Plastic Slip Research Articles

Study of the interplay between lower-order and higher-order energetic strain-gradient effects in polycrystal plasticity

Strain-gradient (SG) plasticity refers to a class of non-local theories in which gradients of plastic slip determine the storage of geometrically necessary dislocations, introducing a length-scale dependence in the mechanical behavior of crystalline materials, which is otherwise lacking in local theories. In this work, we incorporate lower-order (LO) and higher-order energetic (HOE) strain-gradient effects into a crystal plasticity fast Fourier transform (FFT)-based formulation to investigate the interplay of the length scale that each strain-gradient term introduces at the microscale, and the mechanical properties that result at the macroscale. For an applicable range of length scales, we consider two systems: a 1-D two-phase face centered cubic (FCC) laminate and a 3-D FCC polycrystal, and two uniaxial deformation modes: monotonic tension and cyclic tension–compression. We show that increases in the individual LO and HOE length scales increase the hardening rate and strength of the material, respectively. When combined, the strong LO hardening is less pronounced than the effect alone due to the lowering of the gradients due to the HOE microstress. We demonstrate that the LO and HOE hardening manifest as “isotropic” (yield surface expansion) and “kinematic” (yield surface shift) effects, respectively, consistent with their theoretical origins. We show that in cyclic loading, the Bauschinger effect emerges in both local and non-local calculations and link its origins and severity to the behavior in the strain field, slip-system rates, and the HOE microforce.

Consistent modeling of the coupling between crystallographic slip and martensitic phase transformation for mechanically induced loadings

AbstractA computational framework is proposed to model anisotropic metallic polycrystals subjected to mechanically induced loadings. It enables the simulation of crystal‐plasticity‐like phenomena at finite strains. The unified framework of thermodynamically consistent constitutive equations is formulated such that it couples the crystallographic slip and martensitic transformation theories. The constitutive description for the slip plasticity evolution incorporates an anisotropic hyperelastic law with self and latent‐hardening. The mechanically induced martensite formation kinematics is based on the crystallographic theory of martensitic transformations. The complete set of highly coupled equations is expressed in a single system of equations and solved by a monolithic solution procedure. It is based on the Newton–Raphson methodology and incorporates the complete linearisation leading to asymptotic quadratic rates of convergence. The quasi‐static discretized evolution equations are integrated with a fully implicit scheme, except for the critical resolved slip stresses, which employ the generalized midpoint rule. The plastic flow is integrated with an implicit exponential integrator to exactly preserve the plastic incompressibility. Viscous regularizations for both deformation mechanisms are pursued to overcome numerical difficulties and model the behavior over a wide range of strain‐rate sensitivities. Numerical examples are presented to demonstrate the efficiency and predictive capability of the methodology.

A novel crystal plasticity model incorporating transformation induced plasticity for a wide range of strain rates and temperatures

Transformation induced plasticity (TRIP) is an effect common to several classes of advanced high strength steels (AHSS) with promising automotive applications. This effect is characterized by the transformation of retained austenite (RA) to martensite, resulting in increased hardening, increased fracture resistance, and improved formability. Accurate thermo-mechanical modeling over a range of strain-rates and temperatures is critical to fully utilize the improved performance of AHSS exhibiting the TRIP effect. In this work, a novel thermodynamically consistent rate-dependent crystal plasticity formulation is developed, which incorporates strain-rate and temperature dependent strain-induced martensitic transformation. Thermodynamic arguments are used to derive plastic slip and transformation driving forces accounting for various physical mechanisms (e.g. applied stress, temperature, crystal orientation, stored dislocation energy), as well as a constitutive law governing temperature evolution. RA and transformed martensite mechanical thermo-elasto-viscoplastic behavior is explicitly modeled, and a modified Taylor homogenization law is proposed to determine strain partitioning while accounting for transformation. The model is then calibrated and validated for a QP3Mn alloy over a large range of temperatures (-10°C–70°C) and strain-rates (5 × 10-4s−1–200s−1). The evolution of the Taylor–Quinney coefficient and the orientation dependence of transformation are found to match well with trends in literature. The fully calibrated model is compared to a model recalibrated without strain-rate dependent transformation, demonstrating that capturing strain-rate dependent transformation may be necessary even for materials where no direct experimental strain-rate dependence. Plane strain and equibiaxial tension simulations are conducted using the calibrated model, showing that increasing triaxiality results in increased transformation. An extension to the calibrated model is proposed for materials which do not match the predicted trend.

