Schmid Factor Analysis Research Articles

Microstructure, texture and mechanical properties of commercial high-purity thick titanium plates jointed by electron beam welding

Electron beam welding (EBW) is a fusion joining process particularly suitable for the welding of thick titanium plates. In the present work, commercial high-purity titanium plates with a thickness of 30mm were welded by EBW. Color metallography and electron backscattered diffraction (EBSD) were used to investigate the microstructure and texture after welding. The results show that the grains become elongated or coarsened in the weld zone (including the fusion zone and the heat-affected zone). Meanwhile, as revealed by the (0001) pole figures, the texture of the weld zone is enhanced. Despite the grain coarsening, the welded plates exhibit higher yield strength than the base metal. A Schmid factor analysis revealed that this increase in yield strength could be attributed to texture strengthening. Specifically, the grains in the weld zone are re-oriented. For the weld zone, the Schmid factor is relatively small for prismatic slip, which is the most easily activated deformation mode for titanium at room temperature. Compared to the base metal, the Schmid factors for {101¯2} twinning and {112¯2} twinning are larger for the weld zone. The EBSD observations confirmed that a large number of {101¯2} twins and {112¯2} twins are formed in the weld zone during tension. However, the plastic strain caused by the twin formation is much smaller than that caused by the prismatic slip in the base metal. As a result, necking occurred in the base metal during the transverse tensile tests.

Characteristics of cross grain boundary contraction twin pairs and bands in a deformed Mg alloy

With the help of trace analysis, cross-grain boundary (cross-GB) contraction twin (CTW) pairs and bands can be identified more easily in a deformed Mg alloy. Cross-GB CTW pairs can form in two neighboring grains with misorientations from 5° to 60°. Schmid factor (SF) analysis reveals that the majority of them are high SF twin variants, indicating that the applied macro stress plays the most important role in their nucleation. Twinning shear compatibility over GB has been explicitly evaluated by a geometrical compatibility parameter (m′). It is found that nearly half of the cross-GB contraction twin pairs have high m′ values greater than 0.7, indicating that their formation is mainly due to twinning shear transmission over GBs. However, dramatically different from cross-GB extension twin pairs and bands reported before, the rest of the cross-GB contraction twin pairs have low m′ values smaller than 0.4. Their formation is due to the dominance of the applied macro stress near GBs.

Abnormal migration of twin boundaries in rolled AZ31 alloy containing intersecting [formula omitted] extension twins

Twin boundary (TB) migration under the condition of the interaction between different {10–12} twin variants with a high misorientation of 60.4° was investigated by using in-situ electron backscattered diffraction technique combined with Schmid factor analysis. It was found that TBs would continue to migrate when the sides of intersecting twin bands enclose an acute angle, but cease to migrate on the sides making an obtuse angle. Besides, due to the twin-twin interaction, half locked and entirely locked twin boundaries occurred as deformation progressed. Moreover, strain accommodated by double twin and new active twin was found at further imposed strain in current study.

Experimental deformation of coarse‐grained rock salt to high strain

AbstractThe processes and deformation mechanisms (e.g., dislocation creep, pressure solution, grain boundary sliding, and recrystallization) of rock salt are still a matter of debate. In order to fill this gap, high strain constriction experiments at 345°C, atmospheric pressure and a strain rate of ~10−7 s−1 have been conducted on natural halite cuboids (60 × 60 × 45 mm) from the Morsleben mine of Northern Germany. Most samples were almost single crystals and contain a small amount of smaller grains (10–26%). The grain boundaries are decorated with fluid inclusions. The experiments were stopped at different final strains (εy = z of ~10, 20, 30, and 40%) corresponding to a maximum strain (εx) range of 20–170%. The halite is deformed by dislocation creep, and the size of developed subgrains corresponds to the applied stress. The combined Schmid factor and subgrain boundary analysis indicate that slip was largely accommodated by the {110} < 110 > slip systems, with possible minor contribution by slip on the {100} < 110 > slip systems. Some of the deformed samples show evidence of grain boundary migration. In addition, subgrains with small misorientations form that result in large cumulative misorientations within a single grain (>40°). However, no subgrain rotation recrystallization is observed (i.e., misorientation angles are <10°). All the experiments show strain hardening, suggesting that recrystallization by grain boundary migration was not extensive and did not reset the microstructure. The experiments show that high finite strain in coarse‐grained relatively dry rock salt can be accommodated by dislocation creep, without extensive dynamic recrystallization.

