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Chapter 19: Problem 24

(a) Briefly explain why thermal stresses may be introduced into a structure by rapid heating or cooling. (b) For cooling, what is the nature of the surface stresses? (c) For heating, what is the nature of the surface stresses?

Short Answer

Expert verified
Answer: Thermal stresses occur when a material experiences a temperature change, causing it to expand or contract. In scenarios of rapid heating or cooling, there is a significant temperature gradient between the structure's surface and its inner core, leading to uneven expansion or contraction, which induces thermal stresses. During cooling, the surface contracts faster than the inner core, resulting in compressive surface stresses. In contrast, during heating, the surface expands faster than the inner core, leading to tensile surface stresses.

Step by step solution

01

(a) Understanding thermal stresses and how they're introduced by rapid heating or cooling

Thermal stresses occur when a material experiences a temperature change, causing it to expand or contract. If the expansion or contraction is constrained (e.g., by fixtures or other components), this results in stresses within the material. In case of rapid heating or cooling, the temperature gradient between the structure's surface and its inner core could be significant, which causes uneven expansion or contraction, leading to induced thermal stresses.
02

(b) Surface stresses during cooling

During cooling, the surface of a structure contracts faster than its inner core, as it loses heat and temperature drops more rapidly at the surface compared to the core. This temperature gradient causes the surface to be in a state of compression, meaning that the surface molecules are being "squeezed" together.
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(c) Surface stresses during heating

On the contrary, during heating, the surface of a structure expands faster than its inner core, as it gains heat and temperature increases more rapidly at the surface compared to the core. In this situation, the temperature gradient leads to the surface being in a state of tension, meaning the surface molecules are being "stretched" apart.

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Most popular questions from this chapter

The constant \(A\) in Equation \(19.2\) is \(12 \pi^{4} R / 5 \theta_{\mathrm{D}}^{3}\), where \(R\) is the gas constant and \(\theta_{\mathrm{D}}\) is the Debye temperature \((\mathrm{K})\). Estimate \(\theta_{\mathrm{D}}\) for copper, given that the specific heat is \(0.78 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\) at \(10 \mathrm{~K}\).

Briefly explain why the thermal conductivities are higher for crystalline than noncrystalline ceramics.

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