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.     

EFFECTS OF AIR AND INERT ENVIRONMENTS ON THE NEAR THRESHOLD FATIGUE CRACK GROWTH BEHAVIOR OF ALLOY 718

The near threshold fatigue crack growth behavior of alloy 718 was studied in air and helium environments at room temperature and at 538°C. Tests were performed at 100 Hz and at load ratios of 0.1 and 0.5. At room temperature and at 538°C, the ΔK_th values in helium were lower than in air. The ΔK_th values in air decreased with increasing load ratio. These results can be explained with a model that involves the accumulation of oxide in the crack which enhances crack closure. In the air tests, the oxide build-up on the fatigue fracture surfaces at ΔK_th was of the order of magnitude as the crack tip opening displacement. In the helium tests, no significant build-up of oxide on the fracture surface at threshold was found.     

Effect of corrosive medium on fatigue crack growth behaviour and fracture in high martensite dual phase steel

Fatigue crack growth (FCG) behaviour in both near-threshold and higher stress intensity range (ΔK) in intercritically annealed dual-phase (DP) steel containing martensite between 32% and 76% in ferrite has been studied in 3·5% NaCl solution. It is shown that the amount of martensite content in dual phase steel has a significant effect on threshold (ΔK _th) values and FCG rates. Higher content of martensite in ferrite leads to higher threshold values and lower FCG rates. Further, ΔK _th is much higher in 3·5% NaCl solution as compared to that in laboratory air. Fractography studies reveal that in the near-threshold region, fracture surfaces are characterized mainly by intergranular cracking in corrosive (3·5% NaCl solution) environment. Higher threshold values in 3·5% NaCl solution is attributed to the higher crack closure induced by rougher fracture surface and by the strong wedge effects of corrosion products.     

Fatigue behaviour of friction stir welded AA2024‐T3 alloy: longitudinal and transverse crack growth

The fatigue crack growth properties of friction stir welded joints of 2024‐T3 aluminium alloy have been studied under constant load amplitude (increasing‐ΔK), with special emphasis on the residual stress (inverse weight function) effects on longitudinal and transverse crack growth rate predictions (Glinka's method). In general, welded joints were more resistant to longitudinally growing fatigue cracks than the parent material at threshold ΔK values, when beneficial thermal residual stresses decelerated crack growth rate, while the opposite behaviour was observed next to K_C instability, basically due to monotonic fracture modes intercepting fatigue crack growth in weld microstructures. As a result, fatigue crack growth rate (FCGR) predictions were conservative at lower propagation rates and non‐conservative for faster cracks. Regarding transverse cracks, intense compressive residual stresses rendered welded plates more fatigue resistant than neat parent plate. However, once the crack tip entered the more brittle weld region substantial acceleration of FCGR occurred due to operative monotonic tensile modes of fracture, leading to non‐conservative crack growth rate predictions next to K_C instability. At threshold ΔK values non‐conservative predictions values resulted from residual stress relaxation. Improvements on predicted FCGR values were strongly dependent on how the progressive plastic relaxation of the residual stress field was considered.     

Microstructure variation effects on room temperature fatigue threshold and crack propagation in Udimet 720Li Ni-base superalloy

An assessment of the effects of microstructure on room temperature fatigue threshold and crack propagation behaviour has been carried out on microstructural variants of U720Li, i.e. as‐received U720Li, U720Li‐LG (large grain variant) and U720Li‐LP (large intragranular coherent γ′ variant). Fatigue tests were carried out at room temperature using a 20 Hz sinusoidal cycling waveform at an R‐ratio = 0.1 on 12.5 mm × 12.5 mm square cross‐section SENB specimens with a 60° starter notch. U720Li‐LG showed the highest threshold ΔK (ΔK_th), whilst U720Li‐LP showed the lowest ΔK_th value. U720Li‐LP also showed higher crack growth rates in the near‐threshold regime and at high ΔK (although at higher ΔK levels the difference was less marked). Crack growth rates of U720Li and U720Li‐LG were relatively similar both in the near‐threshold regime and at high ΔK. The materials showed crystallographic stage I type crack growth in the near‐threshold regime, with U720Li showing distinct crystallographic facets on the fracture surface, while U720Li‐LG and U720Li‐LP showed mostly microfacets and a lower proportion of large facets. At high ΔK, crack growth in the materials becomes flat and featureless indicative of stage II type crack growth. The observed fatigue behaviour, which is an effect of the combined contributions of intrinsic and extrinsic crack growth resistances, is rationalized in terms of the microstructural characteristics of the materials. Enhanced room temperature fatigue threshold and near‐threshold long crack growth resistance are seen for materials with larger grain size and higher degree of planar slip which may be related to increased extrinsic crack growth resistance contributions from crack tip shielding and roughness‐induced crack closure. Differences in the deformation behaviour, either homogeneous or heterogeneous due to microstructural variation in this set of materials may provide approximately equivalent intrinsic crack growth resistance contributions at room temperature.     

