Crystal Plasticity Research Articles

Crystal Plasticity based Constitutive Model for Deformation in Metastable β Titanium Alloys

Crystal Plasticity based Constitutive Model for Deformation in Metastable β Titanium Alloys

Utilizing integrated neutron diffraction and elastoplastic self-consistent crystal plasticity model to quantitatively assess the strengthening mechanism in Al-12.5Ce and Al-12.5Ce-0.4Mg alloys

Abstract An integrated in-situ neutron diffraction and elastic plastic self-consistent crystal plasticity (EPSC-CP) modeling scheme is performed on a binary Al-12Ce alloy and a ternary Al-12Ce-0.4Mg alloys. Using this scheme, the constitutive parameters, i.e. elastic constants and slip system parameters of individual phases can be calibrated which can be used in microstructure-based crystal plasticity models to predict materials performance. From this study, it is shown that the elastic constants of Al11Ce3 intermetallics calculated from DFT calculation in the literature are rather accurate. When applied to the EPSC-CP model, the lattice strains of both the binary and ternary alloys are correctly predicted as compared with experiments, and large lattice strain differences between Al (100) plane and Al11Ce3 (010) plane are demonstrated. The slip system parameters calibrated by the scheme shows that the addition of 0.4 wt% Mg in the alloy has little influence on the critical resolved shear stress (CRSS) of initial dislocation glide in the Al matrix which caused plastic yield in the material. This can be explained by the very dilute Mg solute content in the Al solid solution, causing large spacing of Al-Mg lattice misfit sites and little impact on resistance of dislocation glide at initial yield. The 0.4 wt% Mg addition, on the other hand, has a large influence on the hardening term in the slip system parameters, indicating those Al-Mg misfit sites do help dislocation accumulation during the deformation. The impact of dilute Mg addition on the Al slip system parameters is also reflected in the flow behavior of the ternary alloy: little impact on the yield stress, but a large impact on working hardening and tensile strength of the materials which is consistent with the literature.

Microstructure Design of Multiphase Compositionally Complex Alloys II: Use of a Genetic Algorithm and a Vanishing Cracked Particle Model

AbstractAchieving high strength, ductility, and toughness via microstructure design is challenging due to the interrelated dependencies of strength and ductility on microstructural variables. As a natural extension of the microstructure design work in Bhattacharyya and Agnew (Microstructure design of multiphase compositionally complex alloys I: effects of strength contrast and strain hardening, 2024), an optimization framework to obtain the microstructure that maximizes the toughness is described. The strategy integrates a physics-based crystal plasticity model, which accounts for damage evolution within the reinforcement through a “vanishing cracked particle” model that is governed by Weibull statistics, and a genetic algorithm-based optimization routine. Optimization constraints are imposed in the form of bounds on the microstructure parameters such that they are most likely attainable by conventional thermomechanical processing. Various matrix strain hardening behaviors are considered, as well as the strength contrast between the two phases and fracture behavior of the reinforcement. It is shown that the addition of a fine-grained (hard) reinforcing phase is preferred as is a matrix that exhibits sustained strain hardening such as is observed under TRIP/TWIP scenarios. Finally, the Pareto-optimal set of solutions for several scenarios are presented which offer new insights into the linkages between microstructure and mechanical properties.

Boosting the Ionic Conductivity of Pyrrolidinium-Based Ionic Plastic Crystals by LLZO Fillers

Boosting the Ionic Conductivity of Pyrrolidinium-Based Ionic Plastic Crystals by LLZO Fillers

Design of Fluorinated Elastomeric Electrolyte for Solid-State Lithium Metal Batteries Operating at Low Temperature and High Voltage.

