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.     

Analysis of high temperature fatigue crack growth behavior

High temperature fatigue crack growth has been examined in the light of the new concepts developed by the authors. We observe that the high temperature crack growth behavior can be explained using the two intrinsic parameters ΔK and K_max, without invoking crack closure concepts. The two-parameter requirement implies that two driving forces are required simultaneously to cause fatigue cracks to grow. This results in two thresholds that must be exceeded to initiate the growth. Of the two, the cyclic threshold part is related to the cyclic plasticity, while the static threshold is related to the breaking of the crack tip bonds. It is experimentally observed that the latter is relatively more sensitive to temperature, crack tip environment and slip mode. With increasing test temperature, the cycle-dependent damage process becomes more time-dependent, with the effect that crack growth is dominated by K_max. Thus, in all such fracture processes, whether it is an overload fracture or subcritical crack growth involving stress corrosion, sustained load, creep, fatigue or combinations thereof, K_max (or an equivalent non-linear parameter such as J_max) remains as one essential driving force contributing to the final material separation. Under fatigue conditions, cyclic amplitude ΔK (or an equivalent non-linear parameter like ΔJ) becomes the second necessary driving force needed to induce the characteristic cyclic damage for crack growth. Cyclic damage then reduces the role of K_max required for crack growth at the expense of ΔK.     

Analysis of the effects of compressive stresses on fatigue crack propagation rate

In this study, the effects of compressive stresses on the crack tip parameters and its implication on fatigue crack growth have been studied. Elastic–plastic finite element analysis has been used to analyse the change of crack tip parameters with the increase of the applied compressive stress level.The near crack tip opening displacements and the reverse plastic zone size around the crack tip have been obtained. The finite element analysis shows that when unloading from peak tensile applied stress to zero applied stress, the crack tip is still kept open and the crack tip opening displacement gradually decreases further with the applied compressive stress. It has been found that for a tension–compression stress cycle these crack tip parameters are determined mainly by two loading parameters, the maximum stress intensity K_max in the tension part of the stress cycle and the maximum compressive stress σ_maxcom in the compression part of the stress cycle.Based on the two parameters, K_max, and σ_maxcom, a fatigue crack propagation model for negative R ratios only has been developed to include the compressive stress effect on the fatigue crack propagation rate.Experimental fatigue crack propagation data sets were used for the verification of this model, good agreements have been obtained.     

A numerical investigation of 3-D small-scale yielding fatigue crack growth

The 3-D small-scale yielding (SSY) model provides a computational framework to study fatigue crack growth in thin, metallic components (and test specimens) containing an initially sharp, straight-through crack. This work describes a finite element study of plasticity-induced crack closure in the 3-D SSY model under mode I, constant amplitude cyclic loading with a ratio R=K_min/K_max. A purely kinematic hardening model with constant modulus represents the material constitutive behavior. This paper first addresses key computational issues and proposes modeling guidelines leading to 3-D numerical results for fatigue crack growth in SSY that exhibit convergence with mesh refinement. Specifically, computed crack opening loads show an independence of finite element mesh refinement when (a) the plastic zone at peak load encloses more than 10 eight-noded brick elements (b) the reverse plastic zone encloses at least two elements, and (c) the half-thickness has at least five element layers. The paper also describes stress and deformation fields at the crack front for a growing fatigue crack and provides an understanding of localized 3-D effects on the normalized remote opening load value K_op/K_max. In addition, the computational studies demonstrate that the similarity scaling relationship established for R=0 [Roychowdhury and Dodds, Fatigue Fract. Engng. Mater. Struct. (accepted for publication)] also holds for the non-zero ratio R=0.1--a value commonly adopted in experimental programs. In particular, K_op/K_max, at each location along the crack front remains unchanged when the peak load (K_max), thickness (B) and material flow stress (σ₀) all vary to maintain a fixed value of .     

