Evaluation of the period of subcritical growth of a high-temperature creep crack in the wheel of a steam turbine

The computational model of propagation of high-temperature creep cracks in metallic materials proposed earlier is used to develop a method for the evaluation of residual life of the wheels of steam turbines. Examples of annular and disk-shaped wheels are analyzed.     

A phenomenological theory of subcritical creep crack growth under constant loading in an inert environment

The subcritical creep crack growth under constant loading is considered as due to the repeated rupture of the plastic zone in the vicinity of the crack tip. Fracture mechanics concepts are used to derive the rupture life of a centre-cracked thin sheet loaded in plane stress. The formulation is such that numerical results can readily be obtained for crack growth. Approximate analytical formulae are also given for crack growth against time.     

Formal analysis of subcritical crack growth under monotonic loading

The article analyzes the equation of energy balance in integral form which made it possible to formulate a number of considerations concerning the conditions of applicability of criterial characteristics used in fracture mechanics, and to suggest a new criterion which, in the present author's opinion, characterizes more rigorously the conditions of failure of brittle materials.Translated from Problemy Prochnosti, No. 7, pp. 19–23, July, 1990.     

The kinetics of subcritical crack growth under sustained loading

The kinetics of subcritical crack growth under sustained loading for an AISI 4340 steel tempered at 400°F in distilled water were determined. Crack growth experiments were carried out over a range of temperatures from 10–75°C, using the crack tip stress intensity factor, K, to characterize the mechanical driving force. Results show that crack growth in distilled water is controlled by a thermally activated process with apparent activation energies that depend on K. Crack growth occurred only above a threshold K level with growth rates showing a strong K dependence at lower values of K and attaining constant, rate limiting values at higher K levels. The rate limiting velocities correspond to an apparent activation energy of 8000±1000 cal/mole, in essential agreement with values reported for crack growth in similar steels. This apparent activation energy corresponds to that for hydrogen permeation in AISI 4340 steel and lends further support to the concept that the rate limiting process for crack growth in high strength steels in water is that of hydrogen permeation into the crack-tip region. Because of the differences in the apparent activation energies for crack growth in water and in gaseous hydrogen, the rate limiting step in the permeation process still needs to be defined.

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Zusammenfassung Die Kinetik der subkritischen Rißausbreitung bei konstanter Belastung in distilliertem Wasser wird für ein Stahl AISI 4340, der auf 400°F Wärme behandelt wurde, aufgestellt.Die Rißausbreitungsversuche wurden, unter Verwendung des Spannungsintensitätfaktors K an der Spitze des Risses zur Charakterisierung der mechanischen Fortbewegungskraft, in einem Temperaturbereich von 10 bis 75°C ausgeführt.Die Ergebnisse zeigen daß die Ausbreitung des Risses im distillierten Wasser durch ein thermisches Beschleunigungsverfahren regiert wird, wo die Beschleunigungsenergie von K abhängt. Rißausbreitung kann nur über einem gewissen Niveau der Höhe von K zu stande kommen mit Rißausbreitungsgeschwindigkeiten die stark von K abhängen für die Werte die nahe über diesem Niveau liegen, die aber einen Konstanten Oberwert anstreben für höhere Werte von K.Diesem Oberwert der Geschwindigkeit gehört eine Beschleunigungsenergie von 8000±1000 Kal/mole an was mit den Werten die man für ähnliche Stähle gefunden hat übereinstimmt.Diese Beschleunigungsenergie ist die gleiche wie die, die zur Diffusion von Wasserstoff in Stahl AISI 4340 nötig ist. Dies ist ein zusätzliches Argument zur Annahme daß die Rißausbreitungsgeschwindigkeit für Stähle, mit hoher Bruchlast, im Wasser durch ein Diffusionsverfahren vom Wasserstoff in der Gegend der Spitze des Risses begrenzt wird.

