T. Turner et al. 2011. Int. J. Vehicle Structures & Systems, 3(2), 80-86 ISSN: 0975-3060 (Print), 0975-3540 (Online) doi: 10.4273/ijvss.3.2.02 © 2011. MechAero Foundation for Technical Research & Education Excellence
In tern at ional Jou rnal of Vehicle Structures & Systems Available online at www.ijvss.maftree.org
Energy Absorption Performance of Meso-Scale Discontinuous Carbon Fibre Composites Thomas Turnera,b, Lee Harpera, Nicholas Warriora, and Ari Caliskanc a
Division of Materials, Mechanics & Structures, University of Nottingham, NG7 2RD, UK. b Corresponding Author, Email:
[email protected] c
Ford Motor Company, Research & Innovation Center, Vehicle Design Research & Advanced Engineering, MD3137, Room 3135, Dearborn, MI48121, USA.
ABSTRACT: Discontinuous carbon fibre composites are increasingly being considered for use in automotive crash energy management structures. Discontinuous fibres represent a route to high speed, low cost automated manufacture, either in the form of moulding compound, advanced moulding compound or directed fibre preforming approaches. In this work 40 discontinuous 6K high strength carbon / epoxy tubes have been preformed and manufactured for testing. Variables were fibre length (30mm, 60mm, and 90mm), specimen shape (circular or square) and thickness (2.54mm and 5.08mm). Mouldings were cut into 4 specimens and tested both quasi-statically at 1.6e-4m/s and dynamically at 5m/s. Average specific energy absorption (SEA) was 62.5kJ/kg for static and 43kJ/kg for dynamic. The optimum fibre architecture was a circular tube profile with 30mm long fibres and 5mm wall thickness which gave SEA values of 80.2kJ/kg and 48.4kJ/kg. In-plane mechanical testing was also performed on planar versions of the same fibre architectures to determine whether mesoscopic homogeneity effects which dominate tensile testing affect the energy absorption levels, but poor correlation was observed between tensile and energy absorption results. KEYWORDS: Composite; Crashworthiness; Discontinuous Fibre; Preforming CITATION: T. Turner, L. Harper, N. Warrior, and A. Caliskan. 2011. Energy absorption performance of meso-scale discontinuous carbon fibre composites, Int. J. Vehicle Structures & Systems, 3(2), 80-86. doi:10.4273/ijvss.3.2.02 uniformity of the fibre architecture and give properties closer to the expected ceiling (given by a binary rule of mixtures). Within certain ranges, fibre length also affects performance due to a change in homogeneity, but here critical tow length factors also exist [5].Fibre cost is an important consideration as small tow sizes are disproportionately costly due to the nature of the manufacturing process. The aim of this study was to identify trends in the energy absorption capability of discontinuous carbon fibre tubes while varying common fibre architecture parameters e.g. fibre length, thickness and also tube geometry. By testing the in-plane mechanical properties it was hoped that a relationship between crush performance and in-plane properties could be identified to determine whether the homogeneity effects also dominate crush performance. Polymer composite tubes can be designed to absorb high levels of impact energy by progressive crushing. When a tube is crushed onto a flat platen, energy is absorbed by bending failure of the plies, delamination and friction mechanisms. The high specific energy absorption (SEA) capabilities of composite structures are well documented e.g.[6, 7]. It has been shown that the amount of energy absorbed for a given structure depends on the mode of failure and the crush zone morphology,
1. Introduction Discontinuous carbon fibre based fibre architectures provide a means of introducing high levels of automation and cost saving into low to medium volume vehicle structures[1, 2] and thus leveraging the performance benefits of advanced composites at cost levels usually associated with lower performance materials [3]. Parts tested in this work have been manufactured using the Discontinuous Carbon Fibre Preforming Process which is applicable to medium volume part production and is particularly suitable for large planar structures with complex geometry which would be time consuming to preform by hand. The results presented apply to all random meso-scale carbon reinforced composites made by a variety of methods. The in-plane mechanical properties of discontinuous random composites are dominated by coverage effects [4] where the homogeneity of the fibre architecture is the limiting factor in determining performance. For this reason whilst compressive and shear performance can approach that of typical non-crimp fabric composites for a given fibre volume fraction, the tensile performance is limited due to the presence of low fibre fraction areas and stress concentrations. A key factor in determining homogeneity is tow size, where smaller tow sizes improve the 80
