H. A. Elliot

Bio: H. A. Elliot is an academic researcher. The author has contributed to research in topics: Internal pressure & Crack tip opening displacement. The author has an hindex of 1, co-authored 1 publications receiving 259 citations.

The opening of a Griffith crack under internal pressure

Abstract: 1. The determination of the distribution of stress in the neighbourhood of a crack in an elastic body is of importance in the discussion of certain properties of the solid state. The theory of cracks in a two-dimensional elastic medium was first developed by Griffith1 who succeeded in solving the equations of elastic equilibrium in two dimensions for a space bounded by two concentric coaxial ellipses; by considering the inner ellipse to be of zero eccentricity and by assuming that the major axis of the outer ellipse was very large Griffith then derived the solution corresponding to a very thin crack in the interor of an infinite elastic solid. Because of the nature of the coordinate system employed by Griffith the expressions he derives for the components of stress in the vicinity of the crack do not lend themselves easily to computation. An alternative method of determining the distribution of stress in the neighbourhood of a Griffith crack was given recently by one of us2 making use of a complex stressfunction stated by Westergaard.3 This method suffers from the disadvantage that the Westergaard stress-function refers only \"to the case in which the Griffith crack is opened under the action of a uniform internal pressure; the stress-function corresponding to a variable internal pressure does not appear to be known. In the present note we discuss the distribution of stress in the neighbourhood of a Griffith crack which is subject to an internal pressure, which may vary along the length of the crack, by considering the corresponding boundary value problem for a semi-infinite two-dimensional medium. The analysis is the exact analogue of that for the three-dimensional \"circular\" cracks developed in the previous paper2 except that now we employ a Fourier cosine transform method in place of the Hankel transform method used there. A method is given for determining the shape of the crack resulting from the application of a variable internal pressure to a very thin crevice in the interior of an elastic solid, and for determining the distribution of stress throughout the solid. The converse problem of determining the distribution of pressure necessary to open a crevice to a crack of prescribed shape is also considered. As an example of the use of the method the expressions for the components of stress, due to the opening of a crack under a uniform pressure, are derived and are found to be in agreement with those found in the earlier paper.2 2. We consider the distribution of stress in the interior of an infinite two-dimensional elastic medium when a very thin internal crack — c^y^c, * = 0 is opened under the action of a pressure which may be considered to vary in magnitude along the length of the crack. For simplicity we shall consider the symmetrical case in which the applied pressure is a function of |y| but the analysis may easily be extended to the

The mathematical theory of equilibrium cracks in brittle fracture

Abstract: Publisher Summary In recent years, the interest in the problem of brittle fracture and, in particular, in the theory of cracks has grown appreciably in connection with various technical applications. Numerous investigations have been carried out, enlarging in essential points the classical concepts of cracks and methods of analysis. The qualitative features of the problems of cracks, associated with their peculiar nonlinearity as revealed in these investigations, makes the theory of cracks stand out distinctly from the whole range of problems in terms of the theory of elasticity. The chapter presents a unified view of the way basic problems in the theory of equilibrium cracks are formulated and discusses the results obtained thereby. The object of the theory of equilibrium cracks is the study of the equilibrium of solids in the presence of cracks. However, there exists a fundamental distinction between these two problems, The form of a cavity undergoes only slight changes even under a considerable variation in the load acting on a body, while the cracks whose surface also constitutes a part of the body boundary can expand even with small increase of the load to which the body is subjected.

Numerical Modeling of Hydraulic Fractures Interaction In Complex Naturally Fractured Formations

Abstract: A recently developed unconventional fracture model (UFM) is able to simulate complex fracture network propagation in a formation with pre-existing natural fractures. A method for computing the stress shadow from fracture branches in a complex hydraulic fracture network (HFN) based on an enhanced 2D displacement discontinuity method with correction for finite fracture height is implemented in UFM and is presented in detail including approach validation and examples. The influence of stress shadow effect from the HFN generated at previous treatment stage on the HFN propagation and shape at new stage is also discussed.

Numerical Modeling of Hydraulic Fractures Interaction in Complex Naturally Fractured Formations

Abstract: A recently developed unconventional fracture model (UFM) is able to simulate complex fracture network propagation in a formation with pre-existing natural fractures. A method for computing the stress shadow from fracture branches in a complex hydraulic fracture network (HFN) based on an enhanced 2D displacement discontinuity method with correction for finite fracture height is implemented in UFM and is presented in detail including approach validation and examples. The influence of stress shadow effect from the HFN generated at previous treatment stage on the HFN propagation and shape at new stage is also discussed.

Depth and spacing of tension cracks

Abstract: Contraction cracks in basalt, permafrost, and mud, and crevasses in glaciers are examples of geological phenomena that might be studied by reference to a theoretical model of tension cracks in a semi-infinite solid. The effect of the crack in relieving stress at the ground surface bears on the problem of crack spacing, and the rate of energy dissipation at the advancing crack tip bears on the problem of crack depth. Even though the stresses that cause cracking develop slowly, an elastic model of the stress near a crack can be useful as long as the cracks, once initiated, propagate rapidly. Results are presented for the elastic stress perturbation caused by a crack in an infinite or semi-infinite medium in which the initial stress is a step function or a linear function of depth. Tables and graphs are presented which can be applied directly to problems in which the variation of stress with depth is arbitrary. These results, used with the modified Griffith theory of macroscopic fracture introduced by Irwin [1948] and Orowan [1950], suggest a means of predicting depth and spacing of tension cracks in terms of the stress field and measurable properties. The method is illustrated with a discussion of cooling joints in basalt, and other problems of tension fracture in geology.