BCC Polycrystals Research Articles

Effect of irradiation-induced strength anisotropy on the reorientation trajectories and fragmentation behavior of grains in BCC polycrystals under tensile loading

We present a combined experimental and computational study exploring the effects of strength anisotropy on the grain reorientation trajectories in neutron-irradiated BCC polycrystals subjected to uniaxial tensile loading. We observe through in situ high-energy X-ray diffraction microscopy measurements of a model BCC alloy, Fe-9wt.%Cr, that the grains in irradiated samples exhibit reorientation trajectories that deviate more substantially from classical expectations than those in the unirradiated counterpart. We hypothesize that irradiation-induced strength anisotropy is a major influence on this behavior. Utilizing crystal plasticity finite element modeling, we isolate the effects of strength anisotropy by performing a suite of simulations in which we systematically strengthen select slip systems. Reorientation trajectories are compared against a datum of Taylor model predictions, and the deviation from classical expectations is analyzed through the lens of slip activity and availability. We further describe observations regarding the propensity of samples with high degrees of strength anisotropy to exhibit grain fragmentation. Overall, computational results provide insight on and quantification of the effects of strength anisotropy on reorientation trajectories and grain fragmentation, and align well with experimental observations, suggesting strength anisotropy as a plausible contributing mechanism to the observed phenomena.

Microstructurally-sensitive fatigue crack growth in HCP, BCC and FCC polycrystals

Microstructurally sensitive fatigue crack growth in four material systems with BCC, FCC and HCP crystallography was investigated through integrated crystal plasticity eXtended Finite Element (XFEM) modelling and experiment. The mechanistic drivers for crack path tortuosity and propagation rate have been investigated and crack propagation found to be controlled by crack tip stored energy and the crack direction by anisotropic crystallographic slip at the crack tip. Experimentally observed microstructurally-sensitive fatigue crack path tortuosities and growth rates in titanium alloy (Ti–6Al–4V), ferritic steel, nickel superalloy and zirconium alloy (zircaloy 4) have been shown to be captured, supporting the underpinning mechanistic arguments. Very short crack growth is dominated by local slip, but with increasing length, crack tip stresses begins to predominate, increasing the availability of slip systems and giving smaller amplitude oscillations between slip systems. This leads to overall crack paths which are in fact crystallographic but which appear not to be. Key features of crack retardation at grain boundaries, changes in rate resulting from crystallography, and intragranular crack path deflections have been experimentally observed and captured.

Autowave nature of plasticity. Scale invariance

The generality of localization of plastic deformation, which is observed at the stage of linear work hardening for HCP, BCC and FCC monoand polycrystals of pure metals and alloys, is considered. It was found previously that the motion rate of localized flow autowave is related to the reciprocal value of the work hardening coefficient by a linear law, which is universal in character. This is further substantiated by the results of the given study. The waves of plastic flow localization are found to have dispersion law. It has been established that in order to address the autowave of localized deformation, a quasi-particle may be introduced. The quasi-particle’s characteristics have been defined.

Understanding the deformation mechanism of individual phases of a dual-phase beta type titanium alloy using in situ diffraction method

An in situ tensile X-ray diffraction (XRD) set-up with an area detector was employed to characterize deformation behaviors of individual phases in a commercial dual-phase β-Ti alloy. A developed analytical approach based on the modified Williamson-Hall plot accounting for dislocation evolution was proposed to elucidate the deformation mechanism of each phase from the in situ XRD data. A commercial purity titanium (alpha type, α-Ti) alloy was examined as a comparison to assist identifying the influence of inter-phase interaction on the deformation behavior of the β-Ti alloy. We found that the small amount of the fine lamella shaped hcp (α) precipitates, which is only 5% in volume, has great effects on the deformation mechanism of the bcc (β) matrix in the β-Ti alloy due to the Burger's orientation relationship (BOR) between the two phases. Due to the reason that slip on the coherent plane of (211)β of the β phase (i.e. (10 1̅0)α plane of the α phase) is more predominant than that of (110)β plane (i.e. (0002)α plane) in a hcp ploycrystal, slip on (211)β plane is easier than that on (110)β plane in the β-Ti alloy (cf. {110} < 111 > is the typical slip system in single phase bcc polycrystals). Although slip on (211)β plane is the most facile, lattice strain on (211)β plane is not the smallest, manifesting that stress/strain redistribution between α precipitates and β matrix occurred to accommodate the inter-phase interaction.

Numerical investigation of the influence of rolling texture and microstructure on fatigue crack initiation in BCC polycrystals

The study aims to investigate the influence of the grain morphology and rolling texture on the fatigue crack initiation in BCC polycrystals. Several 2D polycrystalline aggregates having different grain size and shape distributions are generated based on an anisotropic tessellation and an ellipse packing algorithm. Uniform and typical BCC rolled textures containing both the α and γ fibers are considered for the crystallographic texture of the material. Finite element simulations using a crystal plasticity model are performed under cyclic uniaxial tension-compression condition. Twenty simulations are conducted for each type of microstructure in order to obtain significant statistical data. A critical plane fatigue indicator parameter (FIP) following the Tanaka-Mura model is applied to quantify the sensitivity of the microstructure against fatigue crack initiation. The distributions of relevant geometrical, crystallographic and mechanical quantities are analyzed. The effect of the grain size distribution, morphology and texture on the fatigue performance and scattering are discussed.

Average intragranular misorientation trends in polycrystalline materials predicted by a viscoplastic self-consistent approach

This work presents estimations of average intragranular fluctuations of lattice rotation rates in polycrystalline materials, obtained by means of the viscoplastic self-consistent (VPSC) model. These fluctuations give a tensorial measure of the trend of misorientation developing inside each single crystal grain representing a polycrystalline aggregate. We first report details of the algorithm implemented in the VPSC code to estimate these fluctuations, which are then validated by comparison with corresponding full-field calculations. Next, we present predictions of average intragranular fluctuations of lattice rotation rates for cubic aggregates, which are rationalized by comparison with experimental evidence on annealing textures of fcc and bcc polycrystals deformed in tension and compression, respectively, as well as with measured intragranular misorientation distributions in a Cu polycrystal deformed in tension. The orientation-dependent and micromechanically-based estimations of intragranular misorientations that can be derived from the present implementation are necessary to formulate sound sub-models for the prediction of quantitatively accurate deformation textures, grain fragmentation, and recrystallization textures using the VPSC approach.

Experimental and Visco-Plastic Self-Consistent evaluation of forming limit diagrams for anisotropic sheet metals: An efficient and robust implementation of the M-K model

In the present work, an efficient formulation for the prediction of forming-limit diagrams (FLDs) based on the well-known Marciniak and Kuczynski (M−K) theory using a Visco-Plastic Self-Consistent (VPSC) crystal-plasticity model has been detailed. The present model extends the previous MK-VPSC implementation (Signorelli et al., Predictions of forming limit diagrams using a rate-dependent polycrystal self-consistent plasticity model, International Journal of Plasticity 25 (2009) 1–25) based on the Newton–Raphson (N-R) method, which gives no guarantee of a robust iterative procedure. In order to avoid convergence problems and to reduce the computational cost of the coupled MK-VPSC scheme, a direct approach (DA) is proposed. The DA eliminates the need of the Jacobian evaluation associated with the N-R method as well as the iterative procedure tied to other possible minimization techniques. Moreover, the mechanical states outside and inside the groove are solved in the sample reference frame, avoiding the need to rotate the crystallographic orientations and the internal variables to the current band reference frame at each increment. In this way, only two calls to the material law are required per M−K increment, obtaining a more robust numerical procedure with a significant computational cost reduction. Interestingly, the requirement of more complex boundary conditions does not substantially increase the number of internal VPSC iterations to achieve a given tolerance. Simulation results show that the direct MK-VPSC approach is consistent with that based on the N-R method. The generalized boundary conditions in the polycrystal model allowed us to calculate either strain-rate ratio or stress ratio based FLDs. The effect of using either strain-rate ratio or stress ratio paths on the FLDs has been investigated by imposing three types of pre-straining on the sheet metals. Formability predictions for a randomly-textured FCC material and for textured FCC, BCC and HCP polycrystals are presented and discussed. Finally, by considering dissimilar metals – extra deep-drawing quality steel (EDDQ), dual-phase steel (DP-780) and pure zinc (Zn20) – we evaluated the MK-VPSC model's ability to predict forming-limit strains irrespective of microstructure and crystallography. The predicted results have been compared with experimental data and good agreement was found.

