Dual-time scale crystal plasticity FE model for cyclic deformation of Ti alloys

A dual-time scale finite element model is developed in this paper for simulating cyclic deformation in a Titanium alloy Ti-6242. The material is characterized by crystal plasticity constitutive relations. Modeling cyclic deformation using conventional time integration algorithms in a single time scale can be prohibitive for crystal plasticity computations. Typically 3D crystal plasticity based fatigue simulations found in the literature are in the range of 100 cycles. Results are subsequently extrapolated to thousands of cycles, which can lead to considerable error in fatigue predictions. However, the dual-time scale model enables simulations up to a significantly high number of cycles to reach local states of damage initiation leading to fatigue crack growth. This formulation decomposes the governing equations into two sets of problems, corresponding to a coarse time scale (low frequency) cycle-averaged problem and a fine time scale (high frequency) oscillatory problem. A statistically equivalent 3D polycrystalline model of Ti-6242 is simulated by the crystal plasticity finite element model to study the evolution of local stresses and strains in the microstructure with cyclic loading. The comparison with the single time scale reference solution shows excellent accuracy while the efficiency gained through time-scale compression can be enormous.     

Fatigue crack initiation life prediction for aluminium alloy 7075 using crystal plasticity finite element simulations

An experimentally-validated approach for predicting fatigue crack initiation life of polycrystalline metals is developed based on crystal plasticity finite element (CPFE) simulations. In this approach, the microstructure used in the simulations possesses statistically the same grain size and crystallographic orientations as those obtained from electron back-scatter diffraction experiments. A backstress model is incorporated into the CP constitutive model to describe the mechanical behaviour of aluminium alloy (AA) 7075 under cyclic loading. The key variables of the prediction model, the energy efficiency factor and plastic strain energy density, are calibrated using a fatigue test on a round-notched AA7075 specimen at room temperature. The proposed approach is then validated by using another fatigue test to predict 69.1–87.3% of the experimentally measured fatigue crack initiation life. The effects of the microstructure and texture on the energy efficiency factor and fatigue life prediction are quantitatively determined. It is shown that for a given range of energy efficiency factors a similar range of life prediction is obtained. Since the proposed approach considers the heterogeneity of the microstructure, it can well capture the grain scale deformation localisation and therefore improve the precision of fatigue life prediction.     

Modeling the effect of microstructural features on the nucleation of creep cavities

A crystal plasticity based finite element model has been applied to study the deformation of metals at the microstructural length scale, in order to determine the effect of various microstructural features on the nucleation of creep cavities. The deformation model captures the non-uniform distributions of the equivalent plastic strain and the hydrostatic stress within the different grains of the microstructure when subjected to cyclic loading conditions. The influence of various microstructural features such as grain boundaries, triple junctions, and second-phase particles, on the strain and stress fields is examined through the simulations. The results indicate that the various microstructural parameters, such as grain orientation, presence of the precipitates and their shape, and alignment of the boundaries with respect to the loading direction influence the strain and stress distributions, and therefore, the conditions that favor the nucleation and growth of creep cavities.     

Simulated extreme value fatigue sensitivity to inclusions and pores in martensitic gear steels

The objective of this work is to model the sensitivity of high cycle fatigue resistance of secondary hardening martensitic gear steels to variability in extrinsic inhomogeneities such as primary inclusions, and pores, coupled with intrinsic microstructure variability. A simplified approach is presented to quantify the variability in the driving force for fatigue crack formation in the matrix at non-metallic inclusions and pores in lath martensitic gear steels using a three-dimensional crystal plasticity constitutive model. The utility of a simulation-based strategy for exploring sensitivity of minimum fatigue lifetime (low probability of failure) to microstructure lies in its inherent capability to consider parametric simulations of hundreds of inclusions and microstructures in contrast to limited numbers of physical experiments. Experiments are used to calibrate the polycrystalline cyclic stress–strain response and mean (50% probability) fatigue crack formation life. Several remote loading conditions are considered in the high cycle fatigue (HCF) regime relevant to typical gear applications. Idealized inhomogenieties (spherical) in the form of hard (Al₂O₃), soft inclusions (La₂O₂S), and pores are systematically investigated in this parametric computational study. Relations between remote loading conditions and local plasticity are discussed as a function of stress amplitude and microstructure. The maximum plastic shear strain range is used in the modified form of Fatemi–Socie parameter evaluated at the grain scale as a measure of the driving force for fatigue crack formation (nucleation and early growth to lengths on the order of several times the average grain size). Multiple realizations of the polycrystal microstructure are considered to obtain a statistical distribution of this fatigue indicator parameter (FIP). The results are used to construct an extreme value Gumbel distribution of the FIPs for the selected microstructures. Subsequently, a computational micromechanics based minimum life estimate that corresponds to 1% fatigue crack formation probability is calculated.     

