, where:

 = Density (kg/m^3)

m = Mass (kg)

V = Volume (m^3)

Energy Dissipated at Fracture

 , where:

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

 = Surface Energy of Material (J/m^2)

GP = Plastic Dissipation of Material (J/m^2)

Euler-Bernoulli Equation

 , where:

q = Distributed Load (N/m)

E = Young's Modulus (Pa)

I = Area Moment of Inertia (m^4)

w = Deflection of Beam (m)

x = Length of Beam (m)

First Moment of Area

 , where:

M = First Moment of Area about the x-axis (m^3)

y = Distance of elements from x-axis (m)

A = Area (m^2)

Fracture Toughness


Note:  Fracture occurs when KC < KI ,  where:

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

KI = Stress Intensity (Pa*m^.5)

E = Young's Modulus of Material (Pa)

G = Strain Energy Release Rate (Pa*m)