Query: InSb,Energy release rate

title: Effects of strain rate on fracture toughness and energy release rate of gas shales
abstract: Understanding the aspect of enhanced energy extraction through an approach of rock mechanics requires a detailed interpretation of rock fracture mechanism. Common examples are hydraulic fracturing of gas shales and geothermal energy systems. Resolving rock fracture behavioural patterns and its properties such as fracture toughness and energy release rate during fracturing is important for the successful implementation of such projects. These properties are a function of different environmental factors such as temperature, humidity, water vapour, pressure, and strain rate. In this study, the effects of various strain rates on the fracture toughness as well as the energy release rate of gas shales were investigated. The three point bending method was applied using notched semicircular bending shale specimens that were prepared as per the international standards. The fracture toughness and the energy release rates were measured for three different modes, namely, mode I, mixed mode (I II) and mode II. In addition, X ray diffraction analysis was carried out to identify the composition of the selected shales. Finally, scanning electron microscope (SEM) analyses were performed in order to acquire an insight into the effects of strain rate on fractures at microstructural scales. The experimental results indicate that the fracture toughness and the energy release rate for all the three modes are a function of strain rate. At lower strain rates, the fracture toughness and the strain energy release rates for all the modes are comparable but vary significantly at higher strain rates. At high strain rates, the strength and stiffness of the shale increases, which in turn increases the fracture toughness and, eventually, the energy release rate of the shale. For all the strain rates, mode I requires the minimum application of energy, while mode II requires maximum energy for the onset of crack growth. The energy release rate in mode I is maximum, in comparison with the two other modes. The findings of this investigation will be useful in achieving a better and comprehensive understanding of some aspects such as initiation, propagation and failure of shales during hydraulic fracturing for the extraction of hydrocarbons.

title: Discussion on the use of the strain energy release rate for fatigue delamination characterization
abstract: This paper discusses the use of the strain energy release rate (SERR) as a parameter to characterize fatigue delamination growth in composite materials. Based on the observed difference in fatigue delamination response, it is argued that the fibre bridging generated during quasi static and fatigue loading is significantly different and normalization of fatigue data with quasi static SERR becomes meaningless. From the physical view, bridging fibres should not impose any strain energy release during fatigue delamination, unless they fail. This is supported by analyzing the earlier mentioned experiments with an energy approach. When the measured strain energy release normalized against the applied number of cycles is plotted against the fatigue delamination growth rate, all data approximately coincides to a single curve. It is therefore concluded that the current use of SERR to characterize fatigue delamination growth is not in agreement with the physical concept of strain energy release.

title: Energy release rate and stress intensity factor in antiplane elasticity
abstract: In the setting of antiplane linearized elasticity, we show the existence of the stress intensity factor and its relation with the energy release rate when the crack path is a C 1 1 curve. Finally, we show that the energy release rate is continuous with respect to the Hausdorff convergence in a class of admissible cracks.

title: Energy release rate along a three dimensional crack front in a thermally stressed body
abstract: Based on a line integral expression for the energy release rate in terms of crack tip fields, which is valid for general material response, a (area/volume) domain integral expression for the energetic force in a thermally stressed body is derived. The general three dimensional finite domain integral expression and the two dimensional and axisymmetric specializations for the energy release rate are given. The domain expression is naturally compatible with the finite element formulation of the field equations. As such it is ideally suited for efficient and accurate calculation of the pointwise values of the energy release rate along a three dimensional crack front. The finite element implementation of the domain integral corresponds to the virtual crack extension technique. Procedures for calculating the energy release rate using the numerically determined field solutions are discussed. For illustrative purposes several numerical examples are presented.ResumeEn sa basant sur une integrale simple exprimant le taux de relaxation d'energie afferant aux champs de contrainte a l'extremite d'une fissure, expression applicable a la reponse d'un materiau quelconque, on a deduit une integrale de domaine (superficielle ou volumique) decrivant l'energie dans un corps soumis a contraintes thermiques.On fournit l'integrale generale relative a un domaine fini tridimensionnel et a des cas particuliers bidimensionnels et axisymetriques, exprimant le taux de relaxation d'energie. L'integrale de domaine est naturellement compatible avec une formulation par elements finis des equations de champ. Comme telle, elle convient idealement pour un calcul facile et precis des valeurs ponctuelles du taux de relaxation de l'energie le long du front d'une fissure tridimensionnelle. L'implantation d'elements finis dans l'integrale de domaine correspond a une technique d'extension virtuelle de la fissure. On discute des procedures de calculs du taux de relaxation de l'energie, qui utilisent les solutions relatives au champ determinees par voie numerique. A titre d'illustration, on presente plusieurs exemples numeriques.

