Section 2.3. Residual Strength Methodology
The strength of a structure can be
significantly affected by the presence of a crack and is usually substantially
lower than the strength of the undamaged structure. To prevent catastrophic failure, one must evaluate the load
carrying capacity that will exist in the potentially cracked structure
throughout its expected service life.
The load carrying capacity of a cracked structure is the residual
strength of that structure and it is a function of material toughness, crack size,
crack geometry and structural configuration.
The determination of residual strength for uncracked structures
is straightforward because the ultimate strength of the material is the
residual strength. A crack in a
structure causes a high stress concentration resulting in a reduced residual
strength. When the load on the
structure exceeds a certain limit, the crack will extend. The crack extension may become immediately
unstable and the crack may propagate in a fast uncontrollable manner causing
complete fracture of the component.
In general, unstable crack propagation results in fracture of
the component. Hence, unstable crack
growth is what determines the residual strength. In order to estimate the residual strength of a structure, a
thorough understanding of the crack growth behavior is needed. Also, the point at which the crack growth
becomes unstable must be defined and this necessitates the need for a failure
criterion. There are several criteria
available; these criteria are tailored to represent the ability of a material
to resist failure.
A material’s toughness depends on thickness. When the thickness is such that the crack
tip plastic zone size is on the order of the plate thickness, the toughness
reaches a maximum value, Kc(max). With increasing thickness of the plate, the
plastic zone size reduces and thus the toughness gradually decreases, from Kc(max) to KIc. When the thickness is large enough that the
crack tip deformation is not affected by the thickness, plane strain conditions
prevail at the crack tip. The toughness
in the plane strain regime is virtually independent of thickness. For increasing thickness, the toughness
asymptotically approaches the plane strain fracture toughness, KIc.
The critical Kcr
for abrupt fracture mode is denoted as KIc
for plane strain conditions and Kc
for plane stress conditions; the conditions for plane stress or plane strain
are determined by experiment. The test
requirements necessary for generating KIc
and Kc are discussed in
When the crack extends by a tearing mode of fracture, which
typically occurs in thin metal sheets or in tough materials, the crack
extension is essentially slow and
stable. The failure condition for
tearing fractures depends on the crack growth resistance (KR) behavior of the material and the applied
stress-intensity factor K, which in
turn depends on the crack and structural configurations.
The crack growth resistance curve (KR) has shown good promise for materials where limited
(small-scale) yielding occurs in front of the crack tip. Difficulties in estimating crack tip
plasticity under large-scale yielding conditions, led Wilhem  to an
alternate failure criterion based on the J-integral
[Rice, 1968]. For a basic introduction
to the J-integral see Section 11.
An important element in the process of
predicting residual strength of a structure experiencing ductile tearing is
having a criterion that predicts the onset and rate of this phenomenon. Tests
and numerical simulations have been performed to assess the critical crack tip
opening angle (CTOAc) criterion for predicting residual strength of
structures containing MSD. Section 4 section details the theoretical background
behind the CTOAc criterion, and describes experimental and
computational investigations into it.