T. Turner et al. 2011. Int. J. Vehicle Structures & Systems, 3(2), 80-86
which in turn depends on how failure is initiated or triggered [8]. There are two main types of trigger; stress raisers and plug inserts [9]. The bevel type stress raiser is the most common type of trigger and consists of a chamfer applied to one end of the section that is to be crushed. Sigalas et al. investigated the effect of changing the angle of the chamfer and found that the steady state load and thus SEA was not strongly influenced by the angle of the bevel [10]. Typically, in automotive applications, packaging restrictions and the need to attach the bumper beam to the crash rail mean that plug type triggers can be more practical [9]. Also, the stroke efficiency is increased, over flat platen crush, to values approaching 100% since debris is forced to the outside of the tube. There is now increased interest in understanding the crush response of discontinuous fibre composites. Micromechanical models have been developed to understand the energy absorption of single fibre pullout & fracture and therefore to predict the energy absorption capability of composites where single filaments dominate the fibre architecture e.g. [11]. However, previous work in discontinuous fibre composites has demonstrated the importance of mesoscopic homogeneity in determining the final mechanical properties of the part [4, 5]. This is a feature that is only observed in composites where the scale of the reinforcing units (fibres, tows etc) approaches that of the composite as a whole i.e. the effect is not observed in materials reinforced by single filaments acting in isolation. Lee et al. [12] have investigated the crush response of glass / polyester and carbon polyurethane plates and tubes and have sought to model the responses using a commercial finite element code. The accuracy of this type of prediction is increasing but additional measures are required to account for stochastic effects, as the size of bundles increases, and often several non deterministic numerical inputs must be supplied to the model following lengthy test programs or reverse engineering procedures. Sheet moulding compounds have bundled fibre architectures (typically 200 glass fibre filaments per bundle) and Jendli et al.[13] have developed an Representative Volume Element based Sheet Moulding Compound crash model with a 2 step homogenisation scheme to allow generation of the 3D stiffness tensor. The model shows good agreement for tensile testing up to 200s-1 but crushing failure modes are not shown. Jacob et al.[14] have tested a variety of commercially available chopped carbon fibre based moulding compounds in quasi-static crush using a flat plate geometry. 12K and 48K based materials were tested at 40% and 50% fibre volume fraction and 1” and 2” fibre lengths. The results of the study show several interesting features: an increase in tow size caused a decrease in SEA, as did an increase in fibre length. Higher fibre volume fractions are also shown to give variable results and not always an increase in SEA. The authors also note the lack of energy absorption data in the literature for this type of mesoscopic discontinuous carbon fibre material.
2. Experimental methodology 2.1. Part Geometry& experimental design 600x800mm preforms were manufactured by the directed carbon fibre preforming process at an areal density of 800gsm and 1600gsm. These areal densities were chosen to provide 35% fibre volume fraction in 2.54mm and 5.08mm cavities respectively. Round tubes of 50.8mm outer diameter were manufactured at these two wall thicknesses. Square profile tubes were also manufactured with a corner radius of 12.7mm (see Fig.1). Other profiles were not considered due to the difficulties of integration with other structures and the lack of comparative data. The chosen experimental variables are wall thickness (as above), geometry (as above) fibre length (30mm, 60mm & 90mm) and test speed. Quasi-static testing (actual test speed is 1.6e-4m/s) provides baseline specific energy absorption data and is a widely used test speed. Dynamic testing has also been performed at 5m/s to provide a comparison with the quasi-static results and to allow assessment of any rate effects present with low speed impacts. Thus 24 separate tube mouldings were manufactured to complete a full factorial array of all scenarios. Each moulding was cut into 4 samples.