Effects of tempered structure on the near threshold fatigue crack growth behavior of a coarse grained high strength steel

Near threshold fatigue crack growth behavior of a high strength steel under different temper levels was investigated. It is found that the observed variations in ΔK_th could predominantly be attributed to roughness induced crack closure. The closure-free component of the threshold stress intensity range, ΔK_eff,th showed a systematic variation with monotonic yield strength.     

Analysis of vacuum fatigue crack growth results and its implications

Conventionally, the reduction of ΔK_th with load ratio R has been interpreted in terms of crack closure arising from plasticity, oxide or crack surface roughness. Since, plane-strain conditions exist near-threshold, plasticity-induced closure is absent. Therefore, to account for R-ratio effects near-threshold, the oxide and roughness closure mechanisms have been proposed. Further analysis has shown that these other two closure effects also are small, when the results taken in vacuum were included. The present analysis shows that there is a unique relation of the oxide thickness with a threshold K_max, rather than with a threshold ΔK. This threshold K_max (K*_max,th) depends on environment. When the applied K_max<K*_max,th, the crack is stationary in the presence of the oxide formation and grows only when the applied K_max>K*_max,th. Thus, the oxide thickness—K_max relation seems to have a bearing on the criterion for crack growth in the presence of the environment. Oxide formation passivates the crack surfaces and retards the environmental damage ahead of the crack-tip. Examples from CrMo and NiCrMo steels support this viewpoint and suggest that there is a pressing need for quantifying the crack-tip environmental effects and fatigue thresholds.     

The micromechanics of fatigue-induced delamination of a graphite/epoxy composite

Fatigue crack growth in the resin layer between 0 and 90 plies of an AS/3501-5A graphite fibre/epoxy composite is discontinuous. Regularly spaced extensions of the crack front occur after periods of arrest. Crack compliance and tip strain fields have been measured to determine how the local minimum (K _min ^l) and maximum (K _max ^l) crack tip stress intensities affect growth. Contact of the fracture surfaces and swelling of the 90° ply modify these local stress intensities by an amount sensitive to load ratio (R), and the resulting propagation rate depends strongly onR. A model capable of describing thisR effect relates the distance of each individual crack advance to K_max ^l and the duration of each arrest toK _mnax ^l -K _min ^l, i.e., to K _eff. We discuss the genesis of this model, and its explanation of the large Paris law coefficient which results if growth rates are instead expressed against the applied cyclic stress intensity.     

Fracture toughness of selectively reinforced Al2124 alloy: precrack tip in the aluminium alloy side

Abstract

The fracture toughness of Al2124/Al2124+SiC bimaterials is affected by thermal residual stresses, elastic/plastic mismatch, precrack tip position, and failure mechanism. When the precrack tip is in the Al2124 side, final catastrophic failure occurs when ductile fracture of the Al2124 layer between the precrack tip and the composite side takes place, followed by fracture of the composite layer. For a precrack tip 2·0 mm from the interface, K _Q(5%) values are lower than the 'Al2124 only' value due to the near crack tip tensile residual stresses and higher stress triaxiality within the Al alloy ligament. At 0·5 mm from the interface, K _Q(5%) values increase and are usually as high as the 'Al2124 only' value due to the stronger shielding of the elastic/plastic mismatch. If the precrack tip is 2·0 mm from the interface, K _crit values of the bimaterial are higher than the 'Al2124 only' value and this is deduced to be due to the elastic/plastic mismatch shielding. At 0·5 mm from the interface, K _crit values are reduced because both the near tip tensile residual stress is higher and stress triaxiality levels of the ductile ligament are higher, although the elastic/plastic mismatch shielding is also higher at this position.     

