Poisson's ratio is fundamentally related to stress and strain in materials, quantifying lateral expansion or contraction when a stress is applied. In the case of a free rod subjected to uniform heating, the change in diameter can be accurately calculated using the formula Δd = αΔΤd, where α is the coefficient of linear thermal expansion and ΔΤ is the change in temperature. This approach is valid under the condition that the linear expansion remains small (i.e., ##\frac{\delta }{L} \ll 1##). The discussion emphasizes that while Poisson's ratio is significant under mechanical loading, it does not apply in scenarios without stress, such as thermal expansion.
PREREQUISITESMaterial scientists, mechanical engineers, and anyone involved in thermal analysis and mechanical design will benefit from this discussion, particularly those interested in the effects of temperature on material properties.
Poisson's Ratio is stress related. If you apply a stress in a given direction causing a strain, it quantifies what happens in lateral directions in terms of expansion/contraction for a given material.question4 said:
So in order to find the change of the diameter is it enough to say that : Δd= α*ΔΤ*d ?erobz said:
Well, I believe that formula is for ##\frac{\delta }{L} \ll 1##, but basically...yes.question4 said:
