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Measurement and modeling of micro residual stresses in zirconium crystals in three dimension
Abstract
The performance of the zirconium alloys used in nuclear reactors can be affected by the state of the residual stresses that develop during manufacturing of the reactor core components. In this paper, residual stresses within individual grains of a textured α-zirconium polycrystal are studied. For this purpose, three-dimensional synchrotron X-ray diffraction is used to measure elastic strain tensor, center-of-mass (COM), orientation, and stress tensor of more than 11000 grains in a zirconium sample. The grain measured COMs and orientations are used to reconstruct the 3D microstructure of the sample using the weighted Voronoi tessellation technique. The microstructure is subsequently imported into Abaqus to simulate the experiment using a crystal plasticity finite element model. The state of the thermal residual stresses that develop during slow cooling from 700 °C, and those that develop after unloading from 1.2% applied tensile strain are discussed. It is shown that both thermal and mechanical micro residual stresses, and their variations within a grain, are correlated with grain size. Also, due to strong anisotropy of the single crystal, residual stresses are significantly affected by the configuration of local grain neighborhood.
... For example, the coefficient of thermal expansion (CTE) is an isotropic tensor for cubic materials, whereas it is anisotropic for transversely isotropic materials. Therefore, in a transversely isotropic material, the anisotropic nature of the CTE tensor can result in significant internal stress if the material is cooled down or heated up (see, for example, (Abdolvand et al., 2015;Alawadi and Abdolvand, 2020;Lim et al., 2021;Zheng et al., 2020)). However, similar observations cannot be made in cubic materials unless multiple phases are present with a mismatch in CTE values. ...
... In the literature, thermal residual stress has been incorporated within CPFE simulation (Abdolvand et al., 2015;Alawadi and Abdolvand, 2020). In these studies, it has been shown that if the residual stress within a material is a priori known to be primarily due to thermal effects, a simple cooling simulation, mimicking material processing conditions, may be sufficient to initialize type III residual stress. ...
... Due to their higher penetration depth compared to electron-based techniques, synchrotron X-ray diffraction (XRD) based methods have been employed to measure stresses in bulk polycrystalline materials [30]- [32] For the concurrent measurement of strains, stresses, orientations, and the centroid of individual grains, 3D-XRD can be used as it provides a good compromise between the spatial and angular resolution [33], [34]. Since in-situ experiments can be performed, it is possible to study the evolution of stress or orientation for each grain using 3D-XRD [35]- [38]. For instance, Abdolvand et. ...
... First, the state of is investigated by comparing the measured and calculated average . Two grains, one 'hard' and one 'soft', from the notch section of each specimen are selected to analyze their for cycles 20, 35 Following the results shown in section 5.3, a good agreement is generally achieved between the measured and calculated values. It is evident that the measured average stresses fall into the domain produced by the gaussian distributions. ...
Engineering components are often exposed to various cyclic loading conditions. The development of microscale stresses under such conditions depends on the material texture, local microstructure, the degree of crystals elastic and plastic anisotropy, as well as the presence of geometrical irregularities. In this study, the three-dimensional synchrotron X-ray diffraction (3D-XRD) technique is used and coupled with a crystal plasticity finite element (CPFE) model to deconvolute the contribution of such parameters on the magnitude of localized stresses. Special attention is paid to the notch geometry, where two double-edge-notched α-zirconium specimens with different geometries but the same texture were deformed in-situ while grain-scale stresses were measured both in the vicinity of the notches and in the far-field zones. Deep and shallow notches were cut to the dimensions comparable with the specimens’ average grain sizes. For each specimen, the center of mass, orientation, elastic strain, stress, and relative volume of more than 6,000 grains were measured and studied. Post-deformation analysis with Electron Backscatter Diffraction (EBSD) was conducted to further validate the observed trends. It is shown that the distribution of grain-scale stresses is asymmetric within each specimen. This asymmetry develops from the early stages of the applied cyclic load and remains intact with further loading. A new method is introduced for quantifying the effects of grain neighbourhood on load sharing, where it is shown that such effects relax the stresses acting on “hard” grains, altering grain-scale stress concentration factors.
... The slip resistance of different HCP crystal slip systems varies significantly. Hence, plastic deformation in polycrystalline zirconium alloys strongly depends on crystallographic texture [4][5][6]. For instance, a cold-rolled zirconium alloy sheet with a specific crystallographic texture shows strong anisotropic deformation behavior [7,8]. ...