title: Strain Energy Release Rate for a Crack Under Combined Mode I and Mode II
abstract: The energy release rate for a crack subjected simultaneously to mode I and mode II conditions is computed. The energy was computed by path independent integrals, using the elastic solution of a deflected crack, having a main branch and a propagation branch. The elasticity solution was obtained from the functional integral equations by the process of iterations. This process leads to a point wise exact solution in the limit as the propagation branch goes to zero. Using the Griffith Irwin criterion, incipient paths of propagation of such a crack were obtained from the maximum value of the energy release rate. An experiment, which gives a pure mode II condition at the tip of the crack, was devised. The results were in excellent agreement with the theory. The energy release rate, in parametric form, can be used for any crack subjected to mode I and mode II loading conditions.

title: An energy release rate based plastic damage model for concrete
abstract: A new plastic damage constitutive model for concrete is proposed in this paper. A tensile and a shear damage variable are adopted to describe the degradation of the macromechanical properties of concrete. Within the framework of continuum damage mechanics, the elastic Helmholtz free energy is defined to establish the plastic damage constitutive relation with the internal variables. Regarding the specific format for the effective stress space plasticity, the evolution law for the plastic strains and the explicit expression for the elastoplastic Helmholtz free energy are determined and the damage energy release rates that are conjugated to the damage variables are derived. Thus, damage energy release rate based damage criteria can be established in conformity to thermodynamical principles. In accordance with the normality rule, evolution laws for the damage variables are obtained to complete the proposed plastic damage model. Some computational aspects concerning the numerical algorithm implementation are discussed as well. Several numerical simulations are presented at the end of the paper, whose results allow for validating the capability of the proposed model for reproducing the typical nonlinear performances of concrete structures under different monotonic and cyclic load conditions.

title: Application of the energy release rate approach for delamination growth in Glare
abstract: Fatigue crack growth in a fibre metal laminate such as Glare is accompanied by delamination growth at the interface between the aluminium and glass fibre/adhesive layers. To incorporate this delamination growth in crack growth prediction methods, the energy release rate approach is applied to describe the delamination growth rate. Tests were performed to determine the relationship between the delamination growth rate and the calculated energy release rate.

title: An energy release rate criterion for mixed mode fracture
abstract: The initial energy release rate for a branch crack propagating at an arbitrary angle from an existing crack tip is obtained in a simple fashion and in closed form by using a continuity assumption. It is then postulated that the branch crack propagates in the direction which causes the energy release rate to be a maximum and that initiation occurs when the value of this release rate reaches a critical value. It is shown that these postulates yield results identical to the maximum stress theory, since the direction in which the maximum circumferential stress occurs is also the direction causing the maximum energy release rate.ResumeLa vitesse de relaxation de l'energie initiale d'une fissure arborescente qui se developpe suivant un angle arbitraire au depart de l'extremite d'une fissure preexistante est obtenue sous une presentation simple et une forme fermee en utilisant une hypothese de continuite. On postule donc que la fissure laterale se propage dans la direction correspondant a un maximum de relaxation de l'energie, et que l'amorcage se produit lorsque la vitesse de relaxation atteint une valeur critique. On montre que ces postulats conduisent a des resultats identiques a ceux de la theorie de la contrainte maximale, puisque la direction suivant laquelle se presente la contrainte circonferentielle maximum est egalement celle suivant laquelle la vitesse de relaxation de l'energie est maximale.ZusammenfassungDie Anfangsgeschwindigkeit der Energiefreilassung fur einen Zweigrib, der sich unter einem willkurlichen Winkel von einer bestehenden Ribspitze ausbreitet, wird unter einer einfachen Darstellung und in einer geschlossenen Form durch Gebrauch einer Kontinuitatsannahme aufgestellt. Es wird dann vorausgesetzt dass der Zweigrib sich in der Richtung ausbreitet welche ein Maximum der Energiefreilassungsgeschwindigkeit bewirkt und dass die Ribauslosung eintritt wenn der maximum Wert dieser Energiefreilassungsgeschwindigkeit einen kritischen Wert erreicht. Es wird gezeigt dass diese Annahmen zu den selben Ergebnissen wie die der maximalen Spannungstheorie fuhren, da die Richtung der maximalen Kreisspannung dieselbe ist als die der maximalen Energiefreilassungsgeschwindigkeit.

title: Maximum energy release rate criterion applied to a tension compression specimen with crack
abstract: The title problem is studied by using the explicit asymptetic analysis presented in the accompanying paper. The asymptotic analysis indicates that the very basic problem is a semi infinite L shaped crack governed by a single integral equation. This equation is discretized to a system of complex algebraic equations and solved by a standard HARWELL subroutine. It is found that the maximum energy release rate criterion has two branches, one for tensile loads and one for compressive loads. Our numerical results indicate that the maximum energy release rate is always associated with maximum K1 and K2=0, where K1 and K2 are the stress intensity factors at the fractured tip. Thus, the well known K G relation valid for crack parallel propagation also holds for non crack parallel propagations. This conclusion is, however, purely numerical.

title: On the energy release rate in quasi static elastic crack propagation
abstract: This paper presents a rigorous derivation of several results concerning the energy release rate for a sharp crack in a homogeneous hyperelastic body.