EBSD Study of Delamination Fracture in Al–Li Alloy 2090

Aluminum–lithium (Al–Li) alloys offer attractive combinations of high strength and low density for aerospace structural applications. However, a tendency for delamination fracture has limited their use. Identification of the metallurgical mechanisms controlling delamination may suggest processing modifications to minimize the occurrence of this mode of fracture. In the current study of Al–Li alloy 2090 plate, high quality electron backscattered diffraction (EBSD) information has been used to evaluate grain boundary types exhibiting delamination fracture and characterize microtexture variations between surrounding grains. Delamination was frequently observed to occur between variants of the brass texture component, along near-Σ3, incoherent twin boundaries. EBSD analyses indicated a tendency for intense deformation along one side of the fractured boundary. A through-thickness plot of grain-specific Taylor factors showed that delaminations occurred along boundaries with the greatest difference in Taylor factors. Together, these suggest a lack of slip accommodation across the boundary, which promotes significantly higher deformation in one grain, and stress concentrations that result in delamination fracture.     

随机晶界分布和连通性对晶间破坏行为的影响

采用随机有限元方法研究了两个具有相同不均匀材料属性和相同随机晶界含量但不同随机晶界分布的特殊多晶体样本在准静态拉伸下的晶间破坏行为,发现随机晶界连通性强的样本的断裂能比较低．在不同随机晶界含量下分别构造的50个晶界随机分布的样本的计算结果表明,断裂能与平均晶界连通数的关联并不明显,甚至还出现了相反的结果,即在相同随机晶界含量下,平均晶界连通数大的计算样本的断裂能反而大．     

Non-equilibrium grain boundary structure and inelastic deformation using atomistic simulations

Grain boundary influence on material properties becomes increasingly significant as grain size is reduced to the nanoscale. Nanostructured materials produced by severe plastic deformation techniques often contain a higher percentage of high-angle grain boundaries in a non-equilibrium or energetically metastable state. Differences in the mechanical behavior and observed deformation mechanisms are common due to deviations in grain boundary structure. Fundamental interfacial attributes such as atomic mobility and energy are affected due to a higher non-equilibrium state, which in turn affects deformation response. In this research, atomistic simulations employing a biased Monte Carlo method are used to approximate representative non-equilibrium bicrystalline grain boundaries based on an embedded atom method potential, leveraging the concept of excess free volume. An advantage of this approach is that non-equilibrium boundaries can be instantiated without the need of simulating numerous defect/grain boundary interactions. Differences in grain boundary structure and deformation response are investigated as a function of non-equilibrium state using Molecular Dynamics. A detailed comparison between copper and aluminum bicrystals is provided with regard to boundary strength, observed deformation mechanisms, and stress-assisted free volume evolution during both tensile and shear simulations.     

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.     

Role of grain boundary energetics on the maximum strength of nanocrystalline Nickel

Numerical simulations are used to investigate the competing grain boundary and dislocation mediated deformation mechanisms in nanocrystalline Ni with grain sizes in the range 4-32 nm. We present a 3D phase field model that tracks the evolution of individual dislocations and grain boundaries. Our model shows that the transition from Hall-Petch to inverse Hall-Petch as the grain size is reduced cannot be characterized only by the grain size, but it is also affected by the grain boundary energetics. We find that the grain size corresponding to the maximum yield stress (the transition from Hall-Petch strengthening with decreasing grain size to inverse Hall-Petch) decreases with increasing grain boundary energy. Interestingly, we find that for grain boundaries with high cohesive energy the Hall-Petch maximum is not observed for grains in the range 4-32 nm.     

An experimental and numerical study on the formability of textured AlZnMg alloys

The influence of texture and grain structure on strain localisation and formability is investigated experimentally and numerically for two AlZnMg alloys. The considered alloys have recrystallised or non-recrystallised grain structure and strong or nearly random texture. The textured materials have rotated cube texture or β-fibre texture of high intensity. A comprehensive test programme, including uniaxial tension tests in three directions, through-thickness compression tests, plane-strain tension tests and double-plate formability tests, is completed to determine the work hardening, plastic anisotropy and formability of the materials. Strain localisation and failure are examined by optical microscopy. Using parts of the test data, an anisotropic plasticity model is calibrated and applied in calculation of forming limit curves, using the Marciniak–Kuczynski (M-K) analysis for anisotropic materials. The formability tests show that the materials with nearly random texture exhibit superior formability. This is mainly attributed to enhanced work hardening for these materials. For the material exhibiting strong β-fibre texture significantly lower formability is found in equibiaxial stretching than in plane strain, while this characteristic is not seen for the material with strong cube texture. The M-K analysis is capable of predicting the major trends of the experiments, and captures the low formability of the alloy with strong β-fibre texture under equibiaxial straining. A numerical study is performed to evaluate the sensitivity of the predicted forming limit curves to parameters not determined experimentally.     

