Dislocation-based Crystal Plasticity Research Articles

A dislocation-based crystal plasticity model for single-crystal micropillars based on strain burst with stochastic characteristics

A dislocation-based crystal plasticity model for single-crystal micropillars based on strain burst with stochastic characteristics

Understanding the strain localization in additively manufactured materials: Micro-scale tensile tests and crystal plasticity modeling

Metallic parts fabricated by additive manufacturing (AM) usually exhibit unique microstructures and non-negligible residual stresses compared with the counterparts produced by conventional manufacturing. These inherent microstructural factors strongly affect the mechanical response of the as-built AM parts. In this study, we focus on the strain localization behavior of 316L stainless steel produced by laser powder-bed-fusion. In-situ tensile tests under a scanning electron microscope are performed, and the digital image correlation method is used to measure the strain distribution combined with electron backscatter diffraction. Meanwhile, a dislocation-based crystal plasticity finite element model incorporating residual stresses is developed to study the origins of the strain localization in the AM material. The results indicate that strain localization in AM materials is closely associated with microstructural features, encompassing behaviors related to slip activities, interactions with neighboring grains and dislocation evolutions. Additionally, the columnar grain features also render the strain distribution sensitive to the loading direction. The strain localization is serious in some small grains with high residual stresses, while in large grains the effect is less significant. These factors collectively contribute to the increasing likelihood of strain localization occurring in the AM microstructures with heterogeneous grain size and texture distribution. This work provides detailed insights into the strain localization in AM materials and would facilitate the manufacturing parameter optimization of AM materials by tuning the microstructure to reduce deformation inhomogeneity.

Effect of micron-scale nonmetallic inclusions on fatigue crack nucleation in a nickel-based superalloy

Micron-level nonmetallic inclusions are likely to be a limiting factor for further improvement in the fatigue resistance of nickel-based superalloys. To investigate the fatigue response of nickel-based superalloys containing micro-inclusions, a dislocation-based crystal plasticity model was employed for numerical simulations, and the local energy storage density criterion was used for damage evolution analysis. The results showed that, as a hard phase, micro-inclusions interfered with the plastic deformation of the matrix, as evidenced by the inhomogeneous slipping of the main slip systems and the activation of new slip systems. Additionally, micro-inclusions induced the accumulation of geometrically necessary dislocations (GNDs) around them. When micro-inclusions appeared on grain boundaries, the above factors changed the energy required for local deformation through potential hardening effects in the model and ultimately affected the evolution of the local energy storage density. When micro-inclusions appeared inside grains, the evolution of local energy storage was often dominated by plastic deformation only. The above mechanism is microstructure sensitive and spatially limited, which leads to the dispersion of lifetimes and negligible effect of micro-inclusions on distal grains.

Shear localization in polycrystalline metal at high-strain rates with dynamic recrystallization: Crystal plasticity modeling and texture effect

Shear localization is an important failure mode, or even the dominant mode in metals at high-strain rates. However, it is a great challenge to accurately predict the occurrence and evolution of shear localization in metals at the high-strain rate deformation. Here, a dislocation-based crystal plasticity constitutive model with a crucial mechanism of shear instability, namely dynamic recrystallization, was developed. The evolution equations of dislocation density and grain size in the process of dynamic recrystallization were proposed and incorporated into the new constitutive model. The threshold of the stored energy in crystals was used as the criterion for the occurrence of dynamic recrystallization. Dynamic compression of a nanograin Cu-Al alloy was performed using the crystal plasticity finite element method based on the new constitutive model, and good agreement of the numerical prediction with the existing experimental data validates the new constitutive model. The results show dynamic recrystallization can be a more dominant mechanism for the occurrence of shear instability than thermal softening. In addition, dynamic tension and shear of the Cu-Al alloys with five typical textures were also simulated, showing that both loading mode and texture can significantly affect the formation of shear localization. This work is helpful for us to understand the role of microstructural evolution in the formation of shear localization at high-strain rates and to design the microstructure for artificially controlling or preventing the formation of shear localization.

Multi-phase-field and dislocation-based crystal plasticity analysis of martensitic transformation in metastable austenitic steels

Multi-phase-field and dislocation-based crystal plasticity analysis of martensitic transformation in metastable austenitic steels

Crystal plasticity analysis of the evolutions of temperature, stress and dislocation in additively manufactured tungsten

Additive manufacturing (AM) has brought new opportunities for the fabrication of refractory metal tungsten (W). However, the cracking issue in additive manufactured pure W has not been solved, restricting its application. The cracking behavior is associated with the high residual stress, which is caused by the high temperature gradient and cooling rate during AM, as well as the internal brittleness of W. In order to solve this problem, the evolution of the internal microstructure and the corresponding thermal and loading conditions during AM has to be systematically investigated, but the related work is very rare. In the current work, a thermal-mechanical coupled dislocation-based crystal plasticity model is developed, which considers the temperature dependent plasticity induced by the thermal-activated kink-pair mechanism of screw dislocation. This model is applied to investigate the evolution of temperature, stress, and dislocation behaviors in single crystal and polycrystalline W during AM. The influences of crystal orientation and adding alloying element Ta are also discussed from the microscopic and macroscopic perspectives.

