Transcript НАЗВАНИЕ ДОКЛАДА

DEPARTMENT OF MECHANICS AND MATHEMATICAL SIMULATION
Tensile testing of Ti-6Al-4V alloy
superplasticity
Sergey Aksenov, Ph.D.
Tarusa
July 09-11, 2013
Introduction
As a titanium alloys have remarkable properties in terms of mechanical
characteristics, low density and elevated corrosion resistance, it is
widely used in many fields including aerospace, automotive,
electronics and even bio-medical industry. At the same time the semifinished parts of titanium alloys are rather expensive in particular
because of the number and complexity of technological operations.
The superplastic forming (SPF) is an effective way to manufacture very
complex thin-shape components, which allows at the same time to
decrease its cost.
The major advantages of SPF:
• The possibility of form a large and complex workpieces
in one operation
• Excellent precision of a finished products
• Fine surface finish of a products
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Typical titanium alloys SPF applications
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Material
Ti-6Al-4V is the most popular titanium alloy which
covered more than 50% of titanium alloy production
Physical properties:
Chemical composition
Density
Melting Range
Specific Heat
C
Fe
N2
O2
Al
V
H2
Ti
4.42
g/cm3
1649±15°C
560
J/(kg °C)
Mechanical properties:
Tensile Strength 1000
Elastic Modulus 114
Mpa
Gpa
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<
<
<
<
0.08%
0.25%
0.05%
0.2%
5.5-6.76%
3.5-4.5%
< 0.015%
Balance
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Constitutive model
The main goal of the mechanical properties investigation for an alloy in the
hot forming state is the establishment of the relationship:
𝜎 = 𝐹 𝜀, 𝜀, 𝑇 ,
where 𝜎 is the flow stress,𝜀 – effective strain rate, ε – effective strain and
𝑇 – temperature.
Backofen equation:
𝜎 = 𝐾𝜀
𝑚
where
K – material constant,
m – strain-rate sensitivity
exponent
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Constitutive model
O. M. Smirnov proposed the rheological model of elasto-viscoplastic (EVP) medium which describes the behavior of
superplastic materials in a wide range of strain rates.
σ0 + k v ε m v
σ = σs
σs + k v ε m v
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Constitutive model
The strain rate sensitivity exponent
𝑑𝑙𝑛(σ)
𝑚𝑣 𝑘𝑣 𝜀 𝑚𝑣 𝜎𝑠 − 𝜎0
𝑚 𝜀 =
=
𝑑𝑙𝑛(𝜀)
𝜎0 + 𝑘𝑣 𝜀 𝑚𝑣 𝜎𝑠 + 𝑘𝑣 𝜀 𝑚𝑣
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Dynamic materials model
Y.V.R.K. Prasad et al. suggested the dynamic materials modeling (DMM)
approach for describing the material behavior under processing conditions by
means of processing maps.
𝝈 = 𝒇(𝜺)
Efficiency of power dissipation:
𝜂=
𝐽
𝐽𝑚𝑎𝑥
2(𝜎𝜀 − 𝐺)
=
𝜎𝜀
Instability criterion (Zingler):
𝜕𝐽
𝜕𝜀
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<
𝐽
𝜀
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Dynamic materials model
Y.V.R.K. Prasad et al.
(𝝈 = 𝑲𝜺𝒎 )
Narayana Murty
(𝝈 = 𝒇(𝜺))
Efficiency of power dissipation
𝜂 = 2𝑚/(𝑚 + 1)
1
𝜂 =2 1−
𝜎𝜀
𝜀
𝜎𝑑 𝜀
0
Instability criterion
𝜕𝑙𝑛 𝑚 1 + 𝑚
𝜕𝑙𝑛𝜀
+𝑚 <0
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2𝑚 < 𝜂
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Experiment
As received Ti-6Al-4V alloy was used in the investigation.
Each specimen was set in clamps of the test machine,
placed in the furnace and heated up to the preset
temperature. Then isothermal tensile-tests were carried
out in the temperature range of 700 – 925 °С.
