Porous bulk metallic glasses (BMGs) exhibit an excellent combination of superior mechanical properties such as high strength, high resilience, large malleability, and energy absorption capacity. However, a mechanistic understanding of their response under diverse states of stress encountered in practical load-bearing applications is lacking in the literature. In this work, this gap is addressed by performing three-dimensional finite element simulations of porous BMGs subjected to a wide range of tensile and compressive states of stress. A unit cell approach is adopted to investigate the mechanical behavior of a porous BMG having 3% porosity. A parametric study of the effect of stress triaxialities T = 0, ±1/3, ±1, ±2, ±3, and ±∞, which correspond to stress states ranging from pure deviatoric stress to pure hydrostatic stress under tension and compression, is conducted. Apart from the influence of T, the effects of friction parameter, strain-softening parameter and Poisson’s ratio on the mechanics of deformation of porous BMGs are also elucidated. The results are discussed in terms of the simulated stress-strain curves, pore volume fraction evolution, strain to failure, and development of plastic deformation near the pore. The present results have important implications for the design of porous BMG structures.

References

References
1.
Schuh
,
C. A.
,
Hufnagel
,
T. C.
, and
Ramamurty
,
U.
,
2007
, “
Mechanical Behavior of Amorphous Alloys
,”
Acta Mater.
,
55
(
12
), pp.
4067
4109
.
2.
Schroers
,
J.
,
2010
, “
Processing of Bulk Metallic Glass
,”
Adv. Mater.
,
22
(
14
), pp.
1566
1597
.
3.
Hofmann
,
D. C.
,
2013
, “
Bulk Metallic Glasses and Their Composites: A Brief History of Diverging Fields
,”
J. Mater.
2013, p.
517904
.
4.
Telford
,
M.
,
2004
, “
The Case for Bulk Metallic Glass
,”
Mater. Today
,
7
(
3
), pp.
36
43
.
5.
Miller
,
M.
, and
Liaw
,
P.
,
2007
,
Bulk Metallic Glasses: An Overview
,
Springer
,
New York
.
6.
Spaepen
,
F.
,
1977
, “
A Microscopic Mechanism for Steady State Inhomogeneous Flow in Metallic Glasses
,”
Acta Metallurgica
,
25
(
4
), pp.
407
415
.
7.
Pampillo
,
C. A.
,
1975
, “
Flow and Fracture in Amorphous Alloys
,”
J. Mater. Sci.
,
10
(
7
), pp.
1194
1227
.
8.
Alpas
,
A.
, and
Embury
,
J.
,
1988
, “
Flow Localization in Thin Layers of Amorphous Alloys in Laminated Composite Structures
,”
Scr. Metall.
,
22
(
2
), pp.
265
270
.
9.
Leng
,
Y.
, and
Courtney
,
T. H.
,
1989
, “
Some Tensile Properties of Metal-Metallic Glass Laminates
,”
J. Mater. Sci.
,
24
(
6
), pp.
2006
2010
.
10.
Leng
,
Y.
, and
Courtney
,
T. H.
,
1990
, “
Fracture Behavior of Laminated Metal-Metallic Glass Composites
,”
Metall. Trans. A
,
21
(
8
), pp.
2159
2168
.
11.
Leng
,
Y.
, and
Courtney
,
T. H.
,
1991
, “
Multiple Shear Band Formation in Metallic Glasses in Composites
,”
J. Mater. Sci.
,
26
(
3
), pp.
588
592
.
12.
Lewandowski
,
J. J.
,
Wang
,
W. H.
, and
Greer
,
A. L.
,
2005
, “
Intrinsic Plasticity or Brittleness of Metallic Glasses
,”
Philos. Mag. Lett.
,
85
(
2
), pp.
77
87
.
13.
Hofmann
,
D. C.
,
Suh
,
J.-Y.
,
Wiest
,
A.
,
Duan
,
G.
,
Lind
,
M.-L.
,
Demetriou
,
M. D.
, and
Johnson
,
W. L.
,
2008
, “
Designing Metallic Glass Matrix Composites with High Toughness and Tensile Ductility
,”
Nature
,
451
(
7182
), pp.
1085
1089
.
14.
Conner
,
R.
,
Dandliker
,
R.
, and
Johnson
,
W.
,
1998
, “
Mechanical Properties of Tungsten and Steel Fiber Reinforced Zr41.25Ti13.75Cu12.5Ni10Be22.5 Metallic Glass Matrix Composites
,”
Acta Mater.
,
46
(
17
), pp.
6089
6102
.
15.
Kim
,
C. P.
,
Busch
,
R.
,
Masuhr
,
A.
,
Choi-Yim
,
H.
, and
Johnson
,
W. L.
,
2001
, “
Processing of Carbon-Fiber-Reinforced Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 Bulk Metallic Glass Composites
,”
Appl. Phys. Lett.
,
79
(
10
), pp.
