Abstract

The stress field, constraint effect, and fracture mode transition at crack tip of mixed mode I-II-III inclination surface crack under compression have been investigated. The effects of geometrical configurations (relative crack depth and aspect ratio), friction coefficient, and biaxial scale factor on stress intensity factor (KII and KIII) and in-plane constraint parameter T-stress are quantitatively studied, the stress field at different crack inclination angles under tension and compression are compared, the failure mode at special locations along crack front of inclination surface crack is analyzed according to the generalized maximum tangential stress criterion (GMTS). The relative crack depth has slight effect on stress intensity factor and T-stress, and aspect ratio has a significant effect on stress intensity factor and T-stress. The friction coefficient decreases the magnitude of stress intensity factor and increases the magnitude of T-stress, the greater the crack inclination angle is, the more pronounced the effect is when crack inclination angle greater than 30 deg. The stress distribution around crack tip under tension and compression is completely different. At free surface, the crack will failure in-plane shear mode II sliding crack, and at the deepest part of crack, the crack will start as out-plane shear mode III tearing crack under compression.

References

1.
Lin
,
H.
,
Yang
,
H.
,
Wang
,
Y.
,
Zhao
,
Y.
, and
Cao
,
R.
,
2019
, “
Determination of the Stress Field and Crack Initiation Angle of an Open Flaw Tip Under Uniaxial Compression
,”
Theor. Appl. Fract. Mech.
,
104
, p.
102358
.10.1016/j.tafmec.2019.102358
2.
Westergaard
,
H. M.
,
1939
, “
Bearing Pressures and Cracks
,”
ASME J. Appl. Mech.
,
6
(
2
), pp. A
49
–A
53
.10.1115/1.4008919
3.
Irwin
,
G. R.
,
1957
, “
Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate
,”
ASME J. Appl. Mech.
,
24
(
3
), pp.
361
364
.10.1115/1.4011547
4.
Larsson
,
S. G.
, and
Carlsson
,
A. J.
,
1973
, “
Influence of Non-Singular Stress Terms and Specimen Geometry on Small-Scale Yielding at Crack Tips in Elastic-Plastic Materials
,”
J. Mech. Phys. Solids
,
21
(
4
), pp.
263
277
.10.1016/0022-5096(73)90024-0
5.
Betegon
,
C. H.
,
1991
, “
Two-Parameter Characterization of Elastic-Plastic Crack-Tip Fields
,”
ASME J. Appl. Mech.
, 58(1), pp.
104
110
.10.1115/1.2897135
6.
Du
,
Z. Z.
, and
Hancock
,
J. W.
,
1991
, “
The Effect of Non-Singular Stresses on Crack-Tip Constraint
,”
J. Mech. Phys. Solids
,
39
(
4
), pp.
555
567
.10.1016/0022-5096(91)90041-L
7.
Guo
,
W.
,
She
,
C.
,
Zhao
,
J.
, and
Zhang
,
B.
,
2006
, “
Advances in Three-Dimensional Fracture Mechanics
,”
Key Eng. Mater.
,
312
, pp.
27
34
.10.4028/www.scientific.net/KEM.312.27
8.
Zhao
,
J.
,
Guo
,
W.
, and
She
,
C.
,
2007
, “
The in-Plane and Out-of-Plane Stress Constraint Factors and K - T - Tz Description of Stress Field Near the Border of a Semi-Elliptical Surface Crack
,”
Int. J. Fatigue
,
29
(
3
), pp.
435
443
.10.1016/j.ijfatigue.2006.05.005
9.
Ayhan
,
A. O.
,
2004
, “
Mixed Mode Stress Intensity Factors for Deflected and Inclined Surface Cracks in Finite-Thickness Plates
,”
Eng. Fract. Mech.
,
71
(
7–8
), pp.
1059
1079
.10.1016/S0013-7944(03)00153-X
10.
Ayhan
,
A. O.
,
2007
, “
Mixed Mode Stress Intensity Factors for Deflected and Inclined Corner Cracks in Finite-Thickness Plates
,”
Int. J. Fatigue
,
29
(
2
), pp.
