structural geology, propagation mechanics and - Stanford School of ...

Normalized stress magnitude
3
2.5
2
1.5
1
0.5
0
−0.5
−1
(a)
−1.5
−200 −150 −100 −50 0 50 100 150 200
θ in degrees (local tip coordinate system
Normalized stress magnitude
4
3
2
1
0
−1
−2
(b)
−3
−200 −150 −100 −50 0 50 100 150 200
θ in degrees (local tip coordinate system
Figure 4.12. Plots of the near-tip stress magnitudes expressed in polar coordinates as a
function of θ for a fixed r (see Figure 4.10). (a) Distribution of stresses for a pure closingmode
sense of displacement discontinuity. (b) Distribution of stresses for mixed-mode
displacement discontinuity (shear component positive). Blue lines are σθθ, red lines are
σrr and green lines are σrθ.
(a)
r
σ22 (b)
r
σ22 r
σ11 r
σ11 Figure 4.13. Schematic representation of the effect of remote differential stress on
propagation path stability. (a) When the least compressive remote stress acting parallel to
the anticrack band is significantly less than the maximum compressive remote stress
(high differential stress) any deviation from symmetric propagation results in shear
stresses being resolved on the deviant tip such that it turns back toward the original path.
(b) When the remote stress state is nearly isotropic, the tendency for self-correction is
diminished.
102
α
α
β
β