## How to Calculate and Solve for Partial Dislocation Separation | Fracture Mechanics

The image above represents partial dislocation separation.

To compute for partial dislocation separation, four essential parameters are needed and these parameters are Shear Modulus (G), Burger Vector (b2), Burger Vector (b3and Stacking Fault Energy (γ).

The formula for calculating partial dislocation separation:

d = Gb2b3 / 2πγ

Where:

d = Partial Dislocation Separation
G = Shear Modulus
b2 and b3 = Burger Vectors
γ = Stacking Fault Energy

Let’s solve an example;
Find the partial dislocation separation when the shear modulus is 4. the burger vectors is 8 and 10, the stacking fault energy is 14.

This implies that;

G = Shear Modulus = 4
b2 and b3 = Burger Vectors = 8 and 10
γ = Stacking Fault Energy = 14

d = Gb2b3 / 2πγ
d = (4)(8)(10) / 2π(14)
d = 320 / 87.96
d = 3.64

Therefore, the partial dislocation separation is 3.64 m.

## How to Calculate and Solve for Shear Modulus | Rock Mechanics

The image above represents shear modulus.

To compute for shear modulus, two essential parameters are needed and these parameters are young’s modulus (E) and Poisson’s ratio (v).

The formula for calculating the shear modulus:

G = E / 2(1 + v)

Where:

G = Shear Modulus
E = Young’s Modulus
v = Poisson’s Ratio

Let’s solve an example;
Find the shear modulus when the young’s modulus is 32 and the Poisson’s ratio is 24.

This implies that;

E = Young’s Modulus = 32
v = Poisson’s Ratio = 24

G = E / 2(1 + v)
G = 32 / 2(1 + 24)
G = 32 / 2(25)
G = 32 / 50
G = 0.64

Therefore, the shear modulus is 0.64.

Calculating the Young’s Modulus when the Shear Modulus and the Poisson’s Ratio is Given.

E = G (2 + 2v)

Where:

E = Young’s Modulus
G = Shear Modulus
v = Poisson’s Ratio

Let’s solve an example;
Find the young’s modulus when the shear modulus is 12 and the Poisson’s ratio is 10.

This implies that;

G = Shear Modulus = 12
v = Poisson’s Ratio = 10

E = G (2 +2v)
E = 12 (2 + 2(10))
E = 12 (2 + 20)
E = 12 (22)
E = 264

Therefore, the young’s modulus is 264.