AN ANALYSIS OF THE EFFECTS OF SYMMETRICAL TILT GRAIN BOUNDARIES ON THE PLASTIC DEFORMATION

A numerical investigation on the simple polycrystals containing threesymmetrical tilt grain boundaries(GBs)is carried out within the framework of crystalplasticity which precisely considers the finite deformation and finite lattice rotation aswell as elastic anisotropy.The calculated results show that the slip geometry and theredistribution of stresses arising from the anisotropy and boundary constraint play animportant role in the plastic deformation in the simple polycrystals.The stress levelalong GB is sensitive to the load level and misorientation,and the stresses along GB aredistributed nonuniformly.The GB may exhibit a softening or strengthening feature,which depends on the misorientation angle.The localized deformation bands usuallydevelop accompanying the GB plastic deformation,the impingement of the localizedband on the GB may result in another localized deformation band.The yield stresseswith different misorientation angles are favorably compared with the experimentalresults.     

Effect of microstructure on the nucleation of deformation twins in polycrystalline high-purity magnesium: A multi-scale modeling study

A multi-scale, theoretical study of twin nucleation from grain boundaries in polycrystalline hexagonal close packed (hcp) metals is presented. A key element in the model is a probability theory for the nucleation of deformation twins based on the idea that twins originate from a statistical distribution of defects in the grain boundaries and are activated by local stresses at the grain boundaries. In this work, this theory is integrated into a crystal plasticity constitutive model in order to study the influence of these statistical effects on the microstructural evolution of the polycrystal, such as texture and twin volume fraction. Recently, a statistical analysis of exceptionally large data sets of {101?2} deformation twins was conducted for high-purity Mg (Beyerlein et al., 2010a). To demonstrate the significantly enhanced accuracy of the present model over those employing more conventional, deterministic approaches to twin activation, the model is applied to the case of {101?2} twinning in Mg to quantitatively interpret the many statistical features reported for these twins (e.g., variant selection, thickness, numbers per grain) and their relationship to crystallographic grain orientation, grain size, and grain boundary misorientation angle. Notably the model explains the weak relationship observed between crystal orientation and twin variant selection and the strong correlation found between grain size and the number of twins formed per grain. The predictions suggest that stress fluctuations generated at grain boundaries are responsible for experimentally observed dispersions in twin variant selection.     

The role of intergranular constraint on the stress-induced martensitic transformation in textured polycrystalline NiTi

The influences of grain boundaries and relative grain misorientations on stress-induced martensitic transformations in NiTi are studied using unique experiments and finite element modeling. Tensile and compressive mechanical tests reveal that polycrystalline NiTi with a dominant <111> fiber texture and single crystal NiTi oriented along the [111] direction exhibit nearly identical stress–strain curves during a stress-induced martensitic transformation. Micro-mechanical finite element simulations of fiber textured polycrystals and single crystals undergoing a multi-variant martensitic transformation confirm the relative indifference of the macroscopic transformation attributes to the presence of grain boundaries. On the microscale, the finite element simulations further reveal that the insensitivity of the transformation to intergranular constraint is linked to the local stress disturbance created by transforming grains. The transformation of grains that are favorably oriented with respect to the loading axis creates local stresses that invariably assist the transformation in neighboring grains, effectively lowering the influence of grain misorientations and boundaries on the macroscopic transformation behavior.     

Dislocation nucleation in Σ3 asymmetric tilt grain boundaries

Atomistic simulations were used to investigate dislocation nucleation from Σ3 asymmetric (inclined) tilt grain boundaries under uniaxial tension applied perpendicular to the boundary. Molecular dynamics was employed based on embedded atom method potentials for Cu and Al at 10 K and 300 K. Results include the grain boundary structure and energy, along with mechanical properties and mechanisms associated with dislocation nucleation from these Σ3 boundaries. The stress and work required for dislocation nucleation were calculated along with elastic stiffness of the bicrystal configurations, exploring the change in response as a function of inclination angle. Analyses of dislocation nucleation mechanisms for asymmetric Σ3 boundaries in Cu show that dislocation nucleation is preceded by dislocation dissociation from the boundary. Then, dislocations preferentially nucleate in only one crystal on the maximum Schmid factor slip plane(s) for that crystal. However, this crystal is not simply predicted based on either the Schmid or non-Schmid factors. The synthesis of these results provides a better understanding of the dislocation nucleation process in these faceted, dissociated grain boundaries.     

