Dilatational component of the stress tensor

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 ... 

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]

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... 

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,... 

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

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... 

A general state of stress at a point or the stress tensor at a point can be separated into two components, one of which results in a change of shape (deviatoric) and one which results in a change of volume (dilatational). Shape changes due to a pure shear stress such as that of a bar in torsion given in Fig. 2,2 are easy to visualize and are shown by the dashed lines in Fig. 2.16(a) (assuming only a horizontal motion takes place). 

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... 

The viscous properties of a liquid are defined in relation to the rate of distortion and dilatation of a local region R in response to stresses applied at the surface S which encloses it. In the analysis, we consider an element SS of the surface and construct a unit normal vector n directed outwardly from the surface. The applied stress can then be resolved into components tending to stretch the vector and components tending to rotate it. The force F per unit area can then be represented in terms of a tensor P(r) operating... 

The importance of the concept of a separating the stress (and strain) tensors into dilatational and deviatoric components is due to the observation... 

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