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• A nonproportional parameter at the mesoscale is proposed. • The modified isotropic hardening and kinematic hardening rules are proposed. • The cyclic deformation features under uniaxial and multiaxial loading are predicted. • The ratcheting behaviors under different nonproportionally multiaxial loading paths are predicted. The theoretical investigations of cyclic deformation behavior and deformation mechanism of the rail steels under multiaxial loadings are of great significance to the study of rolling contact fatigue. Based on the classical crystal plasticity framework, a new nonproportional parameter at the mesoscale is proposed, and the isotropic and kinematic hardening models are modified. A series of finite element simulations of U75V rail steel under uniaxial and multiaxial cyclic loading are carried out using the proposed model. The simulation results show that the proposed model can reasonably reflect the cyclic softening under strain-controlled uniaxial cyclic loading, cyclic hardening under strain-controlled multiaxial cyclic loadings, and ratcheting behavior under stress-controlled uniaxial and multiaxial cyclic loadings of U75V rail steel. Moreover, the influence of multiaxial loading paths on the plastic strain is explained from a mesoscopic perspective. The values of nonproportional parameters of different slip systems under uniaxial and multiaxial paths are compared, and the difference of nonproportional parameters at the macroscale and mesoscale are discussed. Finally, the simulation results of the proposed model and the existing model with modified kinematic hardening rules are compared. The results show that the proposed model has better predictions on the evolution of ratcheting strain and nonproportionally additional hardening effect caused by nonproportionally multiaxial loadings. [ABSTRACT FROM AUTHOR]

• The Lemaitre model of low cycle fatigue damage is modified and incorporated into the crystal plasticity theory. • The grains with low Schmid factor generally generate higher Von Mises stress as well as lower dislocation density, and suffer more severe low cycle fatigue damage, compared with those with high Schmid factor. • Low cycle fatigue damage is generally more severe in the vicinity of the grain boundaries with high misorientation angles. To capture the mechanical behavior and low cycle fatigue damage of metals, a crystal plasticity model combined with isotropic continuum damage mechanics model of low cycle fatigue is developed. In this constitutive model, the Lemaitre model of low cycle fatigue damage is modified accounting for the effect of stress triaxiality and Lode parameter, the slip strength is associated with the evolution of the density of statistically stored forest dislocations and debris dislocations, and a non-linear kinematic hardening rule is employed to capture the cyclic response. Simulation is implemented by applying this developed constitutive model to the Voronoi polycrystalline aggregation of 7075 aluminum alloy. The studied results show that the grains with low Schmid factor generally suffer more severe damage compared to those with high Schmid factor. In addition, due to the orientation mismatch of adjacent grains, localized stress concentrations and the resulting severe damage generate near the grain boundaries, especially near the grain boundaries with high misorientation angles. The proposed constitutive model manifests the capacity for the determination of damage evolution of the polycrystalline metals. [ABSTRACT FROM AUTHOR]

• Cyclic torsion of Mg alloy is studied by experiment and crystal plasticity model. • Deformation mechanism is revealed by active operation modes, TVF, internal stress. • "Butterfly" shaped axial strain-shear strain curve is led by twinning-detwinning. • Gradient twin structure could be regulated in Mg alloy through cyclic torsion. This work investigated the cyclic torsional behaviors of extruded AZ61A Mg alloy tubes through experiments and simulations. To capture the Bauschinger effect, the elastic viscoplastic self-consistent model with the twinning and detwinning scheme, together with a torsion-specific finite element approach was improved by adding a back-stress. A unique Swift effect with the "butterfly" shape was observed and reasonably reproduced by our model. Furthermore, the relative activities of deformation mechanisms, internal stress distributions, and twin volume fraction distributions under cyclic torsion were discussed. The findings could be beneficial to the design, manufacturing, and service of Mg alloys, particularly under cyclic torsion. [ABSTRACT FROM AUTHOR]

