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Model of effect of environmental attack on flaw growth kinetics of glass

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Abstract

The time rate of extension of a single slit-like flaw in glass is modeled assuming the same corrosion mechanism as previously invoked for modeling delayed failure in glass containing a multiplicity of microscopic scratches or flaws. The rate of extension is expressible in terms of the stress intensity K and is in good agreement with the experimental results reported by Wiederhorn and Bolz and others. The model considers a moisture-induced corrosive attack occurring on the exposed flaw surfaces to be governed by local chemical kinetic and thermodynamic considerations, producing a rounding of the flaw tip. This mechanism accounts for the possibility of threshold behavior. The remotely applied stress becomes magnified as shown by Inglis to require the combined effect of the flaw length and tip curvature. These geometric factors in combination with the remotely applied stress mutually interact through the corrosion kinetics to define the net rate of flaw extension.

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Abbreviations

A :

Rate of environmental corrosion at the exposed planar sample surface

B :

Abbreviation for log[4A/(ω/L)(1 − α)

E :

Young’s modulus

K :

Stress intensity =\({S}\surd\pi{L}\)

L :

Length from free surface to tip of flaw

RT :

Gas constant times temperature in degrees Kelvin

S :

Tensile stress applied to the sample normal to the flaw axis

S N :

Tensile stress causing catastrophic failure at 78 K

V* :

Activation volume for transport of molecular entity causing corrosive attack

t :

Time over which the stress S is applied

u :

Stress multiplication factor at tip of flaw

u 0 :

σ u /S N  = initial stress multiplication factor at tip of flaw obtained at 78 K

u max :

That value of u the maximizes the growth rate

v :

Local rate of advance of environmental corrosion front

v 0 :

Rate of flaw advance at crack tip = dL/dt

x :

Tranverse distance from flaw centerline to free surface; the value of the abscissa

y :

The lengthwise coordinate measured from the free surface of the sample

y(x,t):

Curve describing flaw geometry

α :

The angle between the normal to the flaw contour and the y axis

α :

Also contraction for 3(1 − λ)/4 (dependent on context).

β :

 = V */RT

\(\Gamma\) :

Surface free energy of the matrix/void interface

\(\Phi\) :

\(=\,1/cos(\alpha) = \surd(1 + {(y(x, t)^\prime)}^{2})\)

\({\Psi(u)}\) :

= Factor that controls rate of increase of tip curvature

\(\Omega\) :

Molar volume of the solid subjected to environmental attack

λ:

A constant that defines the shape of the flaw tip region

k :

Curvature at flaw tip = \({1/\rho}_{\rm 0}\)

ρ:

Radius of curvature at the flaw tip

\(\rho_{\rm o}\equiv\rho_{\rm o}(t)\) :

Time dependent radius of curvature at tip of flaw

σ:

Tangential tensile stress anywhere at flaw surface

σ:

Tangential tensile stress at flaw tip

σu :

Ultimate strength of sample

\(\Omega\) :

\(={\Omega/RT}\)

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  1. Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, NY, 12180-3590, USA

    William Bruno Hillig

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Hillig, W.B. Model of effect of environmental attack on flaw growth kinetics of glass. Int J Fract 143, 219–230 (2007). https://doi.org/10.1007/s10704-006-9020-y

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