Effects of the transverse stress on biaxial fatigue crack growth predicted by plasticity-corrected stress intensity factor

The transverse stress has an important effect on the biaxial fatigue crack behavior. However, the experimental evidence has provided conflicting indications: it is sometimes considered to increase, decrease or have no effect. These complex phenomena cannot be rationally explained by the existing mechanical models. The effect of the transverse stress on the fatigue crack growth behavior is still one of the most puzzling questions in biaxial fatigue. Physically, this effect is a transverse stress induced plasticity phenomenon. In this paper, a plasticity-corrected stress intensity factor (PC-SIF) is proposed to describe the effect of transverse stress on biaxial fatigue. By use of this new crack driving force some important phenomena associated with transverse stress are predicted. Comparisons with experimental results showed that the PC-SIF as an effective mechanical parameter is capable of predicting the effects of the crack length, the stress level, cyclic stress ratio, biaxial stress ratio and phase difference on the biaxial fatigue crack growth. Consequently, the alleged conflicting experimental results have been rationally explained by the PC-SIF.     

The effect of braking energy on the fatigue crack propagation in railway brake discs

Thermal fatigue cracks can often be found on the friction surface of brake discs used in railway vehicles after a period of usage and include crackle, radial and circumferential patterns. These cracks typically exhibit different initiation and propagation behavior under different braking conditions. In this paper, the effect of braking energy on fatigue crack evolution is analyzed by using experimental testing and numerical simulations. Macro observations show that a significant number of radial cracks appear on the surface of brake discs which operate at 300 km/h, while crackles typically appear after repeated emergency braking (EB) at 200 km/h. No crack growth was observed on disc surfaces after routine braking. The cyclic load that leads to the fatigue crack propagation consists of compressive stress during braking and residual tensile stress after cooling. Simulation results show that the depth of cracks correlates well with the residual tensile stress distribution in brake discs. Breaking tests exposed that the fracture surface of fatigue cracks which were covered by oxides shows nearly elliptic-type. Higher braking energy leads to a hardened layer on the friction surface and oxide generation near the crack edges, which are also important factors that contribute to accelerating crack propagation.     

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.     

The effect of crack surface interaction on the stress intensity factor in Mode III crack growth in round shafts

Turbine-generator shafts are often subjected to a complex transient torsional loading. Such transient torques may initiate and propagate a circumferential crack in the shafts. Mode III crack growth in turbo-generator shafts often results in a fracture surface morphology resembling a factory roof. The interaction of the mutual fracture surfaces results in a pressure and a frictional stress field between fracture surfaces when the shaft is subjected to torsion. This interaction reduces the effective Mode III stress intensity factor.The effective stress intensity factor in circumferentially cracked round shafts is evaluated for a wide range of applied torsional loading by considering a pressure distribution between mating fracture surfaces. The pressure between fracture surfaces results from climbing of asperities respect to each other. The pressure profile not only depends on the fracture surface roughness (height and width (wavelength) of the peak and valleys), but also depends on the magnitude of the applied Mode III stress intensity factor. The results show that asperity interactions significantly reduce the effective Mode III stress intensity factor. However, the interactions diminish beyond a critical applied Mode III stress intensity factor. The critical stress intensity factor depends on the asperities height and wavelength. The results of these analyses are used to find the effective stress intensity factor in various Mode III fatigue crack growth experiments. The results show that Mode III crack growth rate is related to the effective stress intensity factor in a form of the Paris law.     

The effect of single overloads in tension and compression on the fatigue crack propagation behaviour of short cracks

The crack propagation behaviour in cast quenched and tempered steel after one overload cycle in tension as well as in compression on short cracks is investigated in deep notched specimens. The overload cycle exhibits a significant influence on the fatigue life endurance, due to the formation of an overload plastic zones in front of the crack tip. The crack propagation after overload cycles is investigated by inspection of the fatigue threshold R-curve and fatigue crack propagation rate. Tension overload increased the long crack threshold and reduced the R-curve effect, whereas overloads in compression reduced the crack growth resistance and shifted the threshold value to larger crack extension. A simple FE simulation was also performed to investigate the variation in the contribution of plasticity induced crack closure during crack propagation after the overload. Macroscopic mechanistic and dislocation models are introduced to explain the results obtained.     

