Crack Turning/Arrest Behavior of Integral Structure
Richard G. Pettit, 1-22-98
1.0 Introduction
The residual strength of stiffened panels with large damage, such as a two-bay crack,
is an important design parameter for large transport aircraft typically required
to satisfy fail-safety criteria. The crack-stopping role of the stiffeners has long
been recognized and utilized for structures with mechanically fastened structure, but
has historically been considered less effective for integrally stiffened structures
[1], due to the potential of the crack to spread directly from the skin into an integral
stiffener. A recent study at NASA [2] has shown that crack turning phenomena can enhance
the residual strength of integrally stiffened structure by turning a crack as it approaches
a stiffener as shown in Figure 1. The results of that study also suggested
that even in cases where the crack did not turn, the observed residual strength of integral test
panels was higher than would have been anticipated, possibly due to the peculiar
three-dimensional profile of the crack as it tunnels under the stiffener. Fracture
orthotropy is also believed to play a significant role [3]. Better understanding of these
phenomena could enable future aerospace programs to utilize low-cost integral structures
with greater freedom and confidence than at present.
Figure 1. Up-Close Photographs of Failed 2096-T8X Panel With Integral Stiffeners
As part of the Integral Airframe Structure (IAS) program now in progress at NASA Langley Research Center, it is proposed to further the development of the theory of crack
turning and other phenomena relative to the residual strength of integrally stiffened structures.
2.0 Scope
In keeping with the present emphasis of the IAS program on metallic structures, the
primary focus of the proposed program would be on crack turning phenomena in metallic
structures. However, the behavior of non-metallic materials may also be considered
where appropriate to the theoretical development and validation (i.e. the ideally elastic
vs. the elastic-plastic behavior). Also, crack turning in composite wing structure
has been observed in tests at NASA, and the proposed effort would coordinate with
and support efforts at NASA and elsewhere to understand these phenomena. Crack tunneling and other phenomena relevant to integral metallic structure may also be studied as
appropriate.
3.0 Approach
Based on Reference [2], and more recent developments under the IAS program [4], there
are several concepts/observations which should guide this work with regard to metallic
structures. First, the effect of the T-stress (the second order term in the Williams
expansion of the stress field about a crack tip) is much more pronounced on tearing
cracks than on fatigue cracks. Also, fracture orthotropy has been observed to play
a large role in directing the crack, and the fracture orthotropy can be much different
in the fatigue and tearing regimes. It has further been proposed that for stable tearing,
two regimes of crack path behavior exist--one which is mode I driven, and another
driven by mode II, or some other shear phenomenon. The physical mechanism by which
the crack path develops still remains somewhat mysterious, and new criteria are still
being brought forth which deserve further scrutiny. A discussion of the proposed
approach based on these principles follows.
3.2 T-Stress Effect on Crack Path
The dramatic difference in fatigue and tearing crack paths in a high T-stress environment
of a Double Cantilever Beam (DCB) specimen is well documented in References [2], see also Figure 2. The first order orthotropic theory of FRANC2D [3] is seen to predict the fatigue crack growth path quite well, but not the stable
tearing path. A second order isotropic theory [5, 6] explains this behavior, but
lacks the orthotropic capability (though formulation of such a theory is already
showing promise under the IAS program, as will be discussed in the next section). The FRANC codes do not presently include any second-order turning theory. Nevertheless, the relevance of the T-stress effects to crack turning in integral structure was validated in Reference [2] (high T-stresses were found to occur as a growing crack nears a stiffener
in a pressurized fuselage, promoting crack turning). Thus, the theory developed
under this program must properly account for the influence of the T-stress. This
also suggests that method for calculating the T-stress must be robust and coded into the
FRANC software.
Figure 2. Comparison of Fatigue and Tearing Crack Paths
in T-L 2024-T3 DCB Specimens
3.3 Fracture Orthotropy
Fracture orthotropy is defined by the ratio of the crack growth resistance in the
two principle material orientations, which for an isotropic material is unity. It
should be distinguished from elastic orthotropy, which describes a difference in principal
moduli.
New isotropic theories are constantly being put forth, but the real metallic materials
used in structures are typically fracture orthotropic, though elastically isotropic.