• A test platform was set up to investigate the combined high and low cycle fatigue behavior. • A new CCF life prediction model is proposed based on CPFEM. • The new model can predict fatigue life through parameters with clear physical meaning. Combined low and high cycle loading of AISI 4140 steel during service has a significant effect on its fatigue performance, compared to pure low or high cycle loading. In this study, we analyzed the combined low and high cycle fatigue (CCF) responses of AISI 4140 steel under different frequency ratios (20%-30%), and stress amplitude ratios (100–1000). The results indicated that the higher the stress amplitude ratio and frequency ratio, the shorter was the fatigue life of CCF. The fatigue life prediction model was established based on the crystal plasticity theory, the fatigue indicator parameters were obtained from the microstructure evolution, and then fatigue life under different stress amplitude ratios and frequency ratios was predicted. Comparison of the predicted and experimental results demonstrated that the predicted lives were located within thrice the scatter band. [ABSTRACT FROM AUTHOR]

[Display omitted] • Crack tip stored energy density captures short fatigue crack growth rates across samples with strongly differing texture. • Elastic anisotropy and yield stress mismatch at grain boundaries in HCP Zircaloy-4 drive short crack growth rate fluctuations. • Crack path tortuosity in HCP single crystals is linked with the cyclic development of a shear back stress. Rates of fatigue crack growth in Zircaloy-4 are highly microstructurally sensitive and dependent upon texture. Crystal plasticity finite element modelling with the eXtended Finite Element Method and a stored energy density fracture criterion are used to simulate crack propagation in single crystals and polycrystalline microstructures for comparison with experimental crack growth rate data. Results demonstrate that growth rate fluctuations at microstructural features are driven primarily by elastic anisotropy and yield stress mismatch. Additionally, reduced rate of growth in soft hexagonal close packed grains (relative to the remote loading direction) can be linked with crack path tortuosity, which is shown to be controlled by the cyclic development of an in-plane shear back stress. Most importantly, stored energy density is shown to accurately capture major microstructure-driven differences in crack growth rate. Comparison of simulated fatigue crack growth rates with experimental data enables estimation of the critical stored energy density for crack propagation in Zircaloy-4 to be 250 J/m2. [ABSTRACT FROM AUTHOR]

• A dislocation motion-based failure indicator parameter (FIP) has been proposed. • The physical meaning of the proposed FIP has been interpreted. • Life predictions for low cycle fatigue and creep-fatigue loadings have been conducted. A dislocation movement-based physical failure indicator parameter (FIP) was proposed and incorporated into crystal plasticity finite element to assess the damage for components subjected to low cycle fatigue (LCF) and creep-fatigue interaction (CFI) loadings. The concept of net slip was introduced through the distance of dislocation movement whose evolution was analyzed and compared with other FIPs. The creep damage can only be captured by the proposed physical FIP. Life prediction based on net slip was developed and validated for different materials under LCF and CFI loadings at different temperatures. Most of the predicted life falls in the ± 1.5 error bands. [ABSTRACT FROM AUTHOR]

• Basal slip and 10 1 ¯ 2 < 11 2 ¯ 0 > tensile twins were found active on hard orientated grains and colonies respectively. • Observations of Rogue pairs were experimentally observed matching hypothesis crystal plasticity models for quasi-cleavage facet formation. • A common slip was observed at Rogue colony-grain combinations in a bimodal microstructure. In this paper, quasi-cleavage facet formation and deformation mechanisms in dwell fatigue have been studied on specimens from a Ti834 compressor disc alloy with a bimodal microstructure by ex-situ dwell fatigue testing at temperatures between 80 °C and 200 °C. Basal slip was observed in grains with their c-axis near parallel the loading direction, while colonies similarly oriented accommodate deformation by tensile twins 10 1 ¯ 2 < 11 2 ¯ 0 >. This type of slip in basal planes is the most critical damage mode leading to failure during dwell fatigue loading. A Rogue colony-grain combination is presented and a possible criterion for slip transfer in bimodal titanium alloys is introduced. The requirements cited for quasi-cleavage facet formation leading to dwell fatigue failure have been experimentally observed in agreement with the suggested hypothesis in previously presented crystal plasticity models. [ABSTRACT FROM AUTHOR]

