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Effect of microstructure on the mechanical properties of Ti–5Al–5Mo–5V–1Cr–1Fe alloy
Journal Pre-proof Effect of microstructure on the mechanical properties of Ti–5Al–5Mo–5V–1Cr–1Fe alloy Chun Ran, Zemin Sheng, Pengwan Chen, Wangfeng Zhang, Qi Chen PII:
S0921-5093(19)31514-X
DOI:
https://doi.org/10.1016/j.msea.2019.138728
Reference:
MSA 138728
To appear in:
Materials Science & Engineering A
Received Date: 2 September 2019 Revised Date:
22 November 2019
Accepted Date: 23 November 2019
Please cite this article as: C. Ran, Z. Sheng, P. Chen, W. Zhang, Q. Chen, Effect of microstructure on the mechanical properties of Ti–5Al–5Mo–5V–1Cr–1Fe alloy, Materials Science & Engineering A (2019), doi: https://doi.org/10.1016/j.msea.2019.138728. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
1
Effect of microstructure on the mechanical properties of
2
Ti-5Al-5Mo-5V-1Cr-1Fe alloy
3
Chun Rana,b*, Zemin Shengb, Pengwan Chenb†, Wangfeng Zhangc, Qi Chena
4
a. School of Materials Science and Engineering, Beijing Institute of Technology, Beijing
5
100081, China
6
b. State Key Laboratory of Explosion Science and Technology, Beijing Institute of
7
Technology, Beijing 100081, China
8
c. Beijing Institute of Aeronautical Materials, Aero Engine Corporation of China,
9
Beijing 100095, China
10
Abstract—Systematic investigation of microstructure on the dynamic behavior of
11
titanium alloys are seldom reported in the literature. In order to further understand this
12
topic, four types of heat treatment and hot processing are designed, resulting in the
13
following microstructures: e.g., bimodal structure, equiaxed structure, basketweave
14
structure
15
Ti-5Al-5Mo-5V-1Cr-1Fe (Ti-55511) is characterized over a wide range of strain rates
16
and temperatures. The findings of this experimental demonstrate that Ti-55511 alloy is a
17
strain rate and temperature sensitive material. The results also show that the
and
Widmanstatten
structure.
The
mechanical
response
*
Corresponding author. School of Materials Science and Engineering, Beijing Institute of Technology, Beijing
100081, China †
Corresponding author. State Key Laboratory of Explosion Science and Technology, Beijing Institute of
Technology, Beijing 100081, China
E-mail address: [email protected] (Chun Ran) and [email protected] (Pengwan Chen) 1
of
18
Johnson-Cook constitutive equation can be utilized to predict the dynamic behavior of
19
Ti-55511 alloy. Moreover, adiabatic shear susceptibility is affected by microstructures
20
and temperature. Microstructural observation of the samples deformed at high strain
21
rates indicate that the formation of the adiabatic shear band is highly influenced by the
22
microstructure type, and shear failure is the main failure mechanism. To fully utilize the
23
potential of the material, engineers can choose the optimal microstructure to fabricate
24
components according to the service requirements.
25
Keywords: Ti-55511; High strain rate; Temperature; Microstructures; Adiabatic Shear
26
bands
27
1. Introduction
28
Ti-5Al-5Mo-5Al-1Cr-1Fe (Ti-55511), a typical near β titanium alloy, is of great
29
importance in aerospace and automotive industrial applications due to its highly
30
attractive properties, such as high strength-to-weight ratio, excellent combinations of
31
corrosion, toughness and crack growth resistance [1, 2].
32
Compared to Ti-6Al-4V alloy [3, 4], Ti-55511 alloy is superior as an aircraft structural
33
material considering its 15-20% weight reduction due to its higher strength-to-weight
34
ratio [5]. This has attracted increasing attention to Ti-55511 alloy over the past decade [6,
35
7]. The mechanical properties have been extensively studied, including strength, fatigue,
36
creep and fracture toughness. Chen et al. [1] pointed out that the sample with higher
37
rolling reduction exhibits higher strength and better ductility due to the refined grain size 2
38
and fragmentation of the grain boundary α phase. Li et al. [2] found that, due to the
39
evolution of dislocation substructures, the strength of Ti-55511 alloy increased while the
40
ductility decreased with increasing thickness reduction. Ning et al. [8] reported that
41
strain rate sensitivity coefficients increase with increasing deformation temperature. Shi
42
et al. [9, 10] studied the crack initiation behavior and fatigue limit of Ti-55511 alloy with
43
basketweave microstructure. They claimed that the yield strength and subsurface-crack
44
initiation ratio in high cycle fatigue regime can both exert positive influences on its
45
fatigue limit. Moreover, the fracture toughness is sensitive to the microstructure. Lin et
46
al. [11] found that strain rate or deformation amount can reduce the fraction of α. In
47
addition, when deformed at larger deformation amounts or higher strain rates, the
48
original lamellar α phases can easily transform into the spheroidal and bulk α phases.
49
However, the focus of the above-mentioned studies was primarily on low strain rate
50
loading (<100 s-1). In fact, in practical application, components made of Ti-55511 alloy
51
are often loaded at higher strain rate, and the mechanical behavior and failure
52
mechanism of Ti-55511 alloy under high strain rates are still not totally understood
53
though some dynamic experimental investigations have been reported recently [12-15].
54
Moreover, except for these two above mentioned investigations [1, 9], systematic
55
assessments of microstructural effects on mechanical behavior of Ti-55511 alloy are
56
rather scarce, and in dynamic loading conditions are nearly non-existent. In general, the
57
mechanical properties of Ti-55511 alloy are sensitive to the microstructures [16].
58
Therefore, one of the goals of this contribution is to gain deeper insight into 3
59
microstructure effect on the dynamic behavior and failure mechanism of Ti-55511 alloy,
60
and determine the constants of Johnson-Cook constitutive law (J-C model) to enrich the
61
database of J-C model for a larger group of materials. For that purpose, four types of heat
62
treatment and hot processing are designed, and the effect of microstructure on the
63
mechanical behavior of Ti-55511 alloy have systematically studied.
64
A related subject is that of adiabatic shear susceptibility. The term “adiabatic shear
65
band” (ASB) has been widely accepted by scholars since it was first proposed by Zener
66
and Hollomon [17], and ASBs are found in different dynamic loading processes, such as
67
impact deformation, dynamic punching, and ballistic impact etc. ASB is an important
68
failure mechanism of titanium alloys in high strain rate deformation [18]. The classical
69
explanation of ASB formation is the competition between hardening effect (strain and
70
strain rate) and thermal softening effect [17], and a large amount of analytical and
71
numerical work has been dedicated to the subject [19, 20]. Recht [21] noted that
72
“catastrophic shear failure” would occur when materials deformed above the critical
73
cutting speed. Batra and Kim [22] pointed out that shear band begins to grow when the
74
shear stress has dropped to 90% of its maximum value. Culver [23] claimed that thermal
75
instability could occur at a strain value near the static fracture strain. To date, researchers
76
usually using critical strain rate [21], critical stress [22], and critical strain [23] to
77
evaluate the adiabatic shear susceptibility of materials. However, all of the
78
aforementioned criteria are univariate, in which strain effect, strain rate effect, and
79
thermal conductivity were not considered simultaneously. A different viewpoint show 4
80
that the value of dynamic mechanical energy is constant, implying that it is a true
81
material property [24].
82
Hence, the other goal of this contribution is trying to find an effective way to evaluate
83
the adiabatic shear susceptibility for future guidance in titanium alloys processing when
84
subjected to dynamic loading.
85
2. Material and Methods
86
The material used in the present investigation was in the form of forged bar with a
87
diameter of 61 mm from Beijing Institute of Aeronautical Materials, Aero Engine
88
Corporation of China. The chemical composition of the as-received bar is listed in table
89
1, the contents of impurities (wt%) are as follows: 0.02C, 0.03N, 0.01H, 0.1O, 0.15Zr,
90
0.1Si, and readers are referred to Ran et al. [5] for further details of the investigated
91
materials.
92
Table 1 Chemical composition of Ti-55511 alloy (wt%)
Al
Mo
V
Cr
Fe
Ti
5.50
4.82
4.82
1.02
1.02
balance
93
To investigate the microstructural effect on the dynamic behavior of Ti-55511 alloy,
94
four types of heat treatment and hot processing were designed. The bimodal structure
95
was achieved through typical double annealing after forging at 1133 K (below Tβ). For
96
equiaxed structure, it was forged at 1113 K (below Tβ) and then heated to 1123 K for 2
97
h prior to air cooling (AC). For basketweave structure, it was forged at 1183 K (above 5
98
Tβ) and then cooled to 1123 K for 2 h prior to AC. For Widmanstatten structure, it was
99
forged at 1133 K (below Tβ) and then heated to 1173 K for 2 h before furnace cooling
100
(FC). The schemes of processing parameters and corresponding microstructure were
101
summarized in table 2, and the initial microstructures are shown in Fig. 1.
102
Table 2 Heat treatment processing of Ti-55511 alloy Microstructure
Processing parameters
BS
(Tβ-30) K+Double Annealing
ES
(Tβ-50) K+1123 K/2 h+AC
BWS
(Tβ+20) K +1123 K/2 h+AC
WS
(Tβ-30) K+1173 K/2 h+FC
103
Note: BS, ES, BWS, WS shown in the tables indicate bimodal structure, equiaxed structure,
104
basketweave structure and Widmanstatten structure, respectively. Tβ is the β-transus temperature. AC
105
and FC are air cooling and furnace cooling, respectively.
106
107 6
108
Figure 1 Typical microstructures of Ti-55511 alloy (100 X): a) Bimodal structure, b) Equiaxed structure,
109
c) Basketweave structure and d) Widmanstatten structure.
110
As depicted in Fig. 1, the grain boundaries of basketweave structure and
111
Widmanstatten structure are significant, while the grain boundaries of bimodal structure
112
and equiaxed structure are hard to discern.
