Creep temperature dependence

Four modes of characterization are of interest chemical analyses, ie, quaUtative and quantitative analyses of all components mechanical characterization, ie, tensile and impact testing morphology of the mbber phase and rheology at a range of shear rates. Other properties measured are stress crack resistance, heat distortion temperatures, flammabiUty, creep, etc, depending on the particular appHcation (239). 

The theory relating stress, strain, time and temperature of viscoelastic materials is complex. For many practical purposes it is often better to use an ad hoc system known as the pseudo-elastic design approach. This approach uses classical elastic analysis but employs time- and temperature-dependent data obtained from creep curves and their derivatives. In outline the procedure consists of the following steps ... 

Figure 9.6. (a) The temperature dependence of the flow stress for a Ni-Cr-AI superalloy containing different volume fractions of y (after Beardmore et al. 1969). (b) Influence of lattice parameter mismatch, in kX (eflectively equivalent to A) on creep rupture life (after Mirkin and Kancheev... 

The viscoelastic nature of the matrix in many fibre reinforced plastics causes their properties to be time and temperature dependent. Under a constant stress they exhibit creep which will be more pronounced as the temperature increases. However, since fibres exhibit negligible creep, the time dependence of the properties of fibre reinforced plastics is very much less than that for the unreinforced matrix. 

This is then replaced by a period of steady state creep which, depending on the temperature and stress level, takes up the greatest part of the creep life. 

The time/temperature-dependent change in mechanical properties results from stress relaxation and other viscoelastic phenomena that are typical of these plastics. When the change is an unwanted limitation it is called creep. When the change is skillfully adapted to use in the overall design, it is referred to as plastic memory. 

As shown in Sect. 2, the fracture envelope of polymer fibres can be explained not only by assuming a critical shear stress as a failure criterion, but also by a critical shear strain. In this section, a simple model for the creep failure is presented that is based on the logarithmic creep curve and on a critical shear strain as the failure criterion. In order to investigate the temperature dependence of the strength, a kinetic model for the formation and rupture of secondary bonds during the extension of the fibre is proposed. This so-called Eyring reduced time (ERT) model yields a relationship between the strength and the load rate as well as an improved lifetime equation. 

For the investigation of the time and the temperature dependence of the fibre strength it is necessary to have a theoretical description of the viscoelastic tensile behaviour of polymer fibres. Baltussen has shown that the yielding phenomenon, the viscoelastic and the plastic creep of a polymer fibre, can be described by the Eyring reduced time (ERT) model [10]. The shear deformation of a domain brings about a mutual displacement of adjacent chains, the... 

If up to 40% of ESI is blended with LDPE then foamed, the foam properties are closer to those of LDPE foams. Ankrah and co-workers (33) showed that the ESI/LDPE blends have slightly lower initial compressive yield strengths than the LDPE alone, allowing for the density of the foam. The temperature dependence of the yield stress is similar to that of LDPE foam (Figure 3). Although the yield stress is higher than EVA foam of the same density, the compression set values are lower. The ESI/LDPE foams have improved impact properties, compared with EVA foams of similar density. Analysis of creep tests shows that air diffuses from the cells at a similar rate to EVA foams of a greater density. 

For a semi-crystalline polymer the E-modulus shows between Tg and (in which region it is already lower than below Tg), a rather strong decrease at increasing T, whereas with amorphous polymers, which are used below Tg, the stiffness is not much temperature dependent (apart from possible secondary transitions). The time dependency, or the creep, shows a similar behaviour. 

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. ... 

The mechanical properties of Shell Kraton 102 were determined in tensile creep and stress relaxation. Below 15°C the temperature dependence is described by a WLF equation. Here the polystyrene domains act as inert filler. Above 15°C the temperature dependence reflects added contributions from the polystyrene domains. The shift factors, after the WLF contribution, obeyed Arrhenius equations (AHa = 35 and 39 kcal/mole). From plots of the creep data shifted according to the WLF equation, the added compliance could be obtained and its temperature dependence determined independently. It obeyed an Arrhenius equation ( AHa = 37 kcal/mole). Plots of the compliances derived from the relaxation measurements after conversion to creep data gave the same activation energy. Thus, the compliances are additive in determining the mechanical behavior. 

These differences in the mechanical behavior are not reflected, within the experimental error, in the temperature dependence of the mechanical properties. As shown by the examples of Figures 1 and 3, the relaxation modulus and creep compliance data showed very little scatter and could be shifted smoothly into superposition along the logarithmic time axis. The amounts of shift, log Or, required to effect superposition are plotted against the temperature, T, in Figure 5 for the relaxation data, and in... 

Figure 6. Temperature dependence of the creep compliance of Kraton 102 cast from benzene solution...

Below a characteristic temperature, T0, of about 15° to 16°C, the shift factors appear to follow the WLF equation, Equation 2, with C = 7.1, C2 = 135.9°C, and Tr — 0°C. The coefficients were determined in the usual way (6). The temperature dependence of both the relaxation moduli and the creep compliances could be described with the same WLF equation within the experimental scatter. It appears that below T0 the triblock copolymer behaves essentially as a filled rubber, the polystyrene domains acting only as inert filler. However, the WLF equation which describes the temperature dependence of the mechanical properties in this region is not identical with that of pure 1,4-polybutadiene, for which Maekawa, Mancke, and Ferry (20) find cx — 4.20, c = 161.5°C,... 

