Creep models reinforcement

Boltzmann s constant, and T is tempeiatuie in kelvin. In general, the creep resistance of metal is improved by the incorporation of ceramic reinforcements. The steady-state creep rate as a function of appHed stress for silver matrix and tungsten fiber—silver matrix composites at 600°C is an example (Fig. 18) (52). The modeling of creep behavior of MMCs is compHcated because in the temperature regime where the metal matrix may be creeping, the ceramic reinforcement is likely to be deforming elastically. 

The 1-D concentric cylinder models described above have been extended to fiber-reinforced ceramics by Kervadec and Chermant,28,29 Adami,30 and Wu and Holmes 31 these analyses are similar in basic concept to the previous modeling efforts for metal matrix composites, but they incorporate the time-dependent nature of both fiber and matrix creep and, in some cases, interface creep. Further extension of the 1-D model to multiaxial stress states was made by Meyer et a/.,32-34 Wang et al.,35 and Wang and Chou.36 In the work by Meyer et al., 1-D fiber-composites under off-axis loading (with the loading direction at an angle to fiber axis) were analyzed with the... 

To gain a better understanding of the creep behavior of fiber-reinforced ceramics, a simple 1-D analytical approach will be used to examine the effects of constituent behavior on composite creep deformation and changes in internal stress. Since the derivation of the model provides valuable insight into the parameters that influence composite creep behavior, the derivation of the 1-D concentric cylinder model will be outlined first. 

It seems unlikely that long-fiber ceramic matrix composites with strong bonds will find application because of their low temperature brittleness. However, for completeness, a model which applies to the creep of such materials can be stated. It is that due to Kelly and Street.21 It is possible also that the model applies to aligned whisker-reinforced composites since they may have strong bonds. In addition, the model has a wide currency since it is believed to apply to weakly bonded composites as well. However, the Mileiko18 model predicts a lower creep strength for weakly bonded or unbonded composites and therefore is considered to apply in that case. 

No attempt has been made to discuss, in a comprehensive manner, models which are based on finite element calculations or other numerical analyses. Only some results of Schmauder and McMeeking10 for transverse creep of power-law materials were discussed. The main reason that such analyses were, in general, omitted, is that they tend to be in the literature for a small number of specific problems and little has been done to provide comprehensive results for the range of parameters which would be technologically interesting, i.e., volume fractions of reinforcements from zero to 60%, reinforcement aspect ratios from 1 to 106, etc. Attention in this chapter was restricted to cases where comprehensive results could be stated. In almost all cases, this means that only approximate models were available for use. 

A comprehensive analytical model for predicting long term durability of resins and of fibre reinforced plastics (FRP) taking into account viscoelastic/viscoplastic creep, hygrothermal effects and the effects of physical and chemical aging on polymer response has been presented. An analytical tool consisting of a specialized test-bed finite element code, NOVA-3D, was used for the solution of complex stress analysis problems, including interactions between non-linear material constitutive behavior and environmental effects. 

Fig. 60. Comparison of experimental (circles) creep and recovery behavior of a glass-reinforced phenolic resin with the predictions from the Schapery (147-149) nonlinear viscoelastic model. o Experimental Data A Predicted Recovery Data (Nonlinear Theory). After Schapery (147), with permission.

The door-mounted rear view mirror with a plastic body, now a virtually universal feature, was a French innovation, introduced with the Renault 14 in 1976. The great majority of today s mirror housings are moulded in glass reinforced nylon, in a variety of formulations based on both PA 6 and PA 66. Black UV-stabilized grades are normally used, with body colours an added refinement for high series models (see Fig. 5.20). Reinforced nylon is used because of the mechanical performance requirements of remote-controlled mirrors, especially the creep resistance needed for the mechanisms to survive the touch-up ovens. The precise grade selection depends on whether die-castings are used for any of the structural elements (still the... 

The reliable formulae and extensive test results for polymer and fibre-reinforced composites are scarce. Simple relations for the prediction for shrinkage and creep of ordinary concretes for application in structural design were given already in CEB-FIP Model Code (1990) with coefficients to allow for actual conditions. Later, so-called Model B3 was recommended by ACI (1999) and extensively discussed by Bazant and Baweja (1995). A sHghtly different approach was proposed in EN 1992 (2004) and detailed comments may be found in Vandewalle (2000). 

Fiber composite plastics are not creep-rupture resistant. Therefore, admissible loads have to be obtained. When determining creep strength for unidirectional reinforcing rods and strips, it must be ensured that enough measurements for statistical evaluation are obtained. Also, it has to be considered that considerable grip problems occur during the tests, and that operational service life significantly exceeds the times that can be achieved in the laboratory, so that extrapolation models have to be utilized [1017]. 

Creep Equivalent strut model Finite element model Infilled frame Masonry Nonlinear analysis Reinforced concrete... 

---