Creep strain limit

By assuming that creep rupture occurs at a constant creep strain limit (2), Eq. (13.4) can be transformed into an expression of creep rupture time tcR as a function of stress and temperature ... 

Figure 11.21 Design stress domains recommended forNb-lZr, Ta-8W-2Hf, TZM [112], and V tCr-4Ti [113], The creep strain limit was made by two-thirds of creep rupture stress for 10 h for V-4Cr-4Ti and 1% creep strain in 7 years for the others.

Creep strain limit the Tcs value of the applied load which produces a creep strain of 10% in... 

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. 

Each phase in a composite will typically have different elastic and creep properties. However, assuming strong interfacial bonding as a limiting case, compatibility requires that the total strain, and the total strain rate, of each constituent be equal. The total strain rate of each constituent, eiitot, is given by the sum of the elastic strain rate, ki ei, and the creep strain rate, e,. To satisfy compatibility, this sum must equal the total creep rate of the composite eCjto, ... 

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... 

Soils stabilized with urea-formaldehyde have strengths comparable to the phenoplasts and like those materials are less sensitive to testing strain rate than other chemical grouts. (For optimum mechanical properties and to keep free formaldehyde levels low, one molecule of urea should be provided with three molecules of formaldehyde.) Little data are available, but it is probable that aminoplasts break down comparatively quickly under cyclic wet iry and freeze thaw conditions. The creep endurance limit is probably a relatively high percentage of the UC. Except as noted above, the resins have good stability and are considered permanent. 

The creep-strength limit, which is the initial stress that will just cause rupture or a specified strain in a specified time (under the stated environmental conditions). 

Most non-aerospace CMC applications require long service lives. For these applications CMC components must avoid creep rupture and must exhibit creep strains lower than 1 percent after 10,000 hours of service (e.g., at 1,200°C [2,192°F] and 100 MPa [14.5 ksi]) components must also be chemically and microstructurally stable. These stringent demands present major challenges to researchers and engineers, particularly for material development and accelerated testing. The performance objectives limit the material choices to polycrystalline oxides, SiC, or amorphous Si-C-N-B compositions (single-crystal fibers are not affordable). 

Buckley and McCrum have recently published work on the anisotropy of creep obtained using a tensile creep apparatus based on precision measurement of clamp displacement. Creep strains up to a maximum of 0 1% were used. The creep compliance was subject to error limits of 5% but the scatter of points on a given creep curve was always less than 0-5% provided creep was terminated after 60 s below room temperature or after 180 s above room temperature. Details of the apparatus have not yet been published. 

FIGURE 2. Creep strength of SiC fibers for strain limit of 0.4% at 1400°C for 10 hrs in air open points = as-produced condition closed points = after second phase removal. 

In general, the maximum temperature/time/stress capability of the more creep-prone fibers is limited by the fiber tendency to display excessive creep strains (for example, > 1%) before fracture. On the other hand, the temperature/time/stress capability of the more creep-resistant fibers is limited by fiber fracture at low creep strains (<1%), the values of which are often dependent on the environment. These limitations are illustrated in Table 3, which shows the approximate upper use-temperature for some SiC fibers, as determined from the... 

Table 4. No observable creep strain was obtained at 8I5°C, though one sample did rupture after 460 hours at 140MPa. At 1093°C and 1204°C measurable strain rates were obtained, though few samples attained a steady state strain rate before the end of the 1000 hour test or at rupture. Over the range of temperature and stress evaluated (1093 and 1204°C and 125 to 160MPa) the measured strain rates at 1000 hours for the test run-out samples ranged from 2 x 10 s to 2 x 10 " s . This range of strain rates is very low compared to creep rates currently accepted for metallic hardware in turbine engines, and thus creep deformation is not expected to be a limiting factor for the application of HiPerCompTM composites.

In designs that are strain-limited, the maximum strain for the purposes of specifying creep modulus is simpfy the maximum allowable strain for the material in question. In designs that are deflection-limited, the maximum strain is not known in advance. In these cases, a short iteration is used an initial estimate is made, and the stress anafysis is repeated a few times until consistent results are obtained. 

Fig. 5.21. Schematic illustration of craze formation in the creep test on transparent amorphous thermoplastics. Visible crazes occur at a certain time and strain dming the creep test. These times are indicated in the creep curves measured at different stresses. The connecting line of these points provides a curve which describes the strain limit at which craze formation occnrs as a function of time or deformation rate respectively. An extrapolation of the cnrve towards great times yields the critical limiting strain for craze formation...

Thus, for linearly viscoelastic behavior, by measuring the creep strains it is possible to draw time-modified modulus curves. Having established these curves, it is then possible to use these data to predict the behavior of the plastic under other conditions. Such time-modified modulus curves for several common thermoplastics were shown in Figure 3-58. It is important to remember that such curves are valid only for a specific temperature and for strains that do not exceed the limits of the validity of the data. 

The Kelvin will not have a sudden increase in strain as the damper will not allow a sudden jump in strain. Under the condition of constant stress, each model with a free damper (Maxwell and four parameter fluid) will have an ever-increasing creep strain and will be similar to the response for a thermoplastic polymer described in Fig. 3.13. Those with a free spring (Kelvin and three parameter solid) will creep to a limiting constant strain and will be similar to the response of thermoset polymers described in Fig. 3.13. In relaxation, the stress will decay to zero for those models with a free damper (Maxwell and four parameter fluid) and the stress will decay to a limiting value for those without a free damper (Kelvin and three parameter solid) as shown in Fig, 3.12 for thermoplastic and thermosetting materials respectively. Note that a simple stress relaxation test is not possible for a Kelvin model as the damper will prohibit a sudden increase in strain. 

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