Thermal Expansion Stress

[Seraph042]

I'm designing a system that will thermally cycle a stainless steel substrate up to 1200C from room temperature; right now my design consists of clamping the substrate onto a plate using a bolt head/washer with a nut on the other end of the screw, as shown on the attached figure.

I want to determine the minimum distance I can put the substrate away from the bolt so that buckling will not occur during thermal expansion. The substrate in question is 4"x1"x1/16" (the 1" is into the figure). The bolts I have selected have a 3mm nominal diameter and are made of Monel.

I calculated the critical compressive stress on the substrate to be 22.9 ksi, but I am having trouble incorporating the thermal expansion of both the sample and the bolt in order to determine the compressive stress on the sample. What steps should I take?

Here's some material info I got from matweb.com:

[tex]\alpha_{stainless steel}[/tex]=15.1E-06 /degC, E[tex]_{stainless steel}[/tex]=28.5E+06 psi, S[tex]_{y, stainless steel}[/tex]=89.6E+03 psi

[tex]\alpha_{bolt}[/tex]=13.9E-06 /degC, E[tex]_{bolt}[/tex]=24.5E+06 psi

 

[minger]

When looking at thermal stresses, the typical approach is superposition. Assume that you have a beam fixed between two supports and heat it. You can think of there being two loads: one thermal, and one mechanically imposed by the support.

Typically one would allow a free end to move as if it were not being constrained. You would then calculate the load required to move it back into place.

I hope that gets you on the right track. If you need an example I'm sure someone can provide one.

 

[oswaler]

, S_{y, bolt}=76.5E+03 psi

First, it is important to understand the concept of thermal expansion stress. Thermal expansion stress occurs when a material experiences a change in temperature, causing it to expand or contract. This can create internal stresses within the material, which can lead to deformation or failure if not properly accounted for in the design process.

In your case, you are designing a system that will thermally cycle a stainless steel substrate at high temperatures. This means that both the substrate and the bolt will experience thermal expansion, which can result in compressive stress on the substrate. To determine the minimum distance to prevent buckling, you will need to consider the thermal expansion coefficients, Young's modulus, and yield strength of both the substrate and the bolt.

To calculate the thermal expansion stress on the substrate, you can use the following equation:

\sigma_{th} = \alpha \Delta T E

Where \sigma_{th} is the thermal expansion stress, \alpha is the thermal expansion coefficient, \Delta T is the change in temperature, and E is the Young's modulus.

Using the information provided, the thermal expansion stress on the stainless steel substrate can be calculated as:

\sigma_{th, SS} = (15.1E-06 /degC) (1200C - 25C) (28.5E+06 psi) = 4.03 ksi

Similarly, the thermal expansion stress on the bolt can be calculated as:

\sigma_{th, bolt} = (13.9E-06 /degC) (1200C - 25C) (24.5E+06 psi) = 3.71 ksi

Next, you will need to consider the compressive stress that the bolt will exert on the substrate. This can be calculated using the following equation:

\sigma_{c} = F/A

Where \sigma_{c} is the compressive stress, F is the force applied by the bolt, and A is the cross-sectional area of the substrate.

In this case, the force applied by the bolt can be calculated as:

F = (3mm)^2 \pi (76.5E+03 psi) = 2180 lbf

The cross-sectional area of the substrate can be calculated as:

A = (1/16 in) (1 in) = 0.0625 in^2

Thus, the compressive stress exerted by the bolt