Effect of material plasticity on fatigue crack propagation under complex stress state

The maximum energy release rate criterion, i.e., G _max criterion, is commonly used for crack propagation analysis. However, this fracture criterion is based on the elastic macroscopic strength of materials. In the present investigation, a modification has been made to G _max criterion to implement the consideration of the plastic strain energy. This criterion is extended to study the fatigue crack growth characteristics of mixed mode cracks in steel pipes. To predict crack propagation due to fatigue loads, a new elasto-plastic energy model is presented. This new model includes the effects of material properties like strain hardening exponent n, yield strength σ_y and fracture toughness and stress intensity factor ranges. The results obtained are compared with those obtained using the commonly employed crack growth law and the experimental data.     

Influence of effective stress intensity factor range on mixed mode fatigue crack propagation

ABSTRACT The behaviour of fatigue crack propagation of rectangular spheroidal graphite cast iron plates, each consisting of an inclined semi‐elliptical crack, subjected to axial loading was investigated both experimentally and theoretically. The inclined angle of the crack with respect to the axis of loading varied between 0° and 90°. In the present investigation, the growth of the fatigue crack was monitored using the AC potential drop technique, and a series of modification factors, which allow accurate sizing of such defects, is recommended. The rate of fatigue crack propagation db/dN is postulated to be a function of the effective strain energy density factor range, ΔS_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The mixed mode crack growth criterion is discussed by comparing the experimental results with those obtained using the maximum stress and minimum strain energy density criteria. The threshold condition for nongrowth of the initial crack is established based on the experimental data.     

Crack growth prediction and non-linear analysis for an elasto-plastic solid

In this paper, a variable radius for the plastic zone is introduced and a maximum principal stress criterion is proposed for the prediction of crack initiation and growth. It is assumed that the direction of crack initiation coincides with the direction of the maximum principal stress. The von Mises yield criterion is applied to define the plastic zone, instead of assuming a plastic zone with a constant distance r from the crack tip. An improvement is made to this fracture criterion, and the criterion is extended to study the crack growth characteristics of mixed mode cracks. Based on the concept of frictional stress intensity factor, k_f, the rate of fatigue crack propagation, db/dN, is postulated to be a function of the effective stress intensity factor range, Δk_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The proposed crack growth model is discussed by comparing the experimental results with those obtained using the maximum principal stress criterion.     

Fracture indentation beneath flat and spherical punches

The mechanics of crack initiation and propagation beneath an axisymmetric flat punch are investigated. The stress tensor given by Sneddon in 1946 is described. Numerical integration along stress trajectories gives the strain energy release rate as a function of both the crack length and its position relative to the indenter. Comparison with Hertzian fracture is made. The initiation of crack outside the circle of contact is shown to be due to the steepest gradient of stresses along the flaws near the circle of contact. The meaning of Auerbach's law is discussed. The Auerbach range is shown to correspond to the relatively flat maximum of the envelope of theG againstc/a curves for various starting radii. The influence of subcritical crack growth is also discussed. The model proposed in 1978 by Maugis and Barquins for kinetics of crack propagation between punches and viscoelastic solids is used. It is assumed that the static fatigue limit corresponds to the true Griffith criterion with intrinsic surface energy , and that the critical strain energy release rateG _c corresponds to a criterion for crack speed instability and velocity jump, so that no stress corrosion is needed to explain subcritical crack growth for 2<G<G _c. The 1971 experimental results of Mikosza and Lawn are easily interpreted by this model. Finally, experiments performed on a borosilicate glass give results that agree satisfactorily with the theory. Due to kinetic effects, an apparent surface energy of about 4.5 J m^–2 is obtained, larger than the intrinsic surface energy and slightly lower than the fracture energy derived from high-speed experiments.     

Fatigue crack growth model for constant amplitude loading

A fatigue crack growth model under constant amplitude loading has been developed considering energy balance during growth of the crack. The plastic energy dissipated during growth of a crack within cyclic plastic zone and area below cyclic stress–strain curve was used in the energy balance. The near crack tip elastic–plastic stress and strain were calculated on the basis of Hutchinson, Rice and Rosengren (HRR) formulations. Fatigue crack growth rate in linear and near threshold region of da/dN versus ΔK curve can be determined on the basis of the proposed model in terms of low cycle fatigue (LCF) properties determined on smooth specimen. The predictions of the model have been compared with the experimental and theoretical results available in the literature using mechanical and fatigue properties. The model compares well in the threshold and intermediate region of the da/dN versus ΔK curve for wide range of material tested.     