Microstructure-scale modeling of HCF deformation

Computational crystal plasticity (ABAQUS FE) simulations are presented for dual phase alloy Ti–6Al–4V subjected to cyclic loading in the high cycle fatigue (HCF) regime. Relations between remote loading conditions and local plasticity are discussed as a function of stress amplitude and microstructure. Based on computational micromechanics, effects of microstructure heterogeneity and R-ratio are examined in terms of their influence on cyclic microplastic strain within the microstructure of unnotched specimens. It is shown that bulk-dominated fatigue damage at high R-ratios (>0.7) is associated with the onset of percolation of ratcheting of shear strain in the HCP α phase through connected channels within the microstructure. A high cumulative plastic strain gradient across the α–β phase boundaries is the likely driving force for decohesion at phase boundaries as the manifestation of bulk damage in the HCF regime. Effects of texture are also examined using random periodic microstructure representations. Application of the same crystal plasticity model for Ti–6Al–4V in fretting fatigue contact at positive R-ratios for the bulk fatigue stress also reveals a dominance of ratcheting strain in shear bands emanating from the contact surface, ostensibly in the HCF regime.     

Micromechanical finite element modelling of thermo-mechanical fatigue for P91 steels

In this paper, the cyclic plasticity and fatigue crack initiation behaviour of a tempered martensite ferritic steel under thermo-mechanical fatigue conditions is examined by means of micromechanical finite element modelling. The crystal plasticity-based model explicitly reflects the microstructure of the material, measured by electronic backscatter diffraction. The predicted cyclic thermo-mechanical response agrees well with experiments under both in-phase and out-of-phase conditions. A thermo-mechanical fatigue indicator parameter, with stress triaxiality and temperature taken into account, is developed to predict fatigue crack initiation. In the fatigue crack initiation simulation, the out-of-phase thermo-mechanical response is identified to be more dangerous than in-phase response, which is consistent with experimental failure data. It is shown that the behaviour of thermo-mechanical fatigue can be effectively predicted at the microstructural level and this can lead to a more accurate assessment procedure for power plant components.     

Effect of saline solution environment on the cyclic deformation of Ti-6Al-4V alloy

The present investigation studies the effect of physiological solution at 37°C on the cyclic deformation behaviour of a Ti-6Al-4V alloy, with a microstructure corresponding to that obtained in the substrate when a sintered metallic porous coating is produced. Cyclic deformation tests have been carried out up to fracture and the fatigue crack nucleation mechanisms have been analysed. Since fatigue is a phenomenon related with plastic deformation, which is enhanced at corrosion and/or at stress concentration sites, cyclic deformation tests conducted at a level of stress above the elastic limit can provide a clear picture of the crack nucleation mechanisms involved.     

Micromechanical methodology for fatigue in cardiovascular stents

A finite element based micromechanical methodology for cyclic plasticity and fatigue crack initiation in cardiovascular stents is presented. The methodology is based on the combined use of a (global) three-dimensional continuum stent-artery model, a local micromechanical stent model, the development of a combined kinematic–isotropic hardening crystal plasticity constitutive formulation, and the application of microstructure sensitive crack initiation parameters. The methodology is applied to 316L stainless steel stents with random polycrystalline microstructures, based on scanning electron microscopy images of the grain morphology, under realistic elastic–plastic loading histories, including crimp, deployment and in vivo systolic–diastolic cyclic pressurisation. Identification of the micromechanical cyclic plasticity and failure constants is achieved via application of an objective function and a unit cell representative volume element for 316L stainless steel. Cyclic stent deformations are compared with the J₂-predicted response and conventional fatigue life prediction techniques. It is shown that micromechanical fatigue analysis of stents is necessary due to the significant predicted effects of material inhomogeneity on micro-plasticity and micro-crack initiation.     

