Maximum Stress Intensity Factor Kmax Research Articles

Analytical prediction of fatigue resistance of additively manufactured aluminium alloy based on Murakami method

This research is devoted to analyze the stress state and fatigue strength of two specimens made by a newly developed high-strength aluminium alloy produced by the wire arc additive manufacturing (WAAM) process. The relationship between fatigue strength and flaw size was calculated based on the root squared area – a parameter by conventional Murakami’s equation which is a widely used analytical approach for predicting fatigue resistance in metallic materials. The research involves the metallographic preparation process on two aluminum alloy labeled HS-Al-A and HS-Al-B followed by Vickers hardness measurement. Further, the image of the observed pores was processed and dimensioned using an open-sourced software ImageJ by considering pixels and actual distance as well as by defining image threshold value for measuring pore sizes. The analytical approach is conducted in order to describe the maximum stress intensity factor Kmax at the crack front and to assess the fatigue strength σFS. As final results, specimen A has an average pore area of ≈65 µm with Kmax of 333.75 MPa∙√m and σFS of 137 MPa, while specimen B has an average pore area of ≈42 µm with Kmax of 325.13 MPa∙√m and σFS of 153 MPa. Overall, this research allows the formulation of a method for estimating fatigue strength of large defects leading to a conclusion that flaws can influence the fatigue resistance of the material so that the bigger the flaw size is, the lower σFS and the higher the Kmax.

Investigation of subsurface fatigue crack growth behavior of D2 tool steel (JIS SKD11) based on a novel measurement method

In our preliminary study of the fatigue properties of D2 tool steel (JIS SKD11), it was found that owing to grinding in the specimen preparation process, high compressive residual stresses were introduced in the surface layers of the fatigue specimens, and as a result, the fatigue crack growth of the specimen was entirely subsurface. As relatively little is known about the subsurface growth of fatigue cracks, this finding gave us the opportunity to learn more about the subsurface fatigue crack growth process. An S–N curve covering fatigue lifetimes from 103 to 108 cycles was established for R = −1 loading condition. The velocity of fatigue crack growth as a function of the maximum stress intensity factor Kmax was determined to be in the range of 10−11–10−7 m/cycle. The Murakami √area method and a new experimental procedure were used to estimate the stress intensity factor and crack growth velocity under the specimen surface, respectively. An analytical equation for the velocity of crack growth as a function of the maximum stress intensity factor Kmax was developed, which agrees with the experimental results. The integration of this equation led to estimates of the fatigue lifetime for given stress ranges. These estimates were also in agreement with the experimental results.

Modeling R-dependence of near-threshold fatigue crack growth by combining crack closure and exponential mean stress model

A previously proposed equivalent driving force model was modified to account for crack closure for modeling stress ratio, R, dependence of fatigue crack growth in near-threshold regime. A new fatigue crack growth driving force model was established in the form of ΔK⋅f(R), where the f(R) includes both crack closure and mean stress contributions, and well informs the shift from dominance of stress intensity factor range ΔK to maximum stress intensity factor Kmax with increasing R. The model was validated widely with sound agreement between modeling results and experimental data.

A two-parameter analysis of surface fatigue crack growth behavior of fine-grained WC-Co cemented carbide at different stress ratios

In this study, the fatigue crack growth (FCG) characteristics of the short surface crack was studied at various stress ratios, R, using the fine grained cemented carbide. The FCG law for the material was studied using two parameters, the maximum stress intensity factor Kmax and the stress intensity factor range ΔK. It was found that the relationship between the rate of FCG, da/dN and ΔK depends on the R value. In the da/dN vs. Kmax relation, at the region of high crack growth rate, the FCG rate was nearly constant by the value of Kmax without depending on R. However, in the low FCG rate region, the FCG rate tended to accelerate as R became lower. Therefore, it was difficult to specify da/dN as a single value at different R ratios using either ΔK or Kmax from the low speed region to the high-speed region. For that reason, the FCG behaviour of the material was studied based on the crack growth law, da/dN = AKmaxmΔKn. The values of m and n were obtained as 6.6 and 1.4, respectively. Therefore, it was found that the FCG rate of the cemented carbide was strongly dependent on Kmax rather than ΔK, like the FCG characteristics of ceramics.

