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).     

Subsurface crack formation and propagation of fretting fatigue in Ni‐based single‐crystal superalloys

The fretting fatigue crack formation and propagation behaviors of Ni‐based single‐crystal (NBSX) superalloys are investigated in this paper. Subsurface crack formation process is revealed by in situ fretting fatigue experiment. The crack is observed to form on subsurface area, then propagates to the contact surface. Inclusions in materials are found to have obvious effects on crack propagation, and slip lines are closely related to the crack propagation direction. Crystal plastic finite element method (CPFEM) simulation is used to simulate crack formation position. The accumulative plastic strain peaks at the edge of contact zone and the subsurface area. The results show that the CPFEM simulation and in situ observation achieve good agreements.     

Mechanism‐based life model for out‐of‐phase thermomechanical fatigue in single crystal Ni‐base superalloys

This paper describes an enhanced physics‐inspired model to predict the life of the second‐generation single crystal superalloy PWA 1484 experiencing out‐of‐phase (OP) thermomechanical fatigue (TMF). Degradation due to either pure fatigue or a coupling between fatigue and environmental attack are the primary concerns under this loading. The life model incorporates the effects of material anisotropy by utilizing the inelastic shear strain on the slip system having the highest Schmid factor while accounting for the effects of temperature‐dependent slip spacing and stress‐assisted γ′ depletion. Both conventional TMF and special bithermal fatigue (BiF) experiments were conducted to isolate and therefore better understand the interactions between these degradation mechanisms. The influences of crystallographic orientation, applied mechanical strain range, cycle maximum temperature and high temperature hold times were assessed. The resulting physics‐inspired life estimation model for OP TMF and OP BiF predicts the number of cycles to crack initiation as a function of crystal orientation, applied strain amplitude and stresses, temperature, cycle time (including dwells), and surface roughness within a factor of 2.     

Investigation the effect of crystal orientation of nickel‐based single crystal superalloys on bending creep tests

The relationship between the three points bending creep test and the uni‐axial creep test on the single crystal superalloy was investigated by using crystal plasticity slip theory with a three‐dimensional (3D) finite element model. The purpose of the present work is to build the relationship between bending creep and conventional uni‐axial tensile creep in determining crystallographic creep parameters for face centered cubic (FCC) nickel‐based single crystal superalloys. To this aim, the bending creep performed on [001]‐, [011]‐, and [111]‐oriented nickel‐based single crystal superalloys were respectively investigated, and the data was compared with those obtained with uni‐axial tensile creep counterparts. It shows that the determination of crystallographic creep stress exponent is independent of crystallographic orientations, and the results agree reasonably well between bending creep test and uni‐axial tensile creep test. The findings may shed some light on understanding of the crystal structures and its time‐dependent deformation mechanisms with the bending creep method.     

Fatigue crack initiation in AA2024: A coupled micromechanical testing and crystal plasticity study

A new combined experimental and modelling approach has been developed in order to understand the physical mechanisms that lead to crack nucleation in a polycrystalline aluminium alloy AA2024 undergoing cyclic loading. Four‐point bending low‐cycle fatigue tests were performed inside the chamber of a scanning electron microscope on specimens with a through‐thickness central hole, introduced to localize stresses and strains in a small region on the top surface of the sample. Fatigue crack initiation and small crack growth mechanisms were analyzed through high‐resolution scanning electron microscope images, local orientation measurements using electron‐back‐scattered‐diffraction, and local strain measurements using digital image correlation. A crystal plasticity finite element model was developed to simulate the cyclic deformation behaviour of AA2024. Two‐dimensional Voronoi‐based microstructures were generated, and the material parameters for the constitutive equations (including both isotropic and kinematic hardening) were identified using monotonic and fully reversed cyclic tests. A commonly used fatigue crack initiation criterion found in the literature, the maximum accumulated plastic slip, was evaluated in the crystal plasticity finite element model but could not predict the formation of cracks away from the edge of the hole in the deformed specimens. A new criterion combining 2 parameters: The maximum accumulated slip over each individual (critical) slip system and the maximum accumulated slip over all slip systems were formulated to reproduce the experimental locations of crack nucleation in the microstructure.     

