M6 Elasticity and Brittle Behavior

Topic

The elastic response of this glass to an applied load follows Hooke's law linearly from the initial moment of loading right up to the instant of fracture, with no intervening phase of plastic behavior; unlike a polycrystal—where grain boundaries can introduce additional deformation mechanisms—this glass, completely lacking grain boundaries, responds according to Hooke's law without interruption until it fractures. The absence of grain boundaries—as opposed to the granular microstructure of a polycrystal—ensures that the glass's elastic response is free from any additional mechanisms that would cause it to deviate from linear Hookean behavior, even near the point of fracture.

Because the glass responds in this Hookean manner up to the moment of fracture, all the energy absorbed during elastic deformation is stored as elastic energy, without any portion being dissipated through plastic deformation; it is precisely this stored elastic energy that is suddenly released at the moment of fracture to drive crack propagation. The fact that the glass accumulates more elastic energy prior to fracture—for a given amount of deformation—means that a greater amount of energy becomes available to drive crack propagation at the instant of fracture.

This elastic stiffness—characterized by Hooke's law—can be determined experimentally by measuring the speed of sound within the material itself: an ultrasonic pulse traveling through the glass moves at a speed directly dependent on its Young's modulus and density; thus, measuring the speed of sound allows the Young's modulus to be calculated without subjecting the glass to destructive testing. A higher measured speed of sound within the glass implies—for a given density—a higher calculated Young's modulus. For this reason, this model—characterized by the elastic response and Hooke's law with which it was introduced—is formally identical to another model in a different set: the one describing the elastic-brittle behavior of a ceramic based on that same Hooke's law and elastic energy. The only difference is that the ceramic must account for the contribution of its grain boundaries, a feature absent in this glass. The fact that this ultrasonic method determines the glass's Young's modulus from an easily measurable indirect quantity—without requiring destructive testing—means it shares the same logic of indirect characterization with two other models in this set: the one determining the glass transition temperature from the slope of a thermal expansion curve, and the one determining the glass's viscosity from the deformation rate of a specimen under constant load.

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