Nafems benchmarks for composite delamination

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- 1. AVAVAVAVAV AVA VAVAVAV AVAVA VAVAV AVAVAVA VAV Committed to Professional Development AVAVAVAVAV for Engineering Analysis I. Simulation Benchmarks For Composite T Delamination by G A 0 Davies Published by NAFEMS Ref: - R0084 Issue 1 www. nafems. org
- 2. Benchmarks For Composite Delamination Author: G A 0 Davies Current trends towards more efﬁcient and cost-effective component design and manufacture have resulted in an increasing interest and emphasis on the use of laminated composite materials, particularly ﬁbre-reinforced composites, as a viable economic alternative to traditional engineering materials. Modern composites have major beneﬁts in terms of their strength, stiffness and fatigue performance. Signiﬁcant weight reductions can be achieved and there is now a wide choice of general purpose and more sophisticated materials for both the ﬁbre and matrix. Analysis of component designs which utilise composite materials is not straightforward in view of the complexity of the material behaviour. In order to address these design problems, almost all commercial ﬁnite element programs now include composite element formulations and facilities for predicting composite material failure traditionally derived from in-plane and transverse shear stress criteria. Previous NAFEMS reports have derived linear elastic benchmarks concerning the prediction of such stress ﬁelds in composites. The four 2D benchmarks described in this report concern delamination between the plies in which the resin matrix fails in tension, shear, or both. They encompass mode II— shear driven delaminations with a curved crack front in a circular plate, subject to either point loading or external pressure, and mode I tensile non-linear delamination in a double cantilevered beam composed of a carbon/ epoxy T800/924 or T300-PEI thermoplastic material. These benchmarks have been selected from a European Union research program concerned with designing and testing adaptive ﬁnite element techniques for predicting delamination in composites. The work was performed by Professor Glyn Davies, Department of Aeronautics, Imperial College of Science and Medicine, London, under the auspices of the NAFEMS New Technology Working Group. J McVee QinetiQ Rosyth (Chairman) P Bartholomew QinetiQ Farnborough T Edmunds Rolls Royce Bristol S Hardy University of Wales, Swansea A Ramsay MSC. Software P Hopkins Astrium Ltd. N Warrior University of Nottingham Approved for issue Signed 33* Q .33”). /42¢ Date 9th August 2002 Issue: 1 J McVee — Chairman of NT Working Group.
- 3. Disclaimer Whilst this publication has been carefully written and subject to peer group review, it is the rea¢ler's responsibility to take all necessary steps to ensure that the assumptions and results from any finite element analysis which is made as a result of reading this document are correct. Neither NAFEMS nor the authors can accept any liability for incorrect analyses.
- 4. BENCHMARKS FOR COMPOSITE DELAMINATION CONTENTS Page 1. INTRODUCTION 3 2. THE NEED FOR BENCHMARKS 5 3. BENCHMARKS 9 Benchmark l(A) 10 Benchmark l(B) 13 Benchmark 2 15 Benchmark 3 17 4. REFERENCES 19 Benchmark speciﬁcations 21-24 Figures 1 — 14 25-34
- 5. BENCHMARKS FOR COMPOSITE DELAMINATION
- 6. INTRODUCTION 1. INTRODUCTION High performance composite materials have been in use for 20 years in the Aerospace industry. The speciﬁc stiffness of carbon ﬁbre reinforced plastics is unmatched by any metal, and most agile and high speed military aircraft could not have met their speciﬁcation without using it. Figure l for example shows the amount used in Euroﬁghter. The expense has restricted their use, outside Aerospace, to rather specialist areas like sporting goods, racing cars, medical equipment, nuclear fuel processing and the like. Hybrid structures have also been effective, using carbon composite skins as a way of rescuing aging concrete structures. However the costs of the basic materials and their processing have come down of late and the engineering community has also realized that composite structures may actually be cheaper due to the small number of parts compared with traditional metal structures assembled from many components. The buzz word is ‘unitisation’. Any form of transport will beneﬁt from being light, as fuel costs and environmental pressures begin to bite, and mass produced cars will contain more composites, probably thermo-plastics. These can be formed quickly from cured ﬂat sheets, in contrast to thermosets in which the fibres and the resin are brought together and cured in an autoclave or heated press. The use of composite structures represents a challenge to the designers and the ﬁnite element community because their strengths and failure modes are not as easy to predict as in metals. This is the reason for this report and the research programme which underpinned it.
