Maximum Schmid Factor Research Articles

{332}〈113〉 Twinning system selection in a β-type Ti–15Mo–5Zr polycrystalline alloy

The orientational dependence of {332}〈113〉 twinning and its system was examined in a 4.0% tensile-strained Ti–15Mo–5Zr (mass%) polycrystalline alloy by electron backscatter diffraction analysis combined with Schmid factor analysis. Twinning and system selections were found to obey the Schmid law in grains with tensile axes close to the [1̄11] and [001] directions, in which the maximum Schmid factors of an easily operative (233)[3̄11] twinning system were larger than 0.46 and smaller than 0.34, respectively. However, when the maximum Schmid factor ranged from 0.34 to 0.46, both selections became complex and not entirely explainable by the Schmid law around the center of a stereographic triangle. Twinning systems other than (233)[3̄11] were also activated in grains with a Schmid factor even below 0.1 and inside twins with a negative Schmid factor. We conclude that additional factors, specifically local stress concentrations and geometric constraints between neighboring grains, should also be considered in regard to {332}〈113〉 twin formation, even in a polycrystalline β-titanium alloy that has been only slightly deformed.

Influence of the crystalline orientations on microcrack initiation in low-cycle fatigue

Present study aims at analyzing the crack initiation in an austenitic stainless steel in low-cycle fatigue. A fatigue test was carried out using a polished specimen. The surface of the specimen was observed in situ during the fatigue test, in order to establish the time of slip activity or crack initiation. After a number of cycles sufficient to initiate small cracks, the test was stopped and the surface observed by scanning electron microscopy. The electron backscattered diffraction technique (EBSD) was used to identify the orientations of surface grains in the central zone of the fatigue specimen. Crack-initiation sites and slip systems associated to the initiated microcracks were identified. The criterion of the maximum Schmid factor explains two-thirds of the cracks initiated in slip systems; however if the favorably oriented slip band with respect to this criterion makes an angle of around 45° to the loading direction, a crack may initiate in another slip system.

Deformation and damage behavior of colonies in a small-sized α/β Ti alloy

The mechanical behavior of small-sized Ti alloy containing only a few colonies is expected to be different from that of its bulk counterpart. Here, we found that depending on the relation between the geometrical and colony scales of the small-sized Ti alloy, fracture did not always occur preferentially in the colony with the maximum Schmid factor. The proposed model suggests that the local strain level in the colony is a dominant factor.

Effect of Grain Rotation on the Strain-Softening Behavior in Nanocrystalline Materials

We postulated a softening model involving grain rotation that results in diffusion-accommodated grain-boundary sliding. This numerical model was used to compute the proportion evolution of grains within shear bands and was also employed to predict the softening of nanocrystalline materials considering non-homogeneous plastic deformation due to shear bands. The effect of softening mechanism for total stress-strain relation and the grain size and mean maximum Schmid factor effect was also considered in our model.

Grain rotation dependent non-homogeneous deformation behavior in nanocrystalline materials

Many experimental observations have indicated a transition from homogeneous to non-homogeneous plastic deformation on nanocrystalline materials. Based on a grain rotation theory of diffusion-accommodated grain-boundary sliding, a new phase mixture model was developed to predict the softening of nanocrystalline materials considering non-homogeneous plastic deformation due to shear bands subjected to quasi-static rates of loading. In this phase mixture model, nanocrystalline materials were treated as composites consisting of grain interior and grain boundary phases. Grain interior phase was divided into soft-grain interior part with soft orientation and hard-grain interior part with hard orientation. The grain rotation rate driving force for grain rotation was derived from energy considerations, including the dissipation induced by mass diffusion and that by GB sliding viscosity. The model predicts the effect of softening mechanism for total stress–strain relation; the grain size and mean maximum Schmid factor effect was considered in the phase mixture model. Further discussion was presented for calculation results and relative experimented observations.

Angular Distribution of Slip Steps by Three-Dimensional Polycrystalline Model for Stainless Steel

Localized deformation plays an important role in the initiation of irradiation-assisted stress corrosion cracking, and it can be characterized by the spacing and inclination of slip steps observed on the surface. In order to examine the contribution of mechanical factors (stress) to slipping, the angular distribution of slip steps was evaluated by using a three-dimensional polycrystalline model generated by Voronoi tessellation. An elastic finite element analysis was performed to derive the resolved shear stress (RSS) acting on each slip system. Random crystallographic orientations assigned to each grain caused the microstructural inhomogeneity of local stress due to anisotropic elastic properties. The angular distribution obtained was compared with the experimental results observed in irradiated and deformed stainless steel. It was shown that mechanical factors dominate the slipping behavior of the irradiated stainless steel and that not only RSS but also normal stress acting on the slip plane affects the crystallographic slip. The angular distribution was also evaluated from the maximum Schmid factor of individual grains, in which the inhomogeneous local stress was not taken into account. The angular distributions obtained using RSS and the Schmid factor were almost the same. This suggests that the inhomogeneity of local stress negligibly affects the angular distribution of slip steps, although the change in the local stress in the polycrystalline material is significant.