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.     

The fracture toughness of Ni/Al2O3 laminates by digital image correlation I: Experimental crack opening displacement and R-curves

The crack opening displacement of laminates made of alumina/nickel was measured using digital image correlation (DIC). The crack opening displacements were validated with a finite-element model that uses the characteristic bridging-stress bridging-displacement relationship obtained experimentally by testing a constrained nickel sandwich in tension. The method is a simple, accurate way of measuring the crack opening displacement (COD) in ceramic/metal laminates.     

Evaluation of fatigue crack propagation by mode I and mixed mode in 1050 aluminium

The mechanism of mixed‐mode fatigue crack propagation was investigated in pure aluminum. Push‐pull fatigue tests were performed using two types of specimens. One was a round bar specimen having a blind hole, one was a plate specimen having a slit. The slit direction cut in the specimen was perpendicular or inclined 45 degrees relative to the centre of the specimen axis. In both cases, cracks propagated by mode I or by the mixed mode combining mode I and shear mode, depending on the testing conditions. In these cases the crack propagation rate was evaluated with a modified effective stress intensity factor range. Crack propagation retardation was observed in some specimens. However, it was found that the crack propagation rate could also be evaluated by the effective stress intensity factor range independent of the crack propagation mode.     

Effect of the stress distribution in simple welded specimens and complex components on the crack propagation life

While a long stable crack propagation phase was observed during experiments of complex welded components, very conservative estimations of the fatigue life were achieved in the past. The difference was explained by the stress gradient occurring over the plate thickness. This paper deals with numerical crack propagation simulations which were performed for geometrically different variants. The variants differ in global geometry, boundary conditions and weld shape. The analyses aim to investigate how the crack propagation is altered if the structural configuration gets more complex. In conclusion, the stress gradient over the plate thickness, the effective plate thickness due to vertical web plates and high notch effects slow down the crack propagation rate if the same stress value being effective for fatigue appears at the weld toe. Thereby, the load-carrying grade of the weld, the weld flank angle and the geometrical configuration also have an impact on both the notch effect and the local stress concentration.     

In situ Al3Ti and Al2O3 nanoparticles reinforced Al composites produced by friction stir processing in an Al-TiO2 system

Al and TiO₂ powders were selected to fabricate in situ Al composites via multiple pass friction stir processing (FSP) based on the thermodynamic analysis. The microstructural investigations indicated FSP would induce reaction between Al and TiO₂. Al₃Ti and Al₂O₃ particles were formed after 4 pass FSP with 100% overlapping. The in situ particles were about 80 nm in size at various FSP conditions, and ultrafine matrix grains 602 nm in size were obtained when water cooling was applied during FSP. Tensile tests indicated that the in situ nanocomposites exhibited pronounced work hardening behavior and a good combination of strength and ductility.     

Minimization of stress concentration factors in fatigue crack repairs

A numerical study is reported of a repair by flaw removal on a conventional welded joint. The repair profile is optimized with respect to the flaw and joint dimensions in order to minimize the resulting stress concentration factor (SCF). Two dimensional (edge repair) and three dimensional (surface repair) finite element analyses were made for the determination of SCF values and a graphical representation of results is presented. A relation between edge repair and surface repair is obtained and short and long repairs are defined. The weld geometry and repair orientation effects on SCF values are discussed. Finally, implications on using short and long repairs on fatigue initiation and inspection are presented.     

Raman study of stress effect on Ge nanocrystals embedded in Al2O3

Ge nanocrystals (NCs) embedded in Al₂O₃ were grown by RF-sputtering. X-ray diffraction, high resolution transmission electron microscopy, and Raman spectroscopy techniques were used to characterize the stresses on the NCs. While small NCs (< 10 nm) have been observed to be spherical and fully relaxed in the matrix, the larger ones (> 17 nm) demonstrated a compressive stress effect. This could be linked to the crystal structure of the adjacent Al₂O₃ matrix.     

