Nonlinear crack dynamics and scaling aspects of fracture (experimental and theoretical study)

Nonlinear dynamics of crack propagation are investigated experimentally and theoretically with the goal of clarifying the nature of limiting crack velocity, the transition from steady state to branching regimes of crack dynamics, and the dynamics of crack arrest. The theoretical explanation of limiting steady-state crack velocity and the transition to a branching regime was proposed due to the study of collective behavior of a microcrack ensemble at the crack tip area. The experimental study of crack dynamics was carried out in a preloaded plate PMMA specimen using the high-speed camera coupled with the photo-elasticity method, the point stress recording with a laser system, and the failure surface roughness measurement.     

An experimental and theoretical study of crack propagation in crossply fiber composites

Rectangular specimens of a cross-ply fiberglass composit e (Scotchply 1002) in which sharp edge notches have been cut along one of the fiber directions parallel to a specimen edge have been tested in an “Instron” testing machine. Tensile stress was applied perpendicular to the direction of the notch. The commencement and growth of the crack has been observed. It has been found that if the notch is sufficiently close to one edge of the specimen the crack instead of propagating along the direction of its axis, i.e. perpendicular to the applied stress runs along the stress direction; when the notch is sufficiently far from the edge the crack propagates in the direction of its axis right across the specimen while at intermediate notch positions the crack runs along in its axial direction and then turns sharply through a right angle and continues in the direction of the applied stress. The theory of this behavior has been studied and it is shown that if a criterion of a critical tensile force rather than a critical energy density is used, the observed phenomena can, at least qualitatively, be accounted for. The comparable situation for a brittle isotropic specimen of “Plexiglass” is also described. This shows a quite different response and conventional linear fracture mechanics can be used to describe this behavior.     

Recent theoretical and experimental results on fast brittle fracture

Some recent and important results of the theory of crack extension in elastic bodies are summarized. The theory can adequately account for most of the features of fast brittle fracture observed experimentally. In particular, the fact that the maximum crack speeds observed in practice are considerably lower than the speed of Rayleigh waves may be attributed to a sharp increase in the effective surface energy with increasing crack speed. This increase in surface energy would make branching more likely, but it is recognized that there is still no satisfactory explanation of the phenomenon of crack branching. It is probable that branching of a main crack is the result of its interaction with microcracks generated ahead of it. The difficulties involved in a theoretical analysis of this interaction are outlined and certain suggestions for further research are given.The present review complements that given by Erdogan [1].

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Résumé On rappelle brièvement certains résultats récents et importants de la théorie décrivant l'allongement d'une fissure dans un corps elastique. Cette théorie permet d'expliquer la plupart des aspects connus de la rupture rapide de matériaux fragiles. Par exemple, les vitesses maximales qu'on observe en pratique sont bien inférieures à la vitesse des ondes de Rayleigh, et ceci peut être expliqué comme conséquence de l'augmentation rapide de l'énergie requise pour la formation des surfaces à mesure que la vitesse augmente. La bifurcation d'une fissure est plus probable en vue de cette augmentation, mais il faut reconnaître qu'il n'y a jusqu'à l'heure aucune explication acceptable de ce phénomène. Il paraît que la bifurcation d'une fissure principale resulte d'une interaction avec des fissures d'ordre microscopique qui la précèdent. Une analyse théorique d'une telle interaction est presqu'inabordable pour des raisons qu'on discute brièvement, et l'on soumet quelques suggestions pour des recherches futures. Notre revue supplée à celle d'Erdogan [1].

     

MOCVD of ZrO2 films from bis(t-butyl-3-oxo-butanoato)zirconium(IV): some theoretical (thermodynamic) and experimental aspects

The equilibrium concentrations of various condensed and gaseous phases were calculated from thermodynamic modeling of MOCVD of ZrO₂ films using a β-ketoesterate complex of zirconium as precursor. This leads to the construction of the ‘CVD phase stability diagram’ for the formation of solid phases. In the reactive ambient of oxygen, the calculations predict carbon-free ZrO₂ film over a wide range of process conditions. The thermodynamic yields are in reasonable agreement with experimental observations, though the removal of carbon from the MOCVD grown films is not as complete as the thermodynamic calculations predict.     

Scale invariance in brittle fracture and the dynamics of crack fusion

The brittle fracture of solids subject to extreme differential stress is assumed to be a consequence of the sequential fusion of smaller cracks into larger ones. Renormalization methods quantitatively describe the dynamics of the cascade of fusion events that culminates in failure, including the observed time-to-failure versus stress scaling law.

