Mechanism-based Crystal Plasticity Research Articles

A microstructure-informed constitutive model for hierarchical materials with subgrain features

Additively manufactured metal alloys often have a hierarchical microstructure consisting of subgrain features. The subgrain features, being smaller in size than grains, significantly influence the mechanical properties and anisotropy of the material. Recognizing the critical role of subgrain features, this work proposes a novel generalized microstructure-informed constitutive modeling framework for hierarchical materials using a mechanism-based crystal plasticity formulation. Considering direct energy deposited (DED) stainless steel (SS) 316 L as the reference material we first categorize subgrain features as a network of solidification cells and a scattered distribution of secondary phases. Then we advanced the state-of-the-art mechanism-based crystal plasticity formulation by explicitly accounting for the geometric and mechanistic effects of both cellular network and scattered secondary phase subgrain features. Homogenization schemes are developed to implement the constitutive model on a finite element analysis (FEA) framework. The anisotropy is realized as a natural outcome of a preferred alignment of cells in the build direction. The model is then calibrated using experimental data. Limited validation of the model is also performed. Results show that explicitly accounting for the subgrain features in a constitutive model allows one to accurately capture the macroscopic and microscopic response of a hierarchical material.

Crystal plasticity analysis of temperature-sensitive dwell fatigue in Ti-6Al-4V titanium alloy for an aero-engine fan disc

This study investigates the temperature-dependent dwell fatigue behavior of Ti-6Al-4V alloy using crystal plasticity finite element method. The dislocation mechanism-based crystal plasticity parameters are calibrated with the data of quasi-static tensile and constant load creep tests at ambient and intermediate temperatures. In particular, the rate-dependent parameters related to slip property are employed to establish the relationship between strain rate sensitivity of a soft α-titanium single crystal and temperature. The variation of strain rate sensitivity with temperature influences the stress redistribution occurring within the hard-soft grain combination, which in turn affects the dwell fatigue sensitivity. Further, the structural analysis for a Ti-6Al-4V fan disc provides the stress fields at takeoff and cruise phases to examine the in-service stress redistribution. The highly localized hoop stress and presence of large macrozones at the bore of the fan disc, rather than the fair rate sensitivity of soft macrozones at working temperatures, are responsible for triggering basal stress enhancement and dwell facet nucleation in hard macrozones.

Examining deformation localization of irradiated tungsten under uniaxial compression with crystal plasticity

In this work, the deformation behavior of irradiated tungsten at elevated service temperatures is examined using mechanism-based crystal plasticity finite element framework by considering multiple mechanisms, including thermal softening and irradiation hardening. The previously developed mechanism-based crystal plasticity model is first utilized to assess the yield stress of unirradiated and irradiated tungsten upon low-temperature irradiation. The engineering stress-strain response under uniaxial compression is then predicted by considering the effect of irradiation-induced defect clusters on the motion of deformation-induced dislocations, and the predicted results agree well with the experimental measurements. More importantly, the formation and evolution of plastic strain localization zones in the form of shear bands are qualitatively captured, and the maximal principal strain distribution is quantitatively linked to the dose of irradiation damage. Finally, the deformation-induced shear band as a result of plastic instability in the compressed tungsten specimen is discussed.

Cyclic plasticity of an interstitial high-entropy alloy: experiments, crystal plasticity modeling, and simulations

The development of high-entropy alloys (HEAs) comprising multiple principal components is an innovative design strategy for metallic materials from the perspective of thermodynamic entropy. However, despite their potential candidacy for engineering applications, the lack of research on the cyclic loading responses as well as constitutive modeling of the HEAs is a major constraint. Therefore, the present work focuses on the cyclic plasticity of a typical carbon-doped interstitial HEA (iHEA) with nominal composition Fe49.5Mn30Co10Cr10C0.5 (at.%). The results of stress-controlled cyclic tests with nonzero mean stress showed that the iHEA exhibits significant cyclic hardening and stress level–dependent ratcheting. Owing to its improved cyclic hardening, the saturated ratcheting strain rate of the iHEA is lower than that of conventional steels such as the 316L stainless steel. Furthermore, microscopic characterizations revealed that the cyclic deformations caused massive martensitic phase transformation and hierarchical structures in the iHEA. The experimental results were used to develop a physical mechanism-based crystal plasticity constitutive model that is capable of describing the cyclic plasticity of the iHEA, which was implemented into a finite element framework. The simulation results showed that the loading stress significantly affected the microstructural evolutions, leading to a stress level–dependent cyclic plasticity. Thus, this investigation provides a fundamental basis for fatigue tests and service life prediction/optimization of the iHEA in the future, which can promote its engineering applications.

Influence of crystal structure on size dependent deformation behavior and strain heterogeneity in micro-scale deformation

Crystal structure determines the distinct deformation mode of crystalline materials and thus plays a critical role in micro-scale deformation. The micro-deformation mechanism at grain level, however, is still not well understood and the knowledge of how crystal structure affects size effect and its affected deformation behaviors in micro-scale deformation is not yet systematic and extensive enough to support micro-manufacturing and microproduct development. To explore the influence of crystal structure on size dependent deformation, strain heterogeneity and fracture in micro-scale deformation, a series of micro-scale tensile tests using polycrystalline pure copper (FCC), pure iron (BCC) and pure α-titanium (HCP) sheets with various thicknesses and microstructural grain sizes were conducted. A mechanism-based crystal plasticity (CP) model incorporating size-dependent slip and twinning was proposed. The CP model successfully predicted the influence of grain size and thickness on the flow stress as well as the dependence of twinning volume fraction on the grain size of Ti samples. Full-field simulation was carried out to thoroughly explore the influence of crystal structure on grain-scale strain heterogeneity and fracture behavior via examining strain localization, lattice rotation, slip and twinning activity. Results showed that when only few grains exist in the thickness direction, slip activation is particularly limited in HCP Ti sample, leading to strain concentration and generation of wide and long shear bands thus sharply reduce the fracture toughness. Lattice rotation of Cu samples is most uniform. The large strain in samples of BCC Fe is distributed more dispersedly and more shear bands are formed. This work presents a comprehensive understanding of the effect of crystal structure on the size effect affected micro-scale deformation of metallic materials at grain level and a basis to support the applications of micro-scale deformation for making different crystal structured micro-parts.

