Formulas For Final

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21 Terms

1
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What is the Hall Petch equation?

What does it do?

See figure

σyield = yield stremgth

σo = Stress for dislocation movement

ky = strengthening coefficient

d = diameter

Shows how smaller grains make materials stronger

<p>See figure</p><p><span>σyield = yield stremgth</span></p><p><span>σo = Stress for dislocation movement </span></p><p><span>ky = strengthening coefficient</span></p><p><span>d = diameter</span></p><p><span>Shows how smaller grains make materials stronger</span></p>
2
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What is the cold work equation?

What does it do?

See figure

%CW = cold work percentage

Ao = Original cross sectional area

Ad = Cross sectional area after deformation

measures the percentage change in the cross-sectional area of a material after cold working

<p>See figure</p><p>%CW = cold work percentage</p><p>Ao = Original cross sectional area</p><p>Ad = Cross sectional area after deformation</p><p>measures the percentage change in the cross-sectional area of a material after cold working</p>
3
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What is the Griffith equation?

What does it do?

See figure

σm = stress at crack tip [Pa]

σo = applied stress [Pa]

pt = radius of curvature [m]

a = one half length of internal crack [m]

predicts the critical stress required for a crack to propagate in a brittle material

<p>See figure</p><p><span>σm = stress at crack tip [Pa]</span></p><p><span>σo = applied stress [Pa]</span></p><p><span>pt = radius of curvature [m]</span></p><p><span>a = one half length of internal crack [m]</span></p><p>predicts the critical stress required for a crack to propagate in a brittle material</p>
4
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Stress concentration factor?

Whats it used for?

See figure

σm = max stress at crack tip

σo = average applied stress

quantifies the stress concentration at a point of discontinuity in a structure

<p>See figure</p><p>σm = max stress at crack tip</p><p>σo = average applied stress</p><p>quantifies the stress concentration at a point of discontinuity in a structure</p>
5
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What is the critical stress formula?

What is it used for?

See figure

σc = critical stress [Pa or MPa]

E = Youngs modulus [Pa]

ys = specific surface energy [J/m²]

a = one half length of internal crack [m]

for ductile materials replace ys with ys+yp where yp is the plastic deformation energy

predicting the stress required to propagate a crack in a brittle material.

<p>See figure</p><p><span>σc = critical stress [Pa or MPa]</span></p><p><span>E = Youngs modulus [Pa]</span></p><p><span>ys = specific surface energy [J/m²]</span></p><p><span>a = one half length of internal crack [m]</span></p><p><span>for ductile materials replace ys with ys+yp where yp is the plastic deformation energy</span></p><p><span>predicting the stress required to propagate a crack in a brittle material.</span></p>
6
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What is the formula for fracture toughness?

What is it used for?

See figure

Kc = Fracture toughness [MPa sqrt m]

Y = Dimensionless parameter

σc = critical stress [MPa]

a = one half length of internal crack [m]

Measures the materials resistance to brittle fracture when a crack is present

For thick samples replace Kc with KIC which is plane strain fracture toughness

<p>See figure</p><p>Kc = Fracture toughness [MPa sqrt m]</p><p>Y = Dimensionless parameter</p><p>σc = critical stress [MPa]</p><p>a = one half length of internal crack [m]</p><p>Measures the materials resistance to brittle fracture when a crack is present</p><p>For thick samples replace Kc with KIC which is plane strain fracture toughness</p>
7
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What is the mean stress for cyclic loading equation?

See figure

<p>See figure</p>
8
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What is the range of stress equation?

See figure

<p>See figure</p>
9
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What is the stress amplitude equation?

See figure

<p>See figure</p>
10
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What is the stress ratio equation?

See figure

<p>See figure</p>
11
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Weight percent and atom percent formula?

See figure

<p>See figure</p>
12
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Burgers Vector Calculation for BCC and FCC lattices?

For SC lattices?

See figure

<p>See figure</p>
13
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Vacancy concentration formula?

See figure

Nv = number of defects [atom/m³]

N = total number of atomic sites [atom/m³]

Qv = activation energy [J/atom] or [eV/atom]

k = boltszman’s constant [1.38×10^-23 J/atom] or [8.62×10^-5 eV/atom K]

T = temp [K]

<p>See figure</p><p>Nv = number of defects [atom/m³]</p><p>N = total number of atomic sites [atom/m³]</p><p>Qv = activation energy [J/atom] or [eV/atom]</p><p>k = boltszman’s constant [1.38×10^-23 J/atom] or [8.62×10^-5 eV/atom K]</p><p>T = temp [K]</p>
14
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Fick’s 2nd Law?

See figure

∂C/​∂t = The rate of change of concentration with respect to time

D = The diffusion coefficient

∂²C/∂x²​: The second derivative of concentration with respect to position

<p>See figure</p><p><span>∂<em>C/</em>​</span>∂t<span> = The </span>rate of change of concentration <span>with respect to </span>time</p><p>D = <span>The </span>diffusion coefficient</p><p><span>∂²<em>C/</em></span>∂x²<span>​: The </span>second derivative of concentration with respect to position</p>
15
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Arrhenius equation for diffusion?

See figure

<p>See figure</p>
16
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Ficks 1st Law of Diffusion?

J = -D [(dC)/(dx)]

D = Diffusion coefficient [m²/s]

J = Flux = [moles or mass diffusing] / [surface area times times] in mol/cm²s or kg/m²s

17
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Poissons ratio

v = ex/ey

18
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Relationship for isotropic materials for elastic shear?

See figure

tau = Gy

<p>See figure</p><p>tau = Gy</p>
19
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Relationship for isotropic materials for elastic bulk?

See figure

P = -K [delta V / Vo]

<p>See figure</p><p>P = -K [delta V / Vo]</p>
20
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Percent elongation?

Percent reduction in area?

See figure

<p>See figure</p>
21
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Resilience equation?

Ur = ½ σy ey