Crack opening, displacements

For tough polyethylenes, the craze angle remains approximately constant as the damage zone grows so the growth of the craze in the crack direction is linearly related to the COD. 

The use of CRDF measurements was shown by Ward and co-workers [78] to be understood in terms of the relationship of creep behaviour to plastic strain following the concept of the true stress-true strain - strain rate surface (see Section 12.6). Ward and co-workers 

In several publications, Brown and co-workers [82] developed the idea that the reduction in growth rate in polyethylene due to incorporation of branches relates to a difference in the tie molecules in the initial structure. The extensive studies of Capaccio and coworkers [80] confirmed by the computer model of Ward et al. suggest that the critical factor is the creep failure of the fibrils in the craze and is not related directly to the initial morphology [83]. 

In several publications. Brown and co-workers [79] developed the idea that the 

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In the traditional Dugdale model [56], a = Oy and the familiar result is obtained, Gic = cTySc- In the EPZ model, cr exceeds critical crack opening displacement <5c is proportional to the maximum stresses cr in the deformation zone... 

Effective molecular mass between crosslinks tvtc/kg mol 1 Tensile yield strength cry/MPa Energy release rate Gic/Jm 2 Half crack opening displacement w = 6/2 = Gic/2cry w/pm Chain contour length (Eq. 7.9) lc/nm... 

The boundary of the proposed deformation zone is shown in Fig. 7.3 according to Eq. (7.2). The displacement at the crack tip at x = 0 is called crack opening displacement 5 or critical crack opening displacement 8C if the crack is going to propagate. 

Fig. 7.4. Half the crack opening displacement 8C, is plotted against the effective molecular mass N4C between crosslinks. 5C = GIC/uy was calculated from the results in Table 6.1, measured at 23 °C. Mc was determined from the moduli of the polymers in the rubbery state...

Polymer Network A/E = 1 [105] Glass transition temperature T/C Molecular mass of strands (experimental) Mc/kg moF1 Critical stress intensity factor (crack initiation) KIC/MPa ]/m Yield stress, taken from Fig. 9 [110] cry/MPa Half crack opening displacement w = Kfc/2E[Pg.347]

Both sets of experiments seem to support the proportionality of crack opening displacement 5C = 2w and molecular mass Mc between crosslinks as indicated by the slope 1 in the double logarithmic plot (Fig. 7.5). Even if Mc had to be adjusted due to doubts about the front factor in Eq. (4.3), the proportionality would stay unaffected. Consequently, the size of the deformation zone ahead of the crack is determined by the length of the molecular strands in the chemical network. 

Fig. 7.5. Half the crack opening displacement 6C is plotted against the effective molecular mass Mc between crosslinks.

The repeat unit in the Phenoxy molecule is longer by two carbon atoms than that of PC. Otherwise the molecular structures of the two polymers are similar. Eq. (7.8) should, therefore, apply also to PC, at least approximately. 8C = 8.9 pm was measured for the crack opening displacement in a Makrolon sheet (Mn = 9.5 kg/mol) by Fraser and Ward [80], An estimate of the molecular mass between entanglements according to Eq. (7.8) yields Mc = 1.7 kg/mol. This result is not very different from the value of 2.5 kg/mol for IVIC in PC as given in Table 3.2. 

The presented results and the additional information taken from various references indicate the direct relevance of the size of the network strands for the crack opening displacement and consequently for the toughness of the polymer. In polymers under load, the molecular chains at the tip of the crack break after the deformation zone ahead of the crack has grown to a critical width 5C, that is the crack opening displacement. This value 5C is proportional to the length of the molecular strands of the network and is linked in this way to the molecular structure of the polymer. However, the molecular mechanism for chain breakage in the deformation zone is not known at present. 

Claus, R. O. Gunther, M. F. Wang, A. Murphy, K. A., Extrinsic Fabry Perot sensor for strain and crack opening displacement measurements for 200 to 900° C, J. Smart Mater. Struct 1992, 1, 237 242... 

Various models 1-2,42 43) have been proposed to describe the extent and shape of the localised plastic deformation zone at the crack tip. From these models one may define a parameter known as the crack opening displacement, 5, (see Fig. 16) and the value of 5,c for the onset of crack growth is given by... 

Fig. 14. Crack opening displacement, 8te, as a function of test temperature for a rubber-modified epoxy polymer 44)...

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