Fracture macroscopic stress

Failure. When a stress, however small, is applied to a Newtonian liquid, it flows, implying that all bonds between the constituting molecules frequently break, while new ones are formed. When an increasing stress is applied to a piece of an elastic solid, it becomes deformed, and when a certain stress is reached, the test piece starts to fracture. Macroscopic fracture is characterized by... 

Deformation, fracture and stress relaxation at high temperatures in many respects are similar to these phenomena at low temperatures. The major distinction between fracture at high and low temperatures lies in the fact that at high temperature the direction of crack propagation occurs at the angle 90° to the nanotube axis. As a result, the fracture surface has numerous steps. At the macroscopic level it corresponds to tough fracture. 

The stress that causes fracture is not the overall macroscopic stress a that acts on the dried body, but it is the stress concentrated at the flaw tip of length c, having radins r at the tip. 

All cement-based composites are heterogeneous and the notion of a macroscopic stress has only very limited sense. Clear images of stress and strain variations in concrete were shown for the first time by Dantu (1958) and are presented in Figures 8.1 and 8.2. The fracture is initiated by the local stress concentrations where stress values are much higher than the mean value. 

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]. 

It is important to note that we assume the random fracture approximation (RPA) is applicable. This assumption has certain implications, the most important of which is that it bypasses the real evolutionary details of the highly complex process of the lattice bond stress distribution a) creating bond rupture events, which influence other bond rupture events, redistribution of 0(microvoid formation, propagation, coalescence, etc., and finally, macroscopic failure. We have made real lattice fracture calculations by computer simulations but typically, the lattice size is not large enough to be within percolation criteria before the calculations become excessive. However, the fractal nature of the distributed damage clusters is always evident and the RPA, while providing an easy solution to an extremely complex process, remains physically realistic. 

The strength and extensibility of a noncrystallizable elastomer depend on its viscoelastic properties (28,29), even when the stress remains in equilibrium with the strain until macroscopic fracture occurs. In theory, such elastomers have a time- or rate-independent strength and ultimate elongation, but such threshold quantities apparently have not been measured, though rough estimates have been made (28,30). 

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