Analyses of the fatigue crack propagation process and stress ratio effects using the two parameter method

In situ SEM observations (Zhang JZ. A shear band decohesion model for small fatigue crack growth in an ultra-fine grain aluminium alloy. Eng Fract Mech 2000;65:665–81; Zhang JZ, Meng ZX. Direct high resolution in-site SEM observations of very small fatigue crack growth in the ultra fine grain aluminium alloy IN 9052. Script Mater 2004;50:825–28; Halliday MD, Poole P, Bowen P. New perspective on slip band decohesion as unifying fracture event during fatigue crack growth in both small and long cracks. Mater Sci Technol 1999;15:382–90) have revealed that fatigue crack propagation in aluminium alloys is caused by the shear band decohesion around the crack tip. The formation and cracking of the shear band is mainly caused by the plasticity generated in the loading part of a load cycle. This shear band decohesion process has been observed to occur in a continuous way over the time period during the loading part of a cycle. Based on this observation, in this study, a new parameter has been introduced to describe fatigue crack propagation rate. This new parameter, da/dS, defines the fatigue crack propagation rate with the change of the applied stress at any moment of a stress cycle. The relationship between this new parameter and the conventional da/dN parameter which describes fatigue crack propagation rate per stress cycle is given.Using this new parameter, it is proven that two loading parameters are necessary in order to accurately describe fatigue crack propagation rate per stress cycle, da/dN. An analysis is performed and a general fatigue crack propagation model is developed. This model has the ability to describe the four general type of fatigue crack propagation behaviours summarised by Vasudevan and Sadananda (Vasudevan AK, Sadananda K. Fatigue crack growth in advanced materials. In: Fatigue 96, Proceedings of the sixth international conference on fatigue and fatigue threshold, vol. 1. Oxford: Pergamon Press; 1996. p. 473–8).     

Effect of stress ratio on the mechanism of environmentally-assisted fatigue crack growth in high strength steels

The environmentally-assisted fatigue crack growth (FCG) behavior of high strength steels, the effect of cathodic potential on the FCG rates, and fracture surfaces were examined in some aqueous solutions. The effect of stress ratio on the critical values of maximum stress intensity, as well as cyclic stress intensity range and da/dN, which define quantitatively the role of hydrogen-induced cracking and local anodic dissolution in crack propagation, were also examined.Published inProblemy Prochnosti, Nos. 1–2, pp. 94–102, January–February, 1995.     

A crack propagation criterion based on ΔCTOD measured with 2D‐digital image correlation technique

The fatigue cracks growth rate of a forged HSLA steel (AISI 4130) was investigated using thin single edge notch tensile specimen to simulate the crack development on a diesel train crankshafts. The effect of load ratio, R, was investigated at room temperature. Fatigue fracture surfaces were examined by scanning electron microscopy. An approach based on the crack tip opening displacement range (ΔCTOD) was proposed as fatigue crack propagation criterion. ΔCTOD measurements were carried out using 2D‐digital image correlation techniques. J‐integral values were estimated using ΔCTOD. Under test conditions investigated, it was found that the use of ΔCTOD as a fatigue crack growth driving force parameter is relevant and could describe the crack propagation behaviour, under different load ratio R.     

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.     

Mode I fatigue crack growth under biaxial loading

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

In situ characterization of humidity effect on the fatigue damage evolution of a cast aluminium alloy

In this paper, the feedback signal of ultrasonic fatigue system was used to deduce the accumulated fatigue damage in situ using the ultrasonic nonlinearity parameter. It was observed that, compared with the decrease in resonant frequency, the ultrasonic nonlinearity parameter shows a greater sensitivity to fatigue damage evolution (i.e. crack initiation and propagation). Ultrasonic nonlinearity parameters obtained from tests conducted under various environmental humidity levels were monitored and analysed. Through changes in the ultrasonic nonlinearity parameter, it was concluded that both of the fatigue crack initiation life and crack propagation life were reduced by increasing the humidity levels.     

