The effect of fracture surface morphology on the crack mechanics in a brittle material (original) (raw)
Related papers
Relationship of energy to geometry in brittle fracture
Journal of the European Ceramic Society, 2020
Numerous investigators have noticed that there is a relationship between the energy of branching and the energy of initiation during a fracture event in materials that fail in a brittle manner. Usually, this is measured in terms of the stress intensities, i.e., K B /K c. The ratio has been reported between 3 and 4, implying a constant value. However, data suggests that it is a constant for a material, but not a universal constant. The fractal dimension of the fracture surface is related to the critical stress intensity factor. It is a measure of the tortuosity of the fracture surface. We show that the K B /K C ratio is directly related to the square root of the fractal dimensional increment, indicating a relationship between the energy of crack propagation and the tortuosity of the fracture surface.
Theoretical aspects of fracture mechanics
Progress in Aerospace Sciences, 1995
In this review we try to cover various topics in fracture mechanics in which mathematical analysis can be used both to aid numerical methods and cast light on key features of the stress field. The dominant singular near crack tip stress field can often be parametrised in terms of three parameters I~j, I¢ u and K m designating three fracture modes each having an angular variation entirely specified for the stress tensor and ,displacement vector. This is true for cracks in homogeneous elastic media, and for cracks against bimaterial interfaces although the stress singularity is different in this latter case. For cracks lying on bimaterial interfaces the classical elastic solution produces complex stress singularities and associated unphysical interpenetration of the crack faces. These results and contact zone models for removing the interpenetration ~Lnomaly are described.
Journal of Physics and Chemistry of Solids, 1987
This article first presents introductory material which should make it possible for the person unfamiliar with fracture to read the papers of this series. Then material of a basic physical nature regarding cracks in materials is presented. Emphasis is placed on the effects of chemical attack of bonds at a crack tip, and on the basic physical cause for a material to exhibit a tough (desirable) or a brittle (undesirable) overall aspect.
Determination of Fracture Energy from Size Effect and Brittleness Number
ACI Materials Journal, 1987
A series of tests on the size effect due to blunt fracture is reported and analyzed. It is proposed to define the fracture energy as the specific energy required for crack growth in an infinitely large specimen. Theoretically, this definition eliminates the effects of specimen size, shape, and the type of loading on the fracture energy values. The problem is to identify the correct size-effect law to be used for extrapolation to infinite size. It is shown that Bazant's recently proposed simple size-effect law is applicable for this purpose as an approximation. Indeed, very different types of specimens, including three-point bent, edge-notched tension, and eccentric compression specimens, are found to yield approximately the same fracture energy values. Furthermore, the R-curves calculated from the size effect measured for various types of specimens are found to have approximately the same final asymptotic values for very long crack lengths, although they differ very much for short crack lengths. The fracture energy values found from the size effect approximately agree with the values of fracture energy for the crack band model when the rest results are fitted by finite elements. Applicability of Bazant's brittleness number, which indicates how close the behavior of specimen or structure of any geometry is to linear elastic fracture mechanics and to plastic limit analysis, is validated by test results. Comparisons with Mode II shear fracture tests are also reported.
Engineering Fracture Mechanics, 1983
THE AUTHORS of the above referenced paper have recently attempted to modify the strain energy density criterion as applied to predict the onset of rapid fracture [l]. A mean value of the strain energy density factor 3 obtained by averaging S around the crack tip from 0 = 0" to 360" was used to determine the onset of fracture while the direction of crack initiation is still governed by the minimum value of S or Smin. The results based on 9 led to the false conclusion that /I = 72" gave the lowest critical stress rather than /I = 90" when the applied stress is normal to the crack plane. The discrepancy is due to Mode I and III interaction of the experimental data and not that of Mode I and II as concocted by the authors in their modified version of the strain energy density criterion. A discussion of the work in [l] can be found in 121. The same senior author used the strain energy density in its original form for the same angle crack problem and claimed agreement between theory and experiment .
Interpretation Of Apparent Fracture ToughnessBased On The Use Of Non-singular Terms
WIT transactions on engineering sciences, 1970
The account for non-singular terms of the near-crack-tip stress concentration makes it possible to explain experimentally observed dependence of the fracture toughness upon the crack length. Formulae for the stress intensity factor and the leading non-singular terms for an arbitrarily loaded edge crack are obtained in closed form. The influence of remote boundaries is discussed. Two examples of fitting the theoretical curves to the experimental data on the size effect in fracture toughness are presented.
2008
An incremental description of (linear elastic) fracture mechanics is presented which shows a perfect analogy with plasticity theory. The formulation of a generic criterion stemming from the associated plasticity theory is presented and its feature discussed. The analogy between plasticity and quasi-static crack growth leads also to a new algorithm for crack propagation for an arbitrary number of cracks in multi-connected materials, which is driven by the increment of external actions. Stability of crack path under mode I loading is finally analyzed. Introduction Fracturing process reveals three distinct phases [1]: loading without crack growth, stable crack growth an unstable crack growth. During crack advancing, energy dissipation takes place in the processregion, in the plastic region outside the process region, and eventually in the wake of plastic region. When the fracture process is idealized to infinitesimally small scale yielding, energy dissipation during crack growth is con...
Fracture Mechanics Fundamentals and Applications - Surjya Kumar Maiti
ISBN 978-1-107-09676-9 (hardback), 2015
Fracture mechanics studies the development and spread of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture. The subject has relevance to the design of machines and structures in application areas including aerospace, automobiles, power sector, chemical industry, oil industry, shipping, atomic energy and defense. This book presents the gradual development in the fundamental understanding of the subject and in numerical methods that have facilitated its applications. The subject can be studied from the viewpoint of material science and mechanics; the focus here is on the latter. The book, consisting of nine chapters, introduces readers to topics like linear elastic fracture mechanics (LEFM), yielding fracture mechanics, mixed mode fracture and computational aspects of linear elastic fracture mechanics. It also discusses the calculation of theoretical cohesive strength of materials and the Griffith theory of brittle crack propagation and its Irwin and Orowan modification. Explaining analytical determination of crack tip stress field, it also provides an introduction to the airy stress function approach of two dimensional elasticity and Kolosoff-Mukheslishvili potential formulation based on analytic functions. In addition a chapter deals with the characteristics of fracture in terms of crack opening displacement (COD) and J integral and the interpretation of J as potential energy release rate for linear elastic materials. Other relevant topics discussed in the book include stress intensity factor (SIF); factors that affect cyclic crack growth rate and Elber's crack closure effect; fundamentals of elastic plastic fracture mechanics (EPFM) and the experimental measurements of fracture toughness parameters KIC, JIC, crack opening displacement (COD), K-resistance curve etc.