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.     

Threshold stress intensity factor and crack growth rate prediction under mixed-mode loading

A new mixed-mode threshold stress intensity factor is developed using a critical plane-based multiaxial fatigue theory and the Kitagawa diagram. The proposed method is a nominal approach since the fatigue damage is evaluated using remote stresses acting on a cracked component rather than stresses near the crack tip. An equivalent stress intensity factor defined on the critical plane is proposed to predict the fatigue crack growth rate under mixed-mode loading. A major advantage is the applicability of the proposed model to many different materials, which experience either shear or tensile dominated crack growth. The proposed model is also capable to nonproportional fatigue loading since the critical plane explicitly considers the influence of the load path. The predictions of the proposed fatigue crack growth model under constant amplitude loading are compared with a wide range of fatigue results in the literature. Excellent agreements between experimental data and model predictions are observed.     

Shear stress intensity factor near semi-infinite cylindrical crack edges under their shock loading

The discontinuous solution of the torsional vibration equation for an elastic medium with a flaw in the form of a semi-infinite cylindrical crack is constructed. The method of solving the integro-differential equation describing the distribution of shear stresses along the edges of a cylindrical crack is presented. The evaluation procedure for a stress intensity factor and its numerical calculation for the case of short times under the shock loading of cylindrical crack edges are given. It is established that the magnitude of a dynamic stress intensity factor can be used to determine the condition of shock wave interactions with structural heterogeneities at the high-rate deformation of treated surfaces containing flaws in the form of cylindrical cracks. Translated from Problemy Prochnosti, No. 3, pp 63–72, May–June, 1999.     

The stress intensity factor due to normal impact loading of the faces of a crack

The plane strain problem of a half-plane crack in an unbounded elastic solid is considered. The faces of the crack are subjected to suddenly applied, equal but opposite concentrated normal forces which tend to separate the crack faces. The elastic wave propagation problem, which contains a characteristic length, is solved exactly by linear superposition over a fundamental solution arising from a particular problem in the dynamic theory of elastic dislocations. Attention is focused on the time-dependent stress intensity factor. For an applied load with step function time dependence, the stress intensity factor is negative from the time the first wave arrives at the crack tip until the arrival of the Rayleigh wave. At that instant, it takes on its appropriate static value, which is thereafter maintained. Generalizations are discussed for spatially distributed and/or time-varying normal impact loads.     

Thermal effect of plastic dissipation at the crack tip on the stress intensity factor under cyclic loading

Plastic dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic plastic zone. The proposed analytical solution of the thermo-mechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated analytically for the infinite plate and by finite element analysis. The heat flux within the reverse cyclic plastic zone is the key parameter to quantify the effect of dissipation at the crack tip on the stress intensity factor.     

Effects of the transverse stress on biaxial fatigue crack growth predicted by plasticity-corrected stress intensity factor

The transverse stress has an important effect on the biaxial fatigue crack behavior. However, the experimental evidence has provided conflicting indications: it is sometimes considered to increase, decrease or have no effect. These complex phenomena cannot be rationally explained by the existing mechanical models. The effect of the transverse stress on the fatigue crack growth behavior is still one of the most puzzling questions in biaxial fatigue. Physically, this effect is a transverse stress induced plasticity phenomenon. In this paper, a plasticity-corrected stress intensity factor (PC-SIF) is proposed to describe the effect of transverse stress on biaxial fatigue. By use of this new crack driving force some important phenomena associated with transverse stress are predicted. Comparisons with experimental results showed that the PC-SIF as an effective mechanical parameter is capable of predicting the effects of the crack length, the stress level, cyclic stress ratio, biaxial stress ratio and phase difference on the biaxial fatigue crack growth. Consequently, the alleged conflicting experimental results have been rationally explained by the PC-SIF.     

Variations of stress intensity factor of a semi-elliptical surface crack subjected to mixed mode loading

Maximum stress intensity factors of a surface crack usually appear at the deepest point of the crack, or a certain point along crack front near the free surface depending on the aspect ratio of the crack. However, generally it has been difficult to obtain smooth distributions of stress intensity factors along the crack front accurately due to the effect of corner point singularity. It is known that the stress singularity at a corner point where the front of 3 D cracks intersect free surface is depend on Poisson's ratio and different from the one of ordinary crack. In this paper, a singular integral equation method is applied to calculate the stress intensity factor along crack front of a 3-D semi-elliptical surface crack in a semi-infinite body under mixed mode loading. The body force method is used to formulate the problem as a system of singular integral equations with singularities of the form r ⁻³ using the stress field induced by a force doublet in a semi-infinite body as fundamental solution. In the numerical calculation, unknown body force densities are approximated by using fundamental density functions and polynomials. The results show that the present method yields smooth variations of mixed modes stress intensity factors along the crack front accurately. Distributions of stress intensity factors are indicated in tables and figures with varying the elliptical shape and Poisson's ratio.     

The influence of biaxial loading on branching of a dissolution driven stress corrosion crack

Stress corrosion cracking occurs due to the synergistic interaction between mechanical load and corrosion reactions. In this study, branching during anodic dissolution driven crack growth is studied using an adaptive FE procedure. The crack has an inherent blunt tip due to the dissolution, and the growth is treated as a moving boundary problem with a strain-assisted evolution law. Simulations are performed with different degrees of load biaxiality. It is found that increasing biaxiality promotes branching. No conditions for when branching takes place are found. Crack growth rates for branches are investigated, and it is found that, after an initial acceleration, constant growth rates can be reached, as well as decreasing speed and eventual arrest. The influence of T-stresses and perturbations sensitivity are discussed.     