Prediction of Transient Hardening after Strain Path Change by a Multi-scale Crystal Plasticity Model with Anisotropic Grain Substructure

Multi-scale modelling offers physical insights in the relationship between microstructure and properties of a material. The macroscopic anisotropic plastic flow may be accounted for by consideration of (a) the polycrystalline nature and (b) the anisotropic grain substructure. The latter contribution to anisotropy manifests itself most clearly in the event of a change in the strain path, as occurs frequently in multi-step forming processes. Under monotonic loading, both the crystallographic texture and the loading-dependent strength contribution from substructure influence the macroscopically observed strength.The presented multi-scale plasticity model for BCC polycrystals combines a crystal plasticity model featuring grain interaction with a substructure model for anisotropic hardening of the individual slip systems. Special attention is given to how plastic deformation is accommodated: either by slip of edge dislocation segments, or alternatively by dislocation loop expansion. Resultsof this multi-scale modelling approach are shown for a batch-annealed IF steel. Whereas both model variants are seen to capture the transient hardening after different types of strain path changes, the dislocation loop model offers more realistic predictions under a variety of monotonic loading conditions.

Stress localization in BCC polycrystals and its implications on the probability of brittle fracture

The evaluation of the reliability of pressure vessels in nuclear plants relies on the evaluation of failure probability models. Micromechanical approaches are of great interest to refine their description, to better understand the underlying mechanisms leading to failure, and finally to improve the prediction of these models. The main purpose of this paper is to introduce the stress heterogeneities arising within the polycrystal in a probabilistic modeling of brittle fracture. Stress heterogeneities are evaluated from Finite-Element simulations performed on a large number of Statistical Volume Elements. Results are validated both on the measured averaged behavior and on the averaged stresses measured by neutron diffraction in five specific orientations. A probabilistic model for brittle fracture is then presented accounting for the carbide distribution and the stress distribution evaluated previously inside an elementary volume V 0. Results are compared to a “Beremin type” approach, assuming a homogeneous stress state inside V 0.

Fast estimates of evolving orientation microstructures in textured bcc polycrystals at finite plastic strains

The paper presents a framework for a fast computational estimate of the texture evolution in bcc polycrystals. The underlying basis is a Taylor-type approach to rigid plasticity in bcc crystals, where the decision of slip activity is based on a purely geometric argument in terms of the rate of total deformation. The core part of the method is a new algorithm for rate-independent rigid crystal plasticity, which uses lattice rotations parametrized by Rodrigues vectors as history variables. We show that such a geometric estimate of the orientation microstructure provides very good approximations when compared with experimental results of bcc crystals. It is shown for several deformation modes of polycrystalline aggregates, that the geometric approach predicts the texture evolution very well at large strains. In contrast to standard approaches for the analysis of texture, the proposed new method is extremely robust and fast even for a high number of discrete grain orientations. As a consequence, such an approach provides a perfect base for large scale computations of texture development in polycrystals.