Hardening and softening analysis of pure titanium based on the dislocation density during torsion deformation

The hardening and softening phenomena during torsion deformation are studied based on the Taylor dislocation model for pure titanium. The hardening and softening phenomena are observed through the hardness analysis during micro-indentation test and micro-hardness test. Besides, the variations of indentation size also verify the existence of hardening and softening phenomena during torsion. The variations of geometric necessary dislocations (GNDs) and statistic store dislocations (SSDs) state that the positions of high dislocation density and low dislocation density correspond to the positions of hardening and softening. The results from the microstructure, grain boundaries evolution and twins analysis indicate the twins play an important role in appearance of hardening and softening phenomena. The appearance of hardening and softening phenomena are attributed to the combination of different slip systems and twinning systems combining with the Schmid Factor (SF) analysis and the transmission electron microscope (TEM). The appearance of hardening and softening phenomena can be explained by the Taylor dislocation theory based on TEM analysis.

The effect of twin–twin interaction in Mg[sbnd]3Al[sbnd]1Zn alloy during compression

Electron backscattered diffraction serial image analyses on AZ31 magnesium alloy compressed along RD at different strain levels revealed that twin–twin interactions are found to correlate with mechanical hardening. Four typical twin–twin structures are investigated: (1) Parallel twins with single variant; (2) Interacting twins with single variant; (3) Parallel twins with double variants; (4) Interacting twins with double variants. We studied twin–twin interactions by combining experimental observations and Schmid factor analysis. Due to twins intersecting with each other, the limited growth rate of twins was observed in EBSD maps. The intersection between different twin variant pairs was found to retard the twin growth and promote the nucleation of new twins near intersection region. Besides, “Apparent crossing” twin structure is a limiting case, in which the twin is crossed by a couple of twins, and the interaction region grow slowly. Twin–twin boundary migration is also observed during deformation in this paper, which is considered as an important cause to prohibit twins for further propagate and growth. All these features can be related to twinning-induced hardening.

Experimental and numerical investigation of anisotropic and twinning behavior in Mg alloy under uniaxial tension

In plane tension of magnesium alloy sheets is accommodated by prismatic and basal slip, whereas {10−12} twinning is activated when grains are elongated along the <c> axis. The plastic behavior of Mg-3Al-1Zn in tension has been investigated using a thick rolled plate with a strong basal texture. Tensile tests were performed along five directions distributed between the normal direction and the transverse direction, allowing various amount of {10–12} twinning, basal, and prismatic slip to take place. The twinning behavior has been investigated using EBSD measurement and EVPSC modeling, and Schmid factor analysis was performed. The observed amount of variants with a Schmid factor of high rank is higher than predicted, emphasizing the necessity of strain accommodation between grains and twins. Compared with compression, even when twinning activity is low, more {10–12} twin variants are predicted in tension. This study confirms extension twinning as a major deformation mechanism in all tensile directions and an efficient way to harden Mg alloys by twin-twin boundaries.

Are quartz LPOs predictably oriented with respect to the shear zone boundary?: A test from the Alpine Fault mylonites, New Zealand

AbstractThe Alpine fault self‐exhumes its own ductile shear zone roots and has a known slip kinematics. Within ∼1 km of the fault, the mylonitic foliation is subparallel to the boundary of the amphibolite‐facies ductile shear zone in which it formed. Using EBSD, we analyzed quartz Lattice Preferred Orientations [LPOs) of mylonites along a central part of the Alpine Fault. All LPOs feature a strongest girdle of [c]‐axes that is forward‐inclined ∼28 ± 4° away from the pole to the fault. A maximum of &lt;a&gt; axes is inclined at the same angle relative the fault. The [c]‐axis girdle is perpendicular to extensional (C') shear bands and the &lt;a&gt; maximum is parallel to their slip direction. [c]‐axis girdles do not form perpendicular to the SZB. Schmid factor analysis suggests that σ1 was arranged at 60–80° to the Alpine Fault. These observations indicate ductile transpression in the shear zone. The inclined arrangement of [c]‐axis girdles, &lt;a&gt; axes, and C' planes relative to the fault can be explained by their alignment relative to planes of maximum shear‐strain‐rate in a general shear zone, a significant new insight regarding shear zones and how LPO fabrics may generally develop within them. For the Alpine mylonite zone, our data imply a kinematic vorticity number (Wk) of ∼0.7 to ∼0.85. Inversions of seismic focal mechanisms in the brittle crust of the Southern Alps indicate that σ1 is oriented ∼60° to the Alpine Fault; that shear bands form at ∼30° to this direction, and that σ2 and σ3 flip positions between the brittle and ductile parts of the crust.

