Resolved Shear Stress Research Articles

Subsurface hardening of Al irradiated with ultrafast infrared laser

The effect of femtosecond laser shock peening on a model Al-0.3Mn alloy was investigated experimentally and numerically by molecular dynamics. Micro-diffraction experiments performed at synchrotron source revealed the depth profiles of the residual stress and the stored energy of dislocations, a measure of local plasticity. The depth of the maximum compressive stress did not coincide with that of the maximum dislocation energy, which was found at the surface. The interaction between the laser and the metal was simulated with LAMMPS using a two-temperature molecular dynamics package. The model accurately described the equation of state of aluminum and showed nearly equal resolved shear stresses on all slip systems at the wavefront. The dislocation density at a depth of 1 μm, predicted by the Meyers' model [1], was higher than the experimental data, suggesting possible recovery due to the increased temperature of the sample after repeated shock loading.

Effects of grain size and stacking fault energy on twinning stresses of single-phase CrxMn20Fe20Co20Ni40-x high-entropy alloys

Deformation twinning was investigated in single-phase face-centered-cubic (FCC) high-entropy alloys of the CrxMn20Fe20Co20Ni40-x system (14 ≤ x ≤ 26 at.%). The intrinsic stacking fault energies (γisf) of these alloys varied systematically across this composition range, but other physical properties that have the potential of affecting deformation twinning remained constant allowing us to isolate the effects of γisf on twinning. Tensile tests were performed at 293 and 77 K, and the tests interrupted at several different strains to evaluate deformation-induced changes in microstructure by transmission electron microscopy. The critical stress above which deformation twinning occurs was thus determined. We also evaluated how grain size (19 ≤ d ≤ 237 µm) affects the yield stress (σy) and the uniaxial critical twinning stress (σtw), which allowed us to subtract the corresponding Hall-Petch contributions and compare our polycrystalline results with experimental and theoretical data reported for single crystals. Taking into account the critical resolved shear stresses for deformation twinning in our alloys (τtw) along with those of FCC pure metals and binary alloys reported in the literature, we derived the following relationship that rationalizes most of the experimental data: τtw = 10-3G + γisf/(3·bp), where G is the shear modulus and bp is the magnitude of the Burgers vector of a Shockley partial dislocation. This expression, involving only measurable material properties, can serve as a basis for the design and optimization of new HEAs with tunable twinning stresses and, in turn, exceptional strength-ductility combinations.

3D in situ observations of stress redistribution in Ti-6Al-4V within rogue grain neighborhoods during monotonic and cyclic loading

Grain-scale stress redistribution events are characterized within the Ti-6Al-4V (Ti64) hexagonal close-packed α phase using far-field high-energy X-ray diffraction microscopy. Specimens were deformed in monotonic uniaxial tension and under cyclic tensile loading with approximately 7000 grains probed in each specimen. Analyses focused on the evolution of the resolved shear stresses applied to the basal 〈a〉, prismatic 〈a〉, and pyramidal 〈c+a〉 slip systems, as well as normal stresses applied to basal planes, within individual grains. Slip system softening is observed in the basal 〈a〉 and prismatic 〈a〉 slip systems across the ensemble, while hardening is observed for the pyramidal 〈c+a〉 slip systems during both monotonic and cyclic loading. In addition, discrete stress redistribution events in which increases of normal stresses in grains not favorably oriented for slip that may lead to crack initiation are analyzed. It is observed that these increases in normal stresses are correlated to crystallographic slip in multiple neighboring grains favorably oriented for slip.

