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.

     

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.     

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.     

Asymptotic expansions for constant-composition dew-bubble curves near the critical locus

Explicit functional representations are developed for constant-composition dew and bubble curves near critical according to the modified Leung-Griffiths theory. The pressure and temperature incrementsP=P–P _c andT= T–T _c, where c denotes critical, are linearly transformed to new variablesP andT. In the transformed space, the coexistence curves are no longer double-valued and can be expressed as a nonanalytic expansion, where the coefficients are functions of the critical properties and their derivatives. A similar asymptotic expansion is developed forT in terms of the density increment=– _c. In the approximation that the critical exponents=0 and=1/3, the critical point in temperature-density space is shown to be a point of maximum concave upward curvature, rather than an inflection point as previously conjectured.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.Formerly National Bureau of Standards     

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.     

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.     

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.     

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 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.     

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.     

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.     

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.     

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.     

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.     

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.     

Using criteria of the nonlinear fracture mechanics in examining the growth of surface fatigue cracks

The authors propose a method of evaluating the cyclic cracking resistance of high-ductility corrosion-resisting steels using the method of the cyclic J-integrals. In constructing kinetic diagrams of fatigue failure of specimens with surface semielliptical cracks of 07Kh13N4AG20 and 12Kh18N10T steels the geometrical parameter of the crack was represented by the quantity l proposed by the authors. Comparison of the diagrams constructed for the parameters a (depth of the surface crack), C (the length of the surface crack), and l showed that the evaluation of the cracking resistance by the dependence dl/dN-J_l; is accurate and that the information content of da/Dn-J_a, dC/dN-gDJ_c diagrams is low. Variation of the thickness of the examined material (t = 4–12 mm) and of test temperature (T = 293-77 K) has no marked effect on the form of the dl/dN-gDJ_l dependence.Translated from Problemy Prochnosti, No. 6, pp. 3–12, June, 1993.     

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.     

Experimental investigation of the effects of stress rate and stress level on fracture in polystyrene

The effects of stress rate and stress level on fatigue crack propagation in compression-moulded single-edge notched specimens (0.25 mm in thickness) of polystyrene are reported. Values of the stress rate are obtained from the formula = 2v(_max – _max),, wherev is the frequency and _max, _min are the maximum and minimum stresses of the fatigue cycle. Different levels of are achieved by changing the frequency while keeping _max, _min at fixed values. The effect of the stress level is investigated by keeping and _min constant and varying _max andv. The results show that when the kinetic data are plotted as l/t against the energy release rateG ₁, a relatively small effect of the stress rate is observed. If the same data are treated as l/N againstG ₁, a decrease in l/N with test frequency is seen. The increase in the level of _max results in a higher crack speed. The critical crack length is found to be practically the same for all stress-rate experiments. A decrease in the critical crack length is observed with the increase in stress level. Analysis of craze distribution around the crack path shows that the extent of crazing decreases with the increase in stress rate and increases with the increase in stress level. For all experimental conditions, the ratio of the second moment to the square root of the fourth moment of the histograms of craze density along directions normal to the crack path is found to be constant throughout the slow phase of crack propagation. This result supports a self-similarity hypothesis of damage evolution proposed in the crack layer model.     

On the driving force for fatigue crack formation from inclusions and voids in a cast A356 aluminum alloy

Monotonic and cyclic finite element simulations are conducted on linear-elastic inclusions and voids embedded in an elasto-plastic matrix material. The elasto-plastic material is modeled with both kinematic and isotropic hardening laws cast in a hardening minus recovery format. Three loading amplitudes (/2=0.10%, 0.15, 0.20%) and three load ratios (R=–1, 0, 0.5) are considered. From a continuum standpoint, the primary driving force for fatigue crack formation is assumed to be the local maximum plastic shear strain range, _max, with respect to all possible shear strain planes. For certain inhomogeneities, the _max was as high as ten times the far field strains. Bonded inclusions have _max values two orders of magnitude smaller than voids, cracked, or debonded inclusions. A cracked inclusion facilitates extremely large local stresses in the broken particle halves, which will invariably facilitate the debonding of a cracked particle. Based on these two observations, debonded inclusions and voids are asserted to be the critical inhomogeneities for fatigue crack formation. Furthermore, for voids and debonded inclusions, shape has a negligible effect on fatigue crack formation compared to other significant effects such as inhomogeneity size and reversed loading conditions (R ratio). Increasing the size of an inclusion by a factor of four increases _max by about a factor of two. At low R ratios (–1) equivalent sized voids and debonded inclusions have comparable _max values. At higher R ratios (0, 0.5) debonded inclusions have _max values twice that of voids.