Crack propagation at supersonic velocities

A theoretical model for laser-induced supersonic cracks in crystals with weak cleavage planes is developed. The crack is pictured as being driven by a laser-induced expanding plasma. The theory predicts the crack length-time history to be expected for a given energy-time input curve. The conditions for laser-induced supersonic crack production are seen to be a large input energy relative to fracture energy, a short loading time, and a weak fracture plane. The theoretical calculations are in rough agreement with experimental observations.

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Zusammenfassung Es wird eine Theorie aufgestellt, nach der laserinduzierte Brüche, die mit Überschallgeschwindigkeit in Kristallebenen leichter Spaltbarkeit laufen, beschrieben werden sollen. Dabei wird angenommen, daB der Bruch durch ein sich ausdehnendes Plasma—hervorgerufen durch den Laserstrahl—vorangetrieben wird. Die Abhängigkeit der Rißlange von der Zeit wird für eine bekannte Energie-Zeit Kurve angegeben. Die Bedingungen für die Erzeugung von laserinduzierten Überschallbrüchen sind: eine große Anfangsenergie, eine kurze Belastungszeit und eine schwache Spaltebene. Die theoretischen Berechnungen stimmen größenordnungsmäßig mit den experimentellen Ergebnissen überein.

     

Crack propagation velocities in bi-phase plates under static and dynamic loading

An investigation of the dependence of the crack-propagation velocity in complex bimaterial plates at different loading rates was undertaken. The specimens were fractured under the influence of both static and dynamic loadings and the crack-propagation velocities were detected by high speed photography with the optical method of caustics.The investigation was concentrated in detecting the influence that the different loading rates have on the fracture velocities in both phases of the plates and how this influence interferes—counteracting or superimposing—with the other factors that determine the crack propagation process in bi-material specimens. These factors are the effect of interface, the influence of the mechanical characteristics of each phase on the crack-propagation velocity etc.The results show that for constant and given material characteristics of the bi-phase plate the crack propagation velocity in the first (notched) phase tends to increase with increasing strain rates.The same is valid for the crack propagation velocity in the second phase, but only for the case when fracture occurs under the influence of a dynamic load. A significant discrepancy of the latter statement occurs, however, in the case of fracture under a continuously-increasing static load. In this case the crack-propagation velocity in the second phase reaches some remarkably high values, which are of the order of high strain-rate dynamic crack propagation velocities.In this way, the crack-arrest effect on the crack propagation velocity appears to be more significant in the case of a static loading than it is for the case of dynamic loading.     

Crack velocities in natural rubber

Measurements are reported of the limiting velocity of a running crack in biaxially stretched sheets of unfilled and carbon-black-filled natural rubber. The crack velocity was found to increase with the cleavage strain,e _y , and also with the strain,e _x , parallel to the direction of tearing, reaching values of over 100 m sec^–1 at the highest strain levels employed. These crack velocities are shown to be close to those predicted by Mott's theory, i.e., about one-third of the velocity of sound, when a strong strain-dependence is recognized for the velocity of sound in rubber.     

Crack propagation and failure prediction in silicon nitride at elevated temperatures

A technique for studying high temperature crack propagation in ceramic materials is developed. The technique is used to obtain relationships between the crack propagation rate and the stress intensity factor for hot-pressed silicon nitride up to 1400° C. The data are then used to develop proof test diagrams which give values for the safe working stress levels for this material after proof testing (or any other flaw detection procedure).     

Crack propagation in gaseous atmospheres

Environmentally-assisted cracking is studied for an Al-Zn-Mg alloy in different gaseous atmospheres. A sophisticated experimental installation with an ultra-high-vacuum chamber (10^-5) is used to maintain and monitor a high-purity atmosphere surrounding the specimen. The experimental data show that water vapor is the main factor responsible for the enhancement of the crack growth rates as compared with those in the high vacuum. Embrittlement is attributed to the influence of hydrogen produced as a result of the surface reaction of water vapor with the fresh metal surface near the crack tip. Departamento de Ciencia de Materiales, Escuela de Ingenieros de Caminos; Universidad Politecnica de Madrid. Madrid, Spain. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 4, pp. 65–70, July–August, 1998.     

Crack propagation during fatigue experiments

In the present paper a very simple phenomenological theory of crack propagation during fatigue experiments is presented. It is shown that an important role is played by work-hardening to explain both the existence of a fatigue limit and the well known deviations from Miner's Rule in the case of tests conducted at varying maximum applied stresses. Although approximate, the theory can account for the main phenomena involved in fatigue experiments.

