An experimental technique for evaluation of the M-integral in an elastic-plastic material containing multiple defects is proposed by using digital image correlation (DIC). This technique makes direct use of the definition of M by experimentally evaluating the integrand of M at various points along a square contour and determining the integral by numerical integration. The nonlinear Ramberg–Osgood model is used to capture the elastic-plastic behavior such as the elastic-plastic stress and the total strain energy density in terms of the measured displacements by DIC used in an ARAMIS 4M instrument. Compared with the previous experimental method proposed by King and Herrmann (King and Herrmann, 1981, “Nondestructive Evaluation of the J and M Integrals,” ASME J. Appl. Mech., 48, pp. 83–87), the present technique could be suitable to measure the M-integral for the various complicated damages, specimen geometries, loading conditions, and material behaviors. The path-independence or path-dependence of the M-integral is investigated under small-scale and large-scale yielding conditions, respectively. It is found that the values of M are path independent when the contours entirely enclose the nonlinear plastic region near the multiple defects. In contrast, the path-dependence is concluded for an elastic-plastic solid under large-scale yielding condition when the contours have to pass through the plastic zone. This interesting path-dependence of the M-integral is consistent with numerical prediction via the finite element method and theoretical analysis developed in this paper.

References

References
1.
Knowles
,
J. K.
, and
Sternberg
,
E.
,
1972
, “
On a Class of Conservation Laws in Linearized and Finite Elastostatics
,”
Arch. Rational Mech. Anal.
,
44
, pp.
187
211
.10.1007/BF00250778
2.
Budiansky
,
B.
, and
Rice
,
J. R.
,
1973
, “
Conservation Laws and Energy Release Rates
,”
ASME J. Appl. Mech.
,
40
, pp.
201
203
.10.1115/1.3422926
3.
Eischen
,
J. W.
, and
Herrmann
,
G.
,
1987
, “
Energy Release Rates and Related Balance Laws in Linear Elastic Defect Mechanics
,”
ASME J. Appl. Mech.
,
54
, pp.
388
392
.10.1115/1.3173024
4.
Chen
,
Y. H.
,
2001
, “
M-Integral Analysis for Two-Dimensional Solids With Strongly Interacting Microcracks, Part I: In an Infinite Brittle Solids
,”
Int. J. Solids Struct.
,
38
, pp.
3193
3212
.10.1016/S0020-7683(00)00242-0
5.
Chen
,
Y. H.
,
2001
, “
M-Integral Analysis for Two-Dimensional Solids With Strongly Interacting Microcracks, Part II: In the Brittle Phase of an Infinite Metal/Ceramic Bimaterial
,”
Int. J. Solids Struct.
,
38
, pp.
3213
3232
.10.1016/S0020-7683(00)00243-2
6.
Chen
,
Y. H.
,
2002
,
Advances in Conservation Laws and Energy Release Rates
,
Kluwer Academic Publishers
,
The Netherlands
.
7.
Chen
,
Y. H.
, and
Lu
,
T. J.
,
2003
, “
Recent Developments and Applications of Invariant Integrals
,”
ASME Appl. Mech. Rev.
,
56
, pp.
515
552
.10.1115/1.1582199
8.
Chang
,
J. H.
, and
Chien
,
A. J.
,
2002
, “
Evaluation of M-Integral for Anisotropic Elastic Media With Multiple Defects
,”
Int. J. Fract.
,
114
, pp.
267
289
.10.1023/A:1015561313059
9.
Chang
,
J. H.
, and
Peng
,
D. J.
,
2004
, “
Use of M Integral for Rubbery Material Problems Containing Multiple Defects
,”
J. Eng. Mech.
,
130
, pp.
589
598
.10.1061/(ASCE)0733-9399(2004)130:5(589)
10.
Hu
,
Y. F.
, and
Chen
,
Y. H.
,
2009
, “
The M-Integral Description for a Brittle Plane Strip With Two Holes Before and After Coalescence
,”
Acta Mech.
,
204
, pp.
109
123
.10.1007/s00707-008-0051-5
11.
Hu
,
Y. F.
, and
Chen
,
Y. H.
,
2009
, “
The M-Integral Description for a Brittle Plane Strip With Two Cracks Before and After Coalescence
,”
ASME J. Appl. Mech.
,
76
, p.
061017
.10.1115/1.3130818
12.
Li
,
Q.
, and
Chen
,
Y. H.
,
2008
, “
Surface Effect and Size Dependence on the Energy Release Due to a Nanosized Hole Expansion in Plane Elastic Materials
,”
ASME J. Appl. Mech.
