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The derivation of CRSS in pure Ti and Ti-Al alloys

The work focuses on the determination of the critical resolved shear stress (CRSS) in titanium (Ti) and titanium-aluminum (Ti-Al) alloys, influenced by an array of factors such as non-symmetric fault energies and minimum energy paths, dislocation core-widths, short-range order (SRO) effects which alter the local atomic environment, and tension-compression (T-C) asymmetry affected by intermittent slip motion. To address these multifaceted complexities, an advanced theory has been developed, offering an in-depth understanding of the mechanisms underlying slip behavior. The active slip systems in these materials are basal, prismatic, and pyramidal planes, with the latter involving both $\langle$a$\rangle$ and $\langle$c + a$\rangle$ dislocations. Each slip system is characterized by distinct Wigner-Seitz cell configurations for misfit energy calculations, varying partial dislocation separation distances, and unique dislocation trajectories—all critical to precise CRSS calculations. The theoretical CRSS results were validated against a comprehensive range of experimental data, demonstrating a strong agreement and underscoring the model's efficacy.

Critical stress

The correlation between the temperature dependence of the CRSS and the formation of superlattice-intrinsic stacking faults in the nickel-base superalloy PWA 1480

The PWA 1480 nickel-base superalloy is known to exhibit a unique minimum in the critical resolved shear stress (CRSS) at about 400 C. This paper reports an observation of a deformation mechanism whose temperature dependence correlates exactly with the reduction in the CRSS. It was found that, after monotonic or cyclic deformation of PWA 1480 at 20 C, the deformation substructures typically contain high density of superlattice-intrinsic stacking faults (S-ISFs) within the gamma-prime precipitates. As the temperature of deformation is increased, the density of S-ISFs is reduced, until finally no faults are observed after deformation in the range from 400 to 705 C. The reduction in the fault density corresponds exactly to the reduction in the CRSS, and the temperature at which the fault density is zero corresponds with the minimum in the CRRS. Two possible mechanisms related to the presence of the S-ISFs in the alloy are considered.

Milligan, Walter W.

Cross-slip and easy-glide CRSS in titanium: Theoretical predictions and in-situ TEM measurements

This study investigates the mechanics of prismatic and first-order pyramidal $\langle$a$\rangle$ slip in titanium (Ti), elucidating the physics of easy-glide and cross-slip through a combination of theory and experiments. Screw-character prismatic (Pr) dislocations in Ti are of particular interest because their complex cores can be stable or unstable, leading to activation by either cross-slip or planar glide. To investigate these mechanisms, site-specific micro tensile samples were prepared using focused ion beam (FIB) milling and mounted on a push-to-pull (PTP) device for in-situ transmission electron microscopy (TEM) tensile testing. The in-situ experiments provide direct observations of the onset of dislocation motion and the precise determination of the critical resolved shear stress (CRSS) for the activated mechanisms, and its evolution with load cycling. A comprehensive theory has been developed to predict the CRSS values for easy glide, cross-slip, and multiplication of dislocations. Predicted critical stresses for pyramidal (π)-to-Pr and reverse cross-slip agree closely with the experimental measurements. The latter cross-slip stress is a factor of two higher than that of unobstructed planar slip. The model accounts for overlapping dislocation cores and employs a Wigner-Seitz based cell to evaluate misfit energies. By combining ab initio density functional theory (DFT) with anisotropic elasticity, the framework identifies minimum energy pathways for dislocation glide, which can be intermittent and zig-zag. A simplified expression utilizing (π) and Pr Schmid factor ratios is proposed for critical stress corresponding to (π)-to-Pr cross-slip transition. The results are strongly dependent on crystal orientation, underscoring non-Schmid behavior. Overall, this study explores key critical stress parameters essential for informing higher-scale simulations of plasticity in Ti.