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- 8. THE NEED FOR BENCHMARKS 2. THE NEED FOR BENCHMARKS NAF EMS was founded in 1983, largely in response to the concems that the ﬁnite element codes were full of bugs, and anyway the method itself was approximate wasn’t it? Thus the early efforts were directed at producing benchmarks which code developers were then invited to try, and the results were then published for all to see [Refs. 1 & 2]. The emphasis was entirely on the ability of a code to simulate stress ﬁelds, probably with a stress concentration and gradient somewhere, but no further expectation of what to do with the answers. Simulating failure came later with benchmarks on elasto-plasticity and on fracture [Refs. 3 & 4]. Here the emphasis was on the numerical procedures and algorithms to mimic the physics; and, since the procedures were mostly non-linear, to converge to the right answer. At this time it was thought that non-linear problems were computationally expensive, and required much skill on behalf of the user. In fact many structural codes of practice (such as for pressure vessels) actively discouraged non-linear analysis, preferring to take the simpler elastic solution and then tune it with empiricism to allow for plasticity or limit state analysis. Hopefully ﬁnite element codes are now much more sophisticated, are geared to helping the user create a ﬁnite element model quickly (possibly from an existing CAD description) and are able to present the results as user- ﬁiendly maps of stress/ damage contours etc. Computing power is now incredibly cheap and should be no barrier to iterative non-linear analysis. Without going too much back to basics, the behaviour of high-performance laminated structures can be brieﬂy described. Thin-walled structures will usually be made from laminates as shown in Figure 2, consisting of individual plies in which the uni- directional ﬁbres are embedded in a resin. The brittle ﬁbres (carbon, glass, aramid) are strong and stiff and their propensity to crack is overcome by using very ﬁne ﬁbre diameters of microns but knowing the resin will perform a load by—pass route around every ﬁbre crack, even if there are countless numbers of ﬁbre ﬂaws. However the resin has very little strength (often as low as 50MPa) compared to the uni-directional ﬁbres (of order 2000MPa) so properties transverse to the ﬁbres are relatively very poor. This is
- 9. BENCHMARKS FOR COMPOSITE DELAMINATION overcome by assembling a whole series of plies in a single laminate as shown in the ﬁgure, the stacking sequence being chosen to suit the local loading conditions. This approach has worked ﬁne but we must remember that the ‘through-thickness’ strength still relies entirely on the resin and is still poor. Measures to improve it, such as stitching, weaving, and arrays of micro-pirrs are actively being developed. The failure of laminated composite structures therefore needs to be simulated correctly by ﬁnite element codes. The in-plane failure, dominated by the behaviour of the ﬁbres, is reasonably straight---forward, and many ﬁnite element codes have facilities for predicting in-plane failure. The prediction of in-plane stress ﬁelds and what to do with them was covered in earlier NAF EMS benchmarks studies [Refs. l0&l 1]. The approach to in-plane failure is rather like elasto-plastic analysis in that the loading is increased for an elastic model u71til the stresses in a particular ply in any element reach a ‘failure threshold’. The failure criteria in use are many, but they virtually all use a polynomial combination of the various stress components in tension, shear, or compression in the ﬁbre direction or transverse to it. This coupling between the components -when failure occrirs is empirical and based on tests. A very commonly used criteria is the well-known Chang-Chang coupling between tension/ compression and shear[Ref. 5]. When the ﬁrst ply fails in an element its stifﬁiess is then reduced to a nominal value and the loading increased until eventually all the plies in some region reach their failure level and the whole structure loses its stifﬁress. This concept does not differ materially from elasto-plastic failure and the results are a reasonable simulation of real life. The other failure mode, and the one addressed in this report, is delamination between plies in which the resirr matrix fails in tension, shear, or both. Because this transverse strength is so low, these ‘through-thickness’ stresses need not be high to be dangerous. They can be caused by out-of-plane loading such as a concentrated impact force. However they can also be caused by any gradient in the in-plane stress ﬁeld since transverse stresses are proporti anal to these gradients. Examples could be any stress concentration such as a hole or notch. Laminated skins should not therefore have
- 10. THE NEED FOR BENCHMARKS excessive taper, and in Aerospace a safety rule not to exceed a taper l in 20 is common as a design tool aid. Another example is the stress ﬁeld near an edge which can vary rapidly in a ‘boundary layer’ and the consequent through-thickness stresses will depend on the particular stacking sequence. If delamination occurs, and the in-plane stress ﬁeld is tensile, then structural failure may not actually happen, although the structure may be vulnerable to environmental effects. However if the local stress ﬁeld is compressive, then a delaminated zone can be disastrous, and it is essential to predict not only the onset of delamination but also its extent and whether it will propagate in an unstable fashion. This is not straightforward since a simple strength criteria will not work for a brittle material like an epoxy resin. Also any delamination is effectively a crack, and any attempt to examine the stresses at the crack front will reveal inﬁnitely large values if a ﬁne enough FE mesh is used. We will therefore have to use fracture mechanics, in which the energy released, as a delamination propagates, exceeds the energy absorbing ability at the crack tip. This energy absorbing ability (the Fracture Toughness) is measured as the “critical” strain energy release rate and is a material property. It is high for ductile materials but low for brittle ones like the ﬁbres and resins commonly used in carbon/ epoxy composites. (Benchmarks 2 and 3 are in fact based on a standard fracture touglmess test. ) There are two ways in which ﬁnite element codes determine the energy release rate. The ﬁrst one will be familiar to ﬁnite element analysers of fracture toughness in metallics[Ref 4.] A potential crack front is opened up (or closed) and the work done by the nodal forces over the displacements is logged. This direct evaluation of energy release rate can be tricky when the front is curved as shown in Figure 3a, where it is acknowledged that a very ﬁne mesh may be needed to get the strain energy release rate accurately. Another approach is the use of interface elements which can behave rather like a real resin interface as it is stressed and then cracked. These special elements need to have a force/ displacement relationship like Figure 3b in which the initial behaviour is elastic until a ‘strength’ value is achieved. This can be based on real tensile or shear strength. The element then has to degrade such that the area under the curve is equal to the critical energy release rate G C for that material, based on tests using the simple rigs described later. The method of interface elements does of course involve creating more
- 11. BENCHMARKS FOR COMPOSITE l)ELAMINATION elements, and guessing where they are needed, but it does have the advantage that no real crack front has to be monitored. The elements ﬁnd it for you. It tums out that the interface element performance is not very sensitive to the assumed decay law, as long as the area is G C. In Figure 3b the decay is simply linear.
