The stress distribution ahead of a notch tip is the prerequisite to calculating the driving force for cracks emanating from notches. This article first examines whether two commonly used engineering methods, which are often employed to determine the response at a notch tip, can be applied to evaluate the elastic-plastic response ahead of a notch tip. It is found that both methods would significantly underestimate the stress-strain distribution ahead of a notch tip. Based deformation theories of plasticity, and analytical method is then developed, taking into account of the effects of stress redistribution induced by notch plasticity and the in-plane and through-thickness constraints near the notch root. Predictions are shown to be in close correlation with finite element results.

Issue Section:
Technical Papers
Topics:
Deformation, Finite element analysis, Fracture (Materials), Plasticity, Stress, Stress concentration
1.
Ball
D. L.
,
1990
, “
Proposed Integration of Notch-Strain and Fatigue Crack-Growth Analyses
,”
J. Aircraft
, Vol.
27
, pp.
358
–
367
.
2.
Creager
M.
, and
Paris
P. C.
,
1967
, “
Elastic Field Equations for Blunt Cracks with Reference to Stress Corrosion Cracking
,”
Int. J. Fract. Mech.
, Vol.
3
, pp.
247
–
252
.
3.
Gemma
A. E.
,
1985
, “
An Approximate Elastioplastic Analysis of the Effect of Plane Strain at the Surface of a Notch
,”
Engng. Facture Mech.
, Vol.
21
, pp.
495
–
501
.
4.
Glinka
G.
,
1985
, “
Calculation of Inelastic Notch Tip Strain-Stress Histories Under Cyclic Loading
,”
Engng. Fracture Mech.
, Vol.
22
, pp.
839
–
854
.
5.
Glinka
G.
, and
Molski
K.
,
1981
, “
A Method of Elastic-Plastic Stress and Strain Calculation at a Notch Root
,”
Mater. Sci. Engng.
, Vol.
50
, pp.
93
–
100
.
6.
Glinka
G.
, and
Newport
A.
,
1987
, “
Universal Features of Elastic Notch-Tip Stress Fields
,”
Int. J. Fatigue
, Vol.
9
, pp.
143
–
150
.
7.
Guo, W., Wang, C. H., and Rose, L. R. F., 1998, “Elastoplastic Analysis of Notch-Tip Fields in Strain Hardening Materials,” DSTO-RR-0137, Defence Science and Technology Organisation, Melbourne, Australia.
8.
Hill
R.
,
1949
, “
The Plastic Yielding of Notched Bars under Tension
,”
Q. J. Mechanics and Applied Mathematics
, Vol.
2
, pp.
40
–
50
.
9.
Hoffman
M.
, and
Seeger
T.
,
1985
, “
A Generalised Method for Estimating Multiaxial Elastic-Plastic Notch Stresses and Strains—Part 1 and Part 2
,
ASME JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY
, Vol.
107
, pp.
250
–
260
.
10.
Irwin, G. R., 1958, Fracture, Handuch der Physik VI, pp. 551–590, Flugge, ed., Springer.
11.
Lazzarin
P.
, and
Tovo
R.
,
1996
, “
A Unified Approach to the Evaluation of Linear Elastic Stress Fields in the Neighborhood of Cracks and Notches
,”
Int. J. Fracture
, Vol.
78
, pp.
3
–
19
.
12.
Moftahar
A.
,
Buczynski
A.
, and
Glinka
G.
,
1995
, “
Calculation of Elastoplastic Strains and Stresses in Notches Under Multiaxial Loading
,”
Int. J. Fracture
, Vol.
70
, pp.
357
–
373
.
13.
Neuber
H.
,
1961
, “
Theory of Stress Concentration for Shear-Strained Prismatic Bodies with Arbitrary Nonlinear Stress-Strain Law
,”
ASME Journal of Applied Mechanics
, Vol.
23
, pp.
544
–
550
.
14.
Pilkey, W., 1997, Peterson’s Stress Concentration Factors, 2nd Edition, John Wiley, New York.
15.
Shin
C. S.
,
Man
K. C.
, and
Wang
C. M.
,
1994
, “
A Practical Method to Estimate the Stress Concentration of Notches
,”
Int. J. Fatigue
, Vol.
16
, pp.
242
–
256
.
16.
Singh
M. N. K.
,
Glinka
G.
, and
Dubey
R. N.
,
1996
, “
Elastic-Plastic Stress-Strain Calculation in Notched Bodies Subjected to Non-Proportional Loading
,”
Int. J. Fracture
, Vol.
76
, pp.
39
–
60
.
17.
Timoshenko, S. and Gppdier, J. N., 1969, Theory of Elasticity, McGraw-Hill, New York.
18.
Topper
T. H.
,
Wetzel
R. M.
, and
Morrow
J.
,
1969
, “
Neuber’s Rule Applied to Fatigue of Notched Specimens
,”
J. Materials
, Vol.
4
, pp.
200
–
209
.
19.
Wang
C. H.
, and
Rose
L. R. F.
,
1998
, “
Transient and Steady-State Deformation at Notch Root Under Cyclic Loading
,”
Mechanics of Materials
, Vol.
30
, pp.
229
–
241
.
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