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.     

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 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).     

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.     

Evaluating a strain energy fatigue method using cyclic plasticity models

For the development of constitutive equations that describe the behaviour of materials under cyclic plastic strains, different kinds of formulations can be adopted. Recently, an energy‐based fatigue damage parameter has been developed to present energy‐fatigue life curves using a calculation of the total strain energy. In this study, the damage criterion is examined by calculation of the plastic strain energy from stress–strain hysteresis loops in the cyclic plasticity models under condition of multi‐axial fatigue. These cyclic plasticity models are the Garud multi‐surface model and the Chaboche nonlinear kinematic hardening model. The models are briefly explained and the general features of their computational procedure are presented. Then, the hysteresis loops of these models will be obtained and the fatigue lives are predicted and compared to experimental data by the ratio of predicted life to experimental life. Consequently, a weighting factor on shear plastic work is presented to decrease the life factors.     

Combined hardening and softening constitutive model of plasticity: precursor to shear slip line failure

 In this work, we present a finite element model capable of describing both the plastic deformation which accumulates during the hardening phase as the precursor to failure and the failure process leading to softening phenomena induced by shear slip lines. This is achieved by activating subsequently hardening and softening mechanisms with the localization condition which separates them. The chosen model problem of von Mises plasticity is addressed in detail, along with particular combination of mixed and enhanced finite element approximations which are selected to control the locking phenomena and guarantee mesh-invariant computation of plastic dissipation. Several numerical simulations are presented in order to illustrate the ability of the presented model to predict the final orientation of the shear slip lines for the case of non-proportional loading. Dedicated to the memory of Prof. Mike Crisfield, for his cheerfulness and cooperation as a colleague and friend over many years. This work was supported by the French Ministry of Research and ACI research program. This support is gratefully acknowledged.     

Role of dynamic strain ageing in low cycle fatigue

Low cycle fatigue (LCF) at elevated temperatures is known to be influenced by time-dependent processes like creep, oxidation and metallurgical instabilities. Another time-dependent phenomenon namely, dynamic strain ageing (DSA) has been found to exert an influence on LCF behaviour at high temperatures. Research activities carried out in the present author’s laboratory with a view to understanding the effects of DSA on LCF are highlighted in this paper. Occurrence of DSA manifests during total strain-controlled fatigue tests in the form of serrated plastic flow in stress-strain hysteresis loops, increased cyclic work hardening and reduced plastic strain range. Further, DSA causes localization of plastic flow leading to enhanced planarity of slip and widely-spaced slip bands. Impingement of slip bands on grain boundaries causes increased grain boundary decohesion, leading to reduced fatigue life. The influence of prior microstructure such as second phase particles and grain size on the effects of DSA on LCF is also discussed.     

Fatigue life prediction of copper single crystals using a critical plane approach

A critical plane multiaxial fatigue criterion was employed to predict the fatigue life of copper single crystals. The detailed stress-strain response was obtained through the constitutive modeling using a newly developed crystal plasticity theory. The constitutive model was capable of capturing the major deformation features of copper single crystals under cyclic loading including the cyclic stress-strain curves, cyclic hardening behavior, and the evolution of the hysteresis loops with increasing number of loading cycles. Fatigue life prediction of the single crystal copper was conducted based upon the stress-strain response obtained from the cyclic plasticity model. The fatigue criterion takes into account the plastic strain localization within a single crystal. The critical plane (cracking plane) was identified as the material plane where the fatigue damage accumulation first reached a critical value. For copper single crystals with the crystal orientations being within the standard crystallographic triangle, the fatigue criterion can predict both fatigue life and cracking direction consistent with the experimental observations. More importantly, the constants used in the fatigue criterion were found to be identical to those used for the pure polycrystalline copper with different grain sizes and texture.     

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.     

Effects of grain size on cyclic plasticity and fatigue crack initiation in nickel

Fatigue experiments were conducted on polycrystalline nickel of two grain sizes, 24 and 290 μm, to evaluate the effects of grain size on cyclic plasticity and fatigue crack initiation. Specimens were cycled at room temperature at plastic strain amplitudes ranging from 2.5×10⁻⁵ to 2.5×10⁻³. Analyses of the cyclic stress–strain response and evolution of hysteresis loop shape indicate that the back stress component of the cyclic stress is significantly affected by grain size and plastic strain amplitude, whereas these parameters have little effect on friction stress. A nonlinear kinematic hardening framework was used to study the evolution of back stress parameters with cumulative plastic strain. These are related to substructural evolution features. In particular, long range back stress components are related to persistent slip bands. The difference in cyclic plasticity behavior between the two grain sizes is related to the effect of grain size on persistent slip band (PSB) morphology, and the effect this has on long range back stress. Fine grain specimens had a much longer fatigue life, especially at low plastic strain amplitude, as a result of the influence of grain size on fatigue crack initiation characteristics. At low plastic strain amplitude (2.5×10⁻⁴), coarse grain specimens initiated cracks where PSBs impinged on grain boundaries. Fine grain specimens formed cracks along PSBs. At high plastic strain amplitude (2.5×10⁻³), both grain sizes initiated cracks at grain boundaries.     

