Modeling Cracks and Delaminations In Carbon Fiber Composites

Carbon fiber composites are finding increasing usage in manufactured products.   For example, the Boeing 787 Dreamliner is about 50% composite material by weight, with much of that being carbon fiber laminates or sandwiches.  Here we consider laminate structures fabricated by stacking thin plies of composite material atop one another.  Each ply, about 5 mils thick,  contains fine carbon filaments together with a binding agent often referred to as the “matrix”.

787dreamliner with txt-500x309

Carbon Fiber

Composite

Laminates

laminate plies-700x372

 

Carbon fiber composites are quite strong and fairly light weight, but like all materials they can eventually fail.  Here is a photograph, courtesy of David Hsu and Dan Barnard, showing damage in a 4-ply laminated plate that was subjected to thermal shock.  One sees two types of cracks: cracking of the matrix material within a ply, and separation cracks (delaminations) at the boundary between plies.  The carbon fibers give the material the bulk of its strength, but fairly large cracks can be developed without breaking many fibers.

damage in multiply plate

 

No need to break a lot of fibers to have sizeable cracks:crack of resin-600x333

 

 

Two collaborations are underway between CNDE and the NASA Langley Research Center in Virginia.  They deal with matrix cracking and delaminations, respectively.

types of collaborations-700x556

 

The delamination work is being guided by two key questions:

  • Using a given UT Inspection system, how accurately can you determine the size of a delamination ?
  • If a delam in growing, what is the smallest change in size that can be readily detected ?

 

Early collaborative work on the delamination problem was directed at simulating inspections of laminate structures containing so-called hat-shaped stiffeners.   In some of these structures triangle-shaped delaminations can develop where the stiffener joins the base plate.  In some older test specimens, Teflon inserts were added during fabrication to degrade the bonding of the base plate to the stiffener, and hence to provide a crack initiation site.

 
hat-stiffener-iso-300x338hat-stiffener-side-300x388

 

Models were developed at CNDE to simulate the inspection of ply boundaries containing cracks (delaminations).  Below are simulated ultrasonic C-scans of inspections for the case of a small triangular crack that has grown away from the Teflon insert.  Two inspections are simulated: one using an unfocused transducer, and one with the sound field focused at the depth of the delamination.  The focused inspection provides better resolution, and hence a better rendition of the actual size and shape of the delamination.

 

early model simulations-700x470

Is the model accurate?  The best way to find out would be to compare model predictions against measured responses for delaminations having known geometry.  Finding test specimens containing delaminations with known geometry is not easy.  One model test performed last year took a different route.  There we used a small natural disbond found between titanium and ceramic layers in a multi-layer armor panel.  The size and shape of the disbond were unknown.  However, we varied the assumed size and shape of the disbond in order to get reasonable agreement between measured and predicted C-scans.  This demonstrates how model-assisted delamination sizing might be done.

simulation for small disbond-700x507

 

Proper testing of such simulation models requires actual or artificial delaminations having a known size and structure.  The current research plan for the CNDE-NASA collaboration affords that opportunity.  A number of carbon-fiber laminated plates were fabricated containing artificial delaminations, square in shape and measuring 0.25” x 0.25”.  The disbonds consisted of double layers of Teflon tape, likely to prevent intimate contact from occurring between the two plies on either side of the Teflon.  The Teflon inserts will also be used as starting points for growing more realistic delaminations by fatiguing the plates.

The research plan:  (still evolving)

1.  Develop models to predict UT responses from delams. ISU (paraxial beam models), NASA (finite difference).
2.  Fabricate composite plates with teflon inserts.    (Initially inserts serve as artificial delams for study.)
3.  Measure UT properties of the plates (model inputs).
4.  Fatigue some plates to grow more realistic delams outward from the inserts.  When feasible, use X-ray tomography to determine delam size and shape.
5.  Compare measured and predicted UT responses to see how effective the models are.

n. Rules to estimate limits for crack growth detectability for a given  crack geometry and a given UT inspection system.

