Energy Release Rates

Fracture mechanics (qv) tests are typically used for stmctural adhesives. Thus, tests such as the double cantilever beam test (Fig. 2c), in which two thick adherends joined by an adhesive are broken by cleavage, provide information relating to stmctural flaws. Results can be reported in a number of ways. The most typical uses a quantity known as the strain energy release rate, given in energy per unit area. 

ASTM D5045-91, "Plane Strain Fracture Toughness and Strain Energy Release Rate of Plastic Materials," A.nnualBook ofyiSTM Standards, ASTM Puhhcations, Philadelphia, 1993. 

G. Critical strain energy release rate J/m J/m U Fluidization gas velocity cm/s ft/s... 

The critical strain energy release rate is the energy equivalent to fracture toughness, first proposed by Griffith [Phil. Trans. Royal Soc., A22I, 163 (1920)]. They are related by... 

Gf = toughness (sometimes, critical strain energy release rate). Usual units kj m 2 ... 

Broeklehurst [37] has written an exhaustive review of the early work (prior to 1977) on fracture in polyerystalline graphite. Mueh of this work foeused on the fraeture behavior of nuclear graphites. In most investigations eonsidered, conventional fracture meehanies tests and analysis were performed for maeroseopie craeks. LEFM provided an adequate eriterion for failure. Additionally, results on work of fraeture, strain energy release rate, and fatigue eraek propagation were reported. 

For equilibrium systems with no contact hysteresis G = W, which is the classical Griffith criterion in fracture mechanics. For such a system, Eqs. 12 and 37 are the same. That is, the strain energy release rate is given by... 

Fig. 19. Variation of strain energy release rate for a moving viscoelastic crack. G > W for an opening crack, and G < W for a closing crack [111].

Fig. 7. Adhesion (critical energy release rate, Fc) of zinc coatings to steel substrates effect of steel surface roughness (after Ye et al. [68]).

Step 2. After a contact time t, the material is fractured or fatigued and the mechanical properties determined. The measured properties will be a function of the test configuration, rate of testing, temperature, etc., and include the critical strain energy release rate Gic, the critical stress intensity factor K[c, the critical... 

The energy release rate (G) represents adherence and is attributed to a multiplicative combination of interfacial and bulk effects. The interface contributions to the overall adherence are captured by the adhesion energy (Go), which is assumed to be rate-independent and equal to the thermodynamic work of adhesion (IVa)-Additional dissipation occurring within the elastomer is contained in the bulk viscoelastic loss function 0, which is dependent on the crack growth velocity (v) and on temperature (T). The function 0 is therefore substrate surface independent, but test geometry dependent. 

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. ... 

Attention will be restricted to the strain-energy-release rate for the opening mode. This mode occurs for the plate with a centrally located crack of length 2a under load P in Figure 6-11. 

The strain-energy-release rate due to crack extension 28a is the shaded area in Figure 6-11 if the loading-frame head does not move during crack extension, that is,... 

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

The strain-energy-release rate was expressed in terms of stresses around a crack tip by Inwin. He considered a crack under a plane stress loading of a , a symmetric stress relative to the crack, and x°° a skew-symmetric stress relative to the crack in Figure 6-12. The stresses have a superscript" because they are applied an infinite distance from the crack. The stress distribution very near the crack can be shown by use of classical elasticity theory to be, for example. 

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