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Stress-strain rate curves
The experimental (markers) and predicted (solid
lines) stress-strain curves obtained by stepped
tensile-tests
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Stress-strain rate curves
180.00
Ss
160.00
S0
Expon. (S0)
80.00
20.00
Expon.
(Ss)
100.00
y = 1330.9e-0.003x
R² = 0.7359
60.00
40.00
S0
s0 | ss , MPa
s0 | ss , MPa
120.00
Ss
y = 1330.9e-0.003x
R² = 0.7359
Expon. (Ss)
140.00
100.00
1000.00
10.00
y = 343.85e-0.004x
R² = 0.5597
y = 343.85e-0.004x
R² = 0.5597
0.00
1.00
700 725 750 775 800 825 850 875 900 925 950
700 725 750 775 800 825 850 875 900 925 950
T, 0C
T, 0C
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Stress-strain rate curves
3.50E+05
1.00E+06
3.00E+05
1.00E+05
2.50E+05
1.00E+04
K, -
K, -
2.00E+05
y = 5E+10e-0.017x
R² = 0.9465
1.00E+03
1.50E+05
1.00E+02
1.00E+05
y = 5E+10e-0.017x
R² = 0.9465
5.00E+04
0.00E+00
1.00E+01
1.00E+00
700 725 750 775 800 825 850 875 900 925 950
700 725 750 775 800 825 850 875 900 925 950
T, 0C
T, 0C
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Stress-strain rate curves
2.500
2.000
mv, -
1.500
1.000
0.500
0.000
700
725
750
775
800
825
850
875
900
925
950
T, 0C
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Strain rate sensitivity exponent
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Optimum strain rate
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Efficiency of power dissipation
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Processing maps
Narayana Murty
Prasad
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Maximum of 𝜼
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Tension at 825 °C
50
Stress, MPa
40
30
rate 7.57e-4
rate 5.7e-4
rate 3.8e-4
rate 2e-4
rate 1e-4
20
10
0
0
0.2
0.4
0.6
0.8
Strain
1
1.2
1.4
Optimum = 3.8e-4
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Tension at 875 °C
55
50
45
40
Stress, MPa
35
30
25
rate 2.88e-3
rate 1.9e-3
rate 8.54e-4
rate 5e-4
rate 3e-4
20
15
10
5
0
0
0.2
0.4
0.6
0.8
1
1.2
1.6
Optimum = 8.54e-4
Strain
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Tension at 925 °C
45
40
Stress, MPa
35
30
25
rate 4.4e-3
20
rate 2.9e-3
15
rate 1.4e-3
rate 1e-3
10
rate 3e-4
5
0
0.2
0.4
0.6
0.8
1
1.2
1.6
Optimum = 1.4e-3
Strain
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Stress-strain curves
70
Stress [MPa]
60
50
40
30
Temperature [°C]
750
775
800
825
850
875
900
925
950
20
10
0
0
0.5
1
Effective strain [-]
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1.5
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Stress-strain rate curves
70
0.2
0.6
1
stepped
Stress [MPa]
60
50
40
30
20
10
0
650
750
850
Temperature [°C]
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Summary
• The strain-rate ranges which ensure the realization of
superplasticity at forming of Ti-6Al-4V alloy were
determined in the range of temperatures 700-925 °C.
• At the relatively low temperatures 700–775 °C the Ti-6Al-4V
alloy shows all signs of superplasticity if strain-rates do not
exceed 10-5 s-1.
• Maximization of energy dissipation efficiency, which was
calculated by the simplified Prassad formula, leads
automatically to maximize the strain rate sensitivity index 𝑚.
• The method proposed by Narayana Murty, based on the
same theoretical preconditions, but differs in that it does
not use a priori assumptions about the nature of the
exponential curve 𝜎(𝜀) and lays a claim to be more
adequate. At the same, strain rate, which provides maximum
of energy dissipation efficiency calculated according his
approach does not provide the maximum of 𝑚.
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DEPARTMENT OF MECHANICS AND MATHEMATICAL SIMULATION
Thank you for your attention!
Tarusa
July 09-11, 2013