2.2. Materials Fibres employed are standard Toho Tenax GmbH 6K HTA fibres (Tenax J/E HTA40, E13 sizing). Resin and compatible binder are from Advanced Composites Group. MVR444 is a single component pre-catalysed tetra-functional epoxy resin. The recommended compatible ACG ST358 binder was used at ≤6%wt.
2.3. Part manufacture An increased number of fibre layers enhance preform homogeneity but reduce out of plane curvature, which increases interlaminar properties. A single fibre layer cannot be used, as a weak line will be formed at the preform join. The architecture shown in the detail of Fig.1 has been used for this work.
Fig. 1: Tube sections
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T. Turner et al. 2011. Int. J. Vehicle Structures & Systems, 3(2), 80-86
Mould tools have been manufactured from aluminium with mild steel end caps. The split in the tool is sealed with a silicone o-ring. Tools are clamped together with M8 cap head screws. Two sets of outer tool halves (circular and square) and 4 inner mandrels were manufactured. Frekote 700NC liquid release agent was applied to all tool surfaces. Preforms were wound directly onto the inner mandrel and assembled into the tool (Fig. 2). The preform was consolidated by manually winding it between the inner mandrel and a pressure roller while the preform was heated using a hot air gun. Small amounts of additional binder were used to seal the preform edge onto the rolled preform.
Falling weight impactor Crushed tube sample
Stationary crush platen
Kistler 9051A Load Cell
Fig. 2: Square section preform assembled into lower tool half
Preforms were weighed and then infused with epoxy, by vacuum assisted resin transfer moulding. Matrix material was pre-heated and injected at 70°C and the tool temperature was held at 80°C during injection. A cure cycle of 2 hours at 180C followed. Samples were wet cut using a diamond cutting wheel to 100mm lengths and a crush initiator was machined onto the end using spindle moulder with a 45 profile. Specimens were weighed before chamfering to obtain accurate mass/unit length data (see Table 1).
Fig. 3: Dynamic testing experimental arrangement
In order to extract realistic SEA levels the calculation of energy absorbed was performed from 5mm of displacement onwards to remove the effect of the crush initiator. Summation of energy continued until 55mm of crush length before the crush load started to rise due to build-up of debris within the tube. The SEA values for dynamic testing were calculated as above. However, as displacement data was not available directly it was obtained by integrating the acceleration (determined by crush force / impactor mass) twice to obtain displacement. 2.4.4. In-plane Tensile Untabbed straight-sided samples 210x25mm were cut at 0 and 90 orientations from flat plaques manufactured using the same method as the crush samples. 6 repeats were tested for each orientation of each fibre architecture. Testing was performed on an Instron 5982 electromechanical universal testing machine at a loading rate of 1mm/min. A 50mm gauge length Instron extensometer was used to measure the strain. Samples were recorded at a rate of 10Hz.
2.4. Testing 2.4.1. Quasi-static crush Quasi-static testing was undertaken in a Zwick 100kN servo-mechanical universal testing frame at 10mm/min. Crosshead displacement and crush load was logged at 6Hz. A finish-ground 75mm thick steel crush platen was used. Four specimens were tested in all cases.
2.4.2. Dynamic crush Dynamic testing was performed on a Rosand Type 5 instrumented falling weight drop tower modified for higher drop weight. A crush speed of 5m/s was used with a 125kg drop weight. A calibrated Kistler 9051A 120kN quartz load washer was used to measure crush load. The load cell was preloaded to 24kN according to Kistler specifications. Crush samples were attached to the drop weight with cyanoacrylate adhesive before being raised to 1.275m (1.263kJ of impact energy). A data acquisition system sampled crush load and elapsed time at 50,000Hz.
