13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- (the very first step is neglected for reason addressed above). Five steps are filled with drawn and broken fibers. The sixth one, a weakly visible and elongated wedge type domain, is the process zone with freshly drawn intact fibers. The fibrillated process zone is separated by a sharp boundary from a uniform grey domain of the original HDPE. It is also obvious that five completed steps exhibit an increasing size of PZ, in contrast with an equal size PZ in SCK specimen [6]. Figure 6. CL in CT specimen tested at 80°C with an initial SIF 0 18 K MPa mm for 90 hours, Upper: side view; Lower: fracture surface (18). The data presented above clearly indicate that there are two different mechanisms of SCG: continuous and discontinuous ones. The transition from continuous to discontinuous SCG strongly depends on stress and temperature. A SCG mechanisms map has been proposed and discussed in [6, 7]. The equilibrium process-zone sizes are recorded using micrographs similar to that shown in Fig.6 and used for evaluation of CL parameters. Details of such work are presented in the accompanying paper [8]. 3. Constitutive Equations of CL Model As stated above, CL in PE poses the simplest PZ that displays the characteristic features of PZ evolution. Therefore, we use it as a showcase for formulation of CL constitutive equations. 3.1. Crack Layer Thermodynamic Forces The active zone of CL in PE has narrow wedge shape geometry with a sharp boundary separating PZ from the surrounding original material (see upper Fig.5a). It consists of cold drawn fibers connected with original material. The crack propagation is the process of breaking fibers under creep condition and forming a fracture “surfaces” (see lower Fig 5a). The width of CL is very small in comparison to the CL length. Therefore we employ the conventional Fracture Mechanics formalism in modeling the external with respect to CL domain. However, addressing the fracture propagation through AZ we use an effective continuum with properties reflecting discrete fibrillated and oriented AZ material. In energy balance, we also consider the energy of transformation of the original material into cold drawn, highly oriented structure of PZ. For such analysis, it is convenient to decompose the specimen with CL into a specimen with CL cutoff and a thin wedge shape CL domain with variable width 0 of original material that undergoes cold drawing in process of PZ formation (see Figure 8). The stress analysis problem shown in Figure 8 (a) is presented as superposition of the same specimen geometry and external load with a cut of CL. The mechanical interaction between AZ of CL and the specimen is taken into consideration by application of the drawing stress along the boundaryof AZ since there is a mechanical equilibrium between the drawn and original materials along that boundary (see Figure 8,b). The second part of the superposition is CL cutoff with stress acting on the AZ from the specimen side (Figure 8,c). The width of AZ in the reference configuration 0 is a function of
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