Fatigue and fracture of a 316 stainless steel metal matrix composite reinforced with 25% titanium diboride

Fatigue and fracture mechanisms have been studied in a steel-based metal matrix composite (MMC), comprising a 316L austenitic matrix reinforced with 25 wt.% particulate titanium diboride (TiB₂). The fracture toughness was determined in the as-HIPped condition as being slightly below 30 MPa√m. Fatigue crack growth rates have been determined, and corrected for the effects of crack closure. The fracture surfaces have been studied to determine the mechanisms of damage during crack advance, which are determined as matrix fatigue, reinforcement particle fracture, and ductile rupture of the matrix. We show that the occurrence of damage mechanisms during fatigue of the material is linked to K_max, rather than to ΔK. This is rationalised in terms of a semi-cohesive process zone within the monotonic plastic zone ahead of the crack tip.     

Crack-Tip Stress-Strain Fields During Cyclic Loading and Effect of Overload

Finite-deformation elastoplastic analysis of a plane-strain crack subjected to mode I cyclic loading under small scale yielding was performed. The influence of the load range, load ratio and overload on the crack tip stress-strain field is presented. Two independent parameters of cyclic loading, such as ΔK and K _max, both substantially affect the near tip evolutions of cyclic stresses and plastic strains, in agreement with typical experimental trends of fatigue cracking. This implies that the behaviour of cracks is governed by stress and strain fields ahead of the tip, via their control over the key process variables (damage accumulation and rupture, i.e., bond-breaking), so that the coupled process becomes a two-parameter one in terms of fracture mechanics variables ΔK and K _max.     

Classification of environmentally assisted fatigue crack growth behavior

Fatigue crack growth is represented using fracture mechanics parameters, ΔK and K_max. Environmental effects that depend on time and stress affect the fatigue behavior predominantly through K_max parameter. The superimposed effects of environment and stress are seemingly complex. We have developed a methodology for classifying and separating the effects of environment on fatigue crack growth. A “crack growth trajectory map” is constructed from the behavior of ΔK versus K_max for various constant crack growth rate curves. A “pure fatigue” behavior is defined, in terms of environment-free behavior, such as in high vacuum. Deviation from this “pure fatigue” reference of the trajectory map is associated with either monotonic mode of fracture or to the superimposed environmental effects on crack growth. Using such an approach, called “Unified Damage Approach”, we classify the environmental effects in almost all materials into only five types. Each of these types shows the combination of time and stress affecting the crack tip driving force, and thus ΔK and K_max. The trajectory map depicts the changing material resistance due to the changing crack growth mechanisms with increasing crack growth rate, as reflected in terms of the applied stress intensities, ΔK and K_max. Thus the trajectory map provides a useful tool to separate the contributions from pure fatigue and superimposed monotonic modes and the governing crack growth mechanisms as a function of load-ratio, crack growth rate and environment. Understanding and quantification of the governing mechanisms would help in developing a more fundamental and reliable life prediction method.     

Multiple mechanisms controlling fatigue crack growth

Recognizing that fatigue is a two‐parameter problem requiring two load parameters to define cyclic loads unambiguously, a unified approach has been developed to account for crack growth behaviour in terms of ΔK and K_max . Since both driving forces govern the crack growth rate, any analysis based on either ΔK or K_max will provide only partial information about the fatigue behavior of materials. It is shown that ΔK–K_max plots and the associated crack growth trajectory maps reflect the basic mechanisms that contribute to crack growth in a material. These plots also provide a convenient basis to recognize the changes in the micromechanisms that can occur as a function of load ratio or crack growth rate, or both. Taking examples from the literature, crack growth trajectory maps are provided showing such changes in the governing mechanisms of crack growth. It is shown that the ΔK–K_max approach is not an alternative to crack closure models, but it reflects the intrinsic material behaviour that must be understood before reliable crack prediction models can be developed.     

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.     

