Will Heating and Cooling Affect the Force Needed to Stretch a Yielded Rod?

In summary, the answer to this question depends on the specifics of the material and how the thermal cycle was performed.
  • #1
TSN79
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A small test rod is stretched beyond yielding strength with a force F, and then relieved of tension. If it is now heated and cooled, will a force greater or smaller than F be required to stretch the rod further? Personally I think a smaller force will be required since the rod already has began to give way, but I'm not sure how to explain the physics involved. Can someone help me? :confused:
 
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  • #2
The force F' required for additional strain depends a lot on the original yield point, beyond which plastic or permanent deformation occurs. The yield point depends on the amount of cold-work (dislocation density) in the material or the degree of recrystallization.

Fully-annealed material (no cold-work) has the lowest yield point. The yield point increases with the amount of cold work introduced.

The lower the yield point, the less force required to exceed yield. Below the yield point, the stress ([itex]\sigma[/itex])-strain([itex]\epsilon[/itex])- relationship is essentially linear (Hooke's law), [itex]\sigma[/itex] = E [itex]\epsilon[/itex], where E is the elastic (Young's) modulus.

Beyond the yield point, the stress is given by a more complicated stress-strain law, e.g. [itex]\sigma[/itex] = K E[itex]\epsilon^n[/itex].

If cold working increases the yield point, then more force (greater stress) will be needed to further deform the bar. If the heating is sufficient to anneal the material (i.e. lower the yield point), then less force is necessary. That is one reason that thermo-mechanical treatments do repetitive cold-work/anneal cycles.
 
  • #3
TSN79 said:
A small test rod is stretched beyond yielding strength with a force F, and then relieved of tension. If it is now heated and cooled, will a force greater or smaller than F be required to stretch the rod further? Personally I think a smaller force will be required since the rod already has began to give way, but I'm not sure how to explain the physics involved. Can someone help me? :confused:

I'd say it can go both ways, along the lines of Astronuc. If we consider the material to have strain hardened during the streching beyond yield and the effects of the thermal cycle have not produced recrystallization or any other microstructural recovery the stress will be greater to re-initiate yielding. On the other hand, if recrystallization / annealing occur the stress for further plasticity can be lower than the final stress of the first cycle, and even lower than the initial yield. Since the point is to introduce the thermal cycle I'd go with the latter option, giving an exact answer would require more details.
 

FAQ: Will Heating and Cooling Affect the Force Needed to Stretch a Yielded Rod?

What is the "rod stretching physics problem"?

The rod stretching physics problem is a classic problem in physics that involves determining the amount of force required to stretch a rod of a certain length and width to a specific length. It is used to demonstrate concepts like Hooke's Law and stress-strain relationships.

How do you solve the rod stretching physics problem?

To solve the rod stretching physics problem, you need to use the formula F = kΔL, where F is the force applied, k is the spring constant of the rod, and ΔL is the change in length of the rod. You also need to know the initial length and width of the rod, as well as the desired final length. Plug in these values and solve for the force required.

What are the assumptions made in the rod stretching physics problem?

The rod stretching physics problem assumes that the rod is made of a homogeneous material with a constant spring constant throughout. It also assumes that the rod is stretched in a straight line without any bending or twisting. Additionally, it assumes that the rod is stretched slowly enough for the material to behave elastically.

How does the rod stretching physics problem relate to real-world applications?

The rod stretching physics problem has many real-world applications, such as in engineering and construction. It can be used to determine the amount of force needed to stretch materials like metal rods or cables, which is crucial in designing structures that can withstand different types of forces.

What are some variations of the rod stretching physics problem?

Some variations of the rod stretching physics problem include changing the material of the rod, introducing a weight or load at the end of the rod, or stretching the rod at different angles. These variations can demonstrate how different factors can affect the amount of force required to stretch a rod.

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