Contact energy release rate

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... 

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... 

Equation (1) can be used to calculate the applied energy release rate, Q, for the maximum and minimum loads at each cycle. These values are plotted in Fig. 23.11b. The final step in the analysis is to obtain the incremental decrease in contact radius between cycles, and to plot this as a function of AQ, the difference in applied energy release rates between the maximum and minimum load conditions. The results of this analysis are shown in Fig. 23.12. The circular data points are associated with samples that were held at 80 °C for 5 min before cooling back to room temperature square data points were for samples held for 10 min, and triangular data points for those held for 15 min. The lowest values of AQ are obtained at the beginning of the experiment, and are determined by the load amplitude and by the contact radius that develops during the compressive portion of the experiment. For all three tests, a critical Q occurs at about... 

Fig. 23.11 (a) Contact radius for each cycle of the fatigue experiment, (b) Maximum and minimum values of the applied energy release rate for each cycle of the fatigue experiment. 

Our starting point is the definition of the energy release rate, This quantity has the units of a surface energy (energy/area), and describes the amount of energy that is available to decrease the contact area. A, by a unit amount ... 

The results presented in the previous sections assume that the contacting materials have well-defined elastic constants. In fact, most materials have at least some viscoelastic character, and it is important to understand how these effects should be taken into account. Viscoelastic effects enter into our analysis in two ways. First, it is possible that the overall elastic response of the system, described by the effective elastic constant, , is time-dependent. In the case where adhesion is present, the stress near the crack tip will be defined by stress intensity factors, K and K that are themselves time-dependent. A unique energy release rate cannot be defined in this case. We refer to this macroscopic manifestation of viscoelastic behavior as large-scale viscoelasticity . In this case one needs a procedure for determining the stress intensity factor that describes the current state of stress in the vicinity of the contact perimeter. Appropriate expressions for K are an essential result of treatments of large scale viscoelasticity, and these expressions are provided in Section 5.1. 

Reactions in liquids differ markedly from reactions in the gas phase because of the presence of solvent molecules, which are always in intimate contact with the reactants and, in fact, often interact strongly with them. The most important consequence of this interaction is that ions are often stable species in liquid systems. This is because the energy required to dissociate molecules into ions is usually more than compensated by the energy released from the process of ion solvation. According to the results obtained earlier, Eqs. (2-69) and (2-95), the specific rate constant in condensed phases for a nonideal system can be expressed in terms of transition-state theory as... 

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