Resolved Shear Stress For Slip Research Articles

Study on the plasticity enhancing mechanism of silver-based solid solution for electronic packaging

Ag-based solid solutions have gained significant attention in the electronic packaging field due to their remarkable plasticity. In this work, the generalized planar fault energy (GPFE), critical strength and stresses, and electronic properties after adding solutes with different types and size misfits were studied for Ag-based solid solutions. Furthermore, we explored the underlying mechanism behind the impact of solutes on the plasticity of Ag and confirmed it through transmission electron microscopy (TEM) and high-resolution TEM (HRTEM) analyses. Importantly, we introduced the novel concepts of size and chemical misfit factors, electronic factors, and twinning factor into the plasticity enhancement mechanism of Ag-based solution systems. The predictions based on these factors were in agreement with experimental observations using TEM and HRTEM. Remarkably, the (Ag)–Bi system exhibited the lowest critical resolved shear stress for slip and twinning, as well as the most superior plasticity, positioning it as a crucial candidate for future development. This study presents a scientific framework for designing and developing Ag-based solid solutions with excellent plasticity, encompassing size/chemical factors, electronic factors, and twinning factor.

Critical resolved shear stresses for slip and twinning in Mg-Y-Ca alloys and their effect on the ductility

The deformation mechanisms of an extruded Mg-5Y-0.08Ca (wt.%) alloy were analyzed by means of micropillar compression tests on single crystals along different orientations -selected to activate specific deformation modes- as well as slip trace analysis, transmission electron microscopy and transmission Kikuchi diffraction. The polycrystalline alloy presented a remarkable ductility in tension (∼32%) and negligible differences in the yield strength between tension and compression. It was found that the presence of Y and Ca in solid solution led to a huge increase in the CRSS for 〈a〉 basal slip (29 ± 5 MPa), 〈c + a〉 pyramidal slip (203 ± 7 MPa) and tensile twin nucleation (above 148 MPa), while the CRSS for 〈a〉 prismatic slip only increases up to 105 ± 4 MPa. The changes in the CRSS for slip and tensile twinning in Mg-Y-Ca alloys expectedly modify the dominant deformation mechanisms in polycrystals. In particular, tensile twinning is replaced by 〈a〉 prismatic slip during compressive deformation along the a-axis. The reduction of twinning (which generally induces strong anisotropy in the plastic deformation in textured alloys), and the activation of 〈a〉 prismatic slip (which provides an additional plastic deformation mechanism with limited hardening) were responsible for the large tensile ductility of the alloy.

Microstructural factors dictating the initial plastic deformation behavior of an ultrafine-grained Fe–22Mn-0.6C TWIP steel

While leading a great strain hardening capability, carbon-containing twinning-induced plasticity (TWIP) steels exhibit serrations on their stress-strain curves, resulting in barriers to commercial development. Although grain refinement is believed to suppress the serrations, how the grain size, particularly in the ultrafine-grained (UFG) range, and its orientation impacting on the serrations and plastic deformation mechanism are overlooked. Here, we compared the plastic deformation behavior in fine-grained (2 μm) and ultrafine-grained (0.86 μm) specimens, in both macroscopic and microscopic behavior, using digital image correlation (DIC) and scanning transmission and transmission electron microscopy (S/TEM) techniques. Our results showed that the dominant plastic deformation mode was changed from dislocation gliding and tangling to stacking faults and deformation twinning in the grains equal to or smaller than 1 μm (ultrafine grains). This alteration is also strongly influenced by the grain orientation, i.e., the maximum resolved shear stress for slip versus twinning. The enhancement of strain localization and the inhibition of the serrations in the UFG specimens are discussed.