Vibration fatigue behavior and failure mechanism of Ni-based single-crystal film cooling hole structure under high temperature

Film cooling hole structures significantly influence vibration fatigue performance of Ni-based single crystal turbine blades. This study investigates the vibration fatigue behavior and failure mechanism of film cooling hole structure of Ni-based single crystal superalloy at high temperature by using the plate specimens with film cooling holes. The vibration fatigue cracks are all initiated at the edge of the film cooling hole on specimen surface, and the macroscopic crack path is a straight line path. At the microscopic scale, the crack path at 850 °C is a Zigzag path, but the crack path at 980 °C still shows a straight line path. The crack initiation of the specimen shows the oxidation crack nucleation in the stress concentration area under the coupling effect of high temperature and alternating stress. The macroscopic crack propagation direction at high temperature depends on the stress gradient direction of the resolved shear stress. At the microscopic scale, the crack propagation at 850 °C is the dislocation slip-climb mechanism, and the crack propagation at 980 °C more inclined to produce only the dislocation climb mechanism. The vibration fatigue cracks have the temperature dependence. The high temperature environment promotes the activation of slip system and the enhancement of dislocation mobility, the microscopic raft structure promotes the crack propagation along the γ phase with a large number of dislocations, the oxidation crack promotes the oxygen to enter the alloy matrix, which accelerates the Mode-I crack propagation.

Experimental and digital twinning in ZnAlMg coatings

Twinning is a major deformation mechanism in various materials, especially when few dislocation slip systems are operative. It is the case of zinc-rich coatings in galvanised steel sheets, made of pancake grains on a substrate and where the slip systems with a non-vanishing component along the c-axis present high critical resolved shear stress values. In addition, the abrupt lattice orientation change associated to twinning, the stress relaxation during its propagation and the localised nature of its early stages make it difficult to reproduce this deformation mechanism by using classical crystal plasticity models conceived for dislocation slip. In this sense, this work proposes a hierarchy of three twinning models in combination with a dislocation slip crystal plasticity model, for the case of a ZnAlMg coating. These three models are: a relaxed-Taylor model applied to individual crystal orientations of the coating, a “pseudo-slip” model for twinning and a localised twinning model. The latter incorporates a linear softening in the material law accounting for the unstable twinning initiation and enforces twinning lattice reorientation. A microstructure portion extracted from an in-situ SEM tensile experiment on galvanised steel is used to perform 3D full-field finite element simulations within a finite strain formulation. SEM observations and EBSD acquisitions are used to compare simulation and experimental results during the different steps of the in-situ SEM test, regarding the deformation and damage modes of the zinc-rich coating. The focus is set on twinning evolution inside some individual grains, and the pros and the cons of the three models are finally discussed.

Critical Resolved Shear Stress and Work Hardening Determination in HCP Metals: Application to Zr Single Crystals

Obtaining precise parameters of deformation modes remains a significant challenge in materials science research. Critical resolved shear stresses (CRSS) and work hardening, particularly in hexagonal metals, are crucial parameters for constitutive laws in crystal plasticity. This paper presents a novel approach to determine CRSS and specific hardening matrix coefficients for commercially pure zirconium (α-Zr) at room temperature. In situ methods are employed to measure displacement fields using grids applied to the sample surface, while a comprehensive characterization of the activated deformation systems is performed via SEM and TEM. The CRSS for prismatic ⟨a⟩, pyramidal ⟨a⟩, and 101¯2 and 112¯1 twinning systems, as well as the self-hardening for prismatic slip and several work-hardening coefficients (for prismatic/prismatic and prismatic/pyramidal interactions), are reported in Zr single crystals. Finally, the results are compared with findings from the literature and atomistic simulations.

Investigation of failure analysis on fatigue crack initiation influenced by critical resolved shear stress in X10CrMoVNb9-1 steel

This study investigates the influences of the critical resolved shear stress (CRSS) values on calculating the number of cycles for the fatigue crack initiation cycle of X10CrMoVNb9-1 (P91) under cyclic loading conditions at room temperature while considering varied surface roughness on microstructure models. The micropillar compression test was utilized to calculate the CRSS values, incorporating the Schmid factor, the Frank–Read source together with the Hall–Petch effect, measuring the diameter of the micropillar after compression, and the Mlikota and Schmauder equation. Two primary microstructure surface roughness – plane surface roughness (PS) and surface roughness (SR) with an average of 1 µm – were generated using the Voronoi Tessellation (VT) method. Finite Element Method (FEM) simulations were conducted to identify different stress distributions across these artificial microstructures. These stress distributions were subsequently analyzed using the physics-based Tanaka-Mura model (TMM) to estimate the number of cycles for fatigue crack initiation at several stress amplitudes and six types of microstructure. The number of cycles varies significantly at lower stress amplitudes and convergence at higher stress amplitudes. The study of the CRSS of steel P91 offers a significant advancement in fatigue research, particularly with implications for power plants.

