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Fatigue crack initiation in the high cycle fatigue regime is strongly influenced by microstructural features. Research efforts have usually focused on predicting fatigue resistance against crack incubation without considering the early fatigue crack growth after encountering the first grain boundary. However, a significant fraction of the variability of the total fatigue life can be attributed to growth of small cracks as they encounter the first few grain boundaries, rather than crack formation within the first grain. This paper builds on the framework previously developed by the authors to assess microstructure-sensitive small fatigue crack formation and early growth under complex loading conditions. The scheme employs finite element simulations that explicitly render grains and crystallographic directions along with simulation of microstructurally small fatigue crack growth from grain to grain. The methodology employs a crystal plasticity algorithm in ABAQUS that was previously calibrated to study fatigue crack initiation in RR1000 Ni-base superalloy. This work present simulations with non-zero applied mean strains and geometric discontinuities that were not previously considered for calibration. Results exhibit trends similar to those found in experiments for multiple metallic materials, conveying a consistent physical description of fatigue damage phenomena. [ABSTRACT FROM AUTHOR]

The number of cycles required to form and grow microstructurally small fatigue cracks in metals exhibits substantial variability, particularly for low applied strain amplitudes. This variability is commonly attributed to the heterogeneity of cyclic plastic deformation within the microstructure, and presents a challenge to minimum life design of fatigue resistant components. This paper analyzes sources of variability that contribute to the driving force of transgranular fatigue cracks within nucleant grains. We employ crystal plasticity finite element simulations that explicitly render the polycrystalline microstructure and Fatigue Indicator Parameters (FIPs) averaged over different volume sizes and shapes relative to the anticipated fatigue damage process zone. Volume averaging is necessary to both achieve description of a finite fatigue damage process zone and to regularize mesh dependence in simulations. Results from constant amplitude remote applied straining are characterized in terms of the extreme value distributions of volume averaged FIPs. Grain averaged FIP values effectively mitigate mesh sensitivity, but they smear out variability within grains. Volume averaging over bands that encompass critical transgranular slip planes appear to present the most attractive approach to mitigate mesh sensitivity while preserving variability within grains. [ABSTRACT FROM AUTHOR]

The shock wave initiation of ultra-fast chemical reactions in inorganic powder mixtures requires the reactants to be blended within the shock front or shortly behind it. As such, the details of particle deformation are crucial to understanding the sequence of events leading up to the shock initiation of these systems. It is known that the initial configuration of a powder (i.e. the mixture composition and particle morphology) can have a significant effect on the degree of mixing that is achieved under shock wave loading. However, it is difficult to fully resolve this mixing behaviour in shock compression experiments due to the time and length scales involved. In this work, the shock wave deformation and mixing of six distinct Ni/Al powders are studied at the particle level using finite element simulation. Attention is focused on the Ni/Al interfaces that are formed since overall mixture reactivity depends on the specific amount of reactant interfacial area and on conditions induced at those interfaces. The analysis reveals (i) a rank ordering of the powders based on reactant interfacial area formation, (ii) a scaling relation for the rate of Ni/Al interface production and (iii) the distributed nature of Ni/Al interface temperature and dislocation density over a range of shock stress. Finally, it is shown that particle velocity differentials tend to develop across Ni/Al interfaces when the compacted powders are reshocked by reflection waves. The velocity differentials stem from the heterogeneity of the aggregates and are hypothesized to drive fragmentation processes that enable ultra-fast reactions on a sub-microsecond time scale. [ABSTRACT FROM AUTHOR]

Submicron-sized samples with 42,000 finite elements containing up to ∼86million atoms have been simulated using a concurrent atomistic-continuum method. The simulations reproduce not only nucleation and growth of semicircular dislocation loops in Cu and Al, but also hexagonal shuffle dislocation loops in Si, with the loop radius approaching ∼75nm. Details of leading and trailing partial dislocations connected by intrinsic stacking faults, dislocation loop coalescence through annihilation, and formation of junctions are reproduced. [ABSTRACT FROM AUTHOR]