Initiation and short crack growth in austenitic–ferritic duplex steel‐effect of positive mean stress

The effect of the mean stress on the crack initiation and short crack growth of austenitic–ferritic duplex steel has been studied. High mean stresses and stress amplitudes result in appreciable mean strain relaxation and long‐term hardening. Mean stress produces unidirectional slip bands and slip steps that serve as nuclei for persistent slip bands and persistent slip markings. It leads to the acceleration of the crack initiation and production of a high density of cracks. Crack linkage contributes to the growth of short cracks. The concept of equivalent crack was used to describe the crack growth. The kinetics of short crack growth with positive mean stress is similar to that in symmetric loading, that is, exponential growth is observed. Positive mean stress results in earlier crack initiation and in the acceleration of the crack growth rate. Both factors contribute to the decrease of the fatigue life.     

The influence of crystal orientations on fatigue life of single crystal cooled turbine blade

A method based on the orthotropic elastic finite element analysis (FEA) has been presented to analyze the fatigue life of cooled turbine blades made of nickel-based single crystal superalloy (SC). Special attention was put on the influence of the crystallographic orientations on the strength and fatigue life of SC cooled turbine blades. It is shown that, due to the influence of the temperature distribution and complexity of cooling tunnel, the place of the maximum resolved shear stress in the blade is not corresponding to the most dangerous place, where results in the minimum fatigue life. For the SC cooled turbine blades studied in the paper, as the same of the most commercial SC blades in the world market, the axial direction is cast to [0 0 1] crystallographic orientation within 15° deviation, and the other two directions are in random. It is found that the randomness of the two directions has only limited influence on the distributions of Mises stress and the maximum resolved shear stress in the blade. But the deviation of the axial direction of the blade has obvious influence on the stress distribution, and the influence of the deviation and randomness orientations on the fatigue life is also obvious. Finally, the benefit of the optimization of the crystallographic orientations of SC cooled turbine blades on the fatigue life is highlighted.     

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.     

Crack tip displacements of microstructurally small cracks in 316L steel and their dependence on crystallographic orientations of grains

The paper presents an analysis of the effect of the grain orientations on a short Stage I surface crack in a 316L stainless steel. The analysis is based on a plane‐strain finite element crystal plasticity model. The model consists of 212 randomly shaped, sized and oriented grains that is loaded monotonically in uniaxial tension to a maximum load of 1.12R_p0.2 (280 MPa). The influence of random grain structure on a crack is assessed by calculating the crack tip opening (CTOD) and sliding displacements (CTSD) for single crystal and polycrystal models, considering also different crystallographic orientations. In the single crystal case the CTOD and CTSD may differ by more than one order of magnitude. Near the crack tip slip is activated on all the slip planes whereby only two are active in the rest of the model. The maximum CTOD is directly related to the largest Schmid factors. For the more complex polycrystal cases it is shown that certain crystallographic orientations result in a cluster of soft grains around the crack‐containing grain. In these cases the crack tip can become a part of the localized strain, resulting in a large CTOD value. This effect, resulting from the overall grain orientations and sizes, can have a greater impact on the CTOD than the local grain orientation. On the other hand, when a localized soft response is formed away from the crack, the localized strain does not affect the crack tip directly, resulting in a small CTOD value. The resulting difference in CTOD can be up to a factor of 4, depending upon the crystallographic set. Grains as far as 6xCracklength significantly influence the crack tip parameters. It was also found that among grains with favourable orientation the CTOD increased with the size of such a grain. Finally, a significant change in CTOD and CTSD was observed when extending the crack into the second grain and placing it in the primary or the conjugate slip plane.     

The influence of grains’ crystallographic orientations on advancing short crack

A model of microstructurally short cracks that accounts for random grain geometry and crystallographic orientations is coupled with crystal plasticity constitutive model. A short crack is then inserted in the slip plane in one of the grains at the model top boundary and extended into one of the available slip planes of the neighboring grain at monotonic remote load of 0.96R_p0.2. Crack tip opening (CTOD) and sliding (CTSD) displacements are then calculated for several different crystallographic orientations and crack lengths. As the crack is contained in a single grain the crystallographic orientation of the neighboring grain can change the crack tip displacements by up to 26%, however, the displacements change by up to a factor of 10, once the crack is extended beyond the grain boundary into the next grain. Significant CTSD values were observed in all the analyzed cases pointing to mixed mode loading. Another important observation is that the random crystallographic orientations of grains beyond the first two crack-containing grains affect the CTOD by a factor of up to 4.4. This effect decreases slightly with increased crack length.     

