Conditions for crack kinking under stress-wave loading

Kinking of a crack in a prestressed body under the influence of incident stress waves is investigated on the basis of the balance of rates of energies. It is assumed that the crack tip will choose to propagate at a time, in a direction, and at a speed for which the energy flux into the propagating crack tip attains a maximum value with respect to variation of the kinking angle. It is shown that the balance of rates of energies implies that the crack tip speed is zero at the onset of fracture. Consequently, the conditions for the onset of crack kinking and for the computation of the kinking time and kinking angle are completely defined by the elastodynamic field around the original crack tip. Examples of the incidence of step stress waves on a semiinfinite crack in a prestressed body have been investigated. It is shown that for an incident antiplane wave with Mode III fracture, kinking is generally not possible. For an incident inplane wave with mixed Mode I–II fracture, kinking may happen. For that case curves are presented which relate the kinking time and the kinking angle to the state of prestress and to the parameters of the incident wave.     

Crack kinking under high pressure in an elastic-plastic material

Directional crack growth criteria in compressed elastic–plastic materials are considered. The conditions at the crack tip are evaluated for a straight stationary crack. Remote load is a combined hydrostatic stress and pure shear, applied via a boundary layer assuming small scale yielding. Strains and deformations are assumed to be small. Different candidates for crack path criteria are examined. Maximum non-negative hoop stress to judge the risk of mode I and maximum shear stress for mode II extension of the crack are examined in some detail. Crack surfaces in contact are assumed to develop Coulumb friction from the very beginning. Hence, a condition of slip occurs throughout the crack faces. The plane in which the crack extends is calculated using a finite element method. Slip-line solutions are derived for comparison with the numerically computed asymptotic field. An excellent agreement between numerical and analytical solutions is found. The agreement is good in the region from the crack tip to around halfway to the elastic–plastic boundary. The relation between friction stress and yield stress is varied. The crack is found to extend in a direction straight ahead in shear mode for sufficiently high compressive pressure. At a limit pressure a kink is formed at a finite angle to the crack plane. For lower pressures the crack extends via a kink forming an angle to the parent crack plane that increases with decreasing pressure.     

Crack curving under mode-I loading

The whole history of failure of a rectangular panel with two symmetrical notches and a central crack subjected to a progressively increasing tension load normal to the crack plane is studied. The material of the panel exhibits substantial plastic deformation prior to fracture. An elastic-plastic analysis of the plate is first performed based on finite elements. The results of stress analysis are coupled with the strain energy density theory to determine the critical load for crack initiation and the history of stable crack growth up to the point of instability. At instability the crack runs fast through the elastic material bypassing the plastic zone near the plate boundary. The crack deviates from its initial direction and is curved even though the plate is subjected to opening-mode loading. Results for crack trajectories are given for various initial crack lengths and notch radii of the plate.Presented at Fourth Greek National Congress on Mechanics, 26–29 June 1995, held at Xanthi, Greece.     

Crack extension under compressive loading

Non-planar extension (kinking) of a crack subjected to remote biaxial compression is studied to gain insight into compressive failure of brittle solids. Approximate expressions are developed for the stress intensity factors at the tips of the resulting wing cracks. Assuming the wing crack propagates at a constant value of $\text{K}{}_{\mathrm{Ic}}$, one can calculate wing crack extension vs load. The significance of the dependence on various parameters is discussed.     

Crack paths under mixed mode loading

Long fatigue cracks that initially experience mixed mode displacements usually change direction in response to cyclic elastic stresses. Eventually the cracks tend to orient themselves into a pure mode I condition, but the path that they take can be complex and chaotic. In this paper, we report on recent developments in techniques for tracking the crack path as it grows and evaluating the strength of the mixed mode crack tip stress field.     

