The paper discusses two physically based weakest-link approaches, commonly adopted to evaluate the reliability of ceramic components in multiaxial states of stress (namely, Evans’ multiaxial elemental strength method and Batdorf’s flaw density approach) whose equivalence has been recently proven. It is shown here how the two formulations can be simultaneously derived from the basic assumptions and simply regarded as two different ways to evaluate the same integral. Differences in computational efficiency yielded by the two different integration schemes are also illustrated.

1.
Andreasen
J. H.
,
1993
, “
Statistics of Brittle Failure in Multiaxial Stress States
,”
Journal of the American Ceramic Society
, Vol.
76
, pp.
2933
2935
.
2.
Barnett, R. L., Connors, C. L., Hermann, P. C., and Wingfield, J. R., 1967, “Fracture of Brittle Materials Under Transient Mechanical and Thermal Loading,” Report No. AFFDL-TR-66-220.U. S. Air Force Flight Dynamics Laboratory, Wright Patterson Air Force Base, OH.
3.
Batdorf
S. B.
, and
Crose
J. G.
,
1974
, “
A Statistical Theory for the Fracture of Brittle Structures Subjected to Nonuniform Polyaxial Stresses
,”
ASME Journal of Applied Mechanics
, Vol.
41
, pp.
459
464
.
4.
Batdorf
S. B.
, and
Heinisch
H. L.
,
1978
, “
Weakest Link Theory Reformulated for Arbitrary Fracture Criterion
,”
Journal of the American Ceramic Society
, Vol.
61
, pp.
355
358
.
5.
Chao
L.-Y.
, and
Shetty
D. K.
,
1990
, “
Equivalence of Physically Based Statistical Fracture Theories for Reliability Analysis of Ceramic in Multiaxial Loading
,”
Journal of the American Ceramic Society
, Vol.
73
, pp.
1917
1921
.
6.
Evans
A. G.
,
1978
, “
A General Approach for the Statistical Analysis of Multiaxial Fracture
,”
Journal of the American Ceramic Society
, Vol.
61
, pp.
302
308
.
7.
Freudenthal, A. M., 1968, “Statistical Approach to Brittle Fracture,” Fracture, an Advanced Treatise, Vol. II. H. Liebowitz, Editor, Academic Press, New York, pp. 591–619.
8.
Furgiuele
F. M.
, and
Lamberti
A.
,
1991
, “
On the Equivalence of Two Weakest-Link Fracture Statistics Formulation
,”
International Journal of Fracture
, Vol.
51
, pp.
R15–R20
R15–R20
.
9.
Lamon
J.
, and
Evans
A. G.
,
1983
, “
Statistical Analysis of Bending Strengths for Brittle Solids: A Multiaxial Fracture Problem
,”
Journal of the American Ceramic Society
, Vol.
66
, pp.
177
182
.
10.
Nemeth, N. N., Mandersheid, J. M., and Gyekenyesi, J. P., 1990, “Ceramics Analysis and Reliability Evaluation of Structures (CARES),” NASA TP-2916, Washington, DC.
11.
Tucker, W. T., and Johnson, C. A., 1994, “The Multiaxial Equivalent of Stressed Volume,” Life Prediction Methodologies and Data for Ceramic Materials, ASTM STP 1201, C. R. Brinkman and S. F. Duffy, eds., American Society for Testing and Materials, Philadelphia, pp. 265–279.
12.
Weibull, W., 1939, “A Statistical Theory of Strength of Materials,” Ingeniors Vetenskap Akadamiens, Handlingar, No. 151, pp. 1–45.
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