The effect of material behaviour on the analysis of single crystal turbine blades: Part II – Component analysis

This paper describes the analysis of a turbine blade component using a slip system model developed for modern single‐crystal superalloys. Structural elasto‐viscoplastic calculations are carried out for the component. The emphasis throughout is on the effect of micromechanisms of deformation, accounted for in the material model, on the predicted overall behaviour of the component. With the recent proliferation in detailed material models that are available, it is prudent to take a step back and investigate the implications of such models for component analysis and design. This effect is manifested through the determination of a stabilised and redistributed stress state throughout the component. While some components are creep‐limited in design, many are fatigue‐limited and it is stabilised stresses which control the cyclic life of these components. The accuracy of the material model, incorporating various micromechanisms as a function of stress and temperature, can significantly effect these stabilised stresses. The effect of the crystallographic orientation on blade behaviour is illustrated and the implications of shakedown simulations for fatigue lifing of turbine blades are discussed.     

Investigation on crystallographic behaviors of nickel‐base single crystal alloy cooling holes with different spanwise injection angles

Film cooling as an important thermal protection technology is widely used in aviation and ground gas turbine blades. But film cooling holes reduce the strength of blade seriously, which have become a key region of crack nucleation. In this paper, the plastic behaviors of nickel‐base single crystal alloy turbine cooling holes in spanwise injection angles range from 0° to 40° are investigated on basis of crystallographic constitutive theory. The results show that there are both higher stress regions and lower stress regions around multi‐column cooling holes, where suffer stress interference. The maximum Mises stress occurs at the hole in the center column. The places where the maximum resolved shear stresses occurs change with load and spanwise injection angle. The maximum Mises stress around holes with injection angle of 0° is lowest. With the injection angle increases, the maximum Mises stress increases until injection angles up to 30°. In all the slip systems, the resolved shear stress of hexahedral slip system is most sensitive to the changing of spanwise injection angle and load.     

A modified normal strain ratio fatigue life model based on the hybrid approach of critical plane and crystallographic slip theory

Based on the method combining the critical plane with crystallographic slip theory, an anisotropic low cycle fatigue life model is proposed to reflect the effects of orientation dependence and damage factors on fatigue life. According to this method, the crystallographic slip plane is adopted as the critical plane by searching for 30 potential slip systems. In addition, considering the effects of normal strain and strain ratio on fatigue failure, the normal strain ratio is introduced into model and regression model is obtained by fitting method. The proposed model is verified by estimating the low cycle fatigue lives of single crystal nickel–based superalloys PWA1480, CMSX‐2 and DD3 for different loading conditions. The results show that the proposed model is applicable for more complicated loading situations and give a higher prediction accuracy compared to Sun's model.     

Fatigue behaviour and lifing of two single crystal superalloys

A model has been developed to predict the high temperature cyclic life of single crystal superalloys RR2000 and CMSX-4 under conditions of creep and fatigue. A combined creep–fatigue model is used, although it is found that failure always occurs by creep or fatigue separately, and that creep–fatigue interaction has a minor influence. Microstructural investigation of a series of interrupted high- and low-frequency tests are presented, these are combined with the results of a series of interrupted creep tests to identify the separate and interactive mechanisms of creep and fatigue. When creep damage is present the material behaves homogeneously. Under these conditions crack growth is initiation controlled, the mechanism of failure is surface or casting pore-initiated planar crack growth followed by shear on crystallographic planes. As the temperature is lowered or the cyclic frequency increased, the material behaves less homogeneously and shear bands are formed during cycling. Crack growth under these conditions is again initiation controlled and failure is by rapid crystallographic crack growth along shear bands. Such a failure is a distinct fatigue failure and occurs when little creep damage is present. Under certain cyclic conditions, mainly those where the crystallographic failure mechanism is dominant, the material shows an anomalous increase in fatigue resistance with temperature up to approximately 950 °C. This behaviour has been quantified by relating it to the effect of strain rate and temperature on the yield strength of the material.     