A two parameter driving force for fatigue crack growth analysis

A model for fatigue crack growth (FCG) analysis based on the elastic–plastic crack tip stress–strain history was proposed. The fatigue crack growth was predicted by simulating the stress–strain response in the material volume adjacent to the crack tip and estimating the accumulated fatigue damage. The fatigue crack growth was regarded as a process of successive crack re-initiation in the crack tip region. The model was developed to predict the effect of the mean stress including the influence of the applied compressive stress. A fatigue crack growth expression was derived using both the plane strain and plane stress state assumption. It was found that the FCG was controlled by a two parameter driving force in the form of: . The driving force was derived on the basis of the local stresses and strains at the crack tip using the Smith–Watson–Topper (SWT) fatigue damage parameter: D=σ_maxΔε/2.The effect of the internal (residual) stress induced by the reversed cyclic plasticity was accounted for the subsequent analysis. Experimental fatigue crack growth data sets for two aluminum alloys (7075-T6 and 2024-T351) and one steel alloy (4340) were used for the verification of the model.     

Role of elasto-plastic analysis under cyclic loading in fatigue crack growth studies

Linear Elastic Fracture Mechanics (LEFM) has been widely used in the past for fatigue crack growth studies, but this is acceptable only in situations which are within small scale yielding (SSY). In many practical structural components, conditions of SSY could be violated and one has to look for fracture criteria based on elasto-plastic analysis. Crack closure phenomenon, one of the most striking discoveries based on inelastic deformations during crack growth, has significant effect on fatigue crack growth rate. Numerical simulation of this phenomenon is computationally intensive and involved but has been successfully implemented. Stress intensity factors and strain energy release rates lose their meaning,J-integral (or its incremental) values are applicable only in specific situations, whereas alternate path independent integrals have been proposed in the literature for use with elasto-plastic fracture mechanics (EPFM) based criteria. This paper presents certain salient features of two independent finite element (numerical) studies of relevance to fatigue crack growth, where elasto-plastic analysis becomes significant. These problems can only be handled in the current day computational environment, and would have been only a dream just a few years ago. The work presented in this paper is supported by sponsored research projects of the Aeronautics R & D Board, Government of India and their support is acknowledged.     

Prediction of fatigue crack growth under constant amplitude loading and a single overload based on elasto-plastic crack tip stresses and strains

It is generally accepted that the fatigue crack growth (FCG) depends mainly on the stress intensity factor range (ΔK) and the maximum stress intensity factor (K_max). The two parameters are usually combined into one expression called often as the driving force and many various driving forces have been proposed up to date. The driving force can be successful as long as the stress intensity factors are appropriately correlated with the actual elasto-plastic crack tip stress-strain field. However, the correlation between the stress intensity factors and the crack tip stress-strain field is often influenced by residual stresses induced in due course.A two-parameter (ΔK_tot, K_max,tot) driving force based on the elasto-plastic crack tip stress-strain history has been proposed. The applied stress intensity factors (ΔK_appl, K_max,appl) were modified to the total stress intensity factors (ΔK_tot, K_max,tot) in order to account for the effect of the local crack tip stresses and strains on fatigue crack growth. The FCG was predicted by simulating the stress-strain response in the material volume adjacent to the crack tip and estimating the accumulated fatigue damage. The fatigue crack growth was regarded as a process of successive crack re-initiations in the crack tip region. The model was developed to predict the effect of the mean and residual stresses induced by the cyclic loading. The effect of variable amplitude loadings on FCG can be also quantified on the basis of the proposed model. A two-parameter driving force in the form of: was derived based on the local stresses and strains at the crack tip and the Smith-Watson-Topper (SWT) fatigue damage parameter: D = σ_maxΔε/2. The effect of the internal (residual) stress induced by the reversed cyclic plasticity manifested itself in the change of the resultant (total) stress intensity factors controlling the fatigue crack growth.The model was verified using experimental fatigue crack growth data for aluminum alloy 7075-T6 obtained under constant amplitude loading and a single overload.     