Even in 2024-T3, the fracture orthotropy ratio is on the order of 0.9 (Figure 2)
for mid-range fatigue crack growth, which substantially alters the crack path compared
to the isotropic case. 7050-T7451 plate has been observed to have a mid-range fatigue
orthotropy ratio of about 0.9 as well (Figure 3), but IAS data indicates that the
tearing orthotropy ratio is more like 0.6, which has a tremendous effect on crack paths,
as shown in Figure 4.
Figure 3. A FRANC2D Study of DCB Crack Turning Behavior, Including 7050-T7451 Plate Fatigue Crack Growth Data for Comparison
Notably, the developmental IAS 2nd order fracture orthotropic theory shown for comparison in Figure 4 appears extremely promising for predicting tearing paths in orthotropic metals. It is based on a combination of the theories of References [3] and [6].
However, the methods to measure the material constants used in the analysis are not
well developed at this point for the case of fracture orthotropy (the characteristic
length, rc, associated with the 2nd order theory was based on an educated guess), and the apparent accuracy of the method is still viewed with some hesitation. Also the calculations
involved in this method are extremely tedious at present, and need to be added to
the FRANC codes.
If all goes well with the metals work, a further advance which could be explored under
this program is the formulation and of a 2nd order theory with both elastic and
fracture othotropy for use with composite materials. Emerging work by colleagues
on development of the orthotropic version of the Williams stress field expansion
could soon bring this within reach.
Figure 4. Fatigue Crack Paths for 7050-T7451 DCB Specimens Compared with 2nd Order
Turning Theory with Fracture Orthotropy
3.4 Other Turning Criteria
It is an object of this undertaking to gain understanding of the physical process
by which the crack path is determined. This is particularly significant if the crack
passes from one regime into another, and the crack directing process changes. Just
such a scenario has been observed by Mike Sutton [7] for cases where KII/KI >1, and explained based on void growth phenomena. Recent formulations for void growth
and other potential drivers are given by Shirmohamadi [8], and should be examined
to see if they have merit in structurally important regimes. A potentially important
crack turning case in at least one IAS test configuration appears to be related to
a shear phenomenon of a regime unlike that described by the (mode I dominated) 2nd
order theory described above. A composite damage growth behavior of an apparently
similar regime was observed in the NASA Advanced Composite Technology (ACT) program, and was successfully modeled using an entirely different approach [9] (which incidentally does not predict crack turning in properly in the mode I dominated regime). The implications of these developments must be considered to develop a robust prediction capability for crack trajectories for a wide range of geometries and loading scenarios.
4.0 References
1. T. Swift, "Application of Damage Tolerance Technology to Type Certification",
SAE Paper #811062, Aerospace Congress and Exposition.
2. R. G. Pettit, J. C. Newman, M.S. Domack, Crack Turning Damage Tolerance Approach for Integrally Stiffened Structure
, 19th ICAF Symposium, Edinburgh, June 1997.
3. T. J. Boone, P. A. Wawrzynek, A. R. Ingraffea, "Finite Element Modeling of Fracture
Propagation in Orthotropic Materials", Engineering Fracture Mechanics, Vol. 26, No.
2, pp. 185-201, 1987.
4. Integral Airframe Structures Program
, Joint NASA/Industry Workshop (compilation of presentations by J. Funk), October 28-29, 1997.
5. I. Finnie, A. Saith; "A Note on the Angled Crack Problem and the Directional Stability
of Cracks", International Journal of Fracture
, Vol. 9, pp. 484-486, 1973.
6. M. Kosai, A. S. Kobayashi, M. Ramulu, "Tear Straps in Aircraft Fuselage", Durability of Metal Aircraft Structures
: Proc. of International Workshop on Structural Integrity of Aging Airplanes, Atlanta
Technology Publications, Atlanta, GA, pp. 443-457, 1992.
7. M. Sutton, University of South Carolina, unpublished papers.
8. M. Shirmohamadi, Stable Crack Growth Trajectories and Fracture Due to Interacting Cracks
, Ph.D. dissertation, UC Berkley, 1995.
9. F. Abdi, GENOA Finite Element Code, Alpha Star Corporation, Long Beach, CA.