Stress 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... 

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... 

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... 

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. 

Abstract This chapter gives a brief description of special mechanical tests for various types of materials and sample geometries, such as blister tests for membranes/adhesives/coatings, tensile tests and shear tests for sealants/foam adhesives, indentation and scratch tests for coatings, tack tests for pressure-sensitive adhesives (PSAs), and bimaterial curvature tests for characterizing residual stress, stress-free temperature (SFT), and coefficient of thermal expansion (CTE) of adhesives bonded to substrates of interest. In addition, some applications of these tests, including the nano-/micrometric scale, are also described in this chapter. 

Illustration of bimaterial curvature technique to measure the product of the glassy coefficient of thermal expansion a, and Young s modulus E, of adhesive layer. In addition, the stress-free temperature Tsf, which can be well below the cure temperature in some materials. Schematic representation of (a) test sample, (b) representative deflection results, and (c) residual stress predictions... 

The coefficient of thermal expansion (CTE) and the stress-free temperature (SET) are measured to estimate residual stresses in adhesives. 

The residual stress in a cell when cooled from stress-free temperature to room temperature can be calculated [39] ... 

Simulations are shown in Fig. 15, for electrolyte supported cells, with typical thickness 20 pm for LSMC, 200 pm for 8YSZ and 20 pm for SCMC. One simulated the effects of stress free temperature on thermal stresses developed on cooling to 800 °C, in air (thin Unes) and for H20,H2/LSCM/8YSZ/SCMC/air cells with fuel conditions H20 H2 = 1 1, and electrode polarisations of t]a — 0.1 V for LSCM and rjc — —0.1 V for the SCMC electrode. The dependence of chemical expansion on oxygen partial pressure [53, 84] was transformed to dependence on gas composition and/or overpotential as described above (Eq. 14). 

Fig. 15 Predictions of dependence of thermochemical stresses on the temperature gap between stress free temperature (T f) and working temperature, for electrolyte supported LSCM/ 8YSZ/SCMC ceUs, at 800 °C, in air thin lines) and for prospective operation of H20,H2/LSCM/8YSZy SCMC/air cells with H20 H2 = 1 1, and polarizations = 0.1 V for LSCM and = -0.1 V for SCMC...

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