Crack growth characteristics of carbon nanotube-based polymer composites subjected to cyclic loading

This paper presents the characterization of crack growth in carbon nanotube (CNT)-based polymer composites under fatigue loading. Fatigue crack growth tests were performed on single-edge cracked plate specimens of CNT/polycarbonate composites at room temperature and liquid nitrogen temperature (77 K). An elastic–plastic finite element analysis was also conducted to determine the J-integral range. The crack growth rate data were expressed in terms of the J-integral range, and the effect of nanotube addition on the fatigue crack growth behavior was examined. In addition, possible mechanisms of the crack growth in the nanocomposites are discussed based on microscopic observations of the specimen fracture surfaces.     

J-Dominance in Mixed Mode Ductile Fracture Specimens

The asymptotic mixed mode crack tip fields in elastic-plastic solids are scaled by the J-integral and parameterized by a near-tip mixity parameter, M _{_p} . In this paper, the validity and range of dominance of these fields are investigated. To this end, small strain elastic-plastic finite element analyses of mixed mode fracture are first performed using a modified boundary layer formulation. Here, a two term expansion of the elastic crack tip field involving the stress intensity factor |K| the elastic mixity parameter M _{_e} as well as the T-stress is prescribed as remote boundary conditions. The analyses are conducted for different values of M _{_e} and the T-stress. Next, several commonly used mixed mode fracture specimens such as Compact Tension Shear (CTS), Four Point Bend (4PB), and modified Compact Tension specimen are considered. Here, the complete range of loading from contained yielding to large scale yielding is analyzed. Further, different crack to width ratios and strain hardening exponents are considered. The results obtained establish that the mixed mode asymptotic fields dominate over physically relevant length scales in the above geometries, except for predominantly mode I loading and under large scale yielding conditions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Effects of various environments on fatigue crack growth in Laser formed and IM Ti–6Al–4V alloys

The fatigue crack growth behaviors of Laser formed and ingot metallurgy (IM) Ti–6Al–4V alloys were studied in three environments: vacuum, air and 3.5% NaCl solution. Taking the Unified Fatigue Damage Approach, the fatigue crack growth data were analyzed with two intrinsic parameters, stress intensity amplitude ΔK and maximum stress intensity K_max, and their limiting values ΔK^* and . Fatigue crack growth rates da/dN were found increase with stress ratio R, highest in 3.5% NaCl solution, somewhat less in air and lowest in vacuum, and higher in IM alloy than in Laser formed one. In 3.5% NaCl solution, stress corrosion cracking (SCC) was superimposed on fatigue at R=0.9 for where K_max>K_ISCC, the threshold stress intensity for SCC. This and environment-assisted fatigue crack growth were evidenced by the deviation in fatigue crack growth trajectory (ΔK^* vs. curve) from the pure fatigue line where . Furthermore, the fractographic features, identified along the trajectory path, reflected the fatigue crack growth behaviors of both alloys in a given environment.     

Investigation of crack closure in stainless steel by laser interferometry

The effect of strain-induced martensite transformed during fatigue on the fatigue crack propagation rate near ΔK _th, as well as low-cycle fatigue behaviour of three differently heat-treated stainless steels, was investigated. The heat treatments were chosen so that austenite stability during fatigue was different. The crack closure stress during fatigue crack propagation near the ΔK _th region was measured using laser interferometry. The sensitized specimen showed the highest value of closure load ratio (K _cl/K _max), which was considered to be due to the roughness-induced crack closure caused by intergranular facets. The specimen with the lowest austenite stability showing the largest amount of strain-induced martensite during fatigue, showed the highest crack growth rate. The effect of brittle fracture through the harder strain-induced martensite was larger than that of possible transformation-induced crack closure.     

Crack propagation behavior under creep conditions

The creep crack propagation behavior of a Cr–Mo–V rotor steel has been investigated at 538°C using time-dependent fracture mechanics concepts. The creep crack propagation lives and the creep deflection rates of double-edge-notched (DEN) specimens were estimated using previous data from compact-type specimens. The predicted crack growth lives and deflection rates compared favorably with the experimental data. When plotted as a function of the C _t parameter, the experimentally determined creep crack propagation rates of DEN specimens were found to be in agreement with those of compact and center-crack-tension specimens. These results provide further experimental verification for the validity of the C _t parameter for characterizing creep crack growth behavior. Some discrepancies between the predicted and the observed behavior are attributed to primary creep deformation behavior which was not considered in estimating the value of C _t .     

