Creep behavior temperature dependence

Creep. The phenomenon of creep refers to time-dependent deformation. In practice, at least for most metals and ceramics, the creep behavior becomes important at high temperatures and thus sets a limit on the maximum appHcation temperature. In general, this limit increases with the melting point of a material. An approximate limit can be estimated to He at about half of the Kelvin melting temperature. The basic governing equation of steady-state creep can be written as foUows ... 

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... 

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...

Initial and Final Creep Mismatch Ratio At low temperatures, or during rapid loading, the stress in the fibers and matrix can be estimated from a simple rule-of-mixtures approach this gives the elastic stress distribution between the fibers and matrix. During creep, the stress distribution is time dependent and is influenced by both the initial elastic stress distribution and the creep behavior of the constituents. Immediately after applying an instantaneous creep load (i.e., at t = 0+), the CMR, =0+ can be found by substituting ef0 = Af (E/ Ec)a-C nf and emfi = Am (Em/Ec)[Pg.176]

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. 

This review is intended to focus on ceramic matrix composite materials. However, the creep models which exist and which will be discussed are generic in the sense that they can apply to materials with polymer, metal or ceramic matrices. Only a case-by-case distinction between linear and nonlinear behavior separates the materials into classes of response. The temperature-dependent issue of whether the fibers creep or do not creep permits further classification. Therefore, in the review of the models, it is more attractive to use a classification scheme which accords with the nature of the material response rather than one which identifies the materials per se. Thus, this review could apply to polymer, metal or ceramic matrix materials equally well. 

Researchers have examined the creep and creep recovery of textile fibers extensively (13-21). For example, Hunt and Darlington (16, 17) studied the effects of temperature, humidity, and previous thermal history on the creep properties of Nylon 6,6. They were able to explain the shift in creep curves with changes in temperature and humidity. Lead-erman (19) studied the time dependence of creep at different temperatures and humidities. Shifts in creep curves due to changes in temperature and humidity were explained with simple equations and convenient shift factors. Morton and Hearle (21) also examined the dependence of fiber creep on temperature and humidity. Meredith (20) studied many mechanical properties, including creep of several generic fiber types. Phenomenological theory of linear viscoelasticity of semicrystalline polymers has been tested with creep measurements performed on textile fibers (18). From these works one can readily appreciate that creep behavior is affected by many factors on both practical and theoretical levels. 

In the preceding sections, we have looked at the various types of relaxation processes that occur in polymers, focusing predominantly on properties like stress relaxation and creep compliance in amorphous polymers. We have also seen that there is an equivalence between time (or frequency) and temperature behavior. In fact this relationship can be expressed formally in terms of a superposition principle. In the next few paragraphs we will consider this in more detail. First, keep in mind that there are a number of relaxation processes in polymers whose temperature dependence we should explore. These include ... 

Hutchings KN, Shelleman DL, Tressler RE. Tensile creep behavior of (Lai xSrx) (Coi y xFeyCux)a03 5 stress, temperature, and oxygen partial pressure dependence. Proceedings of the Material Science and Technology Conference, Pittsburgh, Pennsylvania, 25-28 September 2005. 

The temperature dependence of a was obtained in experiments on copper polycrystals [ ]. From Cu creep curves, values of a were determined in the temperature range 1.4 to 4.2 K for a constant r of 24 MPa. Figure 2 shows a plotted against temperature. From the logarithmic creep theory, based on the thermally activated creep assumption [ one expects the linear- and temperature-proportional behavior of the a factor to be... 

Certain important features of the a(T) curve are (1) there is a temperature dependence of a, a(T although weak and (2) the a(T) curve tends toward saturation in the very low temperature range and, if extrapolated to T = 0 K, ends in a finite nonzero value of ao- Contrary to the thermally activated creep theories, this suggests that there is a creep at 0 K. On the one hand, the temperature dependence of a is apparent on the other hand, its behavior differs from the predictions of the classical thermally activated creep laws. This leads one to assume that at 4 K, creep depends on two mechanisms, and as absolute zero is approached, the athermic component becomes more important [ ]. 

The above-mentioned thermomechanical models only consider the elastic behavior of materials. Boyd et al. [13] reported on compression creep rapture tests performed on unidirectional laminates of E-glass/vinylester composites subjected to a combined compressive load and one-sided heating. Models were developed to describe the thermoviscoelasticity of the material as a function of time and temperature. In their work, the temperature-dependent mechanical properties were determined by fitting the Ramberg-Osgood equations and the temperature profiles were estimated by a transient 2D thermal analysis in ANSYS 9.0. 

Trantina (3) analyzed the creep behavior of talc-filled polypropylene composites under constant uniaxial stress loads. He proposed a general expression for the strain ec attributed to creep alone as a superposition of time (f), stress (a), and temperature (T) dependence. The model equation is written as a product of three separate functions for each parameter ... 

Q. Wei, et al., "High Temperature Uniaxial Creep Behavior of a Sintered In Situ Reinforced Silicon Nitride Ceramics", Ceramic Engineering Science Proceedings, ed. E. Usttlndag and G. Fischman, 20(3), 1999, The American Ceramic Society Westerville, OH, 463-470 G. Ziegler, "Thermo-Mechanical Properties of Silicon Nitride and Their Dependence on Microstructure", Mat. Sci. Forum, 47, 162-203 (1989)... 

The bulk of the results obtained in this study were obtained by analytical transmission electron microscopy. Observations were made on both grades of material in the as-received, untested condition and after tensile testing at 1250°C. Test samples selected for examination covered the range of observed creep behavior, and included samples that failed after times ranging from -10 to -200 hours depending on applied stress and also samples from interrupted tests that survived for up to 2000 hours under lower applied stresses. In addition, a comparison was made of non-reinforced samples tested with and without a 500 hour pre-anneal at the test temperature. In all cases, the gauge sections of crept samples were cut parallel to the stress axis to obtain both near-surface and raid-plane sections. Prior to final TEM specimen preparation, these sections were examined optically for evidence of distributed creep cavitation or crack damage. 

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