Crystal Plasticity Framework Research Articles

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.

Numerical investigations regarding a novel process chain for the production of a hybrid bearing bushing

This contribution deals with the numerical investigations to develop a novel process chain for hybrid solid components using Tailored Forming. For manufacturing a hybrid bearing bushing, co-extrusion is the first step to produce hybrid semi-finished workpieces followed by a die forging process, machining processes and hardening. Combining aluminium with steel, compounds with wear-resistant functional surfaces and reduced weight are realised. Numerical simulations are a decisive part of the process chain design, for example to determine suitable process parameters for the co-extrusion process and to predict the thickness of intermetallic phases in the joining zone using a macroscopic phenomenological model. A numerical design including a tool analysis of the die forging process was carried out taking the experimentally determined material properties and the temperature profile after inductive heating into account. Additionally, the damage and fatigue behaviour of the polycrystalline material of the joining zone are modelled at the microstructure level. Moreover, a new discretization scheme, namely the virtual element method, which is more efficient at grain level, is developed regarding a crystal plasticity framework. Numerical simulations are used to develop inductive heating strategies for the forming process and for the design of the inductive hardening of the functional surface at the end of the process chain. In order to investigate the performance of this hybrid machine element under application-oriented conditions, a contact simulation is linked with a statistical damage model to calculate the bearing fatigue. In this study, a general overview of the individual process steps is given and results of the respective models are presented.

Investigation on ductile fracture of an aluminium alloy using a mean-field crystal plasticity framework

The onset of ductile fracture can be described by a simple damage parameter, which accounts for the accumulation of damage under arbitrary deformation. The damage parameter is usually given as integral form of strain over loading history which also has been described as a function of stress state. While the evolution of strain field can be experimentally determined using digital image correlation, experimental measurement of the multiaxial stress state is still a challenging task. Therefore, various uncoupled fracture criteria rely on stress states calculated from phenomenological plasticity model. As a result, the number of mechanical tests required to calibrate the fracture criterion may significantly increase when an anisotropic constitutive model is used. We propose an alternative approach on the basis of a mean field crystal plasticity (VPSC) model, which accounts for the microstructural features such as slip system, crystallographic texture and its evolution. While stress fields can be obtained from the use of full-field crystal plasticity framework, the proposed method utilizes the mean field crystal plasticity framework and repeat the stress estimation on various spatially resolved locations to which DIC technique provides strain history. The repeated VPSC calculations at various locations efficiently provide the map of stress evolution. The resulting map of spatially resolved stress response is further validated by comparing with the bulge stress strain curves.

Repulsion leads to coupled dislocation motion and extended work hardening in bcc metals

Work hardening in bcc single crystals at low homologous temperature shows a strong orientation-dependent hardening for high symmetry loading, which is not captured by classical dislocation density based models. We demonstrate here that the high activation barrier for screw dislocation glide motion in tungsten results in repulsive interactions between screw dislocations, and triggers dislocation motion at applied loading conditions where it is not expected. In situ transmission electron microscopy and atomistically informed discrete dislocation dynamics simulations confirm coupled dislocation motion and vanishing obstacle strength for repulsive screw dislocations, compatible with the kink pair mechanism of dislocation motion in the thermally activated (low temperature) regime. We implement this additional contribution to plastic strain in a modified crystal plasticity framework and show that it can explain the extended work hardening regime observed for [100] oriented tungsten single crystal. This may contribute to better understanding the increase in ductility of highly deformed bcc metals.

