MSE_2610_HW_5_solutions

# MSE_2610_HW_5_solutions - MSE 2610 Introduction to the...

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MSE 2610 Introduction to the Mechanical Properties of Materials Fall 2008 Homework Assignment #5 1.) A single crystal has only one slip plane with a normal vector that makes an angle of 60° with the tensile axis. The three slip directions have angles of 38°, 45°, and 84° with respect to the tensile axis, and the critical resolved shear stress (CRSS) is 2.3 MPa. The shear modulus G for zinc is 42 GPa. a.) Determine the tensile stress at which plastic deformation commences. Plastic deformation occurs when CRSS R τ () ( ) θ cos λ cos σ τ A CRSS = Because the only choice is among the slip directions, the largest critical resolved shear stress will occur when cos( λ ) is the largest. () () ()() MPa 84 . 5 60 cos 38 cos ) MPa 3 . 2 ( θ cos λ cos τ σ o o CRSS A = = = () () ()() MPa 51 . 6 60 cos 45 cos ) MPa 3 . 2 ( θ cos λ cos τ σ o o CRSS A = = = () () ()() MPa 0 . 44 60 cos 84 cos ) MPa 3 . 2 ( θ cos λ cos τ σ o o CRSS A = = = b.) The lattice parameters for zinc are a = 2.66 Å and c = 4.94 Å. What is the magnitude of the Burgers vector b ? Slip (dislocation motion) will occur in the closest-packed planes in the closest-packed directions. This is the (0001) plane and the <112 0> directions in HCP. Because the lattice must remain unchanged after a dislocation has slipped, the Burgers vector must be 1 lattice parameter in the basal plane. The Burgers vector must be 2.66 b=a Å. c.) What is the critical force per unit length (of dislocation) required to move a straight dislocation in zinc? The critical resolved shear stress is the stress when slip starts. The minimum amount this dislocation can travel is 1 Burgers vector. m / N 10 x 1 . 6 ) m 10 66 . 2 )( MPa 3 . 2 ( b τ l F 4 10 CRSS = × = = d.) What is the length of the shortest dislocation line segment that could act as a double-ended dislocation source ( i.e. , Frank-Read source), if the maximum shear stress acting on the dislocation segment is 5.2 MPa? When the dislocation gets pinned at 2 ends, it can act as a Frank-Read source only if the shear stress is high enough to expand the loop past the critical point.

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m μ 30 . 4 d MPa 2 . 5 ) m 10 66 . 2 )( GPa 42 ( 2 τ Gb 2 d d Gb 2 τ 10 max max = × = = = d d/2 2.) List the five strengthening mechanisms mentioned in class. i.
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## This note was uploaded on 12/24/2008 for the course MSE 261 taught by Professor Sass during the Fall '06 term at Cornell University (Engineering School).

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MSE_2610_HW_5_solutions - MSE 2610 Introduction to the...

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