Crack growth kinetics under impulse loading

The dynamic photoelasticity method has been used to study the effect of the acting wave, and the size and orientation of the incident wave front on crack growth kinetics (under short-term pulse loading). It has also been used to study the mechanism of dynamic stress formation at the crack tip. It has been shown that when compression or tensile waves are incident on the crack at an angle of 0<<80 and 100<<180°, the field of dynamic stress which arises is determined by the transverse shear strain while at an angle of 90±10°, stress formation is caused by strain tearing. When transverse waves act on a crack, there is a considerable amount of stress concentration at the crack tip irrespective of the incident angle. It has been established that one-, two-, or threefold crack growth occurs depending on the pulses and the crack depth.Translated from Problemy Prochnosti, No. 7, pp. 18–21, July, 1992.     

Crack propagation under constant amplitude loading

A crack propagation law is derived on the concept that net energy released in one cycle in the vicinity of crack tip is absorbed in cyclic plastic zone incorporating the concept of crack closure. Further, the derived law is modified by introducing some more material properties, as an attempt towards generalization. The finally developed law is dimensionally correct. The crack growth rates predicted by the developed crack growth rate law are compared with the experimental data of 16 materials and a good correlation is achieved.     

The kinking behaviour of a bimaterial interface crack under indentation loading

The aims of this paper are twofold. The first is to evaluate the applicability of the formula for the crack kink angle—based on the maximum principle stress criterion—for predicting the interface kink angle in a bimaterial sample undergoing indentation loading. This formula was developed for cracks in homogenous materials but in this paper, it is used to predict the kink angle using the mode mixity at the tip of a crack lying on a bimaterial interface. The second aim is to examine the behaviour of the system, in terms of the crack kink angle and contact radius, for various coating thickness', crack lengths and combinations of properties of the coating and substrate. The system that is analysed consists of a planar bimaterial sample undergoing indentation with a tungsten-carbide spherical indenter. Two-dimensional, axisymmetric models are created to represent the system, with subdomains used for modelling the cracks. In order to determine the applicability of the kink angle formula, the angle predicted is compared to the angle that is directly calculated using boundary element method models that establish the angle of the kink which yields the maximum mechanical energy release rate. The second aim of the paper is achieved by varying the material property combinations and coating thickness of the bimaterial sample and observing the effect on the kink angle of the interface crack and the contact radius. The methodologies employed are initially verified on homogenous samples with known solutions.     

Crack closure studies under constant amplitude loading

Crack closure experiments were performed on 6063-T6 Al-alloy using a COD-gauge for various load ranges and stress ratios. Experimental results show that for a given stress ratio, $\text{R}$, the crack closure load goes on decreasing as crack length increases (or $\text{K}{}_{\max }$ increases) and reaches even below minimum load level at higher values of stress ratios. On the basis of these experimental results, a model for effective stress intensity range ratio $\text{U}$, which is found to be a function of stress ratio $\text{R}$ and $\text{k}{}_{\max }$, is developed.     

Crack growth in ferroelectric ceramics under electric loading

Summary A crack with growth in ferroelectric ceramics under purely electric loading is analyzed. The crack tip stress intensity factor for the growing crack under small scale conditions is evaluated by employing the model of nonlinear domain switching. The electrical fracture toughness is obtained from the result of the stress intensity factor. It is shown that the ferroelectric material can be either toughened or weakened as the crack grows. Fatigue crack growth in a ferroelectric material under cyclic electric loading is also examined. The incremental fatigue crack growth under cyclic electric loading is obtained numerically. The fatigue crack growth rate is affected strongly by the electrical nonlinear behavior. It is found that the curve of fatigue crack growth rate versus electric field intensity factor is linear on the log-log plot at intermediate values of the electric field intensity factor.     

Crack trajectories under mixed mode and non-proportional loading

A novel testing procedure for mixed mode crack propagation is presented; it offers the possibility of non-proportional loading and of changing the crack trajectory during testing, features which allow non-traditional mixed mode tests which, in turn, may help in discriminating mixed mode fracture criteria. Detailed experimental stable crack trajectories and corresponding load-CMOD (or load-displacement) curves from these non-traditional tests are proposed as benchmarks for numerical programs of mixed mode crack propagation.     