Understanding of the fatigue crack nucleation in metallic sealing rings by explicitly incorporating the deformation history from manufacturing to service

Fatigue cracking in metallic sealing rings has been a concern for the aerospace industry because the formation of even a micro-crack may cause an aviation accident. In this study, an integrated three-point bending fatigue experiment and dislocation-based crystal plasticity finite element modeling was used to determine the threshold for fatigue crack nucleation. Subsequently, the fatigue lives of the rings under different service conditions were evaluated based on the local stored energy density evolution. The conclusions of this work can provide theoretical guidance for the manufacturing of high-performance metallic sealing rings.

Polyphase crystal plasticity for high strain rate: Application to twinning and retwinning in tantalum

Upon increasing strain rate a switch operates in tantalum response from a plasticity dominated regime to a twinning dominated regime. This transition is investigated by means of a polyphase crystal plasticity model which combines a Phase Field-Reaction Pathway formalism and a dislocation-based crystal plasticity model. The proposed formalism for twinning considers an unbounded number of variants which permits the observation of twinning, detwinning and retwinning phenomena. The crystal plasticity model takes into account slip systems interactions and includes two glide regimes to deal with high strain rates. A model for dislocation inheritance during twinning is proposed. Simulations highlight a dual role of plasticity: strain hardening inside the matrix may, under certain conditions, hinder the formation of twin variants whereas plasticity inside the variants further relaxes the residual stress due to twins interaction and contributes to shape the variant.

Dislocation Density Evolution in Low-Cycle Fatigue of Steels Using Dislocation-Based Crystal Plasticity

Dislocation accumulation caused by a crystallographic slip or plastic flow is one of the most critical factors for the growth of fatigue cracks. The dislocation density-based crystal plasticity method accounting for mobile and immobile dislocation densities has been widely used to evaluate crack behavior in polycrystals. However, the evolution of mobile and immobile dislocation densities in fatigue has not been carefully investigated, especially during the crack nucleation period. In the present study, a dislocation-based crystal plasticity model is employed and verified with experimental results. A representative domain with 39 grains is used to evaluate the dislocation density evolution in fatigue crack nucleation. The results indicate that mobile and immobile dislocation densities evolve at a decreasing rate in low plasticity and a constant rate in large plasticity for loading cases with constant strain amplitudes, whereas an increasing rate of dislocation density evolution is observed for loading cases with variable strain amplitudes. By analogy with cumulative plastic strain, a fatigue crack nucleation criterion is proposed, which is correlated well with the Coffin-Manson relationship. Based on a grain level analysis, a loading case with a low strain rate results in transgranular or mixed-mode (intergranular and transgranular) fatigue damage. In comparison, immobile dislocation density at a high strain rate mainly builds up at the grain boundary, indicating intergranular fatigue damage.

Size dependent creep deformation of elastically constrained compliant metallic joints

The present study proposes a novel method to predict the size dependent creep behavior of bi-material joints formed by constraining a creep compliant metal, such as Sn, having varied thickness ranging from 1.4 mm to 170 µm, between stiff elastic substrates, such as Cu. A dramatic reduction in the secondary or minimum creep rate was observed with decrease in joint thickness. Finite element (FE) analysis using continuum formulations attributed this strengthening to the geometric constraints imposed by Cu, which increases the triaxiality in the joints and hence reduces the effective stress. While FE results were in close agreement with experiment in thick joints, it significantly overpredicted the creep rate of miniature joints. Further, orientation imaging revealed that microstructure varied with length scale, from bulk Sn with multiple grains to miniature joints having a few grains. The additional strengthening was captured using dislocation-based crystal plasticity (CP) creep modeling of Sn-Cu joints by incorporating this microstructural length scale, in addition to the geometric constraints. CP simulations revealed that orientation anisotropy of Sn and the constraints imposed by substrates on dislocation motion lead to higher strength in the miniature joints. Using the insights from FE and CP modeling a unified length scale sensitive model, incorporating both geometric or continuum and microstructural factors, was developed that can accurately predict the creep response of the joints of macro and meso length scale.

