Compressive thermal stress

Maximum in-plane tensile and compressive thermal stresses for square 15 cm thick polymethacrylimide foam bonded to an aluminum plate (foam surface temperature 317 K aluminum temperature 20 K). 

Gas turbine blades (figure 2.13(a)) are facing extreme conditions They have to withstand large mechanical loads due to centrifugal forces at high temperature. To at least partly protect the material from the extreme gas temperatures of 1200 C or more, the blades are cooled from the inside with air of about SOO C. If the wall of the turbine blade has a thickness of about 2 mm and is exposed to the process gas with a temperature of 1200 C, its surface temperature will be about Tout = 1000°C, whereas on the inside it is only Tin = bOO C (figure 2.13(b)). Due to thermal expansion, the material would expand on the outside, but is partly constrained by the cooler inside wall. Thus, large compressive thermal stresses form on the outside and tensile stresses on the inside. In the middle of the wall, there will be a neutral axis at about T =... 

The radial (compressive) stress, qo, is caused by the matrix shrinkage and differential thermal contraction of the constituents upon cooling from the processing temperature. It should be noted that q a, z) is compressive (i.e. negative) when the fiber has a lower Poisson ratio than the matrix (vf < Vm) as is the normal case for most fiber composites. It follows that q (a,z) acts in synergy with the compressive radial stress, 0, as opposed to the case of the fiber pull-out test where the two radial stresses counterbalance, to be demonstrated in Section 4.3. Combining Eqs. (4.11), (4.12), (4,18) and (4.29), and for the boundary conditions at the debonded region... 

Composite materials inherently develop residual stresses during processing. This happens because the two (or more) phases that constitute the composite behave differently when subjected to nonmechanical loading. For example, consider a reinforcing phase that has low thermal expansion characteristics embedded in a matrix phase with high thermal expansion characteristics. If the material is initially stress free and the temperature is decreased, then the matrix will try to shrink more than the reinforcement. This places the reinforcement in a state of compression (i.e. a compressive residual stress). If the phases are well bonded, then models can be developed to predict the residual stress field that is induced during processing. 

Contours of maximum principal stress in the first slice (near the gas inlets) and the sixth slice (near the gas outlet) are shown in Figures 5.11 and 5.12 respectively. It can be seen that the stack is partially under compression and partially under tension due to the mismatch in the thermal expansion coefficient of the materials and non-uniform temperature. In each cross-section, the stresses are higher near the top of the stack than near the bottom. Also, the stresses are higher near the gas outlet than near the gas inlets. Maximum tensile and compressive stresses in all the slices are found to be 60 MPa and 57.2 MPa respectively which are in the electrolyte layer of the last slice. The maximum stresses in all the layers are found to be well within the failure limits of their respective materials and hence thermal stress failure is not predicted for this stack. 

For the c-BN formation a stress threshold was observed in the deposited layers. The h-BN intermediate layer shows a preferred orientation, where the c-axis of the h-BN is parallel to the substrate. Both effects are explained by the compressive biaxial stress induced by the ion bombardment. The mechanism for the conversion of h-BN into c-BN is explained by rather high temperatures originated during thermal spikes (direct h-BN —> c-BN transformation). The stress caused by the bombardment with high energetic ions is considered to be a reason for the growth of the c-BN crystals [190, 191]. A stress within the layer of up to 10 GPa has been observed. This biaxial stress causes a hydrostatic pressure up to the values usual in HP-HT synthesis. 

The presence of mullite and hence compressive surface stresses appears to improve the hardness and fracture toughness (see Table 5.2). These values are at least two to three times higher than those reported for the mullite/ alumina system described above. Clearly, the presence of mullite is desirable for inducing compressive stresses in the vicinity of the surface region by virtue of the mismatch in thermal expansion between ZTA and mullite. This significant improvement in the observed fracture toughness was attributed to... 

For most metal-reinforced nanocomposites the thermal expansion coefficient of the metal phase will be larger than that of the matrix, reversing the expected stress fields compared to SiC-reinforced alumina. Thus while the tensile radial stresses surrounding occluded particles may induce transgranular cracking, the compressive hoop stresses may inhibit crack propagation if the particles are located at grain boundaries. Macrostresses in sub-micron Ni... 

For the calculation of the thermal shock-induced stresses, we consider the plate shown in Fig. 15.1 with Young s modulus E, Poisson s ratio v, and coefficient of thermal expansion (CTE) a, initially held at temperature /j. If the top and bottom surfaces of the plate come into sudden contact with a medium of lower temperature T they will cool and try to contract. However, the inner part of the plate initially remains at a higher temperature, which hinders the contraction of the outer surfaces, giving rise to tensile surface stresses balanced by a distribution of compressive stresses at the interior. By contrast, if the surfaces come into contact with a medium of higher temperature Tm, they will try to expand. As the interior will be at a lower temperature, it will constrain the expansion of the surfaces, thus giving rise to compressive surface stresses balanced by a distribution of tensile stresses at the interior. 

Other types of damage may be produced through thermomechanical effects. For example, when being annealed at 450°C a CVD aluminum film on a Si substrate is subjected to compressive thermoelastic stresses owing to the considerable difference between the thermal expansion coefficients of aluminum (a = 23 x 10 °C 0 and the silicon substrate (a. = 3.5 x 10 °C 0-When cooling, the film may therefore contract by as much as 1%. Due to the combined action... 

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