Crystal Plasticity Framework Research Articles

Modeling cyclic deformation of austenitic stainless steels at elevated temperatures using a physically-based mesoscale crystal plasticity framework

Austenitic stainless steels demonstrate significant changes in key macroscale deformation responses at elevated temperatures; these changes are relatively well-understood at micro- and macroscales in the framework of dynamic strain aging (DSA). At the microscale, temperature-dependent behavior is attributed to enhanced solute mobility and subsequent pinning of dislocations by solute atmospheres. At the macroscale, phenomenological equations are used to approximate microscale material behavior. However, the connection between unit dislocation processes at the microscale and macroscale deformation behaviors is unclear. In the current study, a dislocation density-based crystal plasticity model is used to relate micro- and macroscale responses for cyclic loading of austenitic stainless steels at elevated temperatures. Specifically, the variation in deformation behavior at elevated temperatures is attributed to modifications in the heterogenous distribution of dislocations on the mesoscale. The proposed framework demonstrates good agreement with experiments for strain- and stress-controlled cyclic loading scenarios. The model is also shown to be able to address key phenomena associated with DSA, i.e., negative strain rate sensitivity and stress-strain curve serrations.

Influence of microstructure on the failure of ultra-high molecular weight polyethylene composite beams impacted by blunt projectiles

Increasing the fibre tensile strength is well-known to improve the ballistic performance of ultra-high molecular weight polyethylene (UHMWPE) fibre composite beams. Here we investigate modifying ply microstructure as an alternate way to enhance ballistic performance. Specifically, we numerically investigate the mechanisms via which failure is initiated in [0o/90o]nlaminates comprising UHMWPE tape plies and compare with the commonly used UHMWPE fibre composites. Each ply of the beam is discretely modelled using a pressure-dependent crystal plasticity framework with the deformation mechanisms of the tape and fibre-based microstructures modelled by recognising differences in the available slip system in these two material systems. The numerical calculations are used to construct failure mechanism maps for a range of impact velocities, ply shear strengths and ply tensile strengths. Three dominant failure mechanisms emerged from the study: (i) failure of plies immediately under the projectile via an indirect tension mechanism in which compressive stress imposed normal to the plies by the projectile induces tensile in-plane ply stress due to the anisotropic expansion of the alternating 0o/90o plies; (ii) failure due to tensile straining at the rear of the impacted beam resulting from a combination of beam bending and stretching and (iii) a shear plugging like failure mode due to tensile straining at the edge of the impact site. Tensile stress generation by indirect tension is significantly reduced in the tape-based microstructures due to the unavailability of the slip systems that result in lateral plastic expansion. In fact, our calculations suggest that over the entire range of parameters modelled here the tape-based microstructures outperform the fibre-based microstructures. This suggests an alternate route to enhancing the ballistic performance compared to the traditional methods that rely mainly on increasing fibre strength.

Texture effects and rate-dependent behaviors of notched magnesium bars

It is known that the mechanical behavior of many hexagonal close-packed (HCP) materials is sensitive to textural variations. In the technologically important magnesium (Mg) alloys, the anisotropic plastic behaviors and their dependence on different processing-induced textures have been reasonably well studied under relatively simple stress states. However, a detailed assessment of the rate-dependent microstructure–property linkages under triaxial stress states is relatively less explored. In this work, we present a computational investigation of the role played by strain rate, texture, and stress state in the macro–micro mechanical characteristics of Mg alloys. Three-dimensional boundary value problems using smooth and notched round bar geometries subjected to tensile deformation are modeled using a crystal plasticity framework that includes slip and twinning deformation mechanisms. We examine the responses over six orders of magnitudes of strain rates, for three different initial textures that span a broad spectrum of textural strengths, and three specimen geometries that induce varying levels of stress triaxiality. The simulations reveal a remarkable transition of the tensile response from a conventional power-law type to a sigmoidal type for certain combinations of textures, stress triaxiality levels, and strain rates. While the stress response is strongly rate-dependent, the macroscopic deformation anisotropy has a negligible effect from strain rate compared to the role of the stress state and texture. We discuss the potential implications of these observations on the rate-dependent failure of Mg alloys.