Effect of fracture path on the toughness of weld metal

The crack propagation direction may affect weld metal fracture behavior. This fracture behavior has been investigated using two sets of single edge notched bend (SENB) specimens; one with a crack propagating in the welding direction (B×2B) and the other with a crack propagating from the top in the root direction (B×B) of a welded joint. Two different weld metals were used, one with low and one with high toughness values. For Weld Metal A, two specimen types have been used (B×B and B×2B) both with deep cracks. The weld metal A (with high toughness values) has reasonably uniform properties between weld root and cap. The resulting J-R curves show little effect of the specimen type, are ductile to the extent that the toughness exceeds the maximum J_max, value allowed by validity limits and testing is in the large –scale yielding regime. In the case of weld metal B (with low toughness values) with two specimen types (B×B and B×2B) the B×B specimen has shallow cracks while the B×2B specimen has deep cracks. Both resulting J-R curves show unstable behavior despite the fact that the types of specimen and their constraints are different. The analysis has shown that crack propagation direction is most influential for a weldment with low toughness in the small scale yielding regime, whereas its influence diminishes due to ductile tearing during stable crack growth and large scale yielding. The results have shown that these effects are different in both the crack initiation phase and during stable crack growth, indicating a dependence on weld metal toughness and the microstructure of the weld metal. It can be concluded that, if resistance curves during stable crack growth do not show differences in both notch orientations, the fracture toughness values of the whole weld metal can be treated as uniform.     

FATIGUE CRACK PROPAGATION CHARACTERISTICS OF GLASS FIBRE REINFORCED POLYCARBONATE IN HOT DISTILLED WATER

The fatigue crack propagation behaviour of polycarbonate and glass fibre reinforced polycarbonate was studied in hot distilled water. The effects of temperature, distilled water and glass fibre content on fatigue crack growth rate were determined. In distilled water at 333 K, the fatigue crack growth rate decreased with increasing glass fibre content. A melting was observed of the adhesive bond between the glass fibres and the matrix. It was evident that the fracture morphology closely relates to the fatigue crack growth rate which depends on the ΔK parameter rather than the K_max parameter when the materials are tested in hot distilled water.     

Mixed-Mode Crack Propagation in Cruciform Joint using Franc2D

The focus of this research was on determining the cracking behavior when parameter such as the biaxiality ratio was varied. The crack propagation under mixed-mode loading was simulated by means of finite element method. The stress intensity factors have been calculated by the linear elastic fracture mechanics approach using fracture analysis code-2D (Franc2D). The crack growth under opening mode-I was considered because the crack growth occurs mainly along the direction where the mode-I stress component becomes the maximum. The numerical integration of Paris’ equation was carried out. The effect of normal and transverse applied load (σ _x, and σ _y, respectively) on crack propagation was presented. It was found that the fatigue crack growth was faster at a smaller biaxial stress ratio (λ), i.e., higher σ _y on the horizontal crack plan. Moreover, fatigue strength values decrease as λ decreases. The results confirm the use of fracture mechanics approach in biaxial fracture.     

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.     

Predicting fatigue transverse crack growth in cross-ply carbon–epoxy laminates from quasi static strength tests by using iso-damage curves

Cross-ply laminates made of carbon/epoxy IM7/977-2 system are investigated. The fatigue study is confined to ambient temperature conditions and zero loading ratio. Damage is characterized by the transverse crack density ρ in the central 90°-layer. The family of experimental fatigue cracking curves (ρ versus N, where N is the number of cycles, for each tensile test maximum stress amplitude) can be replaced with a set of “iso-damage curves”, i.e. contour curves of constant ρ in the σ–log (N) plane. The iso-damage curves approximately constitute a fan of straight lines that intersect at a common point (σ_e, log (N_s)), where N_s is a very large number of cycles beyond which no more crack appears, and σ_e is some fatigue limit.Our aim is to propose a simple method to predict fatigue cracking at an arbitrary maximum stress level loading by using data stemming from a constant strain rate test. This method essentially rests upon the construction of the above “iso-damage” curves, using very simple assumptions.     

