Traction, distribution

For elastic materials, the contact problem is usually solved as a unilateral contact problem obeying Coulomb s friction law. The algorithms used here are based on those pioneered by Kalker [66]. The contact area, the stick and slip regions, the pressure and traction distributions are numerically determined first and then the stress and displacement distributions within the elastic bodies can be established at the various stages of the tangential cyclic loading. On the basis of these calculations, the occurrence of crack initiation processes can subsequently be analysed in the meridian plane of the contact, y = 0 (Fig. 12), where the cracks first initiate. As a first approach, parameters based on the amplitude of the shear stress, rm, along a particular direction and the amplitude of the tensile stress, [Pg.174]

Fig. 7 a and b. Sketch of a craze and its tractions for the growth process by repeated cavitation of heterophases at the craze tip. In the process zone A, mature craze matter tufts are established as material points enter at right and exit at left a traction distribution across craze b sketch of traction displacement law for craze matter production... 

Fig. 11.8 Craze surface traction distribution measured in a PS craze (from Lauterwasser and Kramer (1979) courtesy of Taylor Francis).

Fig. 11.22 A schematic representation of the domain-cavitation model of craze growth in spherical-morphology PS/PB diblock copol5mers (a) the idealized stress-strain behavior of a cubical cell containing a cavitated PB sphere and (b) the model of the craze-tip process including the likely craze-tip traction distribution (after Schwier et al. (1985a) courtesy of Taylor and Francis).

In the process the applied distant uniaxial stress principal stresses arr, ( ee, and at the tip of the process zone A by virtue of the special traction distribution that produces the craze-tip driving force of eqs. (11.56). They are given by... 

Figure 1. (Left) Effect of temperature on boundary traction distribution. (Right) Effect of loading...

Fig. 8.40 Measured crack-opening profiles in an ABC-SiC ceramic for a Case I where the crack was grown near instability (at 2 x 10 m/cycle at 92 % Kc), and Case II where the crack was grown near threshold (at 1 x 10 m/cycle at 75 % Kc). In b, the best-fit bridging traction distributions are plotted for each case [4]. With kind permission of Professor Ritchie...

Here, the net crack opening profile, u(X), for a linear elastic crack under an applied far-field stress intensity, Ka, with a bridging traction distribution, p(X), of length, L, acting across the crack faces is expressed in terms of the elastic modulus, E (= E in plane stress of E/(l — v ) in plane strain). X is the integral variable where the stress, p, acts. Also shown are the best-fit profiles determined from Eq. (8.63), shown as the dashed line, and the calculated opening profile for a traction-free track, indicated by the solid line. In Fig. 8.40b, the best fits, p(X) and u(X), were estimated by fitting the data. These data may further used to evaluate p(X) and p(u) in Eq. (8.62). 

Fig. 4.2. A schematic diagram of a film with a free edge bonded to a substrate is shown in the upper portion. The lower portion depicts the same system but with the film and substrate separated to reveal the shear traction distribution q x) through which they interact across their interface and the internal membrane tension t x) in the film.

Fig. 4.6. The solid curves show the distribution of interface normal and shear traction near a film edge for the case when the elastic properties of the two materials are identical as determined by means of the nnmerical finite element method. The corresponding traction distributions based on plate theory and shown in Figure 4.5 are included as dashed curves for purposes of comparison.

Fig. 4.7. The shear traction distributions shown in Figure 4.6 are graphed in a way that reveals the strength of the assumed algebraic singularity in behavior near the film edge. The behavior seems to agree with dependence within the internal...

The pair of dislocations in problem (b) induces a traction distribution Tf- along the surface which coincides in position with the free surface in the... 

Fig. 6.35. Two edge dislocations in an unbounded elastic plane, (a) Schematic showing the traction distribution, represented by Tf, on the planes y = 0 and y = ht which is induced by the dislocations, (b) Complementary boundary value problem which can be solved by the finite element method.

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