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Résumé On a détermine la cinétique de la croissance subcritique des fissures sous charge constante dans l'eau distillée pour un acier AISI 4340 revenu à 400°F.Les essais de propagation de fissure ont été exécutés dans une gamme de températures comprise entre 10 et 75°C, les efforts étant caractérisés par le facteur K d'intensité des contraintes à l'extrémité de la fissure.Les résultats démontrent que la croissance de la fissure dans l'eau distillée est régie par un processus d'activation thermique, dont les énergies d'activation apparente dépendent de K. La propagation de la fissure ne se produit que lorsque K dépasse un certain seuil; les vitesses de propagation dépendent fortement de K à ses niveaux les moins elevés au-dessus de ce seuil, mais tendent vers une valeur limite constante lorsque K est important. Cette vitesse limite correspond à une énergie d'activation apparente de 8000±1000 cal/môle, ce qui est en accord avec les valeurs que l'on a trouvées pour la propagation des fissures dans des aciers similaires.Cette énergie d'activation correspond à celle qui est nécessaire pour la diffusion de l'hydrogène dans l'acier AISI 4340. Ceci constitue un argument supplémentaire en faveur du concept suivant lequel la vitesse de croissance des fissures dans les aciers à haute résistance en présence d'eau est limitée par un processus de diffusion de l'hydrogène dans la région de l'extrémité de la fissure.

     

Influence of the loading path on fatigue crack growth under mixed-mode loading

Fatigue crack growth tests were performed under various mixed-mode loading paths, on maraging steel. The effective loading paths were computed by finite element simulations, in which asperity-induced crack closure and friction were modelled. Application of fatigue criteria for tension or shear-dominated failure after elastic–plastic computations of stresses and strains, ahead of the crack tip, yielded predictions of the crack paths, assuming that the crack would propagate in the direction which maximises its growth rate. This approach appears successful in most cases considered herein.     

Mixed-mode fatigue crack growth under biaxial loading

Studies on crack growth in a panel with an inclined crack subjected to biaxial tensile fatigue loading are presented. The strain energy density factor approach is used to characterize the fatigue crack growth. The crack growth trajectory as a function of the initial crack angle and the biaxiality ratio is also predicted. The analysis is applied to 7075-T6 aluminium alloy to predict the dependence of crack growth rate on the crack angle. The effect of crack angle on the cyclic life of the component and on the cyclic life ratio is presented and discussed.     

Predicting fatigue crack growth under irregular loading

We describe a model for predicting fatigue crack growth (FCG) with the presence in the loading spectrum of peak and block tensile overloads. The model is based on account for the following factors influencing crack growth retardation: change of the quantity K_op as a consequence of the induction of a system of residual compressive stresses at the crack tip and increase of the degree of crack closure that is due to plastic deformation of the material in the wake of the tip of the growing crack; plastic blunting of the crack tip. We propose a technique for quantitative prediction of the residual crack tip opening (radius of the blunted tip) after a peak tensile overload. Experimental verification of the proposed FCG model with differing applied load irregularity showed that the model may serve as the basis of a method for predicting the service life of cracked structural members operating in irregular loading regimes.Translated from Problemy Prochnosti, No. 8, pp. 3–16, August, 1994.     

The effect of periodic-random loading on fatigue crack growth

A theory of fatigue crack growth based on the concept of damage accumulation is presented which takes some account of the effect of periodic-random loading. The Dugdale model of plasticity is used to calculate the distribution of the energy dissipated during stress cycling in the plastic zones of a crack embedded in a material sample of infinite extent. It is shown how to calculate the damage accumulated by decomposing the random group of stress levels into significant complete stress cycles of various amplitudes. A simple short numerical algorithm is presented which performs this decomposition. A crack growth law is derived having a very simple form which automatically incorporates the condition for catastrophic failure.

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Résumé On présente une théorie sur la croissance des fissures de fatigue basée sur le concept du dommage cumulatif, et tenant compte de l'effet de mise en charges aléatoires. On recourt au modèle de plasticité de Dugdale pour le calcul de la distribution de l'énergie dissipée lors du cycle de contrainte dans les zônes plastiques d'une fissure noyée dans un matériau de dimension infinie.On montre comment calculer le dommage cumulatif en décomposant les blocs de contraintes de niveau aléatoire en collectifs de contraintes cycliques d'amplitudes variables. Un algorithme numérique simple est présenté pour effectuer cette décomposition. On en tire une loi de propagation de la fissure dont la forme est très simple et qui comporte automatiquement les conditions susceptibles de conduire à une rupture brutale.

