Rate-dependent Crystal Plasticity Research Articles

Effect of wire diameter compression ratio on drawing deformation of micro copper wire

A crystal plasticity finite element model was developed for the drawing deformation of pure copper micro wire, based on rate-dependent crystal plasticity theory. The impact of wire diameter compression ratio on the micro-mechanical deformation behavior during the wire drawing process was investigated. Results indicate that the internal deformation and slip of the drawn wire are unevenly distributed, forming distinct slip and non-slip zones. Additionally, horizontal strain concentration bands develop within the drawn wire. As the wire diameter compression ratio increases, the strength of the slip systems and the extent of slip zones inside the deformation zone also increase. However, the fluctuating stress state, induced by contact pressure and frictional stress, results in a rough and uneven wire surface and diminishes the stability of the drawing process.

Comparison of Linear and Nonlinear Twist Extrusion Processes with Crystal Plasticity Finite Element Analysis.

The mechanical characteristics of polycrystalline metallic materials are influenced significantly by various microstructural parameters, one of which is the grain size. Specifically, the strength and the toughness of polycrystalline metals exhibit enhancement as the grain size is reduced. Applying severe plastic deformations (SPDs) has a noticeable result in obtaining metallic materials with ultrafine-grained (UFG) microstructure. SPD, executed through conventional shaping methods like extrusion, plays a pivotal role in the evolution of the texture, which is closely related to the plastic behavior and ductility. A number of SPD processes have been developed to generate ultrafine-grained materials, each having a different shear deformation mechanism. Among these methods, linear twist extrusion (LTE) presents a non-uniform and non-monotonic form of severe plastic deformation, leading to significant shifts in the microstructure. Prior research demonstrates the capability of the LTE process to yield consistent, weak textures in pre-textured copper. However, limitations in production efficiency and the uneven distribution of grain refinement have curbed the widespread use of LTE in industrial settings. This has facilitated the development of an improved novel method, that surpasses the traditional approach, known as the nonlinear twist extrusion procedure (NLTE). The NLTE method innovatively adjusts the channel design of the mold within the twist section to mitigate strain reversal and the rotational movement of the workpiece, both of which have been identified as shortcomings of twist extrusion. Accurate anticipation of texture changes in SPD processes is essential for mold design and process parameter optimization. The performance of the proposed extrusion technique should still be studied. In this context, here, a single crystal (SC) of copper in billet form, passing through both LTE and NLTE, is analyzed, employing a rate-dependent crystal plasticity finite element (CPFE) framework. CPFE simulations were performed for both LTE and NLTE of SC copper specimens having <100> or <111> directions parallel to the extrusion direction initially. The texture evolution as well as the cross-sectional distribution of the stress and strain is studied in detail, and the performance of both processes is compared.

Investigation of neighboring grain effects on load shedding in titanium alloys under cold dwell fatigue

Load shedding under cold dwell fatigue in titanium alloys has been a threat to the safety of the aero-engine since it is responsible for crack formation. The strain incompatibility between the soft-hard grain pair arises from the significant creep in the soft grain during the dwell period, which is fundamentally related to the load shedding. Such deformational heterogeneity is not only affected by the soft-hard grain itself but also by its neighboring grains, but the effect of the latter is rarely reported. In this paper, the effect of neighboring grains, including location, crystal orientation, texture, etc., on load shedding is quantitatively investigated using a three-dimensional rate-dependent crystal plasticity model by controlling the microstructural morphology of the grains. In particular, the mechanism that the dwell fatigue cracks tend to nucleate from the sample's interior rather than the free surface is revealed. Restriction of rigid body rotation from neighboring grains can further enhance load shedding. The crystal orientation of individual and group neighboring grains sitting at different locations with respect to the soft-hard grain pair is evaluated. The grain directly attached to the hard grain has the strongest influence. The statistics of load shedding are analyzed by conducting hundreds of simulations with different textures. Stronger textures are found to be able to enhance load shedding and thus deteriorate the service lifetime. The change of locations showing the highest stress during the dwell period arising from plastic deformation in neighboring grain may lead to the phenomenon of reverse load shedding. Understanding the neighboring grain effects from both the mechanistic basis and the statistical point of view is important in integrity evaluations and service life assessments of titanium components in aero-engines.

