Strains strain-hardening at large

What is the molecular origin of strain hardening at large elongations of polymeric networks that do not crystallize on stretching ... 

Rubber becomes harder to deform at large strains, probably because the long flexible molecular strands that comprise the material cannot be stretched indefinitely. The strain energy functions considered up to now do not possess this feature and therefore fail to describe behavior at large strains. Strain-hardening can be introduced by a simple modification to the first term in Eq. (1.18), incorporating a maximum possible value for the strain measure J, denoted Jm (Gent, 1996) ... 

The experimental curves stress-draw ratio (o - A) for SBR and nanocomposite SBR-2 are presented in Fig. A. 1 [ 11]. As one can see, the curves a - A for these materials differ significantly even by exterior appearance one can visually affirmed, that nanocomposite has higher Young s modulus E and much more strong strain hardening (i.e., modulus at large strains) than matrix rubber SBR. For these curves theoretical description the authors of Ref [10] used two approaches classical [3] and fractal [7] ones. The first fi om them supposes the relation between a and A, defined by the equation [3] ... 

Strain Hardening. Annealed Ti-15-3 does not follow the usual strain hardening laws as the spread between the tensile yield and ultimate tensile strengths is quite small. Once stable flow is established (post yield strains), an approximately exponential stress-strain relationship is observed. The stress-strain curve at large strain may be estimated as ... 

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%... 

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