Micromorphic crystal plasticity approach to damage regularization and size effects in martensitic steels

A reduced micromorphic model is formulated in the scope of crystal plasticity and crystalline cleavage damage. The finite strain formulation utilizes a single additional microvariable that is used to regularize localized inelastic deformation mechanisms. Damage is formulated as a strain-like variable to fit the generalized micromorphic microslip and/or microdamage based formulation. Strategies of treating slip and damage simultaneously and separately as non-local variables are investigated. The model accounts for size-effects that simultaneously affect the hardening behavior and allow to predict finite width damage localization bands. The results show that the micromorphic extension introduces extra-hardening in the vicinity of grain boundaries and slip localization zones in polycrystals. At the single crystal level slip band width is regularized. Two ways of dealing with damage localization were identified: An indirect method based on controlling width of slip bands that act as initiation sites for damage and a direct method in which damage flow is regularized together with or separately from plastic slip. Application to a real martensitic steel microstructure is investigated.

Analysis of tangential contact damping mechanism by direct observation using X-ray computed tomography

The damping of metal contact surfaces considerably influences the dynamic characteristics of machines. However, the contact damping mechanism has not yet been sufficiently clarified because it is difficult to directly observe metal–metal contact surfaces. In this study, the deformation of the metal surface asperity caused by a tangential load was analyzed using a combination of X-ray computed tomography and finite element method (FEM) simulations. The FEM simulation considering the elastic–plastic deformation and slip reproduced the experimental results well. The contribution of the elastic–plastic deformation and slip of asperities to contact damping was discussed using the developed simulation.

The mechanism of plasticity and phase transition in iron single crystals under cylindrically divergent shock loading

Cylindrically divergent shock loading significantly influences the plasticity and phase transition of iron. In this study, the mechanisms of plasticity and α→ε phase transition are investigated using large-scale nonequilibrium molecular dynamics simulation. We find that iron undergoes a local bcc–hcp–bcc–hcp (bcc: body-centered cubic; hcp: hexagonal close-packed) phase transition under cylindrically divergent shock loading with cylinder axis lying in [001] and [110] directions. A bcc lattice reorientation driven by resolved shear stress occurs during the hcp–bcc reverse transition and results in bcc twins, which transform into hcp twin structures with an unexpected c-axis, as compared with planar shock. Moreover, we analyze the coupling behavior between plasticity and phase transition and find that collective movement and rearrangement of atoms induced by plastic slip on the shuffle plane play a key role in the activation of phase transition, which significantly differs from that of planar shock.

Microstructure evolution of compressed micropillars investigated by in situ HR-EBSD analysis and dislocation density simulations

With decreasing system sizes, the mechanical properties and dominant deformation mechanisms of metals change. For larger scales, bulk behavior is observed that is characterized by a preservation and significant increase of dislocation content during deformation whereas at the submicron scale very localized dislocation activity as well as dislocation starvation is observed. In the transition regime it is not clear how the dislocation content is built up. This dislocation storage regime and its underlying physical mechanisms are still an open field of research. In this paper, the microstructure evolution of single crystalline copper micropillars with a $\langle1\,1\,0\rangle$ crystal orientation and varying sizes between $1$ to $10\,\mu\mathrm{m}$ is analysed under compression loading. Experimental in situ HR-EBSD measurements as well as 3d continuum dislocation dynamics simulations are presented. The experimental results provide insights into the material deformation and evolution of dislocation structures during continuous loading. This is complemented by the simulation of the dislocation density evolution considering dislocation dynamics, interactions, and reactions of the individual slip systems providing direct access to these quantities. Results are presented that show, how the plastic deformation of the material takes place and how the different slip systems are involved. A central finding is, that an increasing amount of GND density is stored in the system during loading that is located dominantly on the slip systems that are not mainly responsible for the production of plastic slip. This might be a characteristic feature of the considered size regime that has direct impact on further dislocation network formation and the corresponding contribution to plastic hardening.

