Maximum Resolved Shear Stress Research Articles

In situ measurement of three-dimensional intergranular stress localizations and grain yielding under elastoplastic axial-torsional loading

The three-dimensional grain-averaged response of solid bar samples under non-proportional (NP) elastoplastic axial-torsional loading was investigated using in situ high energy diffraction microscopy (HEDM) and companion crystal plasticity finite element (CPFE) modeling. Important stress metrics including applied shear (σθZ) and axial (σZZ) stress tensor components, stress and stress deviator tensor invariants (I1, J2, and J3), von Mises equivalent stress (σVMgrain), maximum resolved shear stress (mRSS), stress triaxiality (η), and lode angle parameter (θ‾) values were tracked for ∼ 300 grains under two different loading conditions: (1) Torsion-dominated loading (low NP) and (2) Tension-torsion loading (high NP) in equiatomic NiCoCr, a representative multicomponent face-centered cubic (FCC) superalloy. Overall, significant stress localizations existed within both samples as evidenced by the radial dependence of grain-resolved σθZ, σVMgrain , and J2; by comparison, I1, J3, η, and θ‾ metrics did not show discernible trends within the volume. These stress localizations reveal a complex interplay between axial and shear stress components (e.g., stress coupling) resulting in grain yielding near the sample surface largely driven by shear stress, whereas internal grain yielding was largely accommodated by axial stress. Grain-resolved stress localization trends were described well by the CPFE model, although some discrepancies in magnitude occurred, particularly for volumetric stress metrics (I1 and η) due to initial type II residual stress distributions. The superposition of initial residual stress states onto CPFE grain-resolved data significantly improved model accuracy for η. This suggests that residual stresses more strongly influence the simulation of volumetric rather than deviatoric (yield) stress metrics.

Molecular dynamics simulation study of void collapse mechanisms in cubic metals under shock compression

Molecular dynamics simulations have revealed the collapse mechanism of a void in cubic metals under shock compression along [100] direction. The results show that the void collapse is caused by emitting dislocations from its surface. The type of cubic metal plays a decisive role in the subsequent microstructural evolution around the void. Void in face-centered-cubic metals collapses by emitting Shockley dislocations from its surface when piston velocity exceeds the threshold; while void in body-centered-cubic metals collapses by emitting prismatic dislocation loops, which are formed by the reaction of edge dislocations. Simulation results also reveal that the type of dislocation that induces void collapse is independent of void size. Finally, based on the elastic theory, we find that the maximum resolved shear stress along the slip direction determines the types of dislocation emitted from the voids.

An arc-tenon attachment for nickel-based single crystal turbine blade with improved high-temperature fretting fatigue performance

Nickel-based single crystal (NBSC) turbine blade tenon is prone to fretting fatigue failure. In this study, an arc-tenon attachment was proposed and its fretting fatigue life increased by up to 408.18 % at 600 ℃ compared with the plane-tenon structure under the applied peak stress of 65 MPa. The arc-tenon attachment could effectively reduce the maximum von-Mises stresses and resolved shear stresses near the contact region, regulating the stress distribution and reducing the stress gradient, which was beneficial to alleviating the activation of octahedral slip systems and delaying crack initiation, thereby improving the fretting fatigue life at high temperature. Meanwhile, high temperature promoted the formation of oxide layer on the contact surface, providing low coefficient of friction and further reducing the contact stress. The large resolved shear stress near the contact leading edge region facilitated the activation of octahedral slip systems, then the resultant multiple slip lines sheared both the γ matrix phase and γ′ precipitates. The further growth of the slip lines accelerated the fretting fatigue crack initiation and propagation. The arc-tenon attachment could provide long fretting fatigue life and showed great potential in engineering application.

Crystal plasticity model of BCC metals from large-scale MD simulations

Accurate crystal plasticity models that faithfully capture the behavior of single crystals under a wide range of loading conditions, such as loading direction, strain rate, and temperature, are still lacking. Here we introduce a novel approach in which a crystal plasticity (CP) model is informed directly from and calibrated to large-scale quantum-accurate MD simulations in which single crystal BCC Ta serves as a testbed material. By analyzing our large set of MD simulations several key insights are obtained leading us to modify constitutive assumptions in order to address deficiencies of existing CP models. Importantly, we observe that the standard notion of fixed slip systems – pairs of slip directions and slip planes – is inadequate for describing high-rate plasticity in BCC tantalum at room temperature. Instead, pencil glide defined as dislocation motion in the maximum resolved shear stress planes (MRSSP) of each Burgers vector is fully consistent with our MD simulation data while providing significant simplifications of the constitutive relations. Our resulting new CP model closely matches the behavior of single crystals observed in high-rate MD simulations while being fully consistent with lower rate experimental results.

