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.     

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.     

Fatigue crack initiation and growth of 16MnR steel with stress ratio effects

The effects of stress ratio on the fatigue crack initiation and growth were investigated by a newly developed unified model, which is based on the cyclic plasticity property of material and a multiaxial fatigue damage criterion in incremental form. The cyclic elastic-plastic stress-strain field was analyzed using the general-purpose finite element software (ABAQUS) with the implementation of a robust cyclic plasticity theory. The fatigue damage was determined by applying the calculated stress-strain responses to the incremental fatigue criterion. The fatigue crack growth rates were then obtained by the unified model. Six compact specimens with a thickness less than 3.8 mm were used for the fatigue crack initiation and growth testing under various stress ratios (−1.0, 0.05, 0.1, 0.2, 0.3 and 0.5). Finite element results indicated that crack closure occurred for the specimen whose stress ratio was less than 0.3. The combined effects of accumulated fatigue damage induced by cyclic plastic deformation and possible contact of cracked surfaces were responsible for the fatigue crack initiation and growth. The predicted results agreed with the benchmark mode I fatigue crack growth experiments very well.     

Thermodynamic entropy generation in the course of the fatigue crack initiation

Evolution of the thermodynamic entropy generation during fatigue crack initiation life of notched specimens is studied. A set of experimental results of AA7075‐T651 is examined to determine applicability of the thermodynamic entropy generation as an index of fatigue crack initiation. Entropy accumulation is calculated from hysteresis energy and temperature rise. An increasing trend of entropy accumulation with the number of cycle to failure is observed on macroscale measurements. Results also determine that the entropy generations from the samples under the same operating conditions are similar as the crack grows. Scanning electron microscope analysis is performed on the fractured surfaces to observe the fatigue striations, and persistent slip bands are observed employing an optical microscope. A discussion is presented regarding the length scales on which crack initiation occurs and entropy calculation is made.     

Prediction of rubber fatigue life under multiaxial loading

The process of fatigue failure of materials is generally described by two phases: crack initiation and crack propagation. This study concerns the crack initiation in rubbers submitted to a cyclic loading. A parameter based on the strain energy density (SED) and predicting the onset of primary crack and its probable orientation has been identified for such materials according to the investigations of Mars and Fatemi. More precisely, this criterion has been analytically developed in the cases of simple tension, biaxial tension and simple shear loadings by assuming large strains. The results denote the possibility to predict the orientation plane in which the primary crack would be expected to occur in a material. Then, it was implemented in a finite‐elements (FE) program in order to be applied to structures under any kind of the strain states. A good agreement was obtained between FE and analytical results for the usual strain states. Finally, to evaluate lifetime up to crack nucleation, we have achieved a set of experimental fatigue tests using uniaxial tension (UT) and pure shear (PS) test specimens containing a hole in order to localize the crack initiation. The obtained results proved the efficiency of the criterion to describe the fatigue life of rubbers under multiaxial loading.     

A stored energy criterion for fatigue crack nucleation in polycrystals

A series of microstructurally-differing, large-grained, notched, polycrystal BCC ferritic steel bend test samples have been analysed to extract the experimentally observed sites of fatigue crack nucleation together with the numbers of cycles to cause crack nucleation. The samples have been modelled with explicit representation of both grain morphologies and crystallographic orientations using crystal plasticity which has enabled a detailed assessment to be made of key microstructure-level quantities such as accumulated slip, slip rate, and densities of both statistically stored and geometrically necessary dislocations local to the experimentally observed sites of crack nucleation. These quantities when considered independently have not been found to correlate with experimentally observed cycles to nucleation.A new criterion for fatigue crack nucleation has been introduced in which a critical stored energy density, G_c, is argued to be necessary in order for crack nucleation. The rate of stored energy density determined at the sites of crack nucleation has been shown to correlate well with experimental measurement of cycles to nucleation, and the number of cycles to cause fatigue crack nucleation, for the samples for which such measurements are available, is well predicted. The criterion enables prediction of cycles to crack nucleation for all of the experimental samples and has been shown to demarcate correctly the crack nucleation lives observed over the range of differing experimental microstructures.     

