Stress relaxation failure process

We can predict tg for stress relaxation failure, where the failure occurs during stress releocation process under a constant strain. From observation of rubbery polymers, we can approximate the stress relaxation behavior by following ecjuation. 

Note that stress relaxation occurs twice during each thermal cycle, while recrystallization (which requires a minimum critical energy) may only occur after a number of cycles. This process is difficult to model because of the discontinuities introduced with crack growth and because not all cracks that are initiated contribute to the final failure. A failure rate prediction model should, however, reflect the aspects noted in Table 17. 

Most pigmented systems are considered viscoelastic. At low shear rates and slow deformation, these systems are largely viscous. As the rate of deformation or shear rate increases, however, the viscous response cannot keep up, and the elasticity of the material increases. There is a certain amount of emphasis on viscoelastic behavior in connection with pigment dispersion as well as ink transportation and transformation processes in high-speed printing machines (see below). Under periodic strain, a viscoelastic material will behave as an elastic solid if the time scale of the experiment approaches the time required for the system to respond, i.e., the relaxation time. Elastic response can be visualized as a failure of the material to flow quickly enough to keep up with extremely short and fast stress/strain periods. 

When the applied stress a is less than Su, creep of the matrix will commence after application of the load. During this creep, the matrix will relax and the stress on the fibers will increase. Therefore, further fiber failure will occur. In addition, the process of matrix creep will depend on the extent of prior fiber failure and, as mentioned previously, on the amount of matrix cracking. The details will be rather complicated. However, the question of whether steady-state creep or, perhaps, rupture will occur, or whether sufficient fibers will survive to provide an intact elastic specimen, can be answered by consideration of the stress in the fibers after the matrix has been assumed to relax completely. Clearly, when the matrix carries no stress, the fibers will at least fail to the extent that they do in a dry bundle. It is possible that a greater degree of fiber failure will be caused by the transient stresses during creep relaxation, but this effect has not yet been modeled. Instead, the dry bundle behavior will be used to provide an initial estimate of fiber failure in these circumstances. 

Several cautions are, however, in order. Polymers are notorious for their time dependent behavior. Slow but persistent relaxation processes can result in glass transition type behavior (under stress) at temperatures well below the commonly quoted dilatometric or DTA glass transition temperature. Under such a condition the polymer is ductile, not brittle. Thus, the question of a brittle-ductile transition arises, a subject which this writer has discussed on occasion. It is then necessary to compare the propensity of a sample to fail by brittle crack propagation versus its tendency to fail (in service) by excessive creep. The use of linear elastic fracture mechanics addresses the first failure mode and not the second. If the brittle-ductile transition is kinetic in origin then at some stress a time always exists at which large strains will develop, provided that brittle failure does not intervene. 

Intermediate - Temperature Relaxations. Secondary relaxations in the glassy state at temperatures intermediate between those of the a- and P- relaxations have been reported, but workers disagree as to their nature, location and origin. Confusion arises in part from a failure to recognize the existence of two separate processes. Krum and MUller [19] observed an intermediate relaxation only for injection-moulded or cold-drawn polycarbonate samples. Since the magnitude was diminished by annealing and the loss was not detected in fully annealed samples, they concluded that the intermediate process is a non-equilibrium effect associated with residual stresses. 

Figure 2.17 Effect of OP-10 (1—3) and MDI (4, 5) content in cured PN 609-2IM resin on temperature of the maximum tan 6 for the dipole-grouped relaxation process at failure stress (1, 5), on the failure stress <7 at static bending of the resin (2,4), and on the optical density /3o of the resin (3).

The cause of brittle fracture in polymers is the inability of the material to quickly dissipate by molecular relaxation processes the internal stresses generated as a result of the imposed deformation. Brittle fracture occurs when the time to failure is the same order of magnitude (or faster) than the speed of the relaxation process that dominates the mechanical behavior in the temperature range of interest. The relevant relaxation processes are the first T < Tg secondary relaxation (p or y). A qualitative criterion for determining whether the relaxation... 

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