The importance of compressive stresses on fatigue crack propagation rate

This paper is concerned with the importance of compressive stresses on crack propagation rate. In a previous paper, namely ‘Crack Closure Inadequacy at Negative Stress Ratios’, Int. Journal of Fatigue, 26, 2004, pp. 241–252, was demonstrated the inadequacy of the crack closure concept and ΔK_eff, at a negative stress ratio, R=−1, to predict crack propagation rate. It that paper was verified that, at negative stress ratios, crack closure changes with P_max, for the same R ratio. The main conclusion was about plastic properties and mainly cyclic plastic properties, the Bauschinger effect included, on crack propagation when compressive stresses exist. It was then suggested that in the place of the crack closure concept, another concept based on plasticity should be used to explain fatigue crack propagation.In this paper, instead of working with the same negative R ratio (R=−1), a study on the behavior of crack propagation rate as a function of R ratio, from negative to positive stress ratios, is made. Both the effect of P_max and of R ratio is taken into consideration. Measurements of roughness and of crack opening loads are made, in order to verify their influence on crack propagation rate. Different materials, in order to cover different cyclic plastic properties and different sensitivities to roughness are studied (Ck45-cyclic hardening; Ti6Al4V-cyclic softening, and aluminum, Al 7175-cyclically neutral) are studied. Aluminium alloys and titanium alloys are considered to be sensitive to roughness induced crack closure (RICC) while steels are more dependent on plastic properties (PICC).In this study it is emphasized the importance of the compressive part of the cycle, and of cyclic plastic properties, on crack propagation rate. It is reassessed the inadequacy of crack closure concept and ΔK_eff to describe crack propagation rate, at negative stress ratios. It is also verified that models based solely on extrinsic properties of materials, like da/dN−ΔK or da/dN−ΔK (K_max) should also incorporate intrinsic properties of the materials in order to properly correlate fatigue crack growth.     

Simulation of fatigue life of constructional steels within the mixed modes I and III loading

The authors analysed influence of a component of the torsional moment M_as under the complex loading state, that is under bending with torsion, on fatigue life during initiation and propagation of fatigue cracks. Simulation of specimen life was performed according to the relationships describing the crack propagation rate and including the equivalent stress intensity factor range K_eq. Under complex loading, increase of amplitude of the torsional moment M_as for a given initial value of the resultant moment M_aw0 caused a higher fatigue life of specimens made of 10HNAP and 18G2A steels. This fatigue life increase was described by a nonlinear equation, the parameters of which had been determined from the experimental results. The fatigue lives estimated according to the assumed models were compared with those obtained from tests.     

FATIGUE LIFE AND SURFACE CRACK PENETRATION BEHAVIOUR OF AN ALUMINIUM ALLOY

Fatigue life and crack retardation behaviour after penetration were examined experimentally using CT specimens and surface pre-cracked specimens of aluminium alloy 5083-0. The fatigue crack shape before penetration is almost semicircular, and the measured aspect ratio is larger than the value obtained by calculation using K values proposed by Newman-Raju. It was found that crack growth behaviour on the back side after penetration is unique, and can be divided into three stages. The Wheeler model retardation parameter was used successfully to predict crack growth behaviour after penetration. By using a crack propagation rule, the change in crack shape after penetration can be evaluated quantitatively.     

Fatigue crack propagation behavior of RC beams strengthened with CFRP under cyclic bending loads

A fatigue crack propagation equation of reinforced concrete (RC) beams strengthened with a new type carbon fiber reinforced polymer was proposed in this paper on the basis of experimental and numerical methods. Fatigue crack propagation tests were performed to obtain the crack propagation rate of the strengthened RC beams. Digital image correlation method was used to capture the fatigue crack pattern. Finite element model of RC beam strengthened with carbon fiber reinforced polymer was established to determinate J‐integral of a main crack considering material nonlinearities and degradation of material properties under cyclic loading. Paris law with a parameter of J‐integral was developed on the basis of the fatigue tests and finite element analysis. This law was preliminarily verified, which can be applied for prediction of fatigue lives of the strengthened RC beams.