Phase Field Fracture Modelling of Crack Initiation and Propagation in Dual-Phase Microstructures

Dual-phase (DP) steel's spread in the industry has been fueled by its highly desirable qualities, which include a unique balance of strength and ductility, making it a valuable material for applications ranging from automotive manufacturing to construction. Despite the continued progress in the research of DP steels, the complex failure mechanisms at the microscale, resulting from the coexistence of brittle martensite phases within the ductile ferrite phase, remain an area of ongoing exploration. This study aims to investigate the micro structural evolution, as well as crack initiation and propagation, in DP steels at the microscale. In this context, to accurately capture the microstructural evolution of DP steels, a rate-dependent crystal plasticity formulation is utilized for the ferrite phase alongside a phenomenological isotropic J2 plasticity model for the martensite phase. A novel ductile phase-field fracture framework has been implemented to predict crack initiation and propagation, integrating both crystal plasticity and J2 plasticity constitutive models with the phase field fracture model. Generic 3D polycrystalline Representative Volume Elements (RVEs) are created and simulated to analyze the trends influencing the failure behavior of DP steels. The numerical study includes examples with two different martensite volume fractions (15% and 37%), each characterized by varying random crystallographic orientation sets and morphologies. The obtained results suggest that despite the similarity in stress concentration regions within two different random orientation sets in a simulation with fixed volume fraction and morphology, the resulting crack paths exhibit significant differences. Additionally, it is inferred that damage appears to accumulate at the junction points of the martensite islands. Moreover, an increase in the martensite volume fraction is found to diminish the influence of crystallographic orientation on the resultant crack path. Therefore, given the aforementioned findings, it is essential to analyze the microstructural evolution, as well as crack initiation and propagation in DP steels, utilizing appropriate material and fracture modeling frameworks at the microscale.

Strain rate-dependent plastic behavior of TWIP steel investigated by crystal plasticity model

A strain rate-dependent crystal plasticity finite element (CPFE) model was developed to describe the plastic behavior of TWIP steel over a wide range of strain rates, encompassing quasi-static to dynamic loadings. The developed model captures the effect of strain rate on the mechanisms governing dislocation motion and temperature rise. The mechanical behavior and underlying micro-mechanisms of TWIP steel during compression at different strain rates were then systematically investigated by combining the CPFE model with experimental tests. The results demonstrate that the developed model can accurately predict the mechanical response of TWIP steel over a wide range of strain rates from 10−3 s−1 to 104 s−1. It was observed that the yield stress presents a gradual increase with increasing strain rates below a threshold value of applied strain rate, beyond which the yield stress increases sharply. The stress drop after yielding under high strain rates is found to be attributed to the decreased viscous drag stress by increased dislocation density. Further quantitative analysis results show that the contribution of deformation twinning to the macroscopic flow stress is negligible for both high and low strain rates, and the strain hardening behavior of TWIP steel is mainly dominated by the forest dislocation stress.

Multi-scale plasticity homogenization of Sn–3Ag-0.5Cu: From β-Sn micropillars to polycrystals with intermetallics

The mechanical properties of β-Sn single crystals have been systematically investigated using a combined methodology of micropillar tests and rate-dependent crystal plasticity modelling. The slip strength and rate sensitivity of several key slip systems within β-Sn single crystals have been determined. Consistency between the numerically predicted and experimentally observed slip traces has been shown for pillars oriented to activate single and double slip. Subsequently, the temperature-dependent, intermetallic-size-governing behaviour of a polycrystal β-Sn-rich alloy SAC305 (96.5Sn–3Ag-0.5Cu wt%) is predicted through a multi-scale homogenization approach, and the predicted temperature- and rate-sensitivity reproduce independent experimental results. The integrated experimental and numerical approaches provide mechanistic understanding and fundamental material properties of microstructure-sensitive behaviour of electronic solders subject to thermomechanical loading, including thermal fatigue.

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.

Crack Initiation and Propagation in Dual-phase Steels Through Crystal Plasticity and Cohesive Zone Frameworks

Ferrite-martensite dual-phase (DP) steels have become popular in weight-reduced automotive components due to their straightforward thermomechanical processing and excellent mechanical properties. Even though it has been a popular and productive area of research, there are still many open questions related to their interesting microstructure. Being composed of brittle martensitic clusters dispersed in a ductile ferrite matrix, DP steels benefit from the properties of both phases, which induce interesting failure mechanisms at the same time. The microstructural parameters such as martensite volume fraction, grain size, carbon content, martensite/ferrite morphology, ferrite grain size, and texture, as well as micro and mesoscale segregation, make them difficult to analyze. However these aspects have to be studied in order to link the underlying microstructural influence to macroscopic behaviour. Therefore, the modelling techniques at the microstructure scale should be utilized for physical understanding. In this work, a multi scale modeling strategy is followed for the analysis of plastic deformation and failure in DP steels. A rate-dependent crystal plasticity framework and the isotropic J2 plasticity model are employed for the simulation of the plastic deformation in ductile ferrite phase and in the hard martensite phase respectively at the RVE scale. Moreover, the intergranular cracking is studied by the incorporation of a cohesive zone model at the ferrite-martensite grain boundaries and the failure in martensite phase is addressed through a ductile failure model. The effect of microstructural parameters on both plastic and fracture behaviour is analyzed under axial loading conditions.

