Single Slip Research Articles

Analyzing shear band formation with high resolution X-ray diffraction

Localization of crystallographic slip into shear bands during uniaxial compression of a copper single crystal is studied using very far-field high-energy diffraction microscopy (vff-HEDM). Diffracted intensity was collected in-situ as the crystal deformed using a unique mobile detector stage that provided access to multiple diffraction peaks with high-angular resolution. From the diffraction data, single crystal orientation pole figures (SCPFs) were generated and are used to track the evolution of the distribution of lattice orientation that develops as slip localizes. To aid the identification of ‘signatures’ of shear band formation and analyze the SCPF data, a model of slip-driven lattice reorientation within shear bands is introduced. Confidence is built in conclusions drawn from the SCPF data about the character of internal slip localization through comparisons with strain fields on the sample surface measured simultaneously using digital image correlation. From the diffraction data, we find that the active slip direction and slip plane are not directly aligned with the orientation of the shear bands that formed. In fact, by extracting the underlying slip system activity from the SCPF data, we show that intersecting shear bands measured on the surface of the sample arise from slip primarily on the same underlying single slip system. These new vff-HEDM results raise significant questions on the use of surface measurements for slip system activity estimation.

In-situ observations of the tensile deformation and fracture behavior of a fine-grained titanium alloy sheet

Deformation and crack initiation of industrial Ti-6Al-4V titanium alloy sheet were investigated using in-situ scanning electron microscopy (SEM) at room temperature. The results showed that slip band originated from α/α and α/β interfaces when the tension reaches the yield stage, and the slip mode develops from single slip to multi slip and finally the cross-slip occurs. Microcracks initiate primarily at the phase boundary or along the slip band within α phase, cracks are mainly connected along the 45° line. The fracture surface is full of dimples. Intergranular cracking is the main fracture mechanism.

Characterization of the Long Crack Propagation Behaviour in a Hardenable Aluminium Alloy in Very High Cycle Fatigue Regime

In the regime of Very High Cycle Fatigue (VHCF), it appears questionable whether all the well-known stages of fatigue crack propagation occur. Deviations must be expected through the very small dimension of the cyclic plastic zone ahead of the crack tip and, hence, a strong interaction with microstructural features seems very likely. Investigations have shown that “natural” crack initiation often takes place underneath the material surface leading to crack propagation without contact to atmospheric components. In order to reproduce the crack growth behaviour, an ultrasonic fatigue testing system (USFT) equipped with a small vacuum chamber was used for fatigue experiments in vacuum. The tests were carried out on the aluminium alloy EN-AW 6082 in the peak-aged (pa) condition. Micro-notches were prepared in the USFT specimens by means of the Focused-Ion-Beam technique. Systematic measurements in laboratory air in the region of the threshold value of long fatigue crack growth revealed that primary precipitates significantly influence the crack growth behaviour. Depending on the spatial distribution of the primary precipitates, strong crack retardation and localized crack arrest take place even far above the threshold value. In vacuum only shear-stress-controlled VHCF long crack propagation were detected in EN-AW 6082 (pa) due to very pronounced single dislocation slip associated with the secondary precipitates of the aluminium alloy.

Fall risk during opposing stance perturbations among healthy adults and chronic stroke survivors.

Studies examining recovery from SLIPS and TRIPS indicate higher incidence of falls during SLIPS than TRIPS however, differences in the recovery mechanisms during these opposing perturbations have not been examined. We therefore aimed to compare the reactive balance responses contributing to fall risk during SLIPS and TRIPS at comparable perturbation intensity among community-dwelling healthy adults and chronic stroke survivors. Younger adults (N = 11), age-matched adults (N = 11) and chronic stroke survivors (N = 12) were exposed to a single SLIP and TRIP through a motorized treadmill (16m/s2, 0.20m). Center of mass (COM) state stability was measured by recording COM position and velocity relative to base of support, i.e., Ḋ COM/BOS and Ẋ COM/BOS, respectively. Trunk and compensatory step kinematics were alsorecorded. During SLIPS, the incidence of falls among stroke survivors was greater than healthy adults (53.83% vs. 0%), however not for TRIPS. All groups showed higher change in postural stability from liftoff to touchdown during TRIPS than SLIPS. Among healthy adults higher change in Ḋ COM/BOS during TRIPS was accompanied by the ability to control trunk flexion at step touchdown and lower peak trunk velocity as compared with SLIPS, with no significant differences in compensatory step length between the perturbations (p > 0.05). Chronic stroke survivors increased compensatory step length during TRIPS versus SLIPS (p < 0.05) contributing to greater stability change. They were unable to control trunk excursion and peak trunk velocity as compared with thehealthy adults leading to lower stability than healthy younger and age-matched adults during SLIPS and lower stability than younger adults during TRIPS. Difficulty in trunk control during SLIPS among all individuals and compensatory step length among stroke survivors emphasizes higher fall risk for SLIPS than TRIPS among these populations.