COMPARISON OF PLASTIC WORK OF FATIGUE CRACK PROPAGATION IN LOW CARBON STEEL MEASURED BY STRAIN-GAGES AND ELECTRON CHANNELING

Abstract— The plastic work to propagate a fatigue crack by a unit area, U, measured by the foil strain gage technique requires an extrapolation to estimate the contribution closer than 100 μm to the crack tip. This is due to the size of the strain-gages used, 200 × 210 μm. Conversely, the electron channeling technique for determining U is useful mainly close to the crack tip where subgrains form. In the present work U was measured by both techniques in the same low carbon steel at ΔK= 8 MN/m^3/2. The contribution to U from closer than 100 μm of the crack tip was determined to be 1·7 × 10⁶ J/m² using electron channeling and 2·0 × 10⁶ J/m² by extrapolation. The measured contribution to U from further than 100 μm from the crack tip was 3·6 × 10⁶ J/m² giving 5·3 × 10⁶ J/m² for U. Thus, a large amount of energy is absorbed outside the region where sub-grains form. The non-hysteretic plastic work was found to be about four orders of magnitude smaller than the hysteretic plastic work, and may be neglected. A map of the plastic zone results from the strain-gage measurement. Rice's theory predicts the measured plastic zone sizeif the proper material's strength is employed in the formula.     

Schwellwert für Ermüdungsrißausbreitung: Bestimmungsmethoden,Kennwerte, Einflußgrößen

Threshold for Fatigue Crack Propagation: Experimental Procedure, Characterizing and Influencing Parameters For the determination of a fatigue crack propagation threshold there exists no “Standard” or other generally accepted experimental procedure. The threshold behaviour of “long” cracks can be characterized by threshold ΔK_th determination as a function of R as well as a function of K_max. The experimental determination of ΔK_th with constant K_max is simpler and a plot of the results versus K_max represents the threshold behaviour of a material more accurate. The whole threshold behaviour is characterized by three parameters. These three parameters can be obtained with relatively little experimental expenditure. The influence of certain conditions, i. e. material, microstructure, environment, ect., on the threshold ΔK_th are discussed. It seems that for a particular material and environment only two of these parameters can be considered as material properties. Test results show that with large change of amplitude ΔK fatigue cracks can grow still at ΔK smaller than ΔK_th. But after some growth, fatigue crack propagation ceases.     

Effect of welding residual stresses on fatigue crack growth thresholds

Fatigue crack growth thresholds ΔK_th were determined for friction stir welded butt joints made from aluminium alloys AA2024 and AA6013. Plotting the thresholds as a function of load ratio R showed distinctly higher amounts for welded joints as compared to those for parent material at small load ratios, but differences became smaller with increasing load ratio, until thresholds became finally identical for the highest R values. Applying Döker’s concept of two controlling parameters, namely ΔK and K_max [1], and plotting ΔK_th versus K_max, however, revealed that the effective threshold ΔK_th,eff determined at very high R ratios was nearly independent on the alloy and, simultaneously, was identical for parent material and respective welded joints. Thus, differences in threshold behaviour were only caused by the second threshold K_max,th, which was significantly higher for welded joints as compared to parent material. Differences in K_max,th coincided with compressive residual stresses determined by cut-compliance measurements in terms of stress intensity factors K_rs acting at the crack tip. Based on the analytical approach described by Döker [1], only one characteristic K_rs value was needed to calculate all thresholds of welded joints for 0 ⩽ R ⩽ 1 provided a base material master curve is available.     

A TECHNICAL NOTE. INFLUENCE OF MEAN STRESS ON FATIGUE IN SEVERAL ALUMINIUM ALLOYS UTILIZING Kcmax THRESHOLD PROCEDURES

Recent interest in the constant K_max (K^c_max) threshold testing procedure has resulted in a more in-depth study of the influence of K_max level on fatigue response and ΔK_th in aluminium alloys. Under R^c= 0.1 conditions, which cause large amounts of closure, ΔK^th levels were typically 2 to 4 Mpam. However, under K^c_max test procedures, associated with no measurable closure at threshold, ΔK_th was typically 1 Mpam. A slight K^c_max level effect on ΔK_th was observed at high K_max values for some of the alloys, and was deemed to be a pure mean stress effect, separate from closure arguments.     

