A material has a Young's modulus E of 50GPa, a Burger's vector b of 0.25nm, and a Poisson's ratio ν of 0.3.
What is the approximate line tension for a dislocation in this material?
To find the approximate line tension for a dislocation in this material, we can use the equation for the line tension of a dislocation:
τ = (μ * b) / (2π * (1 - ν))
where τ is the line tension, μ is the shear modulus, b is the Burger's vector, and ν is the Poisson's ratio.
In this case, we are given the Young's modulus E, which is related to the shear modulus μ by the equation:
E = 2 * (1 + ν) * μ
Rearranging this equation, we can solve for μ:
μ = E / (2 * (1 + ν))
Substituting this value for μ into the equation for line tension:
τ = (E * b) / (4π * (1 - ν))
Now, we can plug in the given values:
E = 50 GPa = 50 * 10^9 Pa
b = 0.25 nm = 0.25 * 10^-9 m
ν = 0.3
Calculating the line tension:
τ = (50 * 10^9 Pa * 0.25 * 10^-9 m) / (4π * (1 - 0.3))
Simplifying this equation:
τ ≈ 2.65 * 10^8 Pa
So, the approximate line tension for a dislocation in this material is approximately 2.65 * 10^8 Pa.