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Leonardo Times MARCH 2014THE CHALLENGE
Impact damage modeling in composites is challenging for two reasons: The over-all damage state is very complex and dif-ferent types of failure must be modeled. Furthermore, the problem is dynamic, which means that after onset of damage the stiff ness properties must be updated, after which the load is increased.
The thesis was broken into two parts: damage resistance and damage toler-ance. “Please, think it over well, if you re-ally want to get into this thesis”, said my supervisor. He emphasized that this was not going to be the average kind of work.
DAMAGE RESISTANCE AND DAMAGE TOLERANCE
In the seventies, Cairns and Lagacé (Cairns & Lagacé, 1989) developed the notion of damage resistance and damage tolerance at MIT. Damage resistance in this context deals with the amount of damage a
com-posite structure sustains for a given im-pact load. Damage tolerance deals with the residual failure load of the damaged structure. Previous work on these two top-ics included work done by Sun and Chat-topadhyay (Sun & ChatChat-topadhyay, 1975), Cairns and Lagacé (Cairns & Lagacé, 1989), Olsson (Olsson, 2001) and Talagani (Ta-lagani, 2013). These eff orts ranged from simple curve fi ts to very detail fi nite ele-ment analyses using cohesive eleele-ments. Simple curve fi ts do not really add to the understanding of the problem and previ-ous work showed that a detailed fi nite ele-ment analyses could take a couple of days to run (Talagani, 2013).
ANALYTICAL METHODS TO MODEL IMPACT DAMAGE
In this thesis, analytical methods were developed for two purposes: To model the types, amount and location of im-pact damage (damage resistance) and
to determine the residual compression strength of a composite laminate (dam-age tolerance). These analytical models should be used in the preliminary design phase avoiding expensive fi nite element analyses and/or test programs.
When developing analytical methods, one needs to be aware of the following: out of ten potential methods, only one or none actually works. Analytical methods are simplifi ed involving many assumptions. The question is: how valid are the assump-tions made? This question is answered by verifying the model with numerical meth-ods and/or by validating the model using test data. What makes a good engineer is being ready to make the proper assump-tions. What makes a great engineer is be-ing ready to abandon these assumptions and search for the right ones. Although diff erent kinds of impact problems exist, this work is limited to quasi-static impact. This is the case when the impactor mass is
Predicting compression after impact (CAI) in composite laminates
Impact damage has been known to seriously limit the performance of composite
aircraft structures. In the preliminary design phase, tens of thousands of subparts
need to be analyzed for impact. Over the years, many approaches have been proposed
to study the creation of impact damage and to determine the residual strength of the
structure. Although the progress has been signifi cant, most of the existent methods
are too prohibitive for large-scale implementation in the industry. In this thesis study,
effi cient analytical models were developed to study impact damage. These models
will help the designer in the preliminary design phase to perform quick trade-off s and
multiple analyses.
TEXT Fardin Esrail, MSc. Graduate Aerospace Engineering, Aerospace Structures & Computational Mechanics
POST-IMPACT PERFORMANCE OF COMPOSITES
Predicting Compression after Impact (CAI) in composite laminates
MARCH 2014 Leonardo Times
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much larger than the mass of the laminate and the impactor velocity is low (one to fi ve m/s). Furthermore, it is assumed that the laminate is quasi-isotropic and the im-pactor is a steel sphere.
IMPACT LOAD AND STRESSES
Considering a composite plate impacted by a spherical object, the impact load is typically modeled as a point load. This load is applied in out-of-plane direc-tion and will cause stresses through the thickness of the plate. By the principle of energy balance, the impact load can be determined. One can now solve for the stresses using the fi nite element method. This can be computationally expensive requiring a fi ne mesh with element di-mensions in the order of 0.05mm in the contact area (Talagani, 2013). In this thesis study, exponential functions were used in an assumed form for the out-of-plane stresses. Using energy minimization, the other stresses and unknowns were solved for. The analytical method as implement-ed in MATLAB takes three seconds to run and it showed to agree well with fi nite element results. This means that one can avoid long fi nite element simulations by using this model. The assumptions made here seemed to be valid for a wide range of parameters.
