Lenoe, EM *Chief mechanic of materials and research mathematician, Army Materials and Mechanics Research Center, Watertown, Mass.*

Neal, DM *Chief mechanic of materials and research mathematician, Army Materials and Mechanics Research Center, Watertown, Mass.*

Pages: 23 Published: Jan 1976

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**Source: **STP601-EB

In the past few years a number of test procedures have evolved as a result of attempts to observe stable crack growth in ceramics under constant stress conditions. The experimental procedures have included double cantilever, double torsion, in-plane moment, and controlled flaws in beam bending tests. These procedures are briefly reviewed. Available slow crack growth data for hot pressed silicon nitride, which has been presented in the literature, is utilized to estimate survival times for various stress levels. The computations are completed in several ways: (*a*) use of strength data obtained at various loading rates; (*b*) deterministic integration of the equations; and (*c*) in a Monte Carlo sense, wherein the controlling parameters are assumed to possess realistic variability. The end product of each set of computations is a design stress-survival time relationship, and the purpose of this paper is to compare these life estimates and comment on the adequacy of each method.

Additional motivations were to assess the status of properties information, and to establish, if possible, reasonable bounds on the accuracy of these probability-based life estimates. Examination of the data and application of the two probability techniques led to the conclusion that the procedures are appropriate for order of magnitude estimates, which are generally but not necessarily conservative. It was evident that additional data, improved experimental procedures, and further analysis of specimens were required.

Since the exponents of the crack velocity-stress intensity functions in a power law form are large and typically cover a wide range for ceramics of interest, that is, 4 < *m* < 50, difficulties were encountered in use of numerical simulation procedures. With *m* ⩽ 10, for example, the resulting life functions were widely distributed. Furthermore, the mean value estimates were highly unstable and for large *m* did not appear amenable to economical digital simulation. Accordingly, a number of different trial functions, including logarithmic, exponential, and polynomial approximations were employed to represent subcritical crack behavior. The final function selected was of the form *F* = *A*^{0}exp(*mK*^{1}), where *F* = *K*^{I}/*V*.

This form seemed appropriate since log *F* versus *K*^{I} resulted in reasonable requirements on number of simulations. The *m* values were appreciably lower than the power law representation. Application of the Monte Carlo method to lifetime estimates of ceramics provided an error tolerance for *K*^{I} and allowed calculation of the probability density function.

**Keywords:**

fractures (materials), ceramics, silicon nitrides, fracture properties life (durability) probability theory, Monte Carlo method, crack propagation

**Paper ID:** STP28638S

**Committee/Subcommittee:** E08.06

**DOI:** 10.1520/STP28638S