The physics of fatigue crack initiation

The fatigue life of a component can be expressed as the sum of two segments of life: (a) the number of loading cycles required to initiate a crack and (b) the number of cycles it takes that crack to propagate to failure. In this review, the primary emphasis is relating the fatigue crack initiation to the microstructure of the material. Many studies have focused on this phenomenon over the years and the goal of this paper is to put this work in perspective and encourage future work of fatigue in polycrystals based on the material’s microstructure. In order to address fatigue, it is necessary to understand the mechanisms that facilitate crack initiation. Slip irreversibilities exist in a material and accumulate during fatigue loading. At the defect level, irreversibilities are a result of dislocations: annihilating, cross-slipping, penetrating precipitates, transmitting through grain boundaries, and piling-up. These slip irreversibilities are the early signs of damage during cyclic loading. The dislocations subsequently form low-energy, stable structures as a means to accommodate the irreversible slip processes and increasing dislocation density during cyclic forward and reverse loading. The result is strain localizing in a small region within the materials, i.e. persistent slip bands and dislocation cells/bundles. Strain localization is a precursor to crack initiation. This review paper will focus on experimental observations of strain localization and the theory and numerical analysis of both slip irreversibilities and low energy configuration defect structures. This fundamental understanding is necessary to study persistent slip bands in FCC metals and alloys including the appropriate characterization, theory, and modeling. From this fundamental knowledge both micromechanical and crystal plasticity models can be used to predict crack initiation, which are also reviewed. Finally, this review ends with a discussion of the future of fatigue modeling and experiments.     

Cyclic stress response and deformation behaviour of precipitation-hardened aluminium-lithium alloys

The cyclic stress response of two lithium-containing aluminium alloys aged to contain ordered precipitates was studied in different environments over a range of plastic strains. The specimens were cycled using tension-compression loading under total strain control. The peak-aged Al---Li---Mn alloy cyclically hardened to failure, whereas the peak-aged Al---Li---Cu alloy displayed softening for most of the fatigue life. The presence of shearable softening for most of the fatigue life. The presence of shearable precipitates in the two alloys results in a local decrease in resistance to dislocation movement, leading to a progressive loss of ordering contributions to hardening and slip concentration. This, coupled with the presence of precipitate free zones, promotes strain localization in intense slip bands and results in early crack nucleation. Transmission electron microscopy observations revealed homogeneous deformation in specimens cycled at high plastic strain amplitudes. However, at lower plastic strain amplitudes, deformation was inhomogeneous in the two alloy systems with the formation of intense planar slip bands. Results of this study reveal that the initial hardening observed is due to dislocation-dislocation and dislocation-precipitate interaction and that the softening observed in the Al---Li---Cu alloy is a mechanical and not an environmental effect.     

基于背应力功的疲劳能量模型及其在轮槽构件寿命预测中的应用

基于局部应力-应变法与疲劳损伤能耗结构,以疲劳过程中背应力塑性功累积为基础,建立了一种新的缺口构件疲劳寿命预测能量模型,并将其应用于某型汽轮机轮槽结构件的疲劳寿命预测.通过与试验结果相比较,初步验证了模型的预测精度(预测寿命与试验寿命误差小于20％).此外,还进一步将上述能量模型与传统疲劳寿命预测能量方法进行了比较.结...     

An investigation on the high stress sensitivity of fatigue life of rolled AZ31 magnesium alloy under constant amplitude fatigue loading

In the present work, an investigation on the high stress sensitivity of the fatigue life of the AZ31 rolled magnesium alloy under constant amplitude fatigue loading has been carried out. Different damage parameters were involved to quantify fatigue damage accumulation at the various scales of material volume corresponding to the changing fatigue damage mechanisms that prevail at the various stages of the fatigue life. The experimental work included mainly nano‐indentation measurements to evaluate hardness evolution at the nano‐scale due to cyclic plasticity, results of micro‐crack monitoring by using the replication technique and fractographic analysis to obtain the fracture characteristics of the fatigue specimens after failure. The hexagonal close‐packed structure of the alloy and the resulting difficulty for the activation of five independent slip systems required for homogeneous plastic deformation were considered to determine the high stress sensitivity of the fatigue life observed for the rolled AZ31 alloy under the investigated loading conditions.     

SMALL FATIGUE CRACKS IN AN AUSTENITIC STAINLESS STEEL

The present study concerns nucleation and growth of small surface cracks during the low-cycle fatigue of a nitrogen-containing austenitic stainless steel. Metallographic replicas as well as longitudinal sectioning were used to record the developing crack pattern on the specimen surface. The influence of grain size and nitrogen content is considered. Small surface cracks are observed after about 10% of the fatigue life. The nucleation of cracks continues until about half of the lifetime, when the crack density saturates. This saturation phenomenon is related to the local unloading effect of growing cracks.
The mean crack length increases continuously as a power-law until specimen failure. However, small grains and a low nitrogen content amplify the effect of crack–grain boundary interactions resulting in an intermediate retardation in growth.
At high nitrogen contents, the crack growth characteristics are very much related to the slip bands formed. This results in a more simultaneous growth of cracks, a more jagged feature of the cracks introducing a higher roughness-induced crack closure effect, and, consequently, better fatigue properties.     