Effect of grain size on tensile behavior and the underlying deformation modes in a Mg-5Y sheet

This work aims to further understand the grain size effects on individual slip/twining activities at grain scale and their correlation with the tensile behavior, for a Mg-5Y sheet with mean grain size range of 3–130 μm, based on slip trace/electron backscatter diffraction (EBSD) analysis. The correlation between tensile yield strength and the corresponding grain size fitted well with the Hall-Petch relationship, i.e., the k value was 191 MPa·μm1/2, with an R2 of 0.96. According to the identified 1004 sets of slip traces in 2477 grains, basal <a> slip was always dominant and tended to increase (from 47.2% to 71.5%) with grain size increased from 3 to 85 μm. Meanwhile, the percentage of pyramidal II <c+a> slip exhibited a marked decline from 34.5% to 8.9%, while that of prismatic <a> and pyramidal I <c+a> slip changed slightly. The decreased pyramidal II <c+a> slip activity was consistent with the decreased tensile yield strength as grain size increased. The twinning activity was limited and insensitive to grain size. In addition, the geometrically necessary dislocation (GND) density was increased with increasing grain size. Based on the slip activity statistics, the critical resolved shear stress (CRSS) ratios were estimated, which exhibited a significant grain size effect. Specifically, CRSSpris/CRSSbas showed negative grain size dependence, while the opposite was true for CRSSpyrIICA/CRSSbas. This study provides valuable grain-scale experimental evidence for the grain size effect on individual slip activity and CRSS ratios, which contributes to a better understanding of the Hall-Petch relationship in Mg-Y alloy.

The crack propagation behaviors, microstructure and mechanical properties of T-welded joints for TIGW with crystal plasticity model and XFEM

In view of the significant impact of welding defects on the fracture behaviors involving the strength, stress concentration and bearing capacity of welded joint, etc., the propagation behaviors and mechanical properties of welded joints with porosity and micro crack are deeply investigated using a multiscale method. In this work, a crack nucleation and propagation model based on crystal plasticity theory, combined with the extended finite element method (XFEM), is established for the T-welded joint. The maximum slip on the predominant slip system method is applied to predict the crack propagation path of pores and micro cracks in the weld zone (WZ), and the effect of crystal orientation on crack growth is explored. Then, a continuous model is used to analyze the micro and macro fracture behaviors near the weld under tensile load, combined with the maximum principal stress method. The WZ and heat affected zone (HAZ) are observed using electron backscatter diffraction (EBSD) to study the microstructure evolution. Considering grain boundaries, the image information of crystal morphology is processed through binary image analysis for FE modeling. The local mechanical properties testing is carried out using micro-specimens of HAZ and WZ to calibrate the crystal plastic parameters. The results show that the resolved shear stress of the predominant slip system of crack initiation and propagation elements is increased by pore and crack defects. The fracture positions of tensile specimens through numerical simulation are in good agreement with the macroscopic experimental results. It will provide an analysis basis for preventing fracture failure and improving the service performance of thin-walled structures in future.

An investigation of phase boundary effect on the cutting force fluctuation in orthogonal micro-cutting of Ti6Al4V alloy

In micro-cutting, microstructure induced anisotropic properties highly affect the machinability of materials because the removal amount is almost on same level as the size of microstructures such as grains and phases. In this paper, cutting force fluctuation induced by different phases is theoretically and experimentally investigated in the micro-cutting of dual-phase Ti6Al4V alloy. Particularly, a significant change of cutting force was observed as the tool traverses phase boundaries. Furthermore, the mechanism of the variation of cutting forces is discussed from perspectives of crystallographic orientation, critical resolved shear stresses and slip systems. Constitutive model and geometrical relationship between the tool and workpiece are also proposed to analyzed the resolved shear stresses of phases with different crystallographic orientations. The results agree well with experimental data, indicating that activation of various slip systems is directly determined by the values of corresponding resolved shear stresses. Additionally, cutting force fluctuation is primarily attributed to the change of slip systems at phase boundaries in the micro-cutting. The main findings of this study present the significant role of crystallographic orientations and slip systems in governing cutting force fluctuations at phases and phase boundaries, which provide valuable insights for optimization of cutting parameters in machining of titanium alloys.