Deformation twinning in the full-α″ martensitic Ti–25Ta–20Nb shape memory alloy

Deformation twinning of the Ti–25Ta–20Nb (mass%) shape memory alloy is characterized using EBSD and TEM. The selfaccommodating α″ microstructure is shown to be first deformed using {111}α″ type I and <211>α″ type II reorientation twinning. Plastic deformation occurs further by plastic twinning with a new {130}<310>α″ twinning system. Maximum lattice deformation calculation is a relevant parameter to predict the variant of martensite that is favored during the reorientation process. Conversely, Schmid factor analysis can be used to predict the selection of {130}<310>α″ twinning variants during deformation. Analogy between {130}<310>α″ and {332}<113>β twinning systems is highlighted.

Deformation anisotropy and associated mechanisms in rolling textured high purity titanium

Plastic anisotropy and associated deformation mechanisms of rolling textured high purity alpha phase titanium were investigated by carrying out uniaxial compression tests along the three featured directions, the rolling direction (RD), normal direction (ND) and transverse direction (TD), in combination with an electron backscatter diffraction measurement and a Schmid factor (SF) analysis. The results revealed that the specific crystallographic feature of the material, caused by rolling texture, influences the activities of dislocation slips and twinning by affecting their SF, and this significantly varies with the loading direction, consequently leading to anisotropic deformation. The material yielding was dominated by dislocation slips, and the change of yielding mechanism with the loading direction (prismatic <a> slip for the RD and TD, and basal <a> slip for the ND) gave rise to yielding anisotropy. As the material deformed beyond the yielding point, deformation twins took place and played a decisive role in the deformation. The twinning characteristics including types of twins, morphology, twin area fraction with strain and related texture modification significantly varied with the loading direction, and this had a completely different effect on strain hardening behavior, thereby causing deformation anisotropy.

Study of Dislocation Boundary Structure in Al–Li Alloy During Bending

The dislocation boundary structures of 2060-T8 alloy during bending were investigated by backscattered electron imaging, electron backscattered diffraction, and misorientation axes maps. Experimental result shows that typical dislocation boundary structures, which depend on grains’ orientation, are formed in grains during bending. The microstructure of type A is mainly observed in grains near brass, copper, and Goss orientations; microstructure of type B is mainly found in grains near S orientation; microstructure of type C is mainly seen in grains near Cube orientation. The angle between geometrically necessary boundaries (GNBs) and force axis is in the range of −45° to −30° and 30° to 45°. Most of the GNBs are approximately parallel to the trace of {111} slip planes which are identified by Schmid factor analysis.

Microstructural evolution and deformation behavior of twinning-induced plasticity (TWIP) steel during wire drawing

The effect of wire drawing on the microstructural evolution and deformation behavior of Fe–Mn–Al–C twinning-induced plasticity (TWIP) steel has been investigated. The inhomogeneities of the stress state, texture, microstructure, and mechanical properties were clarified over the cross section of drawn wire with the aid of numerical simulation, Schmid factor analysis, and electron backscatter diffraction (EBSD) techniques. The analysis of texture in drawn wire shows that a mixture of <111> and <100> fiber texture was developed with strain; however, the distribution of <111> and <100> fibers was inhomogeneous along the radial direction of wire due to uneven strain distribution and different stress state along the radial direction. It has also been shown that the morphology, volume fraction, and variant system of twins as well as twinning rate were dependent on the imposed stress state. The surface area was subjected to larger strain and more complex stress state involving compression, shear, and tension than the center area, resulting in a larger twin volume fraction and more twin variants in the former than in the latter at all the strain levels. While the surface area was saturated with twins at an early stage of drawing, the center area was not saturated with twins even at fracture, implying that the fracture of wire were initiated at the surface area because of the exhaustion of ductility due to twinning. Based on these results, it is suggested that imposing a uniform strain distribution along the radial direction of wire by the control of processing conditions such as die angle and amount of reduction per pass is necessary to increase the drawing limit of TWIP steel.

