For Mode I: Plane Stress: E K I 2   Plane Strain: 16 Plane Strain:   2 2 1   E K I For the general 3-D case, plane strain and anti-plane strain loading:   22 22 1 1       K EE KK   17 For the plane stress case (combination Mode I and Mode II): E KK 22     K Dominance Domain of validity There exists an annular zone where the K solution is valid: 18 The inner radius is given by r p (plastic zone size). The outer radius, r 0 , is the radial distance at which the approximate, asymptotic singular solutions deviate significantly (say, by more than 10%) from full elasticity solutions which include higher order terms. It is found that, 19 ar 1.0 0  where is the crack length. a Example Problem Size Requirements Consider a low strength steel with σ ys =350 MPa, K Ic =250 MPa and E = 210 GPa. What are the Minimum specimen size requirements for a valid K Ic measurement? m 20 Example Problem Size Requirements K Ic Test ASTM standard E399 (1974) for K Ic testing (specimen dimensions large compared to plastic zone): 2 5 . 2 , ,        Ic K B b a  21 5 . 2 , ,        ys B b a  Substitute the known values for σ ys and K Ic . Find that   inchesmBba 50!28.1,,   . For Mode I: Plane Stress: E K I 2   Plane Strain: 16 Plane Strain:   2 2 1   E K I For the general 3-D case, plane strain and anti-plane strain. r p (plastic zone size). The outer radius, r 0 , is the radial distance at which the approximate, asymptotic singular solutions deviate significantly (say, by more than 10%) from full elasticity solutions. Requirements K Ic Test ASTM standard E399 (1974) for K Ic testing (specimen dimensions large compared to plastic zone): 2 5 . 2 , ,        Ic K B b a  21 5 . 2 , ,        ys B b a  Substitute