Free temperature

A candidate interlayer consisting of dual coatings of Cu and Nb has been identified successfully for the SiC-Ti3Al-I-Nb composite system. The predicted residual thermal stresses resulting from a stress free temperature to room temperature (with AT = —774°C) for the composites with and without the interlayers are illustrated in Fig. 7.23. The thermo-mechanical properties of the composite constituents used for the calculation are given in Table 7.5. A number of observations can be made about the benefits gained due to the presence of the interlayer. Reductions in both the radial, and circumferential, o-p, stress components within the fiber and matrix are significant, whereas a moderate increase in the axial stress component, chemical compatibility of Cu with the fiber and matrix materials has been closely examined by Misra (1991). 

Quantification of residual stresses after manufacture. The build up of thermal stresses starts during fabrication of the laminate when it is cooled from the stress free temperature to room temperature. The stress free temperature in the case of an amorphous thermoplastic as used in this study is taken as the glass transition temperature [1] Tg of the Polyetherimide used is 215°C). On a fibre-matrix scale, the contraction of the matrix ( = 57 x 10 /°C) is constrained by the presence of the fibre (cif = -1 x 10 /°C for the carbon in the fibre direction). This results in residual stresses on a fibre-matrix scale (microscale). On a macroscopic scale, the properties of a unidirectional layer can be considered trans ersally isotropic. This means, in turn, that a multidirectional composite will not only contain stresses on a microscale, but also on a ply-to-ply (macroscopic) scale. 

A summary of the experimental locations X2 of the second crack as a function of the first crack xj, for all the specimens tested is shown in Figure 8. Here, X2 is defined as X2/a(Tsurface To)t where X2 is the actual location of the second crack, a is the thermal expansion coefficient of mullite, Tgurface is th temperature at the center of the surface of the coating immediately before cooling, To is the stress free temperature and t is the thickness of the substrate. It can be noted that the prediction of the location of the second crack agrees reasonably well with the experimental results. Another important result is that the location of the second crack varies with the temperature gradient across the entire specimen. 

Calculations for Cases 1 through 3 were all performed assuming a stress-free temperature of 1100 K. Recent model... 

T=100°C (heating) and free temperature (cooling). Free displacement. Impermeable... 

Transverse multiple cracking will be initiated on cooling after cure when exceeds the ply failure strain (C( ). This can occur when either the stress-free temperature (usually, the glass transition temperature of the matrix) and/or the matrix expansion coefficient are high in magnitude. Thermal cracking can occur for similar reasons when the properties of the matrix change as a result of a thermal excursion. 

Previously the authors proposed a model for thermally-induced microcracks This model is refined and adapted for integration with the constitutive model proposed in a subsequent section. The premise of this model is that temperature change from some stress-free temperature causes the standard deviation of the grain boundary tractions to change, but the mean remains unchanged. The relationship between the standard deviation of the distribution and the temperature below the stress free temperature is assumed to be linear such that... 

Maintenance Free, Temperature Endured Roof Sheathings... 

Recent over-moderated light water-Zircaloy-U-235 critical experiments performed in the Pressurized Test Reactor at KAPL afforded an unusual check of analytical techniques, since in some cases two clean critical (rod-free) temperatures were obtained for a single core. ... 

The structural solution computes the full 3D elastic-plastic deformation and stress fields for the solid components of the stack. The primary stress-generation mechanism in the SOFC is thermal strain, which is calculated using the coefficient of thermal expansion (CTE) and the local temperature difference from the material s stress-free temperature. These thermal strains and mismatches in thermal strains between different joined materials cause the components to deform and generate stresses. In addition to the thermal load, the stack will have boundary conditions simulating the mechanical constraints from the rest of the system and may also have external mechanical preloading. The stress solution is obtained based on the imposed mechanical constraints and the predicted thermal field. Figure 26.6 shows... 

Temperature-sensitivity in case of field applications. Strain measmements on-site are perturbed by temperature variations. In order to compensate for this, two superimposed grating elements with different periods A and A2 can be used [33]. The static strain sensitivity of this method is reported to be 0.8 (pm/m)/v Hz. Another method is to combine a FBG with a FBI sensor. The FBG is used as strain-free temperature sensor whereas the FPI sensor acts as strain sensor [34]. 

The global model is cooled from its stress-free temperature (which is usually the adhesive cure temperature) to the lowest temperature to which the package has been thermal cycled (0°C if a 0 to 100°C thermal profile is used). 

Consider a film-substrate bilayer system of circular geometry, where the film and the substrate have the same thicknesses and biaxial moduli h /hs = 1 and Mf/Mg = 1, and the bilayer diameter, d (hg + hf). Let the mismatch strain in this case be a consequence of a temperature change from an initial, stress-free temperature To to another temperature T, and let the thermal expansion coefficients of the film and the substrate be denoted by Of and Og, respectively, (a) Determine the variation of the radial stress and circumferential stress across the thickness of the film and the substrate, (b) Find the magnitude and sign of the thermal mismatch stress as the interface is approached from the film and from the substrate. Show that the magnitude of the stress at the interface is independent of the thickness of the film or the substrate for a fixed thickness ratio. 

Fig. 7.31. Numerical prediction of the average lattice mismatch strain as a function of the change in temperature from a stress-free temperature for three different thicknesses of an aluminum film on an elastic substrate. Adapted from Nicola et al. (2002).

In this equation, G,c is the interfacial toughness, AT is the difference between the stress-free temperature and the specimen temperature, and... 

Due to the choice of material properties, only a single temperature drop from 100 °C (212 was considered. The stress-free temperature was set at 120 °C (248 °F), which is the curing temperature of the ICA paste. In the simulation, the temperature was gradually decreased to -55 °C (-67 °F), corresponding to the lowest temperature in the thermal cycling test. The stresses in the joint at this temperature were calculated. 

T = Temperature load including temperature gradients and due to restrained free temperature displacement under normal operating conditions (if any). 

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