Investigation of microstructure effect on fretting fatigue crack initiation using crystal plasticity

The onset of fretting fatigue is characterized by material microstructural changes in which the extent of the damage is comparable to grain size, and hence, the microstructure characteristics could have a significant effect on fatigue crack initiation. In this paper, a three‐dimensional finite element crystal plasticity framework is presented for simulation of the fretting fatigue. Controlled Poisson Voronoi tessellation (CPVT) method is employed to generate the polycrystalline region. In the CPVT method, regularity parameter controls the shape of grains. In this study, the impact of grain size and regularity parameter on crack initiation life and initiation site has been investigated. Cumulative plastic slip was used as a parameter of microstructure‐sensitive fatigue indicator. This parameter could effectively predict the location of crack initiation and its life. The results show that regularity parameter has a significant effect on the location of crack initiation. Furthermore, the effect of grain size on the fretting fatigue life of 316L stainless steel was investigated experimentally through testing different specimens with different grain sizes, to validate the simulation results.     

A Continuum Mechanics Approach for Crack Initiation and Crack Growth Predictions

Very often, different approaches are used for crack initiation and crack growth predictions. The current article introduces a recently developed approach that can be used for the predictions of both crack initiation and crack propagation. A basic assumption is that both crack nucleation and crack growth are governed by the same fatigue damage mechanisms and a single fatigue damage criterion can model both stages. A rule is that any material point fails to form a fresh crack if the total accumulated fatigue damage reaches a limit. For crack initiation predictions, the stresses and strains are obtained either directly from experiments or though a numerical analysis. For the prediction of crack growth, the approach consists of two steps. Elastic‐plastic stress analysis is conducted to obtain the detailed stress‐strain responses. A general fatigue criterion is used to predict fatigue crack growth. Compact specimens made of 1070 steel were experimentally tested under constant amplitude loading with different R‐ratios and the overloading influence. The capability of the approach to predict both crack initiation and the crack growth under these loading conditions was demonstrated by comparing the predictions with the experimental observations.     

Microstructure and load sensitive fatigue crack nucleation in Ti-6242 using accelerated crystal plasticity FEM simulations

This paper investigates microstructure and load sensitive fatigue behavior of Ti-6242 using cyclic crystal plasticity finite element (CPFE) simulations of statistically equivalent image-based microstructures. A wavelet transformation induced multi-time scaling (WATMUS) method [1], [2] is used to perform accelerated cyclic CPFE simulations till crack nucleation, otherwise infeasible using conventional time integration schemes. A physically motivated crack nucleation model in terms of crystal plasticity variables [3] is extended in this work to predict nucleation. The crack nucleation model is based on dislocation pile-up and stress concentration at grain boundaries, caused by inhomogeneous plastic deformation in the polycrystalline microstructure. The model is calibrated and validated with experiments. The dependence of yield strength on the underlying grain orientations and sizes is developed through the introduction of an effective microstructural parameter Plastic Flow Index or PFI. To determine the effects of the microstructure on crack nucleation, a local microstructural variable is defined in terms of the surface area fraction of soft grains surrounding each hard grain or SAFSSG. Simulations with different cyclic load patterns suggest that fatigue crack nucleation in Ti-6242 strongly depends on the dwell cycle hold time at maximum stress.     

