Exercice 2: Schmid's law(1) Compute the theoretical shear stress in order to have a slippage of two atomicplanes relative to each other (the shear modulus is G = E=2(1 + ν)).
Question
Exercice 2: Schmid's law(1) Compute the theoretical shear stress in order to have a slippage of two atomicplanes relative to each other (the shear modulus is G = E=2(1 + ν)).
Solution
Schmid's law is used to determine the resolved shear stress necessary for dislocation motion in a crystal, which leads to plastic deformation. The law is expressed as:
τ = σ * cos(φ) * cos(λ)
where: τ is the resolved shear stress, σ is the applied stress, φ is the angle between the slip plane normal and the stress axis, λ is the angle between the slip direction and the stress axis.
However, the question asks for the theoretical shear stress for slippage of two atomic planes. This is typically given by the shear modulus (G). The shear modulus is related to the elastic modulus (E) and Poisson's ratio (ν) by the equation:
G = E / 2(1 + ν)
Given that E = G, we can substitute E into the equation to get:
G = G / 2(1 + ν)
Solving for G gives:
G = 2G / (2 + 2ν)
Simplifying gives:
G = G / (1 + ν)
So, the theoretical shear stress for slippage of two atomic planes is equal to the shear modulus G, which is given by G / (1 + ν).
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