Thermodynamic dislocation theory for non-uniform plastic deformations

The present paper extends the thermodynamic dislocation theory developed by Langer, Bouchbinder, and Lookman to non-uniform plastic deformations. The free energy density as well as the positive definite dissipation function are proposed. The governing equations are derived from the variational equation. As illustration, the problem of plane strain constrained shear of single crystal deforming in single slip is solved within the proposed theory.

A reduced micromorphic single crystal plasticity model at finite deformations. Application to strain localization and void growth in ductile metals

A micromorphic single crystal plasticity model is formulated at finite deformations as an extension of Mandel’s classical theory based on a multiplicative decomposition of the deformation gradient. It involves a single microslip degree of freedom in addition to the usual displacement components. Two main variants of the constitutive equations are proposed. The first one relies on a Lagrangian microslip gradient and leads to a Laplace term in the isotropic hardening law. In contrast, the second formulation, based on a generalized strain measure defined with respect to the intermediate configuration, is shown to induce both isotropic and kinematic enhanced hardening. The first formulation is implemented in a 3D finite element code. The model is applied first to strain localization phenomena in a single crystal in tension undergoing single slip. The regularization power of the model is illustrated by mesh-independent simulations of the competition between kink and slip bands. The model is then used to investigate void growth and coalescence in FCC single crystals. Cylindrical and spherical voids are considered successively. The simulations show, for the first time in the case of spherical voids embedded in a single crystal matrix, that smaller voids grow slower than bigger ones, and that the onset of void coalescence is delayed for smaller voids. These results are related to the fact that the field of plastic slip is found to be more diffuse around smaller voids.

Critical stresses estimation by crystal viscoplasticity modeling of rate-dependent anisotropy of Al-rich TiAl alloys at high temperature

Determining critical stresses for different slip systems is one of the most important parts in crystal plasticity modeling of anisotropy. However, the task of finding individual critical resolved shear stress (CRSS) for every single slip system, if not impossible, is formidable and a delicate one especially if the microstructure is very complex. Slip family-based, mechanism-based and morphology-based (e.g., phase interface) slip systems classification and hence determining CRSS consistent with experimental measurements are often used in crystal plasticity. In this work, a novel approach to determining CRSS at high homologous temperature has been proposed by crystal plasticity modeling of rate-dependent anisotropy. Two-internal-variable-based phenomenological crystal viscoplasticity model is adopted for simulating isothermal, two-phase, single-crystal-like Al-rich lamellar Ti–61.8at.%Al binary alloy at high-temperature compression state ( $$1050\,^\circ \hbox {C}$$ ) by employing finite strain and finite rotation framework. To the best of authors’ knowledge, this is the first micromechanical modeling attempt with long-period superstructures. Conventional approaches related to CRSS estimation are also compared with the proposed one. Our material parameters are based on calibrating three different sets of compressive stain rate-controlled plasticity data taken from the loading of two different lamellar directions. It is revealed that the proposed approach works fine for rate-dependent anisotropy modeling, while other conventional approaches highly under- or overestimate available anisotropic experimental behavior of this alloy.

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.

Dislocation-density based description of the deformation of a composite material

Composite materials consisting of hard particles in a ductile metallic matrix are of major interest since their strength and deformability can be dramatically changed by varying volume fraction, size and shape of the particles. Understanding dislocation motion in composite materials as the cause of plastic deformation therefore is an important task. Recently, advanced dislocation-based continuum theories of plasticity have been developed for performing meaningful averages over systems of straight and curved dislocation lines in a continuum approach. In this paper, we focus on a single slip heterogeneous microstructure and investigate how the dislocation interactions can be represented in an averaged dislocation density based continuum description. The representation of strong dislocation density gradients is discussed in the context of a formulation, which aims at a coarse-grained resolution. We introduce a set of dislocation density evolution equations which account for the formation and dissolution of dislocation dipoles. By applying the model to a composite structure, we demonstrate that the dislocation density based description can well describe the physical processes in the microstructure and a comparison to discrete dislocation dynamics simulations shows good agreement for the relaxation behavior of the considered composites.

