Crack-front shapes

Arrest Line. A rtb mark (q.v) defining the crack front shape of an arrested crack, before the crack is spread again by a new stress. 

Double torsion test specimens take the form of rectangular plates with a sharp groove cut down the centre to eliminate crack shape corrections. An initiating notch is cut into one end of each specimen (Hill Wilson, 1988) and the specimen is then tested on two parallel rollers. A load is applied at a constant rate across the slot by two small balls. In essence the test piece is subjected to a four-point bend test and the crack is propagated along the groove. The crack front is found to be curved. 

Wallner lines are formed when sonic waves generated during fracture interact with principal stress driving the propagating crack front. Wallner lines appear as a series of arc shaped steps as shown in Figure 2.33. 

Before we conclude we should mention the following. Firstly the wave discussed in this paper is not related with the crack front wave, which is proved to exist theoretically [9] and experimentally [10], since we did not consider any effect associated with the shape of the crack front. Secondly we have numerically calculated the hoop stress at the center of the plate, afg + dgg, and shown in Fig. 4, which is identical to the hoop stress of the two dimensional crack. In this figure no hoop stress maximum at 0 0 is found up to the crack velocity,... 

The pop-in concept was first developed by Boyle, Sulhvan, and Krafft [3] and forms the basis of the current Kic test method that is embodied in ASTM Test Method E-399 [2]. The basic concept is based on having material of sufficient thickness so that the developing plane stress plastic zone at the surface would not reheve the plane strain constraint in the midthickness region of the crack front at the onset of crack growth (see Fig. 4.2). It flowed logically from the case of the penny-shaped crack, as shown in Fig. 4.4 in the previous subsection. 

A specimen of finite thickness may be viewed simply as a shce taken from the penny-shaped crack specimen (Fig. 4.6). As a penny-shaped crack embedded in a large body, the crack-tip stress field is not affected by the external boundary surfaces and plane strain conditions that prevail along the entire crack front. As a slice, however, the crack in this alternate specimen is now in contact with two free... 

If the specimen is very thick i.e., with thickness B much greater than the plastic zone size, or Kic/oysY), the constraint condition along the crack front in the midthickness region is that of plane strain and is barely affected by plastic deformation near the surfaces. Abrupt fracture crack growth) will occur when the crack-tip stress intensity factor reaches the plane strain fracture toughness Kjc. The load-displacement record, similar to that of the penny-shaped crack, is depicted by Fig. 4.7a. 

In this configuration, shown schematically in Fig. 11.6/), the chevron notch specimen looks quite similar to the SENB except for the vital difference that the shape of the initial crack is not flat but chevron-shaped, as shown by the shaded area. The constant widening of the crack front as it advances causes... 

However, for PSA layers we need to introduce two modifications which complicate the analysis the adhesives are both viscoelastic and strained in the nonlinear elastic regime. In other words the term Gc will include a dissipative term and the term E should be replaced with a high-strain equivalent controlled by the nonlinear elastic properties as shown in Fig. 22.14 and 22.15. As a result, the crack front will not have the same shape as the classical interfacial crack and the exact nature of the stress distribution at the crack tip will be unknown. 

Parallel markings, shaped like a quarter ellipse, occur on some fracture surfaces (Fig. 9.3a). A surface crack has initiated when a blunt object pressed on the product surface (Fig. 9.3b). As this crack spreads sideways, the object penetrates the product and twists the two sides in opposite directions. This double torsion loading causes the crack to advance more rapidly on the lower surface in tension. The characteristic markings are due to momentary hesitations of the crack front. 

If delamination is important, then special cohesive interface elements are needed. Commercial codes now have these, incorporating strength criteria for the initiation of the crack and thereafter a fracture based propagation. In using such cohesive elements at the crack front, it should be remembered that the cohesive zone may be less than 1 mm in size, and the EEs should be chosen to cope with this. Eigure 9.20 shows the experimental scans of a peanut -shaped delamination using 0.2 mm elements. The process zone (with partial crack opening) is indicated [43]. 

To this point, crack fronts have been assumed to be straight or circular. Another important crack shape is the ellipse and analytical expressions for K are available for such cracks. In this case, Eq. (8.19) can be written as... 

For mode I loading of an elliptically shaped crack by a uniform tensile stress, the stress intensity factor varies with position along the crack front and is a maximum at the ends of the minor axis. True or False ... 

Tear Fracture. Normal stresses, such as flexure, that are distributed unevenly across the cross section may cause the material to tear from an external or an internal surface, eg, from a material defect. In such cases, the peaks stand at an angle in the fracture surfaces. If elongation is imiform, rims form at the crack front that remain visible in both fracture surfaces as beads with undulating crests after separation (Fig. 4). Further characteristics of tear fracture are V- and U-shaped ramps, whose tips point against the direction of fracture propagation. 

Assume a periodical array of bridging particles along the crack front and replace each particle by square shaped ligament with side length of 2R. Assume a constant cohesive stress acting over the bridging particles and use the solution (Tada, 1985) for the stress intensity factor K for point forces of magnitude P applied to both faces of the crack at a horizontal distance z and a vertically downwards distance A from the crack front... 

To verify the DEEM and the SIFs calculation method the following problem is considered. In the infinite media stretched by tensile stress a in the direction y the penny-shaped fracture of radius R is placed. The fracture is inclined around the Oz axis at the angle a as it is shown in Fig. 4. The SIFs on the crack front for this problem were previously determined exactly [9]... 

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