We demonstrate the low-temperature operation of solid-state lithium metal batteries (LMBs) through the development of a fluorinated and plastic-crystal-embedded elastomeric electrolyte (F-PCEE). The F-PCEE is formed via polymerization-induced phase separation between the polymer matrix and plastic crystal phase, offering a high mechanical strain (∼300%) and ionic conductivity (∼0.23 mS cm-1) at -10°C. Notably, strong phase separation between two phases leads to the selective distribution of lithium (Li) salts within the plastic crystal phase, enabling superior elasticity and high ionic conductivity at low temperatures. The F-PCEE in a Li/LiNi0.8Co0.1Mn0.1O2 full cell maintains 74.4 and 42.5% of discharge capacity at -10 and -20°C, respectively, compared to that at 25°C. Furthermore, the full cell exhibits 85.3% capacity retention after 150 cycles at -10°C and a high cut-off voltage of 4.5V, representing one of the highest cycling performances among the reported solid polymer electrolytes for low-temperature LMBs. We attribute the prolonged cycling lifetime of F-PCEE at -10°C to the great mechanical robustness to suppress the Li-dendrite growth and ability to form superior LiF-rich interphases. This study establishes the design strategies of elastomeric electrolytes for developing solid-state LMBs operating at low temperatures and high voltages. This article is protected by copyright. All rights reserved.

Crystal plasticity modeling and analysis for the transition from intergranular to transgranular failure in nickel-based alloy Inconel 740H at elevated temperature

The precipitation-strengthened Nickel-based alloy Inconel® 740H® (IN740H) exhibits increased ductility at higher applied strain rates during quasi-static tensile tests at an elevated temperature of 760 °C. The examination of fracture surfaces in this context reveals a noteworthy transition of underlying fracture mechanisms from transgranular to intergranular fracture as the applied strain rate decreases from 1×10−3/s to 0.83×10−4/s. To thoroughly understand the mechanical response of IN740H under these conditions, this study develops a crystal plasticity finite element (CPFE) model. This model incorporates various deformation mechanisms including dislocation slips, climb, and grain boundary sliding, which are relevant to the test conditions. The model is calibrated using data from both tensile tests at different strain rates and creep tests across a broad stress range at 760 °C, enabling the accurate determination of model parameters for each mechanism. Simulation results well captured the experimental observations of different failure modes. At higher strain rates, the model shows a dominance of dislocation slip leading to heterogeneous plastic deformation and formation of transgranular shear bands causing the failure, while at lower strain rates, an increased activity of grain boundary sliding causes grain boundaries crack leading to intergranular failure.

Spatially-resolved cluster dynamics modeling of irradiation growth

We develop here a spatially resolved, three-dimensional continuum model coupling cluster dynamics (SR-CD) and crystal plasticity to investigate irradiation growth in zirconium. The model uses scale separation to divide the population of the irradiation cluster into mobile and immobile families. Small interstitial and vacancy clusters are modeled using anisotropic reaction–diffusion equations. Among the immobile clusters, an atomistically-informed vacancy cluster to vacancy loop transition is taken into account. The coupling between the evolution equation of CD and the plastic deformation of the material is two-fold, with stress-informed bias factors and local inelastic strains computed from the evolution of the evolving cluster population. The numerical implementation of the model utilizes the finite element method to analyze both single-crystal and polycrystalline samples. The growth strains that are computed align well with the experimental data provided by Carpenter for single-crystal Zr. Furthermore, the transformation of a vacancy cluster into a complete vacancy loop, occurring at a size of 14 nm, is in agreement with experimental observations and atomistic simulations. The density, size, and growth rate of the dislocation loops, denoted as 〈c〉 and 〈a〉, also exhibit good agreement with transmission electron microscopy (TEM) analysis of irradiated Zr and its alloys. Our findings demonstrate that there is a spatial correlation between the growth of these dislocation loops and growth strains, significantly influenced by the crystal size. To explain the expansion of the 〈a〉 axis and the contraction of the 〈c〉 axis in irradiated Zr, it is necessary to consider the diffusion anisotropy difference (DAD) of mobile interstitial species. We show that the PWR Kearns parameters, specifically fr = 0.63, ft = 0.32, fa = 0.05, confer enhanced irradiation resistance to Zr along the principal directions when compared to single crystals. Additionally, reducing the grain size to nanograins further enhances the resistance to irradiation-induced growth, particularly along the direction with the highest volume fraction of basal poles [0001].