... Summary of the initial CRSS values for zirconium and its alloys from Refs.[5,14,[50][51][52]. ...
This study focuses on investigating the anisotropic deformation behavior of rolling-textured Zircaloy-4 alloy under uniaxial tension along the rolling direction (RD) and transverse direction (TD). A dislocation density-based crystal plasticity finite element method is used to study the associated mechanisms. The simulation accurately reproduces the experimental results on stress–strain curves and strain hardening rate. The relationship between relative activities in different slip systems and anisotropic plastic deformation is established. It is revealed that in the tensile deformation, prismatic slip dominates plastic deformation in the RD, while both prismatic slip and basal slip dominate plastic deformation in the TD. The difference in the dominant slip modes leads to a lower yield stress and a higher strain hardening rate in the RD. Furthermore, the stress and strain distributions in the tensile direction are also statistically analyzed. It is found that a certain proportion of hard grains results in more severe stress concentration and lower uniform elongation in the TD specimen compared with the RD specimen. In addition, the strain rate sensitivity of the yield stress is investigated. It is shown that Zircaloy-4 alloy has almost the same yield anisotropy (TD > RD in terms of the yield stress) at different strain rates in the RD and TD.
... These studies usually include the contributions of {0001}〈1210〉 basal slip as well as {1012}〈1011〉 extension twinning, however recent CPFE studies have also included the contributions from prismatic and pyramidal dislocation slip [29,31,34]. The separation of deformation systems allows the inclusion of different strain hardening characteristics [34][35][36][37][38][39][40][41] which substantially enhances the predictive accuracy of CPFE simulations, and enables their application to accurately simulate crystal reorientation associated with indentation of Mg single crystals [4,6]. In addition, CPFE modeling has been used to study deformation twinning in Mg alloys. ...
... Another microstructure-based modelling of zirconium alloy containing hydride was done by Kulkarni et al. [24], where the effect of hydride volume fraction and hydride orientation on the mechanical properties of the material are studied using the crystal plasticity finite element (CPFE) model. Likewise, Alawadi and Abdolvand [25],Tondro and Abdolvand [26] studied the hydrogen redistribution near notches in zirconium polycrystalline material using CPFE. The focus of the hydrogen migration and hydride precipitation studies on the zirconium alloys was notches, however, the crack-based studies are rare. ...
... In contrast, Crystal Plasticity Finite Element (CPFE) is a mesoscale modeling method that can capture the realtime deformation of individual grains or clusters of grains by incorporating the effects of plastic slip on active slip systems. For example, CPFE modeling has been used to investigate the effects of crystallographic texture, grain size, and loading conditions on the plastic deformation of zirconium alloys [58][59][60][61][62][63][64]. Liu et al. [65] investigated hydride formation in Zircaloy-4 under cyclic thermomechanical loading using microstructurally representative CPFE modeling. ...
One of the main degradation mechanisms of the zirconium alloys used in nuclear reactors is hydrogen embrittlement and hydride formation. The formation of zirconium hydrides is accompanied by a transformation strain, the effects of which on the development of localized deformation zones are not well-understood. This study uses a crystal plasticity finite element model that is coupled with diffusion subroutines to quantify such effects. For this purpose, a zirconium specimen was hydrided in the absence of any external mechanical loads. With the use of electron backscatter diffraction, the rotation fields around interacting intragranular hydrides as well as those located at grain boundaries or triple points were measured at a high spatial resolution. The as-measured zirconium and hydride morphologies were mapped to the model for numerical simulation. Both numerical and experimental results show that hydride precipitation induces large rotation fields within the zirconium matrix, where such rotations are at their maximum in the vicinity of hydride tips. While the crystallographic orientations and shapes of hydrides affect the magnitude of rotation fields, both experimental and modeling results revealed the development of discrete and parallel geometrically necessary dislocation fields and a strong interaction among neighboring hydrides. It is shown that the stress field resulting from hydride precipitation affects the patterning of hydrogen distribution, which in return affects further hydride interlinking.
