An energy approach to crack closure

Crack closure is analyzed using an energy approach whereby it is shown that crack closure does not completely shield the input mechanical energy to the crack tip at a load below the crack opening load P _op if the compliance below P _op is non-zero. An equivalent shielding stress intensity range is defined by the energy release rate against crack closure. From this energy standpoint, the true effective stress intensity range should be defined as K _eff=K _max–K _op, where is the shielding factor. The conventional definition (K _eff=K _max–K _op) is equivalent to the new definition only when the compliance below P _op is zero such that =1, i.e., for a fully closed crack. The corrected K _eff is found to be effective in correlating fatigue crack growth rates (FCGRs) generated in 8090-T8771 aluminum-lithium alloy with and without crack closure. In contrast, the conventional K _eff fails to reconcile the FCGR data within an acceptable scatter band.The Canadian Government's right to retain a non-exclusive, royalty-free licence in and to any copyright is acknowledged.     

The significance of RPG load for fatigue crack propagation and the development of a compliance measuring system

In can be postulated that fatigue crack does not grow if no damage occurs in the vicinity of the crack tip. Damage may occur beyond the Re-tensile Plastic zone's Generated load (RPG load) in the vicinity of a crack tip under loading process. We propose an effective stress intensity factor range ( K _RP) corresponding to the period in which the re-tensile plastic zone appears, in place of K _eff proposed by Elber [1], for a fatigue crack propagation parameter.We then consider the small change of compliance for a cracked body under cyclic loading, for the purpose of measuring RPG load as well as crack opening load and crack closing load. Moreover a subtraction circuit which can measure the small change of compliance during fatigue test is developed and an automatic controlled system which can control the adequate values of resistance in the circuit and the output voltage range from strain amplifiers for minimizing relative noise level is also developed. Then fatigue crack propagation tests of CT specimens were carried out with various stress ratios of constant amplitude loadings. Moreover K _th tests with the conditions of constant stress ratio and constant maximum load with increasing stepwise minimum load were also carried out. It becomes clear that the logarithmic curve of K _RP—crack propagation rate appears to be linear in a wide range from the region of very slow growth rate to the region of stable growth rate. On the other hand, threshold phenomenon appears only circumstantially due to the particular loading pattern on K _eff based on the crack opening load and K _eff ^cl based on the crack closing load. Moreover K _RP gives the quantitative effect of stress ratio on fatigue crack propagation rate.     

Influence of Hydrogen on the Formation of Fatigue Thresholds in Structural Steels

We analyze certain phenomena related to the influence of gaseous hydrogen and hydrogen dissolved in a metal on the near-threshold growth of fatigue cracks. The significant decrease in crack growth resistance due to the action of hydrogen as compared with that in vacuum is caused mainly by the adsorption decrease in strength due to adsorption. We established three factors of the ambiguous influence of hydrogen on the effective fatigue threshold K _theff, for which a positive influence is replaced by a negative one, namely: the strength level, temperature of testing, and high-temperature degradation of the metal. The following fractographic peculiarities of the near-threshold growth of cracks in a degraded metal are revealed: the local tunneling along the front of a crack and the presence of fatigue grooves. We propose a mechanism of crack closure due to both roughness and the component of longitudinal shear at the tip of the crack. We analyze the scale effect of fatigue thresholds, determine the conditions for invariance of the parameter K _theff under conditions of plane deformation, and established the dependence of K _theff on the thickness of specimens in the case of tests of a hydrogenated degraded metal.     

The unzipping model of fatigue crack growth and its application to a two-phase steel

The unzipping analysis, based on the alternate shear deformation process of two intersecting shear planes at a crack tip, is extended to study fatigue crack growth in a two-phase martensitic-ferritic steel. The unzipping crack increment a _uz is directly related to K and J in the case of small scale yielding. It is preferrable to use a _uz is directly related to K and J in the case of small scale yielding. It is preferable to use a _uz as a physical parameter to correlate with the growth rates of micro-cracks and fatigue cracks in a multi-phase material. In the case of micro-cracks, K is often not applicable because of extensive plastic deformation; and in the case of multi-phase material, neither K nor J is applicable because of material inhomogeneity. The effective K, K _eff, is defined in terms of a _uz. The relations between the endurance limit of a two-phase steel and crack nucleus size, ferrite layer thickness, the constraint by the strong martensite on crack tip deformation in the ferrite domain, and K _th's of the martensite and ferrite are analyzed.