Crack initiation and crack propagation under thermal cyclic loading

Theoretical and experimental investigations of crack initiation and crack propagation under thermal cyclic loading are presented. For the experimental investigation a special thermal fatigue test rig has been constructed in which a small circular cylindrical specimen is heated up to a homogeneous temperature and cyclically cooled down under well defined thermal and mechanical boundary conditions by a jet of cold water. At the end of the cooling phase the specimen is reheated to the initial temperature and the following cycle begins. The experiments are performed with uncracked and mechanically precracked specimens of the German austenitic stainless steel X6CrNi 1811.

In the crack initiation part of the investigation the number of load cycles to initiate cracks under thermal cyclic load is compared to the number of load cycles to initiate cracks under uniaxial mechanical fatigue loading at the same strain range as in the cyclic thermal experiment. The development of initiated cracks under thermal cyclic load is compared with the development of cracks under uniaxial mechanical cyclic load.

In the crack propagation part of the investigation crack growth rates of semi-elliptical surface cracks under thermal cyclic loading are determined and compared to suitable mechanical fatigue tests made on compact-tension and four-point bending specimens with semi-elliptical surface cracks. The effect of environment, frequency, load shape and temperature on the crack growth rate is determined for the material in mechanical fatigue tests.

The theoretical investigations are based on the temperature distribution in the specimen, which is calculated using finite element programs and compared to experimental results. From the temperature distribution, elastic and elastic-plastic stress distributions are determined taking into account the temperature dependence of the material properties. The prediction of crack propagation relies on linear-elastic fracture mechanics. Stress intensity factors are calculated with the weight function method and crack propagation is determined using the Paris relation.

To demonstrate the quality of the crack growth analysis the experimental results are compared to the prediction of crack propagation under thermal cyclic load.     

Two-criterial evaluation of the limiting state of a cracked body under a nonsymmetric loading

Problems of the correct derivation of crack-resistance characteristics under longitudinal or transverse shear are examined. It is proposed that effective values of the stress intensity factor, which are calculated in accordance with the theory of maximum tensile stresses, can be used to calculate the limiting state and critical brittleness temperatures for a cracked body under a combined load. It is recommended that the limiting load of ductile failure be calculated in accordance with the theory of limiting equilibrium using the Tresca strength condition. An approximate method of plotting the weighting function for cracks subject to nonsymmetric loading is developed.In order of discussion.Translated from Problemy Prochnosti, No. 11, pp. 32–38, November, 1991.     

Crack propagation in monolithic ceramics under mixed mode loading

Finite element calculations are presented for a semi-infinite crack in a brittle solid undergoing microcracking normal to the maximum tensile direction. Microcracks are presumed stable and a saturation stage is postulated wherein the effective elastic moduli attain steady state values. Mode I, mode II and mixed mode loading conditions are investigated. In these two latter cases, the method of analysis employed allows for cracks to grow out of their initial planes. The mixed mode loading case investigated corresponds to taking equal values of the remote mode I and II stress intensity factors. Contrary to what is observed in the mode I case, no appreciable R-curve behavior is found under mode II or mixed mode conditions.

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Résumé On présente des calculs par éléments finis pour une fissure semi-infinie dans un corps fragile comportant une micro-fissuration normale par rapport à la direction des tensions principales. On suppose que les microfissures sont stables et on postule un stade de saturation au cours duquel les modules d'élasticité atteignent des valeurs constantes. Les conditions de sollicitation en Mode I, et Mode II et en mode mixte sont étudiées et, dans les deux derniers cas, la méthode d'analyse utilisée autorise les fissures à croître hors de leur plant initial.Le mode mixte de mise en charge étudiée revient à prendre des valeurs égales pour les facteurs d'intensité des contraintes agissant à distance selon les Modes I et II.A l'inverse de ce que l'on observe dans le cas du Mode I, on ne trouve pas de comportement significatif selon une courbe R pour les conditions en Mode II et en mode mixte.