305
317
.10.1016/j.ijfatigue.2006.03.006
11.
Ayhan
,
A. O.
, and
Yücel
,
U.
,
2011
, “
Stress Intensity Factor Equations for Mixed-Mode Surface and Corner Cracks in Finite-Thickness Plates Subjected to Tension Loads
,”
Int. J. Pressure Vessel Pip.
,
88
(
5–7
), pp.
181
188
.10.1016/j.ijpvp.2011.05.009
12.
Shlyannikov
,
V. N.
,
Kislova
,
S. Y.
, and
Tumanov
,
A. V.
,
2010
, “
Inclined Semi-Elliptical Crack for Predicting Crack Growth Direction Based on Apparent Stress Intensity Factors
,”
Theor. Appl. Fract. Mech.
,
53
(
3
), pp.
185
193
.10.1016/j.tafmec.2010.06.003
13.
Ismail
,
A. E.
,
Ariffin
,
A. K.
,
Abdullah
,
S.
,
Ghazali
,
M. J.
,
Abdulrazzaq
,
M.
, and
Daud
,
R.
,
2012
, “
Stress Intensity Factors Under Combined Bending and Torsion Moments
,”
J. Zhejiang Univ. Sci. A
,
13
(
1
), pp.
1
8
.10.1631/jzus.A1100040
14.
Fett
,
T.
,
2001
, “
Stress Intensity Factors and T-Stress for Internally Cracked Circular Disks Under Various Boundary Conditions
,”
Eng. Fract. Mech.
,
68
(
9
), pp.
1119
1136
.10.1016/S0013-7944(01)00025-X
15.
Teh
,
S.
,
Andriyana
,
A.
,
Ramesh
,
S.
,
Putra
,
I. S.
,
Kadarno
,
P.
, and
Purbolaksono
,
J.
,
2021
, “
Tetrahedral Meshing for a Slanted Semi-Elliptical Surface Crack at a Solid Cylinder
,”
Eng. Fract. Mech.
,
241
, p.
107400
.10.1016/j.engfracmech.2020.107400
16.
Lewis
,
T.
, and
Wang
,
X.
,
2008
, “
The T-Stress Solutions for Through-Wall Circumferential Cracks in Cylinders Subjected to General Loading Conditions
,”
Eng. Fract. Mech.
,
75
(
10
), pp.
3206
3225
.10.1016/j.engfracmech.2007.12.001
17.
Hua
,
W.
,
Li
,
Y.
,
Dong
,
S.
,
Li
,
N.
, and
Wang
,
Q.
,
2015
, “
T-Stress for a Centrally Cracked Brazilian Disk Under Confining Pressure
,”
Eng. Fract. Mech.
,
149
, pp.
37
44
.10.1016/j.engfracmech.2015.09.048
18.
Jin
,
Z.
, and
Wang
,
X.
,
2015
, “
Characteristics of Crack Front Stress Fields in Three-Dimensional Single Edge Cracked Plate Specimens Under General Loading Conditions
,”
Theor. Appl. Fract. Mech.
,
77
, pp.
14
34
.10.1016/j.tafmec.2015.01.008
19.
Kirilyuk
,
V. S.
, and
Levchuk
,
O. I.
,
2007
, “
Elastic T-Stress Solutions for Flat Elliptical Cracks Under Tension and Bending
,”
Eng. Fract. Mech.
,
74
(
17
), pp.
2881
2891
.10.1016/j.engfracmech.2007.01.002
20.
Wang
,
X.
,
2003
, “
Elastic T-Stress Solutions for Semi-Elliptical Surface Cracks in Finite Thickness Plates
,”
Eng. Fract. Mech.
,
70
(
6
), pp.
731
756
.10.1016/S0013-7944(02)00081-4
21.
Wang
,
X.
, and
Bell
,
R.
,
2004
, “
Elastic T-Stress Solutions for Semi-Elliptical Surface Cracks in Finite Thickness Plates Subject to Non-Uniform Stress Distributions
,”
Eng. Fract. Mech.