... In contrast, Crystal Plasticity Finite Element (CPFE) is a mesoscale modeling method that can capture the realtime deformation of individual grains or clusters of grains by incorporating the effects of plastic slip on active slip systems. For example, CPFE modeling has been used to investigate the effects of crystallographic texture, grain size, and loading conditions on the plastic deformation of zirconium alloys [58][59][60][61][62][63][64]. Liu et al. [65] investigated hydride formation in Zircaloy-4 under cyclic thermomechanical loading using microstructurally representative CPFE modeling. ...
One of the main degradation mechanisms of the zirconium alloys used in nuclear reactors is hydrogen embrittlement and hydride formation. The formation of zirconium hydrides is accompanied by a transformation strain, the effects of which on the development of localized deformation zones are not well-understood. This study uses a crystal plasticity finite element model that is coupled with diffusion subroutines to quantify such effects. For this purpose, a zirconium specimen was hydrided in the absence of any external mechanical loads. With the use of electron backscatter diffraction, the rotation fields around the inter and intragranular hydrides as well as those located at grain boundaries or triple points were measured at a high spatial resolution. The as-measured zirconium and hydride morphologies were mapped to the model for numerical simulation. Both numerical and experimental results show that hydride precipitation induces large rotation fields within the zirconium matrix, where such rotations are at their maximum in the vicinity of hydride tips. While the crystallographic orientations and shapes of hydrides affect the magnitude of rotation fields, both experimental and modeling results revealed the development of discrete and parallel geometrically necessary dislocation fields. It is shown that the stress field resulting from hydride precipitation affects the patterning of hydrogen distribution, which in return affects further hydride interlinking.
The alloy Zr-2.5Nb is used for manufacturing the pressure tubes installed in the core of Canada Deuterium Uranium (CANDU) nuclear reactors. This alloy consists of α-zirconium with hexagonal close-packed (HCP) crystals and a minor β-zirconium phase with body centered cubic (BCC) crystals that are mainly located in between the α-grains. Due to the significant elastic and plastic anisotropy of HCP crystals as well as the development of strong textures during manufacturing, these tubes exhibit significant mechanical anisotropy. However, both local microstructure and texture can change, affecting the local patterning of stress fields and the subsequent hydrogen embrittlement rate. Resolving the local microstructure variation of Zr-2.5Nb is challenging due to the development of nano-sized grains during manufacturing. This paper focuses on developing a procedure for the consistent characterization of such local variations using high spatial resolution electron backscatter diffraction (EBSD) and imaging. Microstructure variations along the radial and transverse directions of the transverse-radial plane, as well as along the axial direction of the transverse-axial and radial-axial planes are studied. It is shown that microstructure variations are non-negligible. For the locations that the transverse-radial planes are studied, pole figures rotate, and Kearns factors decrease along the radial direction. In addition, the morphologies of both α- and β-crystals change significantly along the radial direction. With the procedure used for characterization, some β-crystals are indexed and their orientation relationship with their neighboring α-grains are examined.
The presence of hydrogen atoms in the lattice of polycrystalline metals can lead to hydrogen embrittlement. The diffusion of hydrogen atoms and formation of hydrides depend on several parameters such as the microstructure of the metal alloy, the presence of stress risers, and the applied loading condition. In this study, a non-local crystal plasticity finite element model is coupled with hydrogen diffusion equations to study the effects of such parameters on the stress-assisted diffusion of hydrogen atoms in zirconium polycrystals. The concentrations of hydrogen atoms in the lattice and dislocation trap sites under different scenarios are studied to deconvolute the effects of texture, microstructure, and applied strain on hydrogen diffusion. It is shown that the concentration of hydrogen in the lattice peaks in the vicinity of grain boundaries and most importantly, at the triple-junction points. It is further shown that in localized deformation zones, such as twin or notch tips where dislocations concentrate, the effects of trap hydrogen content can be significant.
