Fracture Mechanics Theories

Another approach used in LEFM is based on stress intensity factors. This method assumes that for a body containing a crack, the stress applied to the body is intensified to a certain degree at the crack tip. Irwin modified stress functions derived by Westergard to obtain the following equation  

If Kc is defined as the critical stress intensity, then when K is greater than or equal to crack propagation will occur. can be expressed in terms of the crack length, a the critical applied stress, cr and a geometric 

Presented in this manner, is considered a material property and is referred to as the fracture toughness. Values for the factor Y have been derived for many test specimen geometries and can be found in an excellent book on fracture mechanics of polymers by Williams.  

It would seem logical to have a relationship between Gc and since they both represent the toughness of a material based on the presence of voids. These equations have been derived for both plane strain (Eq. 23) and plane stress (Eq. 24)  

Plane strain defines a triaxial stress state at the crack tip, which is, for example, the case for a thick block of material. Plane stress is typical for thin samples where there is no stress acting normal to the plane of the sample. 

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The most-often cited theoretical underpinning for a relationship between practical adhesion energy and the work of adhesion is the generalized fracture mechanics theory of Gent and coworkers [23-25] and contributed to by Andrews and Kinloch [26-29]. This defines a linear relationship between the mechanical work of separation, kj, , and the thermodynamic work of adhesion ... 

Fracture mechanic The fracture mechanics theory developed for metals is also adaptable for use with plastics. The basic concepts remain the same, but since metals and plastics are different they require different techniques to describe their fatigue-failure behaviors. Some of the comments made about crack and fracture influences on fatigue performance relate to the theory of fracture mechanics. The fracture mechanics theory method, along with readily... 

The publication of the ISO and equivalent standards was expected to encourage more workers to apply the fracture mechanics approach which underlies them to the prediction of fatigue in rubber products, although the standard itself does not in fact go into the fracture mechanics theory. Judging from the very considerable volume of literature that has been generated, there has been success in this direction. 

The aim of this review is to concentrate mainly on these fundamental aspects of the fracture behavior of glassy thermoplastics. In the first Section, following an outline of the relevant fracture mechanics theory, the optical interference method is described and the nature of the results obtainable from it is discussed. The next Section then considers the behavior of cracks and crazes in specimens subjected to quasistatic loading, whilst the final Section examines the role of crazing associated with fatigue crack growth. 

The fracture-based approach derives from continuum fracture mechanics theory, which claims the strength of most real solids is governed by flaws within the material [2]. To help predict this type of behavior, many test methods have been developed to determine fracture properties of adhesives. These tests are used to characterize the mode I, II, and III fracture properties of many types of material systems. In this study, the focus will be on the mode I and II characteristics of bonded joints for automotive applications. 

We start with fracture surface examination, which can provide clues to the causes of the fracture. The mechanical causes of crack initiation are then described. Enough fracture mechanics theory is included to explain crack growth criteria, and to link branches of the theory to various fracture phenomena. Finally, impact tests, widely used to characterise polymers and products, are analysed. The product environment, which may affect the failure mechanism, is considered further in Chapter 10. 

Phenomenological models describe the phenomena of craze and crack formation and crack growth in notched tensile bars in die long-term tensile test. The failure behaviour in the tensile tests is quantitatively parameterised and analysed using fracture-mechanics theories. 

In special cases, such as elastomers or other high-elongation materials, bulk plastic or nonlinear behavior of the material does occur. For these cases there have been theories proposed. Chapter 1 discussed the generalized fracture mechanics theory developed by Andrews in which the effect of variables such as crack speed, temperature, and magnitude of strain on the strain energy release rate is considered. ... 

The fracture toughness of poly(vinyl chloride), with a low degree of crystallinity, cannot be readily explained by simple fracture mechanic theories, since there is a marked yielded zone, as well as craze-crack propagation involved in all fractures. 

The fracture mechanics theory described above is a global continuum model which satisfies the conservation of energy principle and the particular equation of state of the materials at large scales. However, we must realise that adhesive failure occurs at an atomistic level. Here the polymer molecules are fluctuating in rapid thermal motion, which can form adhesive bonds and also break them in a dynamic equilibrium of Brownian movement. 

In this section, discussion focuses on the interface fracture mechanics and the details of crack trajectory predictions that are possible with numerical implementation of these concepts. According to the interface fracture mechanics theory discussed in Chapter 2, a crack at the interface between the adherend and adhesive can be represented by a sub-interface crack lying a small distance (St) below the interface and the complex stress intensity factors K and K2 for the interface crack are related to the conventional stress intensity factors and Ku for the sub-interface crack as... 

More specific values of the fracture toughness are obtained by the application of the experimental procedures derived from the fracture mechanics theories. In the case of no plastic deformation in front of the crack tip, the LEFM is employed, obtaining the values of the stress critical intensity factor (fQ) or critical stress energy release rate (G,.). On the other hand, when there is plasticity in front of the crack tip, we must use the principles of the elastoplastic fracture mechanics in this sense, two experimental procedures are widely employed the J-integral analysis and the EWF. 

Service lifetime prediction of polymers and/or polymer based materials may be undertaken from different types of tests, such as creep behavior tests (linear and non-linear creep, physical aging, time-dependent plasticity), fatigue behavior tests (stress transfer and normalized life prediction models, empirical fatigue theories, fracture mechanics theory and strength degradation) and standard accelerated aging tests (chemical resistance, thermal stability, liquid absorption) [32]. 

The Izod and Charpy tests are the test methods usually employed for the determination of the toughness of a material and they are especially useful in comparing the toughness of a particular polymer-particle system. Fracture mechanic theories are the conunonly employed routes for the study and characterization of the toughness of, in particular, ductile polymer composites. 

It is well-known from fracture mechanics theory that the J-integral around a crack-tip is... 

On the other hand, fracture mechanics theory suggests the rupture may be due to weak intercrystalline affinity [18-21], agglomeration of amorphous regions [22-24], or some combination thereof [9,18], However, these broad mechanisms are unlikely to be mutually exclusive, and they lead to similar mathematical representations differing only in the rate-controlling step of many kinetic phenomena [6,10], Because the Zhurkov theory is more widely-accepted and has a well-developed basis in physics, it will be highlighted here. 

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