113
Three types of cylindrical specimens were electro-discharged machined from the bars,
114
i.e. quasi-static tensile specimens with a gage length of 25 mm and a diameter of 5 mm,
115
quasi-static compression samples with a length of 25 mm and a diameter of 10 mm, and
116
dynamic compression samples with a length of 5 mm and a diameter of 5 mm. Based on
117
GB/T 228.1-2010 (Metallic Materials-Tensile testing part I: method of testing at room
118
temperature) [25] and GB/T 7314-2017 (Metallic Materials-Compression testing at
119
room temperature) [26], Quasi-static tensile (0.003 s-1) and compression tests (0.001 s-1)
120
were conducted on cylindrical specimens in an INSTRON 5985 testing machine under
121
displacement-controlled conditions.
122
Dynamic compression tests were carried out at 293 K and elevated temperatures
123
ranging from 373 to 673 K by means of split Hopkinson pressure bar (SHPB) technique
124
(see Fig. 2). For the sake of brevity, we will not describe the technique, and the readers
125
are referred to Chen and Song [27] and Ran et al. [5] for further details. However, the
126
following specific points must be noted. The elevated temperature was regulated by a
127
Delixi TDGC2-3kVA (Hangzhou Zhuochi Instrument Co., Ltd.) controller connected to
128
Nickel-Chromium-Nickel-Silicon thermocouple with a diameter of 1.5 mm, with the 7
129
thermocouple wrapped around the samples. Prior to testing, the maximum temperature
130
of a test sample was reached and kept around 10 minutes to establish a uniform
131
temperature state in the specimens. To reduce friction and specimen barreling, vaseline
132
and molybdenum disulfide were used to lubricate the bar-specimen interfaces at room
133
and elevated temperature, respectively. It should be pointed out that 2~3 samples were
134
tested for each loading condition. Sample
1 2
Furnace
Strain gage εi, εr
Strain gage εt
Striker Incident bar Photo diode
Wheatstone bridge
Transmission bar
Sliding sleeve
Wheatstone bridge
Thermocouple
Pre-amplifier Data acquisition instrument
135 136 137 138 139
140
Figure 2 Schematic representations of the split Hopkinson pressure bar apparatus.
When specimen reaches a state of uniform stress, the strain rate, strain and stress histories in the specimen can be determined by [27, 28]: C0 ε r (t ) Ls
(1)
C0 ε r (t )dt Ls ∫
(2)
ε&(t ) = −2 ε (t ) = 2
2
141 142
A E ε (t ) d σ s (t ) = 0 0 t = 0 E0ε t (t ) As ds
(3)
where A0 is the cross-sectional area of the bars; E0 and C0 are the Young’s modulus and 8
143
elastic bar wave speed in the bar material, respectively; As and Ls are initial
144
cross-sectional area and length of the specimen, respectively; d0 and ds are the diameters
145
of the bar and specimen, respectively. Here εi(t), εr(t) and εt(t) represent incident,
146
reflected and transmitted strain histories in the bars at the specimen ends, respectively.
147
Samples for microstructure observation were sectioned along the axial direction by
148
electrical discharge machining, and metallographic specimens were prepared by
149
standard mechanical grinding, polishing, and etched in Kroll’s reagent. LEICA DMI
150
3000M optical microscope (OM) and HITACHI S-4800 scanning electron microscope
151
(SEM) were utilized to characterize the microstructures.
152
3. Results
153
3.1 Mechanical tests
154
The results of quasi-static (tensile and compression) tests are illustrated in Fig. 3. The
155
small graphs inserted in Fig. 3a is the higher magnification of the dashed region, which
156
shows the Young’s moduli of the four microstructures.
157
As displayed in Fig. 3a, the tensile strength (Rm) of basketweave structure is the
158
highest (1341 MPa), while the Widmanstatten structure is the lowest (1052 MPa). The
159
tensile properties of Ti-55511 alloy are presented in table 3. The measured Young’s
160
moduli of bimodal structure, basketweave structure and Widmanstatten structure are all
161
around 100 GPa, which is about 30 GPa higher than that of equiaxed structure. The Rm
162
and proof strength at εp=0.2% (Rp0.2) for basketweave structure are the highest, which 9
163
can reach around 1341 MPa and 1222 MPa, respectively. For Widmanstatten structure,
164
both of them are the lowest. For the percentage elongation after fracture (A), bimodal
165
structure is almost equal to that of Widmanstatten structure, which is nearly 12% higher
166
than those of basketweave and equiaxed structures. For the percentage reduction of area
167
(Z), Widmanstatten structure is the highest, while basketweave structure is the lowest.
168
Quasi-static compression behavior of Ti-55511 alloy is shown in Fig. 3b. It can be seen
169
that the flow stress of basketweave structure at εp=0.075 is the highest (1480 MPa),
170
which is nearly 270 MPa higher than that of the Widmanstatten structure (1210 MPa).
171
As might be expected, the quasi-static mechanical properties of Ti-55511 alloy are
172
sensitive to the microstructural features. 1500
1500
500
Quasi-static tensile tests
True stress (MPa)
True stress (MPa)
1000
b)
a)
True stress (MPa)
ε=0.003s-1
T=293K
BS BWS ES WS
1000
500
0 0.000
0.005
1000
Quasi-static compression behavior
ε=0.001s
T=293K
-1
BS BWS ES WS
500
0.010
True strain
0 0.00
0.05
0.10
0.15
0 0.00
0.20
0.05
0.10
0.15
0.20
Plastic strain
True strain
173 174
Figure 3 a) Quasi-static tensile behavior and b) Quasi-static compression behavior. BS, BWS, ES, WS
175
shown in the figures indicate bimodal structure, basketweave structure, equiaxed structure, and
176
Widmanstatten structure, respectively.
177
Table 3 The tensile properties of Ti-55511 alloy Tensile properties Microstructure E/GPa Rm/MPa Rp0.2/MPa A% BS
106
1131 10
1070
Z%
17.7 56.4
ES
73
1092
1002
6
26
BWS
100
1341
1222
5.6
17.2
WS
103
1052
934
18.3 38.2
178
Note: E, Rm, Rp0.2, A and Z indicate Young’s modulus, tensile strength, proof strength at 0.2% plastic
179
strain, percentage elongation after fracture and percentage reduction of area, respectively.
180
3.1.1 Strain rate sensitivity
181
To gain deeper insight into strain rate effect, the mechanical behavior of Ti-55511
182
alloy will be discussed at a fixed temperature, e.g. 293 K, as shown in Fig. 4. It should
183
be noted that the results here all displayed using a similar scale to allow for comparison
184
(similarly hereinafter the same below). It was observed that the flow stress of Ti-55511
185
alloys increases with increasing plastic strain when deformed at quasi-static loading
186
(shown in Fig. 3b). By contrast, when deformed at high strain rates, the flow stresses
187
remain nearly constant with increasing plastic strain, indicating a lack of strain
188
hardening.
189
As shown in Fig. 4, the relation between true stress and plastic strain for the four kinds
190
of Ti-55511 alloys deformed at high strain rates is different for each condition. The strain
191
rate sensitivity, β’, can be approximately estimated as the slope of the logarithm of flow
192
stress versus the logarithm of the strain rate [29, 30]:
193
σ ln i σ0 β' = ln(ε&i / ε&0 )
(4)
194
where the quasi-static compressive stresses σ0 and dynamic compressive stresses σi are
195
obtained in tests conducted at constant strain rates ε&0 (0.001 s-1) and ε&i (ranging from
196
350 s-1 to 2900 s-1), respectively. 11
1600
a)
BS
T=293K
b)
1600
ES
True stress (MPa)
True stress (MPa)
T=293K 1400
10-3s-1 900s-1 1200s-1 1500s-1 2000s-1 2200s-1
1200
1000
800 0.00
0.05
1400
1200
1000
0.10
0.15
800 0.00
0.20
10-3s-1 1600s-1 2200s-1
1400s-1 2000s-1 2500s-1
0.05
Plastic strain
0.10
0.15
0.20
Plastic strain
197 c)
1600
True stress (MPa)
True stress (MPa)
1600
1400
1200
10-3s-1 600s-1 -1 900s -1 1200s -1 1600s -1 2000s
T=293K BWS
1000
800 0.00
0.05
0.10
0.15
T=293K
1400
1200
10-3s-1 2000s-1 3100s-1
1000
800 0.00
0.20
Plastic strain
d)
WS
0.05
0.10
1600s-1 2700s-1
0.15
0.20
Plastic strain
198 199
Figure 4 True stress versus plastic strain of Ti-55511 alloy deformed at 293 K and various strain rates:
200
a) Bimodal structure, b) Equiaxed structure, c) Basketweave structure and d) Widmanstatten
201
structure.
202
Fig. 5a shows the flow stress as a function of strain rate. It should be pointed out that
203
the plastic strain is fixed at 5%. It can be seen that the flow stress of Widmanstatten
204
structure remains nearly constant with increasing strain rate, while for the other three
205
structures, the flow stress increases with increasing strain rate. Fig. 5b depicts the strain
206
rate sensitivity as a function of strain rate. As illustrated in Fig. 5b, it can be seen that
207
the strain rate sensitivity is nearly constant for Widmanstatten structure within the
208
range of measured strain rates, and it tends to saturate for basketweave structure. By
209
contrast, for bimodal structure and equiaxed structure, there is a tendency that β’ 12
210
increases with increasing strain rate, especially at higher strain rate. 0.020
εp=5%
a)
Strain rate sensitivity
Flow stress (MPa)
1600
1400
1200
1000
εp=5%
500
BS ES BWS WS Fitting curves
T=293K
1000
1500
2000
2500
0.015
0.010
BS ES BWS WS Fitting curves
0.005
0.000
3000
b)
T=293K
1000
-1
2000
3000
Strain rate (s-1)
Strain rate (s )
211 212
Figure 5. The plot of a) flow stress and b) Strain rate sensitivity as a function of strain rate. Note that
213
the plastic strain (εp) is fixed at 5%.
