Strain hardening modulus

The investigated structure (cf. fig. 1) consists of a pure nickel top layer (1.2mm thick), an FGM zone with a linear variation of the volume fraction (2.2mm thick), and a pure alumina bottom layer (0.45mm thick). Material data of the constituents are given in table 1, where Eh denotes the strain hardening modulus. The boundary conditions force all cross sections perpendicular to the monolithic/FGM interfaces to remain plane, i.e. the lefthand and the righthand side (as well as the viewing plane for three-dimensional considerations). The uniaxial load (which causes extension and bending for the present... 

Figure 8.14 Variation of strain hardening modulus with temperature below Tg, for PS/PPO blends (from van Mellick, H. G. H. et o/., Polymer 44, 4493, 2003) Elsevier.

The general behaviour is characterized by a decrease of the initial modulus as well as the yield stress with temperatiue. Yielding of the material is finished at a strain of about 600. .. 900 %, afterwards there is a strain hardening. The strain hardening modulus (slop>e of the true stress vs. strain curve in the region of strain hardening) decreases with the temperature. 

Kurelec, L. et al. (2005). Strain hardening modulus as a measure of environmental stress crack resistance of high density polyethylene. Polymer, Vol. 46 (2005), p>p. 6369-6379... 

Robbins, M. O. and Hoy, R. S. (2009) Scaling of the strain hardening modulus of glassy polymers with the flow stress, J. Polymer Sci. Part B Polymer Phys., 47, 1406-1411. 

Thus, H again serves the role of uniaxial incremental strain hardening modulus, as in (7.61). Finally, the consistency condition in the case of kinematic... 

From the Eq. (14.15) it follows, that polymers structure fractality < d) results to yield stress essential reduction. From the point of view of thermodynamics Oy indicated reduction is due to accumulation in sample of internal (latent) energy, the relative fraction of which is equal to about [41]. For Euclidean solids d = d) the Eq. (14.15) gives Hooke law. At the same time for the indicated materials extrudates strong increase in comparison with initial samples is due to E and d simultaneous growth. It is follows to note also, that the Eq. (14.15) can be used for description of polymers deformation on the elasticity part (at d = d) and on cold flow plateau (at d = d and elasticity modulus replacement on strain hardening modulus) [32]. 

Fig. 22. Temperature dependence of the strain-hardening modulus of iPP and HOPE.

In terms of the strain-hardening modulus, this has been developed by the use of Kuhn and Griin models and Kratky models to relate the development of molecular orientation and meehanical anisotropy (see Section 8.6.3). With regard to the strain rate sensitivity the strain rate-dependent viscosity has been developed by studies of creep and yield behaviour (see Sections 11.3 and 12.5.1). 

An alternative approach was adopted by Kurelec et al. [84] who determined true stress-true strain curves at 80°C for a range of polyethylenes. It was shown that the slope of the tensile curve above the natural draw ratio (called the strain-hardening modulus) correlated well with the measured stress crack resistance (Figure 13.31). These results are entirely consistent with those obtained by Capaccio and co-workers and Ward and co-workers described above. Kurelec et al. found similar effects on the environmental stress cracking resistance (ESCR) performance with regard to short chain branches, and elaborated these in terms of the exact nature of the branches, particularly with regard to bimodal molecular weight distribution polymers. 

Figure 13.31 Environmental stress cracking resistance (ESCR) plotted against strain-hardening modulus for a range of EIDPEs, both catalyst based with broad molecular weight distribution, and bimodal. Points labelled reproducibility are repeated tests on the same sample. (Reproduced from Kurelec, L, Teeuwen, M., Schoffeleers, El. et al. (2005) Strain hardening modulus as a measure of environmental stress crack resistance of high density polyethylene. Polymer, 46, 6369. Copyright (2005) Elsevier Ltd.)...

Eirst, it is observed that the strain hardening is same for amorphous PET and cold crystallized PET, although the crystalline phase is developed by cold crystallization. Eor example, the slope at large strain is used to define the strain-hardening modulus and the lines are parallel and thus strain-hardening modulus values are the same for PET with 0%, 22%, and 29%... 

Figure 18.14 Effects on the strain-hardening behavior of semicrystallme polymers (a) effect of the crystallinity for PET (b) effect of the molecular weight and processing condition for PE (the slope of the dashed line is defined as strain-hardening modulus). Schrauwen et al. [12], Reproduced with permission of American Chemical Society.

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