Predicting plastic behavior of magnesium alloy tube bending with comprehensive constitutive models

This paper aims to predict defects occurring in magnesium alloy tube bending through finite element simulations. Deformation tests were conducted to identify and characterize plastic anisotropy, tension-compression asymmetry, and anisotropic hardening behaviors of extruded Mg–Al–Zn-RE alloy rectangular tubes. Limited by size, the deformation tests along the wall thickness of specimens were conducted through crystal plasticity analysis. To thoroughly investigate the material constitutive features affecting bending, two constitutive models, Yoon2014 and Hill48, were established and calibrated. The non-associative flow rule was adopted, and anisotropic hardening was depicted using the yield-surface interpolation method. In comparison, the Yoon2014 model accurately predicted the strain distribution and tube shape collapse of the bent tube with negligible deviation from the experimental data, prior to the Hill48 model. This underscores the necessity of considering comprehensive plasticity models in tube bending simulations.

Colossal Reversible Barocaloric Effects in a Plastic Crystal Mediated by Lattice Vibrations and Ion Diffusion.

Solid-state methods for cooling and heating promise a sustainable alternative to current compression cycles of greenhouse gases and inefficient fuel-burning heaters. Barocaloric effects (BCE) driven by hydrostatic pressure (p) are especially encouraging in terms of large adiabatic temperature changes (|ΔT| ≈ 10K) and isothermal entropy changes (|ΔS| ≈ 100JK-1kg-1). However, BCE typically require large pressure shifts due to irreversibility issues, and sizeable |ΔT| and |ΔS| seldom are realized in a same material. Here, the existence of colossal and reversible BCE in LiCB11H12 is demonstrated near its order-disorder phase transition at ≈380K. Specifically, for Δp ≈ 0.23(0.10)GPa, |ΔSrev| = 280(200)JK-1kg-1 and |ΔTrev| = 32(10)K are measured, which individually rival with state-of-the-art BCE figures. Furthermore, pressure shifts of the order of 0.1GPa yield huge reversible barocaloric strengths of ≈2JK-1kg-1MPa-1. Molecular dynamics simulations are performed to quantify the role of lattice vibrations, molecular reorientations, and ion diffusion on the disclosed BCE. Interestingly, lattice vibrations are found to contribute the most to |ΔS| while the diffusion of lithium ions, despite adding up only slightly to the entropy change, is crucial in enabling the molecular order-disorder phase transition.

A Macro-Micro Approach for Identifying Crystal Plasticity Parameters for Necking and Failure in Nickel-Based Alloy Haynes 282

This work develops a two-scales macro-micro approach to address the challenge in calibrating crystal plasticity microstructural models when samples undergo necking prior to fracture. The crystal plasticity models are crucial for predicting the materials’ plastic deformation and failure at the microstructure level, identifying the materials’ intrinsic properties as well as investigating the microstructure-properties relationships. However, after necking occurs, the experimentally measured stress-strain curves fail to reflect the materials ‘true’ stress-strain behavior and cannot be directly fitted into crystal plasticity models. The proposed macro-micro approach employs a top-down strategy to address this challenge, which has been studied with experimental tests on precipitation-strengthened Ni-based superalloy Haynes® 282®. In this approach, a macro rate-dependent anisotropic plasticity model with Voce-type hardening and Rice-Tracey damage law is first utilized to model the deformation and failure of the tensile bar, and calibrated by matching the stress-strain curves, necking strain, and reduction of area. Especially, to match the testing results under different applied strain rates, the rate-sensitivity parameter m and saturation stress in the elasticity model are modified to incorporate dependence on the local strain rate. Then, the ‘true’ stress-strain behaviors are extracted from the necking zone of the macro-model, which are used to calibrate a micro-model with explicit microstructures and governed by an extended crystal plasticity law. The consistency between the micro-model and macro-model are enforced during calibration. The calibration outcomes from the crystal plasticity model elucidate the materials intrinsic properties for slip, hardening, and failure, which is vital for further investigations into the microstructure-properties relationship and for accurate prediction of the material behavior under various test and service conditions.