Abstract: To quantify the effects of interactions between various microstructure attributes on fatigue life in the high cycle fatigue (HCF) regime, we have proposed a new microstructure-sensitive extreme value statistical framework. This framework couples the extreme value distributions of certain fatigue indicator parameters (FIPs) or response functions to the correlated microstructure attributes that exist at the extreme value locations of these FIPs. We demonstrate the application of this statistical framework to investigate the microstructure-sensitive fatigue response of the PM Ni-base superalloy IN100 at 650°C. To accomplish this task, we construct statistical volume elements (SVEs) used to compute the local response for 200 instantiations of IN100. These SVEs are constructed and simulated via the finite element method with crystal plasticity constitutive relations. The results of the simulations are used to explore extreme value statistics of the FIPs for these microstructures. The extreme value distributions of the Fatemi–Socie FIP are fit with high confidence by the Gumbel distribution and are defined in a representative nature with as few as 25 simulated microstructure instantiations (i.e., SVEs). The extreme value marked correlation functions of the apparent Schmid factor based on the geometry of the slip systems relative to the loading direction indicate that cube slip may be important to fatigue crack formation in this material system. This supports previous experimental observations of fatigue crack formation and microstructurally small fatigue crack growth along cube planes in IN100 in grains that are unfavorably oriented for octahedral slip at elevated temperatures. [Copyright &y& Elsevier]

Abstract: Two-dimensional cellular materials (prismatic honeycombs) provide a range of properties that make them suitable for multifunctional applications involving heat dissipation and structural performance. In this paper we present two-scale homogenization-based finite element scheme for convective heat transfer and structural characterization of 2-D cellular metals with uniform and graded cell sizes of various topologies as well as with mixed cell-topologies. For convective heat transfer analysis, the cells are modeled implicitly as temperature-dependent sinks modeling the out-of-plane fluid convection through the cells; the sink strength is determined via a micromechanics problem of heat transfer in a cell. For structural analysis, the cellular material is represented as a micropolar continuum with linear elastic constitutive equations obtained via micromechanics solution of a representative unit cell. The analyses are then used in conjunction with an optimization algorithm to design cellular materials with functionally tailored mesostructures. The analysis and design framework enables tailoring cellular materials with graded cell structures of a given topology as well as with cell structures that combine multiple topologies. [Copyright &y& Elsevier]

Abstract: Deformation micromechanisms of a Ti–6Al–4V alloy under fatigue loading at room temperature are studied using a three-dimensional crystal plasticity constitutive model. The model employs a minimum set of fitting parameters based on experimental data for Ti–6Al–4V. Single slip is strongly favored through a softening law that affects mainly the driving force for slip on the first activated slip system. Cyclic deformation behavior at the macroscopic scale and at the local scale of grains is analyzed through the simulation of 20 cycles of fatigue on a polycrystalline structure of 900 randomly oriented grains. The progressive activation of slip (basal, prismatic, and pyramidal) is analyzed and compared to experimental observations. [Copyright &y& Elsevier]

Abstract: Generalized plane strain finite element fretting simulations of a rigid cylinder in contact with a Ti-6Al-4V half-space represented via 3-D polycrystal viscoplasticity model are performed in the partial slip regime. The dual-phase nature of Ti-6Al-4V and realistic 3-D crystallographic textures are explicitly accounted for in the model. Earlier studies using idealized 2-D slip geometry in 2-D finite element calculations indicate that ratcheting is the dominant mechanism of cyclic plastic deformation for this material under fretting conditions. Herein, changes in the distribution and mode of cyclic microplasticity with respect to different representative 3-D textures are examined and compared to observations from simulations using the 2-D slip geometry. Results are discussed and quantified in terms of cumulative effective plastic strain distributions, plastic strain maps, and the effective ratchet strain increments. [Copyright &y& Elsevier]

Design has traditionally involved selecting a suitable material for a given application. An understanding of structure—property relationships provides a more rigorous and scientific basis for choosing an appropriate material for a given set of performance requirements. Improved designs may be possible if the material microstructures could be tailored for application-specific performance requirement. Honeycombs, two-dimensional prismatic cellular metals extended in the third direction, are emerging as an important material system for multifunctional applications. A specific example of designing prismatic cellular microstructure of rectangular cell topology is considered for optimum heat transfer via forced convection through its cells. As opposed to most existing designs, which assume uniform cell structures a priori, grading the cell structure is considered to achieve optimal heat transfer performance. A two-dimensional finite element methodology is developed to model convective heat transfer through a rectangular cellular structure in an approximate yet efficient way, enabling rapid exploration of the design space for purposes of preliminary design. Novel features of the finite element methodology are that it models the void and convection heat transfer due to fluid flow through it in an implicit manner and that it employs sink terms in the energy equation to address heat transfer due to convection down the length of the cells, employing an isothermal upper bound solution strategy for each cell. The finite element approach is used in conjunction with optimization algorithms to design uniform and graded rectangular cell structures. [ABSTRACT FROM AUTHOR]

