Transverse creep

The creep parameters J and y are obtained through transverse creep experiments. The initial compliance is the elastic response of the material (Equation 8.41). In general, the creep parameters J and y, and the shift factor aT may all be dependent on the cure state of the material. For the current process model the shift factor is assumed to be separable and, as such, is only temperature dependent. As a first approximation the creep parameters are represented as linear functions of the degree of cure. ... 

Steady Transverse Creep with Well-Bonded... 

For materials with a strong bond between the matrix and the fiber, models for steady transverse creep are available. The case of a linear matrix is represented exactly by the effect of rigid fibers in an incompressible linear elastic matrix and is covered in texts on elastic materials.7,11,12 For example, the transverse shear modulus, and therefore the shear viscosity, of a material containing up to about 60% rigid fibers in a square array is approximated well... 

It follows that in the coordinates of Fig. 9.1, steady transverse creep with well-bonded fibers obeys... 

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. 

In order to verify some of the predictive capabilities of the finite element model described in the previous sections, the transverse creep response of a IM7/5260 composite investigated in a earlier study [8] was used as a benchmark case. Two separate load histories were considered (1) transverse creep and recovery of a [90]i6 specimen under isothermal conditions, and (2) transverse creep of a [90]i6 specimen subjected to cyclic thermomechanical loading for extended periods of time. 

Figure 12.6 Comparison of NOVA-3D predictions with exact solution for transverse creep and recovery of an IM7/5260 [901,5 specimen. ----, NOVA-3D +, exact 21 MPa O, exact 70MPa...

The modulus term in this equation can be obtained in the same way as in the previous example. However, the difference in this case is the term V. For elastic materials this is called Poissons Ratio and is the ratio of the transverse strain to the axial strain (See Appendix C). For any particular metal this is a constant, generally in the range 0.28 to 0.35. For plastics V is not a constant. It is dependent on time, temperature, stress, etc and so it is often given the alternative names of Creep Contraction Ratio or Lateral Strain Ratio. There is very little published information on the creep contraction ratio for plastics but generally it varies from about 0.33 for hard plastics (such as acrylic) to almost 0.5 for elastomers. Some typical values are given in Table 2.1 but do remember that these may change in specific loading situations. 

Although nearly all creep and stress-relaxation tests are made in uniaxial tension, it is possible to make biaxial tests in which two stresses are applied at 90° to one another, as discussed in Section VI. In a uniaxial test there is a contraction in the transverse direction, but in a biaxial test the transverse contraction is reduced or even prevented. As a result, biaxial creep is less than uniaxial creep--in cquihiaxial loading it is roughly hall as much for equivalent loading conditions. In the linear region the biaxial strain 2 in each direction is (255.256)... 

Zawada et al.44 showed that the proportional limit, expressed in strain (0.3%) rather than in stress, was identical for unidirectional and cross-ply laminates of SiCf/1723. Moreover, the fatigue limit of the unidirectional composite, expressed in strain, corresponded well with the measured fatigue strain limit of the cross-ply laminates. This indicates that the fatigue limit of a cross-ply laminate is primarily governed by the 0° plies and that the influence of the 90° plies is minimal (this result is expected to hold only for room temperature fatigue—see Chapter 5 for a discussion of how transverse plies influence cyclic creep behavior). The 90° plies develop transverse cracks early... 

The previous paragraph has made it clear that if there are elastic fibers and a constant macroscopic stress is applied, the longitudinal creep rate will eventually fall to zero. With constant transverse stresses applied as well, the process of transient creep will be much more complicated than that associated with Eqns. (27) and (28). However, it can be deduced that the longitudinal creep rate will still fall to zero eventually. Furthermore, any transverse steady creep rate must occur in a plane strain mode. During such steady creep, the fiber does not deform further because the stress in the fiber is constant. In addition, any debonding which might tend to occur would have achieved a steady level because the stresses are fixed. 

This equation suggests that E, unlike Ed, is strongly influenced by the matrix modulus. Therefore, if the modulus of the matrix in practical cases decreases due to water absorption or creep relaxation, the transverse modulus will be seriously affected, in contrast to Ed ... 

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