Grain boundary interface mechanics in strain gradient crystal plasticity

Interactions between dislocations and grain boundaries play an important role in the plastic deformation of polycrystalline metals. Capturing accurately the behaviour of these internal interfaces is particularly important for applications where the relative grain boundary fraction is significant, such as ultra fine-grained metals, thin films and micro-devices. Incorporating these micro-scale interactions (which are sensitive to a number of dislocation, interface and crystallographic parameters) within a macro-scale crystal plasticity model poses a challenge. The innovative features in the present paper include (i) the formulation of a thermodynamically consistent grain boundary interface model within a microstructurally motivated strain gradient crystal plasticity framework, (ii) the presence of intra-grain slip system coupling through a microstructurally derived internal stress, (iii) the incorporation of inter-grain slip system coupling via an interface energy accounting for both the magnitude and direction of contributions to the residual defect from all slip systems in the two neighbouring grains, and (iv) the numerical implementation of the grain boundary model to directly investigate the influence of the interface constitutive parameters on plastic deformation. The model problem of a bicrystal deforming in plane strain is analysed. The influence of dissipative and energetic interface hardening, grain misorientation, asymmetry in the grain orientations and the grain size are systematically investigated. In each case, the crystal response is compared with reference calculations with grain boundaries that are either ‘microhard’ (impenetrable to dislocations) or ‘microfree’ (an infinite dislocation sink).     

3-D simulation of spatial stress distribution in an AZ31 Mg alloy sheet under in-plane compression

A complete 3-D crystal plasticity finite element method (CPFEM) that considered both crystallographic slip and deformation twinning was applied to simulate the spatial distribution of the relative amount of slip and twin activities in a polycrystalline AZ31 Mg alloy during in-plane compression. A microstructure mapping technique that considered the grain size distribution and microtexture measured by electron backscatter diffraction (EBSD) technique was used to create a statistically representative 3-D microstructure for the initial configuration. Using a 3-D Monte Carlo method, a 3-D digital microstructure that matched the experimentally measured grain size distribution was constructed. Crystallographic orientations obtained from the EBSD data were assigned on the 3-D digital microstructure to match the experimentally measured misorientation distribution. CPFEM captured the heterogeneity of the stress concentration as well as the slip and twin activities of a polycrystalline AZ31 Mg alloy during in-plane compression.     

Determination of the minimum entropy configuration and velocity surfaces for elastic–plastic wave scattering at grain boundaries

A recent model based on full elastic anisotropy and crystal plasticity predicted the existence of multiple wave configurations during the interaction of stress waves with grain boundaries. Since the multiple wave configuration scenario cannot exist in nature, the principle of minimum entropy production is applied in the current work to find the most probable configuration. A large amplitude transmitted quasi-longitudinal wave is predicted for the given bicrystal orientation studied due to the wave propagating near a [001] direction and thus requiring large stress given the very low Schmid factor in this direction (for nickel aluminide (NiAl) as a model material). Anisotropic elastic–plastic velocity surfaces for quasi-longitudinal and quasi-shear waves in NiAl have also been constructed to gain an understanding of the general nature of plastic waves as a function of crystallographic direction.     

Effects of lattice misorientations on strain heterogeneities in FCC polycrystals

It is well documented that the highly heterogeneous deformation behaviour and lattice rotation typically observed within grains in a polycrystal are attributed to microstructural features such as grain structure, topology, size, etc. In this work, the effects of low- and high-angle grain boundaries on the mechanical behaviour of FCC polycrystals are investigated using a micro-mechanical model based on crystal plasticity theory. The constitutive framework relies on dislocation mechanics concepts to describe the plastic deformation behaviour of FCC metallic crystals and is validated by comparing the measured and predicted local and macroscopic deformation behaviour in a thin Al-0.5% Mg polycrystal tensile specimen containing a relatively small number of surface grains. Comparisons at the microscopic (e.g. local slip distribution) and macroscopic (e.g. average stress-strain response) levels elucidate the role of low-angle grain boundaries, which are found to have a profound effect on both the local and average deformation behaviour of FCC polycrystals with a small number of grains. However, this effect diminishes when the number of grains increases and becomes negligible in bulk polycrystals. In light of the widely accepted view that high-angle grain boundaries strongly influence the mechanical behaviour of very fine-grained metals, this work has shown that low-angle grain boundaries can also play an equally important role in the deformation behaviour of polycrystals with a relatively small number of grains.     

Precipitate coarsening-induced plasticity: Low temperature creep behaviour of tempered SAE 52100

Hardened and tempered SAE 52100 under uniaxial compressive loading deforms even at temperatures well below the tempering temperature and compressive loads well below the yield strength. The origin of the observed creep is associated with the coarsening of the nanosized precipitates (cementite, χ and η). The local volume changes that occur near dissolving and coarsening carbides in the presence of a uniaxial load cause macroscopic dimensional changes. For such process the kinetics is governed by the volume diffusion of C atoms. The coarsening of precipitates located near grain boundaries has been observed by in situ heating experiments with transmission electron microscopy. The observed logarithmic time dependent plastic strain can be described by the coarsening-induced plasticity model developed in this paper that combines concepts from transformation induced plasticity and precipitate coarsening models.     