Crystal Plasticity Modeling of Grain Boundary Softening and Fatigue in U75V Pearlite Steel under Low Strain Conditions: A Study of Cyclic Rolling Contact Fatigue

Grain boundaries (GBs) exhibit fatigue-induced softening under low strain conditions, making them the weakest and most vulnerable regions within the material. This phenomenon significantly influences plastic deformation, plastic strengthening, and the initiation and propagation of microcracks, leading to material fatigue failure. This investigation presents a comprehensive model for the rolling contact fatigue (RCF) damage mechanism of U75V railway steel. Leveraging data from Electron Backscatter Diffraction (EBSD) and employing the Crystal Plasticity Finite Element Method (CPFEM), intragranular mechanical responses are elucidated. A modified bilinear Traction Separation Law (TSL) Cohesive Zone Model (CZM) is developed to capture the impact of GBs fatigue. Integrating this CZM with CPFEM, mechanical properties, scalar stiffness degradation (SDEG), fatigue damage factors, and crack evolution patterns are analyzed to explore the effects of grain morphology, orientation, GB angle, and area on GB fatigue damage and crack initiation. Results indicate a significant increase in GBs damage with increasing GBs angle or decreasing GBs area, highlighting the potential for reducing RCF damage through deliberate grain morphology design. Additionally, GBs are found to impede crack propagation, suggesting that grain refinement can mitigate crack propagation rates. This study enhances our understanding of intergranular fracture, mechanical responses, and microstructure evolution in U75V rail steel under cyclic rolling contact loading, offering novel methodologies for investigating metallic materials' deformation behavior concerning GB fatigue.

Dynamic strength differential and Bauschinger effects in an extruded AZ80 magnesium alloy

Quasi-static and high-rate tension and compression properties of an extruded AZ80 Mg alloy rod were investigated at loading rates of 0.001 and 500 s−1. Acquired stress – strain results show that tension and compression plastic deformations of AZ80 rod are asymmetric, and such strength differential effect is dependent of strain rate and loading orientation. Strength differential effect is weakened at 500 s−1 when the sample was loaded along the extrusion direction. Crystal plasticity simulations on the basis of the visco-plastic self-consistent method were performed. Numerical results indicate that the rate and orientation dependency of strength differential effect in AZ80 alloy is related to {101‾2} extension twinning. High-rate tests for pretension, unloading and reverse compression were realized to investigate the dynamic Bauschinger effect. Experimental results show that Bauschinger effect of AZ80 alloy is anisotropic and sensitive to the strain rate. A Bauschinger effect parameter considering strength differential effect was proposed, and it was found that the Bauchinger effect in the extrusion direction is reduced significantly at 500 s−1.

Phasing effects on thermo-mechanical fatigue damage investigated via crystal plasticity modeling