• The fatigue life prediction model based on the surface integrity features was developed. • The eigenstrain method was used to restructure the residual stress field after milling. • Simulation of different feed rates impact on fatigue life after milling. • Mapping from microscopic characteristics to macroscopic mechanical properties was established. The surface integrity of AISI 4140 steel after milling at different feed rates (75–125 mm/min) was measured by performing laser scanning microscopy, X-ray diffraction, and electron backscatter diffraction. Subsequently, the fatigue responses under different maximum stress values (650–800 MPa) were analyzed. The results showed that the increase in the feed rate increases the residual stress and roughness, whereas the fatigue life at low stress is reduced. Moreover, the feed rate has a limited effect on the surface grain refinement layer, and fatigue life at high stress. The measured surface integrity models were used to predict the fatigue life based on the crystal plasticity theory, and these yielded results within the three times scatter bands from the corresponding experimental values. [ABSTRACT FROM AUTHOR]

[Display omitted] • Different shear direction results in high stress concentration at soft-soft GBs. • Activated TT boundaries and GBs constitute new triple junctions at soft-soft GBs, leading to micro fatigue cracks. • Strain quantity difference at soft-hard grains is insufficient to fatigue cracks. • The interrupt fatigue tests and EBSD-based CP models was developed. The intergranular stress was investigated at grain boundaries (GBs) of Ti-2Al-2.5Zr alloy under cyclic loading. The crystal plasticity (CP) simulations revealed that the strain incompatibility between soft-soft grains due to shear direction difference, which forced the slight activation of tension twins (TT) near GBs. Twin boundaries (TBs) and GBs constituted new triple junctions, leading to further stress concentration and fatigue damage initiation. While the strain quantity difference at soft-hard GBs induced the moderate stress jump and stable stress evolution, which was insufficient to generate fatigue cracks. The EBSD-based CP model successfully predicted the twin activation and fatigue cracks at GBs. [ABSTRACT FROM AUTHOR]

Although surface roughness significantly influences fatigue, most micromechanical models using crystal plasticity only consider bulk behavior. In this work, a framework is described to include surface roughness in crystal plasticity simulations with emphasis on enabling extensive computational studies. This is achieved by the utilization of a statistical surface roughness generator and the prescription of appropriate boundary conditions. Fatigue lifetimes of a high-strength steel are evaluated for three surface conditions, with the models appropriately parameterized by surface measurements. It is shown that fatigue lifetime prediction considering surface roughness is qualitatively in agreement with experimental observations regarding their mean values and scatter. • A framework is established to integrate three-dimensional surface roughness within crystal plasticity models. • Surface roughness profiles from a statistical generation technique are used. • Fatigue lifetime prediction for three distinct surface conditions is qualitatively in agreement with experimental observations. [ABSTRACT FROM AUTHOR]

• Effects of loading conditions on life distribution are explored by using CPFE. • GND density is predicted to understand dwell-fatigue damage mechanism. • Accurate life prediction under wide loading conditions is presented. • 3-D tolerated damage diagram is developed for residual dwell-fatigue life. In this work, a dislocation-based crystal plasticity finite element (CPFE) framework was implemented to investigate the effects of loading conditions on dwell-fatigue crack initiation life. Experimentally, a large number of strain-controlled dwell-fatigue tests were carried out at 650 °C in a nickel-based superalloy. The combinations of CPFE simulations and post-test examinations were used to reveal the dwell-fatigue crack initiation mechanisms. Then, a life prediction approach was presented on the basis of accumulated energy dissipation at half-life cycle. Good agreement between the experimental and simulated lives verifies the robustness as well as the accuracy of the present approach. Finally, a new three-dimensional (3-D) damage tolerance diagram was proposed by introducing a CP-based physical parameter to describe the degradation levels and evaluate the residual dwell-fatigue life. [ABSTRACT FROM AUTHOR]

• Simulations of hybrid-controlled creep-fatigue interaction (HCFI) were performed. • Simulated results of cyclic deformation matched well with the experimental data. • Increase in computational time of the extended model was limited. A numerical process based on crystal plasticity finite element method was implemented to describe the cyclic stress–strain response and especially the creep deformation of 9 %Cr steel under hybrid stress–strain controlled creep-fatigue interaction loading at 650 °C. An extended model based on Armstrong and Frederick (A-F) hardening law was used to capture the creep strain. Compared with experimental results, the creep strain performed by A-F model was small while extended model predicted well. The cyclic softening and decline tendency of relaxation have been simulated. Simulations of other loading modes with extended model also show a good agreement with experimental results. [ABSTRACT FROM AUTHOR]