Parallel to the stronger temperature dependence of E for semi-crystalline polymers is the stronger dependence on time they show a higher tendency to creep than amorphous, glassy polymers, (Figure 4.20), at least at temperatures above or not too far below Tg. 

The second equation appears to be applicable to a number of glassy polymers, and also to other materials the exponent m is always about 3, so that creep can be described by two parameters, Do and to, while the immediate elastic deformation is also taken into account (Do). As a matter of fact, Do and to are temperature dependent. When the experimentally found creep curves are shifted along the horizontal axis and (slightly) along the vertical axis, they can be made to coincide... 

However, this result is based upon sparse creep-life data for Timken 35-15 Stainless Steel (31), so that Figure 3 should be regarded merely as a qualitative guide to such temperature dependence. Considerably more material on creep-life-cost relations must be gathered before reliable design values of the optimum steam temperature can be obtained. 

Creep properties are very much dependent upon temperature. Well below the glass transition point very little creep will take place, even after long periods of time. As the temperature is raised, the rate of creep increases. In the glass-transition region the creep properties become extremely temperature-dependent. In many polymers the creep rate goes through a maximum near the glass-transition point. 

In Fig. 4.21, creep rupture data from a number of different grades of silicon nitride are plotted in a Monkman-Grant format.30,31,34,115 116 For purposes of comparison with metallic alloys, the temperature dependence of the Monkman-Grant curves has been ignored. As with the metallic alloys, the curves for all of the grades of material tend to plot within a relatively narrow band. These results imply that lifetime can be improved merely by improving creep rate the lower the creep rate, the longer the lifetime. 

Fig. 4.20 Monkman-Grant curves for two commercial grades of silicon nitride. Some grades give curves that are temperature-independent (a) AY6, SiC -reinforced others give a series of curves depending on temperature (b) NT154. The temperature independent curves have creep rate exponents, m, for the Monkman-Grant equation, tf = ce L, that are approximately 1, whereas the creep rate exponent for the temperature-dependent curves are greater than 1 e.g., 1.7 for NT154.

Fig. 5.2 Comparison of creep behavior and time-dependent change in fiber and matrix stress predicted using a 1-D concentric cylinder model (ROM model) (solid lines) and a 2-D finite element analysis (dashed lines). In both approaches it was assumed that a unidirectional creep specimen was instantaneously loaded parallel to the fibers to a constant creep stress. The analyses, which assumed a creep temperature of 1200°C, were conducted assuming 40 vol.% SCS-6 SiC fibers in a hot-pressed SijN4 matrix. The constituents were assumed to undergo steady-state creep only, with perfect interfacial bonding. For the FEM analysis, Poisson s ratio was 0.17 for the fibers and 0.27 for the matrix, (a) Total composite strain (axial), (b) composite creep rate, and (c) transient redistribution in axial stress in the fibers and matrix (the initial loading transient has been ignored). Although the fibers and matrix were assumed to exhibit only steady-state creep behavior, the transient redistribution in stress gives rise to the transient creep response shown in parts (a) and (b). After Wu et al 1...

Suppose that one conducts a series of experiments to determine the stress and temperature dependence of creep behavior for the fibers and matrix these experiments would provide curves such as those shown schematically in Fig. 5.6a and b. Conducting these experiments over a range of temperatures and stresses would provide a family of curves that could be combined to provide a relationship between strain rate, stress, and temperature. Such a temperature and stress dependence of constituent intrinsic creep rates, together with the intrinsic creep mismatch ratio, is schematically illustrated in Fig. 5.6c. In this plot, the creep equations for the two constituents at a given temperature and stress are represented by planes in (1 IT, logo-, logs) space, with different slopes, described by <2/> Qm and ny, nm. The intersection of the two planes represents the condition where CMR = 1, which separates temperature and stress into two regimes CMR< 1 and CMR> 1. 

The stress and temperature dependence of the composite creep rate is governed by the values of the activation energies and stress exponents of the constituents. The initial stress and temperature dependence of composite creep rate is governed by the values of n and Q for the constituent which has the higher creep rate the final stress and temperature dependence is governed by the values of n and Q for the constituent with the lowest creep rate. This is illustrated in Fig. 5.6d, which compares the stress and temperature dependence of the constituent creep rate with the initial and final creep behavior of the composite. 

Fig. 5.6 Relationship between the creep rate of a composite and the stress and temperature dependence of the creep parameters of the constituents.31 (a) Temperature dependence of constituent creep rate, (b) Stress dependence of constituent creep rate, (c) Intrinsic creep rate of constituents as a function of temperature and stress illustrating the temperature and stress dependence of the creep mismatch ratio. In general, load transfer occurs from the constituent with the higher creep rate to the more creep-resistant constituent, (d) Composite creep rate with reference to the intrinsic creep rate of the constituents. The planes labeled kf and em represent the intrinsic creep rates of the fibers and matrix, respectively.

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