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Résumé Une analyse de rupture progressive et continue des liaisons, basée sur un processus de déformation de cisaillement alterné de deux plants de cisaillement s'intersectant à l'extrémité d'une fissure, a été étendue à l'analyse de la propagation des fissures de fatigue dans un acier martensito-ferritique à deux phases. L'accroissement de la fissure a est directement en relation avec K et J dans le cas de déformation plastique de faible étendue. II est préférable d'utiliser a comme paramètre physique en corrélation avec les vitesses de croissance de microfissures et des fissures de fatigue dans un matériau à phases multiples. Dans le cas de microfissures, K n'est souvent pas applicable en raison de la déformation plastique importante. Dans le cas de matériau multiphase ni K ni J ne sont applicables en raison de l'inhomogénéité du matériau. La valeur effective K _eff est définie en terme de a. Les relations entre la limite d'endurance d'un acier à deux phases et la taille du nodule de fissuration, l'épaisseur de la couche de ferrite, la contrainte qu'exerce une zone martensitique dure sur le domaine ferritique, sur la déformation à l'extrémité de la fissure en domaine ferritique, et les valeurs de K de la martensite et de la ferrite sont analysées.

     

Fatigue Propagation of Fibre-Bridged Cracks in Unidirectional Polymer-Matrix Composites

In order to improve the fatigue resistance of polymer-matrix composites by materials design, or to conceive micromechanics based models for life predictions, the underlying micromechanisms must be understood. Experimental investigations have revealed fibre-bridged cracking as a toughening micromechanism that retards further fatigue crack growth in a unidirectional 0° carbon-fibre-reinforced epoxy. The bridging fibres exert a closing traction on the crack surfaces, thereby reducing the driving force for crack growth. In this study, the growth of bridged cracks has been quantified by a surface replication technique. The da/dN–K curve defined in terms of nominal stress-intensity factors shows a crack retarding behaviour. The crack growth curve can be replotted in terms of the effective stress-intensity factor where the contribution of the cohesive crack surface forces from the bridging fibres are taken into account. This curve falls somewhat closer to that of the neat matrix material, but the difference is still considerable, and it shows a decelerating propagation. Therefore, there must be other active toughening mechanisms besides fibre bridging, that slow the crack propagation down, and account for the fatigue resistant behaviour of the tested material. Ways by microstructural design to promote the fatigue resistant mechanisms are discussed.     

Plastic deformation — its role in fatigue crack propagation

Recognizing the fact that the effective driving force (ΔK _eff) determines the fatigue crack propagation (FCP) rate and that the shear strain, which is considered to develop due to an occurrence of crack closure, primarily contributes to the plastic deformation, an effort is made here to elucidate the role of plastic deformation in FCP by developing a correlation between the ΔK _eff and the applied driving force (ΔK) with shear strain as variable. The effect of the degree of plastic deformation (i.e. shear strain level) on the FCP rates at higher values of ΔK, where ΔK _eff approaches ΔK, approaching the Paris regime, appears minimal. On the other hand, the disparity between ΔK _eff and ΔK, which apparently increases with shear strain level, persists at lower values of ΔK. This suggests a strong influence of the degree of localized deformation on the FCP rates in the near threshold level. Hence, an improvement of FCP rates in the near threshold level should follow an effort that promotes the plastic deformation near the crack tip to a greater degree. This approach could, therefore, form the basis to explain the effect of the grain size, microstructure, environment,R-ratio and crack size on the near-threshold FCP rates.     

Fatigue crack closure over the range of stress ratios from −1 to 0.8 down to stress intensity threshold level in HT80 steel and SUS304 stainless steel

The closure phenomena of fatigue cracks were investigated with a 1 mm gage length extensometer over the range of stress ratio, R, from –1 to 0.8. Plate specimens with a center slot of HT80 steel and SUS304 stainless steel were fatigued under push-pull loading, and the crack propagation rate, da/dn, was measured. The stress ratio, R, was found to influence da/dn in both materials. The crack opening stress intensity factor, K _op, was determined from the relationship between the crack tip extensometer displacement and the load. The effective stress intensity range ratio, U(=K_eff/K), decreases with the decrease of the stress intensity amplitude, K/2. As for the data which show the crack closure phenomena (R0.4), the relationship between log(da/dn) and log(K _eff/2) falls on a straight line near the stress intensity threshold level. For R=0.8 where the crack tip is fully open over the whole range of loading, the data show a discrepancy from the same line. The strain at the crack tip was also measured with the Moiré fringe multiplication method. A large amount of plastic strain at the crack tip was observed even below the crack opening load for R=–1 in HT80 steel. These phenomena show that fatigue damage still exists when the crack is closed. These also show that the crack closure cannot fully account for the effect of R on da/dn.

