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tress-induced

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Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Section: Chapter Questions
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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)
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)
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
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
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