High and low cycle fatigue behavior of linear friction welded Ti–6Al–4V

Linear friction welded Ti–6Al–4V was investigated in fatigue at various stress amplitudes ranging from the high cycle fatigue (HCF) to the low cycle fatigue (LCF) regime. The base material was composed of hot-rolled Ti–6Al–4V plate that presented a strong crystallographic texture. The welds were characterized in terms of microstructure using electron backscatter diffraction and hardness measurements. The microstructural gradients across the weld zone and thermomechanically affected zone of the linear friction welds are discussed in terms of the crystallographic texture, grain shape and hardness levels, relative to the parent material. The location of crack nucleation under fatigue loading was analyzed relative to the local microstructural features and hardness gradients. Though crack nucleation was not observed within the weld or thermomechanically affected zones, its occurrence within the base material in LCF appears to be affected by the welding process. In particular, by performing high resolution digital image correlation during LCF, the crack nucleation site was related to the local accumulation of plastic deformation in the vicinity of the linear friction weld.     

Correlation between crack length and load drop for low-cycle fatigue crack growth in Ti-6242

For low-cycle fatigue tests with smooth bars the number of cycles to initiation is commonly defined from a measured relative drop in maximum load. This criterion cannot be directly related to the crack length, which is the actual measure of interest. In order to establish a relation between load drop and crack length for the high strength titanium alloy Ti-6242, this investigation compares data from controlled low-cycle fatigue crack growth tests and numerical simulations of these tests. To achieve sufficient accuracy in this relation, focus is given to modelling of mean stress relaxation. Three constitutive models, the Chaboche, the Ohno–Wang and the Chaboche with threshold, are evaluated with respect to experiments. Furthermore, a straightforward method with cycle-scaling of the material parameters are used to efficiently reduce calculation cost. It is shown that it is possible to determine the relationship between load drop and crack length from numerical simulations, provided that care is taken to relevant aspects of the materials stress–strain response. These results are also used to numerically evaluate the effect on load drop of the extensometer position relative to the crack.     

Crystal plasticity finite‐element modelling of cyclic deformation and crack initiation in a nickel‐based single‐crystal superalloy under low‐cycle fatigue

Nickel‐based single‐crystal superalloys are predominantly used for turbine blades in aircraft engines and land‐based gas turbines. Understanding and predicting the fatigue failure of Ni‐based single‐crystal superalloys are critical to ensure the safety of these components during operation. In this paper, low‐cycle fatigue experiments were carried out to investigate cyclic deformation of a nickel‐based single‐crystal superalloy MD2, recently developed by GE Power, with different crystallographic orientations. Specialty in situ scanning electron microscope (SEM) tests were also conducted to study the slip‐controlled initiation of short cracks under low‐cycle fatigue. In particular, the stress–strain response for both [001] and [111] orientations was used to calibrate a crystal plasticity model, which allowed us to simulate the activation of crystallographic slip systems and predict the initiation of short fatigue crack. Using the accumulated shear strain as a criterion, the simulations confirmed that the slip system with the maximum accumulated shear strain appeared to control the crack initiation. The location and direction of slip traces and short cracks, captured by the crystal plasticity finite‐element simulations, agreed with the in situ SEM observations. The modelling tool will be valuable for assessing the structural integrity of critical gas turbine blades.     