Modeling of fatigue crack growth threshold development for a microstructurally small crack

A method for predicting the fatigue crack growth threshold using finite element analysis is investigated. The proposed method consists of monitoring the plastic strain hysteresis energy dissipation in the crack tip plastic zone, with the threshold being defined in terms of a critical value of this dissipated energy. Two-dimensional plane-strain elastic-plastic finite element analyses are conducted to model fatigue crack growth in a middle-crack tension M(T) specimen. A single-crystal constitutive relationship is employed to simulate the anisotropic plastic deformation near the tip of a microstructurally small crack without grain boundary interactions. Variable amplitude loading with a continual load reduction is used to generate the load history associated with fatigue crack growth threshold measurement. Load reductions with both constant load ratio R and constant maximum stress intensity K_max are simulated. In comparison with a fixed K_max load reduction, a fixed R load reduction is predicted to generate a 35% to 110% larger fatigue crack growth threshold value.     

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.     

基于材料低周疲劳的裂纹扩展预测模型

该文基于疲劳裂纹尖端循环应力-应变场, 定义了基于应变幅的平均单位循环损伤参量D, 并引入Miner累积损伤率, 从而从理论上建立起材料低周疲劳性能和疲劳裂纹扩展行为之间的联系。以裂尖扩展方向上的单调塑性区尺寸作为疲劳过程区大小, 并提出了基于弹塑性应变疲劳累积损伤的疲劳裂纹扩展预测模型。模型改进了前人提出的疲劳裂纹扩展预测模型, 考虑了单调塑性区内所有材料的弹塑性应变疲劳损伤贡献;模型中参数均有物理意义, 不需要人为调试。基于完成的Cr2Ni2MoV 材料的低周疲劳结果所建立的该文新模型对该材料裂纹扩展速率的预测结果与实验结果有良好一致性。并且, 借助手册数据, 在TC4钛合金材料上进一步得到了验证。     

Mode I fatigue crack growth under biaxial loading

This paper is centred on the role of the T-stress during mode I fatigue crack growth. The effect of a T-stress is studied through its effect on plastic blunting at crack tip. As a matter of fact, fatigue crack growth is characterized by the presence of striations on the fracture surface, which implies that the crack grows by a mechanism of plastic blunting and re-sharpening (Laird C. The influence of metallurgical structure on the mechanisms of fatigue crack propagation. In: Fatigue crack propagation, STP 415. Philadelphia: ASTM; 1967. p. 131–68 [8]). In the present study, plastic blunting at crack tip is a global variable ρ, which is calculated using the finite element method. ρ is defined as the average value of the permanent displacement of the crack faces over the whole K-dominance area. The presence of a T-stress modifies significantly the evolution of plastic deformation within the crack tip plastic zone as a consequence of plastic blunting at crack tip. A yield stress intensity factor K_Y is defined for the cracked structure, as the stress intensity factor for which plastic blunting at crack tip exceeds a given value. The variation of the yield stress intensity factor was studied as a function of the T-stress. It is found that the T-stress modifies significantly the yield point of the cracked structure and that the yield surface in a (T, K_I) plane is independent of the crack length. Finally, a yield criterion is proposed for the cracked structure. This criterion is an extent of the Von-Mises yield criterion to the problem of the cracked structure. The proposed criterion matches almost perfectly the results obtained from the FEM. The evolution of the yield surface of the cracked structure in a (T, K_I) plane was also studied for a few loading schemes. These results should develop a plasticity model for the cracked structure taking into account the effect of the T-stress.     