A modified kinematic hardening model considering hetero-deformation induced hardening for bimodal structure based on crystal plasticity

Heterogeneous structures (HS) have been reported to overcome the longstanding challenge of the trade-off between strength and ductility in metallic materials. The deformation incompatibility between the fine grains (FG) and coarse grains (CG), producing hetero-deformation induced (HDI) hardening, is the primary mechanism for superior mechanical properties of HS. In this paper, a kinematic hardening law within the framework of crystal plasticity is modified to quantify the HDI hardening of HS in which a new parameter is established to consider the strength mismatch between FG and CG. Taking bimodal structure (BS) as an example of HS, the good agreement between the experimental and numerical results show that the proposed model can successively predict the mechanical properties, including the evolution of back stress, yield strength and strain hardening of BS with various grain size distributions. Furthermore, the underlying strengthening mechanisms are revealed by switching the HDI hardening term and analyzing the partitioning of the strain and stress in different components of BS. By manipulating the grain size ratio of BS, it is found that the effect of HDI hardening is more sensitive to the size of FG than that of CG. The proposed hardening law can provide a significant guide for heterogeneous material design.

Stress-assisted (γ→α′) and strain-induced (γ→ε→α′) phase transformation kinetics laws implemented in a crystal plasticity model for predicting strain path sensitive deformation of austenitic steels

This paper formulates stress-assisted and strain-induced austenite to martensite transformation kinetics laws within a crystal plasticity framework to enable modeling of strain path sensitive elasto-plastic deformation of austenitic steels taking into account the evolution of crystallographic texture and the directionality of deformation mechanisms in the constituent phases. Consistent with experimental observations for mechanically induced martensitic transformation, the stress-assisted transformation is modeled as direct from γ-austenite to α' -martensite, while the strain-induced transformation is modeled as indirect through an intermediate ε-martensite phase, which subsequently transforms to α' -martensite. While the stress-assisted transformation law is conceived based on an energy criterion, the strain-induced transformation law relies on the local stress state sensitive motion of partial dislocations forming shear bands of ε-martensite phase, which after intersecting with other shear bands give rise to α' -martensite. The kinetic models are implemented in the elasto-plastic self-consistent polycrystal plasticity model to facilitate modeling of strain path and crystallographic texture dependence of martensitic transformation, while predicting deformation behavior of metastable austenitic steels. Due to its morphology, the ε-martensite is modeled using a flat ellipsoid approximation, which is a new numerical feature in the model. Simple tension, simple compression, and simple shear data of an austenitic steel have been used to calibrate and to illustrate predictive characteristics of the overall implementation. In doing so, stress-strain response, texture, and phase fractions of γ-austenite, intermediate ε-martensite, and α′-martensite are all calculated, while fully accounting for the crystallography of the transformation mechanisms. It is demonstrated that the appropriate modeling of phase fractions and crystallography facilitates predicting the experimentally measured data. The implementation and insights from these predictions are presented and discussed in this paper.

A crystal plasticity phenomenological model to capture the non-linear shear response of carbon fibre reinforced composites

A hardening response is often observed for shear-dominated large deformation of Carbon Fibre Reinforced Plastics (CFRP). This non-linear response is often modelled by fitting a strain hardening law against experimental stress-strain curves. Inspired by a crystal plasticity framework, a phenomenological model is developed to capture matrix shearing and fibre rotation of CFRP under finite strain. This phenomenological model is first verified by simple shear and transverse compression tests, followed by comprehensive validations against measured stress-strain responses of unidirectional (UD) and cross-ply composite laminates subjected to quasi-static loading. The analytical and finite element predictions of CFRP lamina under simple shear loading confirm that the initial yielding is governed by the shear yield strength of the matrix, while the hardening behaviour is dependent on the modulus and rotation of the carbon fibres. This model accurately predicts the non-linear behaviour of CFRP under off-axis loading without the need of an empirical curve-fitted strain hardening law.

Phenomenological modeling of the effect of oxidation on the creep response of Ni-based single-crystal superalloys

A new constitutive equation predicting the evolution of oxide thickness is proposed and implemented in a crystal plasticity framework with a hardening-based damage density function. The oxidation model depends on the initial surface roughness as well as on the amount of accumulated plastic strain and stress triaxiality. The description for the effect of oxidation on the mechanical behavior and damage is at the flow-stress level by modifying the amplitude of the kinematic hardening. The oxidation-altered kinematic hardening can predict the effect of oxidizing environments on mechanical behavior, specifically the plastic strain rate in the secondary creep stage, and lifetime. Finally, the oxidation model is verified to predict surface roughness and oxide thickness distributions by performing a finite-element simulation on a notched specimen subjected to creep and developing a complex multiaxial stress field.