Thermomechanical modeling of crystallographic anisotropy effect on machining forces based on crystal plasticity framework

In this work, the effect of the crystallographic anisotropy on machining forces is studied through a thermomechanical approach based on rate sensitive plasticity based model. A crystal plasticity framework is adopted to formulate the required constitutive equations. The present approach takes into account the material thermoviscoplastic response, the shear strain rate distribution in the primary shear zone and their effects on the lattice rotation. The machining forces as well as the corresponding specific energies are calculated using two methods: (a) the total power minimization procedure and (b) the Merchant shear angle procedure. The proposed model is validated using cutting force data available in the literature. Then, it is used to gain insight into the effect of the crystallographic anisotropy on machining forces. According to the results, a strong dependence of the machining forces to the crystallographic orientations is obtained. The model is also used to analyze the of the cutting velocity on the shearing along crystallographic slip systems through the material thermomechanical response. In addition, it is observed that, compared to the total power minimization procedure, the Merchant shear angle procedure allows capturing the specific cutting energy trends due to the crystallographic anisotropy, in terms of peaks and valleys.

Micromechanical crystal plasticity back stress evolution within FCC dislocation substructure

Experiments and theories have suggested the evolution of intragranular back stress is primarily dependent on the characteristics and development of dislocation substructure in face-centered cubic (FCC) metals and alloys. Despite this, continuum modeling of complex cyclic loading phenomena such as inelastic ratchet strain accumulation typically appeals to one of several phenomenological back stress forms with weak connections to physical mechanisms. In the current work, a micromechanically-based back stress evolution law is derived and implemented in a crystal plasticity framework for FCC metals that directly considers the evolution of dislocation substructure. The model is used in a case study of stainless steel 316L (SS316L), and good agreement is found with experiments on single- and poly-crystalline specimens subjected to monotonic, fully-reversed cyclic loading, and stress-controlled cyclic loading with mean stress. Ratcheting is attributed to dislocation substructure formation, dissolution, and stabilization within this physically-based framework.

Numerical treatment of small strain single crystal plasticity based on the infeasible primal-dual interior point method

In this contribution, a small strain single crystal plasticity framework in the context of an infeasible primal–dual interior point method (IPDIPM) is discussed with a focus on the numerical treatment. Related to rate-independent algorithms in the field of single-crystal plasticity, the use of the IPDIPM to solve the constrained optimization problem offers the advantage that it handles the naturally arising redundancy in the slip system intrisically through a barrier term. This formulation penalizes the approach of the unfeasible domain, whereas the penalization term gradually approaches zero in the algorithm. This paper focusses on the numerical treatment and presents different tangent operator formulations and compares their convergency behavior in a numerical example.

The effects of internal stresses on the creep deformation investigated using in-situ synchrotron diffraction and crystal plasticity modelling

In this study we investigated the evolution of meso-scale internal stresses and those effects on local deformation behaviour during incremental plastic and creep deformation in type 316H stainless steel at 550 °C, using in-situ X-ray synchrotron diffraction and crystal plasticity modelling. Owing to the fast data accusation rate of synchrotron diffraction technique, for the first time, the transient behaviour of different grain families was captured during initial fast stress relaxation period of the displacement-controlled creep dwells. Significantly it is found that the evolution of internal stresses during time independent plastic deformation is distinct from that during time dependent creep deformation. During plastic deformation, lattice strains in the {311} grain family exhibit linear behaviour whereas during creep deformation it exhibits non-linear behaviour, instead the {111} grain family exhibit linear behaviour. A novel unified constitutive law was devised within crystal plasticity framework based on the theoretical physics; the model successfully predicts the macroscopic deformation behaviour as well as the distinction between the evolution of meso-scale internal stresses during plastic and creep deformation, therefore, correctly accounting for the effect of internal stresses generated during plastic deformation on the subsequent creep deformation. The validated model has elucidated the grain-neighbouring effects on individual grain deformations.

Crystal plasticity modeling of non-Schmid yield behavior: from Ni3Al single crystals to Ni-based superalloys

A crystal plasticity finite element (CPFE) framework is proposed for modeling the non-Schmid yield behavior of L12 type Ni3Al crystals and Ni-based superalloys. This framework relies on the estimation of the non-Schmid model parameters directly from the orientation- and temperature-dependent experimental yield stress data. The inelastic deformation model for Ni3Al crystals is extended to the precipitate (γ′) phase of Ni-based superalloys in a homogenized dislocation density based crystal plasticity framework. The framework is used to simulate the orientation- and temperature-dependent yield of Ni3Al crystals and single crystal Ni-based superalloy, CMSX-4, in the temperature range 260–1304 K. Model predictions of the yield stress are in general agreement with experiments. Model predictions are also made regarding the tension–compression asymmetry and the dominant slip mechanism at yield over the standard stereographic triangle at various temperatures for both these materials. These predictions provide valuable insights regarding the underlying (orientation- and temperature-dependent) slip mechanisms at yield. In this regard, the non-Schmid model may also serve as a standalone analytical model for predicting the yield stress, the tension–compression asymmetry and the underlying slip mechanism at yield as a function of orientation and temperature.