Geometrically necessary dislocations in viscoplastic single crystals and bicrystals undergoing small deformations

In this study we develop a gradient theory of small-deformation single-crystal plasticity that accounts for geometrically necessary dislocations (GNDs). The resulting framework is used to discuss grain boundaries. The grains are allowed to slip along the interface, but growth phenomenona and phase transitions are neglected. The bulk theory is based on the introduction of a microforce balance for each slip system and includes a defect energy depending on a suitable measure of GNDs. The microforce balances are shown to be equivalent to nonlocal yield conditions for the individual slip systems, yield conditions that feature backstresses resulting from energy stored in dislocations. When applied to a grain boundary the theory leads to concomitant yield conditions: relative slip of the grains is activated when the shear stress reaches a suitable threshold; plastic slip in bulk at the grain boundary is activated only when the local density of GNDs reaches an assigned threshold. Consequently, in the initial stages of plastic deformation the grain boundary acts as a barrier to plastic slip, while in later stages the interface acts as a source or sink for dislocations. We obtain an exact solution for a simple problem in plane strain involving a semi-infinite compressed specimen that abuts a rigid material. We view this problem as an approximation to a situation involving a grain boundary between a grain with slip systems aligned for easy flow and a grain whose slip system alignment severely inhibits flow. The solution exhibits large slip gradients within a thin layer at the grain boundary.     

Assessment of plastic heterogeneity in grain interaction models using crystal plasticity finite element method

Micromechanical models aimed at simulating deformation textures and resulting plastic anisotropy need to incorporate local plastic strain heterogeneities arising from grain interactions for better predictions. The ALAMEL model [Van Houtte, P., Li, S., Seefeldt, M., Delannay, L. 2005. Deformation texture prediction: from the Taylor model to the advanced Lamel model. Int. J. Plasticity 21, 589–624], is one of the models in which the heterogeneous nature of plastic deformation in metals is introduced by accounting for the influence of a grain boundary on the cooperative deformation of adjacent grains. This is achieved by assuming that neighbouring grains undergo heterogeneous shear rates parallel to the grain boundary. The present article focuses on understanding the plastic deformation fields near the grain boundaries and the influence of grain interaction on intra-grain deformations. Crystal Plasticity Finite Element Method (CPFEM) is employed on a periodic unit cell consisting of four grains discretised into a large number of elements. A refined study of the local variation of strain rates, both along and perpendicular to the grain boundaries permits an assessment of the assumptions made in the ALAMEL model. It is shown that the ALAMEL model imbibes the nature of plastic deformation at the grain boundaries very well. However, near triple junctions, the influence of a third grain induces severe oscillations of the stress tensor, reflecting a singularity. According to CPFEM, such singularity can lead to grain subdivision by the formation of new boundaries originating at the triple junction.     

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.     

Continuum framework for dislocation structure,energy and dynamics of dislocation arrays and low angle grain boundaries

We present a continuum framework for dislocation structure, energy and dynamics of dislocation arrays and low angle grain boundaries that are allowed to be nonplanar or nonequilibrium. In our continuum framework, we define a dislocation density potential function on the dislocation array surface or grain boundary to describe the orientation dependent continuous distribution of dislocations in a very simple and accurate way. The continuum formulations incorporate both the long-range dislocation interaction and the local dislocation line energy, and are derived from the discrete dislocation model. The continuum framework recovers the classical Read–Shockley energy formula when the long-range elastic fields of the low angle grain boundaries are canceled out. Applications of our continuum framework in this paper are focused on dislocation structures on static planar and nonplanar low angle grain boundaries and misfitting interfaces. We present two methods under our continuum framework for this purpose, including the method based on the Frank׳s formula and the energy minimization method. We show that for any (planar or nonplanar) low angle grain boundary, the Frank׳s formula holds if and only if the long-range stress field in the continuum model is canceled out, and it does not necessarily hold for a total energy minimum dislocation structure.     