Determination of the controlling parameters for dislocation nucleation in SrTiO3: An investigation by nanoindentation

AbstractWe conduct nanoindentation to investigate dislocation nucleation in SrTiO3 (STO) single crystals with surface orientations of (0 0 1), (0 1 1), and (1 1 1) with loading/unloading rates of 25, 250, and 2500 μN/s. Results reveal that the critical loads (Pc) at which “pop‐in” event occurs depend strongly on surface orientations, but slightly related to loading rate. Based on Pc, the critical shear stress that triggers dislocation nucleation was determined by extracting the maximum resolved shear stress (τmax) along the slip systems of STO using the Hertzian solution. The dislocation activation shear stress (τa) was determined by averaging τmax. The determined τa is 9.0–12.0 GPa, close to the shear strength (∼G/2π) of STO, indicating that homogeneous dislocation nucleation dominates the pop‐in events. The consistency of the determined τa demonstrates that the frameworks for nanoindentation pop‐in analysis established for metals can be extended to ceramics, whereas the influence of the limited slip systems should be taken into consideration. Additionally, we estimated the activation volume and the activation energy via the statistical model proposed by Schuh et al. The small values of the determined activation volume (0.6–9.8 Å3) and the activation energy (0.13–0.70 eV) indicate that the dislocation nucleation possibly begins from a single‐atom migration and local point defects may participate in the dislocation nucleation process. That is, heterogeneous nucleation may exist initially but the homogeneous dislocation nucleation dominates the pop‐in events.

Room-temperature plastic deformation of single crystals of α-manganese - hard and brittle metallic element

The deformation behavior of single crystals of α-manganese has been investigated by micropillar compression at room temperature as a function of crystal orientation and specimen size. When the specimen size is reduced to the micrometer-range, single crystals of α-manganese are found to plastically deform by dislocation motion at room temperature for the first time, accompanied by very high yield stresses of the range of 4–6 GPa. Slip along [111] and [001] are identified to operate for compression axis orientations near [001] and near [011] and [1¯11], respectively. Any low-indexed planes cannot be designated as the slip plane for both slip along [111] and [001], because of the significantly wavy nature of slip lines caused by the occurrence of frequent cross-slip. Slip along [111] tends to prefer the slip plane of {112} rather than {110}. Slip along [001], on the other hand, tends to occur on the maximum resolved shear stress plane. The 1/2[111] dislocation carrying slip along [111] moves as a perfect dislocation without dissociating into partials and does not have any preferred orientation. The [001] dislocation carrying slip along [001] also moves as a perfect dislocation without dissociating into partials. Although the Peierls stress for the motion of these dislocations must be very high, there seems no deep Peierls valleys along particular directions, unlike the screw direction for the 1/2[111] dislocation in body-centered cubic metals.

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.

Influence of boron on the stress-rupture behavior of an additively manufactured Hastelloy X

The influence of minor additions of boron and the as-built (AB) microstructure on stress-rupture behavior of a modified crack-free Hastelloy X fabricated by laser powder bed fusion (L-PBF) was investigated. Isothermal stress rupture tests were performed at 816 °C under a static tensile load of 103 MPa. Micro-void formation in the vicinity of carbide precipitates and their coalescence was only observed at chevron-like high-angle grain boundaries, characteristic of L-PBF process. These grain boundaries, laying on the planes with maximum resolved shear stress with respect to the loading direction, directly governed the intergranular crack propagation. In view of the fracture mechanism and the time to rupture, increasing boron content significantly improves time-to-rupture through a diffusion-controlled mechanism by hindering the carbon diffusion to the grain boundaries. Adequate additions of boron (>10 ppm) guarantee the stress-rupture properties (strength) of the AB components without the need for additional post-thermal treatments. Further increase in boron content (i.e., 30 ppm), led to about five times increase in time to rupture (500 h vs. 110 h), and significantly improved creep elongation (30% vs. 9%) compared with the low boron alloy.