Physical meaning of ΔKRP and fatigue crack propagation in the residual stress distribution field

Previous papers have shown ΔK_RP to be a useful parameter describing fatigue crack propagation behavior, where ΔK_RP is an effective stress intensity factor range corresponding to the excess RPG load (re-tensile plastic zone's generated load) in which the retensile plastic zone appears under the loading process. In this paper, the relationship between ΔK_RP and the zone size ( ) (which is smaller between the tensile plastic zone at maximum load and the compressive plastic zone at minimum load) was investigated using a crack opening/closing simulation model so as to consider a physical meaning of ΔK_RP. As a result, it becomes clear that ΔK_RP dominates the zone size where fatigue damage mostly occurs. This result supports the following crack propagation equation

where C and m are material constants.Simulation and fatigue crack propagation tests were then carried out for compact tension (CT), center cracked tension (CCT) and four points bend (4PB) specimens under constant amplitude loading to obtain C and m values for HT-50 steel. Fatigue crack propagation tests were also carried out under constant amplitude loading using CCT specimens with residual stress distribution due to flame gas heating at the center line or edge lines. The T specimen introduced tensile residual stress at the tip of a notch, and the C specimen introduced compressive residual stress. It therefore becomes clear that tensile residual stress leads to a decrease in RPG load, while compressive residual stress leads to increase in RPG load, and that the simulation results are in good agreement with the experimental RPG load. It also becomes clear that simulated crack growth curve using the simulated and the above equation is in good agreement with the experimental curve. It is understood that tensile residual stress creates only a slight increase in crack propagation rate and compressive residual stress create a big decrease a crack propagation rate.     

High cycle fatigue behaviour of microsphere Al2O3–Al particulate metal matrix composites

The high-cycle stress-life (S–N) curve and fatigue crack growth threshold (ΔK_th) behaviour of COMRAL-85^TM, a 6061 aluminium–magnesium–silicon alloy reinforced with 20 vol.% Al₂O₃-based polycrystalline ceramic microspheres, and manufactured by a liquid metallurgy route, have been investigated for a stress ratio of R = −1 (fully reversed loading). Fatigue testing was conducted on both smooth round bar (S–N) specimens and notched round bar (fatigue threshold) specimens. Unreinforced Al 6061-T6 also processed by a liquid metallurgy route and six powder metallurgy processed composites with particle volume fractions ranging between 5% and 30% were also studied. S–N data revealed that the powder metallurgy processed composites generally gave longer fatigue lives than the matrix alloy, whereas COMRAL-85^TM exhibited a reduced fatigue life. The fatigue threshold results were very similar for all the composites, being lower than for Al 6061-T6. Fatigue failure mechanisms were determined from examination of the fracture surfaces and the crack profiles.     

Numerical analysis of 2-D crack propagation problems using the numerical manifold method

The numerical manifold method is a cover-based method using mathematical covers that are independent of the physical domain. As the unknowns are defined on individual physical covers, the numerical manifold method is very suitable for modeling discontinuities. This paper focuses on modeling complex crack propagation problems containing multiple or branched cracks. The displacement discontinuity across crack surface is modeled by independent cover functions over different physical covers, while additional functions, extracted from the asymptotic near tip field, are incorporated into cover functions of singular physical covers to reflect the stress singularity around the crack tips. In evaluating the element matrices, Gaussian quadrature is used over the sub-triangles of the element, replacing the simplex integration over the whole element. First, the method is validated by evaluating the fracture parameters in two examples involving stationary cracks. The results show good agreement with the reference solutions available. Next, three crack propagation problems involving multiple and branched cracks are simulated. It is found that when the crack growth increment is taken to be 0.5h≤da≤0.75h, the crack growth paths converge consistently and are satisfactory.     