A Crystal Plasticity Simulation on Strain-Induced Martensitic Transformation in Crystalline TRIP Steel by Coupling with Cellular Automata

In transformation-induced plasticity (TRIP) steel, the strain-induced martensitic transformation (SIMT) has a close relationship with the shear band formation. At a small length scale such as that of a crystal, the explicit analysis of the shear band structure with the formed microstructure is quite important for an adequate understanding of the SIMT. Here, a study on the microstructures formed by SIMT, related to shear band formation in both single and polycrystal TRIP steels, is presented. The constitutive equation for single crystal TRIP steel considering the transformation strain on each variant system is derived based on a rate-dependent crystal plasticity theory. To express the martensitic transformation, the cellular automata approach, including a transformation criterion acting as a local rule, is introduced. Numerical simulation is conducted with patterning processes of the martensitic phase at an infinite medium under the plane strain tension. It is found that the similar distributions of the plastic strain and the martensitic phase are dependent on the initial crystal orientation and appear as the shear band structures. In addition, the sizes of embryo and cell strongly influence the shear band formation and the martensitic volume fraction of crystal TRIP steel.

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.

Coupled continuum damage mechanics and crystal plasticity model and its application in damage evolution in polycrystalline aggregates

In the present study, damage initiation and growth in a polycrystalline aggregate are investigated. In this regard, an anisotropic continuum damage mechanics coupled with rate-dependent crystal plasticity theory is employed. Using a thermodynamically consistent procedure, a finite deformation formulation is derived. For this purpose, the damage tensor is incorporated in the crystal plasticity formulation for a cubic single crystal. The damage evolution is considered to be dependent on the history of damage, equivalent plastic strain, stress triaxiality, and Lode parameters. This material model is implemented in the commercial finite-element code Abaqus/Standard by developing a user material subroutine (UMAT). Using the available experimental tests of 316L single crystal in the literature, the crystal plasticity hardening and damage parameters are calibrated considering the stress–strain curve before and after necking, respectively. The damage sites in a single-phase polycrystalline aggregate are also considered using a polycrystalline model consisting of grains with random sizes and orientations. The results show that the damage arises at the grain boundaries and triple junctions. Moreover, growth of the damage mostly occurs in the grains with higher Schmid factor compared to the neighboring grains. The presented model manifests capacity for determination of damage initiation sites and damage evolution in polycrystalline models.

A coupled thermomechanical crystal plasticity model applied to Quenched and Partitioned steel

Quenched and Partitioned (QP) steel is a class of Advanced High Strength Steel (AHSS) that exhibits high strength and good ductility. These desirable properties are a consequence of the Transformation Induced Plasticity (TRIP) effect where retained austenite transforms into martensite under applied stress and strain. Accurate microstructural modeling of these advanced deformation mechanisms is critical for automakers to exploit QP steels for automotive weight reduction applications. In this work, the stress and martensitic transformation response of a QP1180 steel alloy are characterized using in-situ High Energy X-Ray Diffraction (HEXRD) uniaxial tension experiments. The initial microstructure is characterized using Electron Backscatter Diffraction (EBSD) and Scanning Electron Microscope (SEM) data. A novel thermodynamically consistent rate-dependent crystal plasticity formulation is used to simulate the large deformation behavior of QP steels that exhibit the TRIP effect. The TRIP effect is captured through a martensite variant selection and evolution scheme, which is governed by a driving force that accounts for various effects (i.e., temperature, orientation, hydrostatic pressure, and martensite surface energy). The constitutive model is implemented into a thermo-mechanical Crystal Plasticity (CP) Finite Element Method (FEM) formulation to study the effect of texture, phase morphology and temperature on the bulk material properties of QP1180 steel. A new method for incorporating thermal boundary conditions in CPFEM models is proposed. The constitutive model is calibrated using experimental stress-strain and martensite evolution measurements. Significant variance in transformation rate was observed, consistent with preferential transformation in the ⟨100⟩ crystal direction. Numerical experiments are conducted to study the effect of thermal and mechanical boundary conditions. Significant differences are observed between the simulations of interrupted and non-interrupted uniaxial tension as a result of the differences in the evolution of temperature. Additional numerical experiments were conducted that demonstrate the fidelity of the constitutive model for elevated temperatures and strain-rates, for several thermal boundary conditions. These simulations showed that the predicted RA and temperature evolution behaviors under quasi-static deformation were not accurately captured, either with adiabatic or isothermal boundary conditions. Finally, simulations showed that the RA and temperature evolution behavior under moderate strain-rates are accurately captured by adiabatic boundary conditions.