• A crystal plasticity model is developed for Nickel-based superalloys considering δ phase. • Accumulated energy dissipation is more feasible for predicting fatigue crack initiation life. • Damage accumulation sites shift from grain boundary to δ phase boundary by increasing δ phase and applied strain level. • The existence of δ phase leads to the increase of plastic slip and decrease of localized stress level. The fatigue crack initiation life and damage mechanisms of three heat-treated nickel-based alloy with different volume fractions of δ phase have been investigated based on experiment and crystal plasticity simulation. With the help of fatigue indicator parameters (FIPs), the predicted fatigue lives are agreed well with experimental results, where energy dissipation based FIP shows more accurate life prediction than plastic slip based FIP does. Maximum fatigue damage sites shift from grain boundary to δ phase boundary by increasing δ phase and applied strain level. Furthermore, the existence of δ phase leads to the increase of plastic slip accumulation and decrease of localized stress level. [ABSTRACT FROM AUTHOR]

• Load-displacement curves of β single crystal show reasonable agreement between nanoindentation tests and dislocation mechanism-based crystal plasticity modeling. • Intergranular β lath within the rogue grain combination reduces the dwell fatigue sensitivity of titanium alloys with globular structure. • Geometrical compatibility of the α / β interface significantly affects the stress redistribution phenomenon. • Increased peak stress in the intergranular β lath may cause competing dwell fatigue failure modes at the high stress state. Grain-scale dwell fatigue behavior in Ti-Fe-O alloy is elucidated, with attention focused on the stress redistribution phenomenon that occurs within the soft-hard grain combination. Elastoplastic properties of the β phase are determined using nanoindentation and crystal plasticity modeling. On this basis, the role of intergranular β lath on stress redistribution is evaluated. Redistribution of stress from the soft to hard α grain is inhibited in the presence of intergranular β lath during dwell period. Meanwhile, the peak stress in the β lath is enhanced. This may result in the competition of two dwell fatigue failure modes at high stress state. [ABSTRACT FROM AUTHOR]

[Display omitted] • The microstructure evolutions of fatigue of HEA are observed by in-situ SEM. • Fatigue induced misorientation and GND densities at two temperatures are analyzed. • A crystal plasticity modeling method based on real grain morphology is proposed. • In-situ SEM, EBSD and CPFE simulation results are comprehensively compared. The fatigue behavior of Fe 44 Mn 36 Co 10 Cr 10 high entropy alloy (HEA) at room temperature and 300 °C was studied by in-situ SEM observation, electron back-scattered diffraction (EBSD) and crystal plasticity simulation. The microstructure evolution and deformation process was observed by in-situ SEM fatigue experiment. The misorientation and geometrically necessary dislocation (GND) density was analyzed by EBSD. A crystal plasticity finite element (CPFE) modeling method based on the real grain morphology was proposed. The cumulative plastic strain, dominant slip system and dominant slip plane distributions were obtained. CPFE simulation shows multiple dominant slip systems being activated, which agrees with the multiple slip phenomena observed by in-situ SEM. [ABSTRACT FROM AUTHOR]

• Fatigue cracks were initiated at the interface between two micro-textured regions. • Crystal plasticity model was used for quantifying the micromechanical response. • Stress concentration and dislocation pile-up lead to the fatigue crack initiation. Micro-textured regions (MTRs) are the presence of large regions of α grains aggregates with strong local texture, which are detrimental to the fatigue performances in titanium alloys. This work proposes an EBSD map-image based crystal plasticity model to study the fatigue crack initiation in MTRs. Crystal plasticity simulations reveal that the crack initiation may be attributed to the significantly high plastic strain accumulated on prismatic a slip systems leading to significantly high dislocation pile-ups, and high stress concentrations on the cluster of hard grains leading to the stress redistribution and cleavage fracture of the specimen. [ABSTRACT FROM AUTHOR]

