Griffith Theory of Fracture

2012 ◽  
pp. 11-24
Author(s):  
C.T. Sun ◽  
Z.-H. Jin
Keyword(s):  
Griffith Theory

Aspects of the Determination of the Strength of Materials

1947 ◽  
Vol 51 (433) ◽  
pp. 65-68
Author(s):  
E. W. J. Mardles
Keyword(s):  
Brittle Fracture ◽  
Statistical Methods ◽  
Mechanical Test ◽  
Microscopical Examination ◽  
Test Results ◽  
Strength Of Materials ◽  
Recent Developments ◽  
The Subject ◽  
Griffith Theory

Some aspects of the determination of the strength of materials formed the subject of two meetings held jointly with the British Rheologists’ Club (President, Prof. E. N. da C. Andrade) and the Royal Aircraft Establishment in the Assembly Hall, Farnborough, on the 16th June, 1945, and with the Royal Aeronautical Society in the library at 4, Hamilton Place, on the 19th February, 1946, under the chairmanship of Sir Ben Lockspeiser.At the Farnborough meeting three papers were read, namely, “The investigation of failures in wood by microscopical examination” by M. C. Pryor and A. Rayne; “The effect of duration of loading on the strength of brittle materials” by C. Gurney; and “Application of statistical methods to mechanical test results” by B. Chalmers and E. R. W. Jones. At the London meeting Prof. N. F. Mott of Bristol University spoke on the “Griffith theory of cracks in solids and recent developments of this theory, with application to brittle fracture in glass and in metals.”

Griffith theory and development of fracture mechanics criteria

1993 ◽  
Vol 29 (3) ◽  
pp. 316-319 ◽  
Author(s):  
N. A. Makhutov ◽  
Yu. G. Matvienko
Keyword(s):  
Fracture Mechanics ◽  
Griffith Theory

Behavior and Fracture Mechanism of Brittle Rock with Pre-Existing Parallel Cracks

2006 ◽  
Vol 324-325 ◽  
pp. 1055-1058 ◽  
Author(s):  
M.X. Zhang ◽  
X.L. Lee ◽  
A.A. Javadi
Keyword(s):  
Fracture Mechanism ◽  
Rock Fracture ◽  
Strength Criterion ◽  
Brittle Rock ◽  
Fracture Mechanisms ◽  
Stress Equilibrium ◽  
Parallel Cracks ◽  
Micro Cracks ◽  
Griffith Theory ◽  
Almost All

There is a macro-crack and micro-crack system in rock, which affects almost all the mechanical properties of rock, especially for the fracture mechanism. The propagation of pre-existing cracks in rock samples under load is fundamental to understanding of rock fracture mechanisms. It is evident that assumption of Griffith theory was not in accord with the fact that numerous cracks exist in rock. So, it is difficult to explain how the propagation of a micro-crack developed into macro-failure by conventional theories. In order to investigate the cause and results of fracture within the rock, the stress concentration around the micro-cracks was analyzed, which resulted in propagation of wing cracks and connecting adjacent original cracks, eventually leading to macro-failure. The experiments on gypseous samples with pre-existing parallel cracks (flat rectangular in shape) under compression were carried out. The fracture mechanism and the stress equilibrium condition at brittle rock were discussed. Based on the fracture mechanism of brittle rock, a strength criterion of rock was proposed.

WHAT IF SPIDERS MADE METAMATERIAL WEBS USING MATERIALS WITH MECHANICAL SIZE-EFFECTS?

2021 ◽  
Author(s):  
ERIC ROBERT BEHLING ERIC ROBERT BEHLING ◽  
ASHUTOSH SRIVASTAVA ◽  
RAPHAËL GLAESENER ◽  
SIDDHANT KUMAR ◽  
ANIRUDDH VASHISTH
Keyword(s):  
Material Properties ◽  
Spider Webs ◽  
Spider Web ◽  
Size Dependent ◽  
Reinforced Polymer ◽  
Dependent Behavior ◽  
Out Of Plane ◽  
Natural Composites ◽  
Griffith Theory ◽  
Energy Absorbers

