Time dependence of strength

It is useful to analyze two situations that are associated with strength degradation. If a constant stress is applied to a material, the component will fail after a given time period. This process is termed static fatigue and, if one assumes Sp S , Eq. (9.8) can be easily integrated to give the failure time (lifetime) (. of the material as 

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Glass fibres exhibit time-dependent fracture under a static load, which is referred to as static fatigue [36]. Since there is no time dependence of strength in a vacuum, it is considered that water is involved in the reduction in strength. Thus, a stress corrosion mechanism in condensed water is inferred. The chemical reactions associated with this process are given in Figure 12.17. 

It is useful to introduce failure statistics into the time dependence of strength and this can be accomplished by stating the initial inert strength in a Weibull form,... 

Stress-probability-time (SPT) diagrams incorporate the time dependence of strength into failure statistics. They give lifetime predictions. An illustration of the use of SPT diagrams is in bioceramrcs. 

Schatz, R., Shooman, M. and Shaw, L. 1974 Application of Time Dependent Stress-Strength Models of Non-Electrical and Electrical Systems. In Proceedings Reliability and Maintainability Symposium, 540-547. 

Fig. 22. Nomialized pull-off energy measured for polyethylene-polyethylene contact measured using the SFA. (a) P versus rate of crack propagation for PE-PE contact. Change in the rate of separation does not seem to affect the measured pull-off force, (b) Normalized pull-off energy, Pn as a function of contact time for PE-PE contact. At shorter contact times, P does not significantly depend on contact time. However, as the surfaces remain in contact for long times, the pull-off energy increases with time. In seinicrystalline PE, the crystalline domains act as physical crosslinks for the relatively mobile amorphous domains. These amorphous domains can interdiffuse across the interface and thereby increase the adhesion of the interface. This time dependence of the adhesion strength is different from viscoelastic behavior in the sense that it is independent of rate of crack propagation.

Many attempts have been made to obtain mathematical expressions which describe the time dependence of the strength of plastics. Since for many plastics a plot of stress, a, against the logarithm of time to failure, //, is approximately a straight line, one of the most common expressions used is of the form... 

So far we have employed in this discussion a critical shear stress as a criterion for fibre fracture. In Sect. 4 it will be shown that a critical shear strain or a maximum rotation of the chain axis is a more appropriate criterion when the time dependence of the strength is considered. 

Consider a general system described by the Hamiltonian of Eq. (5), where = Huif) describes the interaction between the spin system (7) and its environment (the lattice, L). The interaction is characterized by a strength parameter co/i- When deriving the WBR (or the Redfield relaxation theory), the time-dependence of the density operator is expressed as a kind of power expansion in Huif) or (17-20). The first (linear) term in the expansion vanishes if the ensemble average of HiL(t) is zero. If oo/z,Tc <5c 1, where the correlation time, t, describes the decay rate of the time correlation functions of Huif), the expansion is convergent and it is sufficient to retain the first non-zero term corresponding to oo/l. This leads to the Redfield equation of motion as stated in Eq. (18) or (19). In the other limit, 1> the expan-... 

We choose the time dependence of the field strengths of the pump and Stokes fields to be... 

Fig. 15 Time dependence of the lamellar distance d of aligned lamellae (diamonds), (a) Time dependence with increasing electric field strength (E solid line) for a 50wt% solution of SI51 dissolved in toluene, (b) Time dependence with decreasing electric field strength for the same solution. Adapted with permission from Nature [57]. Copyright (2008) Nature Publishing Group...

Fig. 10.3 Time dependence of continuum coefficients at center of absorption spectrum for narrow absorption band, r, = 50 cm"1. Other parameters are pulse s bandwidth = 120 cm"1, peak intensity = 0.05 a.u., transition dipole strength 5.7 x 10"5. (Taken from Fig. 3, Ref. l326].)...

Abstract. It is shown that reinforcement of PTFE by 15% of multiwall carbon nanotubes (MWNT) results in more than 2 times increase of strength parameters compared to starting PTFE matrix. Non-trivial temperature dependences of electrical resistance and thermal electromotive force were observed. Percolation threshold determined from dependence of the composite specific resistance on MWNT concentration was near 6% mass. Concentration and nature of oxygen-containing MWNT surface groups influence the strength parameters of the composite material. 

Figure 29 shows time dependence of the adhesion force between two identical acrylic acid (AAc)-grafted PET films with a graft density of 190 fig/cm2. Apparently, very weak adhesion was obtained in the initial stage of drying, but the shear strength steeply increased after 30 min and approached... 

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