Twinning behaviors of Mg−Sn alloy with basal or prismatic Mg2Sn

The Mg−Sn alloys, with basal or prismatic Mg2Sn laths, were employed to reveal the effect of precipitate orientation on twinning behavior quantitatively. The Mg−5wt.%Sn alloys with basal or prismatic Mg2Sn were compressed to study the twinning behaviors. Subsequently, an Orowan strengthening model was developed to quantitatively investigate the critical resolved shear stress (CRSS) increment of precipitates on twinning. The results revealed that the prismatic precipitates hindered the transfer and growth of tensile twins more effectively compared with the basal precipitates. The decreased proportion of tensile twins containing prismatic Mg2Sn might be attributed to a larger CRSS increment for tensile twins compared with that for basal precipitates. The obvious decreased twinning transfer in the alloy with prismatic Mg2Sn could be due to its higher geometrically necessary dislocation and enhanced CRSS of tensile twins. Notably, the prismatic precipitates have a better hindering effect on tensile twins during compression.

Effect of microstructure rafting on deformation behaviour and crack mechanism during high-temperature low-cycle fatigue of a Ni-based single crystal superalloy

The low cycle fatigue behaviours of a microstructure rafting Ni-based single crystal superalloy have been experimentally investigated at 980 ℃. Deformation of γ/γ’ phases and the corresponding dislocation configurations were investigated, highlighting rafting γ/γ’ morphology that contributes to crack initiation and propagation, as well as macro-scale accumulated plastic strain. Unlike the discrete slip lines of a virgin superalloy, intense slips developed along the parallel {111} slip plane result in crossed slip bands in the rafting superalloy. The decreased resistance of widened γ channels to dislocation movement, along with the prevention of dislocation cutting through γ’ precipitates in pre-existing dense dislocation networks, facilitates crack propagation in the γ channel in the slightly rafting superalloy. As the rafting state increases, the dislocation network loses its protective effect by reducing coherency stress and acting as a superdislocation source, which facilitates crack propagation along the γ/γ’ interface. Finally, a microstructure-based fatigue model is developed considering the reduction of deformation resistance induced by rafting. The fatigue loading control mode effect is introduced by a combination of resolved shear stress and tensile stress effects on crack initiation. The LCF life of rafting Ni-based superalloys significantly decreases under stress-controlled conditions compared to strain-controlled conditions due to the increase in cumulative plastic strain. However, the insignificant impact of the initial surface oxide layer on LCF life is revealed.

High‐Temperature Mechanical Behavior of Single‐Crystal FeCrAl Alloy Under In Situ Micropillar Compression

FeCrAl cladding is one of the candidate materials for the near‐term accident‐tolerant fuel technologies under development. Research on high‐temperature mechanical behaviors of single‐crystal FeCrAl alloy is rather limited. Previous studies have reported the mechanical property of low‐index orientation in single‐crystal FeCrAl alloy at room temperature. However, the critical resolved shear stress to activate slip systems can be orientation and temperature dependent. Here, single‐crystal grains in a coarse‐grained FeCrAl alloy with different crystallographic orientations are selected to preferentially activate {110}&lt;111&gt; slip systems or {112}&lt;111&gt; slip systems. Micropillars are fabricated in the selected single‐crystal grains and tested at elevated temperatures in situ in a scanning electron microscope. The critical resolved shear stresses of {110}&lt;111&gt; slip systems and {112}&lt;111&gt; slip systems are determined at various temperatures. The critical resolved shear stress shows a temperature dependence and orientation independence. This study provides important insight for understanding the deformation mechanisms of FeCrAl alloys at elevated temperatures.