A study on slip activation for a coarse-grained and single crystalline CoCrNi medium entropy alloy

The new CoCrNi medium entropy alloy (MEA) has emerged to be one of the most promising systems which provide extraordinary ductility and strength at cryogenic temperatures. In this study, utilizing both polycrystalline and single crystal specimens, as well as advanced optical strain measurements, the deformation mechanisms dictating the mechanical behavior at the onset of plasticity were detected and precisely quantified. Independent of deformation temperature, the accumulation of permanent strains at the microstructural level was attributed to plastic slip at the onset of yielding and at low levels of deformation (<10%). The resolved shear stress for slip activation was measured to be 78 MPa at 298 K and between 140 MPa and 160 MPa at 77 K. These unique measurements were used to provide an estimate of the temperature dependent resolved shear stress for slip at temperatures ranging from 77 K to 575 K. In addition, strain heterogeneities at the grain-scale were measured to study the nucleation of slip at the micro-scale in polycrystalline specimens. In summary, the present study aims to quantitatively assess the accumulation of plastic strain and reveal the underlying deformation mechanisms (i.e., slip or/twinning) leading to the buildup of plastic strains at the microstructural level.

Anomalous size-dependent strength in micropillar compression deformation of commercial-purity aluminum single-crystals

An anomalously reduced size-dependent strength of commercial-purity aluminum (Al) single-crystal micropillars with diameters ranging approximately from 1 to 10 μm is reported. High-purity Al (99.99%) single-crystal micropillars exhibited an obvious size dependence of the resolved shear stress for slip. The measured shear stress resolved onto a primary slip system (τi) scaled by the shear modulus (G) and the pillar diameter (d) scaled by the Burgers vector (b) showed the following correlation: τi/G = 0.33(d/b)−0.63, which agreed well with previous works. However, the commercial-purity Al samples exhibited a lower power-law exponent (0.19) for their size-dependent strength, resulting in (τi/G) = 0.006(d/b)−0.19. TEM characterization revealed the local presence of Al–Fe intermetallic precipitates surrounded by relatively high-density dislocations in annealed commercial-purity Al samples. These results indicate the relatively high-density dislocations could be responsible for the reduced size-dependent strength, which was confirmed by the remarkably reduced size dependence of their resolved shear stress by prior cold rolling. The reduced size-dependent strength can be rationalized using the stochastic model of the dislocation source length. Thus, this study provides a new insight to allow the application of the micropillar compression test to commercially produced Al alloys.

Theoretical evaluation of solid solution interaction in Fex(CoCrMnNi)100-x medium- and high-entropy alloys

Solid solution interaction in medium- and high-entropy of Fex(CoCrMnNi)100-x (x = 20, 40, 50, and 60 at. %) alloys was evaluated theoretically. The different Fe contents were found to affect the yield strength (σy) of the Fex(CoCrMnNi)100-x system, with higher Fe content leading to reduced σy. The focus of this study was to investigate, using various theoretical approaches, the effect of different Fe contents on the solid solution interaction in the Fex(CoCrMnNi)100-x system. The theoretical approaches demonstrated a decreasing atomic size misfit with increasing Fe content, which reduced lattice distortion. The critical resolved shear stress for slip to occur also decreased with increasing Fe content, leading to the least solid solution contribution with higher Fe content in the Fex(CoCrMnNi)100-x system. The solid solution interaction of the Fex(CoCrMnNi)100-x system at lower temperature was also observed, showing good agreement with the reresults obtained at room temperature.

Deformation and spallation of shock-loaded graphene: Effects of orientation and grain boundary

We perform molecular dynamic simulations to investigate the effects of orientation and grain boundary (GB) on shock response of graphene, including shock-induced slip and spall. For compression under different loading orientations, the critical resolved shear stress for slip is constant along a given growth direction (armchair or zigzag) in single-crystal graphene, and spall initiates in elastically deformed graphene via tension-induced debonding. For bicrystal graphene, the locations of compression-induced slip and initial spall are influenced by preexisting stress field at GB and the interactions between GB and shock waves, respectively. Both of these two factors are related to GB structure, including the density of pentagon-heptagon pairs at GB. However, bicrystals show negligible anisotropy in shock-compression response. For polycrystalline graphene at high shock strength, slips initiate at GBs and triple junctions under shock compression, develop along GBs or toward grain interior, and serve as nucleation sites for spall damage.

