Effect of temperature on the frequency dependency of crack propagation velocity in delayed failure under cyclic load

The crack propagation velocity and the incubation time in delayed failure under repeating load were examined at various frequency ƒ(0–800 cpm) and temperature T(5–80°C) using the pre-cracked specimen of JIS SNCM8 quenched and tempered. The crack propagation velocity under repeating load (da/dt)_R decreased with increase of frequency ƒ and revealed a minimum value (da/dt)_minat a certain ƒ. The activation energy obtained from the Arrhenius plot of (da/dt)_min vs 1/T was about 10,000 cal/mol, which was a little larger than 8100 cal/mol obtained from the relation between the crack propagation velocity under static load and 1/T. The reason for the existence of the minimum value in the crack propagation velocity was explained by assuming the interaction between hydrogen atoms invaded from crack tip and the cyclic change of the position with tri-axial tensile stress. The incubation time under repeating load did not seem to be controlled by the diffusion or concentration process of hydrogen atoms.     

Effect of specimen thickness on the crack propagation and crack branching in delayed failure

The crack propagation and crack branching behaviors in delayed failure have been investigated on the specimens with various thickness ($\text{B = 1.5–10}\text{mm}$).The crack propagation velocity reveals a maximum value at a medium specimen thickness ($\text{B = 5}\text{mm}$). This fact can be understood by assuming the compound effect of two factors that the triaxiality of stress at crack tip as a driving force for hydrogen diffusion increases with increase of specimen thickness $\text{B}$, and that the invasion of hydrogen atoms from specimen surface increases with decrease of $\text{B}$.The stress intensity factor at crack branching, $\text{K}{}_{\mathrm{IB}}$, increases with decrease of specimen thickness $\text{B}$, and when B is 1.5 mm, the specimen fractures without showing the crack branching. The latter fact can be explained by connecting the necessary and sufficient conditions for crack branching with the decrease in height of plastic region at the crack tip in thin specimens.     

Subcritical crack propagation under cyclic stress impulse

An equipment has been designed to observe subcritical crack propagation under cyclic impulse (impact) loads. The equipment design uses the concept of stress wave propagation in bars. A four point bend notched specimen is struck by an incident bar with a known stress wave. The test specimens were machined from PMMA sheet (Lucite^®). The crack, initiated from the notch, was detected by a step wise increase of a graphitic grid imprinted on one side of the specimen. The data was analyzed using fracture mechanics theory and compared with that of conventional fatigue.Although the applied strain rate was quite high (1s^–1), stable crack propagation was significant. It appears that the elastic energy stored in the specimen within the duration of each impulse is dissipated in craze formation at the tip of the advancing crack. Furthermore, the magnitude of stable crack propagation was larger under impulse loading than under sinusoidal fatigue. On the other hand, cracks were slower under impulse loading. Fractographic evidence attributes these phenomena to the nature of craze growth under each loading condition.     

Fatigue crack propagation under cyclic thermal stress

Structures used at elevated temperature subject to severe cyclic thermal stress. Therefore, accurate prediction procedures for thermal fatigue crack growth should be applied to rationalise component flaw assessment. Fatigue crack propagation tests under thermal stress were carried out using an modified type 316 stainless steel (316FR), which is a candidate material for the fast reactor in Japan. Thermal stress of the tests was generated by cyclically changed temperature distribution through thickness in a plate by induction heating and air-cooling. Numerical analysis was also carried out to examine the applicability of the J integral under cyclic thermal stress. The J integral under elasto-plastic condition under thermal stress is close to the elastically calculated J integral. Prediction by J integral tends to be conservative for deeper cracks, and modification of the J integral value using crack opening ratio gives good agreement with the experimental crack growth.     

An analysis of crack propagation velocity in delayed failure under repeating load using an internal friction model

Frequency and temperature dependency of crack propagation velocity in delayed failure under superposed repeating load was analyzed using an internal friction model which assumes the interaction between hydrogen atoms and the cyclic moving of the position with tri-axial tensile stress at crack tip.