Dislocation-density based crystal plasticity model with hydrogen-enhanced localized plasticity in polycrystalline face-centered cubic metals

Hydrogen-enhanced localized plasticity (HELP) has been recognized as an important mechanism for hydrogen embrittlement. Two recognized explinations have been proposed for HELP. The first one is the elastic shielding theory, in which the elastic stress field of solute hydrogen weakens the interactions between dislocations. Another one is the Gibbs theory of absorption isotherm: the lowered dislocation line energy by segregated hydrogen is considered as the main reason. In this work, a dislocation-density based crystal plasticity framework concerning the explicit incorporation of the dislocation line energy is proposed. The explicit consideration of dislocation line energy leads the way to the modelling of HELP mechanism according to the Gibbs theory of absorption isotherm. It is shown that the experimentally observed hydrogen-reduced activation volume and total activation free energy in thermally activated forest intersection in face-centered cubic (FCC) metals can be easily attributed to the reduction of dislocation line energy in the hydrogen environment. Finite element calculations of tensile tests for polycrystalline Pd-H and Ni-H alloys capture several important hydrogen-affected plasticity behaviors: hydrogen-increased flow stress, hydrogen-enhanced dislocation multiplication, hydrogen-promoted heterogeneity of plastic strain and hydrogen-delayed exhaustion of mobile dislocations, which can be all attributed to hydrogen reduced dislocation line energy in the present model. Besides, the influences of hydrogen-reduced vacancy formation free energy and stacking fault energy on thermal annihilation are also considered. However, the simulation results show that they are less important compared with hydrogen-reduced dislocation line energy. The present work is essential for further physically-based modeling of hydrogen distribution in polycrystals and hydrogen-induced damage and failure.

Modelling-assisted description of anisotropic edge failure in magnesium sheet alloy under mixed-mode loading

An uncoupled fracture criterion based on a simple damage indicator computed using a mean-field crystal plasticity framework is proposed and applied to predict failure of an AZ31 sheet originating from the edges. The damage indicator quantifies the contribution of strain components along the axes of orthotropy leading to material failure. The model is calibrated by uniaxial tension tests. The damage indicator is validated for various mixed-mode deformation histories realized by modified Arcan tests in various loading configurations. The loading history of respective fracture sites obtained from DIC analyses is directly employed to a visco-plastic self-consistent crystal plasticity model to obtain the stress responses. The results indicate that the damage indicator requires – beside the strain history – an input of stress triaxiality, by which an improved predictive accuracy can be achieved. This effect is quantified for various loading scenarios, in which cracks are initiated near or at the edge of the sample.

Modeling the Role of Epitaxial Grain Structure of the Prior β Phase and Associated Fiber Texture on the Strength Characteristics of Ti-6Al-4V Produced via Additive Manufacturing

Due to the rapid cooling and directional heat flow inherent in metal-based additive manufacturing, Ti-6Al-4V results in epitaxial grain growth and a fiber texture of the prior β phase. While Ti-6Al-4V produced via powder bed, electron beam melted processing can exhibit a range of strength characteristics, recent studies have shown superior strength properties, compared to similar orientations, of conventional plate material (AMS 4911) across a range of elevated temperatures (204 to 371 °C). To investigate this phenomenon, a series of crystal plasticity models was developed for the representative grain structures of Ti-6Al-4V to rationalize if the columnar, fiber texture produced by additive manufacturing (AM) was sufficient to explain the observed strength attributes. As a first step towards understanding this behavior, the grain structure was characterized via electron backscattering diffraction for AM material taken from four specimens (with different build directions), as well as material taken from baseline plate material (along and transverse to the rolling direction), and the resulting microstructures were modeled via a crystal plasticity framework. As expected, the results showed the AM material accounting for only the α grain structure was stronger in the vertical builds and weaker in the horizontal builds compared to the conventional plate counterparts. This suggested that grain morphology and α grain orientation alone provided some information about the relative strengths, but did not explain the overall trends observed from the experiments. To account for the role of texture, the characterized α phase was converted, via variant selection, to its prior β phase for use in the simulations. The results showed that each simulation of the AM prior β phase exhibited a higher strength compared to the baseline plate material, except for one specimen (horizontally built), which had large colonies of soft microtextured regions for the prior β structure. This suggests that some variability was experienced (as anticipated), but the texture (especially of the prior β macrozones) was a key contributor for the unusually high strength observed of the AM Ti-6Al-4V material.

