Abstract

The ductile fracture process in porous metals due to growth and coalescence of micron scale voids is affected not only by the imposed stress state but also by the distribution of the voids and the material size effect. The objective of this study is to understand the interaction of the inter-void spacing (or ligaments) and the resultant gradient-induced material size effect on void coalescence for a range of imposed stress states. To this end, three-dimensional finite element calculations of unit cell models with a discrete void embedded in a strain gradient-enhanced material matrix are performed. The calculations are carried out for a range of initial inter-void ligament sizes and imposed stress states characterized by fixed values of the stress triaxiality and the Lode parameter. Our results show that in the absence of strain gradient effects on the material response, decreasing the inter-void ligament size results in an increase in the propensity for void coalescence. However, in a strain gradient-enhanced material matrix, the strain gradients harden the material in the inter-void ligament and decrease the effect of inter-void ligament size on the propensity for void coalescence.

References

References
1.
Tekoğlu
,
C.
,
Hutchinson
,
J.
, and
Pardoen
,
T.
,
2015
, “
On Localization and Void Coalescence as a Precursor to Ductile Fracture
,”
Philos. Trans. R. Soc. A: Math., Phys. Eng. Sci.
,
373
(
2038
), p.
20140121
. 10.1098/rsta.2014.0121
2.
Guo
,
T.
, and
Wong
,
W.
,
2018
, “
Void-Sheet Analysis on Macroscopic Strain Localization and Void Coalescence
,”
J. Mech. Phys. Solids.
,
118
, pp.
172
203
. 10.1016/j.jmps.2018.05.002
3.
Liu
,
Y.
,
Zheng
,
X.
,
Osovski
,
S.
, and
Srivastava
,
A.
,
2019
, “
On the Micromechanism of Inclusion Driven Ductile Fracture and Its Implications on Fracture Toughness
,”
J. Mech. Phys. Solids.
,
130
, pp.
21
34
. 10.1016/j.jmps.2019.05.010
4.
Pardoen
,
T.
, and
Hutchinson
,
J.
,
2000
, “
An Extended Model for Void Growth and Coalescence
,”
J. Mech. Phys. Solids.
,
48
(
12
), pp.
2467
2512
. 10.1016/S0022-5096(00)00019-3
5.
Srivastava
,
A.
, and
Needleman
,
A.
,
2013
, “
Void Growth Versus Void Collapse in a Creeping Single Crystal
,”
J. Mech. Phys. Solids.
,
61
(
5
), pp.
1169
1184
. 10.1016/j.jmps.2013.01.006
6.
Torki
,
M.
,
Benzerga
,
A.
, and
Leblond
,
J.-B.
,
2015
, “
On Void Coalescence Under Combined Tension and Shear
,”
ASME J. Appl. Mech.
,
82
(
7
), p.
071005
. 10.1115/1.4030326
7.
Torki
,
M.
,
Tekoglu
,
C.
,
Leblond
,
J.-B.
, and
Benzerga
,
A.
,
2017
, “
Theoretical and Numerical Analysis of Void Coalescence in Porous Ductile Solids Under Arbitrary Loadings
,”
Int. J. Plast.
,
91
, pp.
160
181
. 10.1016/j.ijplas.2017.02.011
8.
Budiansky
,
B.
,
Hutchinson
,
J.
, and
Slutsky
,
S.
,
1982
, “Void Growth and Collapse in Viscous Solids,”,
Mechanics of Solids
,
H. G.
Hopkins
and
M. J.
Sewell
, eds.,
Pergamon Press
,
Oxford
, pp.
13
45
.
9.
Koplik
,
J.
, and
Needleman
,
A.
,
1988
, “
Void Growth and Coalescence in Porous Plastic Solids
,”
Int. J. Solids. Struct.
,
24
(
8
), pp.
835
853
. 10.1016/0020-7683(88)90051-0
10.
Needleman
,
A.
,
Tvergaard
,
V.
, and
Hutchinson
,
J.
,
1992
,
Void Growth in Plastic Solids
,
A. S.
Argon
, ed.,
Springer Verlag
,
New York
, pp.
145
178
.
11.
Benzerga
,
A. A.
, and
Leblond
,
J. -B.
,
2010
,
Ductile Fracture by Void Growth to Coalescence
,
E.
Van der Giessen
and
H.
Aref
, eds., Vol.
44
,
Elsevier
, pp.
169
305
.
12.
Stelmashenko
,
N.
,
Walls
,
M.
,
Brown
,
L.
, and
Milman
,
Y.
,
1993
, “
Microindentations on W and Mo Oriented Single Crystals: An STM Study
,”
Acta. Metall. Mater.