The decrease of crack propagation velocity (da/dt)_R by the superposition of repeating load, the appearance of minimum value in (da/dt)_R at a certain frequency ƒ₀, and the shift of ƒ₀ by the change of temperature, are well explained by the internal friction model. Another reason for the decrease of (da/dt)_R by the superposition of repeating load appears to be the decrease of effective stress intensity at crack tip, though this cannot explain the appearance of minimum value of (da/dt)_R.     

The effect of repeating load on the crack growth initiation and crack propagation in delayed failure

The delayed failure test under repeating load was carried out with pre-cracked specimen. The incubation time and the crack propagation rate were correlated with the stress intensity factor K.

The incubation time is decreased by the superposition of repeating load, as the range of stress intensity factor ΔK or the repeating frequency f increase. The reason can be explained by the promotion of corrosion reaction due to, e.g. the destruction of oxide film on the crack tip, which facilitates the invasion of hydrogen atoms into the material.

The crack propagation rate da/dt is decreased by the superposition of repeating load, and there exist two valleys of crack propagation rate minima on the da/dt vs f and da/dt vs ΔK curves. One valley corresponds to the interaction between the cyclic movement of the region with tri-axial tensile stress and the hydrogen atoms diffused from crack tip, which disturbs the concentration of hydrogen atoms. Another seems te correspond to the generation of retained compressive stress which reduces the effective stress intensity at crack tip and supresses the invasion and diffusion of hydrogen atoms.     

On the effect of cyclic stress ratio on the fatigue crack propagation

A new model of fatigue crack propagation is proposed which takes the effect of cyclic stress ratio into account. In the model it is assumed that the fatigue crack propagation rate is proportional to the absorbed hysterisis energy per stress cycle at the tip of a crack. The energy is calculated from stress field resulting from the Dugdak-Barenblatt Model and strain field from an experimental result. The model was applied to analyse the experiments on several materials.     

Effect of residual stress on crack propagation in MDPE pipes

Crack propagation behaviour in single edge notched specimens prepared from medium-density polyethylene (MDPE) pipe is examined under creep condition. The crack grown from an exterior notch (inbound) initiated faster than that grown from an interior notch (outbound). Subsequently, the outbound crack propagated monotonically to ultimate failure. The inbound crack showed anomalous behaviour involving two arrest stages prior to ultimate failure. The pipe is found to possess substantial residual stresses. The energy release rate for each case was calculated taking into account the respective residual stream distribution. The fact that the rates of crack propagation are not a unique function of the energy release rate indicates that the fracture is also influenced by morphological gradients imposed by processing conditions.     

On the crack propagation with variable velocity

The plane problem of propagation of a straight crack in an elastic medium under arbitrary variable loading is considered. The locations of the edges of the crack are specified as arbitrary smooth functions of time under the only restriction that crack speed at any instant of time is less than the velocity of Rayleigh wave. Solution for the distribution of plane stress components near the crack tip is obtained. In particular, expressions for stress intensity factors at the crack are given, which thus makes it possible to deduce the crack motion under given loading conditions.     

On the crack propagation with variable velocity

The plane problem of propagation of a straight crack in an elastic medium under arbitrary variable loading is considered. The locations of the edges of the crack are specified as arbitrary smooth functions of time under the only restriction that crack speed at any instant of time is less than the velocity of Rayleigh wave. Solution for the distribution of plane stress components near the crack tip is obtained. In particular, expressions for stress intensity factors at the crack are given, which thus makes it possible to deduce the crack motion under given loading conditions.

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Zusammenfassung Man untersucht das ebene Problem der Ausdehnung eines geraden Risses in einem elastischen Medium unter beliebig veränderlichen Belastung. Die Örter der Ränder des Risses werden als beliebige stetige Funktionen der Zeit angenommen mit der einzigen Einschränkung daß die Rißgeschwindigkeit zu jedem Zeitpunkt kleiner ist als die Geschwindigkeit der Rayleighwelle. Die Lösung der Verteilung der ebenen Spannungskomponenten an der Rißspitze wird aufgestellt. Insbesondere werden die Spannungsintensitätsfaktoren am Riß gegeben, was die Ableitung der Rißausdehnung unter gegebenen Belastungsbedingungen ermöglicht.