Phase-field and dislocation-based crystal plasticity analysis on lath martensitic structures formation in polycrystalline metastable austenitic steel

Although strength of TRIP steels can be compatible with ductility owing to deformation-induced martensitic transformation, there is currently no model describing simultaneously the deformation and microstructure formation processes of TRIP steel. In this report, we introduce the basis vectors of martensitic transformation derived in the previous report into the crystal plasticity model and develop a new material model based on a dislocation-based crystal plasticity model coupled with a multi-phase-field one. Also, we consider plastic deformation of austenite phase for more realistic analyze. After that, we use this model to reproduce the formation process of martensitic lath-block structure in a metastable austenitic polycrystal. As a result, it is shown that the microstructure of lath martensite is numerically formed in a polycrystalline micro-specimen using 6 variants in a CP group.

Dislocation-based crystal plasticity modelling of a nickel-based superalloy under dwell-fatigue: From life prediction to residual life assessment

In this work, a dislocation-based crystal plasticity finite element (CPFE) framework was implemented to investigate the effects of loading conditions on dwell-fatigue crack initiation life. Experimentally, a large number of strain-controlled dwell-fatigue tests were carried out at 650 °C in a nickel-based superalloy. The combinations of CPFE simulations and post-test examinations were used to reveal the dwell-fatigue crack initiation mechanisms. Then, a life prediction approach was presented on the basis of accumulated energy dissipation at half-life cycle. Good agreement between the experimental and simulated lives verifies the robustness as well as the accuracy of the present approach. Finally, a new three-dimensional (3-D) damage tolerance diagram was proposed by introducing a CP-based physical parameter to describe the degradation levels and evaluate the residual dwell-fatigue life.

Comparison of EBSD, DIC, AFM, and ECCI for active slip system identification in deformed Ti-7Al

The use of SEM-DIC, AFM, ECCI, and HR-EBSD to characterize slip-system activity was assessed on the same material volume of Ti7Al. This study presents a robust comparison of the various methods for the first time, including an assessment of their advantages and disadvantages, and how they can be used effectively in a complementary fashion. The analysis of the different approaches was carried out in a blind, round-robin manner at three different universities. A Ti7Al specimen was deformed in uniaxial tension to approximately 3% axial strain, and the active slip systems were independently identified using (i) trace analysis; (ii) in-SEM digital image correlation, (iii) observations of residual dislocations from ECCI, and (iv) long-range rotation gradients through HR-EBSD, with consistent trace identification in all cases. Displacement data from AFM was used to augment SEM-DIC displacement data by providing complementary out-of-plane displacement information. Furthermore, short-range dislocation gradients (measured by DIC) provided insight into the residual geometrically necessary dislocation (GND) content, and was consistent with the GND content extracted from EBSD data and ECCI images, confirming the presence of residual GNDs on the dominant slip systems resulting in visible slip bands. These approaches can be used in tandem to provide multi-modal information on slip band identification, strain and orientation gradients, out-of-plane displacements, and the presence of GNDs and SSDs, all of which can be used to inform and validate the development of dislocation-based crystal plasticity and strain gradient models.

Effects of crystallography on hot-spot formation in porous RDX single crystals

The thermomechanical behavior of porous RDX single crystals is studied under dynamic loading using an anisotropic dislocation-based crystal plasticity model that accounts for deformation-induced heating. A micromechanics-based framework is proposed to account for micro-inertially confined dynamic collapse of pores. A suite of finite element calculations are carried out to systematically elucidate the role of crystallographic orientation on hot-spot formation. Under particular loading orientations, the porous RDX crystals are found to be quite sensitive to deviatoric and volumetric strain localizations, even for loading situations that do not particularly promote strain localization in isotropic materials. Due to the anisotropy-induced strain localizations, fairly severe hot-spots are predicted even under moderate applied strains. The susceptibility of porous RDX to strain localize and form severe hot-spots under particular loading orientations has important implications for accidental detonation of these energetic materials.

Modelling and simulation of dynamic recrystallisation based on multi-phase-field and dislocation-based crystal plasticity models

ABSTRACT The mechanical properties of metals used as structural materials are significantly affected by hot (or warm) plastic working. Therefore, it is industrially important to predict the microscopic behaviour of materials in the deformation process during heat treatment. In this process, a number of nuclei are generated in the vicinity of grain boundaries owing to thermal fluctuation or the coalescence of subgrains, and dynamic recrystallisation (DRX) occurs along with the deformation. In this paper, we develop a DRX model by coupling a dislocation-based crystal plasticity model and a multi-phase-field (MPF) model through the dislocation density. Then, the temperature dependence of the hardening tendency in the recrystallisation process is introduced into the DRX model. A multiphysics simulation for pure Ni is conducted, and then the validity of the DRX model is investigated by comparing the numerical results of microstructure formation and the nominal stress–strain curve during DRX with experimental results. The obtained results indicate that in the process of DRX, nucleation and grain growth occur mainly around grain boundaries with high dislocation density. As deformation progresses, new dislocations pile up and subsequent nucleation occurs in the recrystallised grains. The influence of such microstructural evolution appears as oscillation in the stress–strain curve. From the stress–strain curves, the temperature dependence in DRX is observed mainly in terms of the yield stress, the hardening ratio, and the change in the hardening tendency after nucleation occurs.