Microstructural Influences on Fracture at Prior Austenite Grain Boundaries in Dual-Phase Steels.

Dual phase (DP) steels provide good strength and ductility properties. Nevertheless, their forming capability is limited due to the damage characteristics of their constituting microstructural phases and interfaces. In this work, a specific type of interface is analysed, i.e., prior austenite grain boundaries (PAGBs). In the literature, prior austenite grain boundary fracture has been reported as an important damage mechanism of DP-steels. The influence of the morphology of phase boundaries near the PAGB and the role of the martensite substructure in the vicinity of a PAGB on damage initiation is analysed. The experimentally observed preferred sites of crack nucleation along the PAGB are assessed and clarified. A finite strain rate dependent crystal plasticity model accounting for the anisotropic elasto-plasticity of martensite (and also ferrite) was applied to an idealized volume element approximating a typical small-scale PAGB microstructure. The boundary value problem is solved using a fast Fourier transform (FFT) based spectral solver. The role of crystallography and geometrical features within the volume element is studied using simulations. Results are discussed considering possibly dominant regimes of elasticity and plasticity.

A Crystal Plasticity Formulation for Simulating the Formability of a Transformation Induced Plasticity Steel

Abstract The enhancement in formability of new advanced high strength steels (AHSS), such as duplex stainless steel, arises from increased hardening and ductility from complex deformation mechanisms, such as the transformation-induced plasticity (TRIP) effect. However, the interaction of dislocation and transformation mechanisms during deformation for various strain paths presents a challenge in evaluating formability. High fidelity simulation tools for evaluating formability need to capture these complex deformation mechanisms to allow manufacturers to realize their potential benefits. This work presents a rate-dependent crystal plasticity model with a micro-mechanics based transformation criteria to simulate the mechanical response of TRIP steel. A new stress-based transformation criterion, based on the micromechanics of fault band intersection on habits, was developed to initiate transformation. This model inherently captures the strain path effects of martensite transformation through the accumulated shear strain on slip systems. Simulations are calibrated and compared to experimental measurements of duplex stainless steel. Polycrystalline aggregate simulations show that although high Schmid factor habit planes were favorable for transformation, competition exists between the lower Schmid factor dislocation planes that generate higher elastic stress needed for transformation. The calibrated model is then used to predict the forming limit diagram using the Marciniak-Kuczynski approach. The mechanism of transforming from low strength austenite to high strength martensite showed enhanced formability by at least 20% compared to without transformation. This is achieved by the TRIP mechanism suppressing localization at critical moments during deformation. A parametric study of martensite transformation reveals the sensitivity of controlling the timing of martensite generation for improving formability.

Transient thermal fatigue crack propagation behavior of a nickel-based single-crystal superalloy

Thermal fatigue crack propagation behaviors of a V-notched Ni-based single-crystal superalloy DD6 were tested at 25 °C ↔ 760 °C/900 °C/1000 °C. The propagation directions of the two main cracks were approximately 45° with the dendrite orientation, and the {1 1 1} 〈1 1 0〉 slip family was mainly activated. Based on 3D transient thermo-mechanical coupling theory and rate-dependent crystal plasticity theory, the stress intensity factor and J-integral were calculated to predict the thermal fatigue crack propagation behavior. Three surface heat transfer stages were considered. The predicted crack propagation rates at three heating temperatures all showed good agreement with those obtained in the experiments.

Numerical simulation of polycrystalline aluminum alloy welded joints with micropores

Aluminum (Al) alloy welded structures are widely used in industry and daily life, while welded joints are easily produced defects, including macro and microscopic defects. It is a hot topic to study the effect of microscopic defects on the properties of welded joints. In this paper, a two-dimensional rate-dependent crystal plasticity model is established by using a numerical model, and then the mechanical behaviors of welded joints with micropores under tensile load is simulated in a mesoscale. The mechanical properties are described by varying the sizes and positions of micropores. The stress-strain response, equivalent plastic strain and equivalent stress distributions of polycrystalline Al alloy welded joints with different micropores are obtained. The results verify that those micropores have certain impact on the start of slip systems and the ability of resisting the deformation of polycrystalline joints. Compared with the positions of micropores, the sizes of micropores have a greater impact on the mechanical properties of the polycrystalline joints.

