Energy Approach to Fracture

Note that for a situation where the applied force does no work (i.e. there is no overall change in length of the material) then W = 0 and equation (2.80) becomes 

for a through crack propagating in a sheet of material of thickness, B, we may write 

In the context of fracture mechanics the term 2y is replaced by the Gc so that the condition for fracture is written as 

Gc is a material property which is referred to as the toughness, critical strain energy release rate or crack extension force. It is effectively the energy required to increase the crack length by unit length in a piece of material of unit width. It has units of J/m.  

Equation (2.84) may be converted into a more practical form as follows. Consider a piece of material of thickness, B, subjected to a force, F, as shown in Fig. 2.63(a). The load-deflecdon graph is shown as line (i) in Fig. 2.63(b). From this the elastic stored energy, U i, may be expressed as 

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The value of the energy approach to fracture measurement is that it can be readily used on many very analytically difficult problems. Researchers have demonstrated the ability to directly correlate data measured in one test geometry with data obtained with completely different test geometry. Simple test pieces can... 

The second approach to fracture is different in that it treats the material as a continuum rather than as an assembly of molecules. In this case it is recognised that failure initiates at microscopic defects and the strength predictions are then made on the basis of the stress system and the energy release processes around developing cracks. From the measured strength values it is possible to estimate the size of the inherent flaws which would have caused failure at this stress level. In some cases the flaw size prediction is unrealistically large but in many cases the predicted value agrees well with the size of the defects observed, or suspected to exist in the material. 

An alternative energy approach to the fracture of polymers has also been developed on the basis of non-linear elasticity. This assumes that a material without any cracks will have a uniform strain energy density (strain energy per unit volume). Let this be IIq. When there is a crack in the material this strain energy density will reduce to zero over an area as shown shaded in Fig. 2.65. This area will be given by ka where )k is a proportionality constant. Thus the loss of elastic energy due to the presence of the crack is given by... 

Another approach to fracture behavior characterization is by measuring the work of fracture [110] (i.e.. energy absorbed during the creation of fracture surfaces following the... 

Within this volume, the reader will find several approaches within this general framework. Chapter 2 introduces the concept of fracture mechanics, which is treated in more detail in Chapters 7 and 8. Chapter 3 provides an elegant overview of the energy approach to adhesion. Stresses and driving energies for contact problems relevant to adhesion are given in Chapter II, and Chapter 15 uses fracture mechanics concepts to help interpret the failure modes occurring in bonded joints. 

In order to apply the crack nucleation approach, the mechanical state of the material must be quantified at each point by a suitable parameter. Traditional parameters have included, for example, the maximum principal stress or strain, or the strain energy density. Maximum principal strain and stress reflect that cracks in rubber often initiate on a plane normal to the loading direction. Strain energy density has sometimes been applied as a parameter for crack nucleation due to its connection to fracture mechanics for the case of edge-cracked strips under simple tension loading. ... 

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