A gradient crystal plasticity theory for large deformations with a discontinuous accumulated plastic slip

The implementation of novel material models in the microscale gives a deeper understanding of inner and intercrystalline effects of crystalline materials. For future works, this allows more precise predictions of macroscale models. Here, we present a finite gradient crystal plasticity theory which preserves the single crystal slip kinematics. However, the model is restricted to one gradient-stress, associated with the gradient of the accumulated plastic slip, in order to account for long range dislocation interactions in a physically simplified, numerically efficient approach. In order to model the interaction of dislocations with and their transfer through grain boundaries, a grain boundary yield condition is introduced. The grain boundary flow rule is evaluated at sharp interfaces using discontinuous trial functions in the finite element implementation, thereby allowing for a discontinuous distribution of the accumulated plastic slip. Simulations of crystal aggregates are performed under different loading conditions which reproduce well the size dependence of the yield strength. An analytical solution for a one-dimensional single slip supports the numerical results.

Slip transmission behavior across α/β interface and strength prediction with a modified rule of mixtures in TC21 titanium alloy

Slip transmission behavior across α/β interface has been investigated in an α/β titanium alloy, TC21 alloy (Ti-6Al-2Sn-2Zr-3Mo-1Cr-2Nb-0.1Si). Scanning electron microscopy (SEM) was used to observe slip lines morphology and transmission across the interface in samples which undergo a certain tensile strain. Details of slip traces in α and β lamellae have been observed in detail by Transmission electron microscope (TEM). Atomic Force Microscopy (AFM) technique was used to observe and measure height of a single slip step at the surface of α lamellae. Two processes of slip transmission, direct transmission and a deviation of 10° angle from α to β lamellae, are observed at α/β interface corresponding to basal slip and prismatic slip in α phase, respectively. Slip transmission is not observed across α/βtrans interface when β phase is strengthened by fine α laths. A modified rule of mixtures is developed to predict yield strength of TC21 alloy by introducing an interaction term. Based on experimental data and slip transmission behavior from α to β lamellae, interaction term is calculated by multiplication of barrier stress and a coefficient. The coefficient is closely related to slip transmission behavior. Easy slip transmission across the interface leads to high absolute value of the coefficient, which indicates that the interaction term has an apparent effect on prediction of strength. The low absolute value means that interaction term from interface has less effect on prediction of strength than the high one.

Void nucleation behavior of single-crystal high-purity iron specimens subjected to tensile deformation

Void nucleation plays an important role for determining local deformation properties of ductile materials. In this study, the void nucleation behavior of single-crystal iron was examined in tensile tests.Two micrometer-size single crystals having a different type of slip extracted from electrodeposited pure iron were used to investigate the fracture mechanics during tensile deformation. Scanning electron microscopy (SEM) and high voltage electron microscopy (HVEM) images verified the existence of only a single slip system in the smaller specimen (cross-sectional area A = 16µm2) and furthermore, no voids were observed. However, multiple slips and voids were observed in the larger specimen (A = 28µm2). These findings allowed us to reveal that multiple slips are a necessary criterion for void nucleation in single-crystal iron.

The recovery response to a novel unannounced laboratory-induced slip: The “first trial effect” in older adults

BackgroundAfter a single slip, older adults rapidly make adaptive changes to avoid or eliminate further backward loss of balance or a fall. This rapid adaptation has been termed the “single trial effect”. The purpose of this study was to explore the relationship between the motor errors subjects experienced upon a novel slip and the selection and execution of corrective response by which they modified their ongoing gait pattern and turned it into a protective step. MethodsA forward slip was induced in the laboratory among 145 community-living older (≥65year old) adults who were protected by an overhead full body harness system. An eight-camera motion analysis system recorded subjects' kinematics, which was used to compute their instability (motor error), recovery step placement (response selection), and stability gain (motor correction). FindingsA linear relationship was found between the stability errors at recovery foot liftoff and the distance between the recovery foot and slipping foot at the time of its touchdown, reflecting an appropriate selection of response that was proportionate to the motor error. A linear relationship was also found between this step modification and resulting stability gain, indicating that greater step modification resulted in greater stability gain. This learning behavior was surprisingly consistent regardless whether the outcome was a recovery or a fall. InterpretationsThese results suggest that fallers and non-fallers all have an intact motor learning foundation that has enabled them to rapidly improve their stability in subsequent exposures.