Fracture initiation in a single crystal copper edge-crack specimen for various crystallographic orientations

The motivation of the present study entails the determination of fracture initiation of a single crystal copper edge-crack specimen subjected to tensile load by considering the influence of crystallographic anisotropy, strain hardening and damage accumulation. To accomplish the purpose of this study, a damage criterion coupled with crystal plasticity finite element method was used to determine material softening after the peak load. Damage evolution was chosen as the function of maximum shear strain within the crystal plasticity framework. Coupled with a damage criterion, the crystal plasticity model was used to reproduce the stress-strain responses of copper single crystals until failure. The model was then applied to assess damage evaluation near crack-tip of a single crystal copper edge-crack specimen along two crystallographic orientations of tensile loading directions. The analysis abetted to predict fracture initiation (J-initiation) of a crack lying along various crystallographic orientations, while keeping the loading direction orientation identical in all the cases. The methodology presented here has the scope to analyze single crystal complex structures with cracks subjected to loading along various crystallographic orientations.

Self-consistent, polycrystal rate-independent crystal plasticity modeling for yield surface determination

The evolution of the macroscopically observed yield surface has been the subject of many studies due to its significant effect on the numerical simulation of metal forming processes. Although macroscopic models exist that aim to define this evolution accurate data for calibration as well as validation of these models are difficult to obtain. One common approach is to use crystal plasticity simulations for analyzing the mesoscopic behavior followed by a homogenization scheme for gathering the aggregate behavior. In this study a similar approach is followed the difference being the choice of the crystal plasticity and homogenization methods. A rate-independent crystal plasticity framework where all slip system activities are solved implicitly using a backward Euler approach in combination with an interior point method for constrained optimization is used for single crystal behavior. The aggregate behavior is obtained using a self-consistent analytical homogenization scheme. The results of the homogenization scheme are compared against full-field crystal plasticity finite element simulations. The determination of the yield surface is done by considering the macroscopic behavior where the strain rate direction and magnitude changes over a threshold during stress-based loading.

Atomistically informed crystal plasticity analysis of deformation behavior of alloy 690 including grain boundary effects

In this paper, we predict the deformation behavior of alloy 690 by explicitly modeling finite thickness grain boundaries within the crystal plasticity framework. This is realized by using a blend of quasi-static tensile experiments, microstructural characterization using scanning electron microscopy, atomistic simulations and crystal plasticity finite element analysis. We begin with material characterization to probe the type of grain boundaries present in the Ni-based alloy 690. Inspired by physically justified multiscale modeling schemes, we then use atomistic simulations within the framework of embedded-atom method to quantify activation parameters for dislocation nucleation from those grain boundaries in Ni bicrystals. The kinetic activation parameters are then passed on to a transition state theory based crystal plasticity model. At this scale, the grain boundaries are explicitly modeled using finite elements and prescribed distinct constitutive parameters obtained from lower scale atomistic simulations. The predictive capabilities of the adopted methodology are demonstrated by capturing the uniaxial tensile behavior of alloy 690 at different temperatures (250C–6000C) (stress-strain curves as well as texture evolution). Our implementation of grain boundaries in crystal plasticity is built upon a standard representative volume element used in most polycrystalline simulations. It is envisioned that this comprehensible approach will provide a compelling platform for unifying many other interface related deformation processes at the mesoscale. Eventually, the demonstrated methodology can expedite in apprehending the structure-property relationships through apt use of physically justified multiscale modeling schemes.

Handling tensors using tensorial Kelvin bases: application to olivine polycrystal deformation modeling using elastically anistropic CPFEM

In this work we present a simple and convenient method for handling tensors within computational mechanics frameworks based on the Kelvin decomposition. This methodology was set up within a crystal plasticity framework which permits, using the Kelvin base related to the crystal symmetries, to account for elastic anisotropy. The classical mixed velocity pressure finite element formulation has been modified in order to account for the elastic anisotropic behavior introduced into the crystal plasticity model. Moreover this modification of the mixed formulations allows to account for volume/pressure variations that can stream from constitutive models that could allow present compressible plasticity. Using this numerical framework, we explore the influence of elastic anisotropy onto the mechanical behavior of olivine. Our results suggest that at the polycrystal scale, the elastic anisotropy is not of first order importance. However the local changes on the stress state can be important for some physical phenomena such as recrystallization and damage.