Hexagonal close packed (HCP) Mg and Zr are being used in transportation and nuclear industries, respectively. The ductility and formability of these materials is significantly limited by the activation of prevalent deformation twinning. Twins in HCP polycrystals usually nucleate at grain boundaries (GBs), propagate into the grain, and they either terminate at opposing GBs (isolated-twins) or transmit into a neighboring grain (adjoining-twin-pairs: ATPs). Because twin interfaces provide a path for crack propagation, twin transmission is relevant to material ductility. This study combines electron backscatter diffraction (EBSD) based statistical analysis of twinning microstructures and crystal plasticity modeling, to characterize twin thickening processes away from and near GBs. Analysis of deformed Mg and Zr microstructures reveals that local twin thicknesses at GBs are statistically larger for ATPs compared to isolated-twins. Further, thicknesses are found to decrease with increasing GB misorientation angle. Full-field Fast-Fourier-Transform micromechanics modeling shows that shear-transformation induced backstress are locally relaxed at GBs for ATPs, but not for isolated-twins. As a consequence, ATPs can thicken locally at GBs and the preferential site for twin thickening shifts from the middle of the twin to common GB.
Hydrogen embrittlement of zirconium alloys is a major concern in nuclear industry. It is known that diffusion of hydrogen atoms in zirconium lattice depends on the localized state of stresses, the patterning of which is significantly affected by the elastic and plastic anisotropy of zirconium crystals. This study focuses on developing a model to understand the effects of such localized stress fields on hydrogen diffusion and precipitation. For this purpose, a crystal plasticity finite element code is updated and coupled with a series of newly developed subroutines for simulating stress-assisted-diffusion of hydrogen atoms in zirconium polycrystals. An electron backscatter diffraction experiment is also conducted on a hydrided Zircaloy-2 sample to compare the measured distribution of the hydride phase with the calculated one. It is shown that even in the absence of macroscopic loads, thermal residual stresses within zirconium grains can disturb the uniform distribution of hydrogen atoms by inducing large hydrostatic stresses at the vicinity of grain boundaries. Such stress concentrations can further affect the sequence of hydrides nucleation. Also, it is shown that by alternating local stress fields, hydride induced transformation strain can change the distribution of the hydrogen atoms in zirconium matrix.
The deformation of polycrystalline zirconium is analysed at the individual grain level using three-dimensional Synchrotron X-ray Diffraction (3D-XRD) in combination with a Crystal Plasticity Finite Element (CPFE) model. The effects of elastic strains and lattice rotations on the shape and position of diffracted peaks are studied in detail. For this purpose, the three dimensional measured microstructure of a commercially pure zirconium (CPZr) sample was imported into a crystal plasticity finite element (CPFE) model to simulate the deformation of measured grains. The calculated lattice rotations and strains of the selected most active grains were subsequently used to forward simulate diffracted peaks. The simulated peaks are then compared to the 3D-XRD measured ones. It is shown that although the sample was deformed to 1.2% strain, soft grains exhibit significant peak smearing. Peak broadening is mostly affected by the deformation induced lattice rotation and less affected by the elastic strains. Further, the comparison of CPFE modelling and 3D-XRD results confirms that prism and basal slip are the most active systems and pyramidal <c+a> is present but only slightly active. A method is developed to determine the activity of possible slip systems. As an example, by comparing the simulated and measured peak positions as well as the rotations of the most affected diffraction peaks, it is shown that pyramidal slip system is not active significantly at room temperature.
Anisotropy in single-crystal properties of polycrystals controls both the overall response of the aggregates and patterning of local stress/strain distributions, the extremes of which govern failure processes. Improving the understanding of grain–grain interactions has important consequences for in-service performance limits. Three-dimensional synchrotron X-ray diffraction was used to study the evolution of grain-resolved stresses over many contiguous grains in Zr and Ti polycrystals deformed in situ. In a significant fraction of grains, the stress along the loading axis was found to decrease during tensile plastic flow just beyond the macroscopic yield point; this is in the absence of deformation twinning and is a surprising behaviour. It is shown that this phenomenon is controlled by the crystallographic orientation of the grain and its immediate neighbours, particularly those adjacent along the loading axis.
Grain fracture and crushing are known to influence the macroscopic mechanical behavior of granular materials and be influenced by factors such as grain composition, morphology, and microstructure. In this paper, we investigate grain fracture and crushing by combining synchrotron x-ray computed tomography and three-dimensional x-ray diffraction to study two granular samples undergoing uniaxial compaction. Our measurements provide details of grain kinematics, contacts, average intra-granular stresses, inter-particle forces, and intra-grain crystal and fracture plane orientations. Our analyses elucidate the complex nature of fracture and crushing, showing that: (1) the average stress states of grains prior to fracture vary widely in their relation to global and local trends; (2) fractured grains experience inter-particle forces and stored energies that are statistically higher than intact grains prior to fracture; (3) fracture plane orientations are primarily controlled by average intra-granular stress and contact fabric rather than the orientation of the crystal lattice; (4) the creation of new surfaces during fracture accounts for a very small portion of the energy dissipated during compaction; (5) mixing brittle and ductile grain materials alters the grain-scale fracture response. The results highlight an application of combined x-ray measurements for non-destructive in situ analysis of granular solids and provide details about grain fracture that have important implications for theory and modeling.