Fatigue crack growth of a metastable austenitic stainless steel

The fatigue crack growth behavior of an austenitic metastable stainless steel AISI 301LN in the Paris region is investigated in this work. The fatigue crack growth rate curves are evaluated in terms of different parameters such as the range of stress intensity factor ΔK, the effective stress intensity factor ΔK_eff, and the two driving force parameter proposed by Kujawski K¹.The finite element method is used to calculate the stress intensity factor of the specimens used in this investigation. The new stress intensity factor solution has been proved to be an alternative to explain contradictory results found in the literature.Fatigue crack propagation tests have been carried out on thin sheets with two different microstructural conditions and different load ratios. The influence of microstructural and mechanical variables has been analyzed using different mechanisms proposed in the literature. The influence of the compressive residual stress induced by the martensitic transformation is determined by using a model based on the proposal of McMeeking et al. The analyses demonstrate the necessity of including K_max as a true driving force for the fatigue crack growth. A combined parameter is proposed to explain the effects of different variables on the fatigue crack growth rate curves. It is found that along with residual stresses, the microcracks and microvoids are other factor affecting the fatigue crack growth rate in the steel studied.     

Effect of sudden load decrease on the fatigue crack growth in cold drawn prestressing steel

This paper analyzes the overload retardation effect (ORE) on the fatigue crack growth (FCG) of cold drawn prestressing steel when different loading sequences are used. The ORE is more intense for elevated load decrease or for low initial stress intensity factor (SIF) range ΔK₀. A transient stage can be observed in the Paris curve (da/dN–ΔK) when the K_maxΔK value suddenly decreases, associated with the ORE and with the evolution of the plastic zone and compressive residual stresses near the crack tip. In tests with K_max decrease, a small zone appears related to FCG initiation, with a fatigue fractography resembling the tearing topography surface (TTS) mode, and associated with a decrease of crack tip opening displacement (CTOD).     

Fatigue crack growth resistance of ECAPed ultrafine-grained copper

This work presents the experimental results of fatigue crack growth resistance of ultrafine-grained (UFG) copper. The UFG copper has a commercial purity level (99.90%) and an average grain size of 300 nm obtained by a 8-passes route Bc ECAP process. The fatigue propagation tests are conducted in air, at load ratios R = K_min/K_max varying from 0.1 to 0.7, on small Disk Shaped CT specimens. Both stage I and stage II regime of growth rate are explored. Results are partially in contrast with the few experimental data available in the technical literature, that are by the way about high purity UFG copper. In fact, the present material shows a relatively high fatigue crack resistance with respect to the unprocessed coarse-grained alloy, especially at high values of applied stress intensity factor ΔK. At higher R-ratio a smaller threshold intensity factor is found, together with a lower stage II fatigue crack growth rate. The explanation of such crack growth retardation is based on a diffuse branching mechanism observed especially at higher average ΔK.     

On the dominant role of crack closure on fatigue crack growth modeling

Crack closure is the most used mechanism to model thickness and load interaction effects on fatigue crack propagation. But assuming it is the only mechanism is equivalent to suppose that the rate of fatigue crack growth da/dN is primarily dependent on ΔK_eff=K_max−K_op, not on ΔK. But this assumption would imply that the normal practice of using da/dN×ΔK curves measured under plane-stress conditions (without considering crack closure) to predict the fatigue life of components working under plane-strain could lead to highly non-conservative errors, because the expected fatigue life of “thin” (plane-stress dominated) structures could be much higher than the life of “thick” (plane-strain dominated) ones, when both work under the same stress intensity range and load ratio. However, crack closure cannot be used to explain the overload-induced retardation effects found in this work under plane-strain, where both crack arrest and delays were associated to an increase in ΔK_eff. These results indicate that the dominant role of crack closure in the modeling of fatigue crack growth should be reviewed.     

