Time-stress correspondence, plastics mechanical

The application of force to a stationary or moving system can be described in static, kinematic, or dynamic terms that define the mechanical similarity of processing equipment and the solids or liquids within their confines. Static similarity relates the deformation under constant stress of one body or structure to that of another it exists when geometric similarity is maintained even as elastic or plastic deformation of stressed structural components occurs [53], In contrast, kinematic similarity encompasses the additional dimension of time, while dynamic similarity involves the forces (e.g., pressure, gravitational, centrifugal) that accelerate or retard moving masses in dynamic systems. The inclusion of tune as another dimension necessitates the consideration of corresponding times, t and t, for which the time scale ratio t, defined as t = t It, is a constant. 

Slow Crack Growth. Many thermoplastics exposed to constant and moderate stresses over extended periods of time, as for instance pipes imder internal pressure, fail in either of two different modes, in a ductile or in an apparently brittle manner. The durability is often represented as a stress-lifetime a-t) diagram (Fig. 29). The simultaneous action of two failure mechanisms gives in this case rise to two different branches of the lifetime curves. At moderate stresses (above 50% of cTy) the HDPE pipes fail in a ductile manner because of plastic instability of the creeping material (Fig. 2, which corresponds to Point 1 in Fig. 29). The ductile failures are strongly stress-activated = 307 kJ/mol) giving rise to the flat portions of the cr-t curves. Fracture at smaller stresses and after more extended time periods often occurs in an apparently brittle manner by thermally activated slow crack growth (SCG) (steep branches in Fig. 28, = 181 kJ/mol). Such a... 

Let us consider further reasons of pol5rmer chains breaking at so small stresses, which can be on order lower than ftacture macroscopic stress (i.e., at h5rpothetical k = 0.1). The reasons were pointed for the first time in Refs. [1, 26]. Firstly, anharmonicity intensification in fracture center gives the effect, identical to mechanical overloading effect [26]. Quantitatively this effect is expressed by the ratio of thermal expansion coefficient in fracture center and modal thermal expansion coefficient [5]. The second reason is close inter communication of local yielding and fracture processes [ 1]. This allows to identify fracture center for nonoriented polymers as local plasticity zone [27, 28]. The ratio uJ(X in this case can be reached -100 [5]. This effect compensates completely k reduction lower than one. So, for PC ala 70, K- = 0.44, a. = O.IE. 700 MPa and fiien o = o a /K,a 23 MPa, that by order of magnitude corresponds to experimental value Oj. for PC, which is equal approximately to 50 MPa at T= 293 K [7]. 

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