A supplement to the studies of tralatitious editions of Shangshu and the character issues (II): A version comparison of Yueming

Four sources of the texts of Shangshu are referred to in this article: fragmented texts found on Chu Bamboo Slips of Warring States kept in Shanghai Museum, fragmented texts found on Bamboo Slips of Warring States kept in Tsinghua University, the transcript edition of Shangshu of the Tang Dynasty in ancient script kept in Japan, and the Gengwu edition of Shangshu kept in Korea. These editions represent, respectively, different tralatitious periods of Shangshu. The Tang transcript edition kept in Japan was written in ancient script; the Gengwu edition in Korea contains both ancient and modern scripts; the Bamboo Slips kept in Tsinghua University are regarded as a transcription of the Warring States period. Of the Yueming chapter (part one), many texts in the Bamboo Slips that are kept in Tsinghua University are not compatible with those in the tralatitious editions, or are in contradiction with historical records. Even on a single slip, the texts are often in disorder and unreadable. However, this does not mean that the readable and fluent texts in ancient transcript and print editions testify to the authenticity of the materials. From the level of document dissemination, if the bamboo slip texts are authentic, then we can conclude that there were errors, missing characters, and transcribing errors in the three parts of Yueming in the period as early as the later Warring States period. A comparative study of different editions shows the disagreement in paragraphing and characters in the Tang transcript edition kept in Japan and the Gengwu edition kept in Korea which reflects the version of Shangshu after the merging of the modern and ancient script editions.

Modeling the formability of aluminum alloys at elevated temperatures using a new thermo-elasto-viscoplastic crystal plasticity framework

Industrial processes often use high temperature forming of alloys such as aluminum that have unsatisfactory room temperature formability. Accurate forming models to integrate warm forming in production environment have been hampered by a lack of constitutive relations at elevated temperatures, forcing one to rely on experimental data for such integration. In this paper, the new thermo elasto-viscoplastic (TEV) crystal plasticity constitutive framework developed by Cyr et al. [1] is implemented in an Marciniak–Kuczynski [2] analysis to predict the forming limit diagrams (FLDs) of the AA5754 and AA3003 aluminum alloys at elevated temperatures. The model takes into account the temperature dependence of the single crystal elastic coefficients, single slip hardening parameters, thermal softening, slip rate sensitivity, and the total deformation. Temperature dependent hardening parameters have been determined through curve fitting the simulated stress–strain response with experiments during uniaxial tension at room and elevated temperatures. The calibration of the TEV model for the single slip parameters in uniaxial tension is shown to provide accurate predictions of the experimental forming limit diagrams (FLDs) without the need for further curve fitting. The effects of elastic constants and thermal softening on FLD prediction are discussed, and equations are developed to predict the temperature dependence of single-slip hardening parameters and so-called initial imperfection parameter employed in the Marciniak–Kuczynski (M–K) analysis. The predictive capability of the new model is then demonstrated by FLD simulations for various elevated temperatures.

Non-spherical voids and lattice reorientation patterning in a shock-loaded Al single crystal

An Al single crystal shock loaded in the <1 2 3> direction and captured at incipient spallation was examined by combining X-ray tomography, electron backscatter diffraction on a scanning electron microscope, and transmission electron microscopy (TEM). Octahedral voids with {1 1 1} faces were a characteristic feature in the spall region. Regular patterns of lattice reorientation were found around individual voids, with lattice rotation being up to 25–30°. Each reorientation pattern consists of a number of reoriented zones. The direction of lattice rotation varies systematically from one zone to another. Four groups of reorientation patterns were identified morphologically in the same metallographic section, which result from different sectioning positions relative to the voids and thus provide equivalently a “serial sectioning” investigation of the deformed volume around the voids. An analysis of the observed reorientation patterns based on active slip systems rationalizes the key features observed and suggests that the systematic reorientation patterns result from the dominance of a single slip system in each individual zone. Microstructures revealed by TEM in the spall region show formation of dislocation cells and extended dislocation boundaries, illustrating the importance of plastic deformation during void growth.