- 12. BENCHMARKS 3. BENCHMARKS In 1997 the European Union decided to support a three year research programme ADCOMP [Ref 14] in designing and testing adaptive ﬁnite element techniques for delamination, noting that a ﬁne mesh would be needed in the vicinity of a crack front but not away from it. The consortium consisted of research establishments, industry, and academia , from the UK, France, Germany, the Netherlands and Italy. As part of this programme some nine benchmarks were designed so that the research methods could be evaluated. Four of these are presented in this report. Any benchmark has really to satisfy several criteria which haven’t changed since NAFEMS ﬁrst started publishing them: 0 Although the physics may be complicated, and probably non-linear, the tests should be as simple as possible otherwise no-one will use them. 0 ‘Simple’ means easy to generate the model. 0 The results should be validated by experimental tests, and by an analytical solution if possible. Using another ﬁnite element solution for validation should be a last resort. 0 The target should be a failure load as a deﬁnite quantitative metric, but the history of the non-linear simulation is also very valuable in assessing the credibility of the code modeling. 0 Unlike early benchmarks, no attempt need be made to assess the efﬁciency of a code. This would mean deﬁning the ﬁnite element and mesh in detail and the type of computer. It was felt that capturing the physics was all important. The four benchmarks chosen are laid out as one page speciﬁcations at the end of this report.
- 13. BENCHMARKS FOR COMPOSITE DELAMINATION Benchmark l(A) All benchmarks are presented a: ~. structures subj ected to static loads which are then increased until delamination and failure occurs. However this benchmark is particularly important for analysts wishing to simulate low velocity impact and consequent damage. Composites are vulnerable to impact since they have no ductile energy absorber and it is well known that the compressive strength of plates after impact may be reduced by more than 70% even though the damage (like internal delamination) may be invisible to the observer. The second of Figures 4 shows the experimentally observed delamination areas for a very large number of plate 3, small and large, with both simple supports and clamped boundary conditions, (denoted in the ﬁgure by letters s, l and s, c) and even some stiffened panels, all of three thicknesses l, 2 and 4mm. All plates had a quasi-isotropic lay-up (+45,—45,0,90), .s and the envelopes of the delamination were all nearly circular. For such a large variety of structures, wit h a range of dynamic responses, it is not surprising that the damage maps plotted against impact energy in ﬁg. 4 look like white noise. It is impossible to detect trends. Now the delamination in this case is driven by the impact- induced shear stresses, a so-cal" ed mode II fracture. It is therefore reasonable to suggest that the driving mechanism is t 1e force and not the energy. In all the tests the maximum impact force was recorded and : he ﬁrst of Figures 4 is the consequence. The resulting maps are dramatic. All the damage areas now collapse onto three fairly discrete bands corresponding to the three plate: thicknesses. The plate sizes and boundary conditions are no longer inﬂuential. If we try to explain this in terms of shear stresses we get nowhere. Thus a distance r away from the force the average shear stress is given by P/27r rt , where P is the force. The maximum shear stress in the mid-plane is 1.5 times this, and if we assume that delamination occurs when this maximum shear exceeds the shear strength (1 ), we can ﬁnd the delamination area. If this area was a circle in the middle of the plate the area would be A = 7: r2 = (9/1672 t2 )(P/ T )2 . This relationship is a parabola and the three dotted curves in Figure 4, (using a shear strength of 50 Mpa for this particular material) are shown for the thicknesses 1 =1, 2 and 4mm. Even though this analysis is desperately simpliﬁed, these continuous curves do not begin to capture the physics. To take the case 10