,
71
(
9–10
), pp.
1477
1496
.10.1016/S0013-7944(03)00140-1
22.
Qu
,
J.
, and
Wang
,
X.
,
2006
, “
Solutions of T-Stresses for Quarter-Elliptical Corner Cracks in Finite Thickness Plates Subject to Tension and Bending
,”
Int. J. Pressure Vessel Pip.
,
83
(
8
), pp.
593
606
.10.1016/j.ijpvp.2006.04.003
23.
Shlyannikov
,
V. N.
,
2013
, “
T-Stress for Crack Paths in Test Specimens Subject to Mixed Mode Loading
,”
Eng. Fract. Mech.
,
108
, pp.
3
18
.10.1016/j.engfracmech.2013.03.011
24.
Zhao
,
L. G.
,
Tong
,
J.
, and
Byrne
,
J.
,
2001
, “
Stress Intensity Factor K and the Elastic T-Stress for Corner Cracks
,”
Int. J. Fract.
,
109
(
2
), pp.
209
225
.10.1023/A:1011016720630
25.
Li
,
X. F.
,
Liu
,
G. L.
, and
Lee
,
K. Y.
,
2009
, “
Effects of T-Stresses on Fracture Initiation for a Closed Crack in Compression With Frictional Crack Faces
,”
Int. J. Fract.
,
160
(
1
), pp.
19
30
.10.1007/s10704-009-9397-5
26.
Li
,
X. F.
,
Lee
,
K. Y.
, and
Tang
,
G. J.
,
2012
, “
Kink Angle and Fracture Load for an Angled Crack Subjected to Far-Field Compressive Loading
,”
Eng. Fract. Mech.
,
82
, pp.
172
184
.10.1016/j.engfracmech.2011.12.006
27.
Tang
,
S.
,
Huang
,
R.
,
Tang
,
C.
, and
Zhang
,
H.
,
2016
, “
Study on Fracture Criterion Based on the Maximum Tangential Strain Considering the T-Stress
,”
Tumu Gongcheng Xuebao/China Civ. Eng. J.
,
49
, pp.
87
95
.
28.
Liu
,
H.
,
2018
, “
Wing-Crack Initiation Angle: A New Maximum Tangential Stress Criterion by Considering T-Stress
,”
Eng. Fract. Mech.
,
199
, pp.
380
391
.10.1016/j.engfracmech.2018.06.010
29.
Matvienko
,
Y. G.
,
2020
, “
The Effect of Crack-Tip Constraint in Some Problems of Fracture Mechanics
,”
Eng. Fail. Anal.
,
110
, p.
104413
.10.1016/j.engfailanal.2020.104413
30.
Guo
,
W.
,
1993
, “
Elastoplastic Three Dimensional Crack Border Field-I. Singular Structure of the Field
,”
Eng. Fract. Mech.
,
46
(
1
), pp.
93
104
.10.1016/0013-7944(93)90306-D
31.
Guo
,
W.
,
1993
, “
Elastoplastic Three Dimensional Crack Border Field-II. Asymptotic Solution for the Field
,”
Eng. Fract. Mech.
,
46
(
1
), pp.
105
113
.10.1016/0013-7944(93)90307-E
32.
Wanlin
,
G.
,
1995
, “
Elasto-Plastic Three-Dimensional Crack Border Field-III. Fracture Parameters
,”
Eng. Fract. Mech.
,
51
(
1
), pp.
51
71
.10.1016/0013-7944(94)00215-4
33.
She
,
C.
, and
Guo
,
W.
,
2007
, “
The Out-of-Plane Constraint of Mixed-Mode Cracks in Thin Elastic Plates
,”
Int. J. Solids Struct.
,
44
(
9
), pp.
3021
3034
.10.1016/j.ijsolstr.2006.09.002
34.
Shlyannikov
,
V. N.
, and
Tumanov
,
A. V.
,
2011
, “
An Inclined Surface Crack Subject to Biaxial Loading
,”
Int. J. Solids Struct.
,
48
(
11–12
), pp.
1778
1790
.10.1016/j.ijsolstr.2011.02.024
35.