Microscopic instabilities in single crystal matrix composites

A finite strain micromechanical analysis is presented for the prediction of the loss of microscopic stability of a class of metal matrix composites that are subjected to axial compressive loading and undergoing large deformations. The metallic constituent behavior is modeled by the single crystal anisotropic plasticity theory in which, due to the resolved shear stresses, plastic deformations occur along certain pre-defined slip planes. Thus, this incremental plasticity theory is capable of providing the effect of the applied axial loading on the induced shear stresses which dominate the microbuckling. The composites are assumed to possess slight imperfections at the interfaces, and in order to satisfy the interfacial conditions, a perturbation expansion is employed which yields zero and first order micromechanical analysis problems. The zero order problem corresponds to the micromechanical modeling of the composite with no imperfections, whereas the solution of the first order problem is utilized to obtain the critical stresses and deformations at which bifurcation buckling occurs. Both problems are solved by employing the finite strain high-fidelity generalized method of cells (HFGMC) micromechanics. Applications are given for various types of single crystal matrix composites including layered, particulate, continuous and short fiber composites. Finally, a comparison between the compressive strengths of a standard metal matrix boron/aluminum and SiC/single crystal composites is presented and discussed.

Investigation of Dislocation Behaviors in 4H-SiC Substrate during Post-Growth Thermal Treatment

Dislocation behaviors after post-growth thermal treatment were investigated by X-ray topography and KOH etching. Generation of prismatic dislocations were observed in X-ray topography, and density of basal plane dislocations (BPDs) increases with annealing temperature and radial temperature gradient. Distribution of newly generated BPDs in the wafer after thermal treatment is correlated to the resolved shear stress arising from radial temperature gradient.

Effects of normal strain on pyramidal I and II 〈c + a〉 screw dislocation mobility and structure in single-crystal magnesium

Abstract In this study, atomistic simulations were used to analyze the effects of nonglide stress and temperature on the mobility and structure of pyramidal-I (Pyr-I) and pyramidal-II (Pyr-II) 〈c + a〉 screw dislocations in single-crystal Mg. At a very low temperature (10 K), the pyramidal screw dislocations stably exist on Pyr-II planes and tend to glide on Pyr-I planes. The critical resolved shear stresses (CRSSes) of the pyramidal screw dislocations depend on the migration direction. Once a Pyr-II dislocation is transformed into a stuck core, a very high shear stress (243 and 391 MPa) is required to escape from the immobilized structure. Furthermore, their CRSSes increase with increasing compressive strain and decrease with increasing tensile strain normal to the slip planes. At the intermediate temperature range of 200 K ≤ T ≤ 400 K, the CRSSes of Pyr-I screw dislocations are weakly affected, whereas those of Pyr-II screw dislocations drastically decrease. Thus, both Pyr-I and Pyr-II screw dislocations have similar CRSS values at 400 K. At a higher temperature (500 K), Pyr-I screw dislocations frequently emit basal- 〈 a 〉 \langle a\rangle dislocation loops, and the remained dislocations are momentarily immobilized. The basal- 〈 a 〉 \langle a\rangle dislocation loops emitted from the 〈c + a〉 dislocations are quickly retracted, and the core structure is recovered as the shear deformation continues. This phenomenon can reduce the mobility of Pyr-I 〈c + a〉 screw dislocations at a higher temperature. The emission of basal- 〈 a 〉 \langle a\rangle dislocation loops is enhanced under compression.