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Résumé On considère le problème plan de la propagation d'une fissure droite dans un milieu élastique soumis à une charge arbitraire et variable.On spécifie que les lieux des bords de la fissure sont des fonctions monotones du temps, sous la seule réserve que la vitesse de fissuration est à tout moment inférieure à la vitesse de propagation des ondes de Rayleigh. On obtient une solution pour la distribution des composantes de la contrainte plane au voisinage de la pointe de la fissure.En particulier, des expressions du facteur d'intensité des contraintes à l'extrémité de la fissure sont fournies, qui permettent de déduire le mouvement de la fissure sous des conditions de charge déterminées.

     

有机玻璃疲劳裂纹扩展试验研究

为研究试样形状对有机玻璃疲劳裂纹扩展性能的影响,对M(T)和C(T)两种不同形状试样进行测试,运用Paris公式曲线拟合方法,对比M(T)和C(T)两种试样形状所获得的疲劳裂纹扩展数据,分析实测数据点分散性的大小并分析其原因。实验结果表明:在有机玻璃的疲劳裂纹扩展性能测试试验中,C(T)试样优于M(T)试样,能够更准确地表征有机玻璃的疲劳裂纹扩展性能。     

基于应力强度因子评估WCP形状对WCP/Fe复合材料热疲劳裂纹扩展行为的影响

应力强度因子在断裂力学中广泛应用于预测由远程载荷或残余应力引起的裂缝尖端附近应力状态。本文基于平面应力条件下应力强度因子建立WC_P形状与其尖端应力之间的规律,利用有限元分析软件对含不同形状WC_P的WC_P/Fe复合材料的热应力进行模拟仿真,研究WC_P形状对WC_P/Fe复合材料热疲劳裂纹扩展行为的影响。研究结果表明,WC_P的形状显著影响应力强度因子,进一步影响WC_P/Fe复合材料的热疲劳裂纹扩展行为。含球状和不规则状WC_P的WC_P/Fe复合材料的极限抗压强度分别约为460 MPa和370 MPa。含不规则状WC_P的WC_P/Fe复合材料因应力集中而容易产生脆性开裂现象。通过热震实验进行验证,发现实验结果与模拟仿真结果相近,说明有限元法的准确性,同时为WC_P/Fe复合材料的热疲劳裂纹扩展行为研究提供科学依据和理论基础。      

Stress dependency on ultrasonic wave propagation velocity

The velocity of an ultrasonic wave propagating in the uniformly deformed isotropic solid was analysed by the Eulerian viewpoint. The pseudo elastic coefficient (PEC) was used to solve the equation of motion of the elastic wave under finite deformation. The infinitesimal displacement gradients are connected to the stress increments by thePEC. Using thePEC and the partial differential equation of motion, the velocity of ultrasonic wave was quantitatively related to applied stress, moreover, the stress dependence on longitudinal and transverse wave velocities propagating in the direction parallel or perpendicular to the uniaxial tensile direction could be cleared. Consequently, the Murnaghan's third order elastic constants can be calculated by precisely measuring the uniaxial tensile stress and ultrasonic wave velocity.     

Effect of loading rate on microstructural features of steel failure in crack propagation

A quantitative and qualitative fracture analysis has been carried out on 40Kh and St.3 steel specimens. The existence of a certain loading rate threshold has been established whose exceeding changes the regularities of the effect of the loading rate on the shape and parameters of the fracture microrelief. This corresponds to the speed dependence of dynamic crack resistance of steel.Translated from Problemy Prochnosti, No. 2, pp. 20–24, February, 1991.     

