Creep Fibre orientation

P(6) If data are not available then the guideline data presented in Figure 4.13 may be used. In order to accommodate composites with varying volume fraction and fibre orientations the figure shows normalised creep modulus against time. It is assumed that initial modulus and therefore creep modulus are linearly proportional to fibre volume fraction. This is a reasonable approximation in most circumstances. 

During the creep of PET and PpPTA fibres it has been observed that the sonic compliance decreases linearly with the creep strain, implying that the orientation distribution contracts [ 56,57]. Thus, the rotation of the chain axes during creep is caused by viscoelastic shear deformation. Hence, for a creep stress larger than the yield stress, Oy,the orientation angle is a decreasing function of the time. Consequently, we can write for the viscoelastic extension of the fibre... 

In order to simplify the discussion and keep the derivation of the formulae tractable, a fibre with a single orientation angle is considered. In a creep experiment the tensile deformation of the fibre is composed of an immediate elastic and a time-dependent elastic extension of the chain by the normal stress ocos20(f), represented by the first term in the equation, and of an immediate elastic, viscoelastic and plastic shear deformation of the domain by the shear stress, r =osin0(f)cos0(f), represented by the second term in Eq. 106. 

For crb 0 the lifetime fb °°,so Eq. 115 presents a non-linear relation between log( b) and the creep stress crb, which is different from the Coleman relation. According to Eq. 115, at constant load the lifetime of a fibre decreases with increasing orientation parameter. Figure 61 compares the observed data for a PpPTA fibre by Wu et al. with the calculated lifetime curve using the parameter values /J=0.08, tan =0.1483, g= 1.6 GPa, j O.032 (GPa)-1, which implies a fibre with a sonic modulus of 91.8 GPa [30]. As shown by Wu et al., fibres that were tested at high stresses had shorter lifetimes than those calculated from the experimental lifetime relation. 

Since for a well-oriented fibre f o/E, the total creep strain is given by... 

The strength of a fibre is not only a function of the test length, but also of the testing time and the temperature. It is shown that the introduction of a fracture criterion, which states that the total shear deformation in a creep experiment is bounded to a maximum value, explains the well-known Coleman relation as well as the relation between creep fracture stress and creep fracture strain. Moreover, it explains why highly oriented fibres have a longer lifetime than less oriented fibres of the same polymer, assuming that all other parameters stay the same. 

Plastics, both thermoplastic and thermosetting, will deform under static load. This is known as creep. For this reason those materials whose prime function is mechanical are generally reinforced with mineral filler or short fibres, or else oriented by drawing. Many components have a limit on acceptable deformation, and the predicted creep strain at the end of life will be fed back to define either a maximum load, or mechanical dimensions large enough for the component to remain within the limitations on strain. Creep becomes more pronounced at higher temperatures. 

Most tests will be made on standard test pieces which may be pieces cut from a component or a sheet, or they may have been moulded separately from the same material. Where test pieces or sheet are produced for the trials it is important that they are produced in as near as possible the same way as the product and that the processing conditions are recorded. Different results can be expected from compression and injection moulding or from extrusion (where a choice is possible). Directional properties can result from the conditions of flowing and cooling in a mould. For example, in a study at ERA, the creep strain of unfilled HDPE, either individually moulded or cut from square plaques, varies by up to a factor of two depending on the orientation of flow [40]. This difference becomes even more marked with short fibre reinforcement. 

Figure 8.7 First stage of the stepped isothermal method (SIM) for oriented polyester fibres. Creep strain is measured under a single load while the temperature is increased...

Fig. 10 Sherby-Dorn plots of creep rate versus strain showing the different creep phases a U PVC pipes for constant hoop stresses of 37 to 42 MPa at a temperature of 20 °C (60 K below Tg) (using data of Castiglione et al. [42]) b Highly oriented UHMWPE fibres at room temperature (using data of Berger et al. [43])...

For well-oriented fibres with a single orientation angle 0 the creep equation reduces to... 

Creep and stress relaxation accelerate once the temperature exceeds the Tg of the matrix. Viscoelastic behaviour is obviously relevant to durabiUty, but fortunately the addition of suitably oriented fibre reinforcement can dramatically decrease or suppress viscoelastic behaviour, to an extent that depends on fibre direction, fibre volume fraction, and so on. This is an important reason for using fibrous reinforcement, even when it seems unnecessary from a consideration of short term mechanical behaviour. 

Fig. 6. Variation of lateral compliance with time during tensile creep of specimens cut at 0 and 90° to the fibre axis of a sheet of oriented polymethylmethacrylate (drawn at I24°C, birefringenceO-(X)l). Note that the values of the lateral compliances...

The low creep rates for the oriented material in Fig. 8 indicated that the easy shear process which produced the high anisotropy of modulus occurr before the start of the creep measurements. This is consistent with the dynamic mechanical data of Stachurski and Ward on similar cold drawn LDPE sheets, which showed a highly anisotropic relaxation, attributed to shear parallel to the oriented crystalline chains, at a frequency of 50 Hz and temperature of 0°C. From the above it would be expected that high creep rates would be obtained on specimens cut at 45° to the fibre axis, when the temperature is lowered into the relaxation region. Baker and Darlington (1973, to be published) have confirmed that such high creep rates are observed at times between 5 and 2 x 10 s, when the temperature is lowered to — 10°C. 

Fig. 18. Creep rupture data for specimens cut at various angles, B. to the fibre axis of an oriented PMMA sheet (birefringence 0-0006). ...

Creep testing of oriented polymers, intended to fully characterise the anisotropy of stiffness behaviour, presents formidable difficulties. For materials with fibre symmetry, techniques are now available which allow complete characterisation. These techniques are considerably more sophisticated than simple creep testing in isotropic materials. For lower symmetries it is still not possible to achieve full characterisation. 

Materials made from unidirectional fibre tows laid in parallel to each other or held at precise predetermined orientations should allow volume fractions of fibre to exceed 50% within plies and highly aligned properties to be generated. Materials with no crimp are beneficial to creep behaviour. 

---