Orientation dependence of twinning in single crystalline CoCrFeMnNi high-entropy alloy

Tensile deformation behavior of the equiatomic CoCrFeMnNi high entropy alloy single crystals were studied along three different crystallographic orientations, i.e. [001], [1¯23], [1¯11], in order to reveal the orientation dependence of deformation twinning at room temperature. It was shown that initial yield behavior along these orientations is governed by dislocation slip mechanism and the critical resolved shear stresses for slip are independent of crystal orientation. Twinning starts at different strain levels after slip deformation, depending on the tensile testing orientation: in the [1¯11]-oriented crystals, twinning starts after 5% strain while in the [1¯23]-oriented crystals, it starts after about 25% strain. Deformation twinning was not detected in the [001]-oriented crystals under tensile loading. The critical resolved shear stresses for twinning are determined to be τcrtw = 110–140MPa. Onset of deformation twinning in the [1¯11]-oriented crystals at low strain levels, together with multiple active dislocation slip systems, leads to a significantly higher strain hardening coefficient and stress for fracture in comparison with the [001]-oriented crystals, where the plastic deformation occurs only by multiple slip systems, and the [1¯23]-oriented crystals, in which the deformation mainly occurs by single slip and then twinning in one system at later stages of the deformation.

The dynamic compressive response of a high-strength magnesium alloy and its nanocomposite

The dynamic compressive mechanical properties of the alloy Mg-4Zn-3Gd-1Ca (wt%) and its nanocomposite Mg4Zn3Gd1Ca-2ZnO were investigated at strain rates up to 1×103s−1, using a Split Hopkinson Pressure Bar (SHPB) tester. Under dynamic loading, the addition of 2wt% ZnO nanoparticles into the alloy generated a significant strength increase (~100MPa), attributed largely to grain refinement. Negative strain rate sensitivity of the alloy and its nanocomposite was observed. It is postulated that the strengthening influence of the nanoparticles by retarding twin nucleation/growth at grain boundaries, is significantly weakened as strain rate increases. The yield stress of the materials studied follows the Hall-Petch relationship even when the grain size is less than 1µm. It is proposed that the strong solute strengthening from Gd and Ca enhances the critical resolved shear stress for slip and preserves tension twinning as the dominant deformation mechanism for yielding.

Critical resolved shear stress for slip and twin nucleation in single crystalline FeNiCoCrMn high entropy alloy

High entropy alloys is an emerging class of materials with superior mechanical properties down to cryogenic temperatures. At 77K, and unlike traditional metallic alloys, an increase in strength, strain hardening rate, and ductility has been reported. This enhancement in properties has been attributed to the activation of twinning as an additional deformation mechanism at low deformation temperatures. The tendency for the formation of twinning and the hardening response dependence on crystal orientation has not been fully explored. This study is dedicated to explore the deformation evolution across several crystal orientations for the equiatomic FeNiCoCrMn high entropy alloy at room temperature (RT) and 77K. The works aims to establish the critical resolved shear stresses (CRSS) for slip and twinning and study the orientation and temperature dependence in these magnitudes. The experimental results have revealed a strong temperature dependence in the CRSS for slip, increasing from 56MPa at RT to 153MPa at 77K, with negligible orientation dependence. At 77K, not all crystal orientations developed twinning even at high levels of deformation. The lack of twinning has been attributed to differences in the hardening response resulting in low stress levels below the twinning CRSS of 153MPa, as established in this work. No twinning was observed in any of the crystal orientations deformed at room temperature, regardless of the level of hardening and the achieved stresses. Overall, the results discussed in this work enhances our understanding of the local deformation response in single crystalline FeNiCoCrMn high entropy alloy, particularly the nucleation of slip, nucleation of twinning, and the effect of crystal orientation and loading temperature on these deformation mechanisms.

Nanostructured extension twins in rapidly compressed Mg–3.0Al–1.0Zn alloy

Magnesium alloy components are potentially subjected to dynamic strain rate loading. High strain rate usually results in a mechanical behavior quite different from that under quasi-static loading. In the present study, twin characteristics were investigated in Mg–3.0Al–1.0Zn (AZ31B) alloy compressed at dynamic strain rate of 8.0×10−1s−1. In addition to large extension twins, nanostructured lamella extension twins were found in a large number in the matrix. The reason that such nanostructured twins co-exist with large twins was explained in terms of comparison between dislocation and twinning dynamics, i.e., due to the high strain rate, the dynamic critical resolved shear stress for slip could be so high as to result in a viscous drag and the abundant occurrence of the rapid shear of the extension twinning should be needed in widely oriented grains to accommodate strain.