214
3.1.2 Temperature sensitivity
215 216
To study the effect of the initial test temperatures, the mechanical behavior of Ti-55511 alloy will be discussed at a fixed strain rate, e.g. 2000 s-1, as shown in Fig. 6.
ε=2000 s-1
a)
BS
1500
True stress (MPa)
True stress (MPa)
1500
1000
293 K 373 K 573 K 673 K 500 0.00
0.05
0.10
0.15
b)
1000
293 K 373 K 573 K 673 K 500 0.00
0.20
Plastic strain
ε=2000 s-1 ES
0.05
0.10
Plastic strain
217
13
0.15
0.20
ε=2000 s-1
c)
1000
293 K 373 K 573 K 673 K BWS ε=2000 s
500 0.00
d)
WS
1500
True stress (MPa)
True stress (MPa)
1500
0.05
1000
293 K 373 K 573 K 673 K
-1
0.10
0.15
500 0.00
0.20
Plastic strain
0.05
0.10
0.15
0.20
Plastic strain
218 219
Figure 6 True stress versus plastic strain of Ti-55511 alloy deformed at 2000 s-1: a) Bimodal structure,
220
b) Equiaxed structure, c) Basketweave structure and d) Widmanstatten structure.
221 222 223 224
As displayed in Fig. 6, the flow stress decreases with increasing initial test temperature. Therefore, the thermal softening effect of Ti-55511 alloy is significant. The temperature sensitivity, s, can be approximated as the slope of the logarithm of flow stress at εp=5% versus the logarithm of the initial tests temperature [31]: σT
ln(
225
s=
i
σT )
(5)
0
T ln( i
T0 )
226
where the quasi-static compressive stresses σ T and dynamic compressive stresses σ T
227
are obtained in tests conducted at room (293 K) and elevated temperatures (ranging from
228
373~673 K), respectively. It should be pointed out that the dynamic compression
229
stresses are conducted at the same value of compressive plastic strain (5%).
0
14
i
-0.1
1700
1500 1400 1300 1200
εp=5%
1100
ε=2000 s-1
1000 200
300
400
500
600
BS ES BWS WS Fitting curves
b) Temperature sensitivity
Flow stress (MPa)
1600
BS ES BWS WS Fitting curves
a)
-0.2
-0.3
-0.4
700
300
Initial test temperature (K)
400
500
600
700
Initial test temperature (K)
230 231
Figure 7. The plot of a) Flow stress and b) Temperature sensitivity as a function of the initial test
232
temperature. Note that the plastic strain is fixed at 5%.
233
Fig. 7a shows the flow stress as a function of the initial test temperature. It can be
234
seen that the flow stress of Ti-55511 alloy decreases rapidly with increasing the initial
235
test temperature. Fig. 7b depicts the temperature sensitivity as a function of the initial
236
test temperature. It is interesting to note that the temperature sensitivity varies with
237
initial test temperature. For instance, the temperature sensitivity of Widmanstatten
238
structure decreases rapidly with increasing the initial test temperature; on the contrary,
239
the temperature sensitivity of equiaxed structure increases with increasing the initial test
240
temperature.
241
3.2 Constitutive model
242
The propensity to shear localization can be quantified from the constitutive response.
243
Numerous constitutive equations have been proposed to describe the high strain rate
244
response of materials, e.g. Zerilli-Armstrong model [32], J-C model [33], and
245
Follansbee-Kocks model [34]. Due to the simple multiplication form and various
246
applications, the J-C model was selected to describe the mechanical behavior of 15
247
Ti-55511 alloy. In this work, the temperature rise induced by plastic work is considered.
248
The reference strain rate is 0.001 s-1, detail information about J-C model was addressed
249
in the Appendix. It should be pointed out that the constants of J-C constitutive law are
250
obtained using the least square method.
251
To obtain the best-fit coefficients, based on the above experimental results (Figs. 3, 4
252
and 6), the J-C constants of Ti-55511 alloy were determined by the least square method.
253
The resulting constants of J-C model for the four kinds of Ti-55511 alloys are presented
254
in table 4, and the comparison between the measured, fitting and predicted true stress
255
versus plastic strain curves of Ti-55511 alloy are shown in Fig. 8.
256
Table 4 J-C constitutive constants of Ti-55511 alloys Constitutive constants Microstructures A/MPa B/MPa
C
n
m
0.9
0.8
BS
1190
840
0.009
ES
1100
640
0.014 0.95 0.9
BWS
1300
700
0.012
WS
990
1260
0.022 0.96 1.1
1.1
0.6
257
Figs. 8a~c illustrate the comparison between the measured and fitting true stress
258
versus plastic strain curves. It can be seen that the fitting curves are in good agreement
259
with the experimental results. It should be noted that in this work, experiment data at
260
temperature 673 K, not used for equation fitting, were used for comparing with the
261
prediction of the J-C equation. Fig. 8d shows the comparison between the measured and
262
predicted true stress versus plastic strain at 673 K and 2000 s−1. 16
1600
1600
T=293K
ε=0.001 s-1
1400
True stress (MPa)
True stress (MPa)
1400
1200
BS BWS ES WS J-C model
1000
800 0.00
0.05
0.10
T=293K 1200
1200s-1 2000s-1 2200s-1 J-C model
1000
0.15
800 0.00
0.20
0.05
Plastic strain
263 1600
Bimodal structure
c)
True stress (MPa)
True stress (MPa)
293K 373K 573K J-C model 0.10
BS BWS ES WS J-C model
T=673K
1200
0.05
0.15
0.20
1600
ε=2000 s-1
1400
1000
0.10
Plastic strain
1400
800 0.00
b)
Bimodal structure
a)
ε=2000 s-1
d)
1200
1000
0.15
800 0.00
0.20
0.05
Plastic strain
0.10
0.15
0.20
Plastic strain
264 265
Figure 8 Comparison between the measured and fitting true stress versus plastic strain curves of
266
Ti-55511 alloy: a) Deformed at 293 K and 0.001 s-1, b) Deformed at 293 K and high strain rates, and
267
c) Deformed at a fixed plastic strain and elevated temperatures. d) Comparison between the measured
268
and predicted true stress versus plastic strain curves of Ti-55511 alloy deformed at 673 K and 2000
269
s-1.
270
3.3 Microstructure characteristics of shear localization
271
Fig. 9 depicts the typical microstructures of Ti-55511 alloy deformed at 293 K.
272 17
273
274
275 276
Figure 9 Typical microstructures of Ti-55511 alloy deformed at 293 K: a) Bimodal structure, 900 s-1,
277
b) Bimodal structure, 1500 s-1, c) Equiaxed structure, 1200 s-1, d) Equiaxed structure, 2000 s-1, e)
278
Basketweave structure, 600 s-1, f) Basketweave structure, 1400s-1, g) Widmanstatten structure, 1400
279
s-1 and h) Widmanstatten structure, 2000 s-1.
280
As illustrated in Fig. 9a, comparing with the initial microstructure, no significant
281
changes are observed for bimodal structure deformed at 900 s-1. When the strain rate
282
increases to 1500 s-1, an ASB occurs at the upper left corner of the microstructure
283
(shown in Fig. 9b), and the width of the ASB is around 5 µm. For equiaxed structure, the 18
284
microstructure does not occur significant changes when the strain rate is below 1200 s-1
285
(shown in Fig. 9c), and an ASB with nearly 5.5 µm in width occurs when the strain rate
286
increases to 2000 s-1 (shown in Fig. 9d). As illustrated in Fig. 9e, for basketweave
287
structure, almost nothing has changed when the strain rate is below 600 s-1, while an
288
ASB with closely 1.5 µm in width occurs when the strain rate exceeds 1400 s-1 (shown in
289
Fig. 9f). For Widmanstatten structure, when the strain rate is below 1400 s-1, obvious
290
changes do not occur (shown in Fig. 9g), and an ASB with approximately 1.1 µm in
291
width occurs when the strain rate is 2100 s-1 (shown in Fig. 9h). It is interesting to note
292
that the ASB crosses over the grain during its propagation process (shown in Figs. 9f and
293
9h).
294
The fracture surface was characterized to characterize the fracture mechanism. A
295
sample deformed at room temperature and 1600 s-1, in Fig. 10a, was given as an
296
example. Higher magnification of regions A and B are illustrated in Figs. 10b and 10c,
297
respectively. It can be seen that the fracture surface can be divided into two
298
characteristic zones, namely the smooth region and shear region. The smooth areas are
299
caused by rubbing between the fragment and the fracture surface, and parabolic
300
dimples are the main features of the shear region. As might be expected, similar results
301
have been found in Ti-55511 alloy deformed at elevated temperatures.
19
302 303
Figure 10 Typical fracture morphologies of Ti-55511 alloy deformed at 1600 s-1: a) lower
304
magnification, b) higher magnification of A and c) higher magnification of B.
305
4. Discussion
306
According to the experimental results, Ti-55511 alloy has a slight strain hardening
307
effect (see Fig. 5). Similar findings were observed in Ti-6Al-4V alloy [35, 36]. On the
308
contrary, it is different from that of commercially pure titanium [37]. This discrepancy
309
may come from the presence of the beta phase. As displayed in Fig. 8d, the predicted and
310
experimental results are in good general agreement. As might be expected, the J-C
311
constitutive equation can be used to predict the dynamic behavior of Ti-55511 alloy.
312
Similar results have been found in TC16 titanium alloy [38] and Ti-6Al-4V alloy [39].
313
4.1 Adiabatic shear susceptibility
314
For the sake of brevity, the universal adiabatic shear susceptibility criterion, i.e.
315
critical strain [23], critical stress [22] and critical strain rate [21], of Ti-55511 alloy with
316
bimodal structure will be discussed and shown in Fig. 11.