DAMAGE SIZE DETERMINATION
Moving on to impact damage modeling, simple failure criterion was used to de-termine diff erent types of damage. Any damage creation before the peak impact load reached was neglected here. By the principle of energy balance, the damage created at the peak impact load was de-termined by modifying the previously determined stresses according to their strength allowables. The big question was: Is this assumption a reasonable one? If it is, it means a simple model can be used to determine impact damage accurately neglecting damage creation and stiff ness loss before the peak load is reached. From a validation with test results published by Dost et al. (Dost, 1991) it was found that the damage contours, for example de-laminations at the interfaces of plies, fi ber breakage, and transverse matrix cracks,
were captured quite accurately. Figure 1 for a comparison of the analysis model prediction with the damage contours ob-tained from an ultrasonic C-scan of a dam-aged quasi-isotropic laminate. For some cases however, the discrepancies were signifi cant.
RESIDUAL STRENGTH DETERMINATION
It is recognized that the models that have been developed so far in the thesis study were simplifi ed and as such, they were not valid for all cases. At that point, three to four months passed from the kick-off meeting, taking into account that two months were only spent on an approach that eventually did not work. Only two months of the actual work resulted into a damage resistance model. A decision had to be made here: Do we start refi ning the damage resistance model to make it more versatile? As the model refi nement seemed to be out of the scope of this thesis, the answer was obvious and we moved on to set up a damage tolerance model in order to determine the residual strength of the damaged composite. The damaged region of the laminate was modeled as several concentric ellipses of diff erent stiff ness and strength. This dif-ference in stiff ness will give rise to stress concentrations when the laminate is load-ed under uni-axial compression. Figure 2 depicts the stress concentration in the damaged region consisting of three ellip-tical inclusions. As the ellipellip-tical boundar-ies are reached, a drop in the stress can be observed. This is attributed to the lower stiff ness encountered in these regions. One can imagine that the diff erence in strength may cause some ellipses to fail and redistribute the load to other ellipses until the entire laminate fails as a whole. To determine the failure load, or the re-sidual strength, of the damaged laminate, a progressive damage analysis was carried out.
PROGRESSIVE DAMAGE ANALYSIS
At the damage site, delaminations and transverse matrix cracks can coalesce in individual smaller laminates, or sub laminates. As the laminate is loaded
un-der compression, the sub laminates can buckle, ultimately leading to fi nal failure. In the analysis model, local buckling was not captured and this would have impli-cations on the failure load predictions when compared to test data. The failure load was determined in an iterative pro-cedure: Apply a small compression load, check which ellipse fails, adjust stiff ness/ strength properties, increase the load and continue the iteration until the laminate fails as a whole. When an ellipse fails, it becomes equivalent to an open hole, in-creasing the local stress concentrations. Failure of an ellipse was assessed by using a fi rst ply failure criterion. See fi gure 4 for the comparison of the predicted failure load with published test results from Dost et al. (Dost, 1991) for a quasi-isotropic laminate.
CONCLUSIONS
The effi ciency of the models created make them prime candidates, when refi ned fur-ther, for trade studies and optimization. They can form the basis to accurately predict the compression after impact strength of quasi-isotropic laminates.
References
[1] Cairns, D.S., Lagacé, P.A., “Transient Response of Graphite/Epoxy and Kevlar/ Epoxy to Impact”, AIAA Journal, Vol. 27, No. 11, pp.1590-1596, 1989.
[2] Sun, C.T., Chattopadhyay, S., “Dynam-ic Response of Anisotrop“Dynam-ic Laminated Plates under Initial Stress to Impact of a Mass”, Journal of Applied Mechanics, Vol. 42, pp. 693-698, 1975.
[3] Olsson, R., “Analytical Prediction of Large Mass Impact Damage in Com-posite Laminates”, Elsevier Science Ltd., Composites: Part A 32, pp. 1207-1215, 2001.
[4] Talagani, M.R., A PhD. Dissertation, Chair of Aerospace Structures & Compu-tational Mechanics, TU Delft, 2013. [5] Dost, E.F., Ilcewicz, L.B., Avery, W.B., “The Eff ects of Stacking Sequence on Impact Damage Resistance and Residual Strength for Quasi-Isotropic Laminates”, ASTM STP 1110, Orlando, FL, 1991. Figure 1. A comparison of the damage contours as obtained from an
ul-trasonic scan from (Dost,1991) (left) and the predicted damage contours (right) for a quasi-isotropic laminate, laminate material: IM7/8551-7.
Figure 2. Comparison of the local stress distribution (the stress parallel to the applied displacement) from the analysis model with fi nite element results in the impact damaged region for an orthotropic laminate ([0/0/0/0]s AS4-8552). At the boundary of each ellipse, a sudden drop in the local stress can be seen.
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