- 14. BENCHMARKS of the 4mm plates, there is no damage at all until the force approaches 6000N and then it positively explodes. This suggests an unstable fracture, and a simpliﬁed analysis [Ref. 6] assuming a completely axisymmetrical behaviour conﬁrmed this. Actually it is impossible to have an axisymmetrical lay-up of constant thickness and volume fraction. The quasi-isotropic lay-up, with equal amounts in the [0, +/ - 45 & 90] directions is an approximation. The analysis in Ref. 6 lets a circular delamination in the mid-plane grow by a small radius 6 r, and ﬁnds the work done by the force P due to the increased ﬂexibility of the two delaminated plate halves. Equating this to the work done against the expanding crack front, this delivers a critical load given by Pm, 2 = (87: 2E t3 G, ,C)/9(1—v’) where E, t, and v are the usual modulus, thickness, and Poisson ratio. G , ,C is the mode II critical energy release rate. The results are displayed in the ﬁrst ﬁgure 4 and have clearly captured the physics correctly. No delamination occurs until the force achieves the critical value as indicated by the vertical arrows. This benchmark then consists of a single central force applied to a plate which may be assumed to be isotropic and having a circular delamination in the mid-surface. The value of the critical force above does not depend on the plate size or the plate boundary conditions. This benchmark has the virtue that it is essentially 1-D and the ﬁnite element model can use axisyrnrnetric plate elements or else just take a convenient sector. The benchmark description, material properties, and the experimental results for P are given in the speciﬁcation table, typical of past NAF EMS benchmark speciﬁcations. Examples of a ﬁnite element simulation are now shown, using the code LUSAS, with axisyrnmetrical interface elements lT6XR, rather than using the crack openingclosing approach. These interface elements were inserted along the center middle surface of the model shown in Figure 5. The homogenous plate has a rather ﬁne mesh and the elements are axisyrnrnetric solids QAX8. The boundary condition is effectively a simply supported edge but the critical delamination load is independent of this boundary condition. The benchmark allows the modeler to use any dimensions. For this illustration of an FE solution the circular plate was chosen to have a diameter of 100nm, a thickness of 3mm, and an initial circular delamination of diameter 30mm. When using an interface element the values of the initial elastic stiffness up to a ‘failure’ 11
- 15. BENCHMARKS FOR COMPOSITE DELAMINATION value, whether mode I or mode £1, can be selected arbitrarily. In this benchmark the maximum shear strength is chosen to be 57Mpa and results in the loading stage 0 to A in ﬁg. 6. The non-linear" loading rc utine used by LUSAS is implicit, with an arc-length strategy in case the stiffness changes sign, i. e. a snap-through or a snap-back occurs. Figure 6 shows the history of the applied load and the central displacement response. The initial behaviour up to point: A is entirely elastic but at A the interface elements opened up and a series of displa cements occurred at an almost constant load, which was 98% of the theoretical critical vzilue. For a differently chosen initial delamination the elastic rise to point A would have a different slope but the collapse load would still be the same. The theoretical analytical value indicated an indeterminate delamination length as soon as the critical load is reach ed. This is the bound between stability and instability. The FE simulation in this case predicts the critical load correctly as a constant value whilst the delamination propagates from A to B. This is all that is necessary to show that the code routine works. However in this case th e simulation was allowed to carry on further. The point B corresponds to the delamination front reaching the outer boundary at which the plate should become two halves instantly and the load becomes unsupportable since the two halves have only one quarter of the original stiffness. An explicit code would pick up the consequent dynamic ‘snap-back’. In this case the ﬁnal parting of the two halves takes place more gradually as the interface elements at the edge soﬁen over their process zone and the implicit arc-length routine captures this snap-back to C and ﬁnal recovery to D which is on the load deﬂection curve DE (passing through the origin) for the separated two plates. Figure 7 shows the ﬁnal deformed shape of the separated plates. This is an interesting excursion beyond the target of the benchmark. 12