The mechanical response of engineering materials evaluated through continuum fracture mechanics typically assumes that a crack or void initially exists, but it does not provide information about the nucleation of such flaws in an otherwise flawless micro-structure. How such flaws originate, particularly at grain (or phase) boundaries is less clear. Experimentally, ''good" vs. ''bad" grain boundaries are often invoked as the reasons for critical damage nucleation, but without any quantification. The state of knowledge about deformation at or near grain boundaries, including slip transfer and heterogeneous deformation, is reviewed to show that little work has been done to examine how slip interactions can lead to damage nucleation. A fracture initiation parameter developed recently for a low ductility model material with limited slip systems provides a new definition of grain boundary character based upon operating slip and twin systems (rather than an interfacial energy based definition). This provides a way to predict damage nucleation density on a physical and local (rather than a statistical) basis. The parameter assesses the way that highly activated twin systems are aligned with principal stresses and slip system Burgers vectors. A crystal plasticity-finite element method (CP-FEM) based model of an extensively characterized microstructural region has been used to determine if the stress-strain history provides any additional insights about the relationship between shear and damage nucleation. This analysis shows that a combination of a CP-FEM model augmented with the fracture initiation parameter shows 0749-6419/$-see front matter Ó International Journal of Plasticity journal homepage: www.elsevier.com/locate/ijplas promise for becoming a predictive tool for identifying damage-prone boundaries.
The mechanical response of engineering materials evaluated through continuum fracture mechanics typically assumes that a crack or void initially exists, but it does not provide information about the nucleation of such flaws in an otherwise flawless micro-structure. How such flaws originate, particularly at grain (or phase) boundaries is less clear. Experimentally, ''good" vs. ''bad" grain boundaries are often invoked as the reasons for critical damage nucleation, but without any quantification. The state of knowledge about deformation at or near grain boundaries, including slip transfer and heterogeneous deformation, is reviewed to show that little work has been done to examine how slip interactions can lead to damage nucleation. A fracture initiation parameter developed recently for a low ductility model material with limited slip systems provides a new definition of grain boundary character based upon operating slip and twin systems (rather than an interfacial energy based definition). This provides a way to predict damage nucleation density on a physical and local (rather than a statistical) basis. The parameter assesses the way that highly activated twin systems are aligned with principal stresses and slip system Burgers vectors. A crystal plasticity-finite element method (CP-FEM) based model of an extensively characterized microstructural region has been used to determine if the stress-strain history provides any additional insights about the relationship between shear and damage nucleation. This analysis shows that a combination of a CP-FEM model augmented with the fracture initiation parameter shows promise for becoming a predictive tool for identifying damageprone
boundaries.