20
1400
b)
a) Critical stress (MPa)
Critical strain
0.20
293K 373K 573K 673K Fitting curves
0.15
1200
293K 373K 573K 673K 1000
0.10
1000
1500
2000
2500
3000
1.0x103
3500
1.5x103
-1
3.5x103
175
d) Dynamic failure energy (MJ/m3)
c) Critical strain rate (s-1)
3.0x103
Strain rate (s )
1600
1400
1200
1000 200
2.5x103 -1
Strain rate (s )
317
2.0x103
300
400
500
600
150
125
100
75 1.0x103
700
293K 373K 573K 673K
1.5x103
2.0x103
2.5x103
3.0x103
3.5x103
-1
Initial test temperature (K)
Strain rate (s )
318 319
Figure 11 Plot of: a) The failure strain of Ti-55511 alloy as a function of strain rate, b) The failure
320
stress of Ti-55511 alloy as a function of strain rate, c) The failure strain rate of Ti-55511 alloy as a
321
function of initial test temperature and d) The dynamic failure energy of Ti-55511 alloy as a function
322
of strain rate.
323
Fig. 11a shows that the critical strain as a function of strain rate. Apparently, the
324
critical strain varies with strain rate, which is contrary to the critical strain criterion
325
requiring failure strain to remain constant. Hence, it appears that the critical strain
326
criterion is not the best indicator of adiabatic shear failure for Ti-55511 alloy. Figs. 11b
327
and 11c show the critical stress as a function of strain rate and critical strain rate as a
328
function of the initial test temperature, respectively. It can be seen that critical stress and
329
critical strain rate keep almost constant. However, both of the aforementioned criteria
330
are univariate, in which strain effect, strain rate effect, and thermal conductivity etc, 21
331
were not considered simultaneously.
332
The dynamic failure energy (the area of the dynamic stress-strain curve up to
333
instability) was calculated as W0 = ∫0 σ d ε p , where εf stands for the failure plastic strain
334
[24], as illustrated in Fig. 11d. It can be found that the dynamic failure energy is
335
practically constant. This is similar to the properties of Ti-6Al-4V alloy (annealed
336
condition) and AM50 (one kind of magnesium-aluminum alloy), which was reported by
337
Rittel et al. [24]. Hence, the dynamic failure energy was used to elucidate the adiabatic
338
shear susceptibility in this work. It should be noted that the higher of the dynamic failure
339
energy, the "tougher" of the material.
εp
340
The plot of the dynamic failure energy of Ti-55511 alloys as a function of the initial
341
test temperature is illustrated in Fig. 12. It can be seen that, at a fixed test temperature,
342
the dynamic failure energy of basketweave structure is slightly higher than that of
343
equiaxed structure, and the dynamic failure energy of Widmanstatten structure is nearly
344
equal to that of bimodal structure. In addition, the dynamic failure energy of bimodal
345
structure is much higher than that of equiaxed structure, implying that the former is less
346
sensitive to adiabatic shear localization than that of the latter. This is similar to the
347
features of Ti-6Al-2.5Mo-1.5Cr-0.5Fe-0.3Si alloy reported by Sun et al. [40], while it is
348
contrary to that of Ti-6Al-4V alloy reported by Hu [41]. The observed discrepancies can
349
be attributed to the difference in the investigated materials.
22
Dynamic failure energy (MJ/m3)
200
BS BWS ES WS
150
100
50
0
300
400
500
600
700
Initial test temperature (K)
350 351
Figure 12 Plot of the dynamic failure energy of Ti-55511 alloys as a function of the initial test
352
temperature.
353
4.2 Failure mechanism
354
As illustrated in Fig. 9, it can be concluded that the strain rates for ASB initiation are
355
different with microstructures at the same temperature loading condition. Similar
356
phenomenon has been found in TA 15 (a typical near-α titanium alloy) [42]. Hence, it
357
can be concluded that the mechanical properties of materials vary with microstructures.
358
Characterize the effect of microstructure on the mechanical behavior of materials not
359
only possesses an important scientific significance, but also paves the way for future
360
directions in titanium alloys design against dynamic loading in general.
361
As displayed in Fig. 10, it can be seen that smooth areas and dimple areas coexist in
362
the fracture morphologies. This phenomenon is consistent with the works reported by
363
Goods and Brown [43] and Timothy and Hutchings [44]. In addition, parabolic dimples
364
elongated along the shear direction, implying that large plastic deformation takes place. 23
365
In other words, the parabolic dimples on the fracture surface are the remnant of
366
elongated α phase close to the shear band. This result agrees well with the work reported
367
by Bai et al. [36]. Therefore, for Ti-55511 alloy, the collapse of the specimens is
368
attributed to shear failure mechanisms.
369
The mechanical properties of Ti-55511 alloy can be summarized in table 5 on the
370
basis of mechanical behavior analysis. Engineers can choose the optimal
371
microstructure to fabricate components according to service requirements to fully
372
utilize the potential of Ti-55511 alloy. For instance, bimodal structure might be the
373
optimal microstructure for fabricating structural components serving at high strain
374
rates due to its high strength and good ductility.
375
Table 5 Assessment of the mechanical properties of Ti-55511 alloy Assessment rating Property BS
ES
BWS WS
Quasi-static tensile strength
**
***
****
*
Quasi-static compression strength
**
***
*
****
Ductility
**
**** ***
*
Dynamic compression strength
**
***
*
****
Critical stress for ASB initiation
**
***
*
****
Critical strain-rate for ASB initiation **
***
*
***
Strain-rate sensitivity
**
*
***
****
Dynamic failure energy
**
**** ***
Adiabatic shear susceptibility
+++ +
++
* ++++
376
Note: ****: very high, ***: high, **: low and *: very low. ++++: very unsusceptible, +++:
377
unsusceptible, ++: susceptible and +: very susceptible
24
378
5. Conclusions
379
The mechanical and failure behavior of Ti-55511 alloy with four different
380
microstructures subjected to high strain rates at various temperatures has been
381
investigated by means of SHPB technique. According to the experimental findings, the
382
following conclusions can be drawn:
383
The strength of basketweave structure is the highest, while the ductility is the lowest.
384
By contrast, the strength of Widmanstatten structure is the lowest, while the ductility is
385
the highest. The results also suggest that Ti-55511 alloy is a strain rate and temperature
386
sensitive material.
387
Microstructural observation of the samples deformed at high strain rates indicate that
388
the formation of ASB is highly influenced by the microstructure type. Fracture
389
morphologies analyses confirm that relatively smooth areas and ductile dimple areas
390
coexist in the fracture surface, indicating that shear failure is the main failure mechanism
391
for Ti-55511 alloy deformed at compression loading.
392
J-C constitutive equation can be used to predict the dynamic behavior of Ti-55511
393
alloy. To enrich the database of J-C model for a larger group of materials, the constants
394
of J-C constitutive law are obtained using the least square method.
395
For future guidance in materials processing against dynamic loading in general, the
396
adiabatic shear susceptibility of Ti-55511 alloy with four typical microstructures is
397
evaluated based on the dynamic failure energy, and the adiabatic shear susceptibility is
398
mainly affected by microstructure and temperature. The effect of microstructural on the 25
399
mechanical behavior of Ti-55511 alloy is summarized, to fully utilize the potential of the
400
material, engineers can choose the optimal microstructure to fabricate components
401
according to the service requirements. For instance, bimodal structure might be the
402
optimal microstructure for fabricating structural components serving at high strain rates
403
due to its high strength and good ductility.
404
Acknowledgements
405
This work was financially supported by the National Natural Science Foundation of
406
China (Grant number 11472054). One of the authors (C. Ran) recognize the assistance of
407
Miss L. Li and Mr. X. Zhang in conducting the high strain rate experiments. The authors
408
also would like to express their sincere thanks to Professor D. Rittel at Technion Israel
409
Institute of Technology for his useful suggestions.
410
Appendix
411 412
The J-C model can be expressed as, Eq. (A1): m ε& T − Tr σ = ( A + Bε ) 1 + C ln 1 − ε&0 Tm − Tr n p
(A1)
413
where A is the yield stress; B and n represent the strain hardening modulus and strain
414
hardening exponent; C and m are strain rate sensitivity coefficient and thermal softening
415
exponent, respectively. It should be noted that all the five parameters were determined
416
experimentally. Here, T and Tr are the current and reference (293 K) temperatures,
417
respectively; ε&0 is the reference strain rate (0.001 s-1); σ and εp are the flow stress and
418
plastic strain, respectively. 26
419 420 421 422
As elucidated in Eq. (A1), the flow stress can be divided into three terms, namely strain hardening, strain rate hardening and thermal softening, respectively. By substituting the reference condition (T=293K and ε& =0.001 s-1) in Eq. (A1), the J-C model can be rewritten as follows: σ =A + Bε pn
423
(A2)
424
Then, A, B, and n can be determined.
425
By substituting the reference temperature condition (T=293K) in Eq. (A1), the strain
426 427 428
429 430 431 432
433
rate sensitivity coefficient, C, can be calculated as: C=
1 − σ ( A + Bε n ) ln ( ε& ε&0 )
(A3)
Finally, the thermal softening exponent, m, can be determined as: σ ln 1 − ( A + Bε n ) 1 + C ln ε& ε&0 m= ln (T − Tr ) Tm − Tr
(A4)
The plastic work can be incorporated into an adiabatic temperature rise, namely: =
(A5)
Then, the thermal softening exponent, m, can be written as: σ ln 1 − ( A + Bε n ) 1 + C ln ε& ε&0 m' = T −T β ∫ σ d ε r ln × 1 + Tm − Tr ( T − Tr ) × ρ c
27
(A6)
434
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[19] B. Dodd, Y. Bai, Adiabatic Shear Localization: Frontiers and Advances, Elsevier, Oxford, 2012.
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29
Highlights
Four types of heat treatment and hot processing are designed to obtain four typical microstructures of Ti-55511 alloy. High strain rate response of the four typical microstructures at various temperatures is investigated. The formation of the adiabatic shear band is highly influenced by the microstructure type. This study revealed that the adiabatic shear susceptibility is affected by microstructures and temperature.
1 2 3
Author Contributions Section
4 5
Chun Ran: Conceptualization, Data Curation, Investigation, Validation, Formal
6
analysis, Writing-Original draft preparation.
7
Zemin Sheng: Data Curation, Formal analysis.