Strain‐dependent partial slip on rock fractures under seismic‐frequency torsion

AbstractMeasurements of nonlinear modulus and attenuation of fractures provide the opportunity to probe their mechanical state. We have adapted a low‐frequency torsional apparatus to explore the seismic signature of fractures under low normal stress, simulating low effective stress environments such as shallow or high pore pressure reservoirs. We report strain‐dependent modulus and attenuation for fractured samples of Duperow dolomite (a carbon sequestration target reservoir in Montana), Blue Canyon Dome rhyolite (a geothermal analog reservoir in New Mexico), and Montello granite (a deep basement disposal analog from Wisconsin). We use a simple single effective asperity partial slip model to fit our measured stress‐strain curves and solve for the friction coefficient, contact radius, and full slip condition. These observations have the potential to develop into new field techniques for measuring differences in frictional properties during reservoir engineering manipulations and estimate the stress conditions where reservoir fractures and faults begin to fully slip.

Orientation dependent spheroidization response and macro-zone formation during sub β-transus processing of Ti-6Al-4V alloy

In the present study, sub β-transus static annealing was carried out on a (α+β)-warm-rolled (700 °C, 90% thickness reduction) Ti-6Al-4V alloy at 900 °C for various durations (15, 30, 45, 60, 75 and 90 min). The key observation was that the spheroidization response of the constituent α-colonies from the starting warm-rolled material differs significantly during subsequent (α+β)-annealing treatment. While some of the α-colonies underwent an early morphological conversion from lamellar to equiaxed, some others stayed stable for prolonged durations. This unique phenomenon has been examined, for the first time, from an orientation perspective by coupling slip activation, boundary formation, and interfacial energy anisotropy of individual α-colonies with their response to static spheroidization. Orientation of the α-colonies in reference to the loading directions dictate the nature of slip activation (single versus multiple slip; basal or prism <a> slip plus pyramidal 〈c+a〉 slip) during prior (α+β)-rolling. During subsequent static (α+β)-annealing, this factor translates into the relative ease of boundary splitting and thermal grooving for them. Formation of longitudinal boundaries, then set the order of spheroidization for diffusion based coarsening processes during long term annealing. Anisotropy in interfacial energy, owing to the loss of coherency during prior deformation (warm-rolling), creates further orientation dependency in the spheroidization sequence. An immediate consequence of this orientation dependent spheroidization response is realized in the formation of the macro-zones for two-phase Titanium alloys after secondary thermomechanical processing. Some remedial processing strategies are highlighted therein.

Homogenization of layered materials with rigid components in single-slip finite crystal plasticity

We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense that it admits only local rotations, the other one is softer featuring a single active slip system with linear self-hardening. As a main result, we obtain explicit homogenization formulas by means of Gamma -convergence. Due to the anisotropic nature of the problem, the findings depend critically on the orientation of the slip direction relative to the layers, leading to three qualitatively different regimes that involve macroscopic shearing and blocking effects. The technical difficulties in the proofs are rooted in the intrinsic rigidity of the model, which translates into a non-standard variational problem constraint by non-convex partial differential inclusions. The proof of the lower bound requires a careful analysis of the admissible microstructures and a new asymptotic rigidity result, whereas the construction of recovery sequences relies on nested laminates.

Laue micro-diffraction and crystal plasticity finite element simulations to reveal a vein structure in fatigued Cu

The formation of a vein during cyclic shearing of a single copper crystal oriented for single slip can be followed in transmission Laue diffraction by analyzing the spatially resolved lattice rotation evolution. Because Laue transmission integrates the signal over the thickness of the sample, the structure of the vein in the beam direction is a priori believed to be inaccessible. Here we show that the vein geometry in the beam direction can be retrieved by comparing lattice curvature tensor components from crystal plasticity finite element simulations with those experimentally derived. Virtual sectional analysis facilitates the interpretation of the measured lattice curvatures of quasi-2D dislocation structures, allowing identifying a vein morphology that is slightly vertically and horizontally inclined in the through thickness direction.