Stationary cracks along and near interfaces between two time-dependent materials are simulated using the finite element method (FEM) to examine crack tip fields and candidate driving force parameters for crack growth. Plane strain conditions are assumed. In some cases, a thin transition layer is included between the two materials. This transition layer features a functionally graded blend of properties of the two materials. An example of such a system is that of weld metal (WM) and base metal (BM) in a weldment, with the transition layer corresponding to the heat-affected zone (HAZ). Numerical solutions for the stress and strain fields of homogeneous and heterogeneous Compact Tension (C(T)-type) specimens are presented. The equivalent domain integral technique is employed to compute the J-integral for elastic-plastic cases as well as the C(t)-integral and transition times for creep behavior. Results from parametric studies are curve-fit in terms of transition layer thickness and crack position, inelastic property mismatches, and other independent model parameters. Results indicate that the incorporation of functionally graded transition layer regions leads to less concentrated stress and strain components along interfaces ahead of the crack tip. It is also shown that the computed fracture parameters are influenced by the transition layer properties. [ABSTRACT FROM AUTHOR]

The effects of missing or fractured cell walls on in-plane effective elastic stiffness and initial yield strength of square and triangular cell metal honeycombs are investigated using finite element analysis. Due to the change of localized deformation mode, the in-plane properties of defected honeycombs can differ significantly from those of intact metal honeycombs, depending on cell type and stress state. First, the effect of the size of a statistical volume element of honeycomb cells with randomly removed cell walls is explored by using different numbers of cells with 5% of walls removed, subject to periodic boundary conditions. The size of a representative volume element (statistically homogeneous) is determined for each considered in-plane property. Next, the effective in-plane properties of square cell and triangular cell honeycombs are, respectively, calculated as a function of increasing number density of randomly removed cell walls. Finally, the sensitivities of axial compressive effective properties of these honeycombs to missing cell walls are compared with that of a previously analyzed hexagonal cell honeycomb. The results indicate that some in-plane properties sharply diminish with defect density, while others exhibit more gradual decay. In compression, the effective elastic stiffness and initial yield strength of triangular cell honeycombs are least sensitive to defects among those considered. [Copyright &y& Elsevier]

Finite element analyses of micronotches including pores and silicon particles of an A356 aluminum alloy were performed to elucidate microstructure–property relations for fatigue crack incubation. Several important findings resulted. By varying the particle and pore size, spacing, aspect ratio, and clustering, the relative microstructural differences were quantified related to micronotch root cyclic plasticity. Results from realistic two-dimensional microstructures showed that minimal microstructure-scale cyclic plasticity corresponds well to the measured fatigue strength at 107 cycles for low porosity A356 aluminum alloy specimens. “Realistic” and idealized particles/pores simulations were used to formulate a local Coffin–Manson type law for crack incubation. [Copyright &y& Elsevier]

Deals with a study which performed estimation of the transverse thermal conductivity of continuous fiber reinforced composites containing a random fiber distribution with imperfect interfaces using finite element analysis. Details on finite element modeling; Results and conclusion.

