In this study, mode I stress intensity factors for a three-dimensional finite cracked body with arbitrary shape and subjected to arbitrary loading is presented by using the boundary weight function method. The weight function is a universal function for a given cracked body and can be obtained from any arbitrary loading system. A numerical finite element method for the determination of weight function relevant to cracked bodies with finite dimensions is used. Explicit boundary weight functions are successfully demonstrated by using the least-squares fitting procedure for elliptical quarter-corner crack and embedded elliptical crack in parallelepipedic finite bodies. If the stress distribution of a cut-out parallelepipedic cracked body from any arbitrary shape of cracked body subjected to arbitrary loading is determined, the mode I stress intensity factors for the cracked body can be obtained from the predetermined boundary weight functions by a simple surface integration. Comparison of the calculated results with some available solutions in the published literature confirms the efficiency and accuracy of the proposed boundary weight function method.
Issue Section:
Research Papers
1.
Bahr
H.-A.
Balke
H.
1987
, “Fracture Analysis of a Single Edge Cracked Strip under Thermal Shock
,” Theoretical and Applied Fracture Mechanics
, Vol. 8
, pp. 33
–39
.2.
Bueckner
H. F.
1970
, “A Novel Principle for the Computation of Stress Intensity Factors
,” ZAMM
, Vol. 50
, pp. 529
–546
.3.
Bueckner
H. F.
1987
, “Weight Functions and Fundamental Fields for Pennyshaped and Half-Space Crack in Three-space
,” International Journal of Solids and Structures
, Vol. 23
, pp. 57
–93
.4.
Emery
A. F.
Walker
G. E.
Williams
J. A.
1969
, “A Green Function for the Stress Intensity Factors of Edge Cracks and Its Application to Thermal Stress
,” ASME Journal of Applied Mechanics
, Vol. 36
, pp. 618
–624
.5.
Heckmer
J. L.
Bloom
J. M.
1977
, “Determination of Stress Intensity Factors for the Corner-Cracked Hole Using the Isoparametric Singularity Element
,” International Journal of Fracture
, Vol. 13
, pp. 732
–736
.6.
Hellen
T. K.
1975
, “On the Method of Virtual Crack Extensions
,” International Journal of Numerical Methods in Engineering
, Vol. 9
, pp. 187
–207
.7.
Hellen
T. K.
Cesari
F.
1979
, “On the Solution of the Center Cracked Plate with a Quadratic Thermal Gradient
,” Engineering Fracture Mechanics
, Vol. 12
, pp. 469
–478
.8.
Labbens, R. C., Heliot, J., and Pellissier-Tanon, A., 1976, “Weight Function for Three-Dimensional Symmetrical Crack Problems,” ASTM STP-Vol. 601, pp. 448–470.
9.
Ma
C. C.
Chang
Z.
Tsai
C. H.
1990
, “Weight Functions of Oblique Edge and Center Cracks in Finite Bodies
,” Engineering Fracture Mechanics
, Vol. 36
, pp. 267
–285
.10.
Ma
C. C.
Liao
M. H.
1996
, “Analysis of Axial Cracks in Hollow Cylinders Subjected to Thermal Shock by Using the Thermal Weight Function Method
,” ASME JOURNAL OF PRESSURE VESSEL TECHNOLOGY
, Vol. 118
, pp. 146
–153
.11.
Ma
C. C.
Shen
I. K.
Tsai
P.
1995
, “Calculation of the Stress Intensity Factor for Arbitrary Finite Cracked Body by Using the Boundary Weight Function Method
,” International Journal of Fracture
, Vol. 70
, pp. 183
–202
.12.
Newman Jr., J. C., and Raju, I. S., 1983, “Stress Intensity Factor Equations for Cracks in Three-Dimensional Finite Bodies,” ASTM STP-Vol. 791, pp. 238–265.
13.
Nied
H. F.
1983
, “Thermal Shock Fracture in an Edge-Cracked Plate
,” Journal of Thermal Stress
, Vol. 6
, pp. 217
–229
.14.
Oliveira
R.
Wu
X. R.
1987
, “Stress Intensity Factor for Axial Cracks in Hollow Cylinders Subjected to Thermal Shock
,” Engineering Fracture Mechanics
, Vol. 27
, pp. 185
–197
.15.
Parks
D. M.
1974
, “A Stiffness Derivative Finite Element Technique for Determination of Crack Tip Stress Intensity Factors
,” International Journal of Fracture
, Vol. 10
, pp. 487
–501
.16.
Raju
I. S.
Newman
J. C.
1979
, “Stress Intensity Factor for a Wide Range of Semielliptical Surface Cracks in Finite-thickness Plates
,” Engineering Fracture Mechanics
, Vol. 11
, pp. 817
–829
.17.
Rice
J. R.
1972
, “Some Remarks on Elastic Crack-Tip Stress Field
,” International Journal of Solids and Structures
, Vol. 8
, pp. 751
–758
.18.
Rice, J. R., 1989, “Weight Function Theory for Three-Dimensional Elastic Crack Analysis,” ASTM STP-Vol. 1020, pp. 29–57.
19.
Rooke, D. P., and Cartwright, D. J., 1976, Compendium of Stress Intensity Factors, Her Majesty’s Stationery Office, London, U. K.
20.
Sha
G. T.
1984
, “Stiffness Derivative Finite Element Technique to Determine Nodal Weight Functions with Singularity Elements
,” Engineering Fracture Mechanics
, Vol. 19
, pp. 685
–699
.21.
Sha
G. T.
Yang
C. T.
1985
, “Weight Function Calculations for Mixed-Mode Fracture Problems with the Virtual Crack Extension Technique
,” Engineering Fracture Mechanics
, Vol. 21
, pp. 1119
–1149
.22.
Sham
T. L.
1987
, “A Unified Finite Element Method for Determining Weight Functions in Two and Three Dimensions
,” International Journal of Solids and Structures
, Vol. 23
, pp. 1357
–1372
.23.
Sih, G. C., 1973, Handbook of Stress Intensity Factors, Institute of Fracture and Solid Mechanics, Lehigh University, PA.
24.
Tada, H., Paris, P. C., and Irwin, G. R., 1973, The Stress Analysis of Cracks Handbook, Del Research Corporation, Hellertown, PA.
25.
Tsai
C. H.
Ma
C. C.
1989
, “Weight Functions for Cracks in Finite Rectangular Plates
,” International Journal of Fracture
, Vol. 40
, pp. 43
–63
.26.
Tsai
C. H.
Ma
C. C.
1992
, “Thermal Weight Function of Cracked Bodies Subjected to Thermal Loading
,” Engineering Fracture Mechanics
, Vol. 41
, pp. 27
–40
.27.
Wilson
W. K.
Yu
I. W.
1979
, “The Use of the J-Integral in Thermal Stress Crack Problems
,” International Journal of Fracture
, Vol. 15
, pp. 377
–387
.
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