113_2009_Practice_MT1

# 113_2009_Practice_MT1 - assume that the strain in the joint...

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Problem 1 Two stainless steel rods with a square cross-section, 1 m on both sides and 25 m long, are joined by a silver alloy braze (0.5 mm thick): E (GPa) ν σ y (MPa) σ u (MPa) Stainless Steel 200 0.3 1240 1530 Silver Alloy 30.3 0.367 140 140 The structure is loaded in uniaxial tension, parallel to the long axis of the steel rods and perpendicular to the braze joint. The alignment is such that bending is not allowed to occur. Two modes of mechanical failure are possible: 1) Yielding of the silver braze 2) Yielding of the steel What is the value of the applied uniaxial force ( P ) required to initiate first yield in this joined-steel configuration and where will the yielding occur? Assumptions: 1) Because the silver braze is relatively “thin” compared to the steel bar, the deformation of the silver is controlled by the steel because it is constrained (the stiffness of the steel far exceeds that of the silver); therefore, you can

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Unformatted text preview: assume that the strain in the joint is the strain in the steel. 2) Hint 1: First compute the Poisson’s contraction strains in the silver braze joint using Hooke’s Law; then consider the corresponding strain in the steel where no constraint will exist. 3) Hint 2: Use the Mises criterion to calculate the potential yielding in the silver alloy. Problem 3 Notes: -Make sure you understand how to do the HW sets -Topics covered in lecture that you should be comfortable include (but are not limited to): o Beam bending (esp slender beams) o Stress and strain definitions (normal and shear) o Bar & tube in tension o Pressurization of a thin walled vessel o Bar & tube in torsion o Transformation of stresses (Mohr’s circle) o Dislocations (Types, motion, etc.) o Yield criteria (Tresca and von Mises); constraint o Stress concentrations (i.e. at a small hole in a semi-infinite plane) o Mechanisms of deformation...
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113_2009_Practice_MT1 - assume that the strain in the joint...

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