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Résumé On pose l'hypothèse que la rupture fragile des solides soumis à des contraintes différentielles est une conséquence de la fusion en série de petites fissures en de grandes.Des méthodes de renormalisation décrivant de manière quantitative la dynamique qui préside à la cascade de fusion conduisant à l'extrême à la rupture, y compris la durée à rupture par rapport à la loi de croissance de la contrainte.

     

Contribution of theoretical and experimental results to powder-snow avalanche dynamics

A powder-snow avalanche can be considered as the flow of a turbulent buoyant volume of heavy fluid (air-snow suspension) in an ambient fluid, the air. In the dynamics of such a flow, two mechanisms must be taken into account: the air entrainment and the snow entrainment inside the avalanche. From fluid mechanics equations (mass conservation and momentum equations) formulae were obtained giving velocity and density of the avalanche as a function of the slope path, the growth rate of the avalanche and fresh snow-cover characteristics. On the other hand, laboratory simulations gave (among others) experimental results about the growth rates of buoyant clouds. From these theoretical and experimental studies, practical examples are proposed with given path profiles and snow-cover characteristics. Such examples can be generalised to any other cases.     

Nonlinear fracture dynamics of laminates with finite thickness adhesives

Finite thickness interfaces, such as structural adhesives, are often simplified from the modeling point of view by introducing ideal cohesive zone models that do not take into account the finite thickness properties in the evaluation of the interface stiffness and inertia. In the present work, the nonlinear dynamic response of those layered systems is numerically investigated according to the finite element method. The weak form of the dynamic equilibrium is written by including not only the contribution of cohesive interfaces related to the virtual work exerted by the cohesive tractions for the corresponding relative displacements, but also considering the work done by the dynamic forces of the finite thickness interfaces resulting from their inertia properties. A fully implicit solution scheme both in space and in time is exploited and the numerical results for the double cantilever beam test show that the role of finite thickness properties is not negligible as far as the crack growth kinetics and the dynamic strength increase factor are concerned.     

An experimental and numerical study of crack closure

Fatigue crack propagation and crack closure are studied in Al 2024-T3 under a wide range of ΔK. An elastic-plastic finite element procedure to analyze crack closure for growing cracks is presented. Numerical results are obtained for plane stress and plane strain conditions for different stress ratios. Measurements of opening loads compare well with numerical predictions within the Paris regime. Fractographic observations and compliance measurements indicate that oxide-induced and roughness-induced crack closure substantially increase the opening loads in the near-threshold regime.     

An experimental investigation into dynamic fracture: III. On steady-state crack propagation and crack branching

This is the third in a series of four papers in which problems of dynamic crack propagation are examined experimentally in large, thin sheets of Homalite-100 such that crack growth in an unbounded plate is simulated. In the first paper crack initiation resulting from stress wave loading to the crack tip as well as crack arrest were reported. It was found that for increasing rates of loading in the microsecond range the stress intensity required for initiation rises markedly. Crack arrest occurs abruptly without any deceleration phase at a stress intensity lower than that which causes initiation under quasi-static loading.In the second paper we analyze the occurrence of micro cracks at the front of the running main crack which control the rate of crack growth. The micro cracks are recorded by real time photography. By the same means it is shown that these micro cracks grow and turn away smoothly from the direction of the main crack in the process of branching.In the present paper we report results on crack propagation and branching. It is found that crack propagation occurs at a constant velocity although the stress intensity factor changes markedly. Furthermore, the velocity is determined by the stress wave induced intensity factor at initiation. The terminal velocity in Homalite-100 was found to be about half the Rayleigh wave speed (0.45 C _r ). These observations are analyzed in terms of a microcrack model alluded to in the second paper of this series. A mechanism for crack branching is proposed which considers branching to be a natural evolution from a cloud of microcracks that accompany and lead the main crack. These results are believed to apply to quasi-brittle materials other than Homalite-100 and the reasons for this belief are discussed briefly in the first paper of this series.In the final paper of the series the effect of stress waves impinging on the tip of a rapidly moving crack is examined. Waves affect the velocity and the direction of propagation as well as the process of crack branching.     