A Characterisation of the Boundary Displacements Which Induce Cavitation in an Elastic Body

In this paper we present numerical and theoretical results for characterising the onset of cavitation-type material instabilities in solids. To model this phenomenon we use nonlinear elasticity to allow for the large, potentially infinite, stresses and strains involved in such deformations. We give a characterisation of the set of linear displacement boundary conditions for which energy minimising deformations produce a single isolated hole inside an originally perfect elastic body, based on a notion of the derivative of the stored energy functional with respect to hole-producing deformations. We conjecture that, for many stored energy functions, the critical linear boundary conditions which cause an isolated cavity to form correspond to the zero set of this derivative. We use this characterisation to propose a numerical procedure for computing these critical boundary displacements for general stored energy functions and give numerical examples for specific materials. For a degenerate stored energy function (with spherically symmetric boundary deformations) and for an elastic fluid, we show that the vanishing of the volume derivative gives exactly the critical boundary conditions for the onset of this type of cavitation.     

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).     

Numerical investigation of grain boundary effects on elevated-temperature deformation and fracture

A three-dimensional (3D) polycrystal intergranular model that accounts for grain boundary deformation and intergranular weakening at elevated temperatures is presented. The effects of grain boundaries on the accumulated slip deformation of grain interiors and lattice rotation have been investigated through a comparison between results from a model including grain boundary region (GBM) and a model representing only the grain interiors not the grain boundary region directly (NGBM). It is found that the presence of grain boundaries seems to suppress the grain interior slip deformation, and this suppressive role is reduced with increased relative thickness of the grain boundaries. In addition, grain boundaries promote the lattice rotation of individual grains in shear bands but suppress that of individual grains within non-shear bands. Mutual rotation of grains in both shear and non-shear bands is caused by the introduction of grain boundary regions. Rate-dependence of high-temperature plasticity could be more accurately captured by the GBM than by the NGBM. By considering creep damage of grain boundary, when the damage variable reaches a critical value, the corresponding grain boundary element is eliminated to describe dynamic intergranular fracture processes. The volume-averaged stress–strain curve by a model considering grain boundary damage (DGBM) showed better agreement with experimental results than that by a model not considering grain boundary damage (GBM).     

Studying the effect of grain boundaries in dislocation density based crystal-plasticity finite element simulations

A dislocation density based constitutive model for the face centered cubic crystal structure has been implemented into a crystal-plasticity finite element framework and extended to consider the mechanical interaction between mobile dislocations and grain boundaries by the authors [Ma, A., Roters, F., Raabe, D., 2006a. A dislocation density based constitutive model for crystal-plasticity FEM including geometrically necessary dislocations. Acta Materialia 54, 2169–2179; Ma, A., Roters, F., Raabe, D., 2006b. On the consideration of interactions between dislocations and grain boundaries in crystal-plasticity finite element modeling – theory, experiments, and simulations. Acta Materialia 54, 2181–2194]. The approach to model the grain boundary resistance against slip is based on the introduction of an additional activation energy into the rate equation for mobile dislocations in the vicinity of internal interfaces. This energy barrier is derived from the assumption of thermally activated dislocation penetration events through grain boundaries. The model takes full account of the geometry of the grain boundaries and of the Schmid factors of the critically stressed incoming and outgoing slip systems. In this study we focus on the influence of the one remaining model parameter which can be used to scale the obstacle strength of the grain boundary.     

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.     

Nucleation,kinetics and morphology of displacive phase transformations in iron

An extensive, systematic molecular dynamics (MD) study is performed for analysing the nucleation, kinetics and morphology characteristics of thermally-induced, displacive phase transformations from face-centred cubic (fcc) to body-centred cubic (bcc) iron. At the atomic level these transformation characteristics are influenced by a number of factors, including (i) the appearance of free surfaces, (ii) the initial presence of fcc-bcc grain boundaries, (iii) the existence of point defects (i.e., atomic vacancies) near a grain boundary, (iv) the initial thermal velocities of the atoms, and (v) the specific interatomic potential used. Other MD studies that capture the overall transformation behaviour of iron well have often underestimated or ignored the influence by these factors on the transformation response, with the risk of putting the accuracy, generality and physical explanation of the MD results on loose grounds. The present research illustrates the relative contribution of each of the above factors by means of a detailed comparison study for three different interatomic potentials. The accuracy of the interatomic potentials is established by validating for the fcc and bcc phases the calculated elastic moduli, cohesive energy, vacancy formation energy and interfacial energy against experimental and ab initio data reported in the literature. The importance of calibrating material data of both the stable bcc phase and the metastable fcc phase – instead of the stable bcc phase only – is demonstrated. The numerical results call for general caution when interpreting phenomena that start close to instability points and therefore are sensitive to small disturbances; a large spread in the overall transformation time is found under different initial thermal velocities, interfacial lattice incoherence, boundary conditions (free vs. periodic), and interatomic potentials, where for completely transformed atomic systems the discrepancy between the maximum and minimum transformation time appears to be more than a factor of 150. The transformation time is phenomenologically related to the overall activation energy and the cohesive energy difference of the fcc and bcc phases, which, beyond a certain combination of values, may even prevent the transformation process from occurring. Also, the morphology of the bcc product phase is remarkably sensitive to the type of boundary conditions and the choice of interatomic potential, while the influence by both the set of initial thermal velocities and the interfacial lattice incoherence only becomes apparent for specific atomic samples that transform relatively slowly. The presence of fcc-bcc grain boundaries increases the spatial heterogeneity of transformation events, with the appearance of an increasing number of vacancies at the grain boundary giving rise to a larger overall transformation time. The 10 main results following from the present MD study are conveniently summarised at the end of this communication.     

