Length

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  • Variables : Length

Strain Energy Release Rate

 , where:

G = Strain Energy Release Rate (Pa*m)

a = Length of Crack (m)

 = Stress at Fracture Point (Pa)

E = Young's Modulus (Pa)

Stress Intensity

 ,

Note: Fracture occurs when KI > KC , where:

KI = Stress Intensity (Pa*m^.5)  

= Stress (Pa)

a = Length of Crack (m)

KC = Fracture Toughness (Pa*m^.5)

Stress of Fracture of Crack

 , where:

 = Stress required for fracture at crack (Pa)

E = Young's Modulus (Pa)

G = Energy Dissipated at Fracture (J/m^2)

a = Length of crack (m)

Stretch Ratio

Also known as the extension ratio:

 = Stretch Radio

 = Final Length (m)

L = Original Length (m)

Strain

Also known as the Cauchy Strain

 , where:

 = Strain

 = Final Length (m)

L = Original Length (m)

Shear Modulus

 , where:

G = Shear Modulus (Pa)

 = Shear Stress (Pa)

 = Shear Strain

F = Force (N)

L = Initial Length (m)

A = Area (m^2)

x = Displacement (m)

Shear Force on a Beam

 , where:

M = Bending Moment (N*m)

Q = Shear Force (N)

E = Young's Modulus (Pa)

I = Area Moment of Inertia (m^4)

w = Deflection (m)

x = Length (m)

Strain on a Beam

 , where:

 = Strain

z = Distance to Neutral Axis (m)

w = Deflection (m)

x = Length (m)

Curvature

 , where:

K = Curvature (1/m)

 = Slope

x = Length (m)

w = Deflection (m)

 = Radius of Curvature

Bending Moment in a Beam

 , where:

M = Bending Moment (N*m)

E = Young's Modulus (Pa)

I = Area Moment of Inertia (m^4)

w = Deflection (m)

x = Length (m)

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