Nickel (Ni)-based superalloys have high strength at elevated temperatures, making them ideal candidates for aerospace components exposed to thermo-mechanical loads. Thermo-mechanical fatigue’s (TMF) influence on material failure is highly dependent on the temperature-load phase profile as a consequence of path-dependent thermo-mechanical plasticity. In order to understand the direct influence phasing effects have on TMF performance, a microstructure-based fatigue model has been developed to connect damage mechanisms to crack initiation events. In this work, in-phase (IP) TMF, out-of-phase (OP) TMF, and iso-thermal (ISO) loading profiles are investigated with a temperature-dependent, dislocation density-based crystal plasticity model to pinpoint a relationship between microstructural damage and TMF phasing effects. A crystal plasticity modeling framework with capabilities to isolate phasing (IP, OP, and ISO) effects is presented to locate fatigue damage in a set of statistically equivalent microstructures (SEMs) with an energy-based damage indicative parameter. Local stress, accumulated damage, intragranular misorientiation, grain interactions, and slip alignment activity at the damaged regions are studied under the various temperature-load phase profiles to connect microstructural material damage to TMF performance. Based on the local microstructural material damage, it is postulated the material’s stiffness at maximum load influences OP TMF performance, whereas the hardening/plasticity at maximum load influences IP TMF. The results from the presented framework is consistent with experimental evidence that at high mechanical strain amplitudes IP TMF has a shorter life as a consequence of hardening/plasticity influencing path-dependent thermo-mechanical plasticity, whereas at low strain amplitudes OP TMF has a shorter life due to stiffness influencing path-dependent thermo-mechanical plasticity.

On the Interaction of Grain-scale and Hydride-scale Stresses in Hydrogen Enriched Zirconium Alloy Nuclear Cladding via combined Discrete Dislocation Plasticity and Crystal Plasticity Finite Element modelling

On the Interaction of Grain-scale and Hydride-scale Stresses in Hydrogen Enriched Zirconium Alloy Nuclear Cladding via combined Discrete Dislocation Plasticity and Crystal Plasticity Finite Element modelling

In-situ study of microstructure and mechanical properties of GH3536 alloy manufactured by selective laser melting at 750 °C

Nickel-based GH3536 alloy exhibits high strength but low ductility when produced by selective laser melting (SLM), which hinders its widespread application in aerospace. This paper employed a ‘two-step’ method of heat treatment to optimize the microstructure of the SLM GH3536 alloy and investigated the mechanical properties. Tensile tests were conducted on SLM GH3536 alloy before and after heat treatment at 750 °C, using an in-situ high-temperature tensile stage. The relationship between the microstructural evolution and deformation behavior of the alloys was investigated by combining the in-situ tensile experiments and crystal plasticity finite element method (CPFEM). The results suggested that the elongation can be increased by 80% without a significant reduction in tensile strength. The improved elongation is attributed to the complete recrystallization, formation of annealed twins and serrated grain boundaries after heat treatment. The study also investigated the deformation behavior and fracture mode of the alloy before and after heat treatment. Discussion was done on the influence of the microstructure, particularly the twin and serrated grain boundaries on the alloy's plastic deformation. This study enhanced the understanding of plastic deformation of SLM GH3536 alloy and provided a valuable reference for the design and post-treatment of superalloy.

Transverse difference of activation slip/twin system in wide AZ31 alloy plate during its rolling

The macroscopic finite element method (FEM) and the crystal plasticity finite element method (CPFEM) were combined to study the transverse difference of activation slip/twin system in wide AZ31 magnesium alloy plates during rolling. The macro-deformation and micro-texture evolution along the transverse direction of the plate during rolling were analyzed experimentally. The microscopic CPFEM was developed on the basis of the thermo-force coupling behavior during plate rolling obtained from macroscopic FEM. The CPFEM parameters were fitted by uniaxial compression experiments. This combination of two scale simulations accurately predicted the texture evolution during the rolling process and had been experimentally validated. Further examination of the deformation mechanism reveals that the transverse spread action of the plate is stronger at the edge region compared to center, and this transverse spread action has a more significant impact on the activation of the {10 1‾ 2} tension twin. The comparison of the activation and extension of pyramidal <a> slip in granular and plate-like grains reveals that plate-like grains are more prone to generate slip bands through the grain, leading to cracking of the grain along the slip activation band and further formation of sub-grains.