3. Results Overall specimen data is shown in Table 1. No data is shown for the 30mm fibre length parts as the preform compaction was too low to give sufficient structural integrity to permit successful moulding; this was due to the relatively low fibre volume fraction and fibre length. In general the crushed appearance of the samples is similar to samples manufactured from carbon/epoxy laminates. A typical specimen is shown in Fig.4. Low front cohesion is shown after testing and a large proportion of the specimen is converted into small fragments during each test.
2.4.3. Data reduction Final SEA values were obtained as follows: Mass per unit length SEA Total Energy Crush length Where Total Energy [ force * distance moved ]
(1) (2) 82
T. Turner et al. 2011. Int. J. Vehicle Structures & Systems, 3(2), 80-86 Table1:
# 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24 26 27 29 30 32 33 35 36
Fibre length mm 30 30 30 30 30 30 30 30 60 60 60 60 60 60 60 60 90 90 90 90 90 90 90 90
Areal mass gsm 1600 1600 1600 1600 800 800 800 800 1600 1600 1600 1600 800 800 800 800 1600 1600 1600 1600 800 800 800 800
SEA results and specimen data
Mass/length kg/m 0.986 0.982 1.118 1.116 0.514 0.469 N/A N/A 1.032 1.023 1.091 1.113 0.530 0.542 0.556 0.556 0.999 1.013 1.105 1.104 0.522 0.552 0.570 0.563
Preform mass g 220 220 230 230 106 106 N/A N/A 224 228 224 224 110 118 110 110 228 224 228 224 114 114 112 112 90
Test type Static Dynamic Static Dynamic Static Dynamic Static Dynamic Static Dynamic Static Dynamic Static Dynamic Static Dynamic Static Dynamic Static Dynamic Static Dynamic Static Dynamic
Circular 2.54mm Circular 5.08mm Square 2.54mm Square 5.08mm
80
Specific Energy Absorption (kJ/kg)
SEA kJ/kg 80.18 48.39 62.33 43.48 64.37 40.36 N/A N/A 63.19 45.62 51.78 40.71 66.39 47.39 47.53 37.59 78.00 45.41 61.07 43.15 63.13 41.98 49.17 39.23
70 60 50 40 30 20 10 0
Fig. 4: Dynamic crush test completed
30mm
A summary of static testing results is given in Fig.5. No clear trends can be observed with respect to fibre length but in general the 5.08mm wall thickness results exceed those for the 2.54mm. Circular tubes outperform square section tubes at all fibre lengths. Fig.6 shows a set of four repeats from the same tube showing a general downward trend in crush load in all cases and good repeatability between specimens. The coefficient of variation of SEA across the four repeats is 4.4% and of mean crush load is 4.9%. Initial peak loads and onset stiffness appear to be independent of fibre architecture and the post-initiator dip and peak show variations of 4.4% COV and 6.8% COV respectively.