1456
1458
.
16.
Chen
,
H.
,
Krause
,
J.
, and
Coleman
,
E.
,
1975
, “
Elastic Constants, Hardness and Their Implications to Flow Properties of Metallic Glasses
,”
J. Non. Cryst. Solids.
,
18
(
2
), pp.
157
171
.
17.
Schroers
,
J.
,
Veazey
,
C.
, and
Johnson
,
W. L.
,
2003
, “
Amorphous Metallic Foam
,”
Appl. Phys. Lett.
,
82
(
3
), pp.
370
372
.
18.
Brothers
,
A. H.
, and
Dunand
,
D. C.
,
2005
, “
Ductile Bulk Metallic Glass Foams
,”
Adv. Mater.
,
17
(
4
), pp.
484
486
.
19.
Brothers
,
A.
, and
Dunand
,
D.
,
2006
, “
Amorphous Metal Foams
,”
Scr. Mater.
,
54
(
4
), pp.
513
520
. Viewpoint set no. 38 on: Frontiers on fabrication and properties of porous and cellular metallic materials.
20.
Wada
,
T.
,
Inoue
,
A.
, and
Greer
,
A. L.
,
2005
, “
Enhancement of Room-Temperature Plasticity in a Bulk Metallic Glass by Finely Dispersed Porosity
,”
Appl. Phys. Lett.
,
86
(
25
), p.
251907
.
21.
Sarac
,
B.
,
Klusemann
,
B.
,
Xiao
,
T.
, and
Bargmann
,
S.
,
2014
, “
Materials by Design: An Experimental and Computational Investigation on the Microanatomy Arrangement of Porous Metallic Glasses
,”
Acta Mater.
,
77
, pp.
411
422
.
22.
Sarac
,
B.
,
Wilmers
,
J.
, and
Bargmann
,
S.
,
2014
, “
Property Optimization of Porous Metallic Glasses Via Structural Design
,”
Mater. Lett.
,
134
, pp.
306
310
.
23.
Wada
,
T.
,
Inoue
,
A.
, and
Greer
,
A. L.
,
2007
, “
Mechanical Properties of Porous Bulk Glassy Alloy Prepared in High-Pressure Hydrogen Atmosphere
,”
Mater. Sci. Eng.: A
,
449–451
, pp.
958
961
.
24.
Gouripriya
,
S.
, and
Tandaiya
,
P.
,
2017
, “
Mechanisms of Compressive Deformation and Failure of Porous Bulk Metallic Glasses
,”
Model. Simul. Mater. Sci. Eng.
,
25
(
4
), p.
045006
.
25.
Smelser
,
R.
, and
Becker
,
R.
,
1989
, “
Abaqus User Subroutines for Material Modeling
,”
ABAQUS Users’ Conference Proceedings
,
Stresa, Italy, Hibbitt, Karlsson, and Sorenson, Inc.
, pp.
207
226
.
26.
Koplik
,
J.
, and
Needleman
,
A.
,
1988
, “
Void Growth and Coalescence in Porous Plastic Solids
,”
Int. J. Solids Struct.
,
24
(
8
), pp.
835
853
.
27.
Biner
,
S.
,
2006
, “
Ductility of Bulk Metallic Glasses and Their Composites With Ductile Reinforcements: A Numerical Study
,”
Acta Mater.
,
54
(
1
), pp.
139
150
.
28.
Tekoglu
,
C.
,
2014
, “
Representative Volume Element Calculations Under Constant Stress Triaxiality, Lode Parameter, and Shear Ratio
,”
Int. J. Solids Struct.
,
51
, pp.
4544
4553
.
29.
Needleman
,
A.
, and
Tvergaard
,
V.
,
1984
, “
An Analysis of Ductile Rupture in Notched Bars
,”
J. Mech. Phys. Solids
,
32
(
6
), pp.
461
490
.
30.
McMeeking
,
R.
,
1977
, “
Finite Deformation Analysis of Crack-Tip Opening in Elastic-Plastic Materials and Implications for Fracture
,”
J. Mech. Phys. Solids
,
25
(
5
), pp.
357
381
.
31.
Jeong
,
H.-Y.
,
2002
, “
A New Yield Function and a Hydrostatic Stress-Controlled Void Nucleation Model for Porous Solids With Pressure-Sensitive Matrices
,”
Int. J. Solids Struct.
,
39
(
5
), pp.
1385
1403
.
32.
Worswick
,
M.
, and
Pick
,
R.
,
1990
, “
Void Growth and Constitutive Softening in a Periodically Voided Solid
,”
J. Mech. Phys. Solids
,
38
(
5
), pp.
601
625
.
33.
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
.
34.
Srivastava
,
A.
, and
Needleman
,
A.
,
2015
, “
Effect of Crystal Orientation on Porosity Evolution in a Creeping Single Crystal
,”
Mech. Mater.
,
90
, pp.