Experimental and modeling study on irradiation effect of A508-Ⅲ steel

Irradiation can induce microscopic defects in reactor pressure vessel (RPV) steel, resulting in macroscopic hardening and embrittlement. This paper proposes a micro-meso-macroscale calculation framework for the mechanical properties of irradiated RPV steel based on experimental and numerical investigations. The mean size and number density of Fe-ion-irradiation-induced dislocation loops were measured using transmission electron microscopy (TEM). These parameters were described by a power-function relationship with the irradiation dose at various temperatures and were used as input parameters for the crystal plasticity finite element model (CPFEM). Nano-indentation tests of A508-Ⅲ steel under different irradiation conditions were successfully simulated. In addition, microstructural characterization and molecular dynamics (MD) simulations revealed the phenomenon of dislocation pinning and the sweeping of irradiation defects during dislocation migration, implying that the dislocation-loop interactions could be responsible for the formation of dislocation channels and curved dislocation lines. Furthermore, increase in yield stress and the ductile-brittle transition temperature (DBTT) at various temperatures were investigated. Results indicated that yield stress, DBTT, and the degree of irradiation hardening and embrittlement increased with the irradiation dose and decreased with irradiation temperature. Finally, the adjusted reference temperature (ART), a significant design parameter for nuclear reactors, was calculated and evaluated using the multiscale framework. The framework can serve as a reference text for extending the life of nuclear reactors.

Hydrogen diffusion behavior within microstructures near crack tip: A crystal plasticity study

Hydrogen diffusion behavior within microstructures near crack tip: A crystal plasticity study

Crystal plasticity finite element method investigation of normal tensile deformation anisotropy in rolled pure titanium sheet

Industrial pure titanium with hexagonal close-packed (HCP) crystal structure has a high degree of anisotropy at room temperature. On the mesoscopic scale, this is due to the rolling texture presented by its crystal orientation. Tensile tests were performed on smooth specimens with five angles in the first quadrant at room temperature, and the central deformation region and fracture region were characterized using EBSD and SEM, respectively. The modified Salem anisotropic hardening model is incorporated into the crystal plasticity finite element method (CPFEM) framework in the form of incremental hardening to describe the initial strength and hardening increment evolution of each deformation system of pure titanium. Both slip dislocation and twinning mechanisms are considered in the CPFEM simulation. Three models with different meshing strategies are used to simulate the tensile conditions to capture the evolution of macro and micro variables of pure titanium sheet. The results show that there are anisotropy in stress-strain, system activity, cumulative shear strain, crystal orientation, twin volume fraction, stress triaxiality and Lode parameter. The purpose of this paper is to explore the anisotropy of macro-meso variables in different directions before damage occurs, so as to provide reference for the subsequent construction of related damage models.

The mechanistic origins of heterogeneous void growth during ductile failure

In 1969, Rice and Tracey proposed that the rate of void growth during ductile failure is a strong function of the hydrostatic stress state. Numerous in-situ x-ray computed tomography (XCT) studies demonstrated that the average rate of void growth is well-predicted by modified versions of the Rice-Tracey equation. However, recent in-situ XCT studies of void growth demonstrated that individual voids grow in highly heterogeneous manners in a way that is not predicted by Rice-Tracey or similar models. Model-based studies using crystal plasticity finite element (CP-FE) suggest that local effects of grain orientation play a strong role during void growth, but we lack experimental data to test this hypothesis. The present study leverages recent advances in laboratory-based diffraction contrast tomography (Lab-DCT) and in-situ XCT to systematically examine the effects of grain orientation on void growth experimentally in an Al-2219 alloy. CP-FE modeling was used to assess the local stress states associated with voids and their influence on void growth rates. These data indicate that void growth is not simply controlled by the local hydrostatic stress or stress triaxiality. Additionally, no clear relationship between void growth rates and grain orientation were observed. Instead, void growth rates were highly stochastic in ways that could not be directly linked to the local stress or strain states. The combination of experimental and modeling data suggests that our current assumptions regarding the mechanisms of void growth are flawed and that additional factors, which may include the local dislocation density, affect the rate of void growth.