A crystal plasticity investigation of grain size-texture interaction in magnesium alloys

This work investigates the microstructure-property linkages in magnesium (Mg) with an emphasis on understanding interaction effects between the grain size, texture, and loading orientation. A single crystal plasticity framework endowed with experimentally informed micro Hall-Petch type relations for the activation thresholds for slip and twinning is adopted to resolve polycrystalline microstructures over a broad texture-grain size space. The macroscopic trends from the simulations corroborate with experiments. The synergistic effects of microstructural engineering on the micromechanical characteristics are mapped, which reveal their role in the emergent macroscopic behaviors. The simulations predict reduced extension twinning with grain size refinement even though the micro Hall-Petch coefficient for twinning is smaller than that for the non-basal slip modes. While grain refinement and textural weakening generally reduce the net plastic anisotropy and tension-compression asymmetry, the degree to which these macroscopic behaviors are tempered depends on the loading orientation. The results offer preliminary insight into the roles that texture and grain size may play in the damage behavior of engineered Mg microstructures.

Misorientation and grain boundary orientation dependent grain boundary response in polycrystalline plasticity

This paper studies the evolution of intergranular localization and stress concentration in three dimensional micron sized specimens through the Gurtin grain boundary model (J Mech Phys Solids 56:640–662, 2008) incorporated into a three dimensional higher-order strain gradient crystal plasticity framework (Yalcinkaya et al. in Int J Solids Struct 49:2625–2636, 2012). The study addresses continuum scale dislocation-grain boundary interactions where the effect of crystal orientation mismatch and grain boundary orientation are taken into account through the grain boundary model in polycrystalline metallic specimens. Due to the higher-order nature of the model, a mixed finite element formulation is used to discretize the problem in which both displacements and plastic slips are considered as primary variables. For the treatment of grain boundaries within the solution algorithm, an interface element is formulated and implemented together with the bulk plasticity model. The capabilities of the framework is demonstrated through 3D polycrystalline examples considering grain boundary conditions, grain boundary strength, the orientation distribution and the specimen size. A detailed grain boundary condition and stress concentration analysis is presented. The advantages and the disadvantages of the model is discussed in detail through numerical examples.

Thermodynamically consistent formulation coupling crystal plasticity theory and Johnson-Cook damage model to simulate micromachining of copper

In this work, a microstructural-related model was developed to simulate micromachining of FCC polycrystalline copper. Indeed, a crystal plasticity framework was adopted to describe the anisotropy of the mechanical behavior. Some material microstructure characteristics (such as grain size, grain misorientation and crystallographic orientation) are explicitly considered through the constitutive model. For describing the material removal during chip formation, a modified thermodynamically consistent formulation of the Johnson-Cook damage model was used. The model was implemented in the ABAQUS/Explicit finite element solver with a user-defined subroutine, and the experimental validation was performed using data on the cutting forces available in the literature. Finally, the model was used to investigate the effect of the microstructure on the micro-machining cutting forces and chip formation process. According to the results, the proposed model allows capturing the cutting forces trends due to the crystallographic anisotropy.

Computational rate-independent strain gradient crystal plasticity

Size effects in metal plasticity are widely accepted, and different theoretical approaches to handle the phenomenon are developing in the literature. The present work considers the Fleck and Willis (2009b) framework, and creates a new gradient enhanced rate-independent crystal plasticity FE-implementation. The study considers both energetic and dissipative gradient hardening and strengthening, and adopts a general form of the gradient enhanced effective slip rate. Monotonic and cyclic shearing of an infinite crystal slab containing a single slip system at an angle of 90° to the loading direction is a first benchmark case. A second case considers combined shear and tension in 2D of a constrained HCP single crystal. The HCP crystal is loaded in its basal plane by a so-called butterfly deformation path that inflicts repeated loading and unloading of the three crystallographic slip systems. Finally, the evolution and interaction of multiple plastic zones are demonstrated by considering a notched tensile sample. A direct comparison to visco-plastic (rate-dependent) simulations confirms that the proposed crystal plasticity framework forms a rate-independent limit for the gradient enhanced Fleck–Willis theory. The model response also reduces to that of conventional crystal plasticity in the limit of zero length parameters.