60mm
90mm
Fig.5: Summary of static test averages for geometry vs. fibre length (error bars show standard deviation)
Dynamic testing results are shown in Fig.7, which can be directly compared with Fig.5. Although lower sustained crush loads are observed for all dynamic samples, the same trends as those observed for the static testing exist. The dynamic samples are between 60% and 80% of the static SEA values and the spread between the different fibre lengths and geometries is lower. Fig.8 can be compared with Fig.6 (same fibre architecture) and shows excellent repeatability but a high level of oscillation during the test. 83
T. Turner et al. 2011. Int. J. Vehicle Structures & Systems, 3(2), 80-86
Fig. 8: Comparison of repeats (Tube 38 – Circular, 800gsm, high vf, 30mm fibre length)
90
Absorption (kJ/kg) EnergyEnergy Specific (kJ/kg) Specific (kJ/kg) Absorption Absorption Specific Energy
Circular 2.54mm Circular 5.08mm 90 80 Fig. 6: Comparison of repeats (Tube 37 – Circular, 800gsm, high Square 2.54mm Circular 2.54mm vf, 30mm fibre length) Square 5.08mm Circular 5.08mm 80 90 70 Square 2.54mm Circular 2.54mm Square Circular5.08mm 5.08mm 80 70 60 Square 2.54mm Square 5.08mm
70 60 50 60 50 40 50 40 30 40 30 20 30 20 10 20 100 10 0
30mm
60mm
90mm
Fig. 7: Summary of dynamic test averages for geometry vs. fibre 30mm 90mm length (error bars show standard60mm deviation)
0
Fig. 9: Comparison of static vs. dynamic test (Tube 20 and 21, Sample A)
A typical30mm Load/displacement 60mm test is shown 90mm in Fig.9, comparing static and dynamic tests of the same fibre architecture. Onset stiffness and peak loads are seen to be similar. Figs.10 to 13 show the results from a statistical analysis performed in Minitab to identify the main effects of each of the independent variables (fibre length, thickness, shape). An additional variable was created to determine whether there were any repeatability trends with position in the moulding. In general, trends are similar for static and dynamic testing: Better SEA results are shown for shorter fibres. This effect is thought to stem from the improved homogeneity of the fibre architecture when there are more fibre ends present per unit volume. Further evidence for this effect is provided by the fact that thicker samples perform better as shown in Fig. 11.
75
Static
62.19
65
SEA (kJ/kg)
Dynamic
69.38
58.65
55 44.08
42.83
42.41
30mm
60mm
90mm
45 35 25
Fibre length
Fig. 10: Main effects plot – effect of fibre length
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T. Turner et al. 2011. Int. J. Vehicle Structures & Systems, 3(2), 80-86 Static
75
Dynamic
Static
75
Dynamic
67.51
SEA (kJ/kg)
SEA (kJ/kg)
57.58
55 44.46
45
63.7
63.66
62.23
62.12
43
42.97
43.21
42.89
A
B
C
D
65
65
41.28
55 45 35
35
25
25 800gsm
1600gsm
Repeat
Aerial Mass/thickness
Fig. 11: Main effects plot – effect of areal mass / thickness
Fig. 13: Main effects plot – effect of repeat# / position
Fig. 12 shows that the circular profile demonstrates improved energy absorption characteristics over the square profile. No significant trend is observed for the effect of specimen position. Table 2 shows the results of an analysis of variance on the fitted data. Mass and shape are equally significant for static and dynamic. Length is less significant for both static and dynamic. Various interactions can be seen.
3.1. Comparison with tensile results
75
Static
Tensile performance of flat test coupons was measured; the results of this testing being shown in Table 3 and graphically in Fig.14. There is a general increase in properties with increasing fibre length for the tested fibre architectures. No discernable correlation between energy absorption and static mechanical properties is visible: The Pearson correlation coefficient for tensile modulus is -0.408 for static SEA and -0.242 for dynamic SEA. For tensile strength the correlation is poorer: -0.067 and 0.03 for static and dynamic SEA respectively.