Simulation of Fatigue Crack Propagation in Ductile Metals by Blunting and Re-sharpening

Laird and Smith [(1962). Philosophical Magazine 8, 847–857] proposed a plastic sliding-off mechanism for the stage II fatigue crack growth via striation formation. In their view, the fatigue crack extension results solely from the changing character of deformation at the crack tip during loading and unloading. In particular, the crack tip blunts during the loading stage and folds into a double notch during the unloading stage, resulting in striation formation. In order to verify Laird’s plastic blunting mechanism for ductile polycrystals as well as for ductile fcc single crystals, FE calculations were performed for a rectangular plate with an initially sharp crack under plane strain conditions. The plate was subjected to a fully reversed tension-to-pressure cyclic load perpendicular to the crack plane (Mode 1). In the single crystal case the crack propagation simulations were carried out for cracks with crack plane (001) for two different crack growth orientations [110] and [100]. No initial radius for the crack tip was assumed. The actual shape of the crack tip followed from an initially sharp crack by repeated remeshing. To model the constitutive behavior typical for polycrystalline ductile metals, J₂ hypo-elasto-plasticity model with Armstrong–Frederick kinematic hardening was used. To model the constitutive behavior typical for ductile fcc single crystals, a geometrically nonlinear version of Cailletaud’s model based on the multiplicative elasto-plastic decomposition of the deformation gradient was implemented into the FE program ABAQUS. For simplicity, only octahedral slip systems were considered. Using repeated remeshing for severely distorted elements at the advancing crack tip, deformation patterns in the sense of Laird’s mechanism for fatigue crack propagation with striation formation were obtained in the case of the polycrystal simulation as well as in the case of the single crystal simulation for [110] crack growth direction. The simulation for [100] crack growth direction with the same stress level as for [110] direction also yielded crack extension by progressive large deformations but without striation formation. The dependence of the fatigue striation formation on the crack growth direction as predicted by the simulation of crack propagation in single crystals is verified by the experimental results of Neumann [(1974). Acta Metallurgica 22, 1155–1165] on pure copper single crystals.     

A study of fatigue crack growth from artificial corrosion pits at welded joints under complex stress fields

The paper studies the effects of artificial corrosion pits and complex stress fields on the fatigue crack growth of full penetration load‐carrying fillet cruciform welded joints with 45° inclined angle. Parameters of fatigue crack growth rate of welded joints are obtained from S‐N curves under different levels of corrosion. A numerical method is used to simulate fatigue crack growth using different mixed mode fatigue crack growth criteria. Using polynomial regression, the crack shape correction factor of welded joints is fitted as a function of crack depth ratios. Because the maximum circumferential stress criterion is simple and easy to use in practice, fatigue crack growth rate is modified using this criterion. The relationship of effective stress intensity factor, crack growth angle and crack depth is studied under different corrosion levels. The simulated crack growth path obtained from the numerical method is compared with the actual crack growth path observed by fatigue tests. The results show that fatigue cracks do not initiate at the edge or bottom of pits but at the weld toes where the maximum stress occurs. The artificial corrosion pits have little effect on the effective stress intensity factor ranges and crack growth angle. The fatigue crack growth rates of welded joints with pits 1 and 2 are 1.15 times and 1.40 times larger than that of the welded joint with no pit, respectively. The simulated crack growth path agrees well with the actual one. The fatigue life prediction accuracy using the modified formulation is improved by about 18%. The crack shape correction factor obtained using the maximum circumferential stress criterion is recommended being used to calculate fatigue life.     

Mapping and load response of overload strain fields: Synchrotron X-ray measurements

High energy synchrotron X-ray diffraction measurements have been performed to provide quantitative microscopic guidance for modeling of fatigue crack growth. Specifically we report local strain mapping, along with in situ loading strain response, results on 4140 steel fatigue specimens exhibiting the crack growth retardation “overload effect”. Detailed, 2D, ε_yy-strain field mapping shows that a single overload (OL) cycle creates a compressive strain field extending millimeters above and below the crack plane. The OL strain field structures are shown to persist after the crack tip has grown well beyond the OL position. The specimen exhibiting the maximal crack growth rate retardation following overload exhibits a tensile residual strain region at the crack tip. Strain field results, on in situ tensile loaded specimens, show a striking critical threshold load, F_c, phenomenon in their strain response. At loads below F_c the strain response is dominated by a rapid suppression of the compressive OL feature with modest response at the crack tip. At loads above F_c the strain response at the OL position terminates and the response at the crack tip becomes large. This threshold load response behavior is shown to exhibit lower F_c values, and dramatically enhanced rates of strain change with load as the crack tip propagates farther beyond the OL position. The OL strain feature behind the crack tip also is shown to be suppressed by removing the opposing crack faces via an electron discharge cut passing through the crack tip. Finally unique 2D strain field mapping (imaging) results, through the depth of the specimen, of the fatigue crack front and the OL feature in the wake are also presented.     

