Plastic constraint

The mechanism for craze nucleation and growth describai here is essentially possible in semicrystalline polymers since the criterion is only related with a stress field due to plastic constraint. Therefore, the size and geometry of a local plastic zone at the notch root is responsible for the formation of crazes (sometimes named internal crazes by the authors). 

The w can be obtained if 1/t ratio is large enough to ensure plane-stress condition in the ligament area and it is proved to be a material constant for a given sheet thickness [Mai and Cotterell, 1986 Mai et al., 1987 Mai and Powell, 1991]. With a reduction of 17t ratio, plastic constraint increases and the plane-stress/plane-strain fracture transition may occur at a certain 1/t ratio. Theoretical analysis shows that the specihc essential work of fracture method is equivalent to the J-integral method for all three fracture modes [Mai and Powell, 1991 Mai, 1993]. 

The stearic acid treated CaCOj nanoparticles significantly improve the tensile modulus of PP, and the modulus increases with an increase in coating thickness [40]. The improvement in modulus is attributed to the presence of stiff particles (Table 9.15). The debonding between nanoparticle and the polymer matrix occurred prior to yielding and therefore released the plastic constraint and allowed shearing to occur. 

Mean-square length of a statistical unit of the chain Mv Molecular mass of a statistical skeletal unit nip Plastic constraint factor... 

A very simple explanation of the effect of notching has been given by Orowan [95], For a deep, symmetrical tensile notch, the distribution of stress is identical to that for a flat frictionless punch indenting a plate under conditions of plane strain [102] (Figure 12.31). The compressive stress on the punch required to produce plastic deformation can be shown to be (2 + 7t)K, where K is the shear yield stress. For the Tresca yield criterion the value is l.Sloy and for the von Mises yield criterion the value is 2.82oy, where 0 is the tensile yield stress. Hence for an ideally deep and sharp notch in an infinite solid the plastic constraint raises the yield stress to a value of approximately 2>Oy which leads to the following classification for brittle-ductile behaviour first proposed by Orowan [95] ... 

For line A the ratio Hb /hy 2 rather than unity, but the difference may be accounted for by the measurement of Hb at very low temperatures and possibly by the measurement of aB in flexure rather than in tension. (The latter may reduce the possibility of fracture at serious flaws in the surface.) It is encouraging that even an approximate relationship holds along the lines of the Ludwig-Davidenkov-Orowan hypothesis. Even more encouraging is the fact that line B has a slope Hb/hy 6, which is three times that of A, as expected on the basis of the plastic constraint theory. 

The plastic constraint factor macroscopic yield stresses [32] ... 

The dependence k on G, is presented in Fig. 5.7 and shows that for polymer, as and for metals [31], Gj enhancement ineieases plastic constraint. At Gj = 0 plastic constraint is absent, that is quite obvious, and at the greatest value of sharp notch the value reaches 2.74, that is close enough... 

FIGURE 5.7 The dependence of plastic constraint factor on defomiation energy release critical rate attesting temperature 293 (1), 313 (2), 333 (3) and 353 K (4) for HDPE [32]. 

Hence, the stated above results have shown that plastic constraint factor is dependent on structiual eharaeteristics of polymer and their change in deformation process and influenees essentially on its meehanical properties in impact tests. Growth k results to reduction of both plasticity and strength of polymer samples [32]. 

Kozlov, G. V., Novikov, V. U. (1997). The Physical Significance of Dissipation Processes in Impact Tests of Semicrystalline Polymers. Prikladnaya Fizika, 1,77-84. Kozlov, G. V., Serdyuk, V. D., Beloshenko, V. A. (1994). Plastic Constraint Factor and Mechanical Properties of High Density Polyethylene at Impact Loading. Mekhanika... 

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