National Technical Informaon Service. U. S. DEPARTMENT OF ... deriving and computer programming of complex mathematical expressions is discussed.
:
AD-779 469J
STRESS INTENSITY FACTORS FOR ELLIPTICAL CRACKS Albert S.
Kobayashi,
et al
Washington University
I-0-.
-
M
Prepared for: Army Research. Office-Durham
.,
March 1974
DISTRIBUTED BY:
National Technical Informaon Service U.S. DEPARTMENT OF COMMERCE
5285 Port Royal Road, Springfield Va. 22151
bCMHCONTROL MY,,lt~Ii DA
St~~ctir~Wti .tSee.£ra), ¢lof&l~ ON14lAA11NG
AC T1V1
Y
A R& D
Ei
eufI
y,?
i
gI
MO.1,body of hattc' and inde(xiA nofall fin niut be *tIE,*J when thv overll -epoyl is r splijd
l
~bel~tlfhuhof)
32~0. R
University of Washingto i
EPOT*CLWqtT% CLASSIAEtCATION
...
21) ,
..
.....
Not applicable "Srress lntensity Factors for Elliptical Cracks" 4 0t1CMI1T'vE NoS(1pt
ofpvt d i
ntieivodate*)
Interim Technical Report No. 2, Marcn 1974 Albert S. Kobayashi, Alfred N. Enetanya, and Rameshchandra C. Shah
6
MCP O
O&UE
"10. VOTA6 NO. OPP PAO%$
I
OF aglo'
September 1973 IS.
27
N.RAC? 011 -GRANT 14Q. ...
9*. ORIINATOR'SIMPO1T N
Grant No. DA-ARO-b-31-124-73-G38 b. P'J 0
StiC
No. 2
EC T NO
None 06.
OTNIWt10W MNIJ
d.,Not
(Any~ oth.,- pumhe!, that may boe ahignvi
applicable
,
.
..
.
...
......
. ... . . ...
Approved for public distribution
~Nolr NOSCONSOMING
MILITARAr
12
1
Not applicable
T~IVI'rf
Army Research Office
-
Durham
The combined use of a solution for an elliptical crack subjected to a polynomial distribution of internal pressure together with a free surface solution for the alternating method is reviewed in order to improve the efficiency of this numerical technique. Numerical differentiation to avoid deriving and computer programming of complex mathematical expressions is discussed. A criterion for maximum grid size for the free surface solution is proposed. Also optimum fittings of the first, second and third order polynomial distributions of internal pressure are considered.
DDC Tr'C11 . , .SERVICC-I,-, NA i NAI IN1-(ORN1A11ON
DDORM
7
INICA .:' ,
-A
(PAGE 1)
0 l ot
0 1 4 -
6
0 0SI
cur lty C l s si fc a ti on
', T
~-I
maw,
14r
IKA
-O-LAR i-*
LINK
-wr
Vwc r-
Fracture Mechanics Stre~ss Intensity Factor Thrtue-Dimensional Elasticity
DD Nov 4.14 73 (PAGE
2)
(BACK) fcta
8
w~T
~
L IN K
OL
"
!
....
i
.....
[ill
'FOREWORD This Interim Technical Report No. 2 was prepared for presentation at the Conference on the Prospects of Advanced Fracture Mechanics which is to be held in Delft, Netherland, June 24 - 28, 1974, under the joint sponsorship of the Metal Research Institute T. N. 0. and Delft University of Technology in close cooperation with Lehigh University. The figures in this report were reduced in compliance with the format specified by the Seminar organizers, Full-size, 8 1/2" x 11", figures can be obtained for numerical computation by writing to the undersigned:
Professor Albert S. Kobayashi Department of Mechanical Engineering University of Washington Seattle, Washington 98195
THE FINDINGS OF THIS REPORT ARE NOT TO BE CONSTRUED AS AN OFFICIAL DEPARTMENT OF THE ARMY POSITION, UNLESS SO DESIGNATED BY OTHER AUTHORIZED DOCUMENTS.
.
fl..
$
...
....
'
21
4
STRESS INTENSITY FACTORS FOR ELLIPTICAL CRACKS
A.S. Kobayashi, A.N. Enetanya, and R.C. Shah University of Washington, Seattle, Washington 98195 and The Boeing Aerospace Company, Seattle, Washington 98124
ABSTRACT
The combined use of a solution for an elliptical crack subjected to internal preasure, which is represented by a polynomial expression, together with a free surface solution for the alternating-method is-reviewed-and-methods--for-improving--th-offi-cienc,, of this numerical technique are proposed. Numerical differentiation for avoiding the derivation and computer programming of complex mathematical expressions is discussed. A criterion for maximum grid size for the free surface solution is proposed. Also optimum fittings of the firnt, second and third order polynomial distributions of internal pressure are considered.
INTRODUCTION Post mortem failure analysis of fractured structural components requires modeling of an embedded or surface flaw from which fracture initiated. More often, these flaws can be approximated
by an ellipse and are located in regions of stress concentrations or thin cross-section, such as those shown in Fig. i, where the stress gradient as well as the complex geometry of the structure cannot be ignored. The elliptical crack and its interaction with its adjacent or intersecting boundaries have thus been studied by
various investigators during the past ten years. The earliest paper on stress intensity factor of an elliptical crack is that by Irwin who then derived the approximate expression for the stress intensity factor at the point of deepest