,
41
(
10
), pp.
2855
2865
. 10.1016/0956-7151(93)90100-7
13.
Ma
,
Q.
, and
Clarke
,
D.
,
1995
, “
Size Dependent Hardness of Silver Single Crystals
,”
J. Mater. Res.
,
10
(
4
), pp.
853
863
. 10.1557/JMR.1995.0853
14.
Fleck
,
N.
,
Muller
,
G.
,
Ashby
,
M.
, and
Hutchinson
,
J.
,
1994
, “
Strain Gradient Plasticity: Theory and Experiment
,”
Acta. Metall. Mater.
,
42
(
2
), pp.
475
487
. 10.1016/0956-7151(94)90502-9
15.
Stölken
,
J.
, and
Evans
,
A.
,
1998
, “
A Microbend Test Method for Measuring the Plasticity Length Scale
,”
Acta. Mater.
,
46
(
14
), pp.
5109
5115
. 10.1016/S1359-6454(98)00153-0
16.
Tvergaard
,
V.
, and
Niordson
,
C.
,
2007
, “
Size-Effects in Porous Metals
,”
Modell. Simul. Mater. Sci. Eng.
,
15
(
1
), pp.
51
60
. 10.1088/0965-0393/15/1/E01
17.
Niordson
,
C.
,
2008
, “
Void Growth to Coalescence in a Non-Local Material
,”
Eur. J. Mech. A - Solids
,
27
(
2
), pp.
222
233
. 10.1016/j.euromechsol.2007.07.001
18.
Tvergaard
,
V.
, and
Niordson
,
C.
,
2004
, “
Nonlocal Plasticity Effects on Interaction of Different Size Voids
,”
Int. J. Plast.
,
20
(
1
), pp.
107
120
. 10.1016/S0749-6419(03)00036-6
19.
Li
,
Z.
, and
Steinmann
,
P.
,
2006
, “
Rve-Based Studies on the Coupled Effects of Void Size and Void Shape on Yield Behavior and Void Growth at Micron Scales
,”
Int. J. Plast.
,
22
(
7
), pp.
1195
1216
. 10.1016/j.ijplas.2005.07.004
20.
Monchiet
,
V.
, and
Bonnet
,
G.
,
2013
, “
A Gurson-Type Model Accounting for Void Size Effects
,”
Int. J. Solids. Struct.
,
50
(
2
), pp.
320
327
. 10.1016/j.ijsolstr.2012.09.005
21.
Nielsen
,
K.
,
2016
, “
Size Effects in Void Coalscence
,”
Contributions to the Foundations of Multidisciplinary Research in Mechanics (The 24th International Congress of Theoretical and Applied Mechanics)
,
Montreal, Canada
,
Aug. 22–26
, pp.
2494
2495
.
22.
Holte
,
I.
,
Niordson
,
C. F.
,
Nielsen
,
K. L.
, and
Tvergaard
,
V.
,
2019
, “
Investigation of a Gradient Enriched Gurson-Tvergaard Model for Porous Strain Hardening Materials
,”
Int. J. Mech. A-Solids
,
75
, pp.
472
484
. 10.1016/j.euromechsol.2019.03.001
23.
Gudmundson
,
P.
,
2004
, “
A Unified Treatment of Strain Gradient Plasticity
,”
J. Mech. Phys. Solids.
,
52
(
6
), pp.
1379
1406
. 10.1016/j.jmps.2003.11.002
24.
Fleck
,
N.
, and
Willis
,
J.
,
2009
, “
A Mathematical Basis for Strain-Gradient Plasticity Theory: Part II: Tensorial Plastic Multiplier
,”
J. Mech. Phys. Solids.
,
57
(
7
), pp.
1045
1057
. 10.1016/j.jmps.2009.03.007
25.
Martínez-Pañeda
,
E.
,
Deshpande
,
V.
,
Niordson
,
C.
, and
Fleck
,
N.
,
2019
, “
The Role of Plastic Strain Gradients in the Crack Growth Resistance of Metals
,”
J. Mech. Phys. Solids.
,
126
, pp.
136
150
. 10.1016/j.jmps.2019.02.011
26.
Zhang
,
K.
,
Bai
,
J.
, and
Francois
,
D.
,
2001
, “
Numerical Analysis of the Influence of the Lode Parameter on Void Growth
,”
Int. J. Solids. Struct.
,
38
(
32–33
), pp.
5847
5856
. 10.1016/S0020-7683(00)00391-7
27.
Kim
,
J.
,
Gao
,
X.
, and
Srivatsan
,
T.