- 16. BENCHMARKS Benchmark 1(B) This second benchmark is also axisymmetrical so an easy model to create. However it is physically quite different. In Benchmark 1A it was found that the critical load for delamination propagation was independent of the delamination length. This is almost unheard of since most fracture thresholds vary typically like a crack length to a power -§ . It happened because the energy release rate is proportional to the delamination radius but the energy absorbed also increases with radius due to the expanding crack front. This second benchmark consists of a circular plate with the delamination growing in from the edge and therefore the crack front is now decreasing. For this crack to propagate we need to arrange interlaminar shears to be a maximum at the outer boundary and not in the center. This is achieved by applying a uniform pressure p to the plate and supporting it (clamped) around the outer edge. The mean shear stress varies linearly from 0 in the center to a maximum %pR/ t at the edge where the support reaction is §pR per unit length, R being the radius. If the radial size of the delamination is I, it was shown, using an energy release balance again [Ref. 7] that the critical pressure for delamination growth is given by 1 4 1 . = —2G E3/1- 2 zj pen! 3 [ IIC t ( V _ and is clearly unstable, once started, since p decreases with 1 increasing. For small lengths (l<<R) the critical pressure varies like I” which is a little different from the familiar l E for plane cracks. However as is usual the pressure required to propagate is inﬁnite for a zero crack length. This is typical of conventional elastic fracture mechanics, so some mechanism is required to start the delamination, other than assuming a small crack exists. (Although this route is acceptable in ‘damage tolerance’ exercises). Following the practice for interface elements it is sensible to assume a strength criteria to initiate the delamination, in this case an interlaminar shear strength. Taking the maximum shear stress in the mid-plane as 1.5 times the mean shear p(R-l)/2t , we ﬁnd the critical pressure needed to produce a maximum shear stress 7 at the crack front is given by 13
- 17. BENCHMARKS FOR COMPOSITE DELAMINATION 4: 3(R -1) This benchmark has some experimental data reported in Ref. 7 where carbon ﬁbre P: '5 composite plates were subjected to an increase in pressure until they delaminated in a sudden unstable fashion. Now it is impossible to make an axisymmetrical plate of constant thickness, so the tests employed a quasi-isotropic lay-up so arranged that the middle surface was an interface between the +45 ° and -45 ° plies. This means that the material properties in the radial direction will vary around the assumed circular crack front. The maximum and minimum values of G "C and E were found to be 11001/m2 and 550]/ m2 and 60GPa and 44Gpa respectively. If we tum to the ﬁgures shown in the benchmark there are six experimental test values of the failure pressure. We see that the pressure required to fail with no initial delamination is close to the lower strength criteria but that after delamination has started the strength criteria completely fails to reproduce reality. It predicts an actual increase in pressure required to propagate the delamination into the plate interior where the shear stress decreases linearly. Theisimple fracture criteria however works quite well even though it is based on an axisymmetrical model. In fact the two fracture curves f"om the two touglmess values are quite close and they capture the real failure pressure variation well. The benchmark recommends using average values for fracture toug hness, interlaminar shear strength, and modulus for this isotropic model. A ﬁnite element test of this benchmark has been carried out by ONERA [Ref.13] using their in-house code PREFI 2D. Although the benchmark is actually axisyrnrnetric, and therefore uses average material values, it was decided to model the plate using only double symmetry. The mesh ch osen is shown in Figure 8 for delamination lengths of 5mm. and 25mm. There is mod est reﬁnement at the crack front. The elements used were standard Mindlin plate elements with shear stiffness. For this case the usual fracture mechanics approach was adopted rather than using interface elements. ONERA have coded a strain energy release rate (SERR) routine (the “ (9 ” method in Ref. 13) which is used as a post-processor to their nonlinear FE programme STRATNL [Ref 1:3] This routine models the crack front as a cubic B spline and the crack opening displacements as modes which are unity along the crack from and 14
