What is the exact strain energy per unit length of an edge dislocation for a material that has a Young's modulus E of 50GPa, a Burger's vector b of 0.25nm, a dislocation density ρ of 108cm−2, and a Poisson's ratio ν of 0.3?
Uedge (in J/m):
What is the exact strain energy per unit length of a screw dislocation for a material that has a Young's modulus E of 50GPa, a Burger's vector b of 0.25nm, a dislocation density ρ of 108cm−2, and a Poisson's ratio ν of 0.3?
Uscrew (in J/m):
To calculate the strain energy per unit length of an edge dislocation and a screw dislocation, we can use the following formulas:
The strain energy per unit length of an edge dislocation, Uedge, is given by:
Uedge = (μ * b^2 * ρ) / (2π * (1 - ν))
The strain energy per unit length of a screw dislocation, Uscrew, is given by:
Uscrew = (μ * b^2 * ρ) / (4π * (1 - ν))
Where:
- μ is the shear modulus of the material
- b is the Burger's vector
- ρ is the dislocation density
- ν is the Poisson's ratio
Given:
- Young's modulus, E = 50 GPa
- Burger's vector, b = 0.25 nm
- Dislocation density, ρ = 10^8 cm^(-2)
- Poisson's ratio, ν = 0.3
To calculate the strain energy per unit length, we first need to calculate the shear modulus (μ) using the relationship:
μ = (E) / (2 * (1 + ν))
Calculating the shear modulus:
μ = (50 * 10^9) / (2 * (1 + 0.3))
= 19.23 GPa
Now, we can calculate the strain energy per unit length for the edge dislocation (Uedge) and the screw dislocation (Uscrew) using the given formulas.
Calculating Uedge:
Uedge = (19.23 * 10^9 * (0.25 * 10^(-9))^2 * 10^8) / (2π * (1 - 0.3))
= 7.03 J/m
Calculating Uscrew:
Uscrew = (19.23 * 10^9 * (0.25 * 10^(-9))^2 * 10^8) / (4π * (1 - 0.3))
= 3.515 J/m
Therefore, the exact strain energy per unit length of an edge dislocation (Uedge) is 7.03 J/m, and the strain energy per unit length of a screw dislocation (Uscrew) is 3.515 J/m.