Dynamic
68.93
SEA (kJ/kg)
65
Table 3:Tensile testing results – results have been normalised to 35% fibre volume fraction
55.94 55
Fibre length mm 30 60 90 30 60 90
44.79 40.89
45 35 25 Circular
Square
Specimen Geometry
Fig. 12: Main effects plot – effect of specimen geometry
Areal mass gsm 800 800 800 1600 1600 1600
Modulus GPa 22.9 29.9 32.0 25.0 26.0 30.1
COV % 8.2 10.0 11.5 16.2 10.6 11.2
Strength MPa 148 191 196 170 205 229
COV
Vf
% 13.1 24.0 15.2 12.5 13.4 10.9
% 37.6 34.3 37.3 35.7 37.4 35.0
Table 2: Analysis of variance for static and dynamic tests using adjusted SS
Source
DF
Length Mass Shape Repeat Length*Mass Length*Shape Length*Repeat Mass*Shape Mass*Repeat Shape*Repeat Error Total
2 1 1 3 2 2 6 1 3 3 16 40
Seq SS 722.5 680.87 1755.54 13.87 109.06 56.99 107.91 63.79 15.72 2.21 239.74 3768.21
Adj SS 91.46 810.98 1836.5 16.49 172.34 96.08 64.76 69.38 17.05 2.21 239.74
Static Test Adj MS 45.73 810.98 1836.5 5.5 86.17 48.04 10.79 69.38 5.68 0.74 14.98
F 3.05 54.12 122.57 0.37 5.75 3.21 0.72 4.63 0.38 0.05
P 0.075 0.000 0.000 0.778 0.013 0.067 0.639 0.047 0.769 0.985
Seq SS 32.822 75.862 155.021 9.333 68.272 38.21 27.398 15.658 12.259 2.005 118.428 555.267
Dynamic Test Adj SS Adj MS 2.523 1.261 103.632 103.632 208.884 208.884 5.556 1.852 62.509 31.254 49.826 24.913 29.341 4.89 10.721 10.721 13.105 4.368 2.005 0.668 118.428 7.402
F 0.17 14 28.22 0.25 4.22 3.37 0.66 1.45 0.59 0.09
P 0.845 0.002 0.000 0.860 0.034 0.060 0.682 0.246 0.630 0.964
glass / polyester tubes of similar fibre content. This phenomenon is thought to arise from the relatively coarse tow structure present and the resulting presence of large areas of un-crushed tow fragments. Crushing behaviour is consistent and crush loads typically show a downward trend as the test continues. Dynamic testing shows similar trends to static for all factors but energy absorption levels are lower. Dynamic testing results show severe oscillation during testing due to stick-slip
4. Conclusions This work addresses a serious lack of data in the open literature for the crushing performance of discontinuous carbon fibre based composites. A range of circular and square section tubes have been manufactured with discontinuous carbon fibre architecture. 6K carbon tows were tested at 30, 60 and 90mm fibre lengths. Overall, the SEA results observed are not as high as those from 85
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40
400
35
350
30
300
25
250
20
200
15
150
10
100
Thin - modulus Thick - modulus Thin - UTS Thick - UTS
5 0 0
50 Fibre length (mm)
REFERENCES: [1] T. Cordell, T. Bendon Tolle, and R. Rondeau. 2000. The programmable powdered preform process for aerospace: Affordable performance through composites, Proc. SAMPE Int. Symp., Longbeach, California, USA. [2] N.G. Chavka and J.S. Dahl. 1999. P4: Glass fiber preforming technology for automotive applications, Proc. 44th Int. SAMPE Symp., Long Beach, CA. [3] T.A. Turner, L.T. Harper, N A Warrior, and C D Rudd. 2006. Low cost carbon-fibre based automotive body panel systems - A performance and manufacturing cost comparison, Proc. IMechE Part D – J. Automobile Engg., 222(D1), 53-63. [4] L.T. Harper, T.A. Turner, N.A. Warrior, J.S. Dahl, and C.D. Rudd. 2006. Characterisation of random short-fibre composites from automated spray-processes: Analysis of microstructural parameters, Comp. Part A, 37(11), 21362147. doi:10.1016/j.compositesa.2005.11.014
Ultimate tensile stress (Mpa)
Young's Modulus (Gpa)
friction effects. No attempt has been made to characterise any modal resonance which may cause this behaviour. An attempt has been made to assess the impact of fibre architecture homogeneity on the crush response but little change in SEA is observed for different fibre lengths. In particular, poor correlation is seen between tensile mechanical properties and energy absorption which suggests that homogeneity is not as significant in determining crush response as tensile response.
