Dilatational component of the stress

Unlike the shear yield process, crazing is an inherently non-isovolume event. Cavitation of the material requires a dilatational component of the stress tensor, such as occurs in triaxial stress systems that may be foimd in samples subjected to plane strain conditions. In addition, it is foimd in practice that there is a time dependency on the appearance of crazing. That is, there is generally a time delay between application of the load and the first visible appearance of a craze. A number of models have been proposed which require either a critical cavitation stress, a critical strain, or the presence of inherent microvoids, which can grow under the applied local stress or strain. 

Sternstein and Ongchin (1969). Considering that cavitation was required for craze nucleation, Sternstein and Ongchin (122) postulated that it is the dilatational component of the stress tensor along with a stress bias flow stress) that controls craze initiation ... 

In eq. (7.5) the complete Helmholtz free energy of formation of a ST includes the interaction energy between the dilatational component of the shear transformation and a mean normal stress a, as would be the case in tension or in compression. 

A portion of this volume increase may be attributed to expansion of free volume, and since it is caused by the dilatational component of the applied stress, the proportion can be estimated to be the same as the ratio of the compressibilities 8/ and (Chapter 11, Section Dl) then bf/be = (jS// 8)(l/ )(diVdc). Substitution into equation 49 of Chapter 11, for small tensile strains where d//d can be approximated by (J2 —/i)/f, predicts that all relaxation times will be modified by a shift factor whose value is given by ... 

Studies were made of chemical and physical factors influencing time dependent near-bond failure in NR/steel bonded joints. Chemical studies revealed no evidence to indicate that chemical modifications were substantially weakening the rubber adjacent to the bond. Video observations suggested that a cavitation-like process, probably arising from dilatational components in the stresses near an interface, could lead to time dependent mechanical failure near the bond. 10 refs. 

We want to work this out in three simple cases. First we consider a homogeneous dilatation of a cubic volume V = LxLyLz-We also assume that the shear components of the stress tensor vanish, i.e. Oafi = 0 for a In such a system the normal components of the stress tensor should all be the same, i.e. ct = ctxx = [Pg.5]

The shear component of the applied stress appears to be the major factor in causing yielding. The uniaxial tensile stress in a conventional stress-strain experiment can be resolved into a shear stress and a dilational (negative compressive) stress normal to the parallel sides of test specimens ofthe type shown in Fig. 11-20. Yielding occurs when the shear strain energy reaches a critical value that depends on the material, according to the von Mises yield criterion, which applies fairly well to polymers. 

Negative pressure specifically. With subscripts c, e, i, m, P, ST, TH, oo craze traction, Mises equivalent, one of three principal stresses, maximum level of craze traction where cavitation in PB begins, negative pressure in particle, negative pressure due to one of three principal stresses, negative pressure due to thermal mismatch, uniaxial applied stress at the borders With subscripts xx, yy, zz etc. for components of the local stress tensor Ratio of slope of the falling to the rising part of the traction cavitation law Craze dilatation Time constant... 

The decomposition in deviatoric and dilatational components of both the stress and strain tensors are... 

In subsequent sections the Eshelby theory of shear transformations is broadened by incorporation of strain-induced dilatancy into an interaction-energy component of the transformation free energy to account for interaction of the transformation strains with mean normal stresses, to obtain specific results for the differences among shear, tension, and compression flow and strength-differential effects. 

The components of the surface stress tensor depend upon the extent and the rate of surface deformation, in a relationship involving the resistance of the surface to both changes in area and shape. Either of these two types of resistance can be expressed in a modulus which combines an elastic with a viscous term. This leaves us with four formal rheological coefficients which suffice for a description of the surface stress. Two of these, viz., the surface dilatational elasticity, and viscosity, measure the surface resistance to changes in area, the other two, viz., the surface shear elasticity, e, and viscosity, r describe the... 

Other transformations, such as ferroelastic transformation and twin formation in a system may also induce toughening effects. The former discussion on stress-induced transformation was Martensitic, involving both dilation and shear components of the transformation strain. Twin transformation typically only has a... 

The tangential bulk-phase stress component evaluated at the interface combines an elastic (interfacial tension gradient) effect, e, and an apparent viscous effect, rxj + tIj) -I- e 7o). One of the most convenient methods of measuring capillary waves is to use light scattering (29), which can yield information on both the tension and dilational modulus of the interface. 

The dilational rheology behavior of polymer monolayers is a very interesting aspect. If a polymer film is viewed as a macroscopy continuum medium, several types of motion are possible [96], As it has been explained by Monroy et al. [59], it is possible to distinguish two main types capillary (or out of plane) and dilational (or in plane) [59,60,97], The first one is a shear deformation, while for the second one there are both a compression - dilatation motion and a shear motion. Since dissipative effects do exist within the film, each of the motions consists of elastic and viscous components. The elastic constant for the capillary motion is the surface tension y, while for the second it is the dilatation elasticity e. The latter modulus depends upon the stress applied to the monolayer. For a uniaxial stress (as it is the case for capillary waves or for compression in a single barrier Langmuir trough) the dilatational modulus is the sum of the compression and shear moduli [98]... 

The stress bias criterion [24,25] refers implicitly to two mechanisms of microvoid formation in a dilatational stress field and stabilization of the microvoids through a deviatoric stress component and local plasticity. Its definition is... 

In analogy with the strain, it is possible to express the stress tensor as the sum of a dilatational component, and a deviatoric component, that is,... 

If the viscoelastic material is under the effect of an isotropic deformation (dilatation or compression), the diagonal components of both the stress and strain tensors differ from zero. In analogy with Eq. (4.92), the relationship between the excitation and the response is given by... 

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