Microplasticity in HCF of Ti–6Al–4V

Previous research has shown that Ti–6Al–4V exhibits pronounced stress ratio effects under high cycle fatigue (HCF) loading. At high stress ratios (R>0.7), a transition of failure mode occurs from traditional surface fatigue crack initiation and growth to bulk-dominated damage initiation and coalescence of multiple microcracks consistent with a ductile tensile test. At these high stress ratios, ratchetting was shown to occur (Int. J. Fatigue 21 (1999) 679; Mech. Time-Dependent Mater. 2 (1999) 195), leading to progressive strain accumulation until final failure. This study explores the microstructural origins of this stress ratio transition in HCF using computational micromechanics. The material being studied is a two-phase Ti–6Al–4V plate forging, consisting of a duplex microstructure with a hexagonal close-packed (hcp) α-phase and lamellar grains with layers of body-centered cubic (bcc) β-phase and secondary hcp α-phase. Crystallographic slip is the dominant mode of plastic deformation in this material. A 2-D crystal plasticity model that incorporates nonlinear kinematic and isotropic hardening at the slip system level is implemented into the finite element method to simulate the cyclic plasticity behavior. The finite element model is used to qualitatively understand the distribution of microplasticity in this alloy under various loading conditions. For typical HCF stress amplitudes, it is shown that microstructure scale ratchetting becomes dominant at R=0.8, but is insignificant at R=0.1 and 0.5. Reversed cyclic microplasticity is insignificant at all three stress ratios. The effects of phase morphology and orientation distribution are shown to affect the microscale plastic strain distribution in terms of the location and magnitudes of the plastic shear bands that form within clusters or chains of primary α grains. The results of the finite element modeling are also considered in light of previous experimental results.     

A model for short crack propagation in polycrystalline materials

A model for microstructurally short crack propagation in a grain structure of a polycrystalline material is developed. The crack propagation model is based on a crystal plasticity model and a microstructurally short crack propagation model in the spirit of the model by Navarro and de los Rios [A model for short fatigue crack propagation with an interpretation of the short-long crack transition. Fatigue Fract Eng Mater Struct 1987;10:169-86]. Numerical examples, where the combined crystal plasticity and crack propagation model is implemented in a model of a microstructure representing a duplex stainless steel, concludes the paper. Results showing how the misorientation of the crack- and slip-directions between two adjacent austenitic grains influences the crack propagation rate, as the crack propagates across their common grain boundary, are given.     

Fretting fatigue crack nucleation in Ti–6Al–4V

Fretting fatigue crack nucleation in Ti?6Al?4V when fretted against itself is investigated to determine the influence of contact pressure, stress amplitude, stress ratio, and contact geometry on the degradation process. For the test parameters considered in this investigation, a partial slip condition generally prevails. The resulting fatigue modifying factors are 0.53 or less. Cycles to crack nucleation, frictional force evolution, crack orientations and their relationship to the microstructure are reported. The crack nucleation process volume is of the same order as the microstructural length scales with several non‐dominant cracks penetrating 50 μm or less. The effective coefficient of friction increases during early part of fretting. Observations suggest that cyclic plastic deformation is extensive in the surface layers and that cyclic ratchetting of plastic strain may play a key role in nucleation of the fretting cracks. A Kitagawa–Takahashi diagram is used to relate the depth of fretting damage to the modifying factor on fatigue life.     

Static recrystallization simulations by coupling cellular automata and crystal plasticity finite element method using a physically based model for nucleation

This study presents a 2D cellular automata simulation of static recrystallization (SRX) arising from the subgrain growth in single-phase material following cold deformation by coupling with a crystal plasticity finite element (CPFE) method. The spatial distribution of the stored deformation energy was obtained by CPFE simulation, based on which the initial deformed microstructure consisting of nonuniformly distributed subgrains was predicted. To simulate grain/subgrain growth during annealing, a curvature-driven mechanism was used, in which the grain/subgrain boundary energy and mobility were misorientation-dependent. On the SRX nucleation, a physically based model using critical subgrain size as criterion was adopted, which could provide better insight into the recrystallization nucleation mechanism involving grain boundary bulging. Simulations under different pre-deformation conditions were performed, and the influence of strain rate and strain on the SRX microstructure evolution and the transformation kinetics were investigated. Results show that deformation at higher strain rate can accelerate the SRX kinetics, and the SRX behavior depends more on the deformation state of individual grain than the nominal strain due to the relatively small computational domain.     