A deformation mechanism based crystal plasticity model of ultrafine-grained/nanocrystalline FCC polycrystals

A new crystal plasticity model based on the deformation mechanism for ultrafine-grained/nanocrystalline face-centered cubic (FCC) metals was developed. The deformation mechanism was that dislocations glide from grain boundary to grain boundary (GB). Constitutive equations on the slip system level were developed based on dislocation glide and all stages of dislocation activities were considered especially their interactions with GB. An Arrhenius type rate equation was established based on the thermally activated depinning of dislocations from GB obstacles. The new constitutive equations were incorporated into a 3D crystal plasticity formulation, and this crystal plasticity model was implemented into a UMAT subroutine of the ABAQUS finite element program. The uniaxial deformation responses of the two ufg/nc materials were simulated. Crystal plasticity finite element method (CPFEM) simulations gave flow stress predictions that were very close to the experimental results. The dislocation mechanism-based crystal plasticity UMAT is ready to be used for more advanced simulation studies.

A mechanism-based model for deformation twinning in polycrystalline FCC steel

Deformation twinning, a common and important plastic deformation mechanism, is the key contributor to the excellent combination of strength and ductility in twinning-induced plasticity (TWIP) steel. In the open literature, a significant amount of research has been reported on the microstructural characteristics of deformation twinning and its influence on the overall deformation behavior of TWIP steel. In this study, we examine the feasibility of a mechanism-based crystal plasticity model in simulating the microstructural level deformation characteristics of TWIP steel. To this end, a model considering both double-slip and double-twin is developed to investigate the stress–strain behavior and local microstructural features related to the formation and growth of micro-twins in low stacking fault energy (SFE) TWIP steel. The twin systems are described as pseudo-slips that can be activated when their resolved shear stress reaches the corresponding critical value. A hardening law that accounts for the interaction among the slip and twin systems is also developed. Numerical simulations for different mesh sizes and single crystal patch tests under different loading modes are carried out to verify the modeling procedure. Our simulation results reveal that, despite its simple nature, the double-slip/double-twin model can capture the key deformation features of TWIP steel, including twin volume fraction evolution, continuous strain hardening, and the final fracture in the form of strain localization.

Mechanism-based crystal plasticity modeling of twin boundary migration in nanotwinned face-centered-cubic metals

Nanotwinned (nt) metals are an important subset of nanostructured materials because they exhibit impressive strength and ductility. Several recent investigations on nt face-centered-cubic (FCC) metals indicate that their macroscopic responses emerge from complex microscopic mechanisms that are dominated by dislocation–TB interactions. Under applied stimulus, nt microstructures evolve through migration of twin boundaries (TBs) that may have implications on the material strength and stability. This work focuses on modeling TB migration within finite element framework in an explicit manner and studying its effects on the micromechanics of twinned FCC metals under quasi-static loading conditions. The theoretical setting is developed using three-dimensional single crystal plasticity as a basis wherein the plastic slip on the {111}〈1¯10〉 slip systems in an FCC crystal structure is modeled as visco-plastic behavior. Owing to their governing role, twins are modeled as discrete lamellas with full crystallographic anisotropy. To model TB migration, an additional visco-plastic slip-law for twinning partial systems ({111}〈112¯〉) based on the nucleation and motion of twin partial dislocations is introduced. This size-dependent constitutive law is presumed to prevail in the vicinity of the TB and naturally facilitates TB migration when combined with a twinning condition that is based on the accrual of the necessary shear strain. The constitutive development is implemented within a finite element framework through a User Material (UMAT) facility within ABAQUS/STANDARD®. Detailed micromechanics simulations on model microstructures involving single-grained and polycrystalline topologies are presented.

Fracture of bicrystal metal/ceramic interfaces: A study via the mechanism-based strain gradient crystal plasticity theory

Two continuum mechanical models of crystal plasticity theory namely, conventional crystal plasticity theory and mechanism-based crystal plasticity theory, are used to perform a comparative study of stresses that are reached at and ahead of the crack tip of a bicrystal niobium/alumina specimen. Finite element analyses are done for a stationary crack tip and growing cracks using a cohesive modelling approach. Using mechanism-based strain gradient crystal plasticity theory the stresses reached ahead of the crack tip are found to be two times larger than the stresses obtained from conventional crystal plasticity theory. Results also show that strain gradient effects strongly depend on the intrinsic material length to the size of plastic zone ratio ( l/ R 0). It is found that the larger the ( l/ R 0) ratio, the higher the stresses reached using mechanism-based strain gradient crystal plasticity theory. An insight into the role of cohesive strength and work of adhesion in macroscopic fracture is also presented which can be used by experimentalists to design better bimaterials by varying cohesive strength and work of adhesion.