Critical stress

The Effects of Composition and gamma'/gamma Lattice Parameter Mismatch on the Critical Resolved Shear Stresses for Octahedral and Cube Slip in NiAlCrX Alloys

Prototypical single-crystal NiAlCrX superalloys were studied to examine the effects of the common major alloying elements, Co, Mo, Nb, Ta, Ti, and W, on yielding behavior. The alloys contained about 10 at. pct Cr, 60 vol pct of the gamma' phase, and about 3 at. pct of X in the gamma'. The critical resolved shear stresses (CRSSs) for octahedral and primary cube slip were measured at 760 C, which is about the peak strength temperature. The CRSS(sub oct) and CRSS(sub cube) are discussed in relation to those of Ni, (Al, X) gamma' alloys taken from the literature and the gamma'/gamma lattice mismatch. The CRSS(sub oct) of the gamma + gamma' alloys reflected a similar compositional dependence to that of both the CRSS(sub cube) of the gamma' phase and the gamma'/gamma lattice parameter mismatch. The CRSS(sub cube) of the gamma + gamma' alloys also reflected the compositional dependence of the gamma'/gamma mismatch, but bore no similarity to that of CRSS(sub cube) for gamma' alloys since it is controlled by the gamma matrix. The ratio of CRSS(sub cube)/CRSS(sub oct) was decreased by all alloying elements except Co, which increased the ratio. The decrease in CRSS(sub cube)/CRSS(sub oct) was related to the degree in which elements partition to the gamma' rather than the gamma phase.

Miner, R. V.

Experimental determination of critical resolved shear stress for strain-induced phase transformation

The current investigation reports the first attempt to measure the critical resolved shear stress to initiates strain-induced phase transformation in a three-dimensional polycrystalline aggregate using high-energy diffraction microscopy (HEDM). In situ tensile testing was performed on a Fe38.5Mn20Co20Cr15Si5Cu1.5 metastable alloy exhibiting transformation-induced plasticity (TRIP). Grains with a higher propensity for strain-induced phase transformation were tracked using HEDM. A sharp drop in grain specific stress, coinciding with the appearance of a new ε-hcp grain oriented relative to the parent γ-fcc phase, was taken as evidence of grain-specific stress required to trigger phase transformation. The highest resolved shear stress on the potential transformation systems was identified as the critical resolved shear stress (CRSS) for strain-induced phase transformation. For the studied metastable alloy, CRSS for transformation was determined to be 86±3 MPa which was very close to theoretical CRSS value determined using Schmid factor (89±12 MPa) compared to the value determined using Taylor factor (62±7 MPa).

Jain, Roopam

Hydrogen effects on the deformation and slip localization in a single crystal austenitic stainless steel

Hydrogen is known to embrittle austenitic stainless steels, which are widely used in high-pressure hydrogen storage and delivery systems, but the mechanisms that lead to such material degradation are still being elucidated. The current work investigates the deformation behavior of single crystal austenitic stainless steel 316L through combined uniaxial tensile testing, characterization and atomistic simulations. Thermally precharged hydrogen is shown to increase the critical resolved shear stress (CRSS) without previously reported deviations from Schmid’s law. Molecular dynamics simulations further expose the statistical nature of the hydrogen and vacancy contributions to the CRSS in the presence of alloying. Slip distribution quantification over large in-plane distances (> 1 mm), achieved via atomic force microscopy (AFM), highlights the role of hydrogen increasing the degree of slip localization in both single and multiple slip configurations. The most active slip bands accumulate significantly more deformation in hydrogen precharged specimens, with potential implications for damage nucleation. For $\langle$110$\rangle$ tensile loading, slip localization further enhances the activity of secondary slip, increases the density of geometrically necessary dislocations and leads to a distinct lattice rotation behavior compared to hydrogen-free specimens, as evidenced by electron backscatter diffraction (EBSD) maps. Finally, the results of this study provide a more comprehensive picture of the deformation aspect of hydrogen embrittlement in austenitic stainless steels.

36 MATERIALS SCIENCE

Effects of Zn and Ca on the deformation texture evolution of Mg–Zn–Ca alloys at elevated temperatures