Angular Distribution of Slip Steps by Three-Dimensional Polycrystalline Model for Stainless Steel

Localized deformation plays an important role in the initiation of irradiation-assisted stress corrosion cracking, and it can be characterized by the spacing and inclination of slip steps observed on the surface. In order to examine the contribution of mechanical factors (stress) to slipping, the angular distribution of slip steps was evaluated by using a three-dimensional polycrystalline model generated by Voronoi tessellation. An elastic finite element analysis was performed to derive the resolved shear stress (RSS) acting on each slip system. Random crystallographic orientations assigned to each grain caused the microstructural inhomogeneity of local stress due to anisotropic elastic properties. The angular distribution obtained was compared with the experimental results observed in irradiated and deformed stainless steel. It was shown that mechanical factors dominate the slipping behavior of the irradiated stainless steel and that not only RSS but also normal stress acting on the slip plane affects the crystallographic slip. The angular distribution was also evaluated from the maximum Schmid factor of individual grains, in which the inhomogeneous local stress was not taken into account. The angular distributions obtained using RSS and the Schmid factor were almost the same. This suggests that the inhomogeneity of local stress negligibly affects the angular distribution of slip steps, although the change in the local stress in the polycrystalline material is significant.

Breakdown of Schmid’s law in micropillars

The validity of Schmid’s law in micropillar samples is assessed by a simulation scheme in which the critical stress to operate a slip system is determined by the free lengths of dislocations pinned by intersection points imposed by dislocations lying on other slip planes. At fixed dislocation density, yielding occurs predominantly on the slip system with the maximum Schmid factor when the sample size is large, but as the sample size reduces, other slip systems have an increasing probability of operating.

Fatigue Damage Mechanism of Nanocrystals in ECAP-Processed Copper Investigated by EBSD and AFM Hybrid Methods

Electron backscattering diffraction, EBSD, technique as well as atomic force microscopy, AFM, was employed to investigate fatigue damage mechanism in ultrafine-grained copper processed by equal channel angular pressing, ECAP. The fatigue damage evolution under axial tension compression was investigated. The results show that linearly shaped fatigue damage was introduced in the scale of micrometers in spite of the average grain size of 300 nm. The linear damage was randomly oriented when the shear direction of the last ECAP-pressing in perpendicular to the loading axis. The orientation analysis by EBSD revealed that the linear damage is introduced in the area with the same crystallographic orientation in the direction of the maximum Schmid factor as in the slip deformation in coarse-grained materials. The comparison before and after fatigue tests shows the grain coarsening in the area where large linear fatigue damage was formed. It is considered that strain concentration at the edge of the slips introduced in a relatively coarse ultrafine grain causes the grain rotation and deformation in the adjacent nano-sized grains, resulting in the grain coarsening and subsequent propagation of the slips in the order of micrometers.

Dislocation nucleation in Σ3 asymmetric tilt grain boundaries

Atomistic simulations were used to investigate dislocation nucleation from Σ3 asymmetric (inclined) tilt grain boundaries under uniaxial tension applied perpendicular to the boundary. Molecular dynamics was employed based on embedded atom method potentials for Cu and Al at 10 K and 300 K. Results include the grain boundary structure and energy, along with mechanical properties and mechanisms associated with dislocation nucleation from these Σ3 boundaries. The stress and work required for dislocation nucleation were calculated along with elastic stiffness of the bicrystal configurations, exploring the change in response as a function of inclination angle. Analyses of dislocation nucleation mechanisms for asymmetric Σ3 boundaries in Cu show that dislocation nucleation is preceded by dislocation dissociation from the boundary. Then, dislocations preferentially nucleate in only one crystal on the maximum Schmid factor slip plane(s) for that crystal. However, this crystal is not simply predicted based on either the Schmid or non-Schmid factors. The synthesis of these results provides a better understanding of the dislocation nucleation process in these faceted, dissociated grain boundaries.