Jin
,
L. Z.
,
Pei
,
Q.
,
Yu
,
C. Y.
,
Chang
,
L.
,
He
,
X. H.
, and
Zhou
,
C. Y.
,
2021
, “
T-Stresses Solution and Out-of-Plane Constraint for Central Cracked Plate (CCP) With I-II Mixed Mode Crack Under Uniaxial Compression
,”
Theor. Appl. Fract. Mech.
,
115
, p.
103040
.10.1016/j.tafmec.2021.103040
36.
Liu
,
H.
, and
Lv
,
S.
,
2019
, “
A Model for the Wing Crack Initiation and Propagation of the Inclined Crack Under Uniaxial Compression
,”
Int. J. Rock Mech. Min. Sci.
,
123
, p.
104121
.10.1016/j.ijrmms.2019.104121
37.
ABAQUS Manual, Version 6.14.SIMULIA, 2014.
38.
Wang
,
Y. Z.
,
Miao
,
X. T.
,
Zhou
,
C. Y.
, and
Lv
,
F.
,
2019
, “
A Study of Txx-Stress on Mixed Mode I-II Semi-Elliptical Surface Crack in Plates
,”
Theor. Appl. Fract. Mech.
,
103
, p.
102305
.10.1016/j.tafmec.2019.102305
39.
Tang
,
S. B.
,
2015
, “
The Effect of T-Stress on the Fracture of Brittle Rock Under Compression
,”
Int. J. Rock Mech. Min. Sci.
,
79
, pp.
86
98
.10.1016/j.ijrmms.2015.06.009
40.
Newman
,
J. C.
, and
Raju
,
I. S.
,
1981
, “
An Empirical Stress-Intensity Factor Equation for the Surface Crack
,”
Eng. Fract. Mech.
,
15
(
1–2
), pp.
185
192
.10.1016/0013-7944(81)90116-8
41.
Leevers
,
P. S.
, and
Radon
,
J. C.
,
1982
, “
Inherent Stress Biaxiality in Various Fracture Specimen Geometries
,”
Int. J. Fract.
,
19
(
4
), pp.
311
325
.10.1007/BF00012486
42.
Ayatollahi
,
M. R.
, and
Saboori
,
B.
,
2015
, “
T-Stress Effects in Mixed Mode I/II/III Brittle Fracture
,”
Eng. Fract. Mech.
,
144
, pp.
32
45
.10.1016/j.engfracmech.2015.06.070
43.
Lajtai
,
E. Z.
,
1974
, “
Brittle Fracture in Compression
,”
Int. J. Fract.
,
10
(
4
), pp.
525
536
.10.1007/BF00155255
44.
Petit
,
J.-P.
, and
Barquins
,
M.
,
1988
, “
Can Natural Faults Propagate Under Mode II Conditions
,”
Techniques
,
7
, pp.
1243
1256
.10.1029/TC007i006p01243
45.
Smith
,
D. J.
,
Ayatollahi
,
M. R.
, and
Pavier
,
M. J.
,
2006
, “
On the Consequences of T-Stress in Elastic Brittle Fracture
,”
Proc. R. Soc. A Math. Phys. Eng. Sci.
,
462
(
2072
), pp.
2415
2437
.10.1098/rspa.2005.1639
46.
Bobet
,
A.
, and
Einstein
,
H. H.
,
1998
, “
Numerical Modeling of Fracture Coalescence in a Model Rock Material
,”
Int. J. Fract.
,
92
(
3
), pp.
221
252
.10.1023/A:1007460316400
47.
Erdogan
,
F.
, and
Sih
,
G. C.
,
1963
, “
On the Crack Extension in Plates Under Plane Loading and Transverse Shear
,”
ASME J. Fluids Eng.
,
85
(
4
), pp.
519
525
.10.1115/1.3656897
48.
ASME, 2010, “ASME Boiler and, Code PV. Part D: Properties (metric). 2010 ASME Boil Press Vessel Code An Int Code 2010; Part D Pro:707–44,” ASME, New York.
You do not currently have access to this content.