This work utilized crystal plasticity simulations and experimental thermo-mechanical processing to examine how Zn and Ca content affects texture evolution in Mg–Zn–Ca alloys during simulated hot rolling. Four different compositions were studied: unalloyed Mg and three Mg alloys of ZX0p50 (Mg- 0.5 wt% Zn- 0.1 wt% Ca), ZX30 (Mg-3 wt% Zn- 0.1 wt% Ca), and ZX31 (Mg-3 wt% Zn- 0.3 wt% Ca). Multi-pass Gleeble experiments simulated hot rolling using plane strain conditions. Unalloyed Mg developed a strong basal texture, while the addition of Zn and Ca significantly weakened the texture in ZX30 and ZX31; this reduction was not seen in ZX0p50. Notably, ZX31 exhibited a split basal texture aligned with the rolling direction. Crystal plasticity simulations revealed that the weaker basal texture in ZX30 and ZX31 resulted from reduced activation of basal and twinning modes compared to unalloyed Mg and Zx0p50. Increased Zn and Ca content raised the ratios of basal to pyramidal critical resolved sheer stress (CRSS) and twin to pyramidal CRSS, enhancing pyramidal slip activity and weakening the basal texture. Extension twinning played a critical role in texture development during the first deformation pass. In unalloyed Mg and ZX0p50, twinning led to a strong basal texture, while ZX30 and ZX31 had weak basal textures that increased only slightly with further deformation. The split basal poles simulated in ZX31 were consistent with the experimental findings, highlighting the interplay between alloy composition and texture evolution.

Crystal plasticity finite element

The interaction of edge dislocations with hydrogen-helium bubbles in tungsten

In fusion reactors, plasmas-facing components undergo degradation due to displacement damage and injection of gas impurities. Significant amounts of hydrogen (H) and helium (He) impurities can be introduced into materials through plasma exposure and nuclear transmutation, and their synergistic effects lead to the formation of mixed He/H bubbles under irradiation, changing their hardening mechanisms. In this study, molecular dynamics (MD) models were developed to study the interaction between ½<111> edge dislocations with mixed He/H-bubbles in W. The critical resolved shear stress (CRSS) that is required for dislocation breakaway increases with He/H-to-vacancy ratio at 600 K, indicating strong pinning effects of mixed He/H bubbles. However, as the temperature increases up to 1400 K, the mixed He/H bubbles become unstable as the H atoms are increasingly emitted from the mixed He/H bubbles and migrate into W matrix, which lowers bubble pressure and CRSS. Overall, these results highlight the synergistic effects of He and H on dislocation behavior in irradiated W during deformation.

36 - MATERIALS SCIENCE

Deformation modeling and constitutive modeling for anisotropic superalloys

A study of deformation mechanisms in the single crystal superalloy PWA 1480 was conducted. Monotonic and cyclic tests were conducted from 20 to 1093 C. Both (001) and near-(123) crystals were tested, at strain rates of 0.5 and 50 percent/minute. The deformation behavior could be grouped into two temperature regimes: low temperatures, below 760 C; and high temperatures, above 820 to 950 C depending on the strain rate. At low temperatures, the mechanical behavior was very anisotropic. An orientation dependent CRSS, a tension-compression asymmetry, and anisotropic strain hardening were all observed. The material was deformed by planar octahedral slip. The anisotropic properties were correlated with the ease of cube cross-slip, as well as the number of active slip systems. At high temperatures, the material was isotropic, and deformed by homogeneous gamma by-pass. It was found that the temperature dependence of the formation of superlattice-intrinsic stacking faults was responsible for the local minimum in the CRSS of this alloy at 400 C. It was proposed that the cube cross-slip process must be reversible. This was used to explain the reversible tension-compression asymmetry, and was used to study models of cross-slip. As a result, the cross-slip model proposed by Paidar, Pope and Vitek was found to be consistent with the proposed slip reversibility. The results were related to anisotropic viscoplastic constitutive models. The model proposed by Walter and Jordan was found to be capable of modeling all aspects of the material anisotropy. Temperature and strain rate boundaries for the model were proposed, and guidelines for numerical experiments were proposed.

Milligan, Walter W.