An RVE-Based Study of the Effect of Martensite Banding on Damage Evolution in Dual Phase Steels.

The intent of this work is to numerically investigate the effect of second phase morphology on damage evolution characteristics of dual-phase (DP) steels. A strain gradient enhanced crystal plasticity framework is used in order to capture the deformation heterogeneity caused by lattice orientations and microstructural size effects. The investigation is focused on two different martensite distributions (banded and random) that are relevant for industrial applications. The effects of martensite morphology are compared by artificially generated 2D plane strain microstructures with initial void content. The Representative volume elements (RVEs) are subjected to tensile deformation imposed by periodic boundary conditions. Evolution of voids are analyzed individually as well as a whole and characterized with respect to average axial strain. It is found that during stretching voids exhibit varying evolution characteristics due to generation of inhomogeneous strain fields within the structure. The behavior of individual voids shows that the stress-state surrounding the void is different from the imposed far field macroscopic stress-state. The voids at the ferrite martensite interface and in ferrite grains of the randomly distributed martensite grow more than in the banded structure. On the other hand, voids formed by martensite cracking growth shows an opposite trend.

A physically-based constitutive model for the shear-dominated response and strain rate effect of carbon fibre reinforced composites

A significant hardening response is often observed for the shear-dominated deformation of Carbon Fibre Reinforced Plastics (CFRP). This non-linear response is typically modelled by fitting a strain hardening law against experimental stress-strain curves. Inspired by crystal plasticity framework, we develop a micro-mechanically motivated constitutive model to capture the matrix shearing and fibre rotation of CFRP under finite strain deformation and different strain rates. Strain rate dependency of the shear modulus and yield strength of the matrix was modelled through scaling functions. This physically-based constitutive model is first verified by simple shear and transverse compression tests, followed by comprehensive validations against the measured stress-strain responses of unidirectional (UD) and cross-ply composite laminates subjected to quasi-static and dynamic off-axis loading. The finite element predictions and analytical models of CFRP lamina under simple shear loading confirms that the initial yielding is governed by the shear yield strength of matrix, while the hardening behaviour is dependent on the modulus and rotation of carbon fibres. This model accurately predicts the non-linear behaviour of CFRP under off-axis loading at different strain rates, without the need of a curve-fitted strain hardening law.

Numerical investigation of the brittle-to-ductile transition temperature of rolled high-purity tungsten

With increasing temperature, high-purity tungsten typically shows a sharp transition from fully brittle behaviour to a significantly more ductile response. The brittle-to-ductile transition of tungsten is not an invariant property, but depends on the microstructure and loading conditions. In the current work, this relation is investigated numerically. To this end, a crystal plasticity framework is adopted, combined with a newly proposed cleavage criterion. The crystal plasticity parameters are identified from experimental data, obtained from tensile tests on rolled polycrystalline samples. The brittle-to-ductile transition is subsequently examined for different strain rates, which allows for calculating the activation energy of the brittle-to-ductile transition. The resulting activation energy is in adequate agreement with experimental findings in literature. Finally, different loading directions with respect to the anisotropic microstructure are considered. The numerically obtained transition temperatures in these directions are consistent with experimental data. The proposed model is therefore instrumental for improving the design of the tungsten monoblocks for future fusion reactors.

