic recrystallization mechanisms that occur in both laboratory conditions and naturally deformed ice are likely candidates to explain the observed CPO evolution. In this study, we use electron backscatter diffraction (EBSD) and automatic ice texture analyzer (AITA) to characterize the mechanisms accommodating deformation, the stress and strain heterogeneities that form under torsion of an initially isotropic polycrystalline ice sample at high temperature, and the role of dynamic recrystallization in accommodating these heterogeneities. These analyses highlight an interlocking microstructure, which results from heterogeneity-driven serrated grain boundary migration, and sub-grain boundaries composed of dislocations with a [c]-component Burgers vector, indicating that strong local stress heterogeneity develops, in particular, close to grain boundaries, even at high temperature and high finite shear strain. Based on these observations, we propose that nucleation by bulging, assisted by sub-grain boundary formation and followed by grain growth, is a very likely candidate to explain the progressive disappearance of the c axis CPO cluster at low angle to the shear plane and the stability of the one normal to it. We therefore strongly support the development of new polycrystal plasticity models limiting dislocation slip on non-basal slip systems and allowing for efficient accommodation of strain incompatibilities by an association of bulging and formation of sub-grain boundaries with a significant [c] component.

Development of crystallographic preferred orientation during cataclasis in low-temperature carbonate fault gouge

Grain size reduction due to cataclasis is a key process controlling fault frictional properties during the seismic cycle. We investigated the role of cleavage planes on fracturing and microstructural evolution during cataclasis in wet and dry carbonate fault gouges (50 wt% calcite, 50 wt% dolomite) deformed in a rotary-shear apparatus over a wide range of slip rates (30 μms−1 to 1 ms−1) and displacements (0.05–0.4 m). During shearing, progressive strain localization forms a narrow slip zone that undergoes significant frictional heating (at high slip rates), but the bulk gouge always accommodates low finite shear strains and deforms at low temperatures. Microstructural analysis of the bulk gouges indicates that deformation occurred by brittle fracturing and twinning. Microfractures in calcite are closely spaced, often exploit {101¯4} cleavage r-rhomb planes, and occur mainly subparallel to the expected principal stress orientation (σ1). Instead, twin planes typically occur sub-perpendicular to σ1. Electron backscatter diffraction analysis of the bulk gouges shows that calcite develops a well-defined crystallographic preferred orientation (CPO) at all investigated deformation conditions. The CPO is defined by a clustering of the calcite c-axes around an orientation sub-parallel to σ1. The calcite CPO is interpreted to result from grain rotation during granular flow, followed by brittle fracturing that occurred preferentially along calcite cleavage planes. This interpretation is supported by measurements of calcite grain shape-preferred orientations that show a population of elongate calcite grains oriented with their long axes sub-parallel to σ1. Our experimental results indicate that well-defined CPOs can form at low temperature in cataclastic fault rocks, and that mineral cleavage can strongly influence the evolution of grain sizes and shapes during comminution.

Study the Effect of Anisotropy of Elastic-Plastic Properties on Residual Stress Development in Autofrettage of Thick Cylinder

Thick-walled cylinders subjected to high internal pressure and/or elevated temperatures are widely used in the aircraft, defence, nuclear and chemical industries especially for military applications e.g. the gun barrel in a ballistic event. In the absence of residual stresses, cracks usually form at the bore where the hoop stress developed by the working pressure is highest. To prevent such failure and to increase the pressure-carrying capacity of the pressure vessel, autofrettage process is used. During autofrettage a plastic region within the thick wall of the pressure vessel is produced by loading the pressure vessel in the plastic domain. Upon unloading, a residual compressive hoop stress is established within the plastic zone. This residual compressive stress counters the tensile hoop stress introduced due to service loading, thereby reducing the overall tensile hoop stress at inner surface. Therefore, autofrettage is used to introduce advantageous favourable compressive residual hoop stress inside wall of a cylinder and result in an increase in the fatigue lifetime of the component. Several researchers have studied the autofrettaged cylinders, both analytically and FE simulation. In this paper, effect of orthotropic anisotropy in the material properties will be studied on the stress field generated in the autofrettaged cylinder. Anisotropy in the material properties may result due to manufacturing processes like extrusion or pilgering. Plastic deformation leads to the development of preferred orientation of grains in the components due to slip occurring only in preferred slip planes in a crystal especially in a HCP material like Zr 2.5%Nb. In this paper, a thick cylinder made from Zr 2.5% Nb is loaded till elasto plastic interface is achieved and then unloaded to study effect of anisotropy on the development of residual stresses. Two material models are considered in the analysis i.e. isotropic and anisotropic plastic behaviour. The effect of anisotropy on the residual stress is investigated.