α铁晶界熵及表面张力的分子动力学模拟

晶界也是一种界面。表面张力是晶界的一个重要的热力学量。本文采用计算机分子动力学模拟(CMD)方法计算 α-Fe,∑=9 的晶界在不同温度和压力下的表面张力,结果与实验值的比较是满意的。发现熵对晶界的表面张力的贡献是很小的,通常可以忽略不计。     

Advanced near-wall modeling for engine heat transfer

Recent developments in the engine heat transfer modeling tend to improve existing wall heat transfer models (temperature wall functions) which mostly rely on the standard or low-Re variants of k-ε turbulence model. Presently applied mesh resolutions already allow for first near-wall computational cells reaching the buffer or locally even viscous/conductive sub-layer, thus increasing the importance of more sophisticated modeling approach. As temperature gradient-induced density and fluid property variations become significant, wall heat transfer is strongly influenced by property variations (viscous/conductive sub-layer) and predictive capability of the turbulence model (buffer region), standard wall laws being inadequate anymore, even for attached boundary layers. The present approach relies on the k-ζ-f turbulence model and formulates a compressible wall function of Han and Reitz in the framework of hybrid wall treatment. The model is validated against spark ignition (SI) engine heat transfer measurements. Predicted wall heat flux evolutions on the cylinder head exhibit very good agreement with the experimental data, being superior to similar numerical predictions available in the published literature.     

A dislocation density based crystal plasticity finite element model: Application to a two-phase polycrystalline HCP/BCC composites

We present a multiscale model for anisotropic, elasto-plastic, rate- and temperature-sensitive deformation of polycrystalline aggregates to large plastic strains. The model accounts for a dislocation-based hardening law for multiple slip modes and links a single-crystal to a polycrystalline response using a crystal plasticity finite element based homogenization. It is capable of predicting local stress and strain fields based on evolving microstructure including the explicit evolution of dislocation density and crystallographic grain reorientation. We apply the model to simulate monotonic mechanical response of a hexagonal close-packed metal, zirconium (Zr), and a body-centered cubic metal, niobium (Nb), and study the texture evolution and deformation mechanisms in a two-phase Zr/Nb layered composite under severe plastic deformation. The model predicts well the texture in both co-deforming phases to very large plastic strains. In addition, it offers insights into the active slip systems underlying texture evolution, indicating that the observed textures develop by a combination of prismatic, pyramidal, and anomalous basal slip in Zr and primarily {110}〈111〉 slip and secondly {112}〈111〉 slip in Nb.     

On dislocation models of grain boundaries

Dislocation models of grain boundaries was suggested by Bragg (Proc Phys Soc 52:54–55, 1940) and Burgers (Proc Phys Soc 52:23–33, 1940). The first quantitative study of these models was given by Read and Shockley (Phys Rev 78(3):275–289, 1950). They obtained a formula for the dependence of the grain boundary energy on the misorientation of the neighboring grains, which became a cornerstone of the grain boundary theory. The Read–Shockley formula was based on a proposition that the grain boundary energy is the sum of energies of the two sets of dislocations that come from the two neighboring grains. This proposition was proved under an assumption on a quite special geometry of the slip planes. This paper aims to show that the assumption is not necessary and the proposition holds for arbitrary geometry of slip planes. Another goal of this paper is to provide all basic formulas of the theory: though the dislocation model of grain boundaries is considered in all treatises on dislocation theory, a complete analysis, including the relations for lattice rotations and displacements, has not been given. This analysis shows, in particular, that continuum theory does not yield the proper relations for the lattice misorientations, and these relations must be introduced by an independent ansatz.