Parameter identification of advanced plastic strain rate potentials and impact on plastic anisotropy prediction

In the work presented in this paper, several strain rate potentials are examined in order to analyze their ability to model the initial stress and strain anisotropy of several orthotropic sheet materials. Classical quadratic and more advanced non-quadratic strain rate potentials are investigated in the case of FCC and BCC polycrystals. Different identifications procedures are proposed, which are taking into account the crystallographic texture and/or a set of mechanical test data in the determination of the material parameters.

Prediction of yield functions on BCC polycrystals

ABSTRACT By the nonlinear optimization theory, we predict the yield function of single BCC crystals in Hill's criterion form. Then we give a formula on the macroscopic yield function of a BCC polycrystal Ω under Sachs' model, where the volume average of the yield functions of all BCC crystallites in Ω is taken as the macroscopic yield function of the BCC polycrystal. In constructing the formula, we try to find the relationship among the macroscopic yield function, the orientation distribution function (ODF), and the single BCC crystal's plasticity. An expression for the yield stress of a uniaxial tensile problem is derived under Taylor's model in order to compare the expression with that of the macroscopic yield function.

Salt influence upon the structure of aqueous solutions of branched PEO–PPO–PEO copolymers

Triblock copolymers composed of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO), present an amphiphilic character in aqueous solution. Since PPO is less hydrophilic than PEO and since their solubilities decrease when the temperature increases, the copolymers self-assemble spontaneously, forming micelles at moderate temperature. For higher temperature or concentration, these solutions can form lyotropic liquid crystalline phases. In order to improve their properties for particular applications, these solutions are often used in the presence of salts. The influence of the salts nature is qualitatively well described for linear copolymer solutions of PEO–PPO–PEO type. The presence of a ‘salting out’ electrolyte shifts the cloud point and the critical micelle temperature to lower temperature while ‘salting in’ electrolyte induces opposite effects. In this article, we study the influence of the presence of sodium chloride (NaCl) on the structure of aqueous solutions of a four-branched copolymer. First, we show by viscosimetric studies that NaCl has a ‘salting out’ effect with these star copolymers as with theirs linear counterparts. Secondly, small angle neutron scattering studies make it possible to determine quantitatively the influence of the NaCl amount on the equilibrium unimers–micelles. These experiments allow obtaining the radius of micelles, their volume fraction and their aggregation number. These informations are compared with the data obtained with salt-free solutions. SANS results are also used to demonstrate that the micelles form bcc polycrystals in a significant zone of the phase diagram. The cell parameter of these crystals is determined according to the salinity of the solution. At last, we observe that the solution presents at high temperature a phase separation. Our results show clearly that this phenomenon is due to the dehydration of the PEO external layer of the micelles.

Forming limit comparisons for FCC and BCC sheets

In this paper, numerical simulations of forming limit diagrams (FLDs) are performed based on a rate-sensitive polycrystal plasticity model together with the Marciniak–Kuczynski (M–K) approach. Sheet necking is initiated from an initial imperfection in terms of a narrow band. The deformations inside and outside the band are assumed to be homogeneous, and conditions of compatibility and equilibrium are enforced across the band interfaces. Thus, the polycrystal model need only be applied to two polycrystal aggregates, one inside and one outside the band. Both FCC and BCC crystals are considered with 12 distinct slip systems for an FCC crystal and 24 distinct slip systems for a BCC crystal. The response of an aggregate comprised of many grains is based on an elastic–viscoplastic Taylor-type polycrystal model. With this formulation, the effects of initial imperfection intensity and orientation, crystal elasticity, strain-rate sensitivity, single slip hardening, and latent hardening on the FLD can be assessed. Identical initial textures are considered for both FCC and BCC polycrystals and the predicted FLDs are compared with each other.