Effect of fiber orientation on fatigue crack propagation in short-fiber reinforced plastics

The influence of the fiber orientation on the crack propagation behavior was studied with single edge-notched specimens which were cut from an injection-molded plate of short-fiber reinforced plastics (SFRPs), at five fiber angles relative to the loading axis, i.e. θ=0° (MD), 22.5°, 45°, 67.5°, 90° (TD). Macroscopic crack propagation path was nearly perpendicular to the loading axis for the cases of MD and TD. For the other fiber angles, the crack path was inclined because the crack tended to propagate along inclined fibers. In the relation between the crack propagation rate and the stress intensity factor range, ΔK, the propagation rate of fatigue cracks was slowest for MD, and increased with increasing fiber angle. When the crack propagation rate was correlated to ΔK/E (E=Young’s modulus), the relations for different orientations merged into a single relation. Based on the results of stress-ratio effect, it was concluded that the crack propagation rate was mainly controlled by ΔK at low rates and by the maximum stress intensity factor Kmax at high rates. For injection molded plates, the existence of the core layer accelerated crack propagation in MD direction, and decelerated in TD direction. Mechanisms of crack propagation were discussed based on microscopic observation of the near crack-tip region and fracture surfaces.

Fatigue Lifetime and Crack Growth Behavior of WC-Co Cemented Carbide

It is well known that WC-Co cemented carbides have excellent wear resistance. However, information about their fatigue crack growth behavior and fatigue properties is limited. In the present study, rotating bending fatigue tests were carried out on a fine grained WC-Co cemented carbide to evaluate its fatigue lifetime and crack growth behavior. From observations of the micro-notched specimen surface during the fatigue process, it was revealed that most of the fatigue lifetime of the tested WC-Co cemented carbide is comprised of crack growth cycles. Using the basic equation of fracture mechanics, the relation between the rate of fatigue crack growth da/dN and the maximum stress intensity factor Kmax of the WC-Co cemented carbide was derived. From this relation, both the threshold intensity factor Kth and the fatigue fracture toughness Kfc of the material were determined. Fatigue lifetime of the WC-Co cemented carbide was estimated based on the fatigue crack growth law.

Mechanics of Fatigue Crack Propagation in Submicron-Thick Freestanding Copper Films

The dominant mechanics and mechanisms of fatigue crack propagation in approximately 500-nm-thick freestanding copper films were evaluated at three stress ratios, R = 0.1, 0.5, and 0.8. The fatigue crack propagation rate (da/dN) versus stress intensity factor range (ΔK) relation was dependent on the stress ratio (R): da/dN increased with increasing R. Plots of da/dN versus the maximum stress intensity factor (Kmax) exhibited coincident features in the high-Kmax region (Kmax 4.5 MPam1/2) irrespective of R, indicating that Kmax was the dominant factor in fatigue crack propagation. In this region, the fatigue crack propagated in tensile fracture mode, or chisel-point fracture, irrespective of the R value. In contrast, in the low-Kmax region (Kmax < 4.5 MPam1/2), da/dN increased with decreasing R. In this region, the fracture mechanism depended on R. At the higher R value (R = 0.8), the fatigue crack propagated in the tensile fracture mode similar to that in the high-Kmax region. On the other hand, at the lower R values (R = 0.1 and 0.5), a characteristic mechanism of fatigue crack propagation appeared: within several grains, intrusions/extrusions formed ahead of the crack tip along the Σ3 twin boundaries, and the fatigue crack propagated preferentially through the intrusions/extrusions.

Fatigue crack growth testing at negative stress ratios: discussion on the comparability of testing results

ABSTRACTIt is an accepted fact in fatigue community that compressive loads contribute to fatigue crack growth. Evidences range from fatigue crack growth under fully compressive loads to effects of compressive underloads to negative stress ratio loading. Because the crack closes under compression and the crack flanks transmit compressive stresses, the loading situation is completely different to those of tensile loading. The present paper addresses the comparability of crack growth testing procedures at negative stress ratios. It reveals that compressive loading at the crack tip differs in different specimens for an equal maximum stress intensity factor Kmax and negative stress ratio R. Furthermore, the crack length can significantly influence the loading conditions at the crack tip for tension–compression loading. Depending on the specimen type and crack length, a negative force ratio may lead to a change of algebraic sign of the stresses at the crack tip or not. As a consequence, the comparability of available literature results for R ≤ 0 tests is not ensured. Proposals to improve the comparability of tension–compression crack growth testing will be given.