The effect of mean stress on delay in fatigue crack growth under load stepdown

The effect of mean stress together with decreasing stress range on fatigue crack propagation behaviour in mild steel is investigated. The delay period between crack arrest and reprogation is found to be a function of the maximum stress intensity factor stepdown ration, K_2max/K_1max. Delay only occurs when this ratio is less than unity. For specimen thicknesses of 1.6 to 6.4 mm, non-propagating cracks, where the affected delay cycles are 500 000 cycles or greater, appear to occur when K_2max/K_1max has a value of approximately 0.7 and the stepdown plastic zone size is about half the initial load plastic zone size, which is approximately equal to the affected crack length.     

A unified method of design for fatigue crack growth resistance in structural materials

It is well established that there are two fatigue crack tip driving forces – the cyclic, ΔK, and the static, K_max. In this study, the effects of each crack tip driving force on crack growth were evaluated for various structural materials. A unified method of design that allows for predicting the response of long and physically small fatigue cracks at positive stress ratios is introduced. Good agreement between predicted and experimental long and physically small fatigue crack growth data was obtained. The importance of this method in material and component design is discussed as part of a contemporary design philosophy.     

Plastic mismatch effect on plasticity induced crack closure: Fatigue crack propagation perpendicularly across a plastically mismatched interface

In the present work, comprehensive investigation of both theoretical analysis and numerical simulation was carried out to investigate the plastic mismatch effect on plasticity induced crack closure (PICC) behavior and effective fatigue crack tip driving force. During the process of crack tip approaching interface, crack tip load and crack tip load ratio will change, resulting in the change of PICC degree. When the crack propagates towards higher strength side, K_op/K_max increases; when the crack propagates towards lower strength side, K_op/K_max decreases firstly and then increases. The two mechanisms of “interface plastic mismatch effect on nominal fatigue crack tip driving force” and “interface plastic mismatch effect on PICC degree” were compared. The second mechanism must be considered when building crack tip driving force model for describing fatigue crack crossing plastically mismatched interface, because it is more physically factual and maybe more important than the first mechanism.     

Crack closure under high load-ratio conditions for Inconel-718 near threshold behavior

Fatigue-crack-growth (FCG) rate tests were conducted on compact specimens made of an Inconel-718 alloy to study the behavior over a wide range in load ratios (0.1 ? R ? 0.95) and a constant K_max test condition. Previous research had indicated that high R (>0.7) and constant K_max test conditions near threshold conditions were suspected to be crack-closure-free and that any differences were attributed to K_max effects. During a test at a load ratio of 0.7, strain gages were placed near and ahead of the crack tip to measure crack-opening loads from local load-strain records during crack growth. In addition, a back-face strain (BFS) gage was also used to monitor crack lengths and to measure crack-opening loads from remote load-strain records during the same test. The BFS gage indicated that the crack was fully open (no crack closure), but the local load-strain records indicated significant amounts of crack closure. The crack-opening loads were increasing as the crack approached threshold conditions at R = 0.7. Based on these measurements, crack-closure-free FCG data (ΔK_eff against rate) were calculated. The ΔK_eff-rate data fell at lower ΔK values and higher rates than the constant K_max test results. In addition, constant R tests at extremely high R (0.9 and 0.95) were also performed and compared with the constant K_max test results. The constant R test results at 0.95 agreed well with the ΔK_eff-rate data, while the R = 0.9 data agreed well with constant K_max test data in the low-rate regime. These results imply that the R = 0.7 test had a significant amount of crack closure as the threshold was approached, while the R = 0.9 and K_max test results may have had a small amount of crack closure, and may not be closure free, as originally suspected. Under the high load-ratio conditions (R ? 0.7), it is suspected that the crack surfaces are developing debris-induced crack closure from contacting surfaces, which corresponded to darkening of the fatigue surfaces in the near-threshold regime. Tests at low R also showed darkening of the fatigue surfaces only in the near-threshold regime. These results suggest that the ΔK_eff against rate relation may be nearly a unique function over a wide range of R in the threshold regime.     