Effet de l'anisotropie élastique cristalline sur la distribution des facteurs de Schmid à la surface des polycristaux

Experimental studies of the plasticity mechanisms of polycrystals are usually based on the Schmid factor distribution supposing crystalline elasticity isotropy. A numerical evaluation of the effect of crystalline elasticity anisotropy on the apparent Schmid factor distribution at the free surface of polycrystals is presented. Cubic elasticity is considered. Order II stresses (averaged on all grains with the same crystallographic orientation) as well as variations between averages computed on grains with the same crystallographic orientation but with different neighbour grains are computed. The Finite Element Method is used. Commonly studied metals presenting an increasing anisotropy degree are considered (aluminium, nickel, austenite, copper). Concerning order II stresses in strongly anisotropic metals, the apparent Schmid factor distribution is drifted towards small Schmid factor values (the maximum Schmid factor is equal to 0.43 instead of 0.5) and the slip activation order between characteristic orientations of the crystallographic standard triangle is modified. The computed square deviations of the stresses averaged on grains with the same crystallographic orientation but with different neighbour grains are a bit higher than the second order ones (inter-orientation scatter). Our numerical evaluations agree quantitatively with several observations and measures of the literature concerning stress and strain distribution in copper and austenite polycrystals submitted to low amplitude loadings. Hopefully, the given apparent Schmid factor distributions could help to better understand the observations of the plasticity mechanisms taking place at the free surface of polycrystals. To cite this article: M. Sauzay, C. R. Mecanique 334 (2006).

Deformation twinning in polycrystalline Zr: Insights from electron backscattered diffraction characterization

The response of polycrystalline α-zirconium to various deformation conditions was investigated through electron backscattered diffraction (EBSD) characterization. The range of deformation conditions included quasi-static compression and tension at room and cryogenic temperatures, along with a Taylor cylinder impact experiment. The resultant data provided spatial resolution of individual with system activity as a function of the progression of deformation. Over 300 deformation twins were analyzed to identify the type of twin system and active variant, along with the Schmid factor in the parent orientation. These data supplied information on the distribution of Schmid factor and variant rank as a function of twin system and deformation condition. Results showed significant deviation from a maximum Schmid factor activation criterion and suggest deformation twinning is greatly affected by local internal stress heterogeneities and the sense of the applied stress.

Development of microbands in mild steel during cross loading

Mild steel specimens are submitted to a complex strain path (tension-shear sequence). The stress decrease recorded at the beginning of the second path is associated at the grain scale with a localization of the deformation in microbands. These microbands are associated with a single crystallographic slip system and carry the main part of the imposed strain. The prediction of the active slip systems during both the prestrain and the second path with the Taylor and static models leads to a necessary condition for the development of microbands: the slip system having the maximum Schmid factor must have been latent during the prestrain. At high strain level, the material resumes strain hardening and the dislocation structure is then composed of sheets parallel and/or perpendicular to the shear direction. The origin of the flow localization and the transition between the two types of structures, i.e. microbands and dislocation sheets, are then discussed.

Direct observation of dislocation emission from crack tips in silicon at high temperatures

The emission of dislocations from crack tips in silicon under combined conditions of temperature and stress is observed in situ at 550–750°C, using transmission electron microscopy. The generation and motion of 1 2 [11̄0] shear dislocation loops on (111) planes, corresponding to those having the maximum Schmid factor, occurs in both mode I and mode III cases. Estimation of the emission condition is made based on the observed dislocation mobility and resultant distribution of dislocations around the crack tip. The difference in the values of K 1 = 0.94 ± 0.06 MPa m 1 2 and K m = 0.17± 0.03 MPa m 1 2 for dislocation emission is attributed to Schmid factor differences and ledge energy effects. Substituting the estimated stress intensity, resolved on to the dislocation emission glide plane, into the Rice-Thomson energy analysis indicates that spontaneous dislocation emission occurs without a nucleation barrier. A value for the lattice friction stress of ~ 110 MPa is deduced from the positions around the crack tips that the dislocations adopt after emission. In a modification of the Rice-Thomson energy analysis, the lattice friction stress is shown to influence the nucleation and growth to a stable size of a dislocation loop emitted from a crack tip.

Slip dislocation propagation in In-doped liquid encapsulated Czochralski GaAs during crystal growth

A propagation rule was studied for two types of slip dislocations arising during crystal growth. In order to specify the dislocation distribution revealed by x-ray topography, we considered the relationship among the slip system, thermal gradient, and stress field. One type of slip dislocation was found to propagate on slip systems having a maximum Schmid factor in a uniform radial stress field, while another well known type occurred in a tangential stress field. It was concluded that different slip systems can be activated by specific stress fields caused by different thermal gradients under various growth conditions.

