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IN m ' r m P R E r A T t o N s of the strength of ceramic materials, the size of the fracture-initiating surface flaw is invariably described by a single dimension-depth.A variable factor, @, is then used to account for the flaw shape, and determination of @ requires knowledge of the ratio a / c , wherea and c are the axes of an ellipse which describes the flaw shape. This complexity is not necessary; a, @, and c can be eliminated, and the flaw area, A , used to describe the flaw size.For a flaw much smaller than component dimensions and stresses well below the yield stress, Irwin' gives the following equation for the stress-intensity factor, K I , for the opening mode in plane stress*:where G is the strain energy releaserate, E is Young's modulus, u is applied stress, the angle 0 is as shown in Fig. 1, and Y is a geometrical parameter.'For surface flaws, Y =2.0, and for subsurface flaws, Y 1.8. The integral @ varies only with a/c as follows:Note that ifaic in Eq. (2a) has the same value ascia in Eq. (2b), the expressions under the integrals (i .e. elliptic integrals) are numerically equal, but the values of @ differ as follows:(3) A flaw will extend from that point on its periphery where K i is maximum, and this occurs where the first derivative of K I , dKl/ d8, is zero and the second derivative, d2Kl/d8', is negative. From Eq. (l), the maxima are found at 8 = n / 2 f o r a < c and at 8=0 for u >c. It follows that an elliptical flaw of any a/c ratio will tend to reduce its ellipticity during growth. When a circular shape is achieved, Eq. (1) shows that K I is constant along the periphery.Maximum values of K I are given by:In the case of materials which fracture well below the yield stress, Eqs. (4a), (4h), and (4c) apply with u andKl(,n,,, replaced, respectively, by g f , the fracture stress, andKlp, the critical stress-intensity factor, and the following equations are obtained:Equations (5u) and (5b) show that the smaller dimension of the flaw controls fracture, and not necessarily the depth, a . Equation (5b) can, however, be modified to include a dependence of C T~ on a: U Fig. 1. (A) Semielliptical flaw in plate subjected to uniform tensile stress. In ( B ) , the flaw depth,a, is less than its half-width, c, and in (C), a is greater than c .Equations (5a) and (5c) can now be combined in a general relation:where Z , known as the flaw shape ~arameter,".~ is as follows:The effect of flaw shape, aic, on Z is plotted in Fig. 2 . ' Values of the flaw area, A ( A _ = n u c / 2 ) , were calculated for several a/c ratios, and Z 2 vs a / d A has been plotted in Fig. 3. For practical purposes, the curve in Fig. 3 can be approximated by a straight line, Z 2 = 2 . 8 2 a l f i , which, when substituted into Eq. (6) gives 1.68 Kic (7) uj=-~ The use of Eq. (7) in place of Eq. (6) introduces a maximum error of 5 % in calculating the fracture stress associated with any realistic elliptical flaw including where a =c. For flaws with 0.2>a/c>3, Eqs. ( 6) and (7) differ significantly. Eq. (7) may, however, be quite useful for n...

Bend strengths of two sizes of specimens of an alumina ceramic were determined under conditions that either enhanced or restricted sub critical crack growth. The specimen sizes differed in each linear dimension by a factor of five and the effective size of small specimens was varied by the use of both 3‐ and 4‐point bending. Strength was dependent on specimen size under both crack‐growth conditions, and the dependence was associated with variations in flaws at fracture origins. The experimental data were analyzed for applicability of Weibull's statistical relations and in terms of fractographic examinations of strength‐controlling flaws.