Creep behavior stress dependence

As shown in Fig. 5.4, for stresses far away from a (either a-c cr or crc a ), the initial creep behavior (stress dependence) of the composite is determined primarily by the constituent having the higher creep rate. On the other hand, the final creep behavior of the composite is governed by the constituent with the lower creep rate. For applied creep stresses close to o, a gradual change in creep stress exponent n occurs from rii to n2 (or vice versa). 

Mosedale et al. were the first to publish useful fast flux irradiation creep data on cladding materials (86). They showed that the irradiation creep rate in solution treated 316 stainless steel is approximately proportional to stress and neutron flux at temperatures of about 250°C. Theoretical studies have predicted a creep rate stress dependence of a power less than 2 and a negative temperature dependence, i.e., at lower temperatures a faster creep rate (77). Claudson has observed such behavior with temperature and has suggested that a creep rate proportional to exp(—0.0027T), where T is in kelvins, should fit both solution treated and cold worked stainless steels. 

When a viscoelastic material is subjected to a constant stress, it undergoes a time-dependent increase in strain. This behavior is called creep. The viscoelastic creep behavior typical of many TPs is illustrated in Figs. 2-22 and 2-23. At time to the material is suddenly subjected to a constant stress that is main-... 

Water is a natural plasticizer for many polar polymers such as the nylons (23K). polyester resins (239), and cellulosic polymers (240). It strongly shifts in epoxies (241.242). Thus the creep and stress-relaxation behavior of such polymers can be strongly dependent on the relative humidity or the atmosphere. 

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. 

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. 

It should be noted that the model leading to Eqn. (69) is incomplete since the stress required to cause the enlargement of void space at the fiber breaks is omitted from consideration. At high strain rates this contribution to stress can be expected to dominate other contributions. Therefore, at high stress or strain, the creep behavior will diverge from Eqn. (69) and perhaps exhibit the nth power dependence on stress as controlled by the matrix. The creep rate at these high stresses can be expected to exceed the creep rate of the matrix at the same applied stress since the void space at the fiber ends is a form of damage. 

In some epoxy systems ( 1, ), it has been shown that, as expected, creep and stress relaxation depend on the stoichiometry and degree of cure. The time-temperature superposition principle ( 3) has been applied successfully to creep and relaxation behavior in some epoxies (4-6)as well as to other mechanical properties (5-7). More recently, Kitoh and Suzuki ( ) showed that the Williams-Landel-Ferry (WLF) equation (3 ) was applicable to networks (with equivalence of functional groups) based on nineteen-carbon aliphatic segments between crosslinks but not to tighter networks such as those based on bisphenol-A-type prepolymers cured with m-phenylene diamine. Relaxation in the latter resin followed an Arrhenius-type equation. 

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. 

Viscoelastic behavior is a time-dependent mechanical response and usually is characterized with creep compliance, stress-relaxation, or dynamic mechanical measurements. Since time is an additional variable to deformation and force, to obtain unique characterizing functions in these measurements one of the usual variables is held constant. 

Loads on a fabricated product can produce different t3q>es of stresses within the material. There are basically static loads (tensile, modulus, flexural, compression, shear, etc.) and dynamic loads (creep, fatigue torsion, rapid loading, etc.). The magnitude of these stresses depends on many factors such as applied forces/loads, angle of loads, rate and point of application of each load, geometry of the structure, manner in which the structure is supported, and time at temperature. The behavior of the material in response to these induced stresses determines the performance of the structure. 

Creep resistance is of primary concern in rotating components of a turbine engine. High creep rates can lead to both excessive deformation and uncontrolled stresses. Creep resistance of fiber-reinforced ceramic matrix composites depend on relative creep rates of, stress-relaxation in, and load transfer between constituents. The tensile creep behavior of SiC/RBSN composites containing 24 vol% SiC monofilaments was studied in nitrogen at 1300 C at stress levels ranging from 90 to 150 MPa. Under the creep stress conditions the steady state creep rate ranged from 1.2 x 10 to 5.1 x 10 At stress levels below... 

Despite this large volume of results, there are almost no papers on the thermoviscoelastic behavior of PLCs and their blends with EPs under conditions of creep or stress relaxation. At the same time, it is known that the time dependence of the mechanical behavior of these materials is significant, i.e. they are distinctly viscoelastic. Thus creep and stress relaxation studies can give important information for better understanding of the peculiarities of this type of polymer material and for the application conditions of PLCs as engineering materials. 

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