A new class of micro–macro models for elastic–viscoplastic heterogeneous materials

Abstract The determination of the effective behavior of heterogeneous materials from the properties of the components and the microstructure constitutes a major task in the design of new materials and the modeling of their mechanical behavior. In real heterogeneous materials, the simultaneous presence of instantaneous mechanisms (elasticity) and time dependent ones (non-linear viscoplasticity) leads to a complex space–time coupling between the mechanical fields, difficult to represent in a simple and efficient way. In this work, a new self-consistent model is proposed, starting from the integral equation for a translated strain rate field. The chosen translated field is the (compatible) viscoplastic strain rate of the (fictitious) viscoplastic heterogeneous medium submitted to a uniform (unknown) boundary condition. The self-consistency condition allows to define these boundary conditions so that a relative simple and compact strain rate concentration equation is obtained. This equation is explained in terms of interactions between an inclusion and a matrix, which lead to interesting conclusions. The model is first applied to the case of two-phase composites with isotropic, linear and incompressible viscoelastic properties. In that case, an exact self-consistent solution using the Laplace–Carson transform is available. The agreement between both approaches appears quite good. Results for elastic–viscoplastic BCC polycrystals are also presented and compared with results obtained from Kroner–Weng's and Paquin et al. (Arch. Appl. Mech. 69 (1999) 14)'s model.

Modelling Microstructure-Based Anisotropy in BCC Polycrystals during Changing Strain Paths

Modelling Microstructure-Based Anisotropy in BCC Polycrystals during Changing Strain Paths

217 BCC および HCP 金属多結晶体の硬化特性について

217 BCC および HCP 金属多結晶体の硬化特性について

Taylor ambiguity in BCC polycrystals: a non-problem if substructural anisotropy is considered

The ambiguity of slip system selection inside each grain plaguing the Taylor solution to polycrystal plasticity is caused by neglecting substructural anisotropy, as the critical resolved shear stresses on all slip systems are assumed to be equal. Simulating accurately the dislocation patterns at the grain-scale level, as done in [Acta Mater 49(2001)1607], solves this Taylor ambiguity.

A theoretical investigation of the contribution of texture and dislocation sheets on strain path change effects in BCC metals

Softening/hardening effects are often observed in BCC polycrystals during changing strain paths. They can lead to premature failure of the material. Both the anisotropy due to microstructural features as well as due to the development of preferred crystallographic orientations are considered to be responsible for these effects. This paper addresses a methodology to incorporate cells and cell blocks at the grain scale in a full-constraints Taylor model. This allows the coupling of the full anisotropy due to basic slip processes, crystallographic texture and microstructure. It is demonstrated that the model is capable of simulating the complex softening/hardening effects during changing strain paths. It is shown that the cross effect and the Bauschinger effect are mainly caused by microstructural features and not by textural effects.

A simplified crystallographic approach of bifurcation for single crystals and polycrystals

Localization of the plastic deformation such as necking, kink and shear bands in polycrystal and single crystals leads to inhomogeneous strain field and lattice rotation field. In order to study at microscopic and macroscopic scales the formation and propagation of such instabilities, single copper crystals and steel polycrystals were deformed in tension within a SEM. The strain field and lattice rotation field were analyzed at the micrometer scale for different steps of the plastic deformation, using simultaneously microextensometry (microgrids) and electronic diffraction (EBSD) within the SEM. Three components of the Green Lagrange tensor, of the strain rate and lattice spin were obtained within the band and the matrix before and during bifurcation. Localization in cfc single crystal and steel (bcc) polycrystals, presented similarities conceming the activation of two shear planes in the necking area and the evolution of the inhomogeneous strain field and lattice rotation. These phenomena can be correlated to the activation of two crystallographic slip systems for the single crystal and two families of parallel slip planes within the grains for the polycrystals. The gradients were analyzed by Cosserat theory: a constitutive law taking into account the lattice curvature (through couple stress tensor) and hardening law dependent on a density of geometrically necessary dislocations within the band. Such analysis previously developed for a two dimensional single crystal, is applied to the polycrystal assumed to a super single crystal.