Texture evolution of rolled Mg–3Al–1Zn alloy undergoing a {10-12} twinning dominant strain path change

The texture modification, caused by {10-12}–{10-12} double twinning, in rolled Mg–3Al–1Zn alloy was investigated by carrying out consecutive in-plane compressions along two orthogonal directions in combination with an electron backscatter diffraction measurement and a Schmid factor analysis. The results revealed that the Schmid law still governs twin variant selection, thereby controlling texture evolution, however, the specific crystallographic feature of {10-12} twinned region in which the c-axis orients to the compression direction with a variation of ±30° on the rolling plane and one prismatic plane including the rotation axis of {10-12} twinning, corresponding to an a-axis, is aligned almost parallel to the rolling plane gives rise to a significantly different texture evolution of {10-12}–{10-12} double twinned region as compared to {10-12} twinned region.

In Situ Neutron Diffraction Studies of Large Monotonic Deformations of Superelastic Nitinol

Superelastic Nitinol micromechanics are studied well into plastic deformation regimes using neutron diffraction. Insights are made into the nature of initial transformation, bulk transformation, plastic deformation, and unloading. Schmid factor predictions based on habit plane variants are found to best describe the very first grains that transform, prior to the transformation plateaus. However, the bulk transformation behavior that gives rise to transformation plateaus violates single crystal Schmid factor analyses, indicating that in bulk polycrystals, it is the effect of grain neighborhoods, not the orientations of individual grains, that drives transformation behaviors. Beyond the plateaus, a sudden shift in micromechanical deformation mechanisms is observed at ~8.50 %/4.75 % tension/compression engineering strain. This mechanism results in reverse-phase transformation in both cases, indicating a strong relaxation in internal stresses of the samples. It is inferred that this mechanism is most likely initial bulk plastic flow, and postulated that it is the reason for a transition from fatigue life enhancement to detriment when pre-straining superelastic Nitinol. The data presented in this work provide critical datasets for development and verification of both phenomenological internal variable-driven and micromechanical theories of transformation-plasticity coupling in shape memory alloys.

The beneficial effect of AgIn addition on deformation behavior, microstructure and texture in Mg–Al–Zn alloy during single pass warm rolling

Abstract In this study microstructure, texture and deformation behavior of Mg–3Al–1Zn (alloy-1) and Mg–3Al–1Zn–0.5AgIn (alloy-2) were investigated. The alloys were subjected to single pass thickness reductions of 30%, 50% and 60% at 300 °C (573 K) followed by annealing at 400 °C (673 K). Scanning electron microscopy (SEM), X-ray based macro-texture, transmission electron microscopy (TEM) and electron backscatter diffraction analysis (EBSD) were performed to investigate the effect of AgIn addition on deformation and annealing behavior. A silver-containing second phase in the form of fine precipitates was observed in alloy-2 during rolling which remained thermally stable during subsequent annealing. An ultrafine microstructure was observed for alloy-2 in comparison to alloy-1 after rolling. EBSD based Schmid factor (SF) analysis revealed a significant contribution of extension twinning, basal slip, pyramidal 〈 c + a 〉 slip and prismatic slip in alloy-2. In contrast, contraction twinning was the predominant deformation mode in alloy-1. The combined activity of larger number of deformation modes resulted in improved formability, refined microstructure and a weak deformation texture in alloy-2. The improved rolling response was mainly attributed to the combined contribution of multi deformation modes.

Slip systems and dislocation densities in individual grains of polycrystalline aggregates of plastically deformed CoTi and CoZr alloys

A novel X-ray diffraction-based technique for grain-by-grain assessment of dislocation density within polycrystals is applied. The technique discriminates dislocation densities of different slip modes, slip systems and dislocation character. Data which was formerly confined to the transmission electron microscope (TEM) is now available from X-ray diffraction (XRD). In addition, there is a profound statistical advantage of the XRD approach over the traditional TEM-based approach. Over 130 grains were analyzed for one sample of CoTi, which would be a Herculean task on the TEM, requiring dozens of samples as well as numerous hours on the microscope and analysis of the images generated for each sample. The present experiments were performed in about 30h per sample and the analysis is semi-automated, involving a Monte-Carlo-type algorithm to determine the dislocation structure best representing the single crystal diffraction peak profiles in a polycrystalline aggregate. Conclusive confirmation of a previously suggested explanation for the anomalous ductility of two CsCl structured intermetallic compounds, CoTi and CoZr, is provided: namely, that hard dislocation modes, with b=〈110〉 and 〈111〉, rarely observed in single crystal experiments, are active in nearly every grain. The results call into question the value of employing single crystal deformation experiments alone to understand the deformation behavior of polycrystalline materials. Further, the results re-emphasize that the uniform stress assumption implicit in Schmid factor analysis is a poor one for materials which are highly anisotropic at the single crystal level.