Extreme Clusters of Grains in Random Microstructures of Polycrystals

It was experimentally observed that in polycrystalline materials under low macro loading of the specimen the first sites of failure initiation take place in the specific clusters of few grains. In some grains of these extreme clusters, the local (meso-) strains and stresses are high enough to cause first damages or plastic slips. In the stochastic microstructure of polycrystals, the formation of an extreme cluster is random and rare. Nevertheless, they govern the failure process initiation and can severely affect the reliability of polycrystalline machine parts. It is time and resource consuming to search and investigate extreme clusters on the real specimens of polycrystalline materials experimentally. A theoretical tool is desirable. Here we present the powerful computational method to look for extreme clusters, to investigate their possible patterns, and to evaluate the absolute maximums of local strains/stresses that can be achieved in these clusters. The experimentally observed clusters consist of few (3-4) preferably oriented neighboring grains or even of one big supergrain. The strain and stress bursts arise due to an interaction of the grains. One can expect that in bigger clusters, larger local bursts of fields can be generated. We found the typical forms of the extreme clusters (small and big) in four different polycrystals with grains of a weak and strong anisotropy for the case of uniaxial tension. In all regarded cases, the extreme clusters have the forms of the symmetrical patterns. In big clusters of highly anisotropic grains, the maximum of mesostrain exceeds the macrostrain by several times. In clusters of weakly anisotropic grains, the local strain concentration is rather moderate (tens of percents).

Micropillar compression of single crystal tungsten carbide, part 2: Lattice rotation axis to identify deformation slip mechanisms

The plastic deformation mechanisms of tungsten carbide at room and elevated temperatures influence the wear and fracture properties of WC-Co hardmetal composite materials. The relationship between residual defect structures, including glissile and sessile dislocations and stacking faults, and the slip deformation activity, which produce slip traces, is not clear. Part 1 of this study showed that 101¯0 was the primary slip plane at all measured temperatures and orientations, but secondary slip on the basal plane was activated at 600 °C, which suggests that 〈a〉 dislocations can cross-slip onto the basal plane at 600 °C. In the present work, Part 2, lattice rotation axis analysis of deformed WC micropillar mid-sections has been used to discriminate 〈a〉 prismatic slip from multiple 〈c + a〉 prismatic slip in WC, which has enabled the dislocation types contributing to plastic slip to be distinguished, independently of TEM residual defect analysis. Prismatic-oriented micropillars deformed primarily by multiple 〈c + a〉 prismatic slip at room temperature, but by 〈a〉 prismatic slip at 600 °C. Deformation in the near-basal oriented pillar at 600 °C can be modelled as prismatic slip along 〈c〉 constrained by the indenter face and pillar base. Secondary 〈a〉 basal slip, which was observed near the top of the pillar, was activated to maintain deformation compatibility with the indenter face. The experimentally observed lattice rotations, buckled pillar shape, mechanical data, and slip traces are all consistent with this model.

Resolved Stress of Long-Range Internal Stress Associated with Geometrically Necessary Dislocations

The influence of grain orientation on the resolved stress of long-range internal stress associated with geometrically necessary dislocations ( GNDs ) is numerically investigated. The GNDs accumulated at grain boundaries ( GBs ) do not systematically generate back stress to inhibit the dislocation motion. Surprisingly, relatively low anti-back stress promoting the plastic slip is derived from GNDs at certain GBs , which originates from a dependence of the expansion direction of dislocations on the grain orientation. This discovery on the deformation behavior of polycrystals provides guidelines to improve the physical content of current crystal plasticity models.

Creep-Fatigue Crack Initiation Simulation of a Modified 12% Cr Steel Based on Grain Boundary Cavitation and Plastic Slip Accumulation.

High-temperature components in power plants may fail due to creep and fatigue. Creep damage is usually accompanied by the nucleation, growth, and coalescence of grain boundary cavities, while fatigue damage is caused by excessive accumulated plastic deformation due to the local stress concentration. This paper proposes a multiscale numerical framework combining the crystal plastic frame with the meso-damage mechanisms. Not only can it better describe the deformation mechanism dominated by creep from a microscopic viewpoint, but also reflects the local damage of materials caused by irreversible microstructure changes in the process of creep-fatigue deformation to some extent. In this paper, the creep-fatigue crack initiation analysis of a modified 12%Cr steel (X12CrMoWvNBN10-1-1) is carried out for a given notch specimen. It is found that creep cracks usually initiate at the triple grain boundary junctions or at the grain boundaries approximately perpendicular to the loading direction, while fatigue cracks always initiate from the notch surface where stress is concentrated. In addition to this, the crack initiation life can be quantitatively described, which is affected by the average grain size, initial notch size, stress range and holding time.