• A physically-based crystal plasticity model is used to study crack tip fields. • Monotonic and cyclic loading scenarios are investigated. • The evolution of dislocation substructure fields is discussed. • Certain correlative fatigue crack growth parameters are examined. The fields produced at the tip of a Mode I crack in a ductile single crystal have been previously investigated using theoretical, experimental, and numerical methods. Limitations in the material model complexity used in theoretical approaches and difficulties in experimentally measuring in situ crack tip fields invite consideration of numerical crystal plasticity. Prior crystal plasticity analyses of crack tip plasticity have leveraged simple phenomenological constitutive forms and investigated limited loading scenarios. The current work extends prior approaches by using a recently developed face-centered cubic (FCC) crystal plasticity model that considers dislocation substructures and complex back stress evolutions during cyclic loading in concert with a finite element model of a stationary crack tip. The model is used to i) more thoroughly understand the conditions where theoretical analyses remain valid in the context of dislocation interactions and substructure development and ii) explore potential fatigue crack growth driving forces for microstructurally small and physically small cracks. Specific observations are made regarding the observed formation of alternating bands of forward and reverse shear, unique to the present model with dislocation substructure, as well as the influence of ratcheting strain on the cyclic irreversibility of slip and associated correlative fatigue crack growth relations. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Structure-property linkage developed for transition fatigue performance. • α-Ti polycrystalline microstructures quantified using spatial statistics. • Fatigue responses compared via fatigue indicator parameter distributions. • Fatigue performance accurately ranked despite significant inelastic deformation. Abstract The transition fatigue regime between low cycle fatigue (LCF) and high cycle fatigue (HCF) is often addressed in the design and performance evaluation of load-bearing components used in many structural applications. Transition fatigue is characterized by elevated levels of local inelastic deformation in significant regions of the microstructure as compared to HCF. Typically, crystal plasticity finite element method (CPFEM) simulations are performed to model this phenomenon and to rank-order microstructures by their resistance to crack formation and early growth in the regime of transition fatigue. Unfortunately, these approaches require significant computational resources, inhibiting their use to explore novel materials for transition fatigue resistance. Reduced-order, microstructure-sensitive models are needed to accelerate the search for next-generation, fatigue-resistant materials. In a recent study, Paulson et al. (2018) extended the materials knowledge system (MKS) framework for rank-ordering the HCF resistance of polycrystalline microstructures. The efficacy of this approach lies in the reduced-dimensional representation of microstructures through 2-point spatial correlations and principal component analysis (PCA), in addition to the characterization of the HCF response with a small set of performance measures. In this work, these same protocols are critically evaluated for their applicability to rank-order the transition fatigue resistance of the same class of polycrystalline microstructures subjected to increased strain amplitudes. Success in this endeavor requires the formation of homogenization linkages that account for the significantly higher levels of local inelastic deformation and stress redistribution in transition fatigue as compared to HCF. A set of 12 α -titanium microstructures generated using the open access DREAM.3D software (Groeber and Jackson, 2014) are employed for this evaluation. [ABSTRACT FROM AUTHOR]

Computationally efficient estimation of the fatigue response of polycrystalline materials is critical for the development of next generation materials in application domains such as transportation, health, security, and energy industries. This is non-trivial for fatigue of polycrystalline metals since the initiation and growth of fatigue cracks depends strongly on attributes of the microstructure, such as the sizes, shapes, orientations, and neighbors of individual grains. Furthermore, regions of microstructure most likely to initiate cracks correspond to the tails of the distributions of the microstructure features. This requires the execution of large numbers of experiments or simulations to capture the response of the material in a statistically meaningful manner. In this work, a linkage is described to connect polycrystalline microstructures to the statistically signified driving forces controlling the high cycle fatigue (HCF) responses. This is achieved through protocols that quantify these microstructures using 2-pt spatial correlations and represent them in a reduced-dimensional space using principal component analysis. Reduced-order relationships are then constructed to link microstructures to performance characteristics related to their HCF responses. These protocols are demonstrated for α -titanium, which exhibits heterogeneous microstructure features along with significant elastic and inelastic anisotropies at both the microscale and the macroscale. [ABSTRACT FROM AUTHOR]

The prediction of formation and early growth of microstructurally small fatigue cracks requires use of constitutive models that accurately estimate local states of stress, strain, and cyclic plastic strain. However, few research efforts have attempted to systematically consider the sensitivity of overall cyclic stress-strain hysteresis and higher order mean stress relaxation and plastic strain ratcheting responses introduced by the slip system back-stress formulation in crystal plasticity, even for face centered cubic (FCC) crystal systems. This paper explores the performance of two slip system level kinematic hardening models using a finite element crystal plasticity implementation as a User Material Subroutine (UMAT) within ABAQUS (Abaqus unified FEA, 2016) [1] , with fully implicit numerical integration. The two kinematic hardening formulations aim to reproduce the cyclic deformation of polycrystalline Al 7075-T6 in terms of both macroscopic cyclic stress-strain hysteresis loop shape, as well as ratcheting and mean stress relaxation under strain- or stress-controlled loading with mean strain or stress, respectively. The first formulation is an Armstrong-Frederick type hardening-dynamic recovery law for evolution of the back stress [2]. This approach is capable of reproducing observed deformation under completely reversed uniaxial loading conditions, but overpredicts the rate of cyclic ratcheting and associated mean stress relaxation. The second formulation corresponds to a multiple back stress Ohno-Wang type hardening law [3] with nonlinear dynamic recovery. The adoption of this back stress evolution law greatly improves the capability to model experimental results for polycrystalline specimens subjected to cycling with mean stress or strain. The relation of such nonlinear dynamic recovery effects are related to slip system interactions with dislocation substructures. [ABSTRACT FROM AUTHOR]

