Basic Principles of Fracture Mechanics

The acknowledged father of fracture mechanics is A. A. Griffith [6-13]. His principal contribution is an analysis of crack stability based on energy equilibrium. If a crack is in equilibrium, the decrease of strain energy U must be equal to the increase of surface energy S due to crack extension, that is,  

From Equation (6.2), but, because of Equation (6.4), Then, from Equation (6.3), 

Inwin [6-14] calls the strain-energy-release rate G, so 

The stress singularity for this and the other stress components Oy and 

The stress-intensity factors are quite different from stress concentration factors. For the same circular hole, the stress concentration factor is 3 under uniaxial tension, 2 under biaxiai tension, and 4 under pure shear. Thus, the stress concentration factor, which is a single scalar parameter, cannot characterize the stress state, a second-order tensor. However, the stress-intensity factor exists in all stress components, so is a useful concept in stress-type fracture processes. For example. 

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The discussion of fracture mechanics will be divided in two parts. First, basic principles of fracture mechanics will be described. Second, the application of fracture mechanics concepts to composite materials will be discussed. In both parts, the basic approach is that of Wu [6-12],... 

When building a model to predict the mechanical behavior of heterogeneous materials based on polypropylene, the basic principle of fracture mechanics should be considered that fracture is induced in a material when an energy threshold on the weakest zones is reached. It is also well accepted that such energy threshold consists of at least two components necessary energy to initiate a craze and the necessary energy to propagate it. 

Fracture mechanics was first applied by A. A. Griffith (1921) as an approach to the analysis and evaluation of the material s behaviour. For the basic principles of fracture mechanics and its present development, the reader is referred to one of a number of available books and manuals Anderson (2005). It is sufficient here to recall a few of the most important notions necessary for considerations of the brittle matrix composites. 

One of the purposes of this paper is to differentiate between surface free energy and fracture surface energy. Thus, several basic principles of fracture mechanics are discussed with reference to the Griffith s energy-b J nce concept and the Irwin-Orowan s plastic-zone concept. We also define several frequently misused terms, e.g., effective fracture surface energy, fracture energy and fracture toughness. Actual values of related parameters are presented to illustrate the applicability of fracture mechanics to the selection of polymers for structural materials. 

According to the Cubic Law, fracture is formed by the smooth, flat, infinite long parallel plates without filling medium, and the water flow between the plates is viscous incompressible flow which is permanent laminar flow. Thus, according to the basic principle of fluid mechanics, the discharge per unit width through the crack surface i.e. q can be calculated by the follow formula ... 

Adhesive joints usually fail by the initiation and propagation of flaws and, since the basic tenet of continuum fracture mechanics is that the strength of most real solids is governed by the presence of flaws, the application of such theories to adhesive joint failure has received considerable attention. The reader is referred to reviews for detailed discussions of the general principles of fracture mechanics and to on the application of fracture mechanics to the failure of adhesive joints ". ... 

Composite materials have many distinctive characteristics reiative to isotropic materials that render application of linear elastic fracture mechanics difficult. The anisotropy and heterogeneity, both from the standpoint of the fibers versus the matrix, and from the standpoint of multiple laminae of different orientations, are the principal problems. The extension to homogeneous anisotropic materials should be straightfor-wrard because none of the basic principles used in fracture mechanics is then changed. Thus, the approximation of composite materials by homogeneous anisotropic materials is often made. Then, stress-intensity factors for anisotropic materials are calculated by use of complex variable mapping techniques. 

Fracture mechanics The study, both theoretical and experimental, of the behavior of cracks in stressed bodies. A basic principle is that fracture is driven by the energy released by the growth of the crack, which begins at a small imperfection such as is found in all bodies. 

The Essential Work of Fracture (EWF) technique has received much attention in the past two decades as a tool to evaluate the fracture behavior of ductile materials. EWF is based on the general postulates of the post-yielding fracture mechanics. EWF basic principles were introduced by Broberg [1] when studying the fracture of ductile metals. Later, Mai and Cotterell presented in 1987 the first application of EWF to polymers [2]. 

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