International Journal of Fracture 53: 229-248, 1992.
© 1992 Kluwer Academic Publishers. Printed in the Netherlands.
Energy density approach for calculation of three-dimensional
inelastic strain and stress at the crack tip in compact
tension specimens of polycarbonate
S. DHAR and G.L. CLOUD
Department of Metallurgy, Mechanics and Materials Science, Michigan State University, East Lansin 9, Michigan 48824,
USA
Received 15 April 1990; accepted 11 February 1991
Abstract. An energy-based method is utilized for calculating elastic-plastic strains and stresses near fatigue crack tip in
specimens of Merlon polycarbonate. The stress redistribution caused by the plastic yielding around the crack tip is taken
into account so that theoretical crack tip strain is improved. The estimated values of crack tip strain based on an energy
density approach are compared with experimental results obtained from an embedded grid moire technique and
embedded strain gages. Large-scale yielding seems to dominate near the crack tip. In fact, the measured strain is in
agreement with the elastic solution, which means, in reality, only small-scale yielding takes place near the crack tip. The
strain in the mid-plane (plane strain) is found to be higher than in the surface plane (plane stress). The experimental
and theoretical results are in good agreement.
List of symbols
P
r
rp
n
x
E
Sn
Kt
Re
Rp
Rep
K
KI
Fi, El
SPL
QPL
MPL
nj
T,
Di~
Ul
Ui(ne)
fir
Fr
v
P
{7
Aa
Ae
= Load.
= Radial coordinate in polar coordinate system.
= Radius of plastic zone.
= Strain hardening exponent.
= Distance from center of notch tip curvature in the plane y = 0.
= Modulus of elasticity.
= Nominal stress.
= Theoretical elastic stress concentration factor.
= Elastic region.
= Plastic region.
= Elastic-plastic region.
= Strength coefficient factor.
= Stress intensity factor.
= Force.
= Surface plane.
= Quarter plane.
= Mid plane.
= Unit vector normal to the surface.
= Traction on the surface due to applied force.
= Stress deviator.
= Displacement vector.
= Elastic component of displacement vector at the notch tip.
= Designates body surface.
= Designates notched surface.
= Poisson's ratio.
= Notch tip radius.
= Normal stress.
= Normal strain.
= Stress range.
= Strain range.