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Principal Stress and Strain on a Fracture

  1. Dec 12, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the expressions for principal stresses in both plane strain and plane stress conditions

    sigma(x) = (K/(sqrt(2*pi*r)))*cos(theta/2)*(1-sin(theta/2)*sin(3*theta/2))
    sigma(y) = (K/(sqrt(2*pi*r)))*cos(theta/2)*(1+sin(theta/2)*sin(3*theta/2))
    T(xy) = (K/(sqrt(2*pi*r)))*cos(theta/2)*sin(theta/2)*cos(3*theta/2))

    Since the problem asks for expressions, no variables are given values.

    2. Relevant equations

    Mohrs Circle for Principal Stress
    Principal Strain

    3. The attempt at a solution

    Should I take derivatives of (x), (y), and (xy) and then use that to solve for the angle theta? All I know is I'm supposed to look for sigmas x, y, and xy (not sure if my teacher meant x', y' and xy') and then sigmas 1 and 2. Ideas?
  2. jcsd
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