Physics‐based multiscale damage criterion for fatigue crack prediction in aluminium alloy

In this paper, a physics‐based multiscale approach is introduced to predict the fatigue life of crystalline metallic materials. An energy‐based and slip‐based damage criterion is developed to model two important stages of fatigue crack initiation: the nucleation and the coalescence of microcracks. At the microscale, a damage index is developed on the basis of plastic strain energy to represent the growing rate of a nucleated microcrack. A statistical volume element model with high computational efficiency is developed at the mesoscale to represent the microstructure of the material. Also, the formation of a major crack is captured by a coalescence criterion at mesoscale. At the macroscale, a finite element analysis of selected test articles including lug joint and cruciform is conducted with the statistical volume element model bridging two scale meshes. A comparison between experimental and simulation results shows that the multiscale damage criterion is capable of capturing crack initiation and predicting fatigue life.     

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.     

Shear mode fatigue crack growth in 1050 aluminium

The shear mode crack growth mechanism in 1050 aluminium was investigated using pre‐cracked specimens. A small blind hole was drilled in the centre section of the specimens in order to predetermine the crack initiation position, and a push–pull fatigue test was used to make a pre‐crack. Crack propagation tests were carried out using both push–pull and cyclic torsion with a static axial load. With push–pull testing, the main crack grew by a mixed mode. It is thus apparent that shear deformation affects the fatigue crack growth in pure aluminium. In tests using cyclic torsion, the fatigue crack grew by a shear mode. The micro‐cracks initiated perpendicular and parallel to the main crack's growth direction during the cyclic torsion tests. However, the growth direction of the main crack was not changed by the coalescence of the main crack and the micro‐cracks. Shear mode crack growth tends to occur in aluminium. The crack growth behaviour is related to a material's slip systems. The number of slip planes in aluminium is smaller than that of steel and the friction stress during edge dislocation motion of aluminium is lower than many other materials. Correlation between the crack propagation rate and the stress intensity factor range was almost the same in both push–pull and cyclic torsion with tension in this study.     

Investigations on the high cycle fatigue behaviour of stir cast AA 6061-SiCp composites

The room temperature high cycle fatigue behaviour of stir cast AA 6061-SiC_p composites, with varying reinforcement percentage, is studied. The specimens were tested under fully reversed cyclic deformation in the peak aged condition. Composite with 20% reinforcement exhibit superior fatigue strength over other composites (with 10,15 and 25% reinforcement). The experimental results are correlated with scanning electron micrographs of the failed specimens. Two distinct morphologies namely, crack initiation/ propagation and fast fracture region, were present. Mode-I type cracking was found to have dominated the crack initiation. The final fracture mode was found to be ductile with nucleation, growth and coalescence of cracks in the matrix.     

A study of crack growth retardation due to artificially induced crack surface contact

The contact of the cracked surfaces during a part of a loading cycle generally results in a reduced crack growth rate. A critical experiment was designed to evaluate the influence of the crack surface contact on crack growth. A round compact specimen made of 1070 steel with a round hole at the wake of the fatigue crack was designed. Two mating wedges were inserted into the hole of the specimen while the external load was kept at its maximum in a loading cycle. In this way, the wedges and the hole in the specimen were in firm contact during the entire loading cycle in the subsequent loading. Experiments showed that the addition of the wedges resulted in a reduction of crack growth rate in the subsequent constant amplitude loading. However, crack growth did not arrest. With the increase in the subsequent loading cycles, crack growth rate increased. The traditional crack closure concept cannot explain the experimental phenomenon because the effective stress intensity factor range was zero after the insertion of the wedges. The detailed stress–strain responses of the material near the crack tip were analyzed by using the finite element method with the implementation of a robust cyclic plasticity theory. A multiaxial fatigue criterion was used to determine the fatigue damage based upon the detailed stresses and strains. The crack growth was simulated and the predicted results were in good agreement with the experimental observations. It was confirmed that the stresses and strains near the crack tip governed cracking behavior. Crack surface contact reduced the crack tip cyclic plasticity and the result was the observed retardation in crack growth.     

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.     

