Dundurs parameters

Table 4.1. Values of the Dundurs parameters D and D2 for some common substrate and film materials. The entry DLC in this table refers to...

For any fixed value of Di and Poisson ratios in the range 0 < the parameter D2 must be in the range — (1 — Di) < D2 < (l- -Di). Values of the Dundurs parameters for some common substrate-film material combinations are listed in Table 4.1. 

Eg enter these conditions only through two dimensionless combinations, the Dundurs parameters Di and D2 which were defined in (3.98) and reintroduced in (4.29). To illustrate the effect of modulus difference between the film and substrate, the two cases with Di = —0.6 and 0.6 are compared to the equal modulus case of D = 0, all with D2 = D /A. These cases correspond to Eg = 4 f and Es = f/4, both with i/f t/g = for example. 

Fig. 5.14. Variation of phase angle if a) with normalized circular buckle size a/om for three different values of the Dundurs parameter D (-0.5, 0 and 0.5), all with D2 = 0 and I f = j.

A wide class of elastic plane problems related to bimaterials depends on only two non-dimensional combinations of the elastic moduli known as Dundurs parameter a and (3 ... 

An interface crack in a bimateiial system (Fig. 6) involves elastic mismatch, which is described in terms of the dimensionless Dundurs parameters [91]. For a coating on a substrate, these are ... 

He and Hutchinson (1989) considered a crack approaching an interface as a continuous distribution of dislocations along a semi-infinite half space. The effect of mismatch in elastic properties on the ratio of the strain energy release rates, Gi/Gj, is related to two non-dimensional parameters, the elastic parameters of Dundurs, a and /f (Dundurs, 1968) ... 

It has been demonstrated that any two-dimensional bimaterial problem can be uniquely described in terms of the two Dundur s parameters, defined as... 

Dundur s Parameters for Several Interfaces Relevant to Microfludic Devices... 

Note Interchanging materials 1 and 2 simply changes sign of Dundur s parameters. 

Dundur s parameters dimensionless parameters that functions of the elastic properties of two materials on either side of an interface, which play a critical role in interface mechanics. Coefficient of thermal expansion of the fth layer, used to include the effects of thermal strains introduced during deposition. 

Material-property dependence for traction-loaded, bimaterial-plane elasticity problems can be completely described in terms of two dimensionless parameters [38]. Consequently, Dundurs elastic mismatch parameters, a and are commonly used to define material-property dependence in calibrations. For a bimaterial with material 1 above the interface and material 2 below. 

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