Out-of-Plane Compressive Response of Additively Manufactured Cross-Ply Composites

ABSTRACTDigital manufacturing was employed to 3D print continuous Carbon, Glass and Kevlar fibre reinforced composites in Unidirectional (UD) [0°], Off-axis ±45° and Cross-ply [0°/90°] layup sequence. These 3D printed composites were subjected to quasi-static, in-plane tension and out-of-plane (compression and shear) loading. The tensile strength of 3D printed Carbon, Glass and Kevlar UD laminates was significantly lower than that of 3D printing filaments used to manufacture them. The type of fibre (brittle/ductile) reinforcement was found to be governing the shear yield strength of 3D printed composites despite having the same Nylon matrix in all the composites. Out-of-plane compressive strength of the 3D printed Carbon and Glass fibre reinforced composites was independent of specimen size. Contrary to that, Kevlar fibre composites showed a pronounced size effect upon their out-of-plane compressive strength. A combination of X-ray tomography and pressure film measurements revealed that the fibres in 3D printed composites failed by ‘indirect tension’ mechanism which governed their out-of-plane compressive strength. To gain further insights on the experimental observations, Finite Element (FE) simulations were carried out using a pressure-dependent crystal plasticity framework, in conjunction with an analytical model based on shear-lag approach. Both FE and analytical model accurately predicted the out-of-plane compressive strength of all (Carbon, Glass and Kevlar fibre reinforced) 3D printed composites.

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 indicate that for tempered twinning with grain refinement it is not necessary for the crystallographic size effect on twinning to be stronger than slip. While grain refinement and textural weakening reduce the net plastic anisotropy and tension-compression asymmetry they are sensitive to loading orientation. The results provide insight into the roles that engineered Mg microstructures may play in their damage behavior.

Effect of microstructure evolution on the creep properties of a polycrystalline 316H austenitic stainless steel

Creep deformation and failure is one of the most critical life limiting factors of structural components used at elevated temperatures, such as in nuclear power plants. Understanding of the mechanisms of creep in nuclear power plant steels, such as Type 316H austenitic stainless steels, is still incomplete. It has been observed that long-term creep curves of initially solution-treated (ST) 316H stainless steels exhibit multiple secondary stages at the operational temperature and stress range. This paper probes the internal mechanisms for this complex phenomenon by correlating and quantifying the evolution of microstructural state (dislocations, precipitation and solid solution elements) and its mechanistic influence on the material's creep properties. This is examined for the first time by a multi-scale self-consistent crystal plasticity framework combined with a simple classical phase transformation model and thermal solute strengthening model. The novel integrated model is capable of describing a broad range of physical processes, including dislocation multiplication (hardening) and climb-controlled recovery, precipitation nucleation, growth and coarsening (Ostwald Ripening) and thermal solute dragging. The mechanisms responsible for the observed multiple secondary stages in the creep curves of initially solution-treated 316H stainless steels are explained through the strengthening and softening effects associated with these processes.

Twinning-induced anisotropy of mechanical response of AZ31B extruded rods

Texture and twinning-induced anisotropy of the yield stress and hardening of AZ31B extruded rods is investigated. The multidirectional compression tests involving strain path changes are performed in order to: i. assess which slip and twinning systems are active in the polycrystalline sample with a strong texture, ii. analyze the influence of the preliminary deformation upon twin formation, iii. observe the resulting change of the mechanical response. In order to fulfil these goals mechanical testing is supplemented by microstructure analysis. Experimental observations are used to validate the proposed crystal plasticity framework when it is combined with the viscoplastic self-consistent scheme. On the other hand, the results of numerical simulations are used to confirm an advocated interpretation of experimental findings. Finally, the experimental and numerical results are discussed with respect to the theoretical study of slip and twinning activity on the basis of the generalized Schmid criterion. It is concluded that twinning activity influences the mechanical response predominantly by the texture change and to lesser extent by modification of strain hardening due to slip-twin interactions.