     

Influence of loading path on fatigue crack growth under multiaxial loading condition

In this study, the specimens made of carbon steel S45 with an initial surface straight edge notch were subjected to combined cyclic axial‐torsion loading at room temperature. The fatigue life, surface crack extension direction and crack length were experimentally investigated. The effects of loading path, stress amplitude ratio and phase angle on the crack growth behaviour were also discussed. The results showed that, under the combination of cyclic axial and torsion loading, the tension stress amplitude had more effect on the initial crack growth path than the latter. The shear stress amplitude contributed mainly to the latter crack extension. The crack extension path was mainly determined by the stress amplitudes and the ratio of the normal stress to the shear stress, and almost independent of the mean stresses. The increase of the tension stress amplitude and shear stress amplitude would both accelerate the crack growth rate.     

Short fatigue crack growth behavior under mixed-mode loading

Mixed-mode loading represents the true loading condition in many practical situations. In addition, most of the fatigue life of many components is often spent in the short crack growth stage. The study of short crack growth behavior under mixed-mode loading has, therefore, much practical significance. This work investigated short crack growth behavior under mixed-mode loading using a common medium carbon steel. The effects of load mixity, crack closure, and load ratio on short crack growth behavior were evaluated by conducting experiments using four-point bending specimens with several initial K _II /K _I mixed-mode ratios and two load ratios. Cracks were observed to grow along the paths with very small K _II /K _I ratios (i.e. mode I). The maximum tangential stress criterion was used to predict the crack growth paths and the predictions were found to be close to the experimental observations. Several parameters including equivalent stress intensity factor range and effective stress intensity factor range were used to correlate short crack growth rates under mixed-mode loading. Threshold values for short cracks were found to be lower than those for long cracks for all the mixed-mode loading conditions. Crack closure was observed for the entire crack length regime with all load mixity conditions at R ≈ 0.05 and for short crack regime under high load mixity condition at R = 0.5. Several models were used to describe mean stress effects and to correlate crack growth rate data.     

Mode I fatigue crack growth under biaxial loading

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

Simulation of corrosion fatigue crack growth under mixed-mode loading

The kinking of a corrosion crack due to mixed-mode fatigue loading is studied using an adaptive finite element procedure. The rate of material dissolution is assumed to be proportional to the stretching of the corroding surface. The dissolution of material is governed by a corrosion law, where no criterion is needed for neither crack growth nor growth direction. The problem is treated as a general moving boundary problem. The kink angles are found to be in very good agreement with results for sharp cracks using criteria reported in the literature.     

The prediction of fatigue crack growth under flight-by-flight loading

A large number of crack growth computations were made for flight-by-flight loading using several varieties of a fighter spectrum. Various retardation models were applied. With proper adjustment of the retardation model the experimental data could be closely reproduced in a calculation. It is concluded that satisfactory crack growth predictions can be made. The application of safety factors to predictions is discussed.     

Interlaminar fatigue crack growth of cross-ply composites under thermal cycles

The fatigue growth of a fiber reinforced composite laminate was characterized under thermal cycling using a combined experimental and computational investigation. Twenty-four ply composite laminates ([0°₁₂/90°₁₂]) are fabricated with a pre-existing delamination, and subjected to thermal cycling in an environmental chamber. The large mismatch in the coefficients of thermal expansion is used to grow an interlaminar crack at the interface of the 0° and 90° laminae. This thermal fatigue crack growth behavior is investigated for different amplitudes of temperature change (ΔT = 30–140 °C). The inspection of fracture surfaces, after completion of the fatigue tests, reveals an angled or kinked crack front growth with greater propagation distances near the free-surfaces/edges. Due to the non-uniform crack growth across the specimen thickness, three-dimensional finite element analyses are performed to investigate the fatigue growth mechanisms under thermal load. From the analysis, the energy release rate as well as the mixed-mode stress intensity factors is calculated and the variations of these fracture parameters are found to be consistent with the observed crack front configuration. Using the computed results, the experimentally measured crack growth rates are also correlated with the amplitude of energy release rate, and a power law form of the fatigue law is established. The relevant coefficients as well as the threshold energy release rate are also determined. The present analysis is useful for not only understanding the fatigue delamination mechanisms under thermal cycling but also for estimating the threshold temperature variation that is needed to drive crack growth.