Development of inter- and intragranular stresses during switching of ferroelectric polycrystals

Ferroelectrics are crystalline inorganic materials consisting of domains with different directions of spontaneous polarization. By application of sufficiently high electric fields, these domains can switch into a common direction, thus making the material piezoelectric. Due to ferroelasticity, the domains can be also switched into different states by the application of mechanical stress. In polycrystalline materials, as used in most applications, electric and stress fields interact so as to maintain compatibility. We study the influence of grain-to-grain interactions on the overall and local switching behavior and in particular the induced stresses inside grains and across grain boundaries. The behavior inside each grain is represented by the single-crystal model of [Huber, J.E., Fleck, N.A., Landis, C.M., McMeeking, R.M., 1999. A constitutive model for ferroelectric polycrystals. Journal of the Mechanics and Physics of Solids 47 (8), 1663–1697] and the polycrystal response is obtained through a two-dimensional multi-grain model in which grains are represented individually. We investigate the effect of random grain orientations, both in the plane of consideration and in three directions, and compare plane strain with plane stress conditions. It is found that the overall piezoelectric response under electric loading is not dependent only on the intra- and intergranular stresses in the plane but is also significantly affected by stresses in through-thickness direction.     

Three-dimensional local stress analysis on grain boundaries in polycrystalline material

In order to understand the initiation behavior of microstructurally small cracks in a stress corrosion cracking condition, it is important to know the tensile normal stress acting on the grain boundary (normal GB stress). The local stress in a polycrystalline body is enhanced by the inhomogeneity which stems from the shape and orientation of each grain. The stress in a three-dimensional polycrystalline body consisting of 100 grains with random orientation, under a remote uniform tensile stress condition, is evaluated by the finite element method. It was revealed that the local stress on the polycrystalline body is inhomogeneous under uniform applied stress and becomes large at those grain boundaries that are perpendicular to the load axis, though there is large fluctuation. It was also shown that the normal GB stress tends to be large near the triple points due to the deformation constraint caused by adjacent grains. Finally, the maximum stress on the surface of a large component caused by the inhomogeneity was evaluated by using Gumbel statistics.     

Defect redistribution within a continuum grain boundary plasticity model

The mechanical response of polycrystalline metals is significantly affected by the behaviour of grain boundaries, in particular when these interfaces constitute a relatively large fraction of the material volume. One of the current challenges in the modelling of grain boundaries at a continuum (polycrystalline) scale is the incorporation of the many different interaction mechanisms between dislocations and grain boundaries, as identified from fine-scale experiments and simulations. In this paper, the objective is to develop a model that accounts for the redistribution of the defects along the grain boundary in the context of gradient crystal plasticity. The proposed model incorporates the nonlocal relaxation of the grain boundary net defect density. A numerical study on a bicrystal specimen in simple shear is carried out, showing that the spreading of the defect content has a clear influence on the macroscopic response, as well as on the microscopic fields. This work provides a basis that enables a more thorough analysis of the plasticity of polycrystalline metals at the continuum level, where the plasticity at grain boundaries matters.     

Yield stress strengthening in ultrafine-grained metals: A two-dimensional simulation of dislocation dynamics

The effect of grain size on the tensile plastic deformation of ultrafine-grained copper polycrystals is investigated using a two-dimensional simulation of dislocation dynamics. Emphasis is put on the elementary mechanisms governing the yield stress in multislip conditions. Whatever the grain size, the yield stress is found to follow a Hall-Petch law. However, the elementary mechanism controlling slip transmission through the grain boundaries at yield is observed to change with the grain size. For the larger grain sizes, the stress concentrations due to dislocations piled-up at grain boundaries are responsible for the activation of plastic activity in the poorly stressed grains. For the smaller grain sizes, the pile-ups contain less dislocations and are less numerous, but the strain incompatibilities between grains become significant. They induce high internal stresses and favor multislip conditions in all grains. Based on these results, simple interpretations are proposed for the strengthening of the yield stress in ultrafine grained metals.     

The role of grain boundaries on fatigue crack initiation - An energy approach

In this paper, we construct a model for prediction of fatigue crack initiation based on the material’s microstructure. In order to do so, the energy of a persistent slip band (PSB) is monitored and an energy balance approach is taken, in which cracks initiate and the material fails due to stress concentration from a PSB (with respect to dislocation motion). These PSBs are able to traverse low-angle grain boundaries (GB), thus belonging to clusters of grains. As a consequence of the ongoing cyclic slip process, the PSBs evolve and interact with high-angle GBs, the result of which leads to dislocation pile-ups, static extrusions in the form of ledges/steps at the GB, stress concentration, and ultimately crack initiation. Hence, this fatigue model is driven by the microstructure, i.e. grain orientations, widely distributed grain sizes, precipitates, PSB-GB interactions, as well as the affect of neighboring grains. The results predict that cracks initiate near twin boundaries from PSBs spanning a single large grain with a favorable orientation or multiple grains connected by low-angle GBs. Excellent agreement is shown between model predictions and experimental data.     

