Part A What would be the stress developed in a mullite furnace tube constrained

Question

Part A What would be the stress developed in a mullite furnace tube constrained in the way illustrated in the figure below if it were heated to 1400 Constraint of thermal expansion Fracture due to excessive compressive stress () ree expansion followed by compression TI T1 72 Thermal shock resulting from constraint of uniform thermal expansion. This process is equivalent to free expansion followed by mechanical compression back to the original length Express your answers, separated by a comma, to three significant figures 1ow ,gh= |505,512 MPa, MPa Submit My Answers Give Up Incorrect, Iry Again

Explanation / Answer

Note:
The coefficient of thermal expansion, alpha, for mullite is 5.3 x 10-6 mm/(mmoC)
Young's modulus for mullite if E = 69 x 103 MPa  

The stress developed is the stress necessary to result in a mechanical strain equivalent to the thermal strain:
thermal strain = alpha (deltaT)

thermal strain = [5.3 x 10-6 mm/(mmoC)] [1400-25]oC

thermal strain = 7.2875x10^-3

The mechanical stress necessary to develop this strain:

stress = E strain
stress = (69 x 103 MPa) (7.2875x10^-3)
stress = 502.88 MPa (compressive)

thermal strain = [5.3 x 10-6 mm/(mmoC)] [1400] = 7.420x10^-3

stress = E strain
stress = (69 x 103 MPa) (7.42x10^-3) =511.98 MPa(expansion)

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