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.

---

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.

     

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.     

Deformation approach to the evaluation of the period of initiation and growth of fatigue macrocracks

We performed experimental investigation of the opening displacements of the contours of stress concentrators (notches and cracks) for various amplitudes of cyclic loading. On the basis of experimental results, we propose a new deformation parameter _t which is a function of the notch (crack) tip opening displacement , namely, _t /(+d*), where is the radius of the tip of the notch andd* is the characteristic size of the prefracture zone. It is shown that this parameter uniquely determines the number of cyclesN _l to the initiation of a fatigue macrocrack independently of the geometry of the specimens and stress concentrators in elastic and elastoplastic materials, i.e., the dependence of _t onN ₁ is a characteristic of the material. It is experimentally demonstrated that this dependence enables one to quantitatively describe the process of fatigue fracture both in the stage of initiation of macrocracks and their propagation.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 5, pp. 7–21, September – October, 1995.     

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.

---

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.

     

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.     

ΔK ol level effects on fatigue crack propagation

In order to determine the effects of K _ol level on fatigue life, a single peak load was applied at distinct K levels of 7.8×10.3 and 9.8×10³ p.s.i. in^1/2. Here the K _ol level was defined to be a K level at which overload was applied. Three different overload ratios of 1.5, 2.0, and 2.5 were used to determine the overload ratio effect on the recovery factor. The result showed that the recovery factor, Z, was linearly related to K as Z = qK+Z _o, where q was a function of overload ratio. The value of q decreased as the overload ratio increased in a given K _ol level and seemed to be an important factor as well as retardation cycles in determining the fatigue life. For the same overload ratio, specimens that underwent overload at a smaller K _ol level showed more improved fatigue life.Nomenclature a Crack length - a ^* Overload affected zone size - B Specimen thickness - (da/dN)_ca Crack growth rate due to constant amplitude fatigue load - (da/dN)_ol Crack growth rate after overload is applied - E Young's modulus - K Stress intensity factor - K _min Minimum stress intensity factor - K _max Maximum stress intensity factor - K _ol K level at which overload is applied - N Number of cycles - N _D Number of delayed cycles - N _f Number of cycles needed for a specimen to be completely fractured - r _p Assumed plastic zone size - S Load - _ys Yield stress - W Width - Z Recovery factor     

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.     

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.

---

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.

---

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.

     

General features of fatigue fracture diagrams of metals

In this paper the results of investigations of fatigue fracture diagrams (v-K diagrams) of materials or products (depicting the relationship between the fatigue crack growth rate, v, and stress intensity factor range in a cycle, K) performed in the Physico-mechanical Institute are summarized. Typical diagrams are described and their main features in normalized coordinates are clearly demonstrated. On this basis the defining parameters of crack growth rate curves (v-K curves), K_th, K_fc, m, and K^*, characterizing the crack extension resistance of material are validated. Convenient expressions for analytical approximating v-K curves by splines are proposed. The main observed deviations of v-K curves from typical ones are shown.Paper presented at the XIIth International Colloquium on Mechanical Fatigue (Miskolc, Hungary, 10–12 March, 1994).Published in Problemy Prochnosti, No. 1, pp. 30–35, January, 1996.     

Double influence of hydrogen on fatigue crack growth in heat-resistant steels

We investigate fatigue crack growth in cast heat-resistant steel pipes of reforming furnaces in a vacuum, in air, and in gaseous hydrogen in the temperature range 20 – 800°C. It is shown that the character and intensity of hydrogen-induced effects depend on temperature and loading amplitude. For the crack resistance threshold, we discovered the phenomenon of temperature inversion of these effects. Namely, the value of K _th in hydrogen increases with temperature up to 400°C and then decreases. Under high-amplitude loading, the influence of hydrogen manifests itself only in the acceleration of crack growth. The ambiguity in the influence of hydrogen on the plastic strain resistance of the material at the crack tip is analyzed on the basis of well-known physical concepts of the influence of hydrogen on the processes of generation and displacement of dislocations. The effects discovered in this work are explained by the realization of different fracture mechanisms and different types of hydrogen-induced effects under different conditions. Thus, at low temperatures (up to 400°C) and high K, one observes a decrease in the tearing strength; the case of low temperatures and low K is characterized by the shear fracture mechanism and the strengthening effect of hydrogen; for high temperatures ( 400°C) and low K, the shear fracture mechanism is combined with a decrease in the plastic strain resistance under the influence of hydrogen.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No, 4, pp. 7–15, July – August, 1994.     

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.     

Gravitational flow of superfluid helium through small orifices

We present data on the flow of superfluid helium through channels of diameters 2.5 and 5.0 µm. Three modes of flow are observed: (1) flow that can be identified with the thermal nucleation of vorticity, (2) flow described by z (t – t ₀), where z is the gravitational head andt the time, and (3) flow described by (z)^1/2 (t – t ₀). Associated with the third mode, flows appear with a critical velocity close to that of the Feynman prediction for small channels.Research supported in part by a grant from the National Science Foundation and in part by the U.S. Atomic Energy Commission.     