,
2004
, “
Modeling of Void Growth in Ductile Solids: Effects of Stress Triaxiality and Initial Porosity
,”
Eng. Fract. Mech.
,
71
(
3
), pp.
379
400
. 10.1016/S0013-7944(03)00114-0
28.
Gao
,
X.
, and
Kim
,
J.
,
2006
, “
Modeling of Ductile Fracture: Significance of Void Coalescence
,”
Int. J. Solids. Struct.
,
43
(
20
), pp.
6277
6293
. 10.1016/j.ijsolstr.2005.08.008
29.
Barsoum
,
I.
, and
Faleskog
,
J.
,
2007
, “
Rupture Mechanisms in Combined Tension and Shear–Micromechanics
,”
Int. J. Solids. Struct.
,
44
(
17
), pp.
5481
5498
. 10.1016/j.ijsolstr.2007.01.010
30.
Bao
,
Y.
, and
Wierzbicki
,
T.
,
2004
, “
On Fracture Locus in the Equivalent Strain and Stress Triaxiality Space
,”
Int. J. Mech. Sci.
,
46
(
1
), pp.
81
98
. 10.1016/j.ijmecsci.2004.02.006
31.
Barsoum
,
I.
, and
Faleskog
,
J.
,
2007
, “
Rupture Mechanisms in Combined Tension and Shear–Experiments
,”
Int. J. Solids. Struct.
,
44
(
6
), pp.
1768
1786
. 10.1016/j.ijsolstr.2006.09.031
32.
Srivastava
,
A.
,
Gopagoni
,
S.
,
Needleman
,
A.
,
Seetharaman
,
V.
,
Staroselsky
,
A.
, and
Banerjee
,
R.
,
2012
, “
Effect of Specimen Thickness on the Creep Response of a Ni-Based Single-Crystal Superalloy
,”
Acta. Mater.
,
60
(
16
), pp.
5697
5711
. 10.1016/j.actamat.2012.06.043
33.
Srivastava
,
A.
, and
Needleman
,
A.
,
2015
, “
Effect of Crystal Orientation on Porosity Evolution in a Creeping Single Crystal
,”
Mech. Mater.
,
90
, pp.
10
29
. 10.1016/j.mechmat.2015.01.015
34.
Tekoglu
,
C.
,
2014
, “
Representative Volume Element Calculations Under Constant Stress Triaxiality, Lode Parameter, and Shear Ratio
,”
Int. J. Solids. Struct.
,
51
(
25–26
), pp.
4544
4553
. 10.1016/j.ijsolstr.2014.09.001
35.
Liu
,
Z.
,
Wong
,
W.
, and
Guo
,
T.
,
2016
, “
Void Behaviors From Low to High Triaxialities: Transition From Void Collapse to Void Coalescence
,”
Int. J. Plast.
,
84
, pp.
183
202
. 10.1016/j.ijplas.2016.05.008
36.
Fuentes-Alonso
,
S.
, and
Martínez-Pañeda
,
E.
,
2020
, “
Fracture in Distortion Gradient Plasticity
,”
Int. J. Eng. Sci.
,
156
, p.
103369
. 10.1016/j.ijengsci.2020.103369
37.
Martínez-Pañeda
,
E.
,
Niordson
,
C. F.
, and
Bardella
,
L.
,
2016
, “
A Finite Element Framework for Distortion Gradient Plasticity With Applications to Bending of Thin Foils
,”
Int. J. Solids. Struct.
,
96
, pp.
288
299
. 10.1016/j.ijsolstr.2016.06.001
38.
Voyiadjis
,
G. Z.
, and
Faghihi
,
D.
,
2012
, “
Thermo-Mechanical Strain Gradient Plasticity With Energetic and Dissipative Length Scales
,”
Int. J. Plast.
,
30
, pp.
218
247
. 10.1016/j.ijplas.2011.10.007
39.
Tekoglu
,
C.
,
Leblond
,
J.-B.
, and
Pardoen
,
T.
,
2012
, “
A Criterion for the Onset of Void Coalescence Under Combined Tension and Shear
,”
J. Mech. Phys. Solids.
,
60
(
7
), pp.
1363
1381
. 10.1016/j.jmps.2012.02.006
40.
Martínez-Pañeda
,
E.
,
Deshpande
,
V. S.
,
Niordson
,
C. F.
, and
Fleck
,
N. A.
,
2019
, “
The Role of Plastic Strain Gradients in the Crack Growth Resistance of Metals
,”
J. Mech. Phys. Solids.
,
126
, pp.
136
150
. 10.1016/j.jmps.2019.02.011
You do not currently have access to this content.