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Résumé Les phénomènes de fermeture de fissures de fatigue ont été étudiés à l'aide d'un extensomètre d'une longueur de référence d'un millimètre sur une étendue des rapports de contrainte R variant de –1 à +0,8. Les éprouvettes plates comportant un trou central oblong, étaient en acier HT80 et en acier inoxydable SUS304. Elles ont été soumises à fatigue sous des conditions de traction-compression, et la vitesse de propagation de la fissure, da/dn, a été mesurée. Le rapport des tensions R est apparu avoir une influence sur da/dn, dans le cas des deux matériaux. Le facteur d'intensité des contraintes correspondant à l'ouverture de la fissure K _op a été déterminé à partir de la relation entre le déplacement de l'extensomètre à l'extrémité de la fissure et la charge. Le rapport effectif de la variation de l'intensité de la contrainte U(=K_eff/K) décroit lorsque décroit l'amplitude de l'intensité de contrainte K/2. En ce qui concerne les données montrant le phénomène de fermeture de la fissure (pour R0,4) la relation entre log(da/dn) et log(K _eff/2) tombe sur une ligne droite au voisinage du niveau de seuil de l'intensité des contraintes. Pour R=0,8 qui correspond à une extrémité d'entaille complètement ouverte quelle que soit la charge, les données montrent une déviation par rapport à cette ligne. La déformation à l'extrémité de la fissure a également été mesurée à l'aide d'une méthode de multiplication des franges de Moiré. On a observé une grande quantité de déformations plastiques à l'extrémité de la fissure, même en dessous de la charge d'ouverture de la fissure correspondant à R=–1 pour l'acier HT80. Ces phénomènes montrent que le dommage par fatigue existe encore lorsque la fissure est refermée. Ils montrent également que la fermeture de la fissure ne peut pas tenir complètement compte de l'effet de R sur da/dn.

     

A tentative explanation for two parameters,C and m,in Paris equation of fatigue crack growth

The two parameters, C and m, which characterize the Paris equation for fatigue crack growth are explained in relation to the crack closure concept suggested by Elber. It is proposed that the range of effective incremental change in stress intensity factor (K) needed for crack growth should have a second power correlation with the growth rate. The crack growth is essentially determined by cumulative damage to the material in cycled plastic zone near the crack tip, and is relatively insensitive to the applied K-values and the mechanical properties of material. However, the crack closure behavior is expected to depend on both the stress range and the material properties. Thus it is concluded that the exponent parameter m reflects mainly the dependency of crack closure behavior on K. For example, in the case of m=4 the crack opening level increases linearly with increase in K, while in the case of m=2 it remains constant. It is suggested that the cyclic straining at the crack tip possibly varies with K, thus changing primarily the crack closure behavior rather than the damage accumulation process in the plastic zone.

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Résumé Les deux paramètres, C et m, qui caractérisent l'équation de Paris pour la propagation des fissures de fatigue sont expliqués en relation avec le concept de fermeture d'une fissure suggéré par Elber. On propose que la grandeur du changement effectif du facteur d'intensité de contrainte K nécessaire à l'accroissement d'une fissure figure à une puissance deuxième dans une corrélation avec le taux de croissance. La croissance d'une fissure est essentiellement déterminée par le dommage cumulatif infligé au matériau dans la zône de déformation plastique cyclique au voisinage de l'extrémité de la fissure; il est relativement insensible aux valeurs appliquées de K et aux propriétés mécaniques du matériau. Toutefois, le comportement à la fermeture d'une fissure devrait dépendre à la fois du taux de contrainte et des propriétés du matériau. Il est donc conclu que le paramètre exponentiel m représente principalement la dépendance du comportement à la fermeture d'une fissure par rapport à K. A titre d'exemple, dans le cas de m=4, le niveau de fermeture de la fissure augmente linéairement avec un accroissement de K, tandis que, dans le cas de m=2, il demeure constant. On suggère que les déformations cycliques à l'extrémité de la fissure peuvent varier avec K et modifient ainsi en premier lieu le comportement à la fermeture de la fissure plutôt que le processus d'accumulation de dommages dans la zône plastique.

     

Testing procedures for fatigue crack propagation and the ΔKeffconcept

Two different procedures are available for the experimental determination of fatigue crack propagation (FCP) velocities da/dN as a function of the loading parameters K. The first procedure is the standardized method in accordance with ASTM E 647 [1] and the second procedure is the so-called K_max-constant method. Both procedures are equivalent, meaning that under the same loading conditions (K, K_max, R) the same FCP velocity (da/dN) is measured. But, the ASTM E 647 method emphasizes the effects of closure (contact of fracture surfaces) in the low K and low K_max regime. It is shown for Al 7075–T7351, the Ni-base alloy Nicrofer 5219 Nb (annealed), the Ti-alloys Ti 6Al 4V (annealed), and Ti 6Al 6V 2Sn that K_eff is the sole driving parameter for FCP.Published in Problemy Prochnosti, No. 7, pp. 13–30, July, 1995.     