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Zusammenfassung Es wird eine sehr einfache Grundlagentheorie zur Beschreibung der Fortpflanzungsbedingungen eines Risses unter Dauerbeanspruchung dargelegt.Die Grundlage dieser Theorie besteht darin die Rissfortpflanzung mit der mechanischen Hysteresis in Zusammenhang zu bringen.Es wird auf die wichtige Rolle der Verformung hingewiesen, sowohl für der Begriff der Dauerfestigkeit als auch für die wohlbekannten Abweichungen von dem Miner Gesetz, im falle von Versuchen bei maximaler Beanspruchung mit veränderlichen Amplituden.Trotz einer Anzahl von Vereinfachungen, gibt these Theorie eine gute Beschreibung der wichtigsten Vorgänge beim Dauerversuch.

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Résumé On présente une théorie phénoménologique extrêmement simple pour décrire les conditions de propagation des fissures en fatigue. Cette théorie repose sur le principe d'associer la propagation des fissures an cycle d'hystérésis mécanique. On montre que l'écrouissage joue un rôle important, à la fois dans la notion de la limite d'endurance, et dans les inexactitudes, bien connues, de la règle de Miner, lorsque des essais sent conduits à des contraintes maximales d'amplitude variable.Quoique assez grossière, cette théorie rend compte des principaux phénomènes qui interviennent dans des expériences de fatique.

     

Crack propagation in polymeric composites

The velocities of rapidly moving cracks in polymethylmethacrylate, an epoxy resin, a rubber modified epoxy resin, coupled and decoupled glass bead filled epoxies and randomly oriented glass fiber reinforced epoxies were measured with a crack propagation gage that was electrolissecally plated on the surfaces of the materials.

When fracture was initiated from a natural crack it was found that the velocity conformed to Mott's equation , while fracture initiated from a blunted notch resulted in a velocity that conformed to Dulany and Brace's equation . A general energy balance was used to show how one could develop these two equations as bounds to the velocity of catastrophic crack propagation.

The terminal crack velocity in the unfilled materials and the glass bead filled materials was , where E/ρ was the modulus to density ratio of the matrix phase at the macroscopic strain rate of the fracture test. The proportionality constant of 0.28 was independent of matrix type, temperature and degree of adhesion. Cracks in the rubber reinforced epoxies always tended to become blunt, resulting in breaking loads that were higher than that expected for materials possessing a natural crack. In addition, the average terminal velocity was less than 0.28√E/ρ, indicating the retardation effects of the rubber particles. These facts were used to explain the higher fracture toughness of these composites.

Fracture surface roughness was primarily a function of crack extension and breaking stress and was less sensitive to crack velocity. An empirical modification of the Mott energy balance was used to qualitatively explain this behavior.     

Crack propagation in cylindrical shells

Results of a theoretical study of dynamic steady crack propagation in a circular cylindrical shell are presented. Equations of thin circular cylindrical shells are utilized for theoretical investigation. The semi-analytic crack tip stress solutions to shell equations are obtained by the perturbation method as well as an iterative method. Plots of internal stresses in the shell with a stationary as well as a steadily running crack are presented. These results are compared with those related to flat plates. It is concluded that the shell curvature has a pronounced effect on increasing the values of crack tip stresses. It would also qualitatively affect the variation of stress field around the crack tip. In some cases, the curvature action is shown to be even more pronounced than the inertia effects.     

Crack propagation in two-belt beams

Conclusions The FEM was used to construct a detailed model of contact interaction of a fastening element and the web of a two-belt beam. The super element approach was used as a base for evaluating the SIF in separation and SIF in transverse shearing for cracks in the zone of the fastening hole of the longitudinal joint and in the belt. The results show that inclined cracks (type A) are situated in the normal opening conditions, whereas the vertical (type C) and horizontal (type D) cracks are in the conditions with mainly transverse shear. The nature of crack propagation depends strongly on the material of the web of the beam. For example, in type D16 material in which cracks can grow by the shear mechanism in a wide range of the values of SIF, the type C and D cracks propagate linearly. The predicted rate of their growth is considerably (15–60 times) higher than the rate of growth of opening cracks. This is caused both by a lower-resistance of the material to propagation of fatigue cracks by the shear mechanism and by adding up all the values of k_II in the opposite loading half cycles. However, if the wall is made of V95-type material in which straight growth of shear cracks takes place only in pure shear conditions the type C and D cracks rotate during growth and degenerate to a separation crack propagating at a considerably low rate.Translated from Fiziko-khimicheskaya Mekhanika Materialov, Vol. 27, No. 3, pp. 67–72, May–June, 1991.     