Numerical Analysis of Conjugated Heat Transfer and Thermal Stress Distributions in a High-Temperature Ni-Based Superalloy Turbine Rotor Blade

This paper establishes a multidisciplinary method combining conjugate heat transfer (CHT) and thermal stress for a high-temperature Ni-based superalloy turbine rotor blade with integrated cooling structures. A conjugate calculation is performed to investigate the coolant flow characteristics, heat transfer, and thermal stress of the rotor blade under rotating and stationary conditions to understand the effects of rotation on the multidisciplinary design of the blade. Furthermore, the maximum resolved shear stress among the 30-slip systems and the corresponding dominant slip system are obtained to predict the deformation tendency of the blade by employing the crystal plasticity finite element method (CPFEM) and considering the specified anisotropic blade material (GTD-111). The results show that the forces of rotation, including centrifugal and Coriolis forces, and their induced buoyancy force, alter the coolant flow field and thus affect the rotor blade’s heat transfer distribution compared with the stationary condition. The maximum temperature and thermal stress of the rotor blade under rotating conditions are reduced by 5% and 21% compared with that under the stationary condition, respectively. Compared with the stationary condition, the temperature and thermal stress distribution on the blade under the rotating condition are more uniform, especially on the suction side. In addition, the blade root connecting with the hub, the film holes near the leading-edge region at the blade root, the mid-chord of the suction surface, and the grooved blade tip are easily damaged by the enormous resolved shear stress and the interface effect of different types of dominant slip system under the two conditions. In this work, it was feasible to use the cascade cooling effect test to analyze the dynamic test results for the rotor blade. Furthermore, the thermal stress analysis based on the CPFEM can provide a superior level of blade cooling design than CHT by considering the anisotropic material characteristics of a turbine blade.

Mechanical Properties of GaN Single Crystals upon C Ion Irradiation: Nanoindentation Analysis.

Mechanical properties of gallium nitride (GaN) single crystals upon carbon ion irradiation are examined using nanoindentation analysis at room temperature. Pop-in events in the load-depth curves are observed for unirradiated and irradiated GaN samples. A statistical linear relationship between the critical indentation load for the occurrence of the pop-in event and the associated displacement jump is exhibited. Both the slope of linear regression and the measured hardness increase monotonically to the ion fluence, which can be described by logistic equations. Moreover, a linear relationship between the regression slope as a micromechanical characterization and the hardness as a macroscopic mechanical property is constructed. It is also found that the maximum resolved shear stress of the irradiated samples is larger than that of the unirradiated samples, as the dislocation loops are pinned by the irradiation-induced defects. Our results indicate that the nanoindentation pop-in phenomenon combined with a statistical analysis can serve as a characterization method for the mechanical properties of ion-irradiated materials.

Sweep-tracing algorithm: in silico slip crystallography and tension-compression asymmetry in BCC metals

Direct Molecular Dynamics (MD) simulations are being increasingly employed to model dislocation-mediated crystal plasticity with atomic resolution. Thanks to the dislocation extraction algorithm (DXA), dislocation lines can be now accurately detected and positioned in space and their Burgers vector unambiguously identified in silico, while the simulation is being performed. However, DXA extracts static snapshots of dislocation configurations that by themselves present no information on dislocation motion. Referred to as a sweep-tracing algorithm (STA), here we introduce a practical computational method to observe dislocation motion and to accurately quantify its important characteristics such as preferential slip planes (slip crystallography). STA reconnects pairs of successive snapshots extracted by DXA and computes elementary slip facets thus precisely tracing the motion of dislocation segments from one snapshot to the next. As a testbed for our new method, we apply STA to the analysis of dislocation motion in large-scale MD simulations of single crystal plasticity in BCC metals. We observe that, when the crystal is subjected to uniaxial deformation along its [001] axis, dislocation slip predominantly occurs on the {112} maximum resolved shear stress plane under tension, while in compression slip is non-crystallographic (pencil) resulting in asymmetric mechanical response. The marked contrast in the observed slip crystallography is attributed to the twinning/anti-twinning asymmetry of shears in the {112} planes relatively favoring dislocation motion in the twinning sense while hindering dislocations from moving in the anti-twinning directions.

Grain reorientation and stress-state evolution during cyclic loading of an [formula omitted]-Ti alloy below the elastic limit

High-energy synchrotron x-rays are used to track grain-averaged lattice reorientation and stress-state evolution in Ti–7Al as it is cyclically loaded to 90% of its macroscopic yield stress. This evolution provides clear indication of accumulating plastic strain even though the sample never exceeded the elastic limit. The largest changes in lattice orientation and stress state are observed following the first cycle then evolution continues at a lower rate with subsequent cycles. Variation of the axes about which lattice reorientation occurs is found to be highly dependent on the maximum resolved shear stress and corresponding activation of various families of slip systems.