8
Pengwan Chen: Funding acquisition, Supervision, Project administration.
9
Wangfeng Zhang: Funding acquisition, Resources.
10
Qi Chen: Writing-Review & Editing.
11 12
1
Declaration of Interest Statement
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
S0921-5093(19)31514-X
DOI:
https://doi.org/10.1016/j.msea.2019.138728
Reference:
MSA 138728
To appear in:
Materials Science & Engineering A
Received Date: 2 September 2019 Revised Date:
22 November 2019
Accepted Date: 23 November 2019
Please cite this article as: C. Ran, Z. Sheng, P. Chen, W. Zhang, Q. Chen, Effect of microstructure on the mechanical properties of Ti–5Al–5Mo–5V–1Cr–1Fe alloy, Materials Science & Engineering A (2019), doi: https://doi.org/10.1016/j.msea.2019.138728. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
1
Effect of microstructure on the mechanical properties of
2
Ti-5Al-5Mo-5V-1Cr-1Fe alloy
3
Chun Rana,b*, Zemin Shengb, Pengwan Chenb†, Wangfeng Zhangc, Qi Chena
4
a. School of Materials Science and Engineering, Beijing Institute of Technology, Beijing
5
100081, China
6
b. State Key Laboratory of Explosion Science and Technology, Beijing Institute of
7
Technology, Beijing 100081, China
8
c. Beijing Institute of Aeronautical Materials, Aero Engine Corporation of China,
9
Beijing 100095, China
10
Abstract—Systematic investigation of microstructure on the dynamic behavior of
11
titanium alloys are seldom reported in the literature. In order to further understand this
12
topic, four types of heat treatment and hot processing are designed, resulting in the
13
following microstructures: e.g., bimodal structure, equiaxed structure, basketweave
14
structure
15
Ti-5Al-5Mo-5V-1Cr-1Fe (Ti-55511) is characterized over a wide range of strain rates
16
and temperatures. The findings of this experimental demonstrate that Ti-55511 alloy is a
17
strain rate and temperature sensitive material. The results also show that the
and
Widmanstatten
structure.
The
mechanical
response
*
Corresponding author. School of Materials Science and Engineering, Beijing Institute of Technology, Beijing
100081, China †
Corresponding author. State Key Laboratory of Explosion Science and Technology, Beijing Institute of
Technology, Beijing 100081, China
E-mail address: [email protected] (Chun Ran) and [email protected] (Pengwan Chen) 1
of
18
Johnson-Cook constitutive equation can be utilized to predict the dynamic behavior of
19
Ti-55511 alloy. Moreover, adiabatic shear susceptibility is affected by microstructures
20
and temperature. Microstructural observation of the samples deformed at high strain
21
rates indicate that the formation of the adiabatic shear band is highly influenced by the
22
microstructure type, and shear failure is the main failure mechanism. To fully utilize the
23
potential of the material, engineers can choose the optimal microstructure to fabricate
24
components according to the service requirements.
25
Keywords: Ti-55511; High strain rate; Temperature; Microstructures; Adiabatic Shear
26
bands
27
1. Introduction
28
Ti-5Al-5Mo-5Al-1Cr-1Fe (Ti-55511), a typical near β titanium alloy, is of great
29
importance in aerospace and automotive industrial applications due to its highly
30
attractive properties, such as high strength-to-weight ratio, excellent combinations of
31
corrosion, toughness and crack growth resistance [1, 2].
32
Compared to Ti-6Al-4V alloy [3, 4], Ti-55511 alloy is superior as an aircraft structural
33
material considering its 15-20% weight reduction due to its higher strength-to-weight
34
ratio [5]. This has attracted increasing attention to Ti-55511 alloy over the past decade [6,
35
7]. The mechanical properties have been extensively studied, including strength, fatigue,
36
creep and fracture toughness. Chen et al. [1] pointed out that the sample with higher
37
rolling reduction exhibits higher strength and better ductility due to the refined grain size 2
38
and fragmentation of the grain boundary α phase. Li et al. [2] found that, due to the
39
evolution of dislocation substructures, the strength of Ti-55511 alloy increased while the
40
ductility decreased with increasing thickness reduction. Ning et al. [8] reported that
41
strain rate sensitivity coefficients increase with increasing deformation temperature. Shi
42
et al. [9, 10] studied the crack initiation behavior and fatigue limit of Ti-55511 alloy with
43
basketweave microstructure. They claimed that the yield strength and subsurface-crack
44
initiation ratio in high cycle fatigue regime can both exert positive influences on its
45
fatigue limit. Moreover, the fracture toughness is sensitive to the microstructure. Lin et
46
al. [11] found that strain rate or deformation amount can reduce the fraction of α. In
47
addition, when deformed at larger deformation amounts or higher strain rates, the
48
original lamellar α phases can easily transform into the spheroidal and bulk α phases.
49
However, the focus of the above-mentioned studies was primarily on low strain rate
50
loading (<100 s-1). In fact, in practical application, components made of Ti-55511 alloy
51
are often loaded at higher strain rate, and the mechanical behavior and failure
52
mechanism of Ti-55511 alloy under high strain rates are still not totally understood
53
though some dynamic experimental investigations have been reported recently [12-15].
54
Moreover, except for these two above mentioned investigations [1, 9], systematic
55
assessments of microstructural effects on mechanical behavior of Ti-55511 alloy are
56
rather scarce, and in dynamic loading conditions are nearly non-existent. In general, the
57
mechanical properties of Ti-55511 alloy are sensitive to the microstructures [16].
58
Therefore, one of the goals of this contribution is to gain deeper insight into 3
59
microstructure effect on the dynamic behavior and failure mechanism of Ti-55511 alloy,
60
and determine the constants of Johnson-Cook constitutive law (J-C model) to enrich the
61
database of J-C model for a larger group of materials. For that purpose, four types of heat
62
treatment and hot processing are designed, and the effect of microstructure on the
63
mechanical behavior of Ti-55511 alloy have systematically studied.
64
A related subject is that of adiabatic shear susceptibility. The term “adiabatic shear
65
band” (ASB) has been widely accepted by scholars since it was first proposed by Zener
66
and Hollomon [17], and ASBs are found in different dynamic loading processes, such as
67
impact deformation, dynamic punching, and ballistic impact etc. ASB is an important
68
failure mechanism of titanium alloys in high strain rate deformation [18]. The classical
69
explanation of ASB formation is the competition between hardening effect (strain and
70
strain rate) and thermal softening effect [17], and a large amount of analytical and
71
numerical work has been dedicated to the subject [19, 20]. Recht [21] noted that
72
“catastrophic shear failure” would occur when materials deformed above the critical
73
cutting speed. Batra and Kim [22] pointed out that shear band begins to grow when the
74
shear stress has dropped to 90% of its maximum value. Culver [23] claimed that thermal
75
instability could occur at a strain value near the static fracture strain. To date, researchers
76
usually using critical strain rate [21], critical stress [22], and critical strain [23] to
77
evaluate the adiabatic shear susceptibility of materials. However, all of the
78
aforementioned criteria are univariate, in which strain effect, strain rate effect, and
79
thermal conductivity were not considered simultaneously. A different viewpoint show 4
80
that the value of dynamic mechanical energy is constant, implying that it is a true
81
material property [24].
82
Hence, the other goal of this contribution is trying to find an effective way to evaluate
83
the adiabatic shear susceptibility for future guidance in titanium alloys processing when
84
subjected to dynamic loading.
85
2. Material and Methods
86
The material used in the present investigation was in the form of forged bar with a
87
diameter of 61 mm from Beijing Institute of Aeronautical Materials, Aero Engine
88
Corporation of China. The chemical composition of the as-received bar is listed in table
89
1, the contents of impurities (wt%) are as follows: 0.02C, 0.03N, 0.01H, 0.1O, 0.15Zr,
90
0.1Si, and readers are referred to Ran et al. [5] for further details of the investigated
91
materials.
92
Table 1 Chemical composition of Ti-55511 alloy (wt%)
Al
Mo
V
Cr
Fe
Ti
5.50
4.82
4.82
1.02
1.02
balance
93
To investigate the microstructural effect on the dynamic behavior of Ti-55511 alloy,
94
four types of heat treatment and hot processing were designed. The bimodal structure
95
was achieved through typical double annealing after forging at 1133 K (below Tβ). For
96
equiaxed structure, it was forged at 1113 K (below Tβ) and then heated to 1123 K for 2
97
h prior to air cooling (AC). For basketweave structure, it was forged at 1183 K (above 5
98
Tβ) and then cooled to 1123 K for 2 h prior to AC. For Widmanstatten structure, it was
99
forged at 1133 K (below Tβ) and then heated to 1173 K for 2 h before furnace cooling
100
(FC). The schemes of processing parameters and corresponding microstructure were
101
summarized in table 2, and the initial microstructures are shown in Fig. 1.
102
Table 2 Heat treatment processing of Ti-55511 alloy Microstructure
Processing parameters
BS
(Tβ-30) K+Double Annealing
ES
(Tβ-50) K+1123 K/2 h+AC
BWS
(Tβ+20) K +1123 K/2 h+AC
WS
(Tβ-30) K+1173 K/2 h+FC
103
Note: BS, ES, BWS, WS shown in the tables indicate bimodal structure, equiaxed structure,
104
basketweave structure and Widmanstatten structure, respectively. Tβ is the β-transus temperature. AC
105
and FC are air cooling and furnace cooling, respectively.
106
107 6
108
Figure 1 Typical microstructures of Ti-55511 alloy (100 X): a) Bimodal structure, b) Equiaxed structure,
109
c) Basketweave structure and d) Widmanstatten structure.
110
As depicted in Fig. 1, the grain boundaries of basketweave structure and
111
Widmanstatten structure are significant, while the grain boundaries of bimodal structure
112
and equiaxed structure are hard to discern.