AN ANALYSIS OF LOW CYCLE FATIGUE BASED ON HYSTERESIS ENERGY

Abstract— Cyclic deformation behaviour of medium carbon steel, armco iron and copper has been investigated. A model based on the energy absorbed for the fracture process at the crack tip, given in the form (Δw*_p)^y where Δw*_p is the hysteresis energy at the crack front and the exponent y decides the energy spent for the fracture process, is proposed for the crack growth in low cycle fatigue. The value of the exponent y has been found to be around 0·26 to 0·28 for medium carbon steel and armco iron and around 0·52 for copper. These values of y give good prediction of the relations between the total fracture energy and the stress amplitude and the total fracture energy versus the fatigue life. The energy based approach has been extended to predict the cumulative damage in a single step stress variation. Good correlation has been obtained between the experimental data and the theoretical prediction.     

High cycle fatigue mechanisms in a cast AM60B magnesium alloy

ABSTRACT We examine micromechanisms of fatigue crack initiation and growth in a cast AM60B magnesium alloy by relating dendrite cell size and porosity under different strain amplitudes in high cycle fatigue conditions. Fatigue cracks formed at casting pores within the specimen and near the surface, depending on the relative pore sizes. When the pore that initiated the fatigue crack decreased from approximately 110 µm to 80 µm, the fatigue life increased two times. After initiation, the fatigue cracks grew through two distinct stages before final overload specimen failure. At low maximum crack tip driving forces (K_max < 2.3 MPa√m), the fatigue crack propagated preferentially through the α‐Mg dendrite cells. At high maximum crack tip driving forces (K_max > 2.3 MPa√m), the fatigue crack propagated primarily through the β‐Al₁₂Mg₁₇ particle laden interdendritic regions. Based on these observations, any proposed mechanism‐based fatigue model for cast Mg alloys must incorporate the change in growth mechanisms for different applied maximum stress intensity factors, in addition to the effect of pore size on the propensity to form a fatigue crack.     

Fatigue delamination growth rates and thresholds of composite laminates under mixed mode loading

The effect of delamination resistance on fatigue crack growth behavior of composite laminates is studied. The strain energy release rate normalized to fatigue delamination resistance (G_cf) is proposed as a controlling parameter to evaluate the fatigue crack growth rates and thresholds. Compared to previously developed G_cf determination method, the compliance approach presented in this paper shows obvious advantages, such as no interruption to the fatigue crack growth and independence on the specimen dimensions. Based on this approach, the fatigue delamination growth rates and thresholds of carbon/bismaleimide composite laminates under mixed I/II mode loadings are determined experimentally.     

A strain energy based damage model for fatigue crack initiation and growth

A strain energy based fatigue damage model is proposed which uses the strain energy from applied loads and the strain energy of dislocations to calculate stress-life, strain-life, and fatigue crack growth rates. Stress ratio effects intrinsic to the model are discussed, and parameterized in terms of the Walker equivalent stress and a fatigue crack growth driving force. The method is then validated using a variety of different metals with strain-life data and fatigue crack growth rate data available on the SAE Fatigue Design & Evaluation subcommittee database.     

A model of corrosion fatigue crack growth in ship and offshore steels

A model describing corrosion fatigue crack growth rate da/dN has been proposed. The crack growth rate is assumed to be proportional to current flowing through the electrolyte within the crack during a loading cycle. The Shoji formula for the crack tip strain rate has been assumed in the model. The obtained formula for the corrosion fatigue crack growth rate is formally similar to the author's empirical formulae established previously. The different effects of ΔK and the fatigue loading frequency f on da/dN, in region I as compared to region II of the corrosion fatigue crack growth rate characteristics can be described by a change of one parameter only: the crack tip repassivation rate exponent.