Molecular dynamics simulations of screw dislocation mobility in bcc Nb

The screw dislocation mobility in bcc Nb has been studied by molecular dynamics (MD) simulations at different strain rates and temperatures using an embedded-atom method (EAM) potential. Static properties of the screw dislocation, as determined with the EAM potential, are in agreement with previous density-functional-theory calculations. The elementary slip plane of the screw dislocation remains (110) for all studied strain rates (in the range 6.3 × 107–6.3 × 109 s−1) and temperatures (5 to 550 K). However, the consecutive cross-slip on different symmetry-equivalent (110) planes leads to an effective glide on (112) planes. It is demonstrated that the screw dislocation trajectories, velocities and waviness of the screw dislocation depend on the crystallographic indices, (110) or (112), of the maximum resolved shear stress plane. The waiting time for the start of the screw dislocation motion increases exponentially with decreasing strain rate, substantiating the necessity to apply in future accelerated MD techniques in order to compare with macroscopic stress-strain experiments.

A Novel Maximum Resolved Shear Stress Gradient Criterion and Its Application for Crack Deflection Behavior in Polycrystalline Silicon Materials

A Novel Maximum Resolved Shear Stress Gradient Criterion and Its Application for Crack Deflection Behavior in Polycrystalline Silicon Materials

Evaluating the grain-scale deformation behavior of a single-phase FCC high entropy alloy using synchrotron high energy diffraction microscopy

Although the deformation behavior of high-entropy alloys (HEAs) has been extensively studied at the macroscale, many important properties have yet to be explored for these alloys at the microscale, thus hampering accurate prediction of damage and failure processes. Synchrotron high-energy diffraction microscopy (HEDM) and fast-Fourier transform-based crystal plasticity modeling was conducted to investigate the three-dimensional (3D) grain-resolved micromechanical response for approximately 1,900 constituent grains within a single-phase FCC HEA up to 1% applied strain. The evolution of grain-resolved elastic strains, lattice reorientations, and maximum resolved shear stresses (mRSS) were evaluated to quantify elastic, yield, and fully plastic behavior. Overall, the initial critical resolved shear stress (CRSS), determined via in situ HEDM and companion modeling, was found to be > 20% higher than estimated using the classical polycrystalline Taylor factor (M = 3.06). However, a descriptive parameter based on the average grain-resolved Taylor factor (M¯) was found to show excellent agreement with plastic yielding behavior observed within HEDM datasets. Noticeable deviations in HEDM lattice reorientations compared to both EVP-FFT simulations and classical predictions for FCC polycrystals were discovered, highlighting the complexity in correlating local lattice reorientations, Taylor, and Schmid factors with plastic response for this material at the grain-scale. Therefore, it is anticipated that the overall trends and parameter identification of 3D grain-resolved properties in this study can serve as an important foundation for continued mesoscale investigation on both well-established and newly developed Cantor-like HEAs.

Deformation mechanisms and texture evolution in high entropy alloy during cold rolling

In the present study, equiatomic CoCrFeMnNi high entropy alloy (HEA) was subjected to thickness reductions of 20, 40, and 60% during cold rolling in order to thoroughly investigate the evolutions of both the microstructure and the deformation texture. Important aspects of deformed microstructures such as the activation of multiple twin variants and the formation of shear bands in the matrix were captured using electron backscatter diffraction (EBSD) and electron channeling contrast imaging (ECCI) techniques. Twin trace analysis (TTA) was performed in conjunction with resolved shear stress (RSS) analysis for the identification of active twin variants. The RSS ratio, which is a ratio of the maximum RSS values for corresponding twin and slip systems, was used to reveal the orientation dependence of deformation twinning. Visco-plastic self-consistent (VPSC) simulations were carried out to predict the evolution of the crystallographic texture, the transition routes of ideal orientations subjected to multiple deformation twinning, and the role that deformation modes play in the rotation of orientation. Experimental and simulation results substantiated the key finding of the deformation twinning of a Brass orientation, which established new perspectives concerning the evolution of microstructure and texture. One twin variant of the Copper orientation was moved to a Goss orientation by dislocation slip while the other two variants were rotated towards Brass and S orientations. Meanwhile, twin variants of the S and Brass orientations primarily transitioned to a Brass orientation. The Goss orientation showed great resistance to the twinning mode. Furthermore, dislocation slip and the formation of shear bands contributed to the evolution of a strong texture while deformation twinning had the opposite effect.