Limitations of elastic definitions in Al-Si-Mg cast alloys with enhanced plasticity: linear elastic fracture mechanics versus elastic-plastic fracture mechanics

Linear elastic fracture mechanics describes the fracture behavior of materials and components that respond elastically under loading. This approach is valuable and accurate for the continuum analysis of crack growth in brittle and high strength materials; however it introduces increasing inaccuracies for low-strength/high-ductility alloys (particularly low-carbon steels and light metal alloys). In the case of ductile alloys, different degrees of plastic deformation precede and accompany crack initiation and propagation, and a non-linear ductile fracture mechanics approach better characterizes the fatigue and fracture behavior under elastic-plastic conditions.To delineate plasticity effects in upper Region II and Region III of crack growth an analysis comparing linear elastic stress intensity factor ranges (ΔK_el) with crack tip plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) is presented. To compute plasticity corrected stress intensity factor ranges (ΔK_pl), a new relationship for plastic zone size determination was developed taking into account effects of plane-strain and plane-stress conditions (“combo plastic zone”). In addition, for the upper part of the fatigue crack growth curve, elastic-plastic (cyclic J based) stress intensity factor ranges (ΔK_J) were computed from load-displacement records and compared to plasticity corrected stress intensity factor ranges (ΔK_pl). A new cyclic J analysis was designed to compute elastic-plastic stress intensity factor ranges (ΔK_J) by determining cumulative plastic damage from load-displacement records captured in load-control (K-control) fatigue crack growth tests. The cyclic J analysis provides the true fatigue crack growth behavior of the material. A methodology to evaluate the lower and upper bound fracture toughness of the material (J_IC and J_max) directly from fatigue crack growth test data (ΔK_FT(JIC) and ΔK_FT(Jmax)) was developed and validated using static fracture toughness test results. The value of ΔK_FT(JIC) (and implicitly J_IC) is determined by comparing the plasticity corrected elastic fatigue crack growth curve with the elastic-plastic fatigue crack growth curve. A most relevant finding is that plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) are in remarkably good agreement with cyclic J analysis results (ΔK_J), and provide accurate plasticity corrections up to a ΔK corresponding to J_IC (i.e. ΔK_FT(JIC)). Towards the end of the fatigue crack growth test (above ΔK_FT(JIC)) when plasticity is accompanied by significant tearing, the cyclic J analysis provides a more accurate way to capture the true behavior of the material and determine ΔK_FT(Jmax). A procedure to decouple and partition plasticity and tearing effects on crack growth rates is given.Three cast Al-Si-Mg alloys with different levels of ductility, provided by different Si contents and heat treatments (T61 and T4) are evaluated, and the effects of crack tip plasticity on fatigue crack growth are assessed. Fatigue crack growth tests were conducted at a constant stress ratio, R = 0.1, using compact tension specimens.     

On assumptions associated with ΔKeff and their implications on FCG predictions

In this paper, an assessment of commonly used assumptions associated with ΔK_eff and their implications on FCG predictions in light of existing experimental and numerical data is presented. In particular, the following assumptions are examined: (1). ΔK_eff fully describes cyclic stresses and strains at the crack-tip vicinity. (2). K_op can be determined experimentally or numerically with certain accuracy. (3). Overload alters K_op but not K_max and associated σ_max at the crack-tip ‘process zone’. (4). Contact of crack faces curtails the crack driving force in terms of ΔK_eff.The analysis indicates that there is insufficient support to justify the above assumptions. In contrary, the analysis demonstrates that a two-parameter fatigue crack driving force in terms of ΔK and K_max, which accounts for both applied and the internal stresses should be used in FCG analyses and predictions.     

Phenomenology of the effective stress intensity related to fatigue crack growth thresholds

The fatigue crack growth threshold conditions for effective stress intensity amplitude are examined using simple phenomenological models for crack face interference and internal stresses. We show that behaviors correlating with all pure fatigue classifications can be generated from a single ‘ideal fatigue’ behavior by accounting for internal stress and crack face interference. The possible threshold or near-threshold manifestations of an intrinsic K_MAX threshold, independent of effective ΔK effects, are discussed.