CYCLIC DEFORMATION OF A1‐4%Cu ALLOY POLYCRYSTALS CONTAINING θ″ PRECIPITATES

AbstractThe cyclic deformation of polycrystalline A1‐4%Cu alloy containing θ precipitates was investigated by strain controlled tests, and compared to monocrystalline cyclic behavior. The cyclic deformation of the polycrystals was found to depend on the grain size, and in coarse‐grained material (grain diameter = 1 mm) a definite plateau was observed in the cyclic stress‐strain (CSS) curve. In order to explore the relationship of cyclic behavior between single crystals and polycrystals, three available orientation factors were examined. This relationship can be interpreted by selection from the different types of orientation factors (Taylor factor, Sachs factor and Maximum Schmid factor), which operate to different degrees depending on the magnitude of the strain amplitude and the grain size.

Dislocation Generation in the Initiation of Fractures in Silicon Crystals

Notched silicon crystals were deformed in tension at elevated temperatures, and the incipient microplasticity associated with the notch was studied by in-situ X-ray topographic observation. Above a stress level of about 2 kg/mm2 at 700°C, a plastic zone was formed around the notch tip, accompanied by long-range elastic strain. Dislocations were generated on the slip planes parallel to the tensile axis by the operation of a bending moment induced around the notch tip mainly by the activity of two slip systems with the maximum Schmid factor, and the crack propagation is considered to break out as a result.

α-黄銅単結晶および双結晶の応力腐食割れ

Stress corrosion cracking (SCC) of α-brass single and bicrystals in an ammoniacal atmosphere was examined with regard to applied stress, the orientation of the tensile axis and the misorientation of grain boundary. The results obtained are as follows:(1) The time to fracture of single crystals decreased with the increase of applied stress. The specimens of a larger Schmid factor fractured more rapidly than the specimens of a smaller Schmid factor under the same applied stress.(2) The shear stress in the slip direction on a slip plane more remarkably affected the time to fracture than that normal to a slip plane did. This means that SCC of single crystals occurs by slipping at the tip of crack.(3) As far as single crystals are concerned the crackings occurred in general along (111) traces having a maximum Schmid factor, but the crackings were also observed along the traces of secondary slip planes and cross slips when the applied stress became higher.(4) In bicrystals, fracture occurred generally in the grains when tilt and twist angles of grain boundaries were small, and at grain boundaries when these angles were large. In some bicrystals, however, fracture occurred in grains or at grain boundaries regardless of the degree of the misorientation of grain boundaries.

Si単結晶のひっかき条痕部の転位組織

The present paper deals with the formation mechanism of dislocations by the scratch deformation. (111) single crystal of Si is scratch-deformed by a diamond stylus along [\bar101] and [1\bar21] directions at room and liquid nitrogen temperatures. Thin foils for transmission electron microscope observations were made by thinning down the scratched specimen only from the back side through the jet chemical polishing.The results obtained are as follows: The specimen scratch-deformed at −196°C has less dislocation density than that deformed at room temperature and dislocations have the tendency to align in a certain crystallographic direction by lower temperature deformation. The dislocation half loops observed at the scratched part at −196°C lie on {111} slip planes and have the Burgers vector of a⁄2〈110〉 which is consistent with the direction of the maximum Schmid factor by the scratch deformation. These dislocations are supposed to be induced by slip deformation due to the local excess shear stress during the scratching.

Orientation dependence of yield stress in 4.4% silicon iron single crystals

Single crystals of a 4.4%Si-Fe with systematically selected orientations were deformed in tension or compression at room temperature. Slip bands were observed to be nearly parallel to traces of either {110} or {112} plane in most specimens. Two anomalous results were obtained on orientation dependence of yield stress. First, the Schmid law did not hold for the {110}〈111〉 slip system, that is, the critical resolved shear stress increased as the plane of maximum Schmid factor deviated from the {110} plane towards the neighbouring {112} cross slip plane. This is discussed in relation to differences in the dragging stress for the motion of screw dislocations due to differences in the density of jogs which were produced by cross slip. The difference in density of dragging points among specimens with different stress axes was, in fact, observed by electron microscopy using thin foils parallel to slip planes. Secondly, the critical resolved shear stress for a {112}〈111〉 slip in the twinning shear direction was about 13% lower than that in the opposite direction. This fact is tentatively attributed to different Peierls -Nabarro stress between the two opposite senses of motion of a dislocation on a {112} plane.