Models for Yield

The strain rate in the stress direction is proportional to the net jump rate v+ — v, leading to Eq. (62), where V = xA typically corresponds to a few repeat units and is interpreted as an activation volume. 

Among the better-known efforts to provide a more microscopic description of yield within the general Ree-Eyring framework is the approach of Argon, based on metallurgical models, in which the energy barrier is associated with the elastic displacements necessary to accommodate the elementary shear processes [24]. Another well known, but somewhat different, approach is that of Robertson, who 

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The optimization variables values are SQ = 118.3 kg/m3, tr = lh,R = 0.2, and r = 0.2. The values for % yield and productivity calculated by the statistical models are 0.82 and 26.73 kg/(m3-h), respectively. Using the values calculated for S0, tr/ R, and r in the rigorous model, however, the % yield calculated was 0.69 and productivity was 26.39 kg/(m3-h). Note that although the statistical model for yield developed by Costa et al. (5) has a high correlation coefficient and passed the F-test with 99% confidence, at the calculated optimal conditions, it presents a great deviation from the rigorous model. 

A simple model for yield in disordered solids can be derived from the Eyring model, discussed in Section 1.5.1. If the enthalpy of a hop AH is very large, then flow is essentially impossible unless the applied shear stress is large, so that v a approaches AH in magnitude. Then the frcqueney of forward hops is much larger than that of reverse... 

Young, R. J. (1988) Screw dislocation model for yield of polyethylene, Mater. Forum, 11, 210-216. 

Haward and Thackray Model, in 1968 Haward and Thackray (37) developed a one-dimensional model for yield using a spring in series with a parallel arrangement of a spring and dashpot (Fig. 12). The dashpot, rather than being Newtonian as with the standard Maxwell/Kelvin models, was instead an Eyring... 

Thus the term sq in the original Argon model for yield (eq. 36) is replaced by s to give... 

P. B. Bowden and S. Raha, A Molecular Model for Yield and Flow in Amorphous Glassy Polymers Making Use of a Dislocation Analogue , Philos. Mag. 29, 149-166 (1974). 

Young RJ (1974) Dislocation model for yield in polyethylene. Philos Mag 30 85 Zhou J-J, Liu J-G, Yan S-K, Dong J-Y, Li L, Oian C-M, Schultz JM (2005) Atomic force microscopy study of the lamellar growth of isotactic polypropylene. Polymer 46 4077-4087 Zia Q, Radusch HI, Androsch R (2009) Deformation behavior of isotactic polypropylene crystallized via a mesophase. Polym Bull 63 755... 

Bowden, P.B. and Raha, S. (1974) A molecular model for yield and flow in amorphous glassy polymers making use of a dislocation analogue. Phil. Mag., 29,149. 

Young, R.J. (1988) A dislocation model for yield in polyethylene. Materials Forum,... 

Young R J (1974) Dislocation model for yield in polyethylene, Philos Afa 30 85-94. 

Herschel-Bulkley model for yield stress fluids. 

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