113
Three types of cylindrical specimens were electro-discharged machined from the bars,
114
i.e. quasi-static tensile specimens with a gage length of 25 mm and a diameter of 5 mm,
115
quasi-static compression samples with a length of 25 mm and a diameter of 10 mm, and
116
dynamic compression samples with a length of 5 mm and a diameter of 5 mm. Based on
117
GB/T 228.1-2010 (Metallic Materials-Tensile testing part I: method of testing at room
118
temperature) [25] and GB/T 7314-2017 (Metallic Materials-Compression testing at
119
room temperature) [26], Quasi-static tensile (0.003 s-1) and compression tests (0.001 s-1)
120
were conducted on cylindrical specimens in an INSTRON 5985 testing machine under
121
displacement-controlled conditions.
122
Dynamic compression tests were carried out at 293 K and elevated temperatures
123
ranging from 373 to 673 K by means of split Hopkinson pressure bar (SHPB) technique
124
(see Fig. 2). For the sake of brevity, we will not describe the technique, and the readers
125
are referred to Chen and Song [27] and Ran et al. [5] for further details. However, the
126
following specific points must be noted. The elevated temperature was regulated by a
127
Delixi TDGC2-3kVA (Hangzhou Zhuochi Instrument Co., Ltd.) controller connected to
128
Nickel-Chromium-Nickel-Silicon thermocouple with a diameter of 1.5 mm, with the 7
129
thermocouple wrapped around the samples. Prior to testing, the maximum temperature
130
of a test sample was reached and kept around 10 minutes to establish a uniform
131
temperature state in the specimens. To reduce friction and specimen barreling, vaseline
132
and molybdenum disulfide were used to lubricate the bar-specimen interfaces at room
133
and elevated temperature, respectively. It should be pointed out that 2~3 samples were
134
tested for each loading condition. Sample
1 2
Furnace
Strain gage εi, εr
Strain gage εt
Striker Incident bar Photo diode
Wheatstone bridge
Transmission bar
Sliding sleeve
Wheatstone bridge
Thermocouple
Pre-amplifier Data acquisition instrument
135 136 137 138 139
140
Figure 2 Schematic representations of the split Hopkinson pressure bar apparatus.
When specimen reaches a state of uniform stress, the strain rate, strain and stress histories in the specimen can be determined by [27, 28]: C0 ε r (t ) Ls
(1)
C0 ε r (t )dt Ls ∫
(2)
ε&(t ) = −2 ε (t ) = 2
2
141 142
A E ε (t ) d σ s (t ) = 0 0 t = 0 E0ε t (t ) As ds
(3)
where A0 is the cross-sectional area of the bars; E0 and C0 are the Young’s modulus and 8
143
elastic bar wave speed in the bar material, respectively; As and Ls are initial
144
cross-sectional area and length of the specimen, respectively; d0 and ds are the diameters
145
of the bar and specimen, respectively. Here εi(t), εr(t) and εt(t) represent incident,
146
reflected and transmitted strain histories in the bars at the specimen ends, respectively.
147
Samples for microstructure observation were sectioned along the axial direction by
148
electrical discharge machining, and metallographic specimens were prepared by
149
standard mechanical grinding, polishing, and etched in Kroll’s reagent. LEICA DMI
150
3000M optical microscope (OM) and HITACHI S-4800 scanning electron microscope
151
(SEM) were utilized to characterize the microstructures.
152
3. Results
153
3.1 Mechanical tests
154
The results of quasi-static (tensile and compression) tests are illustrated in Fig. 3. The
155
small graphs inserted in Fig. 3a is the higher magnification of the dashed region, which
156
shows the Young’s moduli of the four microstructures.
157
As displayed in Fig. 3a, the tensile strength (Rm) of basketweave structure is the
158
highest (1341 MPa), while the Widmanstatten structure is the lowest (1052 MPa). The
159
tensile properties of Ti-55511 alloy are presented in table 3. The measured Young’s
160
moduli of bimodal structure, basketweave structure and Widmanstatten structure are all
161
around 100 GPa, which is about 30 GPa higher than that of equiaxed structure. The Rm
162
and proof strength at εp=0.2% (Rp0.2) for basketweave structure are the highest, which 9
163
can reach around 1341 MPa and 1222 MPa, respectively. For Widmanstatten structure,
164
both of them are the lowest. For the percentage elongation after fracture (A), bimodal
165
structure is almost equal to that of Widmanstatten structure, which is nearly 12% higher
166
than those of basketweave and equiaxed structures. For the percentage reduction of area
167
(Z), Widmanstatten structure is the highest, while basketweave structure is the lowest.
168
Quasi-static compression behavior of Ti-55511 alloy is shown in Fig. 3b. It can be seen
169
that the flow stress of basketweave structure at εp=0.075 is the highest (1480 MPa),
170
which is nearly 270 MPa higher than that of the Widmanstatten structure (1210 MPa).
171
As might be expected, the quasi-static mechanical properties of Ti-55511 alloy are
172
sensitive to the microstructural features. 1500
1500
500
Quasi-static tensile tests
True stress (MPa)
True stress (MPa)
1000
b)
a)
True stress (MPa)
ε=0.003s-1
T=293K
BS BWS ES WS
1000
500
0 0.000
0.005
1000
Quasi-static compression behavior
ε=0.001s
T=293K
-1
BS BWS ES WS
500
0.010
True strain
0 0.00
0.05
0.10
0.15
0 0.00
0.20
0.05
0.10
0.15
0.20
Plastic strain
True strain
173 174
Figure 3 a) Quasi-static tensile behavior and b) Quasi-static compression behavior. BS, BWS, ES, WS
175
shown in the figures indicate bimodal structure, basketweave structure, equiaxed structure, and
176
Widmanstatten structure, respectively.
177
Table 3 The tensile properties of Ti-55511 alloy Tensile properties Microstructure E/GPa Rm/MPa Rp0.2/MPa A% BS
106
1131 10
1070
Z%
17.7 56.4
ES
73
1092
1002
6
26
BWS
100
1341
1222
5.6
17.2
WS
103
1052
934
18.3 38.2
178
Note: E, Rm, Rp0.2, A and Z indicate Young’s modulus, tensile strength, proof strength at 0.2% plastic
179
strain, percentage elongation after fracture and percentage reduction of area, respectively.
180
3.1.1 Strain rate sensitivity
181
To gain deeper insight into strain rate effect, the mechanical behavior of Ti-55511
182
alloy will be discussed at a fixed temperature, e.g. 293 K, as shown in Fig. 4. It should
183
be noted that the results here all displayed using a similar scale to allow for comparison
184
(similarly hereinafter the same below). It was observed that the flow stress of Ti-55511
185
alloys increases with increasing plastic strain when deformed at quasi-static loading
186
(shown in Fig. 3b). By contrast, when deformed at high strain rates, the flow stresses
187
remain nearly constant with increasing plastic strain, indicating a lack of strain
188
hardening.
189
As shown in Fig. 4, the relation between true stress and plastic strain for the four kinds
190
of Ti-55511 alloys deformed at high strain rates is different for each condition. The strain
191
rate sensitivity, β’, can be approximately estimated as the slope of the logarithm of flow
192
stress versus the logarithm of the strain rate [29, 30]:
193
σ ln i σ0 β' = ln(ε&i / ε&0 )
(4)
194
where the quasi-static compressive stresses σ0 and dynamic compressive stresses σi are
195
obtained in tests conducted at constant strain rates ε&0 (0.001 s-1) and ε&i (ranging from
196
350 s-1 to 2900 s-1), respectively. 11
1600
a)
BS
T=293K
b)
1600
ES
True stress (MPa)
True stress (MPa)
T=293K 1400
10-3s-1 900s-1 1200s-1 1500s-1 2000s-1 2200s-1
1200
1000
800 0.00
0.05
1400
1200
1000
0.10
0.15
800 0.00
0.20
10-3s-1 1600s-1 2200s-1
1400s-1 2000s-1 2500s-1
0.05
Plastic strain
0.10
0.15
0.20
Plastic strain
197 c)
1600
True stress (MPa)
True stress (MPa)
1600
1400
1200
10-3s-1 600s-1 -1 900s -1 1200s -1 1600s -1 2000s
T=293K BWS
1000
800 0.00
0.05
0.10
0.15
T=293K
1400
1200
10-3s-1 2000s-1 3100s-1
1000
800 0.00
0.20
Plastic strain
d)
WS
0.05
0.10
1600s-1 2700s-1
0.15
0.20
Plastic strain
198 199
Figure 4 True stress versus plastic strain of Ti-55511 alloy deformed at 293 K and various strain rates:
200
a) Bimodal structure, b) Equiaxed structure, c) Basketweave structure and d) Widmanstatten
201
structure.
202
Fig. 5a shows the flow stress as a function of strain rate. It should be pointed out that
203
the plastic strain is fixed at 5%. It can be seen that the flow stress of Widmanstatten
204
structure remains nearly constant with increasing strain rate, while for the other three
205
structures, the flow stress increases with increasing strain rate. Fig. 5b depicts the strain
206
rate sensitivity as a function of strain rate. As illustrated in Fig. 5b, it can be seen that
207
the strain rate sensitivity is nearly constant for Widmanstatten structure within the
208
range of measured strain rates, and it tends to saturate for basketweave structure. By
209
contrast, for bimodal structure and equiaxed structure, there is a tendency that β’ 12
210
increases with increasing strain rate, especially at higher strain rate. 0.020
εp=5%
a)
Strain rate sensitivity
Flow stress (MPa)
1600
1400
1200
1000
εp=5%
500
BS ES BWS WS Fitting curves
T=293K
1000
1500
2000
2500
0.015
0.010
BS ES BWS WS Fitting curves
0.005
0.000
3000
b)
T=293K
1000
-1
2000
3000
Strain rate (s-1)
Strain rate (s )
211 212
Figure 5. The plot of a) flow stress and b) Strain rate sensitivity as a function of strain rate. Note that
213
the plastic strain (εp) is fixed at 5%.
214
3.1.2 Temperature sensitivity
215 216
To study the effect of the initial test temperatures, the mechanical behavior of Ti-55511 alloy will be discussed at a fixed strain rate, e.g. 2000 s-1, as shown in Fig. 6.
