Stress intensity factor
[1] It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials, and is a critical technique in the discipline of damage tolerance.
The concept can also be applied to materials that exhibit small-scale yielding at a crack tip.
Linear elastic theory predicts that the stress distribution (
[5] Practically however, this relation breaks down very close to the tip (small r) because plasticity typically occurs at stresses exceeding the material's yield strength and the linear elastic solution is no longer applicable.
[6] These load types are categorized as Mode I, II, or III as shown in the figure.
Mode II is a sliding (in-plane shear) mode where the crack surfaces slide over one another in a direction perpendicular to the leading edge of the crack.
Mode I is the most common load type encountered in engineering design.
Different subscripts are used to designate the stress intensity factor for the three different modes.
These factors are formally defined as:[7] The mode I stress field expressed in terms of
In plane stress conditions, the strain energy release rate (
The material is assumed to be an isotropic, homogeneous, and linear elastic.
The crack has been assumed to extend along the direction of the initial crack For plane strain conditions, the equivalent relation is a little more complicated: For pure mode III loading, where
For general loading in plane strain, the linear combination holds: A similar relation is obtained for plane stress by adding the contributions for the three modes.
Stress intensity in any mode situation is directly proportional to the applied load on the material.
If a very sharp crack, or a V-notch can be made in a material, the minimum value of
can be empirically determined, which is the critical value of stress intensity required to propagate the crack.
imply that the fracture stress of the material must be reached over some critical distance in order for
The G-criterion is a fracture criterion that relates the critical stress intensity factor (or fracture toughness) to the stress intensity factors for the three modes.
The stress intensity factor for an assumed straight crack of length
perpendicular to the loading direction, in an infinite plane, having a uniform stress field
is [5][7] The stress intensity factor at the tip of a penny-shaped crack of radius
is [1] If the crack is located centrally in a finite plate of width
, an approximate relation for the stress intensity factor is [7] If the crack is not located centrally along the width, i.e.,
can be found from fits to stress intensity curves[7]: 6 for various values of
A similar (but not identical) expression can be found for tip B of the crack.
is the distance from the center of the crack to the boundary closest to point A.
, the stress intensity factor can be approximated by For a slanted crack of length
, the stress intensity factors at point B are[7] If the force is distributed uniformly between
The stress intensity factor at the crack tip of a compact tension specimen is[14] where
The stress intensity factor at the crack tip of a single-edge notch-bending specimen is[14] where