Crack Closure Behavior under High-Load Ratio for AISI 4340 Steel

In this paper, fatigue crack growth rate (FCGR) analyses were conducted on compact specimens of an AISI 4340 alloy to study the behavior over a range in load ratios (0.1 ≤ R ≤ 0.95) and constant maximum stress intensity factor (Kmax) condition. Previous study had indicated that high R > 0.7 and constant Kmax test conditions near threshold conditions were suspected to be free of crack-closure and that any differences were caused by Kmax effects, from threshold to near fracture conditions. Cracks in high-cycle fatigue (HCF) components spend a large portion of their fatigue life near threshold conditions. In order to characterize the evolution of damage and crack propagation during these conditions, fatigue crack growth rate (FCGR) data at threshold and near-threshold conditions are essential in predicting service life and in determining the proper inspection intervals. Fatigue crack growth model, namely the Forman model were examined, this model implicit the effect of R ratio and ease of curve fitting to measured data. The Forman model may be suggested for use in critical applications in studying fatigue crack growth for different load ratios.

Effects of triaxial stress on martensite transformation, stress–strain and failure behavior in front of crack tips in shape memory alloy NiTi

Based on the finite element calculation in the conditions of plane stress and plane strain, effects of triaxial stress on martensite transformation, stress–strain and failure behavior in front of crack tips in shape memory alloy NiTi are analyzed. The results show that in plane strain condition the martensite transformation and the plastic deformation in the fully transformed martensite in front of crack tips are strongly suppressed by the high triaxial stress. The maximum normal stress in front of crack tips in plane strain is higher than that in plane stress, and the equivalent plastic strain in plane strain is much lower than that in plane stress. For the fatigue failure of the superelastic shape memory alloy NiTi in plane strain condition, when the maximum stress-intensity factor Kmax is less than 15 MPa m 1/2 ahead of a crack tip, the martensite transformation at the crack tip can be totally suppressed by the high triaxial stress and the fatigue crack will propagate in the untransformed austenite. In plane stress condition, the martensite transformation can occur at very small Kmax due to the low triaxial stress, the fatigue crack will propagate in the transformed martensite in front of crack tips. This analysis result agrees with the experimental result in [A.L. McKrlvey, R.O. Ritchie, Metall. Mater. Trans. 32A (2001) 731–743]. The analysis on the fracture behavior shows that in plane strain condition with high triaxial stress, the crack propagation in fracture process of shape memory alloy NiTi tends to be in an unstable manner. However, in plane stress condition with low triaxial stress, the crack propagation tends to be in stable manner.

A viewpoint on environmental contributions to fatigue crack growth

Fatigue crack growth behaviour is examined using the Unified Damage Approach developed by the authors since 1994. The approach is based on the understanding that a fatigue damage requires two loading parameters; a requirement manifesting in terms of two fracture mechanics parameters: maximum stress intensity factor Kmax and a stress amplitude ΔK. Kmax governs the breakage of crack tip bonds allowing for crack extension and ΔK controls the extent of cycle damage needed ahead of the crack tip. The overall changes in crack growth depend on several factors like microstructure, deformation mode and its properties and environment. The Unified Damage Approach describes these closely related changes in the damage mechanisms due to synergistic effects of mechanical and environmental driving forces. Crack growth trajectory maps developed using the Unified Damage Approach summarises these changes in mechanisms that occur with increasing crack growth rate or stress intensity.

マイクロメカニックスによるパラメータΔε｀Ｐ´を用いた（α＋γ）二相ステンレス鋼のＸ線フラクトグラフィ

X-ray diffraction observation of metal fractures provides us with useful information on the mechanisms and mechanical conditions of fracturing. This method has been developed especially as an engineering tool for fracture analysis. (α+γ) dual phase stainless steel JIS-SUS329J4L is a composite material which consists of ferrite αFe and austenite γFe phases. This material excels in corrosion-resistance in the chlorinated environment, and is used for chemical plant and the oil pipes. In this study, X-ray fractogarphy technique is applied to fatigue fracture surface of dual phase stainless steel. Fatigue crack propagation tests were conducted under stress ratios of 0.5 and 0.7. Residual phase and macro stresses near the fracture surface were measured using X-ray diffraction method to the depth direction. In addition, the distribution of the misfit of plastic strain ΔeP between αFe and γFe phase obtained from micromechanics beneath the fracture surface was calculated. From the distribution of these X-ray parameters, the depth of the maximum plastic zone ωy was determined. Relations between ωy and fracture mechanics parameter were examined. As the result, ΔeP was related with the maximum stress intensity factor Kmax divided by the 0.2% proof stress σ0.2. Moreover, it is suggested that ΔeP is more effective parameter than residual stresses for determination of ωy of dual phase stainless steel.