Spider’s webs are elegant examples of natural composites that can absorb outof- plane impact energy to capture prey. Different spiders have different methods and structure of webs, and these variations in topologies have a significant effect on the prey catching abilities of the web. Taking inspiration from the spiders, metamaterials that have architectured topology can be fabricated according to end applications such as energy absorbers or impact tolerant materials. In this investigation, we theoretically examined impact loading on various orb-spider webs modeled with metamaterial architecture using materials that show size-dependent behavior. Using the size-dependent properties of nano-reinforced polymer-derived ceramics (PDCs), various metamaterial topologies were evaluated for out-of-plane impact due using ANSYS Ls-Dyna. The material properties capture the size dependency of the ceramics where smaller elements have higher strength due to reduced flaw intensity; the mechanical strength of these elements does not follow the conventional Griffith Theory. In this study, spider web geometries fabricated with PDCs with varying size elements were examined.

Laboratory Investigation of Fracture Initiation Pressure and Orientation

1979 ◽  
Vol 19 (02) ◽  
pp. 129-144 ◽  
Author(s):  
W.L. Medlin ◽  
L. Masse
Keyword(s):  
Hydraulic Fracture ◽  
Field Data ◽  
Laboratory Experiments ◽  
Fracture Initiation ◽  
Stress Conditions ◽  
Elastic Behavior ◽  
Fracturing Fluids ◽  
Initiation Pressure ◽  
Cylindrical Cavities ◽  
Griffith Theory

Abstract The mechanics of hydraulic fracture initiation have been investigated by comparing laboratory experiments with theoretical predictions based on poro-elastic behavior. Experiments were conducted poro-elastic behavior. Experiments were conducted with 4-in. (10-cm) diameter cores containing spherical and cylindrical cavities and loaded in a triaxial cell under variable confining pressure, end load, and pore pressure. Experimental results agreed with theory for nonpenetrating fracturing fluid for limited ranges of hydrostatic confining stresses for four kinds of limestone rock. With penetrating fracturing fluids, the theory was penetrating fracturing fluids, the theory was confirmed only partially. Under nonhydrostatic stress conditions, reproducibility of measurements was too poor to evaluate the theory. Fracture orientation was controlled predominantly by stress conditions and cavity geometry. Notching of cylindrical cavities failed through notch extension only if the notch depth exceeded the value predicted approximately by a simple Griffith theory predicted approximately by a simple Griffith theory equation. Field applications of all results are discussed. Introduction This paper describes a combined theoretical/ experimental investigation of the mechanics of hydraulic fracture initiation. We considered fracture initiation pressure, fracture orientation, and mode of failure for various stress conditions and wellbore geometries. Our intention has been to consider theory applicable for both field and laboratory conditions, to test this theory with laboratory experiments, and to apply the results to interpretation of field data. The laboratory experiments were designed not to duplicate field conditions so much as to provide a critical test of the theory. Some field data are examined, but it is impractical to learn much about fracture initiation from field experiments because of the limited number of quantities that can be measured. The theory presented here is more a generalization of earlier work than a development of new theory. It provides a completely general treatment of fracture initiation in spherical and cylindrical cavities for poro-elastic materials. An extension of this theory poro-elastic materials. An extension of this theory to porous materials with nonelastic behavior already has been developed by Biot and will be referred to later. We begin by presenting theory for fracture initiation in spherical and cylindrical cavities. The theoretical results are followed by descriptions of laboratory experiments that test the equations for failure pressure in these geometries under various stress conditions, using penetrating and nonpentrating fracturing fluids. The effects of notching in cylindrical cavities then are considered, and a simple model based on Griffith crack theory is developed to explain experimental results. Field applications of all results then are discussed in detail. THEORY OF FRACTURE INITIATION The theory of hydraulic fracture initiation in rock materials has been treated in successive degrees of refinement. Cases of interest are hollow sphere and long hollow cylinder geometry with penetrating and nonpenetrating fracturing fluids. penetrating and nonpenetrating fracturing fluids. Refs. 1 through 7 cover various parts of the overall picture; Rice and Cleary give the most complete picture; Rice and Cleary give the most complete analysis. We present here an independent analysis based on Biot's theory for fluid saturated porous solids. Our analysis adds little that is new to the basic literature of fracture initiation theory. It is presented mainly to provide a way to analyze presented mainly to provide a way to analyze scaling effects between field results and our laboratory experiments. We start with Biot's stress-strain relations for a fluid saturated porous solid: (1) SPEJ P. 129

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