• VHCF studied with crystal plasticity theory. • Pores have more signification effect on shortening fatigue life than inclusions. • Fatigue highly depends on microstructure, especially inclusions and pores. • Residual stress near inclusion is harmful to the fatigue life. The high-cycle and very-high-cycle fatigue (VHCF) behaviors of AlSi10Mg alloy produced by additive manufacturing (AM) were studied. A crystal plasticity finite element model (CPFEM) with Voronoi tessellation was developed to simulate the cyclic plastic deformation considering defect effects. Morrow's model and Smith-Watson-Topper (SWT) model were used to predict the fatigue life and the SWT model was in good agreement with the experimental life between 105 and 109. CPFEM simulation indicated that the accumulated cyclic plastic strain is significantly increased near a pore than that of an inclusion. The residual stress near an inclusion led to large plastic strain localization, which is harmful to fatigue performance. [ABSTRACT FROM AUTHOR]

• Explicitly introducing discrete slip bands to crystal plasticity model. • Investigating slip-controlled cyclic deformation and short crack growth. • Normal factor-based CRSS to describe orientation-dependent stress-strain responses. • Using cumulative shear strain and element deletion for crack growth modelling. • Capable of predicting tortuous paths and irregular growth rates for short cracks. For metals under fatigue, microplastic strain localisation leads to the formation of discrete slip bands, which contributes to the initiation and propagation of short cracks. In this paper, a discrete slip band model is introduced to investigate the slip-controlled cyclic deformation and short crack growth in a single crystal alloy. In conjunction with crystal plasticity and normal factor-based critical resolved shear stress, finite element simulations demonstrated the success of the discrete model in describing orientation-dependent cyclic stress-strain responses. The proposed approach is also capable of predicting slip-controlled short crack growth, based on element deletion technique and individual cumulative shear strain criterion. [ABSTRACT FROM AUTHOR]

• Integrating physics-based models for predicting fatigue crack nucleation. • Modelling and experiments in small volumes. • Validation of crack nucleation orientation and nucleation life statistical distribution. • Use of non-local FIPs in microstructure-sensitive models with gradients. The failure of micron-scale metallic components presents significant variability as a result of their size being comparable to microstructural length scales. Indeed, these components do not represent the bulk of the material but correspond to statistical volume elements (SVEs). This work investigates the role of SVEs on fatigue crack nucleation with a novel comparison between microbeam experiments and microstructure-sensitive simulations. We recreate multiple microstructural computational realizations to estimate fatigue crack nucleation lives and orientations by means of physics-based crystal plasticity models. We demonstrate a unique approach to validate microstructure sensitive models and quantify the fatigue crack stochasticity associated with small volumes. [ABSTRACT FROM AUTHOR]

• The rolling contact fatigue damage is investigated using a 3D finite element model. • The effect of traction ratio, friction, and partial slip contact on RCF is studied. • RCF cracks initiate below the surface for large wheel loads and low tractions. • For high tractions, the cracks initiate at the rolling surface. A three-dimensional (3D) finite element model that includes the microstructure of grains and grain boundaries is developed for studying the rolling contact fatigue (RCF) damage caused by a rolling steel wheel on a steel railway. The 3D model uses a crystal plasticity-based micromechanical framework for simulation of stress-strain behavior inside the grains, and cohesive elements with traction-separation law for modeling the intergranular fatigue damages. A combination of moving normal Hertzian load and tangential loads are employed to mimic the rolling contact conditions. The effect of various parameters such as friction coefficient, traction, partial slip contact and wheel load on RCF is studied. The results reveal that RCF cracks initiate slightly below the surface for large wheel loads and low tractions. The cracks migrate toward the surface as the wheel-rail traction increases. For high tractions, the cracks initiate at the rolling surface. Under partial slip contact condition, there is a large change in rail life for small normalized tractions. With a slight increase in the latter, the rail life significantly decreases. For moderate to large tractions, rail life remains relatively unchanged or slightly increases. The results of the study appear to agree with anecdotal observations by the U.S. railroads from revenue service operation. [ABSTRACT FROM AUTHOR]