The change of potency to nucleate cracks in high cycle fatigue (HCF) at a primary non-metallic inclusion in a martensitic gear steel due to the existence of a neighboring inclusion is computationally investigated using two-and three-dimensional elastoplastic finite element (FE) analyses. Fatigue indicator parameters (FIPs) are computed in the proximity of the inclusion and used to compare crack nucleation potency of various scenarios. The nonlocal average value of the maximum plastic shear strain amplitude is used in computing the FIP. Idealized spherical (cylindrical in 2D) inclusions with homogeneous linear elastic isotropic material properties are considered to be partially debonded, the worst case scenario for HCF crack nucleation as experimentally observed for similar systems (Furuya et al., 2004, "Inclusion-Controlled Fatigue Properties of 1800 Mpa-Class Spring Steels," Metall. Mater. Trans. A, 35A(12), pp. 3737-3744; Harkegard, 1974, "Experimental Study of the Influence of Inclusions on the Fatigue Properties of Steel," Eng. Fract. Mech., 6(4), pp. 795-805; Lankford and Kusenberger, 1973, "Initiation of Fatigue Cracks in 4340 Steel," Metall. Mater. Trans. A, 4(2), pp. 553-559; Laz and Hill-berry, 1998, "Fatigue Life Prediction From Inclusion Initiated Cracks," Int. J. Fatigue, 20(4), pp. 263-270). Inclusion-matrix interfaces are simulated using a frictionless contact penalty algorithm. The fully martensitic steel matrix is modeled as elastic-plastic with pure nonlinear kinematic hardening expressed in a hardening minus dynamic recovery format. FE simulations suggest significant intensification of plastic shear deformation and hence higher FIPs when the inclusion pair is aligned perpendicular to the uniaxial stress direction. Relative to the reference case with no neighboring inclusion, FIPs decrease considerably when the inclusion pair aligns with the applied loading direction. These findings shed light on the anisotropic HCF response of alloys with primary inclusions arranged in clusters by virtue of the fracture of a larger inclusion during deformation processing. Materials design methodologies may also benefit from such cost-efficient parametric studies that explore the relative influence of microstructure attributes on the HCF properties and suggest strategies for improving HCF resistance of alloys. [ABSTRACT FROM AUTHOR]

Abstract: Establishing process–structure–property relationships is an important objective in the paradigm of materials design in order to reduce the time and cost needed to develop new materials. A method to link phase-field (process–structure relations) and microstructure-sensitive finite-element (structure–property relations) modeling is demonstrated for subsolvus polycrystalline IN100. A three-dimensional experimental dataset obtained by orientation imaging microscopy performed on serial sections is utilized to calibrate a phase-field model and to calculate inputs for a finite-element analysis. Simulated annealing of the dataset realized through phase-field modeling results in a range of coarsened microstructures with varying grain size distributions that are each input into the finite-element model. A rate-dependent crystal plasticity constitutive model that captures the first-order effects of grain size, precipitate size and precipitate volume fraction on the mechanical response of IN100 at 650°C is used to simulate stress–strain behavior of the coarsened polycrystals. Model limitations and ideas for future work are discussed. [Copyright &y& Elsevier]

