Theory The stress intensity factor is defined from the elastic stress field equations for a stressed element near the tip of a sharp crack under biaxial (or uniaxial) loading in an infinite body. The situation is illust rated below: The direct and shear stresses on the red element are given, to a first order approximation, by: Only these first terms in the series expansion have the 1/rｽ dependency, which causes a stress singularity at the crack tip (i.e. the stresses go to infinity as rgoes to zero). Thus in the near-tip region, which is where frac ture processes occ ur, the stress field is dominated by the singularity. Along the critical plane for cracking ahead of the crack tip (where the angle is zero), the equations reduce to the simple form of: The numerator in these equations essentially gives gives a measure of the magnitude, or intensity, of the near-tip elastic s tress field. Irwin defined the numerator as the stress intensity factor, K, and postulated that fracture would occur at critical values of K. Both numerator and denominator are multiplied by pi for expediency in showing that Kand G(the critical strain energy releas e rate) are related. Thus critical values of K meet both the critical stress a nd the 'energetically favourable' c riteria for crack growth. Generally speaking, finit e geometry and crack shape co rrection factors have to be included in the expression for stress intensity factor, i.e.
The stress intensity factor is defined from the elastic stress
field equations for a stressed element near the tip of a sharp
crack under biaxial (or uniaxial) loading in an infinite body. The
situation is illustrated below:
The direct and shear stresses on the red element are given, to a
first order approximation, by:
Only these first terms in the series expansion have the 1/r
dependency, which causes a stress singularity at the crack tip
(i.e. the stresses go to infinity as r goes to zero). Thus in the
near-tip region, which is where fracture processes occur, the
stress field is dominated by the singularity. Along the critical
plane for cracking ahead of the crack tip (where the angle is
zero), the equations reduce to the simple form of:
The numerator in these equations essentially gives gives a
measure of the magnitude, or intensity, of the near-tip elastic
stress field. Irwin defined the numerator as the stress intensity
factor, K, and postulated that fracture would occur at critical
values of K. Both numerator and denominator are multiplied by pi
for expediency in showing that K and G (the critical strain energy
release rate) are related. Thus critical values of K meet both the
critical stress and the 'energetically favourable' criteria for
crack growth. Generally speaking, finite geometry and crack shape
correction factors have to be included in the expression for stress
intensity factor, i.e.
where Y can be a relatively involved compliance-based function.
This expression can be used to find the stress intensity factor
corresponding to any combination of remote stress and crack length,
but critical values of K at which fast fracture occurs are denoted
K1C when conditions of plane strain apply, and KC otherwise.
Extensive experience has indicated that LEFM can still be
applied in the presence of crack tip plasticity, provided that the
ratio of plastic zone size to crack length is < 1/15.
Further information can be found in the following reference:
H L Ewalds and R J H Wanhill, Fracture Mechanics, Edward Arnold,
London, 1989, pp. 28-42.
