Strain-limited creep

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... 

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 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. 

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 ... 

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...

In Paper 12 it is Implied that Irradiation creep may limit the life of some of the Douglas Point pressure tubes to about 15 years. Could the Author explain whether this estimate is based on a certain limiting creep strain, and if so how has this been chosen ... 

What constitutes failure (section 1.4) will be dictated by the design, but a 10% drop in stiffness is becoming accepted in fatigue. For creep, a strain limit is usually imposed by the design. 

The maximum strain criterion is becoming popular for plastics materials subjected to long-term loads upper strain limits for representative plastics are suggested in Table 2.2. Thus the appropriate design stress at a particular time and temperature can be found in the relevant creep data. 

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.

Figure 9.12 (a) Creep strains measured at various temperatures at 30% UTS and resulting master curve at 20° C reference temperature, (b) creep strains measured at various temperatures at 40% UTS and resulting master curve at 20° C reference temperature, (c) creep strains measured at various temperatures at 50% UTS and resulting master curve at 20° C reference temperature, (d) creep strains measured at various temperatures at 60% UTS and resulting master curve at 20° C reference temperature, and (e) strain-limited master curve showing times to achieve 10% strain at various stress levels. 

Because many geotextile reinforcement design codes specify a limit to allowable creep strain, it is convenient to present the loads at which these strain limits are reached. In this context, the creep data may be presented in an isochronous plot consisting of an array of load—strain curves, similar to the one from a tensile test, but with each curve representing a different duration. Each isochronous (ie, constant time) curve is created by taking load and strain levels from each creep curve at a given constant time and plotting them to form an isochronous curve. Isochronous curves are not an extrapolation tool, but instead are an interpolation tool. 

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

Compared to the previously discussed Maxwell model and actual experimental data, the advantage of the Klevin-Voigt model is that the strain exponentially approaches an ultimate strain limit without any discontinuities. Steady state long-term creep and initial elastic strain, however, are not represented in the overall strain response according to the Klevin-Voigt model. 

Other ways to present creep data include compilation to stress-time diagrams with continuous lines indicating time-dependent strain limits. Therefore, this way of plotting creep data is frequently referred to as an iso-strain diagram. The schematic approach for converting creep data into an iso-strain digram is illustrated in O Fig. 34.8. 

The results of four corresponding creep experiments applying the time-dependent load values fromO Fig. 34.20 indicate that the predicted strain limit of tan y = l was not exceeded in either one of the creep tests and the congruence between relaxation and creep becomes better in the long-term scale (O Fig. 34.21). 

All of the above conclusions have been drawn for isothermal conditions without considering a thermal fluctuation under creep conditions but which in practice represent the usual case during the service life of structural adhesive joints. Considering temperature effects in creep-dependent lifetime, prediction can either follow a worst case scenario in which the definition of the load-dependent fracture envelope or the test for compKance with predefined strain limits is carried out at the maximum temperature to he expected during service life. This conservative approach is likely to lead to excessive contingency reserves. 

Strain controlled limit has been applied in LMFBRs rather than load controlled limit. Inelastic or creep strain have been used as design criteria in LMFBRs. In the Fast Flux Test Facility or CRBRP fuel rod designs, inelastic hoop strain was limited to 0.1% on average and 0.2% as the peak for normal operation conditions, 0.3% at an anticipated transient, and 0.7% at an unlikely event [14]. Inelastic strain limit was an earlier approach used for a failure criterion and is a straightforward concept. 

Another mechanism which normally defines the limiting value for the fuel element design and the limiting temperatures is the combination of creep and strain cycling which results in a certain type of thermal ratcheting. This leads to failure above a certain strain, limited by irradiation effects (/). 

Once the limiting strain is known, design methods based on the creep curves are quite straightforward and the approach is illustrated in the following... 

Example 2.1 A ball-point pen made from polypropylene has the clip design shown in Fig. 2.11. When the pen is inserted into a pocket, the clip is subjected to a deflection of 2 mm at point A. If the limiting strain in the material is to be 0.5% calculate (i) a suitable thickness, d, for the clip (ii) the initial stress in the clip when it is first inserted into the pocket and (iii) the stress in the clip when it has been in the pocket for 1 week. The creep curves in Fig. 2.5 may be used and the short-term modulus of polypropylene is 1.6 GN/m. ... 

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