Question

Problem 3.4 Part A

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An isotropic alloy contains 5% by volume of a precipitate of radius 10nm. Assume the primary metal is in a simple cubic arrangement. The alloy has a Young's modulus E=70GPa and a Poisson's ratio ν=0.35. If Γ=0.9J/m2 (the energy needed to cut through the precipitate lattice per unit surface area), and b=0.25nm, what is the precipitate spacing L in the alloy?

L (in nm):

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Problem 3.4 Part B

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What is the shear stress required to move a dislocation past the precipitates?

τp (in MPa):

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Problem 3.4 Part C

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Instead of introducing a precipitate into the primary metal, alumina, a dispersion compound is introduced.

Consider the dislocation shown below, which bows to a radius of curvature R at an angle θ between two particles a distance L apart. Use the expression for line tension in a dislocation, the geometry of the bowing dislocation, and the force resulting from the applied shear stress to obtain an expression relating the applied shear stress and dislocation radius R. Express your answer in terms of the shear modulus G, the Burgers vector b, and the dislocation radius R.

(Hint: Draw the free body diagram for one of the particles. The force exerted by the stress on the dislocation is F=τbL)

τ=  unanswered

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Problem 3.4 Part D

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Based on your expression in Part C, what is the angle beyond which no additional applied stress is needed to move the dislocation past the particles? (In other words, at what angle does the maximum applied shear stress occur?

θ (in degrees):

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Answer 1