Matrix creep

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... 

Another case is when the fibers creep linearly and the matrix creeps with an index of 2. Then the matrix tends towards a stress... 

A hydrostatic stress can be superposed, but it is caused only by elastic volumetric strain of the composite. The result in Eqn. (39) is, perhaps, not very useful since it is rare that a steady strain rate will be kinematically imposed. When both fiber and matrix creep, the steady solutions for a fixed stress in isothermal states are quite complex but can be computed by numerical inversion of Eqn. (39). The solution can, however, be given for the isothermal case where the fibers do not creep. (For non-fiber composites, this should be... 

The subscripts on B and n have been dropped since only the matrix creeps. The interpretation of time and the initial conditions for Eqns. (41) and (42) are the same as for Eqns. (26) and (27). The fiber deviatoric stresses are given by... 

The latter result indicates that the volumetric strains can be relaxed to some extent by matrix creep. This contrasts with the 3-D case where complete compatibility of strains precludes such relaxation. The extent to which the relaxation occurs has not yet been calculated. However, if it is assumed that the relaxation can be complete so that the matrix volumetric strain is zero, then the fiber stress tends towards aal3lf and, therefore, the composite strain approaches... 

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. 

Fig. 10.10 Curves showing the time needed for crack extension by matrix creep as a function of crack length for various values of the interface viscosity, /. Also shown in the figure is the case wherein fiber bridging is absent. See text for discussion.

Many different fibre/matrix combinations have been proposed some are still in their infancy, some have already reached commercial maturity. Systems based on discontinuous reinforcements (whiskers, chopped fibres) are usually developed to improve selected properties of the matrix (creep resistance, toughness, stiffness) or to extend its temperature range sometimes it happens that improvements are sought to the detriment of other characteristics, first of all ductility. 

A failure indicator was introduced (Ref 25, 26) that proposed that fatigue life was directly proportional to the inverse of the accumulated per-thermal-cycle matrix creep strain. The matrix creep criterion, which is consistent with the Monkman-Grant relation, takes the form ... 

R. lannuzzelli, J. Pitarresi and V. Prakas, Application of Integrated Matrix Creep of Solder Joint Reliability Prediction, ASME IMECE, Nov 1995... 

IMC intermetallic compound integrated matrix creep TEM transmission electron microscopy... 

UV exposure and moisture absorption studies were comparatively performed on long fiber thermoplastics with different matrices, namely PP and PA66 [105], and the first observations were that coloured materials underwent a yellowing process, but all samples displayed cracks at the surface. Depending on time of exposure and the nature of matrix, creep compliance exhibited opposite trends for PP-based composites, it increased, but PA66-based samples showed a moderate decrease probably due to the low oxidation rate, despite the rather constant crystallinity. 

Three principal types of deformation take place upon the application of loads to turbine materials. Elastic deformation is instantaneous reversible deformation that results from the distortion of the crystal lattice. Plastic deformation is the irreversible deformation that takes place instantaneously through the movement of dislocations through the crystal matrix. Creep deformation takes place by a variety of diffusion-controlled processes over time, resulting in continuing strain tmder the applied load. 

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