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.

     

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.     

Ductile-Brittle Transition in Cold-Brittle Metals under High-Cycle Loading

On the basis of the experimental data accumulated under high-cycle loading for cold-brittle steels, we determine the critical characteristics of the ductile-brittle transition. With the help of the criterion of invariance of the effective kinetic diagram of fatigue fracture [bounded current values of the effective range of the stress intensity factor (K_{{fcl.th,T_2}}K_eff K _{eff T1} ^f.inv ), these characteristics determine the limits of existence of the so-called ductile-brittle transition as well as the first T_c1 and second T_c2 critical temperatures of brittleness. It is shown that the effective range of the stress intensity factor K_eff determined by measuring current values of the crack-tip opening displacement is a local characteristic of the crack resistance of the material in the linear elastic fracture mechanics.     

Supercooling of In2Bi and InBi Melts

The effect of melt overheating T ⁺ on the critical supercooling T ^– of liquid In₂Bi and InBi is studied by cyclic thermal analysis. It is shown that, the T ^– for In₂Bi is 2.0 K, independent of the melt preheating temperature. In contrast, the T ^– for InBi varies jumpwise with T ⁺: T ^– 1.0–1.6 K at T ⁺ < 5 K, and T ^– 16 K at T ⁺ = 5–300 K, independent of the cooling rate (varied from 0.002 to 8.0 K/s). The solidification behaviors of In₂Bi and InBi are shown to correlate with the structures of their liquid and solid phases.     

Subgap peak and Tomash-McMillan-Anderson oscillations in the density of states of SNS Bridges

The quasiparticle spectra and the densities of states of superconducting-normal-superconducting junctions are computed from the WKBJ transformed Bogoliubov-de Gennes Equations (BdGE), which are solved by Picard iteration and numerical integration. It is shown that the influence of the proximity effect on the bound states can be modeled by a rectangular pair potential well of effective normal layer thickness 2a*= _–L ^L [1–(z)/]dz, where (z) is the pair potential of the junction, is its asymptotic constant value, and 2L is the total length of the sample. The density of states exhibits a subgap peak at energies less than besides the BCS peak atE=; forE> there are geometrical resonances which are due to electron-hole interferences in finiteS layers of thicknessL-a*.     

Electron fractography and fatigue crack propagation in 7075-T6 aluminum sheet

A centrally slotted thick sheet of 7075-T6 aluminum alloy was cyclically loaded. Striation spacings and crack propagation rates on the specimen surface were measured and compared and the fractographs were examined. The average striation spacing is found proportional to K ^1.8; while the surface crack propagation rate is proportional to K^{2 8}, where K is stress intensity factor range. Cleavage fractures of brittle particles appear to cause a difference between the overall surface crack propagation rate and striation spacings.In the lower K region, there are fewer cleavage fractures, the striations are more distinct and the directions of the striations do not deviate much from the normal to the direction of the overall crack propagation. In the higher K region, there are more cleavage fractures. In this region striations run in divergent directions and become less evident. The differences in fracture surface features result from the cleavage fracture of brittle particles.

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Zusammenfassung Ein zentral geschlitztes Blech aus Aluminium-legierung wurde zyklischen Beanspruchungen unterworfen.Die Abstände zwischen den Verformungslinien sowie die Rißfortpflanzungsgeschwindigkeit an der Proben-oberfläche wurden gemessen und miteinander verglichen; die Mikrofiaktogramme wurden untersucht.Es ergab sick daß der mittlere Abstand zwischen zwei Verformungslinien K ^1.8 proportional ist, während die an der Oberfläche gemessene Rißfortpflanzungsgeschwindigkeit K ^2.8 proportional ist, wobei K der Schwankungsbereich den Span nungsintensitätsfaktors darstellt.Dieses unterschiedliche Verhalten wird durch das Auftreten von Spaltbruchen in den spröden Materialteilen erklärt. Im Bereich kleiner K-Werte gibt es nur wenig Spaltbrüche; die Verformungslinien sind gut ausgebildet and ihre Richtung weicht nur geringfügig von der Normalen zur allgemeinen RiBfortpflanzungsrichtung ab.Im Bereich hoher K-Werte sind die Spaltbrüche zahlreicher und die Verformungslinien entwickeln sich nach verschiedenen Richtungen ; sie Bind auch weniger ausgeprägt. Die Unterschiede in der Ausbildung der Bruchoberfläche stammen von den Spaltbruchen spröder Teilchen her.

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Résumé Une tôle de d'alliage d'aluminium comportant une entaille en son centre a été soumisse à sollicitations cyclicques.On a mesuré et comparé les espacements entre les stries, et les vitesses de propagation de la fissure en surface. Des microfractographies ont également été effectuées. On a trouvé que la distance moyenne séparant deux stries était proportionnelle à K ^1.8, tandis que la vitesse de propagation de la fissure, mesureé en surface, était proportionnelle à K ^2.8, K désignant l'intervalle de variation du facteur d'intensité des contraintes.Des ruptures par clivage de portions fragiles apparaissent être la cause des differences rencontrées.Dans la zone des faibles valeurs de K, il n'y a que peu de ruptures par clivage, les stries sont plus distinctes, et leur orientation ne dévie pas beaucoup de la normale à la direction générale de la propagation de la fissure.Dans la zone des valeurs élevées de K, les ruptures par clivage sent plus nombreuses; les stries se développent selon des orientations divergentes; elles deviennent moins visibles.Les différences qui caractérisent les aspects des ruptures precedent de la rupture par clivage de portions fragiles.