Unravelling Anisotropy Evolution during Spiral Pipe Forming: a Multiscale Approach

Spiral forming of bainitic steel coils into large diameter pipes involves a complex deformation history with several strain path changes. These lead to mechanical properties on pipe which are macroscopically different compared to coil. A detailed understanding of the property evolution during spiral pipe forming is crucial to tailor the coil material and to ensure safe pipe operation. However, it has proven difficult to correctly reproduce the anisotropic strength evolution during pipe forming with available phenomenological hardening models. Unravelling the factors contributing to macroscopic anisotropy is inherently a multi-scale problem due to the complex microstructures exhibited by modern bainitic linepipe steels. They promote a large Bauschinger effect, aside from cross loading-effects and more or less pronounced Lüders banding. Here, we present selected experimental and numerical results related to our efforts to predict the mechanical properties of bainitic steel pipes manufactured from hot rolled coils. Across the scales, we consider sources for anisotropy, such as residual stresses, crystallographic texture and grain substructure. A dislocation-based crystal plasticity model incorporated into a computationally efficient hierarchical multi-scale forming simulation is employed to predict texture and strength changes.

Modeling and simulation of dynamic recrystallization for Mg/LPSO alloys based on multi-phase-field and dislocation-based crystal plasticity models

Modeling and simulation of dynamic recrystallization for Mg/LPSO alloys based on multi-phase-field and dislocation-based crystal plasticity models

Effect of slip transmission at grain boundaries in Al bicrystals

The effect of slip transfer on the deformation mechanisms of Al bicrystals was explored using a rate-dependent dislocation-based crystal plasticity model. Three different types of grain boundaries (GBs) were included in the model by modifying the rate of dislocation accumulation near the GB in the Kocks-Mecking law, leading to fully-opaque (dislocation blocking), fully-transparent and partially-transparent GBs. In the latter, slip transmission is only allowed in pairs of slip systems (SS) in neighbour grains that are suitably oriented for slip transfer according to the Luster-Morris parameter. Modifications of the GB character led to important changes in the deformation mechanisms at the GB. In general, bicrystals with fully-opaque (dislocation blocking) boundaries showed an increase in the dislocation density near the GB, which was associated with an increase in the Von Mises stress. In contrast, the dislocation pile-ups and the stress concentration were less pronounced in the case of partially-transparent boundaries as the slip in one grain can progress into the next grain with some degree of continuity. No stress concentrations were found at these boundaries for fully-transparent boundaries, and there was continuity of strain across the boundary, which is not typical of most experimentally observed GBs (Hémery et al., 2018; Bieler et al., 2019). Simulations of ideal bicrystals oriented for favorable slip transfer on the most highly favored slip system in grains with high Schmid factors for slip transfer depends on the number of active SS in operation in the neighborhood indicating that most boundaries will lead to nearly opaque conditions while some boundaries will be transparent. Finally, the model was applied to a particular experimentally observed GB in which slip transfer was clearly operating indicating that the model predicted a nearly transparent GB.

New insight for mechanical properties of metals processed by severe plastic deformation

The steady state is expected when applying severe plastic deformation (SPD) techniques to process metals. In this study, we propose a method to study the steady state regarding the microstructural features and the mechanical properties, which are verified by the experimental results. More importantly, the initial state of as-prepared metal depending mainly on the processing conditions is critical for the subsequent constitutive relations. Within the framework of dislocation-based crystal plasticity, it is revealed that the dislocation density and flow stress will not change during further deformation when the initial dislocation density is equal to the steady-state value under the loading conditions. In addition, if the initial dislocation density is larger or smaller than the steady-state value, then the dislocation density and flow stress will decrease or increase with increasing strain, and tend to approach the steady-state value. These mechanisms provide not only a physical interpretation for various experimental observations such as near-perfect elastoplasticity, strain hardening and strain softening, but also insightful guidance for investigating the strengthening mechanisms in gradient nano-grained metal produced by SPD.

Grain boundary strengthening of FCC polycrystals

Abstract