- 18. BENCHMARKS decay linearly to zero on all other elements. The magnitude of these modes then serves as an analytical measure( 77) so that a ﬁrst derivative of the potential energy with respect to 77 gives the equilibrium value of the SERR, and the second derivative says whether the propagation will be unstable or not. Although the FE model was not axisyrnrnetric, it was found that the mode 11 SERR varied by less than i 5% around the circular crack front. In this method there is no loading pre-crack history so Figure 9 just displays the critical pressure obtained by putting the SERR equal to the fracture touglmess of 825]/ m 2 given in the benchmark. The agreement between the FE prediction and the given analytical curve is clear. Benchmark 2 The previous two benchmarks were axisynnnetrical and 2-D so that modeling them was cheap, and the ﬁnite element routine for simulating could consequently concentrate on capturing the physics of delamination due to shear propagation against a mode II fracture touglmess. The next two benchmarks are also 2-D but this time involve mode I , (tensile) fracture touglmess. They are in fact the standard double cantilever beam specimens (DCB) for measuring fracture toughness G ,6 . It is assumed that the crack ﬁont, at a delamination distance a from the applied load, is straight, whereas in reality the stress ﬁeld is one of plane strain over most of the crack front but the front curves around a little on both edges where the ﬁeld is plane stress. For a wide specimen these edge effects are not signiﬁcant [Ref. 12] and in this benchmark the width, B = 30n1rn. , is ten times the specimen thickness. It is therefore ﬁne to use simple beam theory and the tip displacement A due to the two applied forces P is given by A : Pa} 2 3E1 where E1 is the ﬂexural rigidity of each arm of the beam. It is now straightforward to . ... ... ... ... ... ... ... ... ... ... ... .. (1) evaluate the work done on the specimen when the crack extends by a small distance 5a. Thus 15
- 19. BENCHMARKS FOR COMPOSITE DELAMINATION 2Pa2 E1 Now this energy is absorbed by the creation of the new surface 2B8a, and if the critical the work done = P. 6A = P. .6 a strain energy release rate is G , C we have propagation if 2P2a2 E1 The crack will propagate when ‘a’ reaches this value and clearly the propagation is 5a = G, C.2B.6a unstable since the left hand side of the equation increases as a increases. The relationship between P and A during this propagation can be expressed by eliminating the crack length a from the above two equations thus 3/2 P2 - . ... ... ... ... ... ... ... ... . . .(2) ie: P needs to decrease as A increases. This benchmark is therefore presented as a test using incremental applied displacements. The experimental values referred to in the Benchmark [Ref. 8] employed carbon epoxy material T800/924 having the values of stifﬁress, strength and touglmess, indicated in the table. There are two ways of simulating this test using standard plane strain elements for the beam, and interface element: -i once again. The approach can either be implicit or explicit. The implicit routine needs a facility once more like the arc-length method, although the force displacement relationship is now merely discontinuous and softening, rather than ‘snap-back’. A model using LUSAS and the loading/ unloading curve is shown in Figures 10 and 11. The switch from the loading to unloading path is fairly well simulated as the agreement with experimental points indicates. The alternative method is to use an explicit dynamic code but to use artiﬁcial mass and damping factors chosen to converge to the static solution as quickly as possible. A new dynamic interi ace element [Ref. 9] has been incorporated into the well- known explicit code DYNA 3-1), and uses the damage mechanics philosophy in degrading the interface stiffness after a strength threshold is reached. . . . as discussed earlier. The solutions presented here in Figure 12 were achieved by using the actual mass of the DCB specimen and a modest amount of viscous structural damping. The results are virtually identical to that obtained using the implicit routine. 16
- 20. BENCHMARKS Benchmark 3 This benchmark is analytically identical to the previous one. It was chosen to test the validity of fracture mechanics for a thermoplastic material which is more ductile in nature than the more conventional thermosets. Moreover when a delamination propagates much ﬁbre bridging takes place. It was by no means certain that classical fracture mechanics would apply. The experimental tests were therefore conducted with great care using the rig shown in ﬁgure 13. The displacement was applied from a hard machine and the resulting load was logged. When the delamination propagated, the crack front position was monitored using a video camera. The experimental results for a large number of tests did show as expected more scatter than in tests on thermoset materials, but the averaged results shown in ﬁgure 14 are quite close to the FE predictions using LUSAS and interface elements once more. Thus the test, the failure model, and the code do seem to be valid. 17
