Abstract

Torsion tests provide important shear stress and shear strain relationships to reveal the fundamental plastic flow response of a material. Bespoke torsion techniques complemented by digital image correlation are developed to accurately measure the shear stress–strain relationship at quasi-static, medium rate 9/s, and high strain rate above 1000/s. The equipment used includes a screw-driven mechanical system, a hydraulic Instron machine and a Campbell thin-walled tube split Hopkinson torsion bar equipped with an ultrahigh-speed camera. A near alpha Ti3Al2.5V alloy was used as a model material in this study. A four-camera digital image system has been constructed to monitor the material deformation and failure during a low rate torsion test, to gain further insight into plastic deformation of the tubular specimen. Shear stress–strain relationship of the Ti3Al2.5V alloy exhibits noticeable strain rate sensitivity. Observations of the strain hardening rate evolution indicate that the hardening capacity of Ti3Al2.5V is both strain and strain rate dependent. High strain rate torsional stress–strain relationship shows lower strain hardening, compared to the response obtained from a shear compression specimen. The present techniques are demonstrated to be suitable for the measurement of pure shear constitutive relationship, including rate sensitivity and failure of the material.

References

1.
Hopkinson
,
B.
,
1914
, “
A Method of Measuring the Pressure Produced in the Detonation of High Explosives or by the Impact of Bullets
,”
Proc. R. Soc. London, A
,
89
(
612
), pp.
411
413
.
2.
Kolsky
,
H.
,
1949
, “
An Investigation of the Mechanical Properties of Materials at Very High Rates of Loading
,”
Proc. Phys. Soc.
,
62
(
11
), pp.
676
700
.
3.
Harding
,
J.
,
Wood
,
E.
, and
Campbell
,
J.
,
1960
, “
Tensile Testing of Materials at Impact Rates of Strain
,”
J. Mech. Eng. Sci.
,
2
(
2
), pp.
88
96
.
4.
Nemat-Nasser
,
S.
,
Isaacs
,
J. B.
, and
Starrett
,
J. E.
,
1991
, “
Hopkinson Techniques for Dynamic Recovery Experiments
,”
Proc. R. Soc. London, A
,
435
(
1894
), pp.
371
391
.
5.
Field
,
J.
,
Walley
,
S.
,
Proud
,
W.
,
Goldrein
,
H.
, and
Siviour
,
C.
,
2004
, “
Review of Experimental Techniques for High Rate Deformation and Shock Studies
,”
Int. J. Impact Eng.
,
30
(
7
), pp.
725
775
.
6.
Chen
,
W. W.
, and
Song
,
B.
,
2010
,
Split Hopkinson (Kolsky) Bar: Design, Testing and Applications
,
Springer Science & Business Media
,
Berlin/Heidelberg, Germany
.
7.
Espinosa
,
H.
,
Patanella
,
A.
, and
Fischer
,
M.
,
2000
, “
A Novel Dynamic Friction Experiment Using a Modified Kolsky bar Apparatus
,”
Exp. Mech.
,
40
(
2
), pp.
138
153
.
8.
Li
,
P.
,
Siviour
,
C. R.
, and
Petrinic
,
N.
,
2009
, “
The Effect of Strain Rate, Specimen Geometry and Lubrication on Responses of Aluminium AA2024 in Uniaxial Compression Experiments
,”
Exp. Mech.
,
49
(
4
), pp.
587
593
.
9.
Lu
,
F.
,
Lin
,
Y.
,
Wang
,
X.
,
Lu
,
L.
, and
Chen
,
R.
,
2015
, “
A Theoretical Analysis About the Influence of Interfacial Friction in SHPB Tests
,”
Int. J. Impact Eng.
,
79
, pp.
95
101
.
10.
Yang
,
G.
, and
Song
,
Y.
,
1985
, “
The TSHB Technique for Material Testing at High Rates of Strain
,”
Appl. Math. Mech.
,
6
(
5
), pp.
393
399
11.
Baker
,
W. E.
, and
Yew
,
C. H.
,
1966
, “
Strain-Rate Effects in the Propagation of Torsional Plastic Waves
,”
ASME J. Appl. Mech.
,
33
(
4
), pp.
917
923
.
12.
Campbell
,
J.
, and
Dowling
,
A.
,
1970
, “
The Behaviour of Materials Subjected to Dynamic Incremental Shear Loading
,”
J. Mech. Phys. Solids
,
18
(
1
), pp.
43
63
.
13.
Lewis
,
J.
, and
Campbell
,
J.
,
1972
, “
The Development and use of a Torsional Hopkinson-Bar Apparatus
,”
Exp. Mech.
,
12
(
11
), pp.
520
524
.
14.
Duffy
,
J.
,
Campbell
,
J. D.
, and
Hawley
,
R. H.
,
1971
, “
On the Use of a Torsional Split Hopkinson Bar to Study Rate Effects in 1100-0 Aluminum
,”
ASME J. Appl. Mech.
,
38
(
1
), pp.