Variation of stress intensity factor and crack opening displacement of semi-elliptical surface crack

In this paper a singular integral equation method is applied to calculate the stress intensity factor along crack front of a 3D surface crack. Stress field induced by body force doublet in a semi infinite body is used as a fundamental solution. Then the problem is formulated as an integral equation with a singularity of the form of r ^-3. In solving the integral equations, the unknown functions of body force densities are approximated by the product of a polynomial and a fundamental density function; that is, the exact density distribution to make an elliptical crack in an infinite body. The calculation shows that the present method gives the smooth variation of stress intensity factors along the crack front and crack opening displacement along the crack surface for various aspect ratios and Poisson's ratio. The present method gives rapidly converging numerical results and highly satisfactory boundary conditions throughout the crack boundary.     

Effect of stress wave shape on the crack propagation velocity in cyclic delayed failure

Crack propagation velocity in delayed failure under superposed repeating load, ($\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{R}}$, was compared with that under static load, ($\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{S}}$Two peaks appear on the relation between decreasing rate of crack propagation velocity, $\text{1-β = 1 ? (}\text{d}\text{a/}\text{d}\text{t))}{}_{\mathrm{R}}\text{/(}\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{S}}$ and frequency, ?, both under sinusoidal and square load. By changing the ratio of holding time at maximum stress intensity factor to that at minimum stress intensity factor in square load, it was deduced that the existence of two peaks on the 1 ? β vs $\text{f}$ curve was caused by an asymmetric interaction between hydrogen atoms and cyclic moving of the position with triaxial tensile stress at crack tip. Moreover, the relation between 1 ? β and $\text{f}$ under the positive or negative saw tooth load could be well explained by the interaction model.     

Local weight functions for stress intensity factor evaluation for a surface semi-elliptical crack under polynomial loading

The stress intensity factor distribution along the front of a surface semi-elliptical crack under polynomial loads is computed. Approximate formulas for the large number of ranges are obtained.     

Collinear stress effect on the crack branching phenomenon

The importance of the non-singular terms of the series representation for the stresses in the crack tip region has been underlined in recent papers. In the present work it is recognized that the stress-intensity factors K_I and K_II are no longer sufficient to define fracture crisis for the plane problem. Some fracture criteria are applied introducing the third parameter λ, which is connected with the stress collinear to the crack's line. The respective fracture loci in the K_I−K_II−λ space are discussed; they depend on the distance from the crack tip at which the crisis conditions are checked. Finally an application of the above mentioned loci to the uniaxial loading condition is shown.

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Résumé Le problème de la mécanique de la rupture a été étudie jusqu'ici en considérant, dans la solution élastique, valable autour des extrémités de fissure, le seul premier terme du développement en autofonctions de Williams. Ce terme de la série qui représente le champ de contrainte est inversement proportionnel à la racine carrée de la distance radiale de l'extrémité de l'axe de fissuration. Cependant, dans cette étude, on considère aussi le deuxième terme de cette série, indépendant de la distance radiale. L'omission du deuxième terme, comme on le souligne dans des travaux assez récents, équivaut à négliger l'effet des tensions normales colinéaires à l'axe de fissuration. Si l'on considère aussi le terme non singulier, on admet que la rupture dépend d'un paramètre ultérieur lié à la contriante normale colinéaire à l'axe de fissuration. Par conséquent, les facteurs d'intensité de contrainte K_I et K_II, introduits par Irwin, ne suffisent plus à décrire la ramification de la fissure. Les endroits de rupture, comme on le montre dans cette étude, sont représentés par des surfaces dans l'espace tridimensionnel K_I−K_II−λ, et non plus par des courbes dans le plan K_I−K_II. Conformément à ces hypothèses, les surfaces varient en fonction de la distance radiale de l'extrémité de la fissure d'après laquelle on estime les conditions de crise (déterminant la rupture). Cette distance est caractéristique du matériau considéré, puisqu'elle est liée à la dimension de la zone plastique à l'extrémité de la fissure. Dans la partie finale de l'étude, on montre ensuite une application dans un cas de sollicitation sous charge monoaxiale en indiquant les résultats expérimentaux obtenus sur des plaques de plexiglass entaillées.

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Research sponsored by the C.N.R. (Consiglio Nazionale delle Ricerche, Italy)     

Effect of microcrack array on stress intensity factor of main crack

An improved technique for solving crack-microcrack interaction problems is developed, based on the Green's function for a dislocation dipole placed in the vicinity of a main crack. The microcrack array is characterized by the microcrack density, orientation and length distributions. The stress field near the main crack tip is taken as a sum of a singular term of an anisotropic problem with stress intensity factor K, and a regular term. K and the regular term are determined from a system of equations obtained by self-consistency arguments. The proposed technique is illustrated by numerical solutions of several interaction problems for particular configurations of microcrack array.     

Investigations on the stress intensity factor field for unstable dynamic crack growth

In this study, the unstable dynamic crack propagation due to static loading in an elastic material is analyzed for both antiplane and inplane conditions. Of particular concern is the investigation of limitations on the assumption that the stress intensity factor field is fully established over a region of given size near the tip of a growing crack. The transient analysis of the stress for a material particle at a small fixed distance from the moving crack tip is examined in detail. Some estimations are made of the time required for the stress at a point near the moving crack tip to reach the value it would have if the stress field were actually given by the near tip stress intensity factor field. In addition, a simple formulation obtained from the equivalent static problem is proposed which can be used as a good approximation to the associated complicated dynamic transient problem.     

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.