ε=2000 s-1
a)
BS
1500
True stress (MPa)
True stress (MPa)
1500
1000
293 K 373 K 573 K 673 K 500 0.00
0.05
0.10
0.15
b)
1000
293 K 373 K 573 K 673 K 500 0.00
0.20
Plastic strain
ε=2000 s-1 ES
0.05
0.10
Plastic strain
217
13
0.15
0.20
ε=2000 s-1
c)
1000
293 K 373 K 573 K 673 K BWS ε=2000 s
500 0.00
d)
WS
1500
True stress (MPa)
True stress (MPa)
1500
0.05
1000
293 K 373 K 573 K 673 K
-1
0.10
0.15
500 0.00
0.20
Plastic strain
0.05
0.10
0.15
0.20
Plastic strain
218 219
Figure 6 True stress versus plastic strain of Ti-55511 alloy deformed at 2000 s-1: a) Bimodal structure,
220
b) Equiaxed structure, c) Basketweave structure and d) Widmanstatten structure.
221 222 223 224
As displayed in Fig. 6, the flow stress decreases with increasing initial test temperature. Therefore, the thermal softening effect of Ti-55511 alloy is significant. The temperature sensitivity, s, can be approximated as the slope of the logarithm of flow stress at εp=5% versus the logarithm of the initial tests temperature [31]: σT
ln(
225
s=
i
σT )
(5)
0
T ln( i
T0 )
226
where the quasi-static compressive stresses σ T and dynamic compressive stresses σ T
227
are obtained in tests conducted at room (293 K) and elevated temperatures (ranging from
228
373~673 K), respectively. It should be pointed out that the dynamic compression
229
stresses are conducted at the same value of compressive plastic strain (5%).
0
14
i
-0.1
1700
1500 1400 1300 1200
εp=5%
1100
ε=2000 s-1
1000 200
300
400
500
600
BS ES BWS WS Fitting curves
b) Temperature sensitivity
Flow stress (MPa)
1600
BS ES BWS WS Fitting curves
a)
-0.2
-0.3
-0.4
700
300
Initial test temperature (K)
400
500
600
700
Initial test temperature (K)
230 231
Figure 7. The plot of a) Flow stress and b) Temperature sensitivity as a function of the initial test
232
temperature. Note that the plastic strain is fixed at 5%.
233
Fig. 7a shows the flow stress as a function of the initial test temperature. It can be
234
seen that the flow stress of Ti-55511 alloy decreases rapidly with increasing the initial
235
test temperature. Fig. 7b depicts the temperature sensitivity as a function of the initial
236
test temperature. It is interesting to note that the temperature sensitivity varies with
237
initial test temperature. For instance, the temperature sensitivity of Widmanstatten
238
structure decreases rapidly with increasing the initial test temperature; on the contrary,
239
the temperature sensitivity of equiaxed structure increases with increasing the initial test
240
temperature.
241
3.2 Constitutive model
242
The propensity to shear localization can be quantified from the constitutive response.
243
Numerous constitutive equations have been proposed to describe the high strain rate
244
response of materials, e.g. Zerilli-Armstrong model [32], J-C model [33], and
245
Follansbee-Kocks model [34]. Due to the simple multiplication form and various
246
applications, the J-C model was selected to describe the mechanical behavior of 15
247
Ti-55511 alloy. In this work, the temperature rise induced by plastic work is considered.
248
The reference strain rate is 0.001 s-1, detail information about J-C model was addressed
249
in the Appendix. It should be pointed out that the constants of J-C constitutive law are
250
obtained using the least square method.
251
To obtain the best-fit coefficients, based on the above experimental results (Figs. 3, 4
252
and 6), the J-C constants of Ti-55511 alloy were determined by the least square method.
253
The resulting constants of J-C model for the four kinds of Ti-55511 alloys are presented
254
in table 4, and the comparison between the measured, fitting and predicted true stress
255
versus plastic strain curves of Ti-55511 alloy are shown in Fig. 8.
256
Table 4 J-C constitutive constants of Ti-55511 alloys Constitutive constants Microstructures A/MPa B/MPa
C
n
m
0.9
0.8
BS
1190
840
0.009
ES
1100
640
0.014 0.95 0.9
BWS
1300
700
0.012
WS
990
1260
0.022 0.96 1.1
1.1
0.6
257
Figs. 8a~c illustrate the comparison between the measured and fitting true stress
258
versus plastic strain curves. It can be seen that the fitting curves are in good agreement
259
with the experimental results. It should be noted that in this work, experiment data at
260
temperature 673 K, not used for equation fitting, were used for comparing with the
261
prediction of the J-C equation. Fig. 8d shows the comparison between the measured and
262
predicted true stress versus plastic strain at 673 K and 2000 s−1. 16
1600
1600
T=293K
ε=0.001 s-1
1400
True stress (MPa)
True stress (MPa)
1400
1200
BS BWS ES WS J-C model
1000
800 0.00
0.05
0.10
T=293K 1200
1200s-1 2000s-1 2200s-1 J-C model
1000
0.15
800 0.00
0.20
0.05
Plastic strain
263 1600
Bimodal structure
c)
True stress (MPa)
True stress (MPa)
293K 373K 573K J-C model 0.10
BS BWS ES WS J-C model
T=673K
1200
0.05
0.15
0.20
1600
ε=2000 s-1
1400
1000
0.10
Plastic strain
1400
800 0.00
b)
Bimodal structure
a)
ε=2000 s-1
d)
1200
1000
0.15
800 0.00
0.20
0.05
Plastic strain
0.10
0.15
0.20
Plastic strain
264 265
Figure 8 Comparison between the measured and fitting true stress versus plastic strain curves of
266
Ti-55511 alloy: a) Deformed at 293 K and 0.001 s-1, b) Deformed at 293 K and high strain rates, and
267
c) Deformed at a fixed plastic strain and elevated temperatures. d) Comparison between the measured
268
and predicted true stress versus plastic strain curves of Ti-55511 alloy deformed at 673 K and 2000
269
s-1.
270
3.3 Microstructure characteristics of shear localization
271
Fig. 9 depicts the typical microstructures of Ti-55511 alloy deformed at 293 K.
272 17
273
274
275 276
Figure 9 Typical microstructures of Ti-55511 alloy deformed at 293 K: a) Bimodal structure, 900 s-1,
277
b) Bimodal structure, 1500 s-1, c) Equiaxed structure, 1200 s-1, d) Equiaxed structure, 2000 s-1, e)
278
Basketweave structure, 600 s-1, f) Basketweave structure, 1400s-1, g) Widmanstatten structure, 1400
279
s-1 and h) Widmanstatten structure, 2000 s-1.
280
As illustrated in Fig. 9a, comparing with the initial microstructure, no significant
281
changes are observed for bimodal structure deformed at 900 s-1. When the strain rate
282
increases to 1500 s-1, an ASB occurs at the upper left corner of the microstructure
283
(shown in Fig. 9b), and the width of the ASB is around 5 µm. For equiaxed structure, the 18
284
microstructure does not occur significant changes when the strain rate is below 1200 s-1
285
(shown in Fig. 9c), and an ASB with nearly 5.5 µm in width occurs when the strain rate
286
increases to 2000 s-1 (shown in Fig. 9d). As illustrated in Fig. 9e, for basketweave
287
structure, almost nothing has changed when the strain rate is below 600 s-1, while an
288
ASB with closely 1.5 µm in width occurs when the strain rate exceeds 1400 s-1 (shown in
289
Fig. 9f). For Widmanstatten structure, when the strain rate is below 1400 s-1, obvious
290
changes do not occur (shown in Fig. 9g), and an ASB with approximately 1.1 µm in
291
width occurs when the strain rate is 2100 s-1 (shown in Fig. 9h). It is interesting to note
292
that the ASB crosses over the grain during its propagation process (shown in Figs. 9f and
293
9h).
294
The fracture surface was characterized to characterize the fracture mechanism. A
295
sample deformed at room temperature and 1600 s-1, in Fig. 10a, was given as an
296
example. Higher magnification of regions A and B are illustrated in Figs. 10b and 10c,
297
respectively. It can be seen that the fracture surface can be divided into two
298
characteristic zones, namely the smooth region and shear region. The smooth areas are
299
caused by rubbing between the fragment and the fracture surface, and parabolic
300
dimples are the main features of the shear region. As might be expected, similar results
301
have been found in Ti-55511 alloy deformed at elevated temperatures.
19
302 303
Figure 10 Typical fracture morphologies of Ti-55511 alloy deformed at 1600 s-1: a) lower
304
magnification, b) higher magnification of A and c) higher magnification of B.
305
4. Discussion
306
According to the experimental results, Ti-55511 alloy has a slight strain hardening
307
effect (see Fig. 5). Similar findings were observed in Ti-6Al-4V alloy [35, 36]. On the
308
contrary, it is different from that of commercially pure titanium [37]. This discrepancy
309
may come from the presence of the beta phase. As displayed in Fig. 8d, the predicted and
310
experimental results are in good general agreement. As might be expected, the J-C
311
constitutive equation can be used to predict the dynamic behavior of Ti-55511 alloy.
312
Similar results have been found in TC16 titanium alloy [38] and Ti-6Al-4V alloy [39].
313
4.1 Adiabatic shear susceptibility
314
For the sake of brevity, the universal adiabatic shear susceptibility criterion, i.e.
315
critical strain [23], critical stress [22] and critical strain rate [21], of Ti-55511 alloy with
316
bimodal structure will be discussed and shown in Fig. 11.