     

On mode I and mode II energy release rates of an interface crack

The opening (mode I) and sliding (mode II) components of the energy that is released during an incremental extension of an interface crack between two different elastic materials are evaluated by the Irwin's crack closure method. Each component of the energies (G _I and G _II ) is expressed in terms of the functions of the length of the incremental crack extension (a) and the real and imaginary part of the complex stress intensity factor defined by Malyshev and Salganik. It is found that values of G _I /a and G _II /a oscillate violently when a approaches zero and that, hence, in contrast with the case for homogeneous materials, each energy release rate should be defined as G _I /a and G _II /a for an actual crack growth step size.     

A correlation of ΔK th-value with the exponent,m, in the equation of fatigue crack growth for various steels

Literature (mainly in Japan) relating to fatigue-crack-growth-data at R=0 in an air environment for a wide range of steels is reviewed with particular attention to the threshold stress intensity, K _th. The collected data are analyzed in terms of the exponent, m(the slope of the linear portion of the log(da/dN)-logD relationship) by taking account of microstructure, material strength, fracture toughness and specimen thickness. The mean rate of fatigue crack growth for ductile steels in the range from the intermediate growth rate to threshold level and the relevant threshold values at R=0, K _th0, can be represented asda/dN = 1.700 × 10^-4(K103.6)^m - 10^-6andK _th0 = 103.6(5.88 × 10^-3)^1/m,where (da/dN) and K are measured by the units of mm/cycle and kgf/mm^3/2, respectively. Contrary to this, in the case of extremely brittle steels with K _IC-value below 200 kgf/mm^3/2 (the fracture occurs by the intergranular separation), the relationships are given byda/dN = 2.893 × 10^-5(K/49.94)^m - 2.5 × 10^-7andK _th0 = 49.94(8.64 × 10^-3)^1/m.

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Résumé La littérature, principalement japonaise, relative aux données sur la propagation des fissures de fatigue pour R=0 dans un environnement d'air et pour une large catégorie d'aciers fait l'objet d'une revue avec une attention particulière pour l'intensité de contrainte de seuil, K _th. Les données collectées sont analysées en terme de l'éxposant m (qui représente la pente de la portion linéaire de la relation log(da/dN)-log K, en tenant compte de la microstructure, de la résistance du matériau, de la ténacité à la rupture et de l'épaisseur de l'éprouvette. La vitesse moyenne de propagation d'une fissure de fatigue dans le cas des aciers ductiles dans la fourchette entre la vitesse intermédiaire de fissuration et le niveau critique, et les valeurs correspondantes de seuil à R=0, K _th0 peuvent être représentées par la relation:da/dN = 1.700 × 10^-4(K103.6)^m - 10^-6etK _th0 = 103.6(5.88 × 10^-3)^1/m,où (da/dN) et K sont mesurés en unités de mm/cycle et en kgf/mm^3/2 respectivement. En contraste, dans le cas d'aciers extrèmement fragiles avec des valeurs K _IC en dessous de 200 kgf/mm^3/2 (la rupture se produit par une séparation intergranulaire), ces relations sont données par:da/dN = 2.893 × 10^-5(K/49.94)^m - 2.5 × 10^-7etK _th0 = 49.94(8.64 × 10^-3)^1/m.

     

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.     

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.     

Changes in surface characteristics of dental resin composites after polishing

The objectives of this study were (1) to determine in vitro changes in surface roughness and color of dental resin composites after application of three finishing and polishing systems; (2) to evaluate the difference in color stability after immersion in a dye solution after polishing; and (3) to evaluate the effects of surface condition, especially roughness, on measured color depending on the color measuring geometries of specular component excluded (SCE) and specular component included (SCI). Color and surface roughness (R_a) of resin composites of four brands of A2 shade and one brand of Yellow Enamel shade were measured after polymerization, after polishing with Enhance (Dentsply), Sof-Lex (3M ESPE), or Super-Snap (Shofu) composite finishing and polishing systems. Color was also measured after immersion in 2% methylene blue solution. Color was measured according to the CIELAB color scale. Color changes (E*_ab) after polishing/staining and by the measuring geometry were calculated by the equation; E*_ab = [(L*)² + (a*)² + (b*)²]^1/2. Ra value was measured with a surface roughness tester. E*_ab and L* values after polishing and after staining varied among polishing systems when measured with SCE geometry. Composites polished with Super-Snap and Sof-Lex systems showed higher E*_ab and L* values than those polished with Enhance polishing system with SCE geometry. E*_ab and L* values between specimens with different surface conditions measured with SCE geometry were significantly higher than those with SCI (p < 0.01). Changes in R_a value after polishing was insignificant in most cases.     

