Abstract

The J-integral is applied to the single cantilever beam (SCB) and double cantilever beam (DCB) test specimens subjected to both mixed-mode I and II loading and large displacements. The methods proposed and resulting closed-form theoretical equations allow for the instantaneous evaluation of J during laboratory tests, requiring only the applied load and angular rotation of the specimen loading link, loading points, and remaining ligament. These measurands can be acquired using a common load cell and markers, a digital video camera, and image analysis software. In general, the equations do require knowledge of the specimen elastic moduli and shear moduli, as well as the specimen linear dimensions. Since the test data can be analyzed and J determined throughout the test instantaneously, and since, due to geometric nonlinearities, the ratio of mode I and mode II loading will likely vary significantly throughout the test, each specimen can be used to generate multiple data points. If crack length is determined throughout the test, presumably by directly measuring the crack length optically, or if the load drops abruptly due to crack growth, then when the crack advances, critical values of J for mixed-mode loading can be determined using the methods and results presented. It is noted that moderate to large translational and rotational displacements may improve the accuracy of the results using these methods. The results are applicable to standard pure mode I or pure mode II SCB and DCB tests as well and reduce to known equations in those special cases.

References

1.
Rice
,
J. R.
,
1968
, “
A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks
,”
ASME J. Appl. Mech.
,
35
(
2
), pp.
379
386
.
2.
Timoshenko
,
S.
, and
Gere
,
J. M.
,
1972
,
Mechanics of Materials
, 1st ed.,
D. Van Nostrand Company
,
New York
.
3.
Williams
,
J. G.
,
1987
, “
Large Displacements and End Block Effects in the DCB Interlaminar Test in Modes I and II
,”
J. Compos. Mater.
,
21
(
4
), pp.
330
347
.
4.
Williams
,
J. G.
,
1989
, “
The Fracture Mechanics of Delamination Tests
,”
J. Strain Anal.
,
24
(
4
), pp.
207
214
.
5.
Paris
,
A. J.
, and
Paris
,
P. C.
,
1988
, “
Instantaneous Evaluation of J and C*
,”
Int. J. Fract.
,
38
(
1
), pp.
19
21
.
6.
Nilsson
,
F.
,
2006
, “
Large Displacement Aspects on Fracture Testing With Double Cantilever Beam Specimens
,”
Int. J. Fract.
,
139
(
2
), pp.
305
311
.
7.
Gunderson
,
J. D.
,
Brueck
,
J. F.
, and
Paris
,
A. J.
,
2007
, “
Alternative Test Method for Interlaminar Fracture Toughness of Composites
,”
Int. J. Fract.
,
143
(
3
), pp.
273
276
.
8.
Gunderson
,
J.
,
Wilber
,
M.
,
Cullin
,
M.
, and
Paris
,
A. J.
,
2019
, “
An Analytical Basis and Experimental Method for the Instantaneous Evaluation of the DCB Test Specimen Mode I Crack Driving Force
,”
56th Annual Technical Meeting of the Society of Engineering Science (SES2019)
,
Washington University, St. Louis, MO
,
Oct. 13–15
.
9.
Paris
,
A. J.
,
2023
, “
Large Displacement Single and Double Cantilever Beam Specimen J-Integral Analyses
,”
21st International Symposium ASTM/ESIS Symposium on Fatigue and Fracture Mechanics (43rd National Symposium on Fatigue and Fracture Mechanics)
,
Washington, DC
,
Nov. 8–10
.
You do not currently have access to this content.