,
75
, p.
061008
.10.1115/1.2965368
13.
King
,
R. B.
, and
Herrmann
,
G.
,
1981
, “
Nondestructive Evaluation of the J and M Integrals
,”
ASME J. Appl. Mech.
,
48
, pp.
83
87
.10.1115/1.3157597
14.
Pan
,
B.
,
Qian
,
K.
,
Xie
,
H. M.
, and
Asundi
,
A.
,
2009
, “
Two-Dimensional Digital Image Correlation for In-Plane Displacement and Strain Measurement: A Review
,”
Measur. Sci. Tech.
,
20
, p.
062001
. 10.1088/0957-0233/20/6/06200110.1088/0957-0233/20/6/062001
15.
Ramberg
,
W.
, and
Osgood
,
W. R.
,
1943
, “
Description of Stress-Strain Curves by Three Parameters
,” Technical Note No. 902, National Advisory Committee for Aeronautics, Washington DC.
16.
McMeeking
,
R. M.
,
1977
, “
Finite Deformation Analysis of Crack-Tip Opening in Elastic-Plastic Materials and Implications for Fracture
,”
J. Mech. Phys. Solids
,
25
, pp.
357
381
.10.1016/0022-5096(77)90003-5
17.
Kuang
,
J. H.
, and
Chen
,
Y. C.
,
1996
, “
The Values of J-Integral Within the Plastic Zone
,”
Eng. Fract. Mech.
,
55
, pp.
869
881
.10.1016/S0013-7944(96)00077-X
18.
Carka
,
D.
, and
Landis
,
C. M.
,
2011
, “
On the Path-Dependence of the J-Integral Near a Stationary Crack in an Elastic-Plastic Material
,”
J. Appl. Mech.
,
78
, p.
011006
.10.1115/1.4001748
19.
Rice
,
J. R.
, and
Rosengren
,
G. F.
,
1968
, “
Plane Strain Deformation Near a Crack Tip in a Power-Law Hardening Material
,”
J. Mech. Phys. Solids
,
16
, pp.
1
12
.10.1016/0022-5096(68)90013-6
20.
Hutchinson
,
J. W.
,
1968
, “
Singular Behavior at the End of a Tensile Crack in a Hardening Material
,”
J. Mech. Phys. Solids
,
16
, pp.
13
31
.10.1016/0022-5096(68)90014-8
21.
Shih
,
C. F.
,
1974
, “
Small Scale Yielding Analysis of Mixed Mode Plane Strain Crack Problems
,”
ASTM STP
,
560
, pp.
187
210
.
22.
Shih
,
C. F.
,
1981
, “
Relationships Between the J-Integral and the Crack Opening Displacement for Stationary and Extending Cracks
,”
J. Mech. Phys. Solids
,
29
, pp.
305
326
.10.1016/0022-5096(81)90003-X
23.
Sivaneri
,
N. T.
,
Xie
,
Y. P.
, and
Kang
,
B. S.-J.
,
1991
, “
Elastic-Plastic Crack Tip-Field Numerical Analysis Integrated With Moire Interferometry
,”
Int. J. Fract.
,
49
, pp.
291
303
. 10.1007/BF00042197
24.
Stump
,
D. M.
, and
Zywicz
,
E.
,
1993
, “
J-Integral Computations in the Incremental and Deformation Plasticity Analysis of Small-Scale Yielding
,”
Eng. Fract. Mech.
,
45
, pp.
61
67
.10.1016/0013-7944(93)90008-G
25.
Wang
,
Y. Q.
,
Sutton
,
M. A.
,
Bruck
,
H. A.
, and
Schreier
,
H. W.
,
2009
, “
Quantitative Error Assessment in Pattern Matching: Effects of Intensity Pattern Noise, Interpolation, Strain and Image Contrast on Motion Measurements
,”
Strain
,
45
, pp.
160
178
.10.1111/j.1475-1305.2008.00592.x
26.
Carlos
,
L.-V.
, and
Carlos
,
H. G.
,
2009
, “
The Need of a Framework to Compare Geometric Conflation Algorithms
,”
12th AGILE International Conference on Geographic Information Science
,
Leibniz Universität Hannover
,
Germany
,
June 2–5, pp
.
1
5
.
27.
Moran
,
B.
, and
Shih
,
C. F.
,
1987
, “
A General Treatment of Crack Tip Contour Integrals
,”
Int. J. Fract.
,
35
, pp.
295
310
.10.1007/BF00276359
You do not currently have access to this content.