20
1400
b)
a) Critical stress (MPa)
Critical strain
0.20
293K 373K 573K 673K Fitting curves
0.15
1200
293K 373K 573K 673K 1000
0.10
1000
1500
2000
2500
3000
1.0x103
3500
1.5x103
-1
3.5x103
175
d) Dynamic failure energy (MJ/m3)
c) Critical strain rate (s-1)
3.0x103
Strain rate (s )
1600
1400
1200
1000 200
2.5x103 -1
Strain rate (s )
317
2.0x103
300
400
500
600
150
125
100
75 1.0x103
700
293K 373K 573K 673K
1.5x103
2.0x103
2.5x103
3.0x103
3.5x103
-1
Initial test temperature (K)
Strain rate (s )
318 319
Figure 11 Plot of: a) The failure strain of Ti-55511 alloy as a function of strain rate, b) The failure
320
stress of Ti-55511 alloy as a function of strain rate, c) The failure strain rate of Ti-55511 alloy as a
321
function of initial test temperature and d) The dynamic failure energy of Ti-55511 alloy as a function
322
of strain rate.
323
Fig. 11a shows that the critical strain as a function of strain rate. Apparently, the
324
critical strain varies with strain rate, which is contrary to the critical strain criterion
325
requiring failure strain to remain constant. Hence, it appears that the critical strain
326
criterion is not the best indicator of adiabatic shear failure for Ti-55511 alloy. Figs. 11b
327
and 11c show the critical stress as a function of strain rate and critical strain rate as a
328
function of the initial test temperature, respectively. It can be seen that critical stress and
329
critical strain rate keep almost constant. However, both of the aforementioned criteria
330
are univariate, in which strain effect, strain rate effect, and thermal conductivity etc, 21
331
were not considered simultaneously.
332
The dynamic failure energy (the area of the dynamic stress-strain curve up to
333
instability) was calculated as W0 = ∫0 σ d ε p , where εf stands for the failure plastic strain
334
[24], as illustrated in Fig. 11d. It can be found that the dynamic failure energy is
335
practically constant. This is similar to the properties of Ti-6Al-4V alloy (annealed
336
condition) and AM50 (one kind of magnesium-aluminum alloy), which was reported by
337
Rittel et al. [24]. Hence, the dynamic failure energy was used to elucidate the adiabatic
338
shear susceptibility in this work. It should be noted that the higher of the dynamic failure
339
energy, the "tougher" of the material.
εp
340
The plot of the dynamic failure energy of Ti-55511 alloys as a function of the initial
341
test temperature is illustrated in Fig. 12. It can be seen that, at a fixed test temperature,
342
the dynamic failure energy of basketweave structure is slightly higher than that of
343
equiaxed structure, and the dynamic failure energy of Widmanstatten structure is nearly
344
equal to that of bimodal structure. In addition, the dynamic failure energy of bimodal
345
structure is much higher than that of equiaxed structure, implying that the former is less
346
sensitive to adiabatic shear localization than that of the latter. This is similar to the
347
features of Ti-6Al-2.5Mo-1.5Cr-0.5Fe-0.3Si alloy reported by Sun et al. [40], while it is
348
contrary to that of Ti-6Al-4V alloy reported by Hu [41]. The observed discrepancies can
349
be attributed to the difference in the investigated materials.
22
Dynamic failure energy (MJ/m3)
200
BS BWS ES WS
150
100
50
0
300
400
500
600
700
Initial test temperature (K)
350 351
Figure 12 Plot of the dynamic failure energy of Ti-55511 alloys as a function of the initial test
352
temperature.
353
4.2 Failure mechanism
354
As illustrated in Fig. 9, it can be concluded that the strain rates for ASB initiation are
355
different with microstructures at the same temperature loading condition. Similar
356
phenomenon has been found in TA 15 (a typical near-α titanium alloy) [42]. Hence, it
357
can be concluded that the mechanical properties of materials vary with microstructures.
358
Characterize the effect of microstructure on the mechanical behavior of materials not
359
only possesses an important scientific significance, but also paves the way for future
360
directions in titanium alloys design against dynamic loading in general.
361
As displayed in Fig. 10, it can be seen that smooth areas and dimple areas coexist in
362
the fracture morphologies. This phenomenon is consistent with the works reported by
363
Goods and Brown [43] and Timothy and Hutchings [44]. In addition, parabolic dimples
364
elongated along the shear direction, implying that large plastic deformation takes place. 23
365
In other words, the parabolic dimples on the fracture surface are the remnant of
366
elongated α phase close to the shear band. This result agrees well with the work reported
367
by Bai et al. [36]. Therefore, for Ti-55511 alloy, the collapse of the specimens is
368
attributed to shear failure mechanisms.
369
The mechanical properties of Ti-55511 alloy can be summarized in table 5 on the
370
basis of mechanical behavior analysis. Engineers can choose the optimal
371
microstructure to fabricate components according to service requirements to fully
372
utilize the potential of Ti-55511 alloy. For instance, bimodal structure might be the
373
optimal microstructure for fabricating structural components serving at high strain
374
rates due to its high strength and good ductility.
375
Table 5 Assessment of the mechanical properties of Ti-55511 alloy Assessment rating Property BS
ES
BWS WS
Quasi-static tensile strength
**
***
****
*
Quasi-static compression strength
**
***
*
****
Ductility
**
**** ***
*
Dynamic compression strength
**
***
*
****
Critical stress for ASB initiation
**
***
*
****
Critical strain-rate for ASB initiation **
***
*
***
Strain-rate sensitivity
**
*
***
****
Dynamic failure energy
**
**** ***
Adiabatic shear susceptibility
+++ +
++
* ++++
376
Note: ****: very high, ***: high, **: low and *: very low. ++++: very unsusceptible, +++:
377
unsusceptible, ++: susceptible and +: very susceptible
24
378
5. Conclusions
379
The mechanical and failure behavior of Ti-55511 alloy with four different
380
microstructures subjected to high strain rates at various temperatures has been
381
investigated by means of SHPB technique. According to the experimental findings, the
382
following conclusions can be drawn:
383
The strength of basketweave structure is the highest, while the ductility is the lowest.
384
By contrast, the strength of Widmanstatten structure is the lowest, while the ductility is
385
the highest. The results also suggest that Ti-55511 alloy is a strain rate and temperature
386
sensitive material.
387
Microstructural observation of the samples deformed at high strain rates indicate that
388
the formation of ASB is highly influenced by the microstructure type. Fracture
389
morphologies analyses confirm that relatively smooth areas and ductile dimple areas
390
coexist in the fracture surface, indicating that shear failure is the main failure mechanism
391
for Ti-55511 alloy deformed at compression loading.
392
J-C constitutive equation can be used to predict the dynamic behavior of Ti-55511
393
alloy. To enrich the database of J-C model for a larger group of materials, the constants
394
of J-C constitutive law are obtained using the least square method.
395
For future guidance in materials processing against dynamic loading in general, the
396
adiabatic shear susceptibility of Ti-55511 alloy with four typical microstructures is
397
evaluated based on the dynamic failure energy, and the adiabatic shear susceptibility is
398
mainly affected by microstructure and temperature. The effect of microstructural on the 25
399
mechanical behavior of Ti-55511 alloy is summarized, to fully utilize the potential of the
400
material, engineers can choose the optimal microstructure to fabricate components
401
according to the service requirements. For instance, bimodal structure might be the
402
optimal microstructure for fabricating structural components serving at high strain rates
403
due to its high strength and good ductility.
404
Acknowledgements
405
This work was financially supported by the National Natural Science Foundation of
406
China (Grant number 11472054). One of the authors (C. Ran) recognize the assistance of
407
Miss L. Li and Mr. X. Zhang in conducting the high strain rate experiments. The authors
408
also would like to express their sincere thanks to Professor D. Rittel at Technion Israel
409
Institute of Technology for his useful suggestions.
410
Appendix
411 412
The J-C model can be expressed as, Eq. (A1): m ε& T − Tr σ = ( A + Bε ) 1 + C ln 1 − ε&0 Tm − Tr n p
(A1)
413
where A is the yield stress; B and n represent the strain hardening modulus and strain
414
hardening exponent; C and m are strain rate sensitivity coefficient and thermal softening
415
exponent, respectively. It should be noted that all the five parameters were determined
416
experimentally. Here, T and Tr are the current and reference (293 K) temperatures,
417
respectively; ε&0 is the reference strain rate (0.001 s-1); σ and εp are the flow stress and
418
plastic strain, respectively. 26
419 420 421 422
As elucidated in Eq. (A1), the flow stress can be divided into three terms, namely strain hardening, strain rate hardening and thermal softening, respectively. By substituting the reference condition (T=293K and ε& =0.001 s-1) in Eq. (A1), the J-C model can be rewritten as follows: σ =A + Bε pn
423
(A2)
424
Then, A, B, and n can be determined.
425
By substituting the reference temperature condition (T=293K) in Eq. (A1), the strain
426 427 428
429 430 431 432
433
rate sensitivity coefficient, C, can be calculated as: C=
1 − σ ( A + Bε n ) ln ( ε& ε&0 )
(A3)
Finally, the thermal softening exponent, m, can be determined as: σ ln 1 − ( A + Bε n ) 1 + C ln ε& ε&0 m= ln (T − Tr ) Tm − Tr
(A4)
The plastic work can be incorporated into an adiabatic temperature rise, namely: =
(A5)
Then, the thermal softening exponent, m, can be written as: σ ln 1 − ( A + Bε n ) 1 + C ln ε& ε&0 m' = T −T β ∫ σ d ε r ln × 1 + Tm − Tr ( T − Tr ) × ρ c
27
(A6)
434
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29
Highlights
Four types of heat treatment and hot processing are designed to obtain four typical microstructures of Ti-55511 alloy. High strain rate response of the four typical microstructures at various temperatures is investigated. The formation of the adiabatic shear band is highly influenced by the microstructure type. This study revealed that the adiabatic shear susceptibility is affected by microstructures and temperature.
1 2 3
Author Contributions Section
4 5
Chun Ran: Conceptualization, Data Curation, Investigation, Validation, Formal
6
analysis, Writing-Original draft preparation.
7
Zemin Sheng: Data Curation, Formal analysis.
8
Pengwan Chen: Funding acquisition, Supervision, Project administration.
9
Wangfeng Zhang: Funding acquisition, Resources.
10
Qi Chen: Writing-Review & Editing.
11 12
1
Declaration of Interest Statement
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.