Continuum fracture mechanics has provided a wealth of methodologies for modeling the evolution of damage, but these methods all depend on knowing where the damage nucleated; hence a pre-existing void or crack is normally introduced arbitrarily. The process by which undamaged material develops damage (here defined as the generation of a new free surface where there was none before) is not very well understood. An understanding of this damage nucleation process in the context of microstructural evolution will allow properties that are of great importance to designers, such as toughness, ductility, and fatigue life, to become more predictable. Damage nucleation frequently develops in two stages, where nascent or pre-damage conditions develop during monotonic deformation resulting from forming operations, followed by growth to a critical size during service, e.g. growth of short cracks at a scale smaller than the grain size, to one larger than the microstructural scale during subsequent loading. In this case nucleation and growth of fatigue cracks depends strongly on microstructure evolution during prior forming history. Thus, a paradigm is needed to understand how the process of plastic deformation interacting with microstructural features leads to the development of subcritical cracks or voids. From both experimental and computational studies, it is commonly held that damage nucleation occurs in locations of large strain concentrations (from the continuum perspective, as in Fig. 1a), or microstructurally, where substantial heterogeneous deformation occurs. If large local strains are effective in accommodating required geometry changes they may prevent damage nucleation, whereas it is conceivable that damage may nucleate where insufficient strain or shape accommodation occurs, as illustrated schematically in Fig. 1b. Such variability in shape accommodation is connected to crystal orientations and crystallographic deformation mechanisms. Experimentally, heterogeneous deformation is often assessed using slip trace analysis, which can be accomplished with both optical and electron microcopy, and can be greatly enhanced and made more quantitative by using tools such as orientation imaging microscopy and strain mapping. However studies that fully analyze the operating deformation mechanisms in the context of the stress–strain history and observed microstructure evolution are rare. More qualitative experiments commonly show cracks and voids developing preferentially in some boundaries but less in others, indicating the significance of heterogeneity in local deformation history. Computationally, two approaches to modeling evolution of microstructure have developed, statistical methods based upon Taylor theory, and finite element polycrystal plasticity approaches (atomistic or discrete dislocation density models can typically model volumes much smaller than a cubic micron (e.g. Farkas, 2005; Arsenlis et al., 2004), making them most useful for modeling nanocrystals). Statistical models developed on the foundation of Taylor theory (e.g. Chen and Gray, 1996; Nemat-Nasser et al., 1998; Nemat-Nasser and Guo, 2000) homogenize deformation characteristics, which is useful for modeling deformation phenomena at the scale of forming operations. This kind of analysis motivates models for yield surface evolution, e.g. Barlat et al. (2003). Homogenization is not helpful for investigating damage nucleation, however, which is a statistically rare event that reflects deviations from homogeneous behavior. This shortcoming can be partially overcome using viscoplastic self-consistent polycrystal plasticity codes that allow strains and stresses to vary in different crystal orientations (e.g. Lebensohn and Tome, 1993; Lebensohn, 2001; Karaman et al., 2000). Nevertheless, self-consistent codes are still based upon a statistical representation of a microstructure. Hence, damage that originates from strain incompatibilities in specific sites cannot be meaningfully predicted with statistical models such as the large body of literature based upon continuum damage mechanics (e.g. review of Lin et al., 2005), because the specific strain history depends on both the local strain behavior near an interface, as well as the strain history in adjacent grains or even within regions of the same grain (non-local strain). Self consistent models homogenize the grain neighborhood and, therefore, cannot provide detailed information at the local scale.
Modeling of site-specific stress–strain histories can be accomplished with crystal plasticity finite element modeling of representative microstructural volumes (oligocrystals or microstructure patches). Several approaches have recently been developed and compared with experimental observations (e.g. Hao et al., 2003, 2004; Heripre et al., 2007; Querin et al., 2007; Dunne et al., 2007; Clayton and McDowell, 2004; Bhattacharyya et al., 2001; Raabe et al., 2001; Ma and Roters, 2004; Ma et al., 2006a,b, Zaafarani et al., 2006, Cheong and Busso, 2004, 2006, Dawson et al., 2002, Kalidindi and Anand, 1993). To date, most modeling attempts of this kind have simulated high ductility damage resistant metals such as steel, copper, or aluminum. Characterizing damage nucleation events microscopically in such high ductility metals is challenging due to the large strains and high dislocation densities that precede damage nucleation. The ability to predict damage nucleation and evaluate whether it will lead to the fatal flaw is one of the major goals of computational plasticity. Such predictions require multiscale modeling approaches that are under development in a number of groups and laboratories (Hao et al., 2003, 2004; Clayton and McDowell, 2004; Voyiadjis et al., 2004; Buchheit et al., 2005; Dunne et al., 2007; Cheong et al., 2007). While heterogeneous deformation is understood to be a precursor to damage nucleation, the actual initiation step between heterogeneous deformation and damage nucleation is not clearly understood. This connection is crucially important, because if the locations of damage are not properly predicted, then any simulations of microstructural evolution that evolve thereafter will be unreliable
(merely fiction). A comprehensive review of multi-scale modeling of plastic deformation shows that solutions to practical problems often have the nanoscale effectively interacting with microscale, which cannot be handled by atomistic methods (Liu et al., 2005, Hao et al., 2003, 2004). Currently, there are no effective handoff methods between atomistic and microstructure scales. Hence, there is an opportunity for bridging across length scales if damage nucleation (intrinsically a nano-scale phenomenon) can be predicted reliably on the basis of heterogeneous microscale deformation. Interfaces represent a profound challenge to modeling heterogeneous deformation and damage nucleation. Damage in particle-free materials normally nucleates at discontinuous interfaces such as grain or phase boundaries.1 At interfaces, strain must be somehow transferred from one grain to another through the boundary. In this process, damage may nucleate at a specific (rather than a generic) interface, due to both local and non-local effects. Rules for predicting which interfaces become damage nucleation sites are not known, though some have used slip transfer criteria as a means to identify suspicious locations (e.g. Ashmawi and Zikry, 2003a,b). From the review that will follow, it will become clear that damage nucleation at interfaces depends on
i. the orientations of crystals on either side of the interface,
ii. the boundary orientation and structure (energy),
iii. the activated deformation systems on either side of the boundary, and
iv. the stress–strain gradient history in the grains on either side of an interface.