FE-simulation of machining processes of epoxy with Mulliken Boyce model

This study simulates the cutting of epoxy-based material with the Mulliken-Boyce constitutive model using the Abaqus package. Two sizes of simulation models were established to represent micro- and macro-machining processes. The formation of epoxy chips is investigated under various finite element cutting conditions. It is found that the continuous, serrated, and broken epoxy chip types found in previous experiments can be realised via this simulation method. It is demonstrated that the machining of epoxy controlled by local deformation should be classified as a shear plastic slip mechanism consistent with experimental results. This simulation can be used to guide industrial production to achieve improvements in manufacturing.

Bauschinger effect and latent hardening under cyclic micro-bending of Ni-base Alloy 718 single crystals: Part I. Experimental analysis of single and multi slip plasticity

Cyclic micro-bending tests on fcc single crystal Ni-base Alloy 718 cantilevers with different crystal orientations were performed to analyze the influence of activated slip systems on dislocation plasticity, latent hardening and the Bauschinger effect. The investigations indicate that plasticity in single crystal micro-cantilevers is significantly influenced by two phenomena - dislocation interaction and dislocation pile-up at the neutral plane. Both phenomena occur at the same time. Their ratio seems to be determined by the activated slip systems. Slip trace analysis indicates that the activation of only one slip system leads to a strong localization of plasticity to a limited number of parallel slip bands. This results in low dislocation interaction and consequently pronounced pile-ups at the neutral plane. In multi slip orientation, the second slip system leads to activation of significantly more dislocation sources, causing a much earlier and more homogeneous elastic-plastic transition zone. In stress-strain hysteresis loops during bending, pronounced dislocation interaction in multi slip orientation leads to a more pronounced latent hardening. The results suggest that on a microstructural length scale, plasticity behavior is strongly affected by activated slip systems, which determine local dislocation phenomena. Based on the results presented in this paper, a finite element analysis of latent hardening and the Bauschinger effect using a single crystal plasticity model with latent kinematic hardening is presented in Part II.

A mechanistic model for creep lifetime of ferritic steels: Application to Grade 91

In this work, a physics-based crystal plasticity model is developed to predict failure in Grade 91 steel. A microstructure-sensitive dislocation kinetics law defines local plastic slip, an Arrhenius creep law is used to model vacancy-mediated plasticity, and strain hardening evolves with local dislocation density. As voids nucleate, a reaction–diffusion framework is adopted to dynamically track the local void size distributions, which grow by coupled viscoplastic and diffusive processes. Upon accurately reproducing the temperature and stress dependencies in primary, secondary, and tertiary creep seen experimentally for Grade 91 steel, the model is exercised to generate a material response database across a wide range of operating conditions. A new reduced-order lifetime predictor is developed from numerical predictions, and a Bayesian framework is used to quantify prediction uncertainties. When compared to current empirically-derived lifetime relations, the proposed lifetime assessment tool predicts rupture times up to several orders more conservative.

A stochastic solver based on the residence time algorithm for crystal plasticity models

The deformation of crystalline materials by dislocation motion takes place in discrete amounts determined by the Burgers vector. Dislocations may move individually or in bundles, potentially giving rise to intermittent slip. This confers plastic deformation with a certain degree of variability that can be interpreted as being caused by stochastic fluctuations in dislocation behavior. However, crystal plasticity (CP) models are almost always formulated in a continuum sense, assuming that fluctuations average out over large material volumes and/or cancel out due to multi-slip contributions. Nevertheless, plastic fluctuations are known to be important in confined volumes at or below the micron scale, at high temperatures, and under low strain rate/stress deformation conditions. Here, we develop a stochastic solver for CP models based on the residence-time algorithm that naturally captures plastic fluctuations by sampling among the set of active slip systems in the crystal. The method solves the evolution equations of explicit CP formulations, which are recast as stochastic ordinary differential equations and integrated discretely in time. The stochastic CP model is numerically stable by design and naturally breaks the symmetry of plastic slip by sampling among the active plastic shear rates with the correct probability. This can lead to phenomena such as intermittent slip or plastic localization without adding external symmetry-breaking operations to the model. The method is applied to body-centered cubic tungsten single crystals under a variety of temperatures, loading orientations, and imposed strain rates.