Laser-speckle angular-displacement sensor: theoretical and experimental study

A novel, to our knowledge, method for the measurement of angular displacement for arbitrarily shaped objects is presented in which the angular displacement is perpendicular to the optical axis. The method is based on Fourier-transforming the scattered field from a single laser beam that illuminates the target. The angular distribution of the light field at the target is linearly mapped on a linear image sensor placed in the Fourier plane. Measuring this displacement facilitates the determination of the angular displacement of the target. It is demonstrated both theoretically and experimentally that the angular-displacement sensor is insensitive to object shape and target distance if the linear image sensor is placed in the Fourier plane. A straightforward procedure for positioning the image sensor in the Fourier plane is presented. Any transverse or longitudinal movement of the target will give rise to partial speckle decorrelation, but it will not affect the angular measurement. Furthermore, any change in the illuminating wavelength will not affect the angular measurements. Theoretically and experimentally it is shown that the method has a resolution of 0.3 mdeg ( approximately 5 murad) for small angular displacements, and methods for further improvement in resolution is discussed. No special surface treatment is required for surfaces giving rise to fully developed speckle. The effect of partially developed speckle is considered both theoretically and experimentally.     

Nonlinear dynamics in meso and nano scales: fundamental aspects and applications

This introduction to the special issue, Nonlinear dynamics in meso and nano scales: fundamental aspects and applications, gives a short overview about different contexts and current challenges posed by the emergence of nonlinearities at meso and nano characteristic sizes. It also addresses different aspects related to classical and quantum chaos. Moreover, it comments on the articles in this thematic publication, briefly summarizing their relevance in helping to understand the uprise of chaos and complex behaviour at those small scales.     

Oscillation of absorption bands of Zn(1-x)Mn(x)S clusters: an experimental and theoretical study

Electroporation of synthetic vesicles is utilized for the preparation of molecular size uncapped Zn(1-x)Mn(x)S clusters. The absence of caps permits (i) continued growth of the Zn(1-x)Mn(x)S clusters formed, (ii) the assessment of their true absorption spectra unaltered by stabilizing ligands, and (iii) the previously inaccessible live observation of the growth of the clusters in the molecular size regime. Upon cluster growth, the UV spectra exhibit novel, time-dependent, oscillation of red and blue shifts of the characteristic absorption band. The structure and electronic properties of Zn(N-1)MnS(N) clusters with N = 1-9 are calculated using the first-principles DMol(3) package. On the basis of similarities between the oscillating trend of the experimentally observed absorption spectra and that of the calculated highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap of Zn(N-1)MnS(N) clusters with N = 1-9, the wavelengths of the sequential spectral peaks can be assigned to Zn(2)MnS(3), Zn(3)MnS(4), Zn(4)MnS(5), Zn(6)MnS(7), and Zn(8)MnS(9), respectively. Our results demonstrate that both the cluster size and the composition can be used to tune the optical properties.     

Data acquisition aspects in experimental research ofelectromechanical systems dynamics

This paper presents results on both experimental research and theoretical analysis of data acquisition aspects for vibration fault detection and isolation systems and in particular, for studying the signature of "real" sampled vibration signals in electric drives with unbalanced rotor. It was revealed that the structure of real vibrations of electric drives with unbalanced rotor is a very complicated nonlinear combination of many factors acting together. Finally, the impossibility of adequate vibration diagnosis without taking into account all effects that may alter the vibration (or stator current) power spectrum was discussed     

Angular displacement fiber-optic sensor: theoretical and experimental study

An optical-fiber sensor based on twist-induced optical activity has been developed for measuring angular displacements at low temperature. The sensing part is composed of a fiber coil rotated between two points, which induces a twist of two sections of fiber. A theoretical study of the evolution of a general input state of polarization in the sensor gave us its main characteristics. Then experimental investigations permitted the construction of a sensor to take angular measurements over a 100-deg range with an accuracy of 0.2 deg. The thermal sensitivity of this kind of sensor is also briefly reported.     

A theoretical and experimental study of chromatothermography at high concentrations

The concentration distribution produced by diffusion is examined; the differential equation has been solved numerically by computer to give working curves that define the physicochemical characteristics. An approximate analytical solution is also given.Translated from Inzhenerno Fizicheskii Zhurnal, Vol.27, No. 3, pp. 466–475, September, 1974.     

A theoretical and experimental study of waveguide coupled SAWresonator filters

The coupling-of-modes (COM) formalism is extended to include coupled transducers and applied to the modelling of surface acoustic wave (SAW) coupled resonator filters. The models do not require the derivation of equivalent circuits and they accommodate finger reflections, electromagnetic feedthrough and external matching circuits. Frequency responses for waveguide-coupled devices are computed and compared to experimental results. Longitudinal mode profiles within the resonant cavities are presented