Physical Metallurgy PSet3 (due October 22)

1: Suppose an isotropically polycrystalline steel has strain hardening exponent n = 0.3, Young’smodulus E = 190GPa, and 0.2%-offset yield strength σY = 400MPa. Use computer to plot thetrue stress-true strain curve σ(ε), and also the engineering stress - engineering strain σ̃(ε̃) curve,in uniaxial tension. Compute the Ultimate Tensile Strength (in true stress). Note: ε ≡ ln(L/L0);ε̃ ≡ L/L0 − 1; σ̃ ≈ σe−ε.

2: Suppose a FCC grain is being pulled uniaxially in its [123̄] direction by σ = 100MPa, find theslip system among its twelve {111}〈11̄0〉 full-slip systems that has the maximum Schmid factor orresolved shear stress, so it will be activated first if everything being equal.

3: Consider two edge dislocations labeled A and B, with

ξA = ξB = ez, bA = −bB = bex (1)

where ex, ey and ez are unit vectors in x-, y-, z-directions, forming a right-handed coordinate frame(ex × ey = ez).

The two dislocation are separated by

x ≡ xB − xA = xex + yey, (2)

with initial separation (at time t = 0)

x(t = 0) = 3y(t = 0) > 0. (3)

Assuming the two dislocations are embedded in isotropic linear elastic medium, calculate theirinteraction forces, and predict how the two edge dislocations will be arranged at t = ∞, if nodiffusion (dislocation climb) is allowed.

For graduate students, now is time to start working on your Term Paper (a critique of 10 pageson a research paper or a topic close to your heart involving metallurgy, with 10+ references).

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