A two-parameter damage criterion and high-temperature fatigue crack growth in a corrosion-resistant steel

Summary The paper is designed to develop the two-parameter failure criterion for describing the growth of fatigue cracks under conditions of high-temperature fatigue. The criterion can be used with laboratory tests on specimens to construct kinetic diagrams for fatigue failure such as would be given if the requirements of linear failure mechanics were met. The initial data are the v-K_eff fatigue failure diagrams, which are effective ones incorporating crack closure, so one can derive v-K_v theoretical diagrams as conservative characteristics for a material for crack growth under conditions of planar strain.The two-parameter criterion enables one to incorporate the effects of frequency and cycle asymmetry at high K, where there are changes in crack growth rate due to changes in the rate of plastic strain at the crack vertex. At low K, the effects of loading frequency are additionally determined by the crack closure, the blunting, and the physicochemical action of the medium, which restricts the scope for using the two-parameter criterion to construct fatigue-failure kinetic diagrams invariant with respect to frequency.Translated from Fiziko-khimicheskaya Mekhanika Materialov., Vol. 26, No. 5, pp. 9–19, September–October, 1990.     

Influence of nonmetallic inclusions on fatigue crack growth in a structural steel

A study of the fatigue behaviour of a hardened and tempered steel, at two inclusion levels, has been carried out according to the linear elastic fracture mechanics criteria. The influence of inclusions on the fatigue crack growth rate has turned out to be a function of the local stress intensity factor range,K _I, at which fracture propagates. At lowK _I values, to which are related crack growth rates less than 10^–5 mm cycle^–1, the crack growth rate in the steel with higher inclusion content is lower than in the steel with lower inclusion content. AsK _I increases, an inversion in the difference between the two rates occurs. In the dirtier steel, the higherK _I, the higher the growth rate than in the other steel. The difference between the two rates becomes nil just below the fast propagationK _Ic level. By fractographic analysis, it has been possible to find out how inclusions affect fatigue behaviour.     

The effects of loading variables on overload induced fatigue crack growth retardation parameters

A growing fatigue crack is known to be retarded on application of an overload cycle. The retardation may be characterized by the total number of cycles involved during retardation, N_D and the retarded crack length, a_D. The loading variables play an important role to influence the retardation behaviour and thereby the retardation parameters N_D and a_D. The important loading variables are considered to be the stress intensity range, K during constant amplitude loading, stress ratio, R and the ratio of the overload stress to the maximum stress in constant amplitude loading, OLR etc. The objective of the present investigation is to study the effect of different loading variables on the retardation parameters. The investigation has been conducted in a 2024-T3 Al-alloy with centre crack tension panels loaded using an Electromagnetic Resonance Machine. The crack extension and crack closure have been measured during cyclic loading under constant amplitude and under overloading situations. The results do indicate dependence of crack opening stress intensity factor, K_OP on loading variables such as K, R and OLR. The delay cycle N_D is found to increase with loading variables K, OLR and R. The functional dependence of retardation zone a_D on loading variables has also been identified.     

Fatigue behaviour of precipitation-hardening medium C steels containing Cu

The presence of Cu precipitates counteracts the cyclic softening present in ordinary quenched and tempered steels. This is expected to result in an increase in fatigue limit. The fatigue crack propagation rate (dc/dN) at constant K in the Cu-C steels was shown to depend on heat-treatment and carbon content. To maximize yield strength and minimize ¦da/dN¦_K for tempering at 500° C, one must choose a low C content and temper for a short time; ¦da/dN¦_K in 0.28 wt % C-1.45 wt % Cu tempered for 13 min was one-third that for 0.45 wt % C-1.45 wt% Cu tempered for 200 min. There is also an advantage in adding Cu while simultaneously lowering the Ccontent. The dc/dN data are discussed in terms of the yield strength and the energy to form a unit area of fatigue crack, U, which was measured using foil strain gauges. The quantity (¦dc/dN ¦_{K y} ² U) where _y is the cyclic yield stress, was found to be nearly constant. In the 0.28 wt % C-1.45wt % Cu alloy, short ageing times at 500° C resulted in greater resistance to initiation of cracks at notches for low Ks than long ageing times.     