Elastic–plastic fatigue crack growth analysis under variable amplitude loading spectra

Most fatigue loaded components or structures experience a variety of stress histories under typical operating loading conditions. In the case of constant amplitude loading the fatigue crack growth depends only on the component geometry, applied loading and material properties. In the case of variable amplitude loading the fatigue crack growth depends also on the preceding cyclic loading history. Various load sequences may induce different load-interaction effects which can cause either acceleration or deceleration of fatigue crack growth. The recently modified two-parameter fatigue crack growth model based on the local stress–strain material behaviour at the crack tip [1,2] was used to account for the variable amplitude loading effects. The experimental verification of the proposed model was performed using 7075-T6 aluminum alloy, Ti-17 titanium alloy, and 350WT steel. The good agreement between theoretical and experimental data shows the ability of the model to predict the fatigue life under different types of variable amplitude loading spectra.     

A finite element study of microstructure-sensitive plasticity and crack nucleation in fretting

This paper is concerned with finite element modelling of microstructure-sensitive plasticity and crack initiation in fretting. The approach adopted is based on an existing method for microstructure-sensitive (uniaxial) fatigue life prediction, which proposes the use of a unit cell crystal plasticity model to identify the critical value of accumulated plastic slip associated with crack initiation. This approach is successfully implemented here, using a FCC unit cell crystal plasticity model, to predict the plain low-cycle fatigue behaviour of a stainless steel. A crystal plasticity frictional contact model for stainless steel is developed for microstructure-sensitive fretting analyses. A methodology for microstructure-sensitive fretting crack initiation is presented, based on identification of the number of cycles in the fretting contact at which the identified critical value of accumulated plastic slip is achieved. Significant polycrystal plasticity effects in fretting are predicted, leading to significant effects on contact pressure, fatigue indicator parameters and microstructural accumulated slip. The crystal plasticity fretting predictions are compared with J₂ continuum plasticity predictions. It is argued that the microstructural accumulated plastic slip parameter has the potential to unify the prediction of wear and fatigue crack initiation, leading in some cases, e.g. gross slip, to wear, via a non-localised distribution of critical crystallographic slip, and in other cases, e.g. partial slip, to fatigue crack initiation, via a highly-localised distribution of critical crystallographic slip with preferred orientation (cracking locations and directions).     

Prediction of fatigue crack nucleation life in polycrystalline AA7075‐T651 using energy approach

A crystal plasticity (CP) simulation and an energy‐based model is presented to predict the fatigue nucleation onset for polycrystalline AA 7075‐T651. Different microstructure morphology and grain sizes are employed in the simulations. Using a simple method, statistically stored dislocation (SSD) and geometrically necessary dislocation (GND) as decoupled with crystal plasticity model are estimated using a double round‐notch specimen test data, and CP simulation. The dislocation density parameter approximated from plastic energy density, stored energy density, elastic energy and accumulated slip validated with double hole experimental data. Sensitivity analysis is performed with respect to different microstructures and dislocation density parameters. Roughly, maximum 30% difference between experimental nucleation life and the simulated one is observed. The simulated predictions are in fair agreement with test data. The proposed strategy is suitable to study the scatter of fatigue nucleation life.     

Modeling cyclic ratcheting based fatigue life of HSLA steels using crystal plasticity FEM simulations and experiments

This paper develops a plastic ratcheting based fatigue failure model for HSLA steels from a combination of results from experiments and finite element simulations using crystal plasticity constitutive relations. It predicts the nucleation of major cracks in the microstructure in ratcheting. Subsequently, the total life is limited by the growth of ductile fracture in the microstructure, which is factored in by comparing the simulated results with experiments. A crystal plasticity based FEM (CPFEM) model is used in this paper to predict the local plastic strain in the microstructure which plays a role in the ratcheting life. Orientation imaging based microstructural information (orientation and misorientation distributions) is incorporated in CPFEM. The model proposed has the ability to represent a range of behavior from low and high cycle behavior in the life models. The predictions from it are found to be in excellent agreement with experimental data.