The effect of load ratio on fatigue life and crack propagation behavior of an extruded magnesium alloy

Fatigue experiments were carried out in laboratory air using an extruded magnesium alloy, AZ31, to investigate the effect of load ratio on the fatigue life and crack propagation behavior. The crack propagation behavior was analyzed using a modified linear elastic fracture mechanics parameter, M. The relation crack propagation rate vs. M parameter was found to be useful in predicting fatigue lives at different R ratios. Good agreement between the estimated and the experimental results at each stress ratio was obtained.     

Effects of surface deformation and crack closure on fatigue crack propagation after overloading and underloading

In the case of a negative baseline stress ratio, the fatigue crack growth rate can actually accelerate after a tensile overload. This crack propagation behavior is related to the local bulging of the specimen in the thickness direction during compression and the resultant tensile residual stress distribution at the crack tip. In the present investigation, the effects of a single tensile overload as well as the effects of a tensile overload followed immediately by a compressive underload on subsequent fatigue crack growth were investigated. The extent of crack opening displacement influences the magnitude of residual stress as well as the crack-tip opening level, and consequently, the subsequent rate of fatigue crack propagation.     

基于应力强度因子评估WCP形状对WCP/Fe复合材料热疲劳裂纹扩展行为的影响

应力强度因子在断裂力学中广泛应用于预测由远程载荷或残余应力引起的裂缝尖端附近应力状态。本文基于平面应力条件下应力强度因子建立WC_P形状与其尖端应力之间的规律,利用有限元分析软件对含不同形状WC_P的WC_P/Fe复合材料的热应力进行模拟仿真,研究WC_P形状对WC_P/Fe复合材料热疲劳裂纹扩展行为的影响。研究结果表明,WC_P的形状显著影响应力强度因子,进一步影响WC_P/Fe复合材料的热疲劳裂纹扩展行为。含球状和不规则状WC_P的WC_P/Fe复合材料的极限抗压强度分别约为460 MPa和370 MPa。含不规则状WC_P的WC_P/Fe复合材料因应力集中而容易产生脆性开裂现象。通过热震实验进行验证,发现实验结果与模拟仿真结果相近,说明有限元法的准确性,同时为WC_P/Fe复合材料的热疲劳裂纹扩展行为研究提供科学依据和理论基础。      

Comparison of the simulation and experimental fatigue crack behaviors in the nanoseconds laser shocked aluminum alloy

This investigation was performed to compare the simulation and experimental results of the fatigue crack growth rates and behaviors of the 7050-T7451 aluminum alloy by nanoseconds laser shock processing (LSP). Forman–Newman–deKoning (FNK) model embedded in the Franc2D/L software was utilized to predict fatigue crack growth rate, which was conducted to weigh the stress intensity factor (SIF) changing on the surface cracks. LSP induced high compressive residual stresses that served to enhance fatigue properties by improving the resistance against fatigue crack initiation and propagation. The circulating times of crack growth obtained from the simulation and experimental values indicated a slower fatigue crack growth rates after LSP. The relationships between the elastic–plastic materials crack growth rates and the SIF changing after LSP are resolved.     

Evaluation of fatigue crack growth behavior of GLARE3 fiber/metal laminates using a compliance method

The objectives of this study were to investigate the effectiveness of a compliance method for analyzing the fatigue crack growth of GLARE3 fiber/metal laminates. The materials tested were GLARE3-5/4 (2.6 mm thick) and GLARE3-3/2 (1.4 mm thick). Centrally notched specimens with two kinds of notch length and two kinds of fiber orientation were fatigue tested under constant amplitude loading. The expression of the experimental stress intensity factor, K_exp, for the 2024-T3 aluminum-alloy layers of a GLARE3 is formulated and K_exp were obtained from the relationship between crack length and specimen compliance. The test results clarified the following: (1) da/dN–ΔK_exp relationships roughly show the linear relationship independent of the maximum stress level, specimen thickness, notch length, and fiber orientations, (2) the da/dN–ΔK_exp relationships approximately agree with the linear part and its extension of Paris–Erdogan’s law obtained for the da/dN–ΔK relationship of the 2024-T3 aluminum-alloy, (3) the compliance method is effective for analyzing fatigue crack growth in GLARE3 laminates.