Constrained shrinkage

Figure 12.15 Temperature dependence of the transverse thermal expansion coefficients of a bismaleimide modified epoxy resin—based carbon fibre composite (Narmco Rigidite 5245C) dry (continuous curve) and wet (dashed curve). The hatching illustrates the differing constrained shrinkages (and hence thermal strain) for wet and dry laminates [23,24].

As shown in Fig. 3.9, the thermal strain in a cross-ply laminate is reduced by moisture absorption because the resin swells in the presence of water [24,25]. Thus the constrained swelling of the plies counteracts the constrained shrinkage which occurred on cooling, after manufacture. The moisture swelling coefficient for the individual plies can be assessed by studying the reduction in tensile residual strains... 

One way of measuring thermal shoek resistanee is to drop a piece of the ceramic, heated to progressively higher temperatures, into cold water. The maximum temperature drop AT (in K) which it can survive is a measure of its thermal shock resistance. If its coefficient of expansion is a then the quenched surface layer suffers a shrinkage strain of a AT. But it is part of a much larger body which is still hot, and this constrains it to its original dimensions it then carries an elastic tensile stress EaAT. If this tensile stress exceeds that for tensile fracture, <7js, the surface of the component will crack and ultimately spall off. So the maximum temperature drop AT is given by... 

The outer side cools and solidifies first the inner part remains fluid the longest its shrinkage in the final stage of solidification is constrained. Its density will, therefore, be lower than at the outer side and tensile stresses are being built up, even with the risk of void formation. 

Assuming planar symmetry, for a two dimensionally constrained film the shrinkage stress would approach 16 MPa in equal biaxial tension. 

Although assumptions of ideal material properties such as linear elasticity and isotropy were considered during simulations of the 3D reconstructed microstructures, the isotropy of the actual microstructures remained questioned. One of the factors responsible for the fact that the microstructures of the films could not possibly be ideally isotropic was that the films experienced constrained sintering which induced greater lateral shrinkage/densification across the direction normal to the surface than that in the other two directions which might result in non-identical... 

It is useful to show a case in which the reduced method does not work at all. Such cases have been hard to find for free sintering. Huang and Pan [18] devised a heavily constrained case which is shown in Fig. 11. A rectangular powder compact is placed between two rigid bodies with perfectly bounded interfaces. The plane strain condition is assumed (i.e. no shrinkage is allowed in the direction normal to the paper). The material is so heavily constrained that only the middle parts of its left and right surfaces can shrink towards each other. 

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