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- 22. 1. l0. 1 1. . Hitchings D, Robinson P, and Javidrad F. "A ﬁnite element model for delamination 13. 15. REFERENCES 4. REFERENCES "The standard NAFEMS benchmarks” NAFEMS ID P18 Davies G A 0. "Background to benchmarks. " NAFEMS ID R0006. "Selected benchmarks for material nonlinearity. " Vols 1 and 2. NAFEMS ID R0026 and R0030. " Two-dimensional test cases in post yield fracture mechanics. " NAFEMS ID R0038 Chang F K and Chang K Y. "A progressive damage model for laminated composites containing stress concentrations. " .1. Composite Materials. 1987 . 21 (9) pp.834-855. Davies G A 0, Zhang X, Zhou G, and Watson S. "Numerical modeling of impact damage. " Composites. 1994. 25(5) pp342-350 Davies G A 0, Robinson P, Robson J, and Eady D. "Shear-driven delamination in 2- D. " Composites partA. 1997.28.pp.757-765. Robinson P, and Song D Q. "A modiﬁed DCB specimen for mode I testing of multi- directional larninates. " .1. Composite Materials. 1992. 26. Pp1554-1577. Iarmucci L. " Dynamic delamination modeling using interface elements. " Computers and Structures 2000. Taig I C. "Finite element analysis of composite materials. " NAFEMS ID R0003. Hardy S. "Composite benchmarks. " NAFEMS ID R0031 . propagation in composites. " Computers and Structures. 1996. 60(6) pp.1093-1 104. Roudolff F. "Development and improvement of delamination models. " ONERA Technical report. RT 28/7256 DMSE/ Y. July 1998. . ADCOMP (Adaptive Composite Delamination Modeling) Brite-Euram III project BE-3580. Monitor J Hernandez. 1999. Roudolff F, and Ousset, Y. “ Comparison between two approaches for the simulation of delamination growth in a D. C.B. specimen. ” Aerospace Science and Technology. No.2/2002
- 23. BENCHMARKS FOR COMPOSITE .5 )ELAMINATION 20
- 24. REFERENCES Benchmark l(A) ORIGIN: Imperial College, Department of Aeronautics ANALYSIS TYPE: Mode II shear-driven delamination with a curved crack ﬁ'ont. GEOMETRY: Axisymmetric An isotropic circular plate loaded by a single point load at the centre. A circular delamination is assumed to start in the centre and midsurface of the plate. LOADING: Incremental point loading until failure at critical load. Failure should be unstable propagation, independent of the delamination size and the plate boundary conditions. MATERIAL PROPERTIES: homogenised isotropic for carbon/ epoxy T800/924 E =60Gpa, Guc=800Jm'2’ v =0.3. r=57MPa LAMINATE LAY-UP: N/ A TARGET RESULTS: Experimental Results: 87r2E(t)3 P P2=TGIIc 1mm 680N 9(1 V ) 2 mm 1895 N 5620 N P = critical force E = ﬂexural modulus t = thickness v = Poisson’s ratio Gnc = Critical mode II strain energy release rate NOTE: The size of the delamination and the plate, and the support conditions are arbitrary. 21
- 25. BENCHMARKS FOR COMPOSITE DELAMINATION Benchmark 1(B) ORIGIN: Imperial College, Department of Aeronautics I ANALYSIS TYPE: Mode II shear-driven delamination with a curved crack front GEOMETRY: Axisymmetric p A circular plate loaded by a uniform applied pressure. The circular sample is clamped around the boundary but is free to slide. Delamination is assumed in the middle surface around the edge of the plate whose radius is 135mm. and thickness 4mm. LOADING: The external applied pressure is increasnxl and the growth of damage from the edge is recorded. MATERIAL PROPERTIES: Homogunised Isotropic T800/924 E = 52 GPa G. = 825 Jm'2 or O.825N/ mm I = 100 MPa (interlaminar shear strengtr1)(ILSS) LAMINATE LAY-UP: This model is isotropic. The test results are for a quasi-isotropic plate, so the curves are upper and lower bounds. TARGET RESULTS: Experimental Results: Initiation P = 4’ 2' 3(R — l) ' Shear strength criterion ILSSﬁ2OMPa | LSS=80MPa Unstable growth after initiation _4 2G, ,CEt3 "2 1 “"3 (1—1/2) '(2R—l)l P = applied pressure R = radius of sample ‘E = interlaminar shear strength 1 = distance from edge of delamination Front delamination length nun i%£¢¢HLH¢ 22
- 26. REFERENCES Benchmark 2 ORIGIN: Imperial College, Department of Aeronautics ANALYSIS TYPE: "Non-linear Delamination GEOMETRY: LOADING: Incremental loading using predetermined displacements (fully supported at right hand end) MATERIAL PROPERTIES: T800/924 Ex, ‘ = 126 GPa, Eyy = 7.5 GPa, Gxy = 4.981GPa, vxy = vy, = vxz = 0.263 Delamination properties : G [C = 0.281 N/ mm, damage initiation stress = 57 MPa. LAMINATE LAY-UP: Unidirectional TARGET RESULTS; Experimental Results: A(mm) P (N) 2.60 86.4 3.25 73.6 4.06 67.2 4.93 57.6 6.07 54.4 7.10 49.6 8.40 43.2 38.4 33.4 33.6 P=3££A 2:10 _ 2(BGCEI)”2 A 2 3EIP = (Pa): BEI G 23