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.     

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.     

Measuring overload effects during fatigue crack growth in bainitic steel by synchrotron X-ray diffraction

In this work we present the results of in situ synchrotron X-ray diffraction measurements of fatigue crack-tip strain fields following a 100% overload (OL) under plane strain conditions. The study is made on a bainitic steel with a high toughness and fine microstructure. This allowed a very high (60 μm) spatial resolution to be achieved so that fine-scale changes occurring around the crack-tip were captured along the crack plane at the mid-thickness of the specimen. We have followed the crack as it grew through the plastic/residually stressed zone associated with the OL crack location. We observed two effects; one when the enhanced plastic zone is ahead of the crack and one after it has been passed. Regarding the former it was found that the compressive stress at the crack-tip initially falls sharply, presumably due to the increased plastic stretch caused by the OL. This is associated with a concomitant fall in peak tensile stress at K_max, the elastic excursion between K_min and K_max remaining essentially unchanged from before OL. Subsequently discontinuous closure as seen previously for plane stress caused by crack face contact at the OL location limits the elastic strain range experienced by the crack tip and thereby retards crack growth.     

On R ratio dependence of threshold stress intensity factor range for fatigue crack growth in type 316(N) stainless steel weld

Abstract

The influence of R ratio in the range 0·05–0·4 on the ambient temperature fatigue crack growth behaviour of an austenitic stainless steel weld, SS 316(N), has been studied. Results indicate that the cyclic threshold stress intensity factor ΔK_th increases with decreasing R ratio. The data are compared with those for SS 316, SS 316L and SS 316L(N) base materials from the literature, and various approaches dealing with the R ratio effects are examined. Zhang’s model considering the contribution of the crack tip plasticity to the fundamental fatigue crack propagation process does provide a consistent interpretation for the data.     

FATIGUE CRACK GROWTH BEHAVIOUR AND FRACTURE RESISTANCE IN CERAMICS

Fatigue crack growth and the fracture resistance curve (R-curve) were investigated in a polycrystalline alumina (AD90) and a silicon carbide whisker-reinforced alumina composite (Al₂O₃-SiC_w) at room temperature in air using a combined loading technique for stabilizing crack growth, and a surface film technique for monitoring crack length. Fatigue crack growth was evaluated successfully with those experimental techniques. Load shedding tests were performed until the crack became dormant, in order to determine the threshold stress intensity factor K_th. Subsequently, the specimens were used for quasi-static crack growth tests under a monotonic loading condition. The R-curves were determined in this experiment; however, fracture resistance did not increase markedly with crack growth. Detailed observations of the crack growth behaviour revealed that the flat R-curve was attributed to the shielding effect of the fatigue crack tip wake. Thus, the fatigue precrack introduced by the load shedding test was not regarded as an ideal crack for determining the R-curve. Fractographic observations were performed to investigate the mechanistic difference between fatigue and quasi-static crack growth. It was found that the cyclic loading produced fretting damage in the wake region and it reduced the shielding effect of the fatigue cracks. Based on the experimental results, the relationship between the fatigue crack growth and the R-curve is discussed as is the significance of K_th as a material parameter.     

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.     

Examination of fatigue crack driving force parameter

Most of the previous parameters that utilized as a crack driving force were established in modifying the parameter K_op in Elber's effective SIF range ΔK_eff(=K_max?K_op). However, the parameters that replaced the traditional parameter K_op were based on different measurements or theoretical calculations, so it is difficult to distinguish their differences. This paper focuses on the physical meaning of compliance changes caused by plastic deformation at the crack tip; the tests were carried out under different amplitude loading for structural steel. Based on these test results, differences of several parameter ΔK_eff in literature are analysed and an improved two‐parameter driving force ΔK_drive(=(K_max)ⁿ(ΔK^∧)^1‐n) has been proposed. Experimental data for several different types of materials taken from literature were used in the analyses. Presented results indicate that the ΔK_drive parameter was equally effective or better than ΔK(=K_max?K_min), ΔK_eff(=K_max?K_op) and ΔK*(= (K_max)^α(ΔK⁺)^1?α) in correlating and predicting the R‐ratio effects on fatigue crack growth rate.