镍基单晶合金多轴非比例加载低周疲劳单胞模型

在680和850℃下对DD3镍基单晶合金进行多轴非比例加载低周疲劳试验,结果表明等效应变范围△ε_e、试验温度、等效应力范围△σ_e对单晶合金的低周疲劳寿命有显著影响。基于能量耗散理论,引入参量k表征多轴非比例加载对疲劳寿命的影响,构造循环塑性应变能作为损伤参量,建立镍基单晶合金低周疲劳寿命预测模型。参量k与循环寿命之...     

一种新的多轴高周疲劳模型

将疲劳强度以上加载等效为塑性应变,建立了塑性应变与加载应力呈线性关系的表达式,由此得到循环加载的塑性应变能。该塑性应变能使材料微观组织结构发生不可逆变化而引起等效宏观应力。假定该应力符合一种特定的分布函数,导出其最大应力与外加应力叠加达到材料本征断裂应力时的裂纹成核寿命,从而并由微裂纹引起上述两部分应力变化,得到继续加载直至宏观裂纹出现的疲劳寿命。所建立的多轴疲劳寿命公式由3个材料参数表达,并通过单轴疲劳试验数据确定。初步研究表明：该模型对所引用的多轴疲劳试验数据有很好的预测能力。     

A MODEL TO PREDICT THE FATIGUE LIFE OF FIBRE-REINFORCED TITANIUM MATRIX COMPOSITES UNDER CONSTANT AMPLITUDE LOADING

A model based on micro-mechanical concepts has been developed for predicting fatigue crack growth in titanium alloy matrix composites. In terms of the model, the crack system is composed of three zones: the crack, the plastic zone and the fibre. Crack tip plasticity is constrained by the fibres and remains so until certain conditions are met. The condition for crack propagation is that fibre constraint is overcome when the stress at the location of the fibre ahead of the crack tip attains a critical level required for debonding. Crack tip plasticity then increases and the crack is able to propagate round the fibre. The debonding stress is calculated using the shear lag model from values of interfacial shear strength and embedded fibre length published in the literature. If the fibres in the crack wake remain unbroken, friction stresses on the crack flanks are generated, as a result of the matrix sliding along the fibres. The friction stresses (known as the bridging effect) shield the crack tip from the remote stress, reducing the crack growth relative to that of the matrix alone. The bridging stress is calculated by adding together the friction stresses, at each fibre row bridging the crack, which are assumed to be a function of crack opening displacement and sliding distance at each row. The friction stresses at each fibre row will increase as the crack propagates further until a critical level for fibre failure is reached. Fibre failure is modelled through Weibull statistics and published experimental results. Fibre failure will reduce the bridging effect and increase the crack propagation rate. Calculated fatigue lives and crack propagation rates are compared with experimental results for three different materials (32% SCS6/Ti-15-3, 32% and 38% SCS6/Ti-6-4) subjected to mode I fatigue loading. The good agreement shown by these comparisons demonstrates the applicability of the model to predict the fatigue damage in Ti-based MMCs.     

Plastic dissipation in mixed-mode fatigue crack growth along plastically mismatched interfaces

A new theory of fatigue crack growth in ductile solids has recently been proposed based on the total plastic energy dissipation per cycle ahead of the crack. This and previous energy based approaches in the literature suggest that the total plastic dissipation per cycle can be closely correlated with fatigue crack growth rates under mode I loading. In a recent paper, the authors have extended the dissipated energy approach to the case of fatigue crack growth in a homogeneous material under sustained mixed-mode loading conditions. The goal of the current study is to further extend the approach to mixed-mode fatigue delamination of ductile interfaces in layered materials. Attention is restricted to material combinations with identical elastic properties, but with mismatches in plastic properties (both yield strength and hardening modulus) across the interface. Such systems can occur in brazing, soldering, welding, and a variety of layered manufacturing applications, where high-temperature material deposition can result in a mismatch in mechanical properties between the deposited material and the substrate. In this study, the total plastic dissipation per cycle is obtained through plane strain elastic–plastic finite element analysis of a stationary crack in a general layered specimen geometry under constant amplitude, mixed-mode loading. Numerical results for a dimensionless plastic dissipation per cycle are presented over the full range of relevant material combinations and mixed-mode loading conditions. Results suggest that while applied mode-mix ratio is the dominant parameter, mismatches in yield strength and hardening modulus can have a significant effect on the total plastic dissipation per cycle, which is dominated by the weaker/softer material.     

Effects of mass layer dimension on a finite quartz crystal microbalance

In this paper, a gradient crystal plasticity model in a polycrystalline grain structure is investigated. Hereby, the focus is on the influence of the grain boundary conditions. A new type of grain boundary conditions is introduced, the so-called micro-flexible boundary condition. In particular, it is compared to existing grain boundary conditions of plastic slip. Numerical results are given for the stress?Cstrain response as well as for the plastic slip field in the grain structure.