Stress-Enhanced Diffusion in Glass. I. Glass under Tension and Compression

McAfee, K. B.

doi:10.1063/1.1744096

Cited by 34 publications

(14 citation statements)

References 6 publications

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“…This same conclusion was reached earlier by Agarwal et al using different reasoning. They noted that noble gases such as helium diffuse through silica glass with little sensitivity to the applied stress . Water molecules are believed to diffuse through silica glass in much the same way as the noble gases.…”

Section: Equilibrium Constant and Hydroxyl Content Under Stress: Detementioning

confidence: 99%

Stress‐Enhanced Swelling of Silica: Effect on Strength

et al. 2016

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From the work of Le Chatelier [1884], it is well known that chemical reactions that exhibit a change in volume are sensitive to the ambient pressure of the reaction. Increasing the pressure will alter the ratio of reaction products to reactants. If the change in volume is constrained to occur at a surface, then such reactions can result in residual stresses that affect the strength of the solid. These effects are applicable to silica glass, which increases in volume when reacting with water. In this paper, we discuss the possibility of using this effect to strengthen silica glass. Using a modification of Le Chatelier's theory to handle applied stresses, we show that water penetration into the surface of silica glass can yield sufficient residual stress to increase the strength of silica glass into the GPa range. Applying these ideas to recent data published by Lezzi et al., we are able to attribute the strengthening they observe to a water/silica reaction under an applied tensile stress.

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Section: Equilibrium Constant and Hydroxyl Content Under Stress: Detementioning

confidence: 99%

Stress‐Enhanced Swelling of Silica: Effect on Strength

et al. 2016

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“…For a given strain field (that is, for a given deformation field), we model the effect of deformation on the diffusivity as follows:

{bold-italicD}_{{bold-italicE}_{l}} (bold-italicx) = {bold-italicD}_{0} (bold-italicx) + ((), {bold-italicD}_{T} (bold-italicx) - {bold-italicD}_{0} (bold-italicx)) ((), \frac{exp [η_{T} I_{{bold-italicE}_{l}}] - 1}{exp [η_{T} E_{ref}] - 1}) + ((), {bold-italicD}_{S} (bold-italicx) - {bold-italicD}_{0} (bold-italicx)) ((), \frac{exp [η_{S} I I_{{bold-italicE}_{l}}] - 1}{exp [η_{S} E_{ref}] - 1})

where η T and η S are non‐negative parameters; D 0 ( x ), D T ( x ) and D S ( x ) are (respectively) the reference diffusivity tensors under no, tensile, and shear strains; and E ref is a reference measure of the strain. This model is partly motivated by the stress‐induced diffusion experiments on glass performed by McAfee . These experiments have clearly shown the following aspects (which have been incorporated in the model given by Equation ): The relative diffusion rate under tension is nearly five times more than that of the relative diffusion rates under compression and shear. The relative diffusion rate varies exponentially with respect to the (circumferential) strain for Pyrex glass (see , Equation 15 and Figure ). The relative diffusion rate under compression is significantly different from that of shear (see , Figure ).…”

Section: A Mathematical Model For Coupled Deformation–diffusionmentioning

confidence: 99%

“…This model is partly motivated by the stress‐induced diffusion experiments on glass performed by McAfee . These experiments have clearly shown the following aspects (which have been incorporated in the model given by Equation ): The relative diffusion rate under tension is nearly five times more than that of the relative diffusion rates under compression and shear. The relative diffusion rate varies exponentially with respect to the (circumferential) strain for Pyrex glass (see , Equation 15 and Figure ). The relative diffusion rate under compression is significantly different from that of shear (see , Figure ).…”

Section: A Mathematical Model For Coupled Deformation–diffusionmentioning

confidence: 99%

A framework for coupled deformation–diffusion analysis with application to degradation/healing

Mudunuru

Nakshatrala

2011

Numerical Meth Engineering

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SUMMARYThis paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation-diffusion in linearized elastic solids. The mathematical model takes into account the effect of the deformation on the diffusion process, and the affect of the transport of an inert chemical species on the deformation of the solid. We then present a robust computational framework for solving the proposed mathematical model, which consists of coupled non-linear partial differential equations. It should be noted that many popular numerical formulations may produce unphysical negative values for the concentration, particularly, when the diffusion process is anisotropic. The violation of the non-negative constraint by these numerical formulations is not mere numerical noise. In the proposed computational framework, we employ a novel numerical formulation that will ensure that the concentration of the diffusant be always non-negative, which is one of the main contributions of this paper. Representative numerical examples are presented to show the robustness, convergence, and performance of the proposed computational framework. Another contribution of this paper is to systematically study the affect of transport of the diffusant on the deformation of the solid and vice versa, and their implication in modeling degradation/healing of materials. We show that the coupled response is both qualitatively and quantitatively different from the uncoupled response.

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“…It is indeed known that mechanical stress has a great influence on diffusion processes. McAfee [34] studied the effect of stress upon the diffusion constant of gases (He, H 2 and other gases) in a borosilicate glass at room temperature. It was shown that an enhanced diffusion of helium (and hydrogen but with lower magnitude) is obtained in glass under high tensile stresses.…”

Section: Discussionmentioning

confidence: 99%