Singular stress

S. G. Larsson and A. J. Carlsson, Influence of Non-Singular Stress Terms and Specimen Geometry on Small Scale Yielding at Crack Tips in Elastic-Plastic Material, J. Mech. Phys. Solids, 21, 263-278 (1973). 

Eq. (38) consists of the well known two dimensional singular stress field, / F(v), multiplied by the factor, J Cj" cos fi z, which makes the field "three dimensional". Thus the... 

When the sound wave generated from the branched microcrack or reflected from the boundary of the plate interact with the crack, the singular stress fields at the tip of the crack are modulated in such form as given by Eqs. (25), which are proportional to cos((wr - P x). On the other hand the 1-st order fields consist of two terms which are proportional either to cos(o>r- p x) or sin(o>r-/5 jX). The latter term, for example, comes from the real part of such term. 

The recorded force first increases, then decreases the maximum value, called the tack force is a measure of the adherence in this experimental condition the area under the curve, called the tack energy, is equal to the work GdA of the singular stress at the crack tip. Tackiness refers to the ability of an elastomer to adhere instantaneously to a solid surface, or to itself, after a brief time of contact under low pressure. Probe tack testing procedure can be analyzed by Eq. 14 and tack curves obtained by computer integration closely coincide with experimental ones (25). ... 

Other relevant articles include Stress distribution bond thickness. Stress distribution Poisson s ratio. Stress distribution stress singularities. Stress distribution shear lag solution and Stress distribution mode of failure. 

Fig. 1. Spew and re-entrant comCTs, snch as those fonnd in a lap joint, can result in singular stress fields...

Relation between G and K. The local singular stress held is described by Ki and it is from this discontinuity that the energy is released by way of G. It is to be expected, therefore, that G and Ki would be related and this can be demonstrated by deriving G around a local contour (2) ... 

The stress within the contact area as given by (8.103) is square-root singular as r a , so that the edge of the contact zone has the character of an elastic crack (Lawn 1993) see Section 4.2.3. The elastic stress intensity factor K associated with the singular stress field along this crack edge is... 

When both materials are compliant, singular stresses can also occur. The situation is more complicated because now there may be multiple singularities and they depend on the elastic properties of each material in addition to the corner angles in each material (Fig. 18). There are several ways to present the state of stress near a bimaterial comer. One common approach is given below. 

The singular stress state at the tip of a crack lying on the interface between two dissimilar, linear-elastic, isotropic materials is well known [7,60]. The interfacial tractions directly ahead of the crack tip (Fig. 15) are given by... 

It was noted in Section 2.3.2 that most of the current interfacial fracture mechanics methodologies describe steady-state crack propagation, but not the initiation of interfacial cracks. A recent approach to the prediction of initiation is based on the calculation of the singular stress field at the free edge of a bimaterial system loaded on the top layer [59,60]. Because the crack is assumed not to exist initially in this analysis, a very different singular field is predicted, and the results can be used to predict initiation of cracks in residually stressed coatings. Because the predictions of this theory sometimes contradict the predictions of the Suo and Hutchinson approach, we shall briefly review it as a final note. 

Singularities. At multimaterial interfaces, as well as crack tips, elastic analysis will report singular stresses (Ref 46,47). The outer surface of the solder-to-pad interface where crack initiation is most likely, is an example of such a multimaterial interface. Except in the case of a perfectly plastic material, derived stresses, strains, and strain energies will he mesh dependent. Einer elements will return higher stress values than will larger elements. Since these derived quantities are most likely used to predict solder joint fatigue life, predictions become inextricably tied to the chosen mesh. 

Here, r and 6 are polar coordinates and a is a characteristic length, as given in Figure 1. The important exponent co depends on the elastic constants of the two materials and on the angles 0, and 02 between the interface and the material boundaries. For positive values of (O, singular stresses are developed at the interface comers. For a flat joint, however, it was shown that there are cases when the... 

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