A Lattice-misfit-dependent Micromechanical Approach in Ni-based Single Crystal Superalloys

In Ni-based single crystal superalloys, the macroscopic properties are intertwined with their complex bi-phased γ (NiAl)/γ’ (Ni3Al) microstructure. This study aims to better understand the coupled effect of lattice misfit and microstructural state on the macro-scale performance by utilizing a faithful representation of the microstructure, via a phase-field model, as a starting point for a micromechanical model embedded in a finite-element crystal plasticity framework. We outlined a micromechanical model with a lattice-misfit-dependent isotropic hardening that takes a unique description depending on the phase: an Eshelby tensor (sphere or penny) for the precipitates (γ’ phase) and a continuous medium for the matrix (γ phase). Finite-element simulations of strain-controlled monotonic tensile and alternate cyclic tests were performed on a set of realistic 3D phase-field microstructures (cuboidal states and directionally coarsened rafted states) defined by their natural (undeformed) or constrained (deformed) lattice misfits and the width of the γ matrix channels. As the magnitude of the natural lattice misfit gets larger for the cuboidal microstructural states, the tensile test simulations predict smaller macroscopic yield stress and strain hardening as well as smaller stress triaxiality at the microstructure level. The model also predicts that having a more pronounced rafted microstructure yields a smaller stress triaxiality at the microscale. The cyclic simulations showed that the averaged stress triaxiality at the microscale during five simulated cycles is the smallest for a natural lattice misfit of -0.3% and a 60% completed rafting process. These insights allow to better understand the experimental studies that investigated the effect of microstructural states on the mechanical response during monotonic and cyclic loading.

Computational analysis of the evolution of the brittle-to-ductile transition of tungsten under fusion conditions

Tungsten components inside fusion reactors are subjected to extreme conditions, including an exceptionally high heat flux. This loading induces high stress levels, that may lead to brittle fracture. The current work aims to provide novel insights by relating the risk for brittle fracture to the tungsten microstructure and loadings conditions. To this end, a crystal plasticity framework is adopted with a temperature dependent slip resistance. The required parameters are obtained from experimental data in the literature. The risk for brittle fracture is assessed by means of Beremin’s weakest-link theory. The brittle-to-ductile transition temperature (BDTT) found in literature can be accurately described with the presented framework. The simulation results reveal that the BDTT decreases linearly with the volume fraction of recrystallized grains in the microstructure. It is also shown that a sharp interface between rolled and recrystallized microscopic grains is more favourable in terms of risk for brittle fracture.

Fatigue Behavior of Additively Manufactured IN718 with Columnar Grains

Fatigue failure of polycrystalline materials is often dominated by crack initiation processes, which are strongly influenced by salient features existing in the microstructure. Herein, a crystal plasticity framework based on the finite element method is used to quantitatively assess the mechanistic drivers existing in columnar IN718 polycrystals for fatigue crack nucleation. To that end, microstructurally differing polycrystalline samples are subjected to strain‐controlled cyclic loading at ambient conditions to elucidate the microstructural mechanisms of fatigue damage. 2D grain structures obtained from the cellular automata (CA) simulations of the additive manufacturing of IN718 are utilized to construct representative 3D microstructures for use in computational analyses. A criterion related to the stored energy density (SED) is used to predict the scatter in fatigue crack nucleation life. This criterion presents a unique and consistent approach toward predicting fatigue crack initiation at the microstructural scale. It is demonstrated that SED is necessary and sufficient to drive crack nucleation in low cycle fatigue. The results show that grain boundaries are the preferred crack initiation sites.

Why is local stress statistics normal, and strain lognormal?

In the present study we elucidate the nature of local strain statistics evolution during tensile deformation in polycrystalline materials. A rate-independent formulation was implemented within a crystal plasticity framework by the means of representative volume element (RVE) analysis. Local elastic strain, as well as stress, were found to obey a normal distribution, whereas the statistics of local plastic strain conforms to a lognormal distribution. In line with experimental observations, the plastic strain becomes progressively localised and the local regions of large strains make significant contribution to the overall average strain increase. The results reveal the nature of strain inhomogeneity at the microscale and emphasize the fact that in metallic materials the elastic strain accumulation represents an additive process, whereas plastic deformation is a multiplicative process.