Fatigue fracture toughness and crack propagation rate

Fatigue crack growth rate, da/dN, of two high strength steels were examined in a laboratory air at different stress ratios, covering almost the entire range of stress intensity, K, from nearly threshold value, Kth, to final fracture. The fatigue fracture toughness, Kfc, corresponding to the final fracture in fatigue, was also determined. The lower the Kfc, the higher da/dN and reduced Kth are revealed.This correlation was analyzed quantitatively based on the four parameter Weibull function. And the stress ratio dependency of the fatigue crack propagation curve can be cleared in a successful manner.The fatigue characteristic stress intensities, Ke and Kv, are proposed to define the transition behaviour in fatigue crack growth curve, from so called region 1 to 2, and from region 2 to 3, respectively. Especially the Kv valua can be specified to be the 0.63Kfc.

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Résumé On a étudié la vitesse de propagation de fissure en fatigue da/dN de deux aciers à haute résistance dans un atmosphère de laboratoire sous des sollicitations couvrant toute la gamme des intensités de contraintes variables K, depuis une valeur voisine de la valeur du seuil Kth jusqu'à celle correspondant à rupture finale.La ténacité à la rupture par fatigue Kfe correspondant à la rupture finale par fatigue a été également déterminée. II s'avère que plus Kfe est faible, plus élevée est da/dN et plus Kth est réduite. Cette correlation est analysée quantitativement en se basant sur la fonction de Weibull à quatre paramètres. On peut ainsi clarifier la manière dont le rapport de contraintes influe les courbes de propagation des fissures de fatigue.On propose de définir pas les facteurs caractéristiques d'intensité de contrainte Ke et Kv les comportements de transition de la courbe de vitesse de propagation de la fissure entre respectivement les régions dénommées 1 et 2, et 2 et 3.En particulier, on peut spécifier que la valeur Kv vaut 0,63 Kfe.

     

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.     

Investigation of the excitonic insulator phase in bismuth-antimony alloys

Pressure-induced metal-semiconductor transitions in bismuth-antimony alloys in a strong magnetic field (up to 70 kOe) at helium temperatures have been investigated. It is found that for values of the overlap-gap |G|1 meV the alloy forms an excitonic insulator (EI) in magnetic fields above a certain threshold (30–40 kOe). It is inferred that the EI energy gap increases with the magnetic field. The maximum gap observed in fields of 70 kOe turns out to be ₀₀7.5 K. An analysis of the results shows that transitions to the EI phase are observed from both the semimetal and the semiconducting states. The critical transition temperatureT _c is related to the EI gap by the expressionT _c0.7. Arguments are advanced in support of the fact that the formation of the EI phase involves the pairing of electrons at theL point with holes at theT point.     

An investigation of the micromechanisms of fatigue crack growth in structural gas turbine engine alloys

This paper presents an overview of fatigue fracture modes in selected structural alloys employed in gas turbine engines. These include the mechanisms of fatigue crack growth in the near-threshold, Paris and high-K regimes obtained from Ti-6Al-4V, Inconel 718 and PWA 1472 (a single crystal nickel-based superalloy of similar chemical composition to Inconel 718). Fatigue fracture modes in these materials are shown to be strong functions of the stress intensity factor range, K, and the maximum stress intensity factor, K _max. Fatigue mechanism maps are also presented to show the parametric ranges of K and K _max corresponding to the different fatigue fracture modes.     

Localized single-particle excitations and the density of states for superconducting composites

The problem of localized single-particle excitations and the density of states (DOS) for an inhomogeneous system consisting of a spherical superconductor (with radius a and order parameter ₁) embedded in another superconductor (order parameter ₂) of infinite size is considered. With the assumption of constant values of ₁ and ₂, the Bogoliubov equations are solved for general values of l (the orbital angular momentum quantum number). For a fixed value of ₁/₂ and different values of ₂/E _F, the dependence of the excitation energy (l=0)/₂ on the particle sizek _F a is shown (k _F is the Fermi wave vector andE _F is the Fermi energy). Fork _F a=300, 450, and 800 and a fixed value of ₂/E _F, the variations in the DOS by changing ₁/₂ are also shown.     

Variational method for measuring dielectric parameters of polar liquids at ultrahigh frequencies

Conclusions Owing to the use of nomograms the above method is universal and rapid. It is independent of the frequency at which the values of and are measured, and it is equally applicable for measuring dielectric parameters of polar liquids which are highly absorbent at ultrahigh frequencies and have one or two clearly expressed minima in the relationship of tol, and for liquids with low dielectric losses in the uhf range, whose measurement with adequate precision is difficult by other methods. Among the deficiencies of the suggested method one should note the two values obtained for _d and tan /2 from the nomogram readings. However, this deficiency can easlly eliminated either by comparing the two values for _d and tan /2 with those obtained for them from a similar nomogram and the second minimum in the relationship of tol, or by an approximate evaluation of _d and tan /2 by means of any other less precise measuring method.Translated from Izmeritel'naya Tekhnika, No. 10, pp. 48–49, October, 1970.     

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.     

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.