83
91
.
15.
Nicholas
,
T.
, and
Lawson
,
J. E.
,
1972
, “
On the Determination of the Mechanical Properties of Materials at High Shear-Strain Rates
,”
J. Mech. Phys. Solids
,
20
(
2
), pp.
57
62
.
16.
Nicholas
,
T.
, and
Campbell
,
J.
,
1972
, “
Shear-Strain-Rate Effects in a High-Strength Aluminum Alloy
,”
Exp. Mech.
,
12
(
10
), pp.
441
447
.
17.
Lawson
,
J. E.
, and
Nicholas
,
T.
,
1972
, “
The Dynamic Mechanical Behavior of Titanium in Shear
,”
J. Mech. Phys. Solids
,
20
(
2
), pp.
65
76
.
18.
Fadida
,
R.
,
Rittel
,
D.
, and
Shirizly
,
A.
,
2015
, “
Dynamic Mechanical Behavior of Additively Manufactured Ti6Al4V With Controlled Voids
,”
ASME J. Appl. Mech.
,
82
(
4
), p.
41004
19.
Garg
,
M.
,
Mulliken
,
A. D.
, and
Boyce
,
M. C.
,
2008
, “
Temperature Rise in Polymeric Materials During High Rate Deformation
,”
ASME J. Appl. Mech.
,
75
(
1
), p.
011009
20.
Chen
,
W.
,
Lu
,
F.
,
Frew
,
D. J.
, and
Forrestal
,
M. J.
,
2002
, “
Dynamic Compression Testing of Soft Materials
,”
ASME J. Appl. Mech.
,
69
(
3
), pp.
214
223
.
21.
Li
,
P.
,
Petrinic
,
N.
,
Siviour
,
C. R.
,
Froud
,
R.
, and
Reed
,
J. M.
,
2009
, “
Strain Rate Dependent Compressive Properties of Glass Microballoon Epoxy Syntactic Foams
,”
Mater. Sci. Eng. A
,
515
(
1–2
), pp.
19
25
.
22.
Hou
,
J. P.
,
Ruiz
,
C.
, and
Trojanowski
,
A.
,
2000
, “
Torsion Tests of Thermosetting Resins at Impact Strain Rate and Under Quasi-Static Loading
,”
Mater. Sci. Eng. A
,
283
(
1–2
), pp.
181
188
.
23.
Fellows
,
N. A.
, and
Harding
,
J.
,
2001
, “
Use of High-Speed Photography to Study Localisation During High-Strain-Rate Torsion Testing of Soft Iron
,”
Mater. Sci. Eng. A
,
298
(
1–2
), pp.
90
99
.
24.
Rittel
,
D.
,
Lee
,
S.
, and
Ravichandran
,
G.
,
2002
, “
A Shear-Compression Specimen for Large Strain Testing
,”
Exp. Mech.
,
42
(
1
), pp.
58
64
.
25.
Rittel
,
D.
,
Ravichandran
,
G.
, and
Lee
,
S.
,
2002
, “
Large Strain Constitutive Behavior of OFHC Copper Over a Wide Range of Strain Rates Using the Shear Compression Specimen
,”
Mech. Mater.
,
34
(
10
), pp.
627
642
.
26.
Dorogoy
,
A.
,
Rittel
,
D.
, and
Godinger
,
A.
,
2015
, “
Modification of the Shear-Compression Specimen for Large Strain Testing
,”
Exp. Mech.
,
55
(
9
), pp.
1627
1639
.
27.
Rittel
,
D.
,
Zhang
,
L.
, and
Osovski
,
S.
,
2017
, “
Mechanical Characterization of Impact-Induced Dynamically Recrystallized Nanophase
,”
Phys. Rev. Appl.
,
7
(
4
), p.
044012
.
28.
Leyens
,
C.
, and
Peters
,
M.
,
2003
,
Titanium and Titanium Alloys: Fundamentals and Applications
,
John Wiley & Sons
,
Hoboken, NJ
.
29.
Macdougall
,
D.
, and
Harding
,
J.
,
1998
, “
The Measurement of Specimen Surface Temperature in High-Speed Tension and Torsion Tests
,”
Int. J. Impact Eng.
,
21
(
6
), pp.
473
488
.
30.
Macdougall
,
D.
, and
Harding
,
J.
,
1999
, “
A Constitutive Relation and Failure Criterion for Ti6Al4V Alloy at Impact Rates of Strain
,”
J. Mech. Phys. Solids
,
47
(
5
), pp.
1157
1185
.
31.
Liao
,
S.
, and
Duffy
,
J.
,
1998
, “
Adiabatic Shear Bands in a Ti-6Al-4V Titanium Alloy
,”
J. Mech. Phys. Solids
,
46
(
11
), pp.
2201
2231
.
32.
Chichili
,
D. R.
,
Ramesh
,
K.
, and
Hemker
,
K. J.
,
2004
, “
Adiabatic Shear Localization in α-Titanium: Experiments, Modeling and Microstructural Evolution
,”
J. Mech. Phys. Solids
,
52
(
8
), pp.