Effect of reflected stress waves on the stress intensity factor of an anti-plane strain edge crack during crack propagation and after crack arrest

Analytic solutions have been obtained for the stress intensity factor for a propagating and arresting anti-plane strain edge crack in a semi-infinite plate. Kostrov's analysis for this system has been used, and solutions have been obtained up to the time it takes for a stress wave emitted from the crack tip at the start of crack propagation to be reflected first from the edge of the plate, then from the crack tip, from the edge of the plate again and to arrive again at the crack tip. To simplify the analysis a constant velocity of crack propagation has been assumed. If the crack arrests before the arrival at the crack tip of a stress wave emitted from the crack tip at the start of propagation and reflected from the edge of the plate, the stress intensity factor remains constant after arrest until this stress wave arrives. The stress intensity factor then increases until the time of arrival of a reflected stress wave emitted at the instant of arrest. After this the stress intensity factor decreases again. If the crack arrests after the arrival of the first reflected stress wave, the stress intensity factor increases after arrest under the influence of reflected stress waves emitted earlier during the propagation of the crack. The changes in the stress intensity factor are more pronounced at higher crack velocities.

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Résumé Des solutions analytiques ont été obtenues pour le calcul du facteur d'intensité de contrainte relatif à une fissure de bord dans une plaque semi-infinie en cours de propagation ou en cours d'arrêt dans des conditions d'état anti-plan de contrainte. Une analyse de Kostrov appliquée à ce système a été utilisée et les solutions ont été obtenues jusqu'au moment où une onde de contrainte émise de l'extrémité de la fissure sur le point du démarrage de la propagation de la fissure se trouvent réfléchie en premier lieu par les bords de la plaque et ensuite par l'extrémité de la fissure, à nouveau par le bord de la plaque et revenant à nouveau à l'extrémité de la fissure. Pour simplifier l'analyse, une vitesse constante de propagation de fissure a été supposée. Si la fissure est arrêtée avant que l'onde de contrainte émise par l'extrémité de la fissure au démarrage de la propagation et après réflexion contre le bord de la plaque n'arrive à l'extrémité de la fissure, le facteur d'intensité de contrainte demeure constant après l'arrêt, jusqu'à ce que l'onde de contrainte arrive. Ensuite, le facteur d'intensité de contrainte augmente jusqu'au moment où arrive l'onde de réflexion émise au moment de l'arrêt de la fissuration. Ensuite le facteur d'intensité de contrainte se réduit à nouveau. Si la fissure s'arrête après l'arrivée du premier train d'ondes réfléchies, le facteur d'intensité de contraintes s'accroît jusqu'à l'arrêt, sous l'influence des ondes réfléchies émises précédemment au cours de la propagation de la fissure. Les changements de facteur d'intensité de contrainte sont plus prononcés lorsqu'augmente la vitesse de fissuration.

     

High frequency cyclic crack propagation in ceramic materials

Techniques and instrumentation for studying high frequency cyclic crack propagation in ceramic materials are described. Tests performed on a silicate glass show that the cyclic slow crack growth mechanism up to 600 Hz is identical to the quasi-static mechanism. Conversely, a strong cyclic effect on the crack growth rate is observed in a tungsten carbide-cobalt material.

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Résumé On décrit les techniques et l'instrumentation utilisées pour l'étude de la propagation des fissures sous sollicitations cycliques à haute fréquence dans des matériaux céramiques.Des essais exécutés sur un verre au silicate montrent que le mécanisme de croissance cyclique lente de la fissure est identique à un mécanisme quasi-statique, pour les fréquences allant jusqu'à 600 Hz.Par contre, un effet important de la fréquence sur la vitesse de croissance de la fissure a été observé dans le cas d'un alliage pour outil de coupe au cobalt et carbure de tungstène.

     

Effect of material plasticity on fatigue crack propagation under complex stress state

The maximum energy release rate criterion, i.e., G _max criterion, is commonly used for crack propagation analysis. However, this fracture criterion is based on the elastic macroscopic strength of materials. In the present investigation, a modification has been made to G _max criterion to implement the consideration of the plastic strain energy. This criterion is extended to study the fatigue crack growth characteristics of mixed mode cracks in steel pipes. To predict crack propagation due to fatigue loads, a new elasto-plastic energy model is presented. This new model includes the effects of material properties like strain hardening exponent n, yield strength σ_y and fracture toughness and stress intensity factor ranges. The results obtained are compared with those obtained using the commonly employed crack growth law and the experimental data.