10
29
.
Proceedings of the IUTAM Symposium on Micromechanics of Defects in Solids
.
35.
Ling
,
C.
,
Besson
,
J.
,
Forest
,
S.
,
Tanguy
,
B.
,
Latourte
,
F.
, and
Bosso
,
E.
,
2016
, “
An Elastoviscoplastic Model for Porous Single Crystals at Finite Strains and its Assessment Based on Unit Cell Simulations
,”
Int. J. Plasticit.
,
84
, pp.
58
87
.
36.
Alves
,
J.
, and
Cazacu
,
O.
,
2015
, “
Micromechanical Study of the Dilatational Response of Porous Solids with Pressure-Insensitive Matrix Displaying Tension-Compression Asymmetry
,”
Eur. J. Mech. - A/Solids
,
51
, pp.
44
54
.
37.
Anand
,
L.
, and
Su
,
C.
,
2005
, “
A Theory For Amorphous Viscoplastic Materials Undergoing Finite Deformations, With Application to Metallic Glasses
,”
J. Mech. Phys. Solids
,
53
(
6
), pp.
1362
1396
.
38.
Tandaiya
,
P.
,
Ramamurty
,
U.
, and
Narasimhan
,
R.
,
2011
, “
On Numerical Implementation of an Isotropic Elastic-Viscoplastic Constitutive Model for Bulk Metallic Glasses
,”
Model. Simul. Mater. Sci. Eng.
,
19
(
1
), p.
015002
.
39.
Anand
,
L.
,
1979
, “
On H. Hencky’s Approximate Strain-Energy Function for Moderate Deformations
,”
ASME J. Appl. Mech.
,
46
(
1
), pp.
78
82
.
40.
ABAQUS/Standard User’s Manual, Version 6.14. Simulia.
41.
Jang
,
D.
, and
Greer
,
J. R.
,
Mar. 2010
, “
Transition from a Strong-Yet-Brittle to a Stronger-And-Ductile State by Size Reduction of Metallic Glasses
,”
Nat. Mater.
,
9
(
3
), pp.
215
219
.
42.
Su
,
C.
, and
Anand
,
L.
,
2006
, “
Plane Strain Indentation of A Zr-Based Metallic Glass: Experiments and Numerical Simulation
,”
Acta Mater.
,
54
(
1
), pp.
179
189
.
43.
Tandaiya
,
P.
,
Narasimhan
,
R.
, and
Ramamurty
,
U.
,
2007
, “
Mode I Crack Tip Fields in Amorphous Materials With Application to Metallic Glasses
,”
Acta Mater.
,
55
(
19
), pp.
6541
6552
.
44.
Tandaiya
,
P.
,
Ramamurty
,
U.
,
Ravichandran
,
G.
, and
Narasimhan
,
R.
,
2008
, “
Effect of Poisson’S Ratio on Crack Tip Fields And Fracture Behavior of Metallic Glasses
,”
Acta Mater.
,
56
(
20
), pp.
6077
6086
.
45.
Tandaiya
,
P.
,
Ramamurty
,
U.
, and
Narasimhan
,
R.
,
2009
, “
Mixed Mode (I and II) Crack Tip Fields in Bulk Metallic Glasses
,”
J. Mech. Phys. Solids
,
57
(
11
), pp.
1880
1897
.
46.
Tandaiya
,
P.
,
Narasimhan
,
R.
, and
Ramamurty
,
U.
,
2013
, “
On The Mechanism and the Length Scales Involved in the Ductile Fracture of a Bulk Metallic Glass
,”
Acta Mater.
,
61
(
5
), pp.
1558
1570
.
47.
Narayan
,
R.
,
Tandaiya
,
P.
,
Garrett
,
G.
,
Demetriou
,
M.
,
Ramamurty
,
U.
,
2015
, “
On the Variability in Fracture Toughness of ’Ductile’ Bulk Metallic Glasses
,”
Scr. Mater.
,
102
, pp.
75
78
.
48.
Raut
,
D.
,
Narayan
,
R.
,
Tandaiya
,
P.
, and
Ramamurty
,
U.
,
2018
, “
Temperature-Dependence of Mode I Fracture Toughness of a Bulk Metallic Glass
,”
Acta Mater.
,
144
, pp.
325
336
.
49.
Tandaiya
,
P. U.
,
2009
, “
Finite Element and Experimental Studies on Fracture Behavior of Bulk Metallic Glasses
”. PhD thesis,
Indian Institute of Science Bangalore
.
50.
Shete
,
M. K.
,
Dutta
,
T.
,
Singh
,
I.
,
Narasimhan
,
R.
, and
Ramamurty
,
U.
,
2017
, “
Tensile Stress-Strain Response of Metallic Glass Matrix Composites Reinforced with Crystalline Dendrites: Role of Dendrite Morphology
,”
Intermetallics
,
83
, pp.
70
82
.
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