1889
1909
.
33.
Yang
,
R.
,
Zhang
,
H.
,
Shen
,
L.
,
Xu
,
Y.
,
Bai
,
Y.
, and
Dodd
,
B.
,
2014
, “
A Modified Split Hopkinson Torsional bar System for Correlated Study of τ–γ Relations, Shear Localization and Microstructural Evolution
,”
Philos. Trans. R. Soc., A
,
372
(
2015
), p.
20130208
.
34.
Zhang
,
L.
,
Rittel
,
D.
, and
Osovski
,
S.
,
2018
, “
Thermo-Mechanical Characterization and Dynamic Failure of Near α and Near β Titanium Alloys
,”
Mater. Sci. Eng., A
,
729
, pp.
94
101
.
35.
Zhang
,
L.
,
Pellegrino
,
A.
,
Townsend
,
D.
, and
Petrinic
,
N.
,
2020
, “
Thermomechanical Constitutive Behaviour of a Near α Titanium Alloy Over a Wide Range of Strain Rates: Experiments and Modelling
,”
Int. J. Mech. Sci.
,
189
, p.
105970
.
36.
Tzibula
,
S.
,
Lovinger
,
Z.
, and
Rittel
,
D.
,
2018
, “
Dynamic Tension of Ductile Polymers: Experimentation and Modelling
,”
Mech. Mater.
,
123
, pp.
30
42
.
37.
Zhang
,
L.
,
Pellegrino
,
A.
,
Townsend
,
D.
, and
Petrinic
,
N.
,
2020
, “
Strain Rate and Temperature Dependent Strain Localization of a Near α Titanium Alloy
,”
Int. J. Impact Eng.
,
145
, p.
103676
.
38.
Pellegrino
,
A.
,
Tagarielli
,
V. L.
,
Gerlach
,
R.
, and
Petrinic
,
N.
,
2015
, “
The Mechanical Response of a Syntactic Polyurethane Foam at low and High Rates of Strain
,”
Int. J. Impact Eng.
,
75
, pp.
214
221
.
39.
Bhujangrao
,
T.
,
Froustey
,
C.
,
Iriondo
,
E.
,
Veiga
,
F.
,
Darnis
,
P.
, and
Mata
,
F. G.
,
2020
, “
Review of Intermediate Strain Rate Testing Devices
,”
Metals
,
10
(
7
), p.
894
.
40.
Zhang
,
L.
,
Pellegrino
,
A.
,
Townsend
,
D.
, and
Petrinic
,
N.
,
2021
, “
Temperature Dependent Dynamic Strain Localization and Failure of Ductile Polymeric Rods Under Large Deformation
,”
Int. J. Mech. Sci.
,
204
, p.
106563
.
41.
Rittel
,
D.
,
1999
, “
On the Conversion of Plastic Work to Heat During High Strain Rate Deformation of Glassy Polymers
,”
Mech. Mater.
,
31
(
2
), pp.
131
139
.
42.
Cowper
,
G. R.
, and
Symonds
,
P. S.
,
1957
, “
Strain-Hardening and Strain-Rate effects in the impact loading of cantilever beams
,” in:
Brown Univ. Tech. Report No. 28
.
43.
Rittel
,
D.
, and
Wang
,
Z.
,
2008
, “
Thermo-Mechanical Aspects of Adiabatic Shear Failure of AM50 and Ti6Al4V Alloys
,”
Mech. Mater.
,
40
(
8
), pp.
629
635
.
44.
Zhou
,
M.
,
Rosakis
,
A. J.
, and
Ravichandran
,
G.
,
1996
, “
Dynamically Propagating Shear Bands in Impact-Loaded Prenotched Plates—I. Experimental Investigations of Temperature Signatures and Propagation Speed
,”
J. Mech. Phys. Solids
,
44
(
6
), pp.
981
1006
.
45.
Rittel
,
D.
,
Zhang
,
L. H.
, and
Osovski
,
S.
,
2017
, “
The Dependence of the Taylor–Quinney Coefficient on the Dynamic Loading Mode
,”
J. Mech. Phys. Solids
,
107
, pp.
96
114
.
46.
Marchand
,
A.
, and
Duffy
,
J.
,
1988
, “
An Experimental Study of the Formation Process of Adiabatic Shear Bands in a Structural Steel
,”
J. Mech. Phys. Solids
,
36
(
3
), pp.
251
283
.
47.
Xu
,
Y.
,
Farbaniec
,
L.
,
Siviour
,
C.
,
Eakins
,
D.
, and
Pellegrino
,
A.
,
2021
, “
The Development of Split Hopkinson Tension-Torsion Bar for the Understanding of Complex Stress States at High Rate
,”
Dynamic Behavior of Materials, Volume 1: Proceedings of the 2020 Annual Conference on Experimental and Applied Mechanics
,
Springer International Publishing
, pp.
89
93
.
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