Generalized fracture mechanics

The puqjose of generalized fracture mechanics (GFM) is to overcome some of the problems raised above. Specifically, GFM addresses (1) nonlinear and inelastic materials, (2) steady-state crack propagation, and (3) the expression of critical fracture parameters in terms of the physical properties of the material(s) involved. 

The generalized approach was first introduced in seeking to explain the fatigue properties of plastics,(6) but was developed in the context of adhesive failure by Andrews and Kinloch.(7) The full theory for cohesive fracture was published in 1974.(8) Since these papers are freely available, we shall only outline the theory here. 

If we first assume that no energy is dissipated and the materials are perfectly elastic, we may obtain the energy release rate - d /dA by simply integrating over the whole specimen to give 

Suppose, on the other hand, that energy is dissipated in the volume elements, so that unloading of an element returns only a fraction (1 — p) of its input energy to the stress field O is the hysteresis ratio and is proportional to tan 8 for small strains). Then it is necessary to divide the specimen into loading and unloading regions and integrate separately over these two domains. Hence in this case 

FIGURE 3. (a) Cohesive and (b) adhesive cases of the center crack in an infinite sheet. Crack length is c and point coordinates are X, Y. 

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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 ... 

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 general fracture mechanics equation (Eq. 20) derived in Chapter 1 is used to derive Gj for the TDCB. The change in compliance with crack length, dC/dA, can be found from simple beam theory ... 

Griffith s Thsory of Fracture. Fracture (qv) of polymers and polymer-based composites is of course a subject on which entire books have been written. General fracture mechanics has been presented fairly succinctly by Pascoe (44). Here we shall quote the most important results. 

The energy required to separate atoms or molecules across a plane of fracture or debonding Generalized fracture mechanics The temperature at which a polymer changes from a glass to a rubber or liquid... 

The assumptions outlined above are not always present and to understand them and cope with the consequences it is useful to set the test in the context of a more general fracture mechanics approach. An energy-based analysis is usually written in terms of the energy release rate, G, for a system where the adhesive fracture energy, Gc, is given by ... 

Ohtsuka K. (1986) Generalized G-integral and three-dimensional fracture mechanics. Surface crack problems. Hirosima Math. J. 16 (2), 327-352. 

Fracture Mechanics. Linear elastic fracture mechanics (qv) (LEFM) can be appHed only to the propagation and fracture stages of fatigue failure. LEFM is based on a definition of the stress close to a crack tip in terms of a stress intensification factor K, for which the simplest general relationship is... 

The few studies which addressed the fracture mechanics behavior of very small cracks generally revealed a quantitative departure from behavior determined at longer crack lengths. This result may be attributed to a departure from perfect mechanical and microstructural similitude between long and small cracks. 

In this book no prior knowledge of plastics is assumed. Chapter 1 provides a brief introduction to the structure of plastics and it provides an insight to the way in which their unique structure affects their performance. There is a resume of the main types of plastics which are available. Chapter 2 deals with the mechanical properties of unreinforced and reinforced plastics under the general heading of deformation. The time dependent behaviour of the materials is introduced and simple design procedures are illustrated. Chapter 3 continues the discussion on properties but concentrates on fracture as caused by creep, fatigue and impact. The concepts of fracture mechanics are also introduced for reinforced and unreinforced plastics. 

In general, the use of FE signals accompanying the deformation and fracture of composites offer elucidation of failure mechanisms and details of the sequence of events leading upto catastrophic failure. The extent of interfacial failure and fiber pull-out are also potential parameters that can be determined. FE can assist in the interpretation of AE and also provide an independent probe of the micro-events occurring prior to failure. FE has been shown to be sensitive to the locus of fracture and efforts are underway to relate emission intensity to fracture mechanics parameters such as fracture toughness (Gjp). Considerable work still remains to fully utilize FE to study the early stages or fracture and failure modes in composites. 

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