Role of glide systems in channel die compression of commercially pure titanium alloy

Plastic deformation process of Ti alloys depends on the competition of active deformation modes: slip and twinning. The specific deformation mechanism depends on the availability of the specific deformation modes as well as on the critical resolved shear stress for slip and the twin activation stress. Effort has been made to provide information on the different slip systems other than prismatic slips, which get activated during the channel die compression process. It is found that, though at the initial stage of deformation, prismatic slip is prevalent, but other slip systems, especially pyramidal types, also appear at the later stage of deformation. Transmission electron microscopy results confirm the presence of pyramidal slips beside prismatic ones. It is also observed that twining does not take place in those grains having the most stable orientation as per the hexagonal close packed system. Information on the critical resolved shear stresses of different glide systems for T40 is also provided.

Effective values of critical resolved shear stress for slip in polycrystalline magnesium and other hcp metals

Critical resolved shear stresses (CRSSs) for slip on different types of slip systems in single-crystal hexagonal close-packed metals show very wide variations. Values derived from measurements and modelling on polycrystals show much less variability and there is often evidence for activation of “hard” slip modes from dislocation observations in transmission electron microscopy. We show that this discrepancy originates in the hardening processes that take place in polycrystals, which must be treated as a term that is additive to the true CRSS.

Strain heterogeneity in deformed Carrara marble using a microscale strain mapping technique

Using high‐resolution surface imaging and a split‐cylinder technique, we mapped the strain heterogeneity in Carrara marble samples deformed to bulk strains &lt;25%, under conventional triaxial loading, at 400–700°C, 300 MPa confining pressure, and strain rates of 10−4 to 10−5 s−1. To map strain, we deposited grid markers on the polished surface of a half cylinder, performed mechanical tests on composites of two half cylinders, compared the positions of each marker in undeformed and deformed samples, and computed the spatial distribution of strain. Strains over the scale of a few microns varied by as much as 300%. Localized deformation occurred along twins and grain boundaries but was also present as patches in intragranular regions. The heterogeneity is more pronounced at scales smaller than grains, but the strain averaged over individual grains also varied by 50%. After deformation, the crystallographic orientation of individual grains relative to the compression direction was measured by electron backscattered diffraction. Inverse pole figures of the aggregate lattice‐preferred orientation (LPO) have a maximum near e(018) and are consistent with previous studies. The observed LPO is qualitatively consistent with that produced by simulations using a simple viscoplastic self‐consistent (VPSC) code that did not include mechanisms other than slip or twinning. The qualitative comparison of observed and simulated LPO was not sensitive to the model for the crystallographic resolved shear stresses for slip. However, the VPSC simulation was ineffective in predicting individual grain rotations.

The Relationship between Activation Parameters and Dislocation Glide in 4H-SiC Single Crystals

4H-SiC single crystals were deformed by compression in the temperature range 550 to 1300 °C and a strain rate range of 3.1 × 10–5 to 6.5 × 10–4 s–1 to determine the critical resolved shear stress for slip on the 〈 2-1-10〉(0001) primary slip system. Two different methods to determine the activation parameters for dislocation glide were examined. In the first method, where the activation enthalpy for dislocation glide ΔHg is assumed to be a function of the applied stress τ, ΔHg drops from ∼7.4 eV at τ ≈ 8 MPa to ∼2.8 eV at τ ≈ 235 MPa. In the second method, where the activation enthalpy for dislocation glide, Q, is assumed to be stress-independent, the values determined at strain rates of less than 6.3 × 10–5 s–1 were Q ≈ (2.1 ± 0.7) eV at low temperatures (T 1100 °C). Transmission electron microscopy investigations of the deformed samples show that very different configurations of dislocations are activated under the action of the applied stress. At 1300 °C, the dislocations were all perfect, albeit dissociated into leading/trailing partials separated by a ribbon of stacking fault, while at 700 °C only single leading partials, each dragging a stacking fault and without their corresponding trailing partials, were observed.

