Knowledge of slow crack growth rate in a window material is required to determine the design life of a window in which cracks grow under the influence of applied service stress. Parameters that characterize crack growth rate can be measured by dynamic fatigue in which coupons are taken to failure at several constant stress rates. The slower the stress rate, the more time is available for cracks to grow during the strength measurement, and the lower the stress at which the coupon fails. That is, coupons tested at a slower stress rate are weaker than coupons tested at a faster stress rate. The rate of slow crack growth is commonly fit to either a power law or an exponential law. The exponential law provides the more conservative estimate of design life and is prescribed for use by the U.S. National Aeronautics and Space Administration to design windows for manned vehicles. Well-established analytical equations are used to derive the power law crack growth parameters from dynamic fatigue measurements of as-polished (unindented) coupons. There are no exact analytical equations to derive power law parameters from indented coupons or to derive exponential law parameters from unindented or indented coupons. Approximate procedures have been used to derive crack growth parameters when there are no exact equations. We now describe a numerical method that gives the power and exponential laws for both unindented and indented coupons by least-squares fitting of dynamic fatigue measurements. A MATLAB code is provided to carry out the calculations.
The slow crack growth rate and inert strength of multispectral zinc sulfide were measured for use in aircraft window lifetime analysis. Dynamic fatigue data for uncoated multispectral zinc sulfide were fit to a power law by linear regression and to an exponential law by computer-aided numerical integration to obtain best-fit slow crack growth rate parameters. For the power law slow crack growth equation, crack velocity ( v ) = A * (KI/KIc)n, we find A * = 0.00769 m / s and n = 14.65, where KI is the stress intensity factor, KIc = 0.72 MPam is the critical stress intensity factor, and we assign the value of the geometric factor to be Y = 2 / π. Parameters for the exponential law slow crack growth equation, crack velocity ( v ) = vo exp ( βKI ) are vo = 3.02 × 10 − 14 m / s and β = 43.64 (MPam) − 1. There were only small differences in the crack growth rate between uncoated and antireflection-coated material. The crack growth rate that we observe is 10 to 200 times faster than previously reported for a stress intensity factor KI = 0.25 MPam, which is a representative value of KI for an aircraft window in service. The faster crack growth rate predicts a correspondingly shorter window lifetime. The inert strength of uncoated biaxial flexure disks (38.1 mm diameter with 15.88 mm load diameter and 31.75 mm support diameter) measured in dry nitrogen exhibited a 50% Weibull failure probability at 115 MPa with an unbiased ASTM C1239 Weibull modulus of 4.68. Antireflection-coated material had a 50% Weibull failure probability at 100 MPa with a Weibull modulus of 5.25.
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