The effect of interference-fit fasteners on the fatigue life of central hole specimens

Fatigue tests were carried out on 2024‐T351, thickness 1.6 mm, central hole specimens containing pins installed with five different interference‐fit levels. Tests clearly demonstrated the beneficial effect of interference fit on fatigue resistance, up to the maximum value examined, 2.5%. A three‐dimensional (3D) finite‐element model was used in order to characterize the stress field around the hole. A large specimen, with a 40‐mm‐diameter hole filled with interference‐fit pin, was instrumented by strain gauges and statically tested in order to check FEM results. A very good correlation existed between measured and numerically evaluated strains. FEM results demonstrated the well‐known effect of interference‐fit fasteners on reducing stress ranges. By increasing the interference level, the stress range was practically unchanged, while the mean stress decreased. Interference‐fit produces a biaxial stress state, which must be taken into account for fatigue evaluation. In the present case, a simple criterion, based on hoop strain, predicted the fatigue results quite well with the exception of open hole fatigue test results, which were overestimated.     

Three-dimensional finite element analysis using crystal plasticity for a parameter study of microstructurally small fatigue crack growth in a AA7075 aluminum alloy

Three-dimensional finite element analysis using a crystal plasticity constitutive theory was performed to understand and quantify various parametric effects on microstructurally small fatigue crack growth in a AA7075 aluminum alloy. Plasticity-induced crack opening stresses (S_o/S_max) were computed, and from these results the crack propagation life N was obtained. A design of experiments (DOE) technique was used to study the influences of seven parameters (maximum load, load ratio, particle modulus, the number of initially active slip systems, misorientation angle, particle aspect ratio, and the normalized particle size) on fatigue crack growth. The simulations clearly showed that the load ratio is the most influential parameter on crack growth. The next most influential parameters are maximum load and the number of initially active slip systems. The particle modulus, misorientation angle, particle aspect ratio, and the normalized particle size showed less influence on crack growth. Another important discovery in this study revealed that the particles were more important than the grain boundaries for inducing resistance for microstructurally small fatigue crack growth.     

Cyclic stress–strain response and crystal plasticity finite element analysis of AISI 9310 steel in biaxial fatigue loading

There are still many gaps in the research on the multiaxial fatigue failure mechanism of the gear shaft. In this paper, cyclic stress–strain response and biaxial fatigue damage characteristics of gear steel AISI 9310 were investigated. The specimens showed obvious cyclic softening characteristics at all phase angles, and the softening rate was directly associated with the initiation and propagation of cracks. The fractographies at different phase angles revealed that the specimens under out-of-phase loading suffered fatigue failure caused by a single crack source on the surface, while the fatigue crack under in-phase loading was gathered together by the propagation of different crack sources. Finally, the established crystal plastic finite element model showed a good prediction of the plastic strain energy density at different phase angles, and the maximum error was 13.03%. Furthermore, a biaxial fatigue life prediction method was proposed, with a maximum error of 39.5%.     

Influence of bulk damage on crack initiation in low‐cycle fatigue of 316 stainless steel

To investigate the effect of bulk damage on fatigue crack initiation, crack initiations due to low‐cycle fatigue of Type 316 stainless steel were observed by electron backscatter diffraction (EBSD) and scanning electron microscopy. The EBSD observations showed that local misorientation developed inhomogeneously due to the cyclic strain, and many cracks were initiated from the slip steps and grain boundaries where the local misorientation was relatively large. The crack initiations could be categorized into two types: enhancement of the driving force by geometrical discontinuity (slip steps and notches), and reduction of material resistance against crack initiation caused by accumulated bulk damage at grain boundaries. In particular, more than half of the cracks were initiated from grain boundaries. However, in spite of the significant bulk damage, the fatigue life was extended by removing the surface cracks under strain of 1 and 2% amplitude. The stress state at the microstructural level was changed by the surface removal, and the damaged portion did not suffer further damage. It was concluded that although bulk damage surely exists, the fatigue life can be restored to that of the untested specimen by removing the surface cracks.