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.     

Interaction between a dislocation and various divalent impurity in KCl single crystals for the Fleischer's model taking account of the Friedel relation

The interaction between a dislocation and the impurity in KCl : Mg²⁺ (0.035 mol% in the melt), KCl : Ca²⁺ (0.035 and 0.065 mol% in the melt) and KCl : Ba²⁺ (0.050 and 0.065 mol% in the melt) was investigated from the strain-rate cycling test during the Blaha effect measurement. This was carried out at 77–254 K. As a result, it was found that the Fleischer's model taking account of the Friedel relation seems to be suitable for KCl : Ca²⁺ and KCl : Ba²⁺. However, it was not appropriate for KCl : Mg²⁺. Furthermore, the values of T _c, H(T _c) and G ₀ were obtained for the specimens. T _c is the critical temperature at which effective stress is zero. H(T _c) and G ₀ are the enthalpy and the Gibbs free energy of activation for the breakaway of the dislocation from the impurity, respectively. H(T _c) was almost the same for the specimens except KCl : Mg²⁺. G ₀ increased with increasing the divalent cation size. In addition, the tetragonality around the divalent ion-positive ion vacancy pair was estimated on the basis of G ₀ for the each specimen.     

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).     

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.     

Magnetic field dependence of zero-sound attenuation close to the pair-breaking edge in3He-B due toJ=1−,J z =±1 collective modes

Our previous theory yielded for the Zeeman splitting of the imaginaryJ=1 collective mode in³He-B the result =2+0.25J _z ( is the effective Larmor frequency). In this paper we take into account the downward shift of the pair-breaking edge from 2 to 2₂– (₂ and ₁ are the longitudinal and transverse gap parameters). This leads to a complex Landé factor: the frequencies of theJ _z =±1 components become =2+0.39J _z , and the linewidths of these resonances become finite: =0.18. The coupling amplitudes of theJ _z =±1 components to density are found to be proportional to gap distortion, (₁–₂/(/)². Our results for the ultrasonic attenuation due to theJ _z =±1,J=1 modes are capable of explaining the field dependence of the attenuation close to the pair-breaking edge as observed by Dobbs, Saunders, et al. The observed peak is caused by theJ _z =–1 component: its height increases due to gap distortion as the field is increased, and the peak shifts downward in temperature and its width increases with the field due to the complex Landé factor. TheJ _z =+1 component gives rise to a corresponding dip relative to the continuum attenuation.     

Fatigue crack growth rates for very short cracks developing at fastener holes in 7075 and 7010 aluminium alloys

Fatigue crack growth rates have been determined for very short corner and bore cracks developing from fastener holes. This was made possible by the use of a simple load programme which provided a contrasting fracture feature or marker. The programme consisted of a high-low-high switch of load ratio (R) usually in blocks of 100 loads. A constant was maintained within each block. The crack growth rate data for short cracks was in reasonable agreement with the published long crack data for 7075 and 7010 alloy. Strong retardation effects were in evidence and certain features of the fractures shed new light on the retardation models, and also on those of fatigue fracture itself.     

Thermodynamic properties of liquid3He-4He mixtures near the tricritical point. II. Data analysis by the scaling-field method

The scaling theory for tricritical phenomena by Riedel is applied to the analysis of thermodynamic properties of liquid³He-⁴He mixtures near the tricritical point. Within this theory experimental data for the phase diagram, the³He molar concentrationX, and the concentration susceptibility (X/) _T are discussed in terms of two scaling fields that are functions of the temperatureT and the difference = ₃ – ₄ of the chemical potentials of the two helium isotopes. The quantitiesX and (X/) _T in terms of thefields T and as independent variables are obtained for the intervals –0.1<T – T _t<0.53 K and –9< – _t <0.8 J/mole, from vapor pressure and calorimetric data described in a previous paper by Goellner, Behringer, and Meyer. The transformed data are analyzed to yield the tricritical exponents, amplitudes, scaling fields, and scaling functions. The values of the tricritical exponents are found to agree with those predicted by the renormalization-group theory of Riedel and Wegner. (Logarithmic corrections are beyond the precision of the present experiment.) Relations between amplitudes are derived and tested experimentally. The (linear) scaling fields are determined by using their relationship to geometrical features of the phase diagram. The data forX and (X/) _T are found to scale in terms of these generalized scaling variables. The sizes of the tricritical scaling regions in the normal and superfluid phases are estimated; the range of apparent tricritical scaling is found to be appreciably larger in the normal-fluid phase than in the superfluid phase. The tricritical scaling function for the concentration susceptibility is compared with the analogous scaling function for the compressibility of pure³He near thecritical gas—liquid phase transition. Finally, when the critical line near the tricritical point is approached along a path of constant < _t , the experimental data are found to exhibit the onset of the crossover from tricritical to critical behavior in qualitative agreement with crossover scaling.Work supported in part by the National Science Foundation through Grant No. GH-36882 and Grant No. GH-32007, and by a grant of the Army Research Office (Durham).