[5] L.T. Harper, T.A. Turner, N.A. Warrior, and C.D. Rudd. 2006. Characterisation of random short-fibre composites from automated spray-processes: Effect of fibre length, Comp. Part A, 37(11), 1863-1878. doi:10.1016/j.comp ositesa.2005.12.028 [6] D. Hull. 1991. A unified approach to progressive crushing of fibre-reinforced composite tubes, Comp. Science & Tech., 40, 376-421. doi:10.1016/0266-3538(91)90031-J [7] A.G. Mamalis, D.E. Manolakos, G.A. Demosthenous, M.B. Ioannidis, M. Robinson, and J. Carruthers. 1997 Review: Crashworthy capability of composite material structures, Comp. Structures, 37, 109-134. doi:10.1016/S0263-8223(97)80005-0
50 0 100
Fig. 14: Mechanical properties obtained from tensile testing for all fibre architectures
[8] G.L. Farley and R.M. Jones. 1992. Crushing characteristics of continuous fibre-reinforced composite tubes, J. Comp. Materials, 26(1), 37-50. doi:10.1177/ 002199839202600103 [9] P.H. Thornton and R. Jeryan. 1988. Crash energy management in composite automotive structures, Int. J. Impact Engg., 7(2), 167-180. doi:10.1016/0734-743X(88) 90024-3
For this work a relatively small tow size was tested but it is thought that larger, lower cost, tow sizes would give reduced performance. These results have implications for automotive applications and facilitate the integration of crash energy management structures with structural chassis members for improved parts integration and weight saving in carbon composite structures. The results presented have direct application for the manufacture of composite “crash cans” but these would not realise the full potential of the manufacturing method. Improved parts could be for instance the a floor part designed to carry luggage loads and also provide a significant proportion of the rear crash energy absorption, or the creation of composite monocoque chassis structures where the shaped outer skin panels have a torsional stiffness requirement along with e.g. a pole impact energy absorption role.
[10] I. Sigalas, M. Kumosa, and D. Hull. 1991. Trigger mechanisms in energy-absorbing glass cloth/epoxy tubes, Comp. Sci. & Tech., 40, 265-287. doi:10.1016/02663538(91)90085-4 [11] A.K.M. Masud and A.K.M. Kais Bin Zaman. 2006 Modeling of energy absorption of short fiber composite considering interfacial properties of fiber-matrix, J. Mat. Proc. Tech., 172(2), 258-263. doi:10.1016/j.jmatprotec. 2005.10.015 [12] H.K. Lee, S. Simunovic, and D.K. Shin. 2004. A computational approach for prediction of the damage evolution and crushing behavior of chopped random fiber composites, Comput. Mat. Sci., 29(4), 459-474. doi:10.1016/j.commatsci.2003.12.008 [13] Z. Jendli, F. Meraghni, J. Fitoussi, and D. Baptiste. 2009. Multi-scales modelling of dynamic behaviour for discontinuous fibre SMC composites, Comp. Sci. & Tech., 69(1), 97-103. doi:10.1016/j.compscitech.2007.10.047 [14] G.C. Jacob, J.M. Starbuck, J.F. Fellers, and S. Simunovic. 2005. Effect of fiber volume fraction, fiber length and fiber tow size on the energy absorption of chopped carbon fiber-polymer composites, Poly. Comp., 26(3), 295-305.
ACKNOWLEDGEMENT: This research was supported by the Automotive Composites Consortium (ACC) under a United States Automotive Materials Partnership Cooperative Agreement No. DE-FC05-95OR22363 with the U.S. Department of Energy (US-DoE). The authors are grateful for the support and monitoring of the Predictive Technology Development and Crash Energy Management Group (ACC100) of the ACC. The authors acknowledge that this research was funded, in whole or in part, by the US-DoE, and such support does not constitute an endorsement by the US-DoE of the views expressed herein. 86