Abstract: A computational strategy is developed to characterize the driving force for fatigue crack nucleation at subsurface primary inclusions in carburized and shot peened C61® martensitic gear steels. Experimental investigation revealed minimum fatigue strength to be controlled by subsurface fatigue crack nucleation at inclusion clusters under cyclic bending. An algorithm is presented to simulate residual stress distribution induced through the shot peening process following carburization and tempering. A methodology is developed to analyze potency of fatigue crack nucleation at subsurface inclusions. Rate-independent 3D finite element analyses are performed to evaluate plastic deformation during processing and service. The specimen is subjected to reversed bending stress cycles with R =0.05, representative of loading on a gear tooth. The matrix is modeled as an elastic–plastic material with pure nonlinear kinematic hardening. The inclusions are modeled as isotropic, linear elastic. Idealized inclusion geometries (ellipsoidal) are considered to study the fatigue crack nucleation potency at various subsurface depths. Three distinct types of second-phase particles (perfectly bonded, partially debonded, and cracked) are analyzed. Parametric studies quantify the effects of inclusion size, orientation and clustering on subsurface crack nucleation in the high cycle fatigue (HCF) or very high cycle fatigue (VHCF) regimes. The nonlocal average values of maximum plastic shear strain amplitude and Fatemi–Socie (FS) parameter calculated in the proximity of the inclusions are considered as the primary driving force parameters for fatigue crack nucleation and microstructurally small crack growth. The simulations indicate a strong propensity for crack nucleation at subsurface depths in agreement with experiments in which fatigue cracks nucleated at inclusion clusters, still in the compressive residual stress field. It is observed that the gradient from the surface of residual stress distribution, bending stress, and carburized material properties play a pivotal role in fatigue crack nucleation and small crack growth at subsurface primary inclusions. The fatigue potency of inclusion clusters is greatly increased by prior interfacial damage during processing. [Copyright &y& Elsevier]

Fatigue Indicator Parameters (FIPs) based on the cyclic plastic strain are used as surrogate measures of the driving force for fatigue crack formation. For a given microstructure, the Extreme Value Distribution (EVD) of FIPs can be populated using results of a number of digital Statistical Volume Element (SVE) instantiations analyzed by the crystal plasticity finite element method. The number of microstructure instantiations affects the maximum FIPs computed. To predict the maximum FIPs in a large volume of material using simulation results from a limited number of SVEs, we proposed a statistical approach based on extreme value theory. The predicted maximum FIP values are compared directly to simulation results of 1000 SVEs to validate the proposed method for duplex Ti–6Al–4V. It is shown that simulations of only 100 SVEs suffice to identify the statistical information for a reliable prediction of the maximum FIPs in polycrystalline duplex Ti–6Al–4V with initial random texture. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Traditionally, crystal plasticity finite element method (CPFEM) simulations have been used to capture the variability in the microstructure-scale response of polycrystalline metals. However, these types of simulations are computationally expensive and require significant resources. To explore the large space of microstructures (reflecting a variety of grain shape, size, and orientation distributions) within the practical constraints of computational resources, a more efficient strategy is required. The purpose of this work is to explore the viability of leveraging the recently established, high-throughput Materials Knowledge System (MKS) for fast evaluation of high cycle fatigue (HCF) performance of candidate microstructures. More specifically, we explore the feasibility of estimating the mesoscale strain fields in hexagonal close packed (HCP) α -titanium polycrystals during HCF loading conditions using the computationally low-cost MKS approach, and subsequently estimating the slip system activities via decoupled numerical integration of the relevant crystal plasticity (CP) constitutive relations. The computed slip activities are then used to arrive at extreme value distributions (EVDs) of fatigue indicator parameters (FIPs). As critical validation of this reduced-cost computational strategy, it is shown that the FIP distributions in the HCF regime estimated using this novel strategy are in reasonable agreement with those computed directly using the conventional CPFEM approach. Additionally, the computational advantages of the MKS and decoupled numerical integration approach over the traditional, computationally-expensive, CPFEM approach are presented and discussed. [ABSTRACT FROM AUTHOR]

Abstract: This paper provides some background and historical review of how microstructure-sensitive finite element simulations can play a role in understanding the effects of stress amplitude, R-ratio, and microstructure on fatigue crack formation and early growth at notches, including pores and non-metallic inclusions for Ti alloys and Ni-base superalloys. The simulations employ fatigue indicator parameters (FIPs) computed over finite volumes that relate to processes of fatigue crack formation and early growth at the scale of individual grains. It is argued that both coarse scale (uncracked, mesoscale) and fine scale FIPs (computed in the vicinity of cracks in single grains or crystals) serve as a driving force for crystallographic fatigue crack growth, and correlate directly with the cyclic crack tip displacement (CTD). Furthermore, variability in high cycle fatigue (HCF) and very high cycle fatigue (VHCF) responses is computationally assessed using multiple statistical volume elements and the distribution of FIPs of extreme value character. The concepts of marked correlation functions and weighted probability density functions are reviewed as a means to quantify the role of multiple microstructure attributes that couple to enhance the extreme value FIPs in the HCF regime. An algorithm for estimation of the cumulative probability distribution of cycles for crack formation and growth from notches in HCF and VHCF is also described. [Copyright &y& Elsevier]