- 27. BENCHMARKS FOR COMPOSITE DELAMINATION Benchmark 3 ORIGIN: University of Twe nte ANALYSIS TYPE: Non-linear Delamination GEOMETRY: Standard DCB test using loading blocks. thickness (2h) : 2.82 mm ‘ width (B) : 20 mm m ‘°”g‘'“ ‘25 “““ pre-crack length (ac) : 53 mm L0] do ' E LOADING Incremental loading using predetermined displacements, ﬁllly supported at right hand end. MATERIAL PROPERTIES: Thermoplastic material (T300-PEI, Ten Cate Advanced Composites) E1 = 120 GPa, E2 = 7.8 GPa, G2 = 3.25 GPa, V12: 0.32, G1, = 1200 J/ m2 LAMINATE LAY-UP: Unidirectional — 20 prepreg layers, with ﬁbre direction along beam and 13p. m starter ﬁlm at mid-point. EXPERIMENTAL RESULTS Deflection 6 Load P Deﬂection 6‘ Load P TARGET RESULTS: (man) 3(1)) (man) (N) 3 5 = 8P3a° from simple beam theory 6-0 Bh E, 10.5 15.5 32 1 _ . 52:3 5 = E P2 3 E1hG, c for crack extension , 3o_() 1 . 34.9 (G = Gk) . 39.4 43.6 with: ' 6 = deﬂection 55:5 P = load 59_() 61.3 61.4 60.4 59.5 58.0 56.3 55.3 54.4 53.2 52.1 51.4 24
- 28. REFERENCES Figures MATERIALS DISTRIBUTION ‘ Carbon Fibre Composite I Titanium I Aluminium Alloy I Glass Reinforced Plastic Fig. 1. Content of composites in Euroﬁghter. (with acknowledgements to BAESysterns) 25
- 29. BENCHMARKS FOR COMPOSITE DELAMINATION 90 ° direction : :-'_. ;.'-'. “.'-‘. -:-‘. -:-. - , . . . . . .-1,.5.-. .-1.. - - Fig. 2. Three ply laminate. MPC for grading Crack Front Fig.3(a) Mesh refinement along a crack front 26
- 30. REFERENCES Force Displacement %: —? Process zone Fig. 3(b) Forcel displacement law for an interface element 27
- 31. I 800 1600 . % StiITPancl2 I %SliITPalIcI I . Q 1400 + 1200 1000 Damage Area (mm x mm) 0 1000 2000 3000 4000 5000 S000 7000 8000 9000 Impact Force (N) Damage Area (mmxmm) 0 A u 0 O A I o I A D + + 0 I O 0 1o _ 5 ’ 20 I I 30 40 ' so ‘ Incident Energy (.1) Fig. 4. Damage maps against force and energy. 28
- 32. REFERENCES EiilllllllllllllllllllllllllllllllllllllllllIIIllllllllllllllllllllll ‘. """"""1!""! "'l'! ""! "'! F'P"""! F!F"! ""'IIllllIlllllllllllllllll ~ IllIIIlllllllllllllllllllllllllIIIIIIIIIIIIIIII nu mmmmnrn Fig. 5. FE mesh used for benchmark 1A 1.00 2.00 3.00 L00 5.00 6.00 7.00 8.00 9.00 10.0 Displt. mm. Fig. 6. Loading history for benchmark 1A 29
- 33. BENCHMARKS FOR COMPOSITE l)ELAMINATION Fig 7 Final deformed shape after delamination reaches the plate edge. rmmlll - I. 3 a . :=ri: =.. -.: '=. -r"l. ..l I = 5mm. 1 = 20mm. Fig. 8. Meshes for quarter plate with delamination propagating from outer edge inwards. 30
- 34. REFERENCES Critical pressure versus delamination length 3 analytical result 8 "I F. E. prediction _. 0 critical pressure (bar) 0 4 -1- 1 . . ——+ 1 0 5 10 15 20 25 30 width of delamination mm. Fig. 9. Critical pressure with delamination width using ONERA fracture mechanics code 111111111111111111111-1111111111»-11:111-rrr1114rrrrrrarrrnnrirrrrrr111-11-1411rrrnuriorrr-111111111411111 Ill rlmmmrmlnl 1 rnmuuun Illnrnl 11Irrrlrrlnruuxrlllllr rm rmmr 1 1 rm 1 rmmmmuumm mm rrlrvvvr I11Ilvrrrrlrllcrrvrrrrrrrrrr Vlllll rlrrrv lmrmrlrrrrrrmrrrrr runmu Fig 10. FE mesh used for benchmark 2 31
- 35. BENCHMARKS FOR COMPOSITE DELAMINATION X E3 Graph Number 1 (‘"20 simple 11n. = LUSAS results circle symbol l| ne= close farm solution 0-100 square symbol line: experimental data 0.080 0.060 R: ltRao1: 0.01.0 0.020 0.0 13.5 0.0 1.93 3.86 5.79 7.71 9.64 11.5 RsltDisp Fig. 11. Simulation of benchmark 2 and test results. (Test data Ref. 8 ) Double Cantilever Beam (DCB) 100.00 I 90.00 ’ - — 50.00 _. . "" Simulation 7000 I I 7 —°“ Experiment result (Robinson 8. Song 1992) 60.00 ' V 5' ’“' 1"“ ‘ 50.00 40.00 30.00 20.00 ’ Vertical Reaction at loading point (N) 10.00 ’ 0.00 1 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 Vertical displacement at loading point (cm) Fig.12. Benchmark 2 simulated by DYNA 3-D explicit procedure 32
- 36. REFERENCES displacement controlled drive -load signal P -data acquisition system displacement signal 8 time signal t counter crack length 0 Fig. 13. DCB rig for displacement-driven mode I delamination BC3 data - experiment versus theory I T? ‘ 9* Experiment I 0 I0 Experiment Theory loo Load N I0 I D } 0 10 20 30 40 50 60 deﬂection lmm Fig. 14. Benchmark 3 for a tough thermoplastic material 33
- 37. BENCHMARKS FOR COMPOSITE I ELAMINATION 34
- 38. 35 NOTES
- 39. Published By NAF EMS Ltd ©2002 NAFEMS, Whitwonh Building, S. :ottish Enterprise Technology Park, East Kilbride, Scotland, G75 OQD Tel: +44 13 55 22 56 88 Fax: +44 13 55 24 91 42 E-mail: infoga7nafems. org Web: www. nafems. org