Influence of the Structure and Asymmetry of Loading Cycles on the Cyclic Crack Resistance of Ti–Si Composites

We analyze fatigue-crack growth rate diagrams for various modifications of a Ti–Si cermet alloy in the initial (as-cast) state and after thermomechanical treatment plotted for beam specimens subjected to three-point bending. It is shown that, for different asymmetries of the loading cycle, the maximum stress intensity factor K max better describes the behavior of the growth rate of fatigue macrocracks in the high-amplitude part of the diagrams than the range of the stress intensity factor ΔK. The threshold crack resistance of the Ti–Si composite under cyclic loading is 2–5 times lower than under long-term static loading. For highly asymmetric loading cycles (R = 0.6), the maximum cyclic crack-growth resistance is exhibited by a modification with the structure of grains of pseudo-α-titanium matrix 20–40 μm in size and 15–30 wt.% of dispersed precipitations of titanium and intermetallic silicides 5–10 μm in size.

A multiparameter approach to the prediction of fatigue crack growth in metallic materials

A multiparameter approach is proposed for the characterization of fatigue crack growth in metallic materials. The model assesses the combined effects of identifiable multiple variables that can contribute to fatigue crack growth. Mathematical expressions are presented for the determination of fatigue crack growth rates, da/dN, as functions of multiple variables, including stress intensity factor range, ΔK, stress ratio, R, crack closure stress intensity factor, Kcl , the maximum stress intensity factor Kmax , nominal specimen thickness, t, frequency, Ω, and temperature, T. A generalized empirical methodology is proposed for the estimation of fatigue crack growth rates as a function of these variables. The validity of the methodology is then verified by making appropriate comparisons between predicted and measured fatigue crack growth data obtained from experiments on Ti–6Al–4V. The effects of stress ratio and specimen thickness on fatigue crack growth rates are then rationalized by crack closure considerations. The multiparameter model is also shown to provide a good fit to experimental data obtained for HY‐80 steel, Inconel 718 polycrystal and Inconel 718 single crystal. Finally, the implications of the results are discussed for the prediction of fatigue crack growth and fatigue life.

Estimation of Applied Stress Based on the Hardness Distribution beneath the Fatigue Fracture Surface.

The micro Vickers hardness distribution just beneath the fatigue crack propagation surface was measured for SUS 316 stainless steel. The increase of hardness occurred in the plastic zone because of the strain hardening. A good correlation was found between the hardened region size and the maximum stress intensity factor Kmax. The relationship can be used to estimete the maximum applied stress on the cracked component which failed by fatigue.

Ｔｉ‐６Ａｌ‐４Ｖ合金の疲労破面におけるＸ線フラクトグラフィ

Fatigue tests were carried out with Ti-6Al-4V alloy CT specimens after three kinds of the heat treatments, namely, 1) solution at 1223K, aging at 813K(STA), 2) annealing at 1123K(AN850) and 3) annealing at 1373K(±β-AN). X-ray fractography, which is a technique to estimate applied stress conditions when a fracture occurs and to be used for analysing a mechanism of fracture, was applied on the fatigue fractured surface. Distributions of residual stress and half-value breadth were measured on the fractured surface along the crack propagation direction as a function of a stress intensity factor. It was found that the residual stress on the fatigue fractured surface had a peak value when maximum stress intensity factor was nearly equal to 25MPa√m. The strain induced transformation was confirmed on the fatigue fractured surface from X-ray diffraction profile pattern. Depth of monotonous plastic zone size was estimated from the distribution of the residual stress beneath fractured surface. Depth of monotonous plastic zone size ωy was expressed by following equation; ωy=α(Kmax/σy)2, where the values of α were 0.17 for STA and 0.13 for AN850. By using X-ray fractography technique on fatigue fractured surfaces of Ti-6Al-4V alloy, a value of maximum stress intensity factor Kmax where the residual stress reach maximum value can be predicted.

Fatigue Crack Growth Behavior of SUS631 Stainless Steel Foil.