Abstract: This paper presents a concurrent atomistic–continuum (CAC) methodology for three-dimensional dynamic simulation of dislocation nucleation, migration and interaction. The method is based on a new continuum field formulation of balance laws with relevant atomistic information (the arrangements and interactions of atoms) considered. In this work, we show that the new CAC method allows the smooth passage of dislocations through sharp interfaces between the atomistic and the coarse-grained finite element domains without unphysical reflection of dislocations or the need for heuristic rules; meanwhile, complex dislocation phenomena such as dislocation nucleation, dynamic strain bursts associated with nucleation and migration avalanches, formations of Lomer–Cottrell locks, dislocation–rigid boundary interactions, formation of intrinsic and extrinsic stacking faults, deformation twinning, and curved dislocation loops can be reproduced by the CAC method. All of the CAC simulations are directly compared with the corresponding atomic-level molecular dynamics (MD) simulations. The efficiency, accuracy and potential applications of the method are discussed along with necessary additional development of criteria for coarse graining. [Copyright &y& Elsevier]

Abstract: The mechanics of high cycle fatigue crack nucleation (formation of a stable crack that can grow away from the influence of the notch root of the inclusion) at subsurface primary inclusions in carburized and shot-peened martensitic steel subjected to cyclic bending is investigated using three-dimensional (3D) finite element (FE) analysis. FE models are constructed using a voxellation technique to address the shape, size, and distribution of primary inclusions within clusters. The critical depth for fatigue crack nucleation is predicted considering the gradient in material properties arising from carburization, prestrain and compressive residual stress distribution due to shot peening, and the gradient of applied bending stress. The influence of inclusion shape and interface condition (intact or debonded) with the matrix on the driving force for fatigue crack nucleation is examined. It is observed that the inclusion shape has minimal influence on the predicted results while the effect of the interface condition is quite significant. For partially debonded interfaces, the predicted critical depth from surface for fatigue crack nucleation agrees qualitatively with experimental observations. [Copyright &y& Elsevier]

Assessing the size of representative volume elements (RVEs) for fatigue-related applications is challenging. A RVE relevant to random microstructure requires a volume of material that is sufficiently large to capture the grain/phase heterogeneity that captures all statistical moments of the distribution of the driving force for fatigue crack formation at "hot spot" grains. Consequently, the large size of a microstructure RVE required to study fatigue phenomena is largely computationally intractable and difficult to explore. A more realistic objective in this work is to systematically study, as a function of the size of a statistical sample of microstructure, trends towards convergence of the simulated distribution of driving force for fatigue crack formation. The present work accordingly leverages the recently developed open-source PRISMS-Fatigue framework [Yaghoobi et al., npj Comput. Mater. , 7, 38 (2021)] to examine the trends in convergence of extreme value distributions (EVD) of Fatigue Indicator Parameters (FIPs) in progressively larger polycrystalline microstructure realizations of FCC Al alloy 7075-T6 using crystal plasticity finite element method simulations. The results are compared to the traditional method in which ensembles of statistical volume elements (SVEs) are simulated to build up statistics intended to approximate those associated with a larger volume of material. The convergence of EVDs with increase of size of a SVE of microstructure is closely related to the extent of grain nearest neighbor (NN) interactions. Accordingly, the sensitivity of the local micromechanical response at hot spot grains is quantitatively investigated by systematically varying the orientations of NN grains. Results indicate that SVEs with cubic crystallographic texture tend towards convergence of the EVD of FIPs with tens of thousands of grains while the random and rolled textures require larger volumes. Simple relationships based on microstructure parameters (e.g., Schmid Factor, grain size, NN misorientation) do not completely correlate to fatigue hot spot grains. Finally, the sensitivity of the extreme value fatigue response at hot spot grains extends to the 3rd NN when a single neighborhood grain orientation is altered. [Display omitted] [ABSTRACT FROM AUTHOR]