Extending Interfaces in 3D to Achieve Superior Nanoscale Strength in Ti/Nb Nanolaminates

Tuning the atomic-level structure of nanolaminates enables high strength, increased deformability, and the ability to absorb and mitigate damage due to varied crystalline defects, including dislocations. Here, we present the enhanced strength of Ti/Nb nanolaminates containing thick 3D interfaces (3DIs), relative to their chemically abrupt 2D counterparts. We examine the effects of crystallographic alignment and compositional gradients on mechanical behavior via experiments and phase-field-dislocation dynamics (PFDD) modeling. Mechanical testing reveals that nanolaminates containing thicker 3DIs demonstrate a 28% hardness enhancement compared with sharp-interface nanolaminates. PFDD modeling shows that the critical resolved shear stress (CRSS) increases with the 3DI thickness. Gradual compositional transitions in 3DIs were confirmed via scanning transmission electron microscopy and high-resolution transmission electron microscopy, showing sharp crystallographic transitions and a heightened interface topography. The findings establish a positive function between the 3DI thickness and mechanical robustness for hexagonal-closest-packed-containing composites, emphasizing the role of defect–interface interactions in tailoring the mechanical performance and providing a foundation for future interfacial engineering.

36 MATERIALS SCIENCE

Computed stress fields in GaAs during vertical Bridgman growth

The thermoelastic stress field of GaAs crystals grown by the vertical Bridgman method has been approximated using a linear elastic, axisymmetric stress model. The model included the effects due to the thermal field and the gravitational field, as well as the interaction with the ampoule, but did not fully account for the elastic anisotropy of the crystal. Realistic thermal fields for different furnace temperatures and insulation zone thicknesses were computed with a similar model. The difference between the Von Mises stress and the critical resolved shear stress (CRSS) was used as a measure of the number of dislocations present. Different sets of growth parameters were examined to determine which produced the lowest amount of stress in the crystal. Results show that the crystal-ampoule interaction is the most important parameter in dislocation generation. In addition, for the same sticking boundary conditions, concave interfaces have lower stress than convex interfaces.

Rosch, William

Slip Analysis in a Ni-base Superalloy

A Ni-base superalloy single crystal with Gamma/Gamma' structure was tested at room temperature along the , <110> and <111> directions. Consistent with previously reported investigations, this alloy did not obey the Schmid law and the CRSS (critical resolved shear stress) was noticeably lower for the <111>-oriented samples. Furthermore, the strain hardening rate decreased and the degree of deformation localization increased in the order of <111>, and <110> orientations. The appearance and orientation of deformation traces were found to depend on the loading orientation as well as the amount of strain. In general, when Gamma'-particles were sheared, the traces followed the expected octahedral shear planes. It is demonstrated that the wavy deformation traces that do not follow the {111} planes are associated with changes in the gamma-channels width and the falling off of the gamma-particles. In this paper the evolution of deformation bands are discussed in terms of plastic localization at microscopic, mesoscopic and macroscopic levels.

Westbrooke, Eboni F.

Utilizing integrated neutron diffraction and elastoplastic self-consistent crystal plasticity model to quantitatively assess the strengthening mechanism in Al–12.5Ce and Al–12.5Ce–0.4Mg alloys

An integrated in-situ neutron diffraction and elastic plastic self-consistent crystal plasticity (EPSC-CP) modeling scheme is performed on a binary Al–12Ce alloy and a ternary Al–12Ce–0.4Mg alloys. Using this scheme, the constitutive parameters, i.e. elastic constants and slip system parameters of individual phases can be calibrated which can be used in microstructure-based CP models to predict materials performance. From this study, it is shown that the elastic constants of Al 11 Ce 3 intermetallics calculated from density function theory calculation in the literature are rather accurate. When applied to the EPSC-CP model, the lattice strains of both the binary and ternary alloys are correctly predicted as compared with experiments, and large lattice strain differences between Al (100) plane and Al 11 Ce 3 (010) plane are demonstrated. The slip system parameters calibrated by the scheme shows that the addition of 0.4 wt% Mg in the alloy has little influence on the critical resolved shear stress of initial dislocation glide in the Al matrix which caused plastic yield in the material. This can be explained by the very dilute Mg solute content in the Al solid solution, causing large spacing of Al–Mg lattice misfit sites and little impact on resistance of dislocation glide at initial yield. The 0.4 wt% Mg addition, on the other hand, has a large influence on the hardening term in the slip system parameters, indicating those Al–Mg misfit sites do help dislocation accumulation during the deformation. The impact of dilute Mg addition on the Al slip system parameters is also reflected in the flow behavior of the ternary alloy: little impact on the yield stress, but a large impact on working hardening and tensile strength of the materials which is consistent with the literature.

36 MATERIALS SCIENCE