Research that considers all four of these factors is rare. For example, the grain boundary engineering paradigm focuses on grain boundary energy (item ii) as a metric for ‘‘good” or ‘‘bad” grain boundaries, but little has been done to examine how slip processes affect the character of ‘‘good” R boundaries differently from their ‘‘bad” random boundary counterparts. Item iii has rarely been examined experimentally or computationally, and when it has, it has not been done with fine detail. Studies of deformation transfer have led to identification of some rules by which a dislocation in one grain can penetrate into a neighboring grain (Clark et al., 1992; de Koning et al., 2002, 2003). However, it is not clear how deformation transfer and damage nucleation are related, and this open question provides the primary motivation for this paper. Clearly, knowledge of a boundary’s propensity to generate damage could provide an effective bridge between atomistic and continuum scale models. To assess the role of slip processes at interfaces on damage nucleation, it is important to have a reliable representation of heterogeneous deformation, the character of the grain boundary, and slip transfer mechanisms. These three topics and current approaches to integrate them are reviewed in some detail in order to provide motivation and a foundation for a new approach that identifies a deformation system based definition of grain boundary character. This new definition of grain boundary character was developed on the basis of experimental observations, and it may be able to determine which kind of deformation system interactions at the boundary will lead to damage nucleation. One example of a deeply characterized microstructure from this experimental work is examined using a current polycrystal plasticity finite element model to identify how mesoscale computational modeling may be used in combination with this new definition of grain boundary character to predict locations of damage nucleation.
A crystal plasticity finite element (CPFE) model is used to study nucleation, elongation, and thickening of deformation twins in a commercially pure titanium. The results of the CPFE simulations are compared with previously published data for an in-situ high resolution electron backscattered diffraction experiment that was conducted on a titanium micro-pillar. The evolution of both local resolved shear stress and elastic energy during twin formation are studied in detail. It is shown that twins are nucleated at the locations where strain energy and resolved shear stress are maximum. After nucleation, resolved shear stresses at the twin tips stay positive which provide the driving force required for twin elongation, however, they are negative at the twin surface for short twins. It is shown that three-dimensional studies are necessary to understand the nucleation of twins [17].
Micro slip activation and localization in Ti-6Al-4V deformed in tension have been examined quantitatively using high-resolution (HR) digital image correlation (DIC), HR-electron backscatter diffraction (EBSD) and crystal plasticity finite element modelling. The measured polycrystal slip, strain, lattice rotation and geometrically necessary dislocation (GND) density distributions are generally well captured by the a priori crystal plasticity model based on the rate-sensitive properties of α-titanium. An overall slip trace analysis showed over 80% agreement between HR-DIC and crystal plasticity modelling of the primary slip activation. The texture beneath the characterised free-surface has been found to affect the local slip, stress distribution, lattice curvature and GND density and three texture variations have been considered. Grain-level slip trace analysis shows that the crystal plasticity modelling can capture single (straight) slip, multiple slip activation and complex wavy slip. The latter has been found to result from the interaction of independently activated basal and prismatic slip systems with common slip direction. Initial inter-granular misorientations greater than about 5° have been shown to influence the subsequent micromechanical grain behaviour including slip, lattice rotation and GND density. This work contributes to the understanding of slip localization and load shedding in dwell fatigue in polycrystalline hexagonal materials.