The fatigue crack growth tests of the SUS 631 stainless steel foil (thickness : 0.05 mm) were carried out in a wide range of fatigue crack growth rate covering the threshold stress intensity factor range ⊿Kth. The effects of aging hardening treatment and the stress ratio on the fatigue crack growth characteristics were investigated on the basis of fracture mechanics. The crack growth rate was measured using the center notched specimens of solution heat treatment (1313K, 2s) foil (STF) and two kinds of aging treatment (703 K, 1 h and 753 K, 1 h) foils. Crack growth tests were conducted at 10 Hz and the stress ratio R=0.1 and R=0.5. The main results obtained are as follows ; (1) The Paris'law could also be applied between da/dN and ⊿K to the SUS 631 stainless steel foil in a special region of da/dN and it was shown to be da/dN=C (⊿K)m. (2) In a low-⊿K region the crack growth rate da/dN of aging treatment foil was higher than that of the STF and was accompanied by a small threshold value ⊿Kth. On the other hand, in a high-⊿K region da/dN of ageing treatment foils was lower than that of STF. (3) Fatigue crack growth resistance of a higher temperature aging material was higher than that of a lower temperature aging material with a higher tensile strength. (4) Crack closure level (Kop/Kmax) was rapidly increased as the maximum stress intensity factor Kmax decrease for each material at R=0.1 and R=0.5.

X-ray Fractography on Fatigue Fractured Surface of Solution and Aging Treated Ti-6Al-4V Alloy.

Fatigue tests were carried out under two kinds of stress ratios in constant amplitude loading of Ti-6Al-4V alloy after heat treatment of solution at 1223K and aging at 813 K (STA). Retardation behavior of fatigue crack propagation was observed. It is considered that this retardation is caused a stress relieving at front of crack tip by growth of secondary cracks. X-ray fractography, which is a technique to estimate the stress conditions and to be used for analysing a mechanisms when a fracture of structures occurs, is applied on fractured surface. Distributions of residual stress and halfvalue breadth by X-ray technique on the fractured surface along the crack propagation direction as a function of a stress intensity factor. It was found that the residual stress on the fatigue fractured surface had a peak value when maximum stress intensity factor was nearly equal to 25MPa√(m). Strain induced transformation was observed on the fatigue fractured surface from X-ray diffraction pattern. The half-value breadth on fractured surfaces increased with increasing maximum stress intensity factors. Depth of monotonous plastic zone size was estimated from a change of the distribution of the residual stress in direction of depth near fractured surface. Depth of monotonous plastic zone size ωy was expressed by following equation ; ωy=a(Kmax/σy)2, where the value of a was 0.17. By using X-ray fractography, maximum stress intensity factor Kmax in fatigue crack propagation of Ti-6Al-4V alloy can be predicted.

FATIGUE CRACK GROWTH OF SILICON NITRIDE WITH CRACK WEDGING BY FINE FRAGMENTS

Abstract— Fatigue crack growth tests of silicon nitride Si3N4 were carried out under four‐point bending using square bar specimens at room temperature. A pre‐crack was introduced by a bridge indentation method. Decreasing K‐type tests at stress ratios of R= 0.1 and 0.6 and also under static load were first carried out, and after observing the cessation of crack growth, K‐increasing tests were performed except for the case of a static load. Crack closure was observed on most specimens by the elastic compliance method. Furthermore, SEM observations of the crack paths were made to see what was happening during crack growth. The threshold and the region of steady crack growth were observed more clearly under cyclic loading, and an effect of load cycling certainly existed which became more evident when the maximum stress intensity factor Kmax approached the threshold. A wedge effect, caused by fine fragments on the crack surface, played an important role in crack closure behaviour of each specimen, and it is suggested that the crack growth rate is controlled by both the effective stress intensity range ΔKeff and the effective mean stress intensity factor Km,eff at least as a first approximation.

RESIDUAL STRESS DISTRIBUTION BENEATH THE FATIGUE FRACTURE SURFACE OF Al/SiC(WHISKERS) COMPOSITE

Abstract The X-ray fractographic technique was applied to characterize the fatigue fracture surface on Aluminium alloy (A6061) reinforced with SiC whiskers (Al/SiCw) prepared by the modified squeeze casting method. The X-ray elastic constant was first determined for the diffraction profiles of Al(222) plane as -88.2 MPa/deg. by using Cr-Ka radiation and a modified four point bending method. Then, the distribution of the residual stress on and beneath the fracture surface was measured, and used for the estimation of the depth of the plastic zone. The results were discussed in connection with the fracture mechanics and a fracture process. The plastic zone size was related to the maximum stress intensity factor Kmax divided by the 0.2% proof stress. The residual stress in the vicinity of the fatigue fracture surface was tension. Its value gradually increased and decreased with increasing the depth below the fracture surface. Its distribution beneath the fracture surface was also characterized as a compositio...