Toughening of titanium alloys by twinning and martensite transformation

Two kinds of titanium alloys, titanium alloy (Ti-10V-2Fe-3Al) and titanium alloy (Ti-5Al-2.5Sn) were used to investigate the toughening mechanisms with new approaches. The results show that Ti-5Al-2.5Sn alloy possesses good combination of strength and ductility as well as satisfied low-cycle fatigue life both at 293 K and 77 K. As for Ti-10V-2Fe-3Al alloy, the microstructure with metastable phase shows lower strength and ductility but higher threshold stress intensity factor (K _th) than solution treated and aged microstructure composed of and phases. The microstructures also show that twinning occurs in deformation of Ti-5Al-2.5Sn alloy at 77 K. Twinning seems to be helpful for improving the low-cycle fatigue life to a great extent at cryogenic temperature. It's also found that owing to stress-assisted martensite transformation in metastable Ti-10V-2Fe-3Al alloy, the fatigue crack propagation path shows a very tortuous way, which decrease the effective stress intensity factor (K _eff) at crack tip, and increase threshold stress intensity factor (K _th).     

Effect of Closure of the Tip of a Fatigue Crack on the Asymmetry of Loading Cycles and on the Thresholds of Crack Resistance

On the basis of the experimental data, it is shown that, in the presence of closure of the tip of a fatigue crack, the imaginary influence of the positive load ratio R on the kinetics of crack growth and on the thresholds of crack resistance expressed via the threshold range of stress intensity factors K _th,R is actually the quantitative representation of changes in the characteristic of crack closure K _cl ^op provided that we use the nominal range of stress intensity factors K.     

Acoustic emission and fatigue crack growth in rigid polyurethane foam

Compact tension specimens of a rigid polyurethane foam have been tested in fatigue and crack growth has been monitored visually and by means of acoustic emission (AE). During the load cycle it has been found possible to resolve the AE activity into four regions: the crack faces un-sticking, fracture events at or close to peak load, a period of zero AE just after peak load, and AE associated with crack closure lower down the unloading part of the cycle. The fracture AE has been found to increase rapidly with crack length — consistent with a seventh power dependence on K — and to occur during every cycle at high K values, but to be absent in an increasingly greater proportion of cycles as K is decreased below about 40 kPa m^1/2. AE data obtained on samples in which crack growth occurred across the layers of foam, through the high density inter-layer skins, show that the technique is very sensitive to the crack retardation effect associated with these skins well before this retardation is detectable visually.     

FATIGUE CRACK GROWTH AND CLOSURE BEHAVIOUR THROUGH A COMPRESSIVE RESIDUAL STRESS FIELD

Behaviour of fatigue crack growth and closure through a compressive residual stress field is investigated by performing fatigue crack growth tests on welded SEN specimens of a structural steel (JIS SM50A). Depending on the type of the initial residual stress in the region of crack growth, the growth and closure of the crack show different behaviour. In particular, in the transition region from a compressive residual stress field to a tensile residual stress field, the fatigue crack growth rates cannot be described by the effective stress intensity factor range ΔK_eff, based on the measured crack opening stress intensity factor K_op. Also it is found that the R'-method using the data of da/dN vs ΔK for residual stress-free specimens, with the effective stress ratio R'[=(K_max+K_r)/(K_min+K_r)], gives non-conservative predictions of the growth rates in the transition region. Observations of crack closure behaviour in this study indicates that partial opening of the crack occurs and this plays an important role in crack growth through a compressive residual stress field. Based on the concept of a partial opening point (defined and measured in this work), fatigue crack growth behaviour can be better explained.     

Fatigue Fracture in VNS-25 Stainless Steel

The paper covers the experimental study of the influence of cycling frequency ranging from 20 Hz to 10 kHz and the cycle asymmetry on the crack growth resistance of VNS-25 stainless steel. It is demonstrated that as the cycling frequency is raised, the crack growth rate decreases monotonically, while threshold values of the stress intensity factor K_th grow. The latter is due to the fact that at high cycling frequencies the plastic deformation processes remain incomplete and the contribution of the fracture mechanisms that facilitate greater energy intensity of fatigue crack growth processes becomes more significant. A comparison of K_th and fatigue life values as a function of cycling frequency for smooth and notched specimens demonstrates that if represented in relative coordinates these functions are described by a common relationship. This allows a quantitative assessment of the effect of the strain cycling rate on the above-mentioned properties of a material from the results of tests of one type only. It has been found that the values K_th in asymmetrical loading cycles are related to those in symmetrical cycles, as well as to a coefficient of material's sensitivity to the static component, and linearly depend on the load ratio.