 

Below is a measured C-scan image formed by scanning an unfocused transducer over one of the plates and displaying the amplitude of the reflected signal from the ply boundary as a function of position.  For this and other C-scan images in this presentation, the scanned region measures 0.8” x 0.8”, the delamination measures 0.25” x 0.25”, and red (blue) coloration indicates a large (small) reflected response.  The small graph above the color image shows the received signal amplitude versus position along the white line in the color image.  When the transducer is far from the delamination little reflected amplitude is seen. As the transducer is scanned over the delamination, the measured response rises slowly, peaks, and then slowly decreases.  The result is a somewhat “blurry” image of the delamination, whose size is indicated by the black dashed line.  The blurring occurs because of the finite lateral size of the interrogating sound pulse, often referred to as the “pulse footprint” or “beam footprint”.  One measure of the footprint is the full width at half maximum (FWHM) of the incident sound intensity field (proportional to pressure squared).  For our inspection, this FWHM region is indicated by the white circle.  About 2/3 of the incident sonic energy is contained within the white circle.  The larger the FWHM (relative to the delamination size), the more blurry the image will be.

 

delam sizing problem-700x527

 

How can one estimate the delamination size from such a blurry image?  A common method is to use the 50% amplitude rule described below.  One argues that when the center of the transducer is aimed at the edge of the delamination, 50% of the incident sound energy misses the delamination, while 50% strikes the delamination and is available for reflection.  Thus the observed sonic signal should be about 50% of the maximum signal that is observed when the beam footprint is fully within the delamination.  As with all rules-of-thumb there are certain disclaimers.  For example, here one assumes that the delamination acts as a perfect reflector and that there is no reflection whatsoever from a well-bonded ply boundary.

 

50 percent rule for delam sizing-700x471

Below we apply the 50% Rule to the earlier measured C-scan.  We locate the highest-amplitude pixel in the image and assign this a value of 100%.  We then color all pixels red which have an amplitude of at least 50% of maximum.  In this case we know that we are dealing with square delamination, so we can find the size of a square which contains the same area as the red region in the processed C-scan.  That square has a side of  0.24”, a bit below the design size of the delamination (0.25”).

 

50 percent rule-700x482

Note the rounding of the corners in the red image which represents our best guess of delamination shape (using the 50% Rule).  This is a well known problem with the rule.  For example, consider the case when the center of the beam footprint is aimed directly at one corner of the delamination.  One can argue that 75% of the incident sound energy will bypass the delamination, so the measured response will be about 25% of maximum.  To get to 50% of maximum, the beam footprint must be shifted inward toward the center of the delamination.  Related problems will occur at all kinks and curves at the edges of a delamination.

50 percent rule for delam sizing-700x471

 

When attempting to ascertain the actual size of a delamination, three profiles are of interest, as shown below.  The first is a step function which defines the physical boundaries of the delamination.  The second is a blurred version which takes into account the finite size of the beam footprint, assuming an “ideal” (perfectly reflecting) delamination and no other complications.  This can be estimated from the models being developed at CNDE and NASA.  The third profile contains additional variations that arise from other real-life factors, such as local variability in the delamination reflectivity, or sound beam distortions that arise due to inhomogeneity within the laminate plate.  Such auxiliary variations can, in principle, be quantified by measurements made on delaminations which are much larger than the beam footprint.  By comparing measured and predicted C-scans, and accounting for typical auxiliary variations, one can estimate delamination sizing errors.

 

1d profiles of interest-700x523

 

For the carbon-fiber laminated plates containing the artificial delaminations, we recently began to compare model predictions with experiment.  Our first comparisons used plates having a “uniaxial layup” where all fibers run in the same direction (left-to-right in the images). The first step was to determine various physical parameters which determine how sound propagates within the plates.  These include elastic stiffness constants (or their “engineering constant” equivalents) and a frequency-dependent attenuation constant.  The latter describes the rate at which a propagating sound pulse loses energy due to absorption and scattering.   CNDE has developed methods to measure such material properties.  The measured values shown below were used as model inputs.

first comparisons of model and exp-700x527

 