Three-dimensional finite element simulations of microstructurally small fatigue crack growth in 7075 aluminium alloy

Three‐dimensional finite element simulations were performed to study the growth of microstructurally small fatigue cracks in aluminium alloy 7075‐T651. Fatigue crack propagation through five different crystallographic orientations was simulated using crystal plasticity theory, and plasticity‐induced crack opening stresses were calculated. The computed crack opening stresses were used to construct small crack da/dN‐ΔK diagrams. The generated da/dN‐ΔK curves compared well with experimental small crack data from the literature. The variance observed among the da/dN‐ΔK results, which occurred as a consequence of the different crystallographic orientations employed, was found to be of the same order of magnitude as commonly observed variability in small fatigue crack growth data. This suggests that grain orientation is a major contributor to observed small fatigue crack data scatter.     

Effect of high-temperature protective coatings on fatigue lives of nickel-based superalloys

This study concerns MCrAlY coatings (M is Ni, Co or both) sprayed by a vacuum plasma spraying process for protection against high-temperature corrosion and oxidation of gas turbine components, such as turbine blades and duct segments. The effect of high-temperature protective coatings on fatigue lives of nickel-based superalloys were investigated at high temperature under push–pull loading and rotary bending and then compared with uncoated superalloys, such as equiaxed IN738LC, unidirectional solidified CM247LC and single-crystal CMSX-2. The high-cycle fatigue lives of MCrAlY-coated superalloys at high temperature under push–pull loading showed an inferior performance when compared with the uncoated superalloys. This was because the crack initiation site was different. The high-cycle fatigue cracks of nickel-based superalloys initiated at casting cavities which were exposed on the specimen surface, whereas the high-cycle fatigue cracks of MCrAlY-coated specimens initiated at interface defects, such as small pores and grid residue, between the MCrAlY coating and the substrate and grew into the MCrAlY coating, and then into the substrate. Similarly, the rotary bending fatigue properties of MCrAlY-coated superalloys at high temperature showed an inferior performance when compared with the uncoated superalloys. This is because of a high stress due to the higher Young's modulus of the MCrAlY coating (in comparison with the substrate) being induced at the MCrAlY coating surface. The crack initiation site was on the specimen surface in both cases of the nickel-based superalloys and the MCrAlY-coated superalloys, respectively. As a result, it was considered that, for rotary bending tests, the fatigue life reduction was due to the high stress that originated from the difference of elastic constants between the MCrAlY coating and the superalloy. Consequently, in fatigue life design it is necessary to take account of the stress levels in a coating layer.     

Propagation behaviour of microstructural short fatigue cracks in the high-cycle fatigue regime

In the high-cycle fatigue regime, it is assumed that crack initiation mechanisms and short fatigue crack propagation processes govern fatigue life of a component. Moreover, it is now becoming accepted that the conventional fatigue limit does not imply complete reversibility of plastic strain and is connected to crack initiation. However, interaction of the crack tip with microstructural barriers, such as, e.g. grain boundaries or second phases, leads to a decrease and eventually to a stop in the crack propagation. In the present contribution, examples for propagating and non-propagating conditions of short fatigue cracks in the microstructure of a duplex steel are given, quantified by means of automated EBSD. To classify the results within the scope of predicting the service life for HCF- and VHCF-loading conditions, a numerical model based on the boundary element method has been developed, describing crack propagation by means of partially irreversible dislocation glide on crystallographic slip planes in a polycrystalline model microstructure (Voronoi cells). This concept is capable to account for the strong scattering in fatigue life for very small strain amplitudes and to contribute to the concept of tailored microstructures for improved cyclic-loading behaviour.     

The microstructure as crack initiation point and barrier against fatigue damaging

From the emission of dislocations till short crack propagation fatigue is a local process determined by the microstructure. We present experiments based on electron channelling contrast imaging (ECCI) as refined application of the scanning electron microscope (SEM) and new focused ion beam (FIB) technique like FIB crack initiation and FIB tomography which give detailed information about crack initiation and the interaction of short fatigue cracks with precipitates and grain boundaries as microstructural barriers. As main result the characteristic fluctuation in the propagation rate of short fatigue cracks in front of grain boundaries that has so far defied calculation can now be calculated analytically from the BCS-model and Tanaka model by using three constants measured in a single crystal.