Thermal Behavior of Materials

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Thermal Behavior of Materials. ME 2105 Dr. R. Lindeke. Some Definitions. Heat Capacity: the amount of heat (energy) required to raise a fundamental quantity of a material 1 K˚ The quantity is usually set at 1 gm-atom (elements) or 1 gm-mole (compounds)

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### Thermal Behavior of Materials

ME 2105

Dr. R. Lindeke

Some Definitions
• Heat Capacity: the amount of heat (energy) required to raise a fundamental quantity of a material 1 K˚
• The quantity is usually set at 1 gm-atom (elements) or 1 gm-mole (compounds)
• Given by the foumula: C=q/(mT) in units of J/gm-atom* K˚ or J/gm-mole* K˚
• Specific Heat: a measure of the amount of heat energy to raise a specific mass of a material 1 K˚
Heat Capacity
• Heat capacity is reported in 1 of two ways:
• Cv – the heat capacity when a constant volume of material is considered
• Cp – the heat capacity when a constant pressure is maintained while higher than Cv these values are nearly equal for most materials
• Cp is most common in engineering applications (heat stored or needed at 1 atm of pressure)
• At temperature above the Debye Temperature Cv 3R  Cp
Definitions
• Thermal Expansion is the “growth” of materials due to increasing vibration leading to larger inter-atomic distances and increasing vacancy counts for materials as temperature increases
Thermal Expansion
• Linear thermal expansion is given by this model:
• As an Example:
• A gold ring (diameter = 12.5 mm) is worn by a person, they are asked to wash the dishes at their apartment – water temperature is 50˚C – how big is the ring while it is submerged?
Definition:
• Thermal Conductivity: the transfer of heat energy through a material (analogous to diffusion of mass)
• Modeled by:
• Note, k is a function of temperature (like  was)
Thermal Conductivity
• Involves two primary (atomic level) mechanisms:
• Atomic vibrations – in ceramics and polymers this dominates
• Conduction by free electrons – in metals this dominates
• Focusing on Metals:
• thermal conductivity decreases as temperature increases since atomic vibration disrupt the primary free electron conduction mechanism
• Adding alloying “impurities” also disrupts free electron conduction so alloys are less conductive than pure metals
Thermal Conductivity
• Focusing on Ceramics and Polymers:
• Atomic/lattice vibrations are “wave-like” in nature and impeded by structural disorder
• Thermal conductivity will, thus, drop with increasing temperature
• In some ceramics, which are “transparent” to IR radiation, TC will eventually rise at elevated temperatures since radiant heat transfer will begin to dominate “mechanical” conduction
• Porosity level has a dramatic effect of TC (pores are filled with low TC gases which limits overall TC for a structure (think fiberglass insulation and ‘stryo-foam’ cups)
Figure 7.5Thermal conductivity of several ceramics over a range of temperatures.

(From W. D. Kingery, H. K. Bowen, and D. R. Uhlmann, Introduction to Ceramics, 2nd ed., John Wiley & Sons, Inc., New York, 1976.)

Definition:
• Thermal Shock: it is simply defined as the fracture of a material (usually a brittle ceramic) as the result of a (sudden) temperature change and is dependent of the interplay of the two material behaviors: thermal expansion and thermal conductivity
• Thermal Shock can be explained in one of two ways:
• Failure stress can be built up by constrained thermal expansion
• Rapid temperature changes lead to internal temperature gradients and internal residual stresses – finite thermal conductivity reasoning – see figure 7.7
By Constrained Thermal Expansion:

Figure 7.6 Thermal shock resulting from constraint of uniform thermal expansion. This process is equivalent to: a. free expansion followed by; b. mechanical compression back to the original length.

Let’s Consider an Example:
• A 400 mm long ‘rod’ of Stabilized ZrO2 ( = 4.7x10-6 mm/mm˚C) is subject to a thermal cycle in a ‘ceramic’ engine – it’s the crank shaft! – from RT (25˚C) to 800˚C. Determine the induced stress and determine if it is likely to fail?
• E for Stabilized ZrO2 is 150 GPa– table 6.4
• MOR for Stabilized ZrO2 is 83 MPa -- table 6.4

Since the Inducted Compressive Stress exceeds the MOR (from Table 6.4) one might expect the ‘rod’ to fail or rupture – unless it is allowed to expand into a designed in ‘pocket’ built into the engine block to accept the shaft’s expansion