Combined grain size, strain rate and loading condition effects on mechanical behavior of nanocrystalline Cu under high strain rates

Molecular dynamics simulations of nanocrys-talline Cu with average grain sizes of 3.1 nm, 6.2 nm, 12.4 nm and 18.6 nm under uniaxial strain and stress tension at strain rates of 10 8 s 1 , 10 9 s 1 and 10 10 s 1 are performed to study the combined grain size, strain rate and loading condition effects on mechanical properties. It is found that the strength of nanocrystalline Cu increases as grain size increases regardless of loading condition. Both the strength and ductility of nanocrystalline Cu increase with strain rate except that there is no monotonic relation between the strength and strain rate for specimens under uniaxial strain loading. Moreover, the strength and ductility of specimens under uniaxial strain loading are lower than those under uniaxial stress loading. The nucleation of voids at grain boundaries and their subsequent growth characterize the failure of specimens under uniaxial strain loading, while grain boundary sliding and necking dominate the failure of specimens under uniaxial stress loading. The rate dependent strength is mainly caused by the dynamic wave effect that limits dislocation motion, while combined twinning and slipping mechanism makes the material more ductile at higher strain rates.     

Dislocation nucleation from bicrystal interfaces and grain boundary ledges: Relationship to nanocrystalline deformation

Molecular dynamics simulations are used to evaluate the primary interface dislocation sources and to estimate both the free enthalpy of activation and the critical emission stress associated with the interfacial dislocation emission mechanism. Simulations are performed on copper to study tensile failure of a planar Σ5 {2 1 0} 53.1° interface and an interface with the same misorientation that contains a ledge. Simulations reveal that grain boundary ledges are more favorable as dislocation sources than planar regions of the interface and that their role is not limited to that of simple dislocation donors. The parameters extracted from the simulations are utilized in a two-phase composite mesoscopic model for nanocrystalline deformation that includes the effects of both dislocation emission and dislocation absorption mechanisms. A self-consistent approach based on the Eshelby solution for grains as ellipsoidal inclusions is augmented by introduction of stress concentration in the constitutive law of the matrix phase to account for more realistic grain boundary effects. Model simulations suggest that stress concentration is required in the standard continuum theory to activate the coupled grain boundary dislocation emission and absorption mechanisms when activation energy of the dislocation source is determined from atomistic calculation on grain boundaries without consideration of impurities or other extrinsic defects.     

A multiscale approach for modeling scale-dependent yield stress in polycrystalline metals

Modeling of scale-dependent characteristics of mechanical properties of metal polycrystals is studied using both discrete dislocation dynamics and continuum crystal plasticity. The initial movements of dislocation arc emitted from a Frank-Read type dislocation source and bounded by surrounding grain boundaries are examined by dislocation dynamics analyses system and we find the minimum resolved shear stress for the FR source to emit at least one closed loop. When the grain size is large enough compared to the size of FR source, the minimum resolved shear stress levels off to a certain value, but when the grain size is close to the size of the FR source, the minimum resolved shear stress shows a sharp increase. These results are modeled into the expression of the critical resolved shear stress of slip systems and continuum mechanics based crystal plasticity analyses of six-grained polycrystal models are made. Results of the crystal plasticity analyses show a distinct increase of macro- and microscopic yield stress for specimens with smaller mean grain diameter. Scale-dependent characteristics of the yield stress and its relation to some control parameters are discussed.     

Numerical simulations of crack deflection at a twist-misoriented grain boundary between two ideally brittle crystals

Finite-element simulations are used to model crack propagation across twist-misoriented grain boundaries, which are an important source of toughness in lamellar microstructures such as TiAl. We consider a twist grain boundary (GB) between two adjacent grains, and assume that each grain has a single cleavage orientation. The cleavage planes and GB are modeled as a set of cohesive surfaces, and the crack path and effective toughness of the system are simulated using a dynamic finite-element method (FEM). As the crack approaches the GB under remote mode I loading, it is allowed to either deflect along the GB and/or induce the nucleation of a periodic array of cracks in the adjacent grain. The simulations predict (i) a critical toughness ratio between the GB and the cleavage planes for the crack to propagate into the adjacent grain; (ii) an array of cracks in the GB and the twisted grain; (iii) the macroscopic mode I toughness of the solid as a function of a generalized measure of crack length; and (iv) the influence of GB toughness and twist misorientation on the effective toughness of the solid.