Investigation on the Effects of Grain Boundary on Deformation Behavior of Bicrystalline Pillar by Crystal Plasticity Finite Element Method

A dislocation density–grain boundary interaction scheme coupled with the dislocation density-based crystalline plasticity finite element method has been established and used to investigate the deformation behavior of bicrystalline pillars with the same grain boundary misorientation angle but different crystal orientations. It is found that the angle between the activated slip systems, which is determined by the crystal orientations, rather than the grain boundary misorientation angle, influences the interactions between the plastic slip and the grain boundary, which further influence the heterogeneous deformation of bicrystalline specimens.

Modeling plasticity of cubic crystals using a nonlocal lattice particle method

In this paper, a novel nonlocal crystal plasticity lattice particle method (CPLPM) is proposed and verified for modeling plasticity of cubic crystals. The proposed CPLPM is fundamentally different from the classical crystal plasticity finite element method, in which the underlying lattice structures are explicitly incorporated in the model formulation and lattice rotation is used to represent the material anisotropy of crystals. As a first attempt to develop a comprehensive CPLPM framework, constitutive relations based on the Schmid’s law and rate-dependent crystal plasticity for infinitesimal deformations are formulated for single crystals of face-centered and body-centered cubic lattice structures. Slip-system-dependent plastic deformation is automatically handled using the underlying crystal topology incorporated in LPM. Numerical solution algorithms for global iteration and plasticity state variables update are discussed in detail. The validity and prediction accuracy of CPLPM are established using several numerical examples, e.g., perfectly plastic deformation of single crystals, plastic slip near crack tip, and the calibration and prediction of experimental results. The performance of the CPLPM algorithm is also discussed considering different viscous properties.

Direct detection of plasticity onset through total-strain profile evolution

Plasticity in solids is dependent on microstructural history, temperature, and loading rate, and sample-dependent knowledge of yield points in structural materials adds reliability to mechanical behavior. Yielding is commonly measured through controlled mechanical testing, in ways that either distinguish elastic (stress) from total deformation measurements or identify plastic slip contributions. In this paper, we show that yielding can be unraveled through statistical analysis of total-strain fluctuations during the evolution sequence of profiles, measured in situ, through digital image correlation. We demonstrate two distinct ways of quantifying yield locations in widely applicable crystal plasticity models for polycrystalline solids, using either principal component analysis or discrete wavelet transforms. We test and compare these approaches for synthetic data of polycrystals and a variety of yielding responses through changes in applied loading rates and strain-rate sensitivity exponents.

Design of Longwall Coal Pillar for the Prevention of Water Inrush from the Seam Floor with Through Fault

Setting up a waterproof coal pillar is an important measure to prevent water inrush from the Weibei mining through fault floor. Based on the plastic slip line field theory, a mechanical model of floor water inrush induced by confined water in the through fault zone was established. The mechanical expressions of confined water pressure and the width of the waterproof coal pillar under the state of limit equilibrium were derived. Combining the laws of floor deformation, failure and fault activation under two kinds of coal pillar width, the safety width of the waterproof coal pillar was determined. Furthermore, the safety threshold is better than the empirical value mentioned in the “coal mine safety regulations.” Following this, grouting transformation was carried out on the K2 sand layer of the cut roadway floor. This provided a theoretical basis and engineering practice for water disaster prevention and the control of the structural floor under similar conditions in the Weibei mining area for future benefit.

Experimental and simulated investigations of low cycle fatigue behavior in a nickel-based superalloy with different volume fractions of δ phase

The fatigue crack initiation life and damage mechanisms of three heat-treated nickel-based alloy with different volume fractions of δ phase have been investigated based on experiment and crystal plasticity simulation. With the help of fatigue indicator parameters (FIPs), the predicted fatigue lives are agreed well with experimental results, where energy dissipation based FIP shows more accurate life prediction than plastic slip based FIP does. Maximum fatigue damage sites shift from grain boundary to δ phase boundary by increasing δ phase and applied strain level. Furthermore, the existence of δ phase leads to the increase of plastic slip accumulation and decrease of localized stress level.