Creep rupture mechanism and microstructure evolution around film-cooling holes in nickel-based single crystal superalloy specimen

The fracture mechanism and microstructure evolution around film-cooling holes in a nickel-based single crystal superalloy specimen under tensile creep at high temperatures were investigated using thin-walled plate specimens with close-packed film-cooling holes. The results demonstrated that the film-cooling hole structure has a weakening effect on the specimen for the creep life and creep ductility. In the specimen with the film-cooling holes, a large number of small cracks formed from initial cracks along the direction of the maximum resolved shear stress during the high-temperature creep process, and the cracks propagated along the direction perpendicular to the loading stress direction. Further, the microstructure evolution of the γ′ phase around the edge of the film-cooling holes was closely related to the local stress. While N-type rafting occurred in the high-stress zone, no significant change of microstructure was observed in the low-stress zone. Further, a modified damage model of the crystal plasticity theory was used to simulate the deformation of the specimen with cooling holes under multi-axial stress state, and the results of finite element analysis (FEA) agreed with both the test results and fracture morphology.

Single crystal yield criterion for chromium based on atomistic studies of isolated 1/2[111] screw dislocations

Using the recently developed Bond Order Potential for Cr, we investigate the mobility of isolated 1/2[111] screw dislocations under stress at 0 K. These studies provide the dependence of the critical resolved shear stress (i.e., the Peierls stress) on the orientation of the maximum resolved shear stress plane and on the shear stress perpendicular to the slip direction. Similar studies are made for loading in tension and compression to show that the onset of yielding in Cr single crystals can be described using a combination of the shear stresses parallel and perpendicular to the slip direction. Based on these results, we develop a single crystal yield criterion for Cr that includes all non-Schmid contributions to the Peierls stress. This criterion is used to predict the shape of the yield surface and compare it with the regular Tresca's hexagon arising from the Schmid law. For all directions of uniaxial load, the criterion is used to quantify the character and magnitude of the tension-compression asymmetry.

Equivalent method of evaluating mechanical properties of perforated Ni-based single crystal plates using artificial neural networks

Creep experiments were performed to study the mechanical characteristics of Ni-based single crystal superalloy samples with densely arranged air film holes. An equivalent model based on crystallographic theory coupled with continuous damage mechanics was developed. The equivalent method was proposed, combining artificial neural networks and the equivalent solid material concept. A series of experiments and calculation results on plates with diverse arrangement patterns and ligament efficiencies were compared to validate the accuracy of the proposed method. The results indicate that the creep curves of the simplified models agree well with the experimental results. The microstructural evolution observed by scanning electron microscopy can be evaluated using the evolution of the maximum resolved shear stress with the creep time. The damage distribution of the simplified models is consistent with the crack initiation location and propagation region of samples. Additionally, the slip system actuation of the simplified models is the same as that of the experimental results. The equivalent errors of the creep time, maximum resolved shear stress and creep damage are less than 15%, except for individual points, indicating that the equivalent method proposed in this study is feasible and accurate.

Multidisciplinary Design Optimization of the Composite Cooling Structure for Nickel-based Alloy Turbine Blade

Abstract A designed method, multidisciplinary coupling computation and multiobjective optimization, has been established for the composite cooling structure of heavy gas turbine blade manufactured with a directionally solidified Ni-based superalloy. The method combines the one-dimensional fluid network gas-thermal coupling computation, three-dimensional flow field coupled with solid stress field, and anisotropic stress calculation based on finite deformation crystal slip. The temperature, flow field, Von-Mises stress and maximum resolved shear stress of the blade before and after optimization were analyzed. The results show that the optimized blade has lower maximum blade temperature, a more uniform temperature distribution, a lower flow resistance of the coolant channel at the leading edge than that of the original blade. The maximum Von-Mises stress of the optimized blade increases by 10.05 % more than the original blade. The maximum shear stress on the suction side and the pressure surface of the optimized blade are improved and slightly deteriorated compared with that of the original blade, respectively. The corresponding relationship of the maximum shear stress distribution with the local temperature gradient reveals further space for the improvement of the composite cooling structure. This paper has a particular guiding significance for the cooling structure design of the turbine blade.