Texture, hardening and mechanical anisotropy in A.A. 8090-T851 plate

An evaluation is made of the effect of preferred crystallographic orientations on the dislocations locking mechanisms underlying the macroscopic yield strength of a 8090-T851 Al-Li alloy plate. The interplay between dislocations-related strengthening mechanisms and textures is made via the Taylor factor for the critical resolved shear stress for slip. By this way, each microstructural contribution to the strengthening (precipitates, solid solution, grain boundaries), independently determined from textures, is projected into a specific direction, with reference to the rolling direction, by multiplying it for the Taylor factor. This one is computed by means of the popLa software package, analysing experimental texture data obtained by X-ray diffraction. The prediction of the strength anisotropy in the 8090-T851 textured alloys is then carried out. Finally, the normal plastic anisotropy of the alloy is investigated experimentally and by means of polycrystal plasticity calculations, pointing out its dependence on the crystallographic textures.

Yield surfaces of b.c.c. crystals for slip on the {110} 〈111〉 and {112} 〈111〉 systems

The single crystal yield surfaces (SCYS) for slip in b.c.c. metals on either {112} 〈111〉 or mixed slip on {112} 〈111〉 and {110} 〈111〉 have been derived. In particular, for the general case of mixed slip, the SCYS is described in terms of ξ, the ratio of the critical resolved shear stresses for slip on the {112} 〈111〉 and {110} 〈111〉 systems. All the possible types of yield vertices are tabulated and classified into crystallographically non-equivalent groups. It is confirmed that there is a limited range of ξ for mixed slip: √ 3 2 ⩽ξ⩽ 2 √3 . Within this range, there are only two different SCYS configurations, depending on whether ξ is greater or smaller than 5 3 √3 . Each of these configurations has 15 groups of vertices and 216 stress states (plus their negatives). The two yield surfaces only differ with respect to 3 of the groups of vertices (72 stress states). The evolution of these vertices near the critical ξ value of 5 3 √3 is described in detail. The mixed slip vertices activate 5, 6 or 8 slip systems depending on the basic group to which they belong. In the vast majority of cases, only 5 slip systems are activated so that, by allowing mixed {110}, {112} glide, the slip ambiguity problem characteristic of {110} 〈111〉 restricted glide is substantially reduced.

Yield strength of MgO to 40 GPa

Using the diamond cell, we have measured the quasi‐static yield strength of polycrystalline and single‐crystal MgO to 40 GPa at room temperature. In contrast to previous studies we find that the yield strength is pressure dependent, increasing from 1.1 GPa at 10 GPa to 4.0 GPa at 40 GPa for polycrystalline samples subjected to small strains. This increase is an order of magnitude larger than the change in the shear modulus over the same pressure range. At 20 GPa the critical resolved shear stress for slip on the system is less than 0.2 GPa, while for slip it is greater than 1.9 GPa. We infer that the critical shear stress is relatively small and independent of pressure. We observe a large variability in the strength of polycrystalline samples depending on the amount of strain achieved in the diamond cell. Samples subjected to large strains are weakest, and they show evidence of a preferred orientation that allows slip on the weak system.

The plastic deformation of potassium single crystals at low temperatures

The yield stress of potassium single crystals was measured in the temperature range of 1.5 to 30 K for a wide range of orientations. The effects of nobs itutional solutes (sodium and rubidium) on the yield strength of potassium single crystals were also investigated. The Schmid law of critical resolved shear stress for slip is invalkid in the temperature-dependent region of yield stress, and the orientation dependence of yield stress is in agreement with the Peierls mechanism for screw dislocation motion. The validity of the Schmid law may be questionable even in the athermal region, as suggested by the observations at 30K. Alloy softening is observed in the temperature-dependent region of yield stress by adding substitutional solutes to potassium.

HARDENING MECHANISMS OF IONIC CRYSTALS ON {110} AND {100} SLIP PLANES

Ionic crystals of the NaCl structure can be deformed on several non-equivalent crystallographic planes. The hardness varies with the type of slip system. This plastic anisotropy depends on temperature, divalent doping and ionicity of the material as is shown by measurements of the critical resolved shear stress for slip on {110} and {100} planes. For a series of NaCl-type crystals hardening mechanisms are discussed based on Peierls and dislocation-solute interactions. The plastic anisotropy is of substantial help in the analysis of these interactions.