Experimental and crystal plasticity finite element study of dynamic shear behavior of CoCrNiSi0.3 medium-entropy alloy

Single-phase CrCoNi-based medium-entropy alloys (MEAs) have garnered considerable attention as a promising class of metallic materials. However, despite this growing interest, the dynamic mechanical response of CrCoNi-based MEAs at high strain rate remains controversial. The dynamic shear mechanical behavior of CoCrNiSi0.3 was characterized through Hopkinson-bar experiment utilizing hat-shaped specimen. In this study, a damage model based on the maximum shear strain of each slip system was chosen to describe the damage initiation and evolution. Combined with this micro-scale damage and dislocation density-based crystal plasticity theory, two constitutive models were proposed to perform predictions of the dynamic shear behavior of CoCrNiSi0.3. The strain rate effect, adiabatic temperature rising, damage evolution, and twin volume fraction during dynamic shear deformation were tracked by investigating the influence of resolved shear stress, dislocation density, texture evolution, and twinning systems shear strain. The presented model effectively predicts the deformation state of specimen, the formation and evolution of Adiabatic Shear Bands (ASBs), and the variations in strain rate and temperature at different locations within the shear region. Adiabatic Shear Bands and texture evolution are caused by the local dislocation density rising and misorientation distributions.

Tension-compression asymmetry in Ti50Ni45Fe5 B2 intermetallic

This work investigates the asymmetry under tension and compression for the homogenized Ti50Ni45Fe5 B2 intermetallic. B2 matrix undergoes localized stress induced martensitic transformation (B2 → B19') under compression, resulting in a visible nonlinear elastic regime in the stress-strain curve. This was absent during deformation under tension; which could possibly be ascribed to lower resolved shear stress required for slip under tension than compression and a higher stress required for stress induced martensite transformation under tension than compression due to different martensite variants. The plastic deformation of B2 matrix under both tension and compression was marked by the presence and movement of stable elongated super intrinsic stacking faults, oriented along particular direction, which could be attributed to the activation of ⟨111⟩ screw dislocations.

In-situ Laue micro-diffraction during compression tests on Ce-TZP single crystal micropillars

The widespread use of ceramics faces challenges due to their limited ductility, stemming from a lack of dislocation-induced plasticity. This study focuses on ceria-stabilized tetragonal zirconia a ceramic that benefits from its unique tetragonal-to-monoclinic phase transformation under stress, leading to transformation-induced plasticity (TRIP). Employing a micro-scale in-situ approach, the study aims to understand the mechanisms governing TRIP, particularly focusing on crystallographic features of the transformation. In-situ compression tests using synchrotron light source and Laue micro-diffraction were conducted on single crystal micropillars with various orientations. Results show that crystal orientation significantly affects the mechanical behaviour, with transformation being most likely when the resolved shear stress on {100} planes of the double-cell and along the <010> direction is highest. The martensite theory validates the correspondences obtained experimentally. This research provides insights into enhancing the mechanical properties of ceramics by leveraging the TRIP mechanisms.

High temperature deformation behaviour and recrystallization mechanism of TiC/Ti6Al4V gradient material fabricated by laser directed energy deposition

Metal-ceramic gradient materials are of considerable interest due to their unique capability to integrate the ductility of metals with the mechanical strength and high-temperature resistance of ceramics, thereby reducing the risk of cracking induced by thermal stress. In this article, TiC/Ti6Al4V gradient materials were prepared through the laser directed energy deposition (LDED) process. Subsequently, high-temperature compression tests were performed at various temperatures to investigate the deformation behaviour and recrystallization mechanism of the gradient materials. The Zener-Holomon constitutive equation was then used to calculate the gradient material at 750–900 °C and 0.001–0.1 s−1 to obtain a deformation activation energy of 362.36 KJ·mol−1. The EBSD was used to analyze the microstructural evolution of the gradient material. The results indicate a significant reduction in the average grain size of the specimens after high-temperature compression, and a more random crystal orientation due to the occurrence of dynamic recrystallisation (DRX). The primary softening mechanism of TiC/Ti6Al4V gradient materials is discontinuous dynamic recrystallisation, with TiC primarily affecting the nucleation of discontinuous dynamic recrystallisation (DDRX) and the subsequent grain growth. The nucleation becomes easier with increasing TiC content. However, the TiC hinders the migration of grain boundaries, resulting in a smaller DDRX grain size. After high-temperature compression, the main slip system of the crystal is converted from Pri to Bas. Pyr is difficult to activate due to its high critical resolved shear stress.