Barenblatt-Dugdale model

Another mathematical approach to modeling cohesive zones is to consider the crack tip fully shielded, that is Keff = 0, rather than partially shielded as in the case considered above. In this case, a cohesive zone lies in front of a traction free crack (Zone 1). This is the classical Barenblatt-Dugdale model in which the stress-intensity factor at the end of the cohesive zone is now zero that is, stress singularities are completely removed by the cohesive forces.29 The requirement of complete shielding results in a cusp-shaped cohesive zone or bridging zone profile. This approach has advantages, particularly for the elevated temperature case, in that the cohesive zone can... 

The deformation zones were calculated for the polymers of Table 5.1 and Table 6.1 according to the Dugdale-Barenblatt-model. Yield stress ay from tensile tests was used instead of the cohesive stress ctc since a reasonable agreement of ay and ctc... 

Fig. 7.3. Deformation zone as calculated from the Dugdale-Barenblatt-model (Eq. 7.2). In order to magnify the displacements, E/cry = 7 was assumed for the diagram, whereas, in reality the ratio is about 38 (Tables 5.1 and 6.1)...

In this section we present a model that applies to a fully shielded crack tip model (Dugdale-Barenblatt-type cohesive zone). We consider the problem of a fully shielded crack (Keff = 0) under small-scale creep/bridging and... 

On the other hand, in glassy polymers the zone of crack tip yielding is often found to be a thin wedge rather than a circle. It is now well documented that a good description of the shape and size of this yielded zone at the crack tip can be provided by the plastic zone size model proposed by Dugdale and by the cohesive force model of Barenblatt " . Similar solutions and further developments have been contributed by other authors... 

The outstanding importance of the Dugdale-Barenblatt-model lies in the fact that yielding occurs by tensile stresses (normal yielding). This becomes obvious if, in the limit of the ellipse becoming a crack, the stresses at the boundary of the plastic zone are considered they are oriented normal to the crack plane. Now, it was shown by Sternstein et coworkers that crazing is a phenomen which essentially occurs under the action of normal stresses. The fibrils in the craze are oriented under the action of the maximum principal tensile stress component and the propagation direction of the craze zone is perpendicular to it and parallel to the axis of the minor principal tensile stress. 

FIGURE 10.7 The schematic picture of crack and local plasticity zone (which is shaded) within the frameworks of the Dugdale-Barenblatt model [22],... 

Fig. 8. Stress distribution in the vicinity of the edge of contact for the Dugdale/Barenblatt cohesive zone model (solid line, Eq. 38), compared to the asymptotic form given by the stress intensity factor (dashed line, Eqs. 30 and 39).

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