Thermal Stress Analysis in a barrel of a T-80 tank

[UsamaHameed]

Homework Statement

I need to find thermal stresses that will be produced in a tank barrel as a result of firing. First of all, I want to know if theses stresses can be small enough to be neglected? And if not, then how can they be calculated? I basically know the solution but I want to be sure. If I can improve my solution in any way or if there can be another way to solve it, I would be interested.
I don't know the temperature after firing so I would be denoting it with T and initial temperature will be T_o.

Homework Equations

Thermal Stress= elastic modulus * coefficient of expansion * change in temperature

The Attempt at a Solution

Using the
E=205 G Pa
coefficient of expansion = 15.69 x 10^-6 m/m.°C
change in temperature = T-T_o
stress= 205*10⁹ * 15.69 x 10^-6 * (T-T_o)

 

[UsamaHameed]

The barrel is constrained only to the turret only. It is smooth bore, auto-frettaged and chrome-platted. It is made up of a single layer of material properties of which I have provided.