Thermal Effects on & Thermal Properties of Materials_Ch19

8/13/2019 Thermal Effects on & Thermal Properties of Materials_Ch19

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Thermal Behavior of Materials

ME 2105

Dr. R. Lindeke


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Some Definitions

Heat Capacity: the amount of heat (energy)required to raise a fundamental quantity of amaterial 1 K

The quantity is usually set at 1 gm-atom (elements) or 1gm-mole (compounds)

Given by the formula: C = q/(mT) in units of J/gm-atom* K or J/gm-mole* K

Specific Heat: a measure of the amount ofheat energy to raise a specific mass of amaterial 1 K


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Heat Capacity

Heat capacity is reported in 1 of two ways: Cvthe heat capacity when a constant volume of

material is considered

Cpthe heat capacity when a constant pressure ismaintained while higher than Cvthese values are nearly

equal for most materials

Cpis most common in engineering applications (heat

stored or needed at 1 atm of pressure) At temperature above the Debye Temperature Cv3R

Cp


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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


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Thermal Expansion

Linear thermal expansion is given by thismodel:

As an Example: A gold ring (diameter = 12.5 mm) is worn by a person,

they are asked to wash the dishes at their apartmentwater temperature is 50C how big is the ring while itis submerged?

dL

LdT


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Thermal Expansion is

Temperature Dependent


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Solving:

0

0 0

50 27 50

50527 27

6

50

6

0

data from table 7.2

* 12.5*3.14159 39.2699

14.1

16.5 14.1

14.21 10 (mm/mm C )

14.21*10 *39.27*12.5 0.007

39.27 .00712.502

avg

f

L L T

L d

x

L L T mm

D mm


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Definition:

ThermalConductivity: thetransfer of heatenergy through a

material (analogousto diffusion of mass)

Modeled by:

at steady state conditions:

dQdtk

dTAdx

Qtk

TAx

Note, kis a function of temperature (like was)


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Modeling Fouriers Law of Thermal Conduction (heat

flow thru a bounded area)


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Thermal Conductivity

Involves two primary (atomic level) mechanisms: Atomic vibrationsin ceramics and polymers this dominates

Conduction by free electronsin metals this dominates

Focusing on Metals: thermal conductivity decreases as temperature increases

since atomic vibrations disrupt theprimary free electron

conduction mechanism

Adding alloying impurities also disrupts free electronconduction so alloys are less conductive than pure metals


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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 on TC (pores are filled

with low TC gases which limits overall TC for a structure

(think fiberglass insulation and strya-foam cups)


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And Continuing:


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Thermal 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.)


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Definition:

Thermal Shock: it is simply defined as the fracture of amaterial (often a brittle ceramic) as the result of a(sudden) temperature change and is dependent on theinterplay 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 stressesbased in finite thermal conductivityreasoning


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By Constrained Thermal Expansion:

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.


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Lets Consider an Example:

A 400 mm long rod of Stabilized ZrO2(=

4.7x10-6mm/mmC) is subject to a thermal

cycle in a ceramic engine its the crank

shaft!from RT (25C) to 800C. Determinethe induced stress and determine if it is likely

to fail?

E for Stabilized ZrO2is 150 GPa MOR for Stabilized ZrO2 is 83 MPa


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exp

0

6

where:

4.7*10 * 800 25 0.00364

150 *0.00364 0.546 546

TI TI

TTI

TI

TI

E

l

l

mmTmm

mmGPa GPa MPamm

Since the Inducted Compressive Stress exceeds the MOR 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 shafts expansion


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Thermal quenches that produce failure by thermal shock are illustrated. The temperature drop

necessary to produce fracture (T0 T) is plotted against a heat-transfer parameter (rmh). More

important than the values of rmh are the regions corresponding to given types of quench (e.g.,

water quench corresponds to an rmh around 0.2 to 0.3).

(From W. D. Kingery, H. K.Bowen, and D. R. Uhlmann,

Introduction to Ceramics, 2nd

ed., John Wiley & Sons, Inc.,

New York, 1976.)


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22

Occurs due to: uneven heating/cooling.

Ex: Assume top thin layer is rapidly cooled from T1to T2:

Tension develops at surface

)( 21 TTE

Critical temperature difference

for fracture (set = f)

E

TT f

fracture21 )(

set equal

Large thermal shock resistance when is large.

E

kf

Result:

E

kf

fractureforrate)(quench

Thermal Shock Resistance

Temperature difference that

can be produced by cooling:

kTT

ratequench)( 21

rapid quench

resists contraction

tries to contract during cooling T2

T1


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Thermal Shock Resistance Parameter

f

l

kTSR

E

Where:

fis fracture strength of a materiallis coeff. Of linear thermal expansionk is thermal conductivity of material

E is modulus of elasticity

Thermal Effects on & Thermal Properties of Materials_Ch19

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