Effect of subsequent tension and annealing on microstructure evolution and strength enhancement of friction stir welded Mg alloys

Friction stir welded (FSW) Mg alloys normally exhibit a lower yield strength compared with the base materials, which is a drawback for their application as structure materials. In this study, subsequent tension along the transverse direction (TD) and then annealing were applied on FSW AZ31 alloys to modify the microstructure and texture in weld zone and to improve the joint strength. The results showed that by subsequent tension ~4.5% strain along TD and then annealing, the yield strength (YS) could be greatly enhanced for the FSW AZ31 alloys. Specifically the YS was improved from ~86 to ~177MPa by subsequent 4.5% tension and then reduced to ~156MPa after annealing. For the initial joint sample, fracture occurred in the stir zone (SZ) side during the transverse tensile test. But after subsequent tension, all the samples fractured in the base materials (BMs) whether subjected to annealing or not. The microstructure and texture evolutions after subsequent tension and annealing were examined by electron backscatter diffraction (EBSD) to understand the underlining mechanisms for the improved mechanical properties. It revealed that a lot of {10−12} extension twins were generated in the SZ side by 4.5% tension along TD, which significantly refined the grains in the SZ side and rotated the grains from soft to hard orientations for the transverse tensile test. Therefore, the formation of {10−12} twin lamellae had significant hardening effects on further transverse tensile tests. Schmid factor (SF) analysis revealed that the texture change by subsequent tension had much more impact on the activation of {10−12} extension twinning than basal slip for the transverse tensile test. This might affect the competition of extension twinning and basal slip and reduce the deformation incompatibility in the SZ side, which was beneficial for the improvement of mechanical properties. Nevertheless the present study showed that it was efficient to improve the YS of FSW Mg alloys by texture modification via subsequent tension and annealing.

Slip-induced texture evolution of rolled Mg–6Al–3Sn alloy during uniaxial tension along rolling and transverse directions

The microstructure and texture evolutions of a rolled Mg–6Al–3Sn (AT63) alloy were investigated during uniaxial tension along the rolling and transverse directions. Combination of experimental examination and Schmid factor analysis indicates that the texture evolution during the two tensions results mainly from dislocation slip. The texture variations in (0002) and (101̄0) poles are related to basal slip and non-basal slips, respectively. The final textures exhibit the lowest SF values not only for basal slip but also for non-basal slips. Our results will be helpful in the investigation of slip mechanism based on texture examination.

Observation and Schmid factor analysis of multiple twins in a warm-rolled Mg–3Al–1Zn alloy

This study aims to understand the features of twinning that occurred during warm-rolling of Mg–3Al–1Zn alloys. The rolling was performed at 150°C with the c-axis of most grains nearly parallel to the transverse direction. Electron backscatter diffraction analysis was conducted to examine microstructural evolution of the rolled sample. Multiple twins including {10−12} extension twin, {10−11} contraction twin, {10−11}–{10−12} and {10−12}–{10−11} double twins and {10−12}–{10−11}–{10−12} tertiary twins were observed in the rolled sample. These twins were present even in the same grain orientation. Based on the applied rolling deformation, an effective Schmid factor was calculated to understand the activation of twinning. Calculated Schmid factor maps were obtained as a function of (0001) pole. The activation of {10−12}–{10−11} double twin was explained by the statistical analysis of Schmid factors for primary {10−12} twin and secondary {10−11} twin.

Effect of microstructure on the uniaxial tensile deformation behavior of Mg–4Y–3RE alloy

This paper reports microstructure–mechanical property correlations for a Mg–4Y–3RE (WE43) alloy. Friction stir (FS) processing was employed to modify the microstructure of hot-rolled (as-received) WE43 alloy. The grain size decreased from 10 to 300µm in as-received condition to an average of 3.1±0.4µm in FS processed condition. The alloy in AR condition contained globular, acicular, and rectangular (cuboidal) shaped precipitates located at twin boundaries, grain boundaries, and intragranular regions, along with fine scale honeycomb network of intragranular β1 precipitates. A very good combination of strength and ductility was observed for the alloy tested in FS processed condition. Detailed fractography was done to differentiate mode of fracture between as-received and FS processed conditions. Based on Schmid factor analysis, it was concluded that basal slip system controlled the yielding of the material in both the conditions. An empirical relationship was developed between work hardening rate and ductility. This can be applied to microstructural design of magnesium alloys used for applications where high uniform ductility is needed.