Previous: ITZ Shrinkage Simulation
A two-dimensional finite element shrinkage algorithm has been used to study the effect of the structure and properties of the interfacial zone on the elastic moduli and elastic shrinkage of portland cement mortars. Using a combination of 2-D computations and 3-D exact analytical results applied to experimental data for 0.35 w/c cement mortars, it has been shown that the interfacial zone cement paste, when its properties are averaged over a 20 micrometer thick region, has a Young's modulus of between 1/3 and 1/2 of the bulk cement paste, and an intrinsic shrinkage strain that is close to the bulk cement paste. The two major simplifications behind this result are: all shrinkage is elastic and reversible, and the properties of the interfacial zone can be taken as constant, averaged across a 20 micrometer thick region.
Both 2-D computations and 3-D analytical results show a minimum in shrinkage, as a function of stiffness in the interfacial zone, for a given unrestrained shrinkage in the ITZ relative to the bulk cement paste. This is directly due to the topology of the interfacial zone, since bulk cement paste can only elastically interact with the aggregate via the interfacial zone, and is valid in 2-D and 3-D. As the interfacial zone becomes very soft, the bulk cement paste essentially decouples from the restraining aggregate, increasing overall shrinkage. On the other hand, as the stiffness of the interfacial zone increases, the coupling becomes stronger, decreasing the magnitude of the overall shrinkage. As the stiffness of the interfacial zone continues to increase, the overall stiffness of the matrix (non-aggregate) phase also increases, enabling it to resist the non-shrinking aggregate better so overall shrinkage starts to increase again. The 2-D computations have also demonstrated that air voids reduce shrinkage by decreasing the modulus of the matrix (non- aggregate) phase and, thus, its ability to resist the non-shrinking aggregate phase.
The quantitative computational accuracy of shrinkage of the non-dilute sand mortars is limited by the 2-D nature of the model, and the assumption of linear elasticity. However, many of the ideas herein should be applicable in future 3-D simulations. As in the case with electrical properties , the 3-D dilute sand-limit calculation can be immediately used to extract quantitative information about interfacial zone properties.
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