Crack propagation in a commercial steel

In this work, the fatigue crack propagation behaviour of commercial steel sheet specimens containing a circular hole, under uniaxial loading conditions at room temperature was investigated.The experimental data have been analysed in terms of variability of material constants. The results were presented in the form of power relationship between the crack growth rate and the stress intensity factor range.

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Résumé Dans ce travail, on a étudié le comportement à la propagation des fissures de fatique d'éprouvettes de tôle mince en acier de construction, présentant un trou circulaire et sujettes à une mise en charge uniaxiale à température ambiante.On a analysé les données expérimentales en termes de variabilité des constantes du matériau. Les résultats sont présentés sous forme d'une relation parabolique entre la vitesse de croissance de la fissure et la variation du facteur d'intensité de contrainte.

     

Crack propagation in a Tantalum nano-slab

Using molecular dynamics with an accurate many-body potential for metallic Tantalum, we studied crack propagation in a pre-notched nano-slab under uniaxial strain in a [100] direction. We study dislocation emission from the crack tip for various strain rate and temperatures, focusing on the influence of the local temperature at the crack tip on the propagation of the crack. We find a close connection between the local temperature at the crack tip and dislocation emission. This revised version was published online in June 2006 with corrections to the Cover Date.     

Crack propagation during steady state creep

A model is proposed tor the steady propagation of a creep crack under steady state creep conditions. Creep is envisaged to take place everywhere in the solid, though higher creep rates at the crick tip lead to a local concentration of the creep strain. A critical local strain criterion is used to describe the condition for crack advance. Local damage is envisaged to accumulate at the crack tip as a result of, or in parallel with the creep strain. The model correctly predicts a dependence of crack propagation rate with the nett section stress varied to the power m, where m is the exponent of stress in the creep equation, for large values of m. An approximate dependence of propagation rate on the elastic stress intensity factor is also shown. Tnese predictions are in accord with experimental work.     

Crack propagation experiments on strip specimens

A method for measuring dynamic fracture properties is briefly described. The method employs the strip specimen and this configuration is discussed from a practical point of view. Results from experiments performed to determine the velocity variation of the fracture energy are presented. Some observations are made regarding the physical nature of the fracture process.     

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.     

Crack propagation behavior under creep conditions

The creep crack propagation behavior of a Cr–Mo–V rotor steel has been investigated at 538°C using time-dependent fracture mechanics concepts. The creep crack propagation lives and the creep deflection rates of double-edge-notched (DEN) specimens were estimated using previous data from compact-type specimens. The predicted crack growth lives and deflection rates compared favorably with the experimental data. When plotted as a function of the C _t parameter, the experimentally determined creep crack propagation rates of DEN specimens were found to be in agreement with those of compact and center-crack-tension specimens. These results provide further experimental verification for the validity of the C _t parameter for characterizing creep crack growth behavior. Some discrepancies between the predicted and the observed behavior are attributed to primary creep deformation behavior which was not considered in estimating the value of C _t .     

Crack propagation studies in brittle materials

An analysis was made of cantilever beam specimens used for crack propagation studies, Included in this analysis were the effects of a plastic zone at the crack tip, beam rotation, and the viscoelastic response of the material. This analysis showed that application of a constant bending moment to the specimen rather than a constant load provides a test in which the strain energy release rate,G, is independent of crack length. Other advantages of this test configuration are that corrections for shear or beam rotation effects are not necessary. Results of this test on both glass and ceramics are reported.List of symbols a crack length - A cross-sectional area of beam - b total thickness of specimen - d deflection of loading arm - E elastic modulus of material - E ₁ dynamic modulus - E ₂ transient response modulus - G shear modulus of material - G strain energy release rate - G _vE strain energy release rate of viscoelastic material - h half height of specimen - I moment of inertia of cantilever beam =bh ^/12 - k modulus of elastic foundation - K stress intensity factor - L distance from point of load application to fulcrum of loading arm - L distance from point at which arm deflection is measured to fulcrum - M applied bending moment - P force applied to beam - r length of plastic zone - t thickness of specimen at groove - T force applied to loading arm - u displacement of beam - V crack velocity - w half height of groove - W stored elastic energy - characteristic length of beam on elastic foundation - reciprocal of the characteristic length of beam - rotation of beam - X viscoelastic creep compliance function - time - inherent opening distance as defined by Wnuk [10] - _y yield strength of material - Poisson's ratio