Investigation of mechanical properties of additive manufactured graphene-reinforced aluminium composites

Graphene considered as an ideal reinforcement for metal matrix composites (MMCs) because of its excellent optical, electrical and mechanical properties has important application prospects in materials science, micro-nano processing and so on. Meanwhile, additive manufactured MMCs becomes the hotspot of current research due to the advantages of precise and controllable structure and easy implementation of modularization. In this paper, a two-dimensional rate-dependent crystal plasticity model using the numerical model is developed to simulate the mechanical behaviors of additive manufactured graphene-reinforced aluminium matrix composites (AMCs) under tensile load in a mesoscale. The mechanical properties are described by varying the volume fractions and distribution patterns of graphene. The results verify that graphene is the main load-bearing part of AMCs. The volume fraction and distribution pattern of graphene play an important role in the crystal dislocation strengthening of AMCs. Moreover, it is proved that the additive manufactured graphene-reinforced AMCs have a potential improvement with increased graphene volume fraction and optimized geometric graphene parameters.

Parametrically homogenized constitutive models (PHCMs) from micromechanical crystal plasticity FE simulations, part I: Sensitivity analysis and parameter identification for Titanium alloys

This is the first of a two part paper that systematically develops a finite deformation elasto-plastic, parametrically homogenized constitutive model (PHCM) for structural-scale macroscopic simulations of Titanium alloy Ti6242S. The PHCMs are thermodynamically consistent, reduced-order continuum models that incorporate functional forms of representative aggregated microstructural parameters (RAMPs) in their constitutive coefficients. These models are designed to represent all characteristics of macroscopic response such as anisotropy, tension-compression asymmetry, strain-rate and temperature dependence, and are consistent with microscopic crystal plasticity relations. An image-based size and rate-dependent crystal plasticity FE (CPFE) model is developed for creating a data-base needed for deriving functional forms of PHCM coefficients using machine learning methods. The first part of this sequence summarizes the generation of microstructure-based statistically equivalent representative volume elements (M-SERVEs) and the image-based CPFE model. Extensive sensitivity analysis is conducted to unravel the effect of specific RAMPs on the overall material response, and hence the PHCM constitutive coefficients. Sobol sensitivity analysis is performed to evaluate the sensitivities of constitutive coefficients in PHCM with respect to RAMPs to examine their suitability for representation. In the second part (Kotha et al., 2019), machine learning will be used with the database to create functional forms of the constitutive coefficients in the PHCMs.

Crystal Plasticity Simulation of Hot Deformation Texture of Titanium Alloy Considering Alpha-beta Transformation

Titanium alloys are usually subjected to hot deformation to optimize its microstructure and mechanical property. In the hot forming process, such as extrusion, texture is of great importance to both manufacturing and performance. In this study, an alpha-beta titanium was used to study the texture evolution during hot extrusion. Large area electronic backscattering scan was used to examine grain orientation distribution. Experimentally measured alpha and beta textures were compared with a rate-dependent crystal plasticity based simulation. The model is capable of predicting the deformation textures of both alpha and beta phases at extrusion temperature. The model also takes into account the transformation of metastable beta phase to alpha phase in the cooling process, considering variant selection. The transformation texture components mostly have [0001] along extrusion direction, forming the primary component of alpha extruded texture. The model works well in predicting hot deformation texture of titanium alloy.

Crack initiation behavior of a Ni-based SX superalloy under transient thermal stress

Based on three-dimensional transient thermo-mechanical coupling theory and rate-dependent crystal plasticity theory, a transient thermal shock constitutive model was developed to investigate the crack initiation behavior under transient thermal stress of a V-notched Ni-based single-crystal superalloy at 25 °C ↔ 760 °C/900 °C/1000 °C. The evolution and distribution of the resolved shear stress and damage were simulated. Three surface heat transfer stages were considered during the water-cooling process in the simulation. The crack initiation lives and locations in the simulation results both showed good agreement with those observed in the experiments. The growth directions of the two main cracks were approximately 45° with the dendrite orientation, and the {111}<110> slip family was mainly activated.