Below is a comparison of measured and predicted C-scans when a 10-MHz, ¼”-diameter, unfocused transducer was used.  Two plates, denoted 8U and 9U, containing nominally identical artificial delaminations were inspected in the same fashion.  The central image is the model prediction, assuming the same UT inspection system with the same equipment settings.  The model is seen to be inaccurate in two regards.  It predicts a larger than observed peak response (about 0.8 Volts compared to 0.5 Volts), with some signals being saturated near the center of the image.  It also predicts the peak response to occur when the transducer is centered over the delamination.  The experimental results display a drop in response at the center.

inspection 10mhz unfocused trans model vs exp-700x502

 

The “broadband” responses shown in the previous slide contain contributions from many frequencies.  It is useful to consider the contributions of the various frequencies individually, since different frequencies have different effective beam footprint sizes.

single freq c scans-700x581

 

Below are selected single-frequency results for the model calculations.  The top row of images show how C-scans of the delamination would appear using only single-frequency data.  The amplitude-to-color mapping has been adjusted in each case so that the highest amplitude pixel always appears red.  The bottom row of images show the beam footprint sizes at the same four frequencies (using the same distance scale as for the C-scans).  As we move up in frequency, the beam footprint narrows, resulting in better resolution of the delamination shape.  At the lowest frequency the corners of the delamination are poorly resolved resulting in a diamond shaped image.  As the frequency increases, the image first becomes round and then takes on a more square-ish appearance.

 

The next two picturees compare the single-frequency model images of the delamination with their experimental counterparts.  Again the colorbar has been adjusted so that the maximum response is always red.  Notice how agreement tends to be better at lower frequencies than at higher ones.

predicted and measured delam c scans-700x507

 

predicted and measured delam c scans 2-700x520

The 50% rule for delamination sizing can be applied to both the single frequency images and the broadband ones.

 

c scan dlam sizing-700x540

Applying the 50% rule to both the model and measured C-scans results in the following graph of the inferred size of the delamination as a function of frequency.  Except at very low frequencies (where the beam footprint diameter exceeds the delamination size), the model predicts that the delamination size is underpredicted by the 50% rule, with the model result approaching the design size (0.25”) from below.  For the experiment data, the inferred size overshoots the design size and then approaches it from above.  Clearly the model is not performing well.

inferred delam graph-700x575

The CNDE model used here makes certain assumptions and approximations.  The laminate plate is treated as a homogeneous, anisotropic material.  Paraxial beam models are used to determine the sound field incident on the delamination, and measured response is computed using a so-called Kirchhoff approximation.  That response is proportional to the square of the incident pressure field integrated over the surface of the delamination.

In addition, the delamination is treated as a flat object which is a perfect reflector of sound.  Below are some conditions not currently treated by the model.

what are we missing-700x607

 

There is some evidence that the last two effects may be present.  Below is a C-scan made using a highly-focused 10-MHz transducer. The beam footprint on the delamination is now much smaller, being only a few hundredths of an inch wide in the vertical direction, but somewhat larger in the horizontal (fiber) direction due to the anisotropy of the plate.  Notice the low-amplitude region slightly left of center.  In this region the delamination may not be a perfect reflector, but rather some of the incident sound energy may be being transmitted into the deeper plies.

Also shown at right (for selected scan lines A, B, and C) are ultrasonic B-scans showing received response as a function of lateral distance and arrival time.  For two of these (B and C) there are variations in echo arrival time that are likely associated with the delamination being “wrinkled” (i.e., non planar).

evidence for any of these-700x507

Efforts are also underway at NASA to grow large delaminations outward from the Teflon inserts.  One method being used is shown below.  A ball indenter is slowly brought to bear on the plate until damage is inflicted.  The ultrasonic C-scan of the indented region reveals a complicated damage pattern that contains delaminations at several ply boundaries rather than just one.  Extending the models to treat non-planar delaminations is the first step toward treating impact damage which spans a range of depths.

 

TOF to 0 crossing-700x531

 

Efforts are also underway at NASA to grow large delaminations outward from the Teflon inserts.  One method being used is shown below.  A ball indenter is slowly brought to bear on the plate until damage is inflicted.  The ultrasonic C-scan of the indented region reveals a complicated damage pattern that contains delaminations at several ply boundaries rather than just one.  Extending the models to treat non-planar delaminations is the first step toward treating impact damage which spans a range of depths.

trying to grow delams-700x550