tress-induced
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
6.8. A shape memory material is in the full martensite phase with 100% temperature martensite and no stress-induced martensite. The temperature of the material is 5◦C. Compute the amount of stress-induced and temperature-induced martensite in the material if the temperature is increased to 35◦C.
![temperatures used earlier in the chapter to model stress-induced transformation. Ex-
perimental evidence demonstrates that a more accurate description of this relationship
is required when the material temperature is initially below the martensitic start tem-
perature. At temperatures below M₁, the critical stresses are assumed to be constant
values, as shown in Figure 6.9. Above M, the critical stresses increase linearly with
the slope C for M, and M, and the slope C₁ for A, and Aƒ.
The transformation equations also require modification to account for the trans-
formation between the different types of martensite. The kinetic law for conversion
from martensite to austenite is
0> A, and C₁(0 - Aƒ) <T<C₁ (0 - A₂)
- 50 {cos [a₁ (0 - A₁-T)] + 1}
Es
ET
§
Es = ESO
ata
0 <M₂
ŠTO -
ST
= STO
The kinetic laws of transformation from austenite to martensite become more elab-
orate, due to the fact that the fraction of stress- and temperature-induced martensite
must also be computed during the process. For temperatures above M₁,
9> M, and T+CM (0-M₂) <T<T+CM (0-M₂)
1- ESO
[T-T-CM (0-M₂)] +
(0 - M₂)]} +
2
ETO
1-550
and for temperatures below M5,
ES =
-COS
Eso
Ero
1-Eso
2
The variable ATE is defined as
Tor-
ATE =
π
TO
and T <T<T
(50 - 5)
(50 - §).
(Es - Eso)
-COS
A
y²-17 (T-17)] +
T-T
(ES - §) + ATE.
Ero
1-Eso
1-ro [cos[am(@_M)] + 1}
2
(6.50)
1 + $SO
2
1+ Eso
2
(6.51)
(6.52)
(6.53)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9990805-875e-498a-8229-128f352d7113%2F2efb506c-d007-4b4f-a26f-988b89c20878%2F62wzor_processed.png&w=3840&q=75)
Transcribed Image Text:temperatures used earlier in the chapter to model stress-induced transformation. Ex-
perimental evidence demonstrates that a more accurate description of this relationship
is required when the material temperature is initially below the martensitic start tem-
perature. At temperatures below M₁, the critical stresses are assumed to be constant
values, as shown in Figure 6.9. Above M, the critical stresses increase linearly with
the slope C for M, and M, and the slope C₁ for A, and Aƒ.
The transformation equations also require modification to account for the trans-
formation between the different types of martensite. The kinetic law for conversion
from martensite to austenite is
0> A, and C₁(0 - Aƒ) <T<C₁ (0 - A₂)
- 50 {cos [a₁ (0 - A₁-T)] + 1}
Es
ET
§
Es = ESO
ata
0 <M₂
ŠTO -
ST
= STO
The kinetic laws of transformation from austenite to martensite become more elab-
orate, due to the fact that the fraction of stress- and temperature-induced martensite
must also be computed during the process. For temperatures above M₁,
9> M, and T+CM (0-M₂) <T<T+CM (0-M₂)
1- ESO
[T-T-CM (0-M₂)] +
(0 - M₂)]} +
2
ETO
1-550
and for temperatures below M5,
ES =
-COS
Eso
Ero
1-Eso
2
The variable ATE is defined as
Tor-
ATE =
π
TO
and T <T<T
(50 - 5)
(50 - §).
(Es - Eso)
-COS
A
y²-17 (T-17)] +
T-T
(ES - §) + ATE.
Ero
1-Eso
1-ro [cos[am(@_M)] + 1}
2
(6.50)
1 + $SO
2
1+ Eso
2
(6.51)
(6.52)
(6.53)
Transcribed Image Text:Table 6.6 Shape memory alloy material properties
Elastic
Properties
YA = 62 GPa
YM = 20 GPa
Transformation
Temperatures
Mf = 10°C
M, = 17°C
A, = 31°C
Af = 44°C
Transformation
Constants
CM = 7 MPa/°C
CA = 11 MPa/°C
Tcr 105 MPa
To
160 MPa
=
Maximum
Recoverable Strain
SL = 0.06
Electrical/Material
Properties
= 66 μΩ · cm
140 J/m²°C.s
resistivity
hc =
p = 6450 kg/m³
Cp = 0.25 kcal/kg. °C
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY