Bachelor of Engineering in Mechanical Engineering. Mysore University ... be accepted in partial fulfillment of the requirements for the degree of Master of Science, ... the design of crashworthy structure in automotive and aircraft applications.
FINITE ELEMENT STUDY OF ENERGY ABSORPTION CHARACTERISTICS OF A HYBRID STRUCTURE - COMPOSITE WRAPPED ON A SQUARE METAL TUBE
A Thesis by Sandeep Kumar Shetty Bachelor of Engineering in Mechanical Engineering Mysore University, India, 2001
Submitted to the Department of Mechanical Engineering and the faculty of Graduate School of Wichita State University in partial fulfillment of the requirements for the degree of Master of Science
May 2006
© Copyright 2006- by Sandeep Shetty All Rights Reserved
FINITE ELEMENT STUDY OF ENERGY ABSORPTION CHARACTERISTICS OF A HYBRID STRUCTURE - COMPOSITE WRAPPED ON A SQUARE METAL TUBE We have examined the final copy of this thesis for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Master of Science, with a major in Mechanical Engineering.
________________________________ Hamid Lankarani, Committee Chair
____________________________________ Babak Minaie, Committee Member
____________________________________ Krishna Krishnan, Committee Member
iii
DEDICATION
To My Parents
iv
ACKNOWLEDGEMENTS As with any endeavor of this magnitude, many people provided invaluable assistance, allowing me to complete all the assigned tasks and reach my desired goals. I would like to express my sincere thanks and appreciation to my advisor Dr. Hamid Lankarani for his excellent guidance, advice, precious time, and constant support throughout my graduate career at Wichita State University, without which my efforts would not have been complete and fruitful. I would also like to express my thanks and appreciation to Dr. Bob Minaie and Dr. Krishna Krishnan for their time and effort in reviewing this manuscript. I am grateful to Avinash Lakkundi for his assistance to complete my task successfully. Finally, I would like thank all my friends who have helped me directly or indirectly during my graduate study.
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ABSTRACT The study of axial crush behavior of metal and composite tube has become a basis for the design of crashworthy structure in automotive and aircraft applications. Unlike metals, polymer composite material displays little or no plastic deformation characteristics. Research has showed that the hybrid tube usually made of inner aluminum tube over-wrapped with Eglass fiber reinforced epoxy have significantly higher energy absorption than either aluminum tube or composite tube. It is therefore important to have a predictive design tool that could simulate the response of the hybrid structure under impact or crush load. This thesis is aimed at the development and validation of finite element simulation methods for hybrid tubes. The axial crushing behavior and the energy absorption capacity of the aluminum-composite hybrid tube under quasi static and impact loading is studied using the LS-Dyna finite element solver. A square aluminum tube externally wrapped with E glass/epoxy composite layer at ±45o to tube axis is used for finite element analysis. A
modified Chang-Chang failure model is used for the composite layers, exhibiting reasonable correlation with the experimental results. Simulations are carried out on composite and aluminum tubes separately. The results indicate that the energy absorption and crush behavior of the hybrid tubes are better than either the composite tubes or the aluminum tubes. In addition, analysis are also conducted on finite element tube to determine the effects of adhesion, ply orientation, and trigger geometry on load displacement response of hybrid tube.
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TABLE OF CONTENTS CHAPTER
1.
PAGE
INTRODUCTION ........................................................................................................... 1 1.1 Crashworthy structure ............................................................................................... 1 1.2 Test Methodologies.................................................................................................. 4 1.2.1 Quasi-static testing ...................................................................................... 4 1.2.2 Impact testing .............................................................................................. 5 1.3 Calculation of Specific Energy Absorption .............................................................. 6 1.4 Crushing Modes and Mechanism.............................................................................. 8 1.4.1 Euler buckling ............................................................................................. 8 1.4.2 Progressive failure mode ............................................................................ 8 1.4.3 Catastrophic failure modes ....................................................................... 10 1.5 Motivation ............................................................................................................... 10 1.6 Objective of this Study............................................................................................ 12
2.
LITERATURE SURVEY .............................................................................................. 13 2.1 2.2 2.3 2.4 2.5
3.
Introduction ............................................................................................................. 13 The Effect of Ply orientation on the Energy Absorption Capability of Tubes ....... 14 Effect of Crush Speed on the Energy Absorption Capability of Tubes .................. 18 Effect of Trigger Geometry and Location .............................................................. 19 Analytical Models ................................................................................................... 21
FINITE ELEMENT MODELING OF HYBRID TUBE ............................................... 26 3.1 Introduction ............................................................................................................. 26 3.2 Classification of Loading ........................................................................................ 28 3.2.1 Static and fatigue loading ......................................................................... 28 3.2.2 High speed or rapid loading ...................................................................... 29 3.2.3 Impact loading .......................................................................................... 29 3.3 Modeling Details of Hybrid Tube ........................................................................... 30 3.3.1 Finite element model ................................................................................ 30 3.3.2 Material model .......................................................................................... 33 3.3.3 Failure criteria for the composite layer ..................................................... 35 3.3.4 Contact modeling ...................................................................................... 38
4.
RESULTS AND DISCUSSION .................................................................................... 40 4.1 Validation of FE Hybrid Model .............................................................................. 40 4.2 Parametric study of hybrid tube .............................................................................. 45 4.2.1 Effect of ply orientation ............................................................................ 45 4.2.2 Effect of adhesive ..................................................................................... 48 4.2.3 Effect of crush speed................................................................................. 50
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TABLE OF CONTENTS (CONTD..) CHAPTER
PAGE
4.2.4 Effect of trigger mechanism ..................................................................... 51 4.2.5 Effect of impact angle ............................................................................... 52 5.
CONCLUSIONS AND FUTURE WORK .................................................................... 54
LIST OF REFRENCES .......................................................................................................... 57 APPENDIX ............................................................................................................................. 60
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LIST OF TABLE
TABLE
PAGE
3.1 Material property of unidirectional e-glass/epoxy lamina .............................................. 34 4.1 Effect of ply orientation under quasi static loading ........................................................ 45 4.2 Effect of ply orientation under impact loading ............................................................... 46
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LIST OF FIGURES FIGURE
PAGE
1.1
Load vs. Displacement Curve. .......................................................................... 3
1.2
Impact testing Machine set up .......................................................................... 6
1.3
Sub floor box structure as energy absorber..................................................... 11
1.4
Hybrid tubes as crash energy absorber in automobiles................................... 11
2.1
Effects of ply orientation on Energy absorption of circular tube.................... 16
2.2
Crush pattern of hybrid tube under axial compression test............................. 17
2.3
Different type of trigger mechanism. .............................................................. 20
2.4
(a) Before Collapse (b) During collapse (c) Final collapse shape. ................. 21
2.5
Effective crushing distance. ............................................................................ 23
3.1
Graph showing load rise time. ........................................................................ 28
3.2
Description of hybrid tube model ................................................................... 30
3.3
A FE model of Hybrid tube using Patran........................................................ 31
3.4
Integration point location in two layered composite....................................... 32
3.5
True stress v/s True plastic strain curve of Aluminum tube. .......................... 33
3.6
Stress-strain curve of unidirectional E-Glass/Epoxy composite material with DFAILT =0.0 and 0.023. ................................................................................ 38
4.1
The progressive crushing of hybrid tube. a) Experimental test tube (b) FE model ......................................................... 41
4.2
Crush pattern of hybrid tube under quasi-static condition .............................. 42
4.3
Comparison of load displacement curve of experimental and numerical mode tube.................................................................................................................. 43
4.4
Crush pattern of (a) Composite tube (b) Aluminum tube (c) Hybrid tube ..... 43
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LIST OF FIGURES (CONTD..) FIGURE
PAGE
4.5
Comparison of load displacement curve of AL and GL/epoxy tube with hybrid tube. ................................................................................................................. 44
4.6
(a) Crush pattern of GL/Epoxy tube (b) Load displacement of GL/Epoxy ........ tube of wall thickness 2.7mm ......... 44
4.7
Load displacement response of hybrid tube under quasi-static loading. ........ 46
4.8
Load displacement response of hybrid tube under impact loading................. 47
4.9
Crush Pattern and time duration to deform a length of 65mm. ...................... 48
4.10
Effect of adhesive strength on the force displacement response of ±45o hybrid tube.................................................................................................................. 49
4.11
Effect of adhesive strength on the force displacement response of hybrid (90 / 0) degree tube.......................................................................................... 49 o Effect of Crsuh speed on Load displacement response of ±45 hybrid tube with bond strength of 150 N. .......................................................................... 50
4.12
4.13 .
Effect of crush speed on Load displacement response of 90 o / 0 o hybrid tube with bond strength of 150 N .............................................................. 50
4.14
FE model of different trigger geometry. ......................................................... 51
4.15
Load displacement curve of hybrid tube with different trigger geometry. ..... 52
4.16
Crush pattern of hybrid tube impacted at an angle to tube axis ...................... 53
4.17
Load displacement curve of Hybrid tube with different impact angle ........... 53
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CHAPTER 1 INTRODUCTION
1.1 Crashworthy structure
Recent years, much importance is given to structures which are light weight and has the highest energy absorption capability in automobile and aerospace industries. Composite and aluminum are two materials where most research work is carried as they provide significant benefit such has enhanced strength and durability, weight reduction and lower fuel consumption. In addition they also behave as a crashworthy structure. Crashworthy structures are those which limit the magnitude of disturbance on the occupants during an impact, thus, minimizing the post-crash injuries. According to the automobile legislation, the occupant of the vehicle with a speed up-to 15.5m/sec (35mph) under an impact should not be exposed to a deceleration greater than 20g. This is basically to avoid any severe internal injuries to the occupant. US helicopter requirements of safely surviving a descent, under no power; at 15 m/sec is another example of crashworthiness legislation. The front rails of a vehicle are designed with proper material and geometry so that it can absorb maximum impact energy during crash. Square, rectangular and hourglass are few non-tailored cross sectional shapes that are considered for vehicles front rail design. The rails under impact can absorb 70% of the energy by deforming in a well controlled mode, metal achieve this through plastic deformation. The crush distance in this stage is about 300 mm so that the resisting force produces a deceleration less than 20 g. Government’s stringent laws
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on both emission and fuel efficiency side, had forced vehicle manufactures to not only look for a clean engine but a lighter material like polymer composite that could replace metal. Polymer composite material show little to no plastic deformation, thus minimizing its use as an energy absorber like metals. The composite such as glass fiber reinforced epoxy are inherently brittle and fail after an elastic deformation of about 2 to 3% elongation. On the other hand micro failure modes like fiber fracture, matrix crazing or cracking, fiber-matrix de-bonding, etc., make up the main failure modes that determine the crushing behavior and energy absorption capability of these shells. Failure mechanism or damage criteria in composite are highly dependent on geometry, lamina orientation, type of crush initiators used in the structure. Hybrid tubes are structures that consist of internal metal tube wrapped with composite prepregs. Hanefi [28] and Song [11] research have shown evidence to say that hybrid tube has better energy absorption capability than either aluminum or composite tube. The external composite material absorbs energy mainly through fiber matrix de-bonding and fiber fracture, whereas metal absorb most of the energy in plastic deformation mode. Many factors contribute to crushing behavior and energy absorption efficiency such as different metal and composites (e.g., plastic and brittle metals, glass, graphite and Kevlar fiber reinforced composites), the specimen fabrication characters (e.g., geometry of the specimen and the ply pattern of the composite), and the volume ratio of metal to composite (often expressed in the ratio of their wall thickness t m / t c ). Thus a crashworthy structure can be optimized to satisfy a certain impact condition according to experiment based analysis. Material Crashworthiness, also expressed around industry as specific energy absorption (SEA), Es, is a characteristic of a particular material and is defined as the energy
2
absorbed per unit mass of the material. Mathematically Es=σ the material and σ
m
m
/ ρ, where ρ is the density of
is the mean crush stress. The correlation study between peak load and
the mean crush load is also valued as of high importance during the energy absorption management analysis. Figure 1.1 depicts the load displacement curve of a gradually crushed tube. As tube undergoes crushing process it sees a peak load (resistive force) for a small interval then drops and maintains a relatively constant crush load. For occupant safety, one doesn’t want the initial resistive force (Pmax) to be of too high of a value than the average crush force (Pm), because this leads to a sudden deceleration and is not well taken in vehicles energy management analysis. The objective of energy management is to minimize transfer of peak load to occupant by absorbing impact energy. Also the load ratio (Pmax to Pm) can’t be the only determinant factor to gauge structures crush efficiency. A structure may have an impressive load ratio but not necessarily has a high energy absorption capability [33]
Figure 1.1
Loads vs. Displacement Curve [34]
3
1.2 Test Methods
Test methodologies commonly used to analyze the specimen’s behavior under crash are listed below. 1.2.1
Quasi-static testing
In quasi-static testing, the test member is compressed at a steady rate using conventional tensional testing machine. Tubes are axial compressed between parallel, flat steel platens, one static and one moving at a constant crosshead speed in the range from 1.5 X 10-3 m/s to 0.1 m/s. Quasi-static tests doesn’t represent an actual crash condition, because during crash, the structure dissipates energy over the entire period thus bringing the object to a complete stop. Many materials used in designing crashworthy structures are rate sensitive. That means their energy absorption capability is dependent on the speeds at which they are crushed. So material selection solely based on qausi-static testing doesn’t ensure a satisfactory performance as crashworthy structure in the event of crash. The following are some advantages of quasi-static testing [33].
Quasi-static test equipment is relatively simple to control and operate
Reduce risk of damaging crosshead and lower maintenance
Impact tests require high frequency data loggers, because a complete testing happens in split second. This drive towards expensive equipment. Therefore, quasi-static test is mainly run to understand the different failure modes in composites material based on crush rate.
4
The following is a major disadvantage of quasi-static testing. Quasi-static test method may not depict a material’s true absorption characteristics as that seen in real vehicle collision. Because most materials are strain rate sensitive. 1.2.2
Impact testing
This test is carried out to understand the absorption capability and failure mechanism of the composite material under impact. The specimen absorbs energy bringing the crosshead from initial high velocity to rest. This test helps to select a good crashworthy material. Impact test condition can be simulated using a drop tower test rigs as shown in Figure 1.2. Test specimen is mounted on the impact plate such as axis of the tube is parallel to the direction of the travel of the dead weight. The drop weight platform is raised to a predefined level depending upon the speed and impact energy and released [33]. Advantage of impact testing
It’s a near to close simulation of an actual vehicle crash condition and also take into account of materials strain hardening affect due to varying impact rate.
Disadvantage of impact testing
Impact testing occurs in a matter of a second and this force to a need of special gadgets (high speed camera and data logger) to record and study crushing process.
5
Figure 1.2
Impact testing Machine set up [11]
1.3 Calculation of Specific Energy Absorption
Specific energy absorption, ES, is defined as the energy absorbed per unit mass of material. Figure 1.1 is a typical load displacement curve obtained from progressive crushing of a hybrid specimen. The area under the load displacement curve is S b W = ∫ Pds 0
(1.1)
where W is the total energy absorbed in crushing of the composite tube specimen. A more characteristic property of progressive crushing mode is S b W = ∫ Pds = Pm ( S − Si ) b 0
6
(1.2)
where Sb and Si are the crush distances as indicated in Figure 1.1 and Pm is the mean crush load. The specific energy absorption capability, ES, of a composite material defined as the energy absorbed per unit mass of material is given by
Es =
W m
(1.3)
where m is the mass of the hybrid tube. Combining the equations (1.2) and (1.3) we get
Es =
W Pm ( Sb − Si ) = m Vρ
(1.4)
where V is the volume of the crushed portion of the hybrid tube specimen and is the density of the hybrid material. We can also write
Es =
W Pm ( Sb − Si ) Pm ( Sb − Si ) = = m Vρ AL ρ
(1.5)
where A and L are the cross sectional area and length of the crushed portion of the hybrid tube specimen respectively.
Es =
Pm ( S − Si ) Pm S b b = AL ρ AL ρ
(1.6)
If Si is much less than Sb. The ratio (Sb/L) = K is a measure of the collapsibility of the hybrid tube. Substituting (Sb / L) = K in the above equation we have
7
P K σ K Es = m = m ρ Aρ
(1.7)
where σ m is the mean crush stress. It is sometime difficult to determine the mean crush load Pm from the load displacement curve, due to erratic behavior of composite material. In such cases energy absorption capability of the material can be found by just considering the area under the whole load displacement curve [33]. 1.4 Crushing Modes and Mechanism
A square tube under axial compression fails by one of the three fundamentally different modes:
1.4.1
Euler buckling
This kind of failure is not common in automotive structures and can be avoided by the choice of tube length, cross section dimension and wall thickness. 1.4.2
Progressive failure mode
Progressive failure mode is common in tubes made from ductile material, but can be achieved in tube made also of brittle material (glass and carbon fibers) if proper trigger mechanism is used. A trigger is a stress concentrator that causes failure to initiate at a specific location within the structure. A trigger reduces the initial load peak that accompanies failure initiation followed by stable collapse. Most common type of trigger or crush initiator that’s in use is chamfer, one end of the tube. A number of other trigger geometries such as bevels, grooves and holes have been investigated in literature.
8
The following are the advantages of progressive failure in the design of crashworthy structures.
Progressive crushing mode illustrates higher energy absorption capability than seen on catastrophic failure mode
The ratio of peak load to mean crush load is less when compared to structures failing catastrophically
Three kinds of basic progressive crushing modes are reported in literature: 1) local buckling or progressive folding, 2) Transverse Shearing or fragmentation mode and 3) lamina bending or splaying mode. Progressive folding or also know as local buckling is mainly exhibited in ductile fibers (Kevlar and Dyneema) reinforced composite tubes. This crush mode is similar to that seen in metal tubes. The ductile fiber composite tubes deform plastically leading to hinge formation and progressive folding under axial compression [33].
The Shearing or fragmentation mode is characterized as the formation of one or more interlaminar and longitudinal cracks in a given lamina bundle during crush process. Tubes with brittle fiber as reinforcement show this type of failure.
In splaying mode the failure occurs due to lamina bending and fronds splitting in a longitudinal direction. Failure mechanism is controlled by matrix cracking and interlaminar crack growth. This type of failures is observed in tubes with brittle fibers as reinforcement.
9
1.4.3
Catastrophic failure modes
Catastrophic failure modes have been of least interest for researcher in the design of crashworthy structure, for following reason [33].
When unstable intra-laminar or inter-laminar crack growth occurs in composite material.
In long thin walled tubes because of column instability
In brittle fiber reinforced tubes, when the lamina bundle do not bend or fracture due to inter-laminar cracks being less than a ply thickness.
Catastrophic failure leads to an immediate rise of peak load followed by a low sustained crush load, consequently the material hold low energy absorption capability and impart high peak load causing internal injuries.
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1.5 Motivation
Engineering structures which are subjected to collision or impact load during service has the ability to absorb energy in a well defined manner. These structures are gaining much needed importance because of their application as energy absorbers in either automotive or aerospace products as shown in Figure 1.3 and 1.4.
. Figure 1.3
Figure 1.4
Sub floor box structure as energy absorber [20]
Hybrid tubes as crash energy absorber in automobiles [33]
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The increasing public demand for safety and government regulation has stipulated the researchers to work on structure which are light weight and has an efficient energy absorbing capability. Polymer composite and aluminum are two materials where most research work is carried as they provide significant benefit such has enhanced strength and durability, weight reduction and also behave as a crashworthy structure when properly designed. Polymer composite material show little to no plastic deformation, thus minimizing its use as an energy absorber unlike metals. Song at al [11] and Mallick [30] reported that the hybrid tube usually made up of inner aluminum tube over-wrapped with Glass reinforced epoxy have higher energy absorbing capabilities than either the composite or aluminum tubes.
1.6 Objective of this Study
The energy absorption capability of hybrid tube is better when compared to metal and composite tubes, as observed by researchers. Before its application as a crashworthy structure in automobiles and aircrafts, it is important to understand the mechanism of energy absorption and failure, and to have design tools for simulating the response of the hybrid structure under impact load. In this research a Finite Element Model using LS-Dyna code was developed to analyze a hybrid tube under static and impact loading. First the FE model was validated with the known experimental results then parametric studies was carried out to study the effect of individual parameters like ply orientation, crush speed, effect of adhesives and geometry of trigger.
12
CHAPTER 2 LITERATURE SURVEY
2.1
Introduction
Among all the crashworthy members, axi- symmetric thin walled metal tubes and thin walled fiber/resin composite tubes have been the focus of study for may researchers in past due to their low cost, ease of fabrication and excellent energy absorption efficiency. As a result, the crush propagation and energy absorption response of metal is well defined. However not until recently the resources were devoted to understand the failure mechanism and energy absorption characteristics in composite tube, consisting both brittle and ductile fiber as reinforcement. Researchers till now have shown enough facts to assume that the energy absorption in most of the composite tube happens through lamina de-fragmentation, bond breakage b/w fiber and matrix and friction[1], whereas metal absorb most of the energy in plasticity mode[1-2]. To perform as an efficient crashworthy structure both metal and fiber reinforced composite under impact should deform in a well defined manner. A stable crushing mode can be achieved in both metal and composite by the inclusion of triggers. Triggers are localized stress concentrators and help in reducing the initial impact force. A stable crushing process is defined as the initiation of localized failure at one end and follows the entire specimen without considerable damage. The most common form of crush initiator is to chamfer one end of the tube. Mamalis et al in 1991 [3] was first to study the energy dissipation capability of bimaterial thin walled tube. Many factors contribute to the crushing behavior and energy absorption efficiency of hybrid tube, such as metal and composite thickness, material used
13
for the tube(e.g. Al, steel, glass, graphite and Kevlar fiber reinforced composites),the specimen fabrication characters (e.g., lay up sequence, fiber –matrix combination, etc.),the geometry of the tube (e.g., square, circular, rectangle and cone) and the volume ratio of metal to composite (often expressed in the ratio of their wall thickness tm/ tc). It was shown that square and rectangular tubes are generally less efficient as energy absorber than circular ones [4-5]. This is due to the fact that the corners of square tube act as stress concentration areas leading to quick splitting of the tubes and may result in unstable collapse and low energy absorption. M.Abdel-Haq et al [6] in his paper describe about the effect of external constraints on energy absorption capability of the tube. He has shown the improvement in energy absorption of the square tube by allowing the tube wall to slide in controlled manner over the steel circular ring. In hybrid tube, since composite material forms a major factor in improving the energy absorption of the tube it becomes important on our part to highlight some of the parameters which affect the energy absorption.
2.2
The Effect of Ply orientation on the Energy Absorption Capability of Tubes
The fiber orientations that enhance the energy absorption capability of the composite material require them to: a) Increase the number of fractured fibers. b) Increase the material deformation. c) Increase the axial stiffness of the composite material. d) Increase the lateral support to the axial fibers.
14
Hull [2] in his work on glass/polyester showed that the fiber lay-up of 0-90o is 50% more effective in absorbing energy than ± 45 o tube. A similar observation is made for glass/epoxy tubes, the difference being a decrease of about 40%. Farley [7] investigated on glass/epoxy, carbon/epoxy and Kevlar/epoxy composite tubes with fiber architecture [0±θ]4, where θ varied from 0o to 90o, showed considerable differences in the energy absorption trend for these materials. The difference in trends can be explained by examination of crushing modes. The specific energy of the glass/epoxy and Kevlar/epoxy tubes remained constant with increasing θ up to 45o and above this value it increased. This trend is not consistent with the general mechanical response of composites. The glass/epoxy and Kevlar/epoxy specimen crushed in a lamina bending and local buckling mode respectively. The increase in energy is attributed to the increased lateral support of the axial fibers with increasing θ. On the other hand, the specific energy of the carbon/epoxy tubes initially decreased with increasing θ up to 45o and then remained constant. The carbon/epoxy specimens crushed in brittle fracturing mode. This initial decrease in the energy absorption is attributed to the reduction in axial stiffness of the composite material with increasing θ. Hamada et al [8] studied the effect of fiber architecture on the energy absorption capability of hybrid composite tubes reinforced with both carbon and dyneema (polyethylene) fibers. The resin used was that of epoxy. It was observed that the energy absorption capability decreased with increasing fiber orientation with respect to the longitudinal axis of the tube. Berry [9] investigated woven glass fabric/polyester tubes by varying the angle of the lay-up. The energy absorption of the tubes with the warp and weft directions at 45ο to the tube axis is observed to be 30% less than that for similar tubes with warp and weft direction parallel to the axial (0o) and hoop (90o) directions respectively. This 15
increase in the energy absorption is due to more material deformation and fracture in the case of the latter tubes. Carbon fiber reinforced composite tubes with different thermoplastic matrices: polyetheretherkeetone (PEEK), polyetherimide (PEI), polyimide (PI) and polyarylsulfone (PAS) were studied by Ramakrishna et al [10]. Fiber orientations of 0o, ±5o, ±10o, ±15o, ±20o, ±25o and ±30o with respect to the axis of the tube were used. The specific
energy absorption capability of the progressively crushed tubes was found to be a function of the θ value. Hong [11] experimentally investigated the effect of ply orientation on the energy absorption of hybrid tube. Hybrid tube was made up of Aluminum wrapped with glass/epoxy composite layers. He examined that the energy absorption of the tube increased with the increasing θ under both quasi-static and impact test condition as shown in Figure 2.1.
Figure 2.1
Effects of ply orientation on Energy absorption of circular tube [11]
Energy absorption capability of Composite wrapped aluminum tubes was investigated by Shin et al [12] under axial compressive and bending load. The effect of ply orientation under these load condition were examined closely. It is seen that tube with 0o ply orientation
16
was crushed catastrophically absorbing less energy, because the two materials were separated each other at interface as shown in Figure 2.2. Further investigations were conducted for tubes wrapped by 90o, 0o/90o and ± 45 ply orientation. The tube with 90o-ply orientation composite material was crushed with stable local buckling failure mode. Hybrid tube with 0 o
/90o and ± 45 ply orientation showed mixed crushing mode. Inner aluminum tube absorbs
energy through plastic deformation, while outer composite material absorbs energy through crack propagation and bending of fronds. It is concluded that the best energy absorption is attained in tubes wrapped with 90o ply orientation.
Figure 2.2 Crush pattern of hybrid tube under axial compression test [12] a) 0o ply orientation
b) 90o ply orientation
c) 0 o/90o ply orientation
d) ± 45 ply orientation
17
In general, as θ increases, the length of the longitudinal cracks decreases. This is due to the increase of fracture toughness with increasing θ. This improved fracture toughness offers more resistance to the crack growth process, thus resulting in an increased specific energy absorption value for the composite material. 2.3
Effect of Crush Speed on the Energy Absorption Capability of Tubes
In past, significant amount of work is done to know the effect of testing speed on the behavior of the material. Schmueser [13] conducted a drop hammer test on circular tubes of (02 / ± θ)s orientation made up of epoxy resin and glass, graphite, Kevlar fiber respectively. It has been seen that the dynamic specific energy was lower than static specific energy for all the three cases. Further research on tubes where conducted by Berry and Hull [14] and farley [15] have shown that the dynamic specific energy absorption values of the tube made from variety of prepreg cloths, using filament winding or form unidirectional taped, with non-0o fibers, can be up to 25% greater than the values obtained form quasi static testing. P.H .Thornton [16] conducted experiments on pultruded glass fiber reinforced tubes, made with either polyester or vinyl ester resin to determine the crush response at high speed. The geometry of the tube considered for the experiments was of square and circular section with bevel or tulip shaped trigger at one end. The results showed that the circular tube made up of polyester resin has an increasing specific energy trend with an increase in crushing speed, on the other hand the tubes made up of vinyl ester resin showed the opposite trend. The study also showed an increasing specific energy trend for tube with square cross section. Farley [17] studied the effect of crushing speed on energy absorption of tubes made from Thornel 300-Fibernate 934 (Gr-E) and Kevlar 49-Fibernate 934(K-E). Circular cross section
18
tubes were crushed at speeds ranging form 0.001 m/s to 12m/s .It was determined that the magnitude of the effect of crushing speed on energy absorption is related to crush mechanism and is a function of strain rate. Experimental investigation carried out by Langseth [18] on thin square walled aluminum subjected to axial loading, showed that the deformation mode is symmetric for static test but shows a mixed mode for tubes under dynamic test. The experiment also showed that the mean force increases with an increase in crushing speed. Mamalis et al [3] was first to study the response of bi-material tube subjected to axial compression. In his experiment he studied the deformation characteristic and energy absorption efficiency of a combination of bi-material tubes. Hong W Song [11] reported the crushing behavior and energy absorption of glass/epoxy composite wrapped on circular metal tube. He also determined the displacement formulae and compared with experimental results. He studied the effect of different parameters like strain rate, composite wall thickness, ply orientation and mechanical properties of metal on energy absorption of tube. 2.4
Effect of Trigger Geometry and Location
Extensive work has been carried out in past to understand the geometry and crush initiator effect on the energy absorption capability of a specimen. In [5] Thornton and Edwards showed that the geometry/shape of the specimen has tremendous effect on energy absorption capabilities of the structure. The geometry chosen in his studies were circular, rectangular and square. Based on the study they concluded that for a given lay up, the energy absorption followed an order, circular > square > rectangle. Farley [20] and Thornton [19] conducted experiment to understand the crushing behavior and
19
specific energy absorption of circular tube with change in diameter to material lay-up thickness. An increase in D/t ratio resulted to a lower energy absorption. Graphite reinforced circular tube depict a stable brittle fracture mode, whereas the kelvar reinforced tube showed a local buckling deformation mode. In [21] Farley documented a similar pattern with elliptical cross section. Farley [20] investigated that the effect of shape variation to thickness is highly noticeable in kelvar/epoxy tubes and not so on glass/epoxy tube. Hamada et al [22] studied the crushing behavior and energy absorption of glass cloth/epoxy tubes and carbon fiber/PEEK tubes with cross sectional shapes full circle, three quarter circle, half circle and quarter circle. His investigation classified that the energy absorption capability of glass/epoxy tube decreased to a 20% range when moved from full circle to quarter circle tube. Whereas the specific energy of carbon fiber/PEEK tube specimens decreased only by 5% with the change in cross sectional shape Thuis H[23] focused his study to understand the affect of trigger mechanism on specific energy absorption, and crushing pattern of the structure. Chamfer, notch, plug are few below listed style of crush initiator that were considered for study. The most popular, stable and easy to manufacture trigger/crush initiator is chamfer. Crush initiators that are widely used is shown in Figure 2.3.
Bevel
Notch type Figure 2.3
Steeple
Flange
Different type of trigger mechanism [34] 20
Plug type
. Mamalis et al [25] conducted test on square, circular and circular cones tubes made up of glass fiber, polyester or vinyl ester resin under static and dynamic crushing condition in a speed range of 18-24m/sec. it was found out that the greater thickness tends to reduce the specific energy absorption, square tube have less specific energy absorption than circular tubes and greater cone angle results in lower SEA.
2.5
Analytical Models
Alexander J.M [26] came up with a model to study the energy absorption capability of metal tubes in 1960. Since then improved models have been presented in many documents e.g. Ref [26-27]. All these models were based on the rigid plastic and moving hinge theory. Hanefi and Wierzbicki [28] have proposed a model for static compression of externally composite reinforced metal tube with a winding angle of 90o. Hanefi assumed that the compound wall deformed as shown in Figure 2.4
Figure 2.4
(a) Before Collapse (b) During collapse (c) Final collapse shape [17]
21
The mean crush force is calculated in an approximate way by equating the rate of external work by rate of internal energy dissipated for a given crushing distance. The rate of internal energy dissipated in the deforming part of the tube. Equating the rate of internal energy to external force gives αf
θf θf 4 HPm = sπR ∫ ⎡t m ∫ σ m dε + t c ∫ σ c dε ⎤ds + ∑ 2πR ∫ M 0i dα i ⎢⎣ 0 ⎥⎦ 0 i 0
(2.1)
Where Pm is the external load applied to tube, H is the hinge length, σ m is the flow stress of the metal, σ c is the ultimate compression stress of the composite in the fiber direction and t m and t c are the wall thickness of metal and composite. The first term on right hand side of equation 2.1 is the energy dissipated in metal tube, Wm , the second term is the energy absorbed by the composite reinforcement Wc , and the third term represent the bending energy dissipated in the wall of the compound tube Wb .
Wm = 4πσ m t m H 2
(2.2)
Wc = (Wc ) com + (Wc ) ten = 2πt c H ( Hσ cf + RE c ε ct )
(2.3)
Wb = 2πRCσ m t m2
(2.4)
where σ cf the ultimate stress of composite in compression, ε ct is the strain of composite in tension and C is a function of material properties and geometry.
22
⎛σ 1⎡ C = ⎢2 + 2⎜⎜ cr 2⎢ ⎝ σo ⎣
⎞⎛ t c ⎟⎟⎜⎜ ⎠⎝ t m
⎞ ⎛ σ cr ⎟⎟ + 2⎜⎜ ⎠ ⎝ σo
⎞⎛ t c ⎟⎟⎜⎜ ⎠⎝ t m
2
⎞ ⎛ σ cr ⎞ ⎟⎟ − ⎜⎜ ⎟⎟ ⎠ ⎝ σo ⎠
2
⎛ tc ⎜⎜ ⎝ tm
⎞ ⎟⎟ ⎠
2
⎤ ⎥ ⎥⎦
(2.5)
Substituting (2.2), (2.3) (2.3) in equation (2.1) we get 4 HPm = 4πσ m t m H 2 + 2πt c H ( Hσ cf + RE c ε ct ) + 2πRCσ m t m2
(2.6)
Defining σ ef as
1 tσ ef = σ o t m + σ cf t c With t =t m +t c 2
(2.7)
Therefore, the expression for Pm takes simple form:
Pm =
(
1 π 2 Rσ m Ct m2 + 4πtσ eq H 2 + 2πRt c E c ε ct2 H 4H
)
(2.8)
An improved expression for the mean crushing force was determined by considering the effective crushing as shown in Figure 2.5 proposed by Abramowicz [29]. The expression for the effective crushing length is given by equation 2.9.
Figure 2.5
Effective crushing distance [11]
23
δ eff = 2 H − 2 x m − t
(2.9)
Where x m = 0.14 H Assuming that the above equation is valid for reinforced tube, the effective crushing length of a 4H section is given by
Δ eff = 2δ eff = 3.44 H − 2t
(2.10)
Replacing 4H by Δ eff in equation (2.8) one gets the following expression for Pm
Pm =
[
1 4πtσ eq H 2 + 2πRt c E c ε ct2 H + 2π 2 Rσ m Ct m2 3.44 H − 2t
]
(2.11)
Hong [11] has extended the above model to the impact loadings with the method used by Abramowicz and Jones [29]. Considering the strain rate effects, the empirical Cowper – Symonds constitutive equation is reviewed
σ dm / σ m = 1 + (ε * / D)1 / p
(2.12)
Where D and p are coefficients. Since the composite response to the strain rate is complex, the strain response of Wc is discounted in the following derivation. Equating the energy dissipation to work of external load is given by 4 HPm = 4 HPm1 + 4 HPm 2 = (Wm + Wb ) + Wc In the impact condition, the dynamic mean crushing load is expressed as
24
(2.13)
d
Pm
⎡ ⎛ ε * ⎞1 / p ⎤ 1 (Wb + Wm )⎢1 + ⎜⎜ ⎟⎟ ⎥ + 1 Wc = 4H ⎢⎣ ⎝ D ⎠ ⎥⎦ 4 H
(2.14)
As in Reference [28, 29], ε * = 2ε pν m / δ eff , where ε p is the mean circumference strain, ν m the mean crushing velocity and is predicted asν m = ν o / 1.93 , and δ eff is the effective crushing distance. Substituting the values of ν m and δ eff in ε * , one has
ε* =
0.518Hν o R(1.72 H − t )
(2.15)
Replacing 4H by δ eff and substituting the expression Wm , Wc and Wb in equation (2.14) gives the dynamic mean crushing load: 1/ p ⎡ 0.518 Hν o ⎞ ⎤ ⎛ m 2 2 ⎟⎟ ⎥ ⎢(2π RCσ t m + 4πσ o t m )⎜⎜1 + 1 Pmd = ⎢ ⎝ DR(1.72 H − t ) ⎠ ⎥ 3.44 H − 2t ⎢ ⎥ c 2 ⎦ ⎣+ 2πt c H ( Hσ + RE c ε ct
The predicted model gives good results for tubes made of inner plastic metal and outer composite material with ply angle 90o.
25
(2.16)
CHAPTER 3 FINITE ELEMENT MODELING OF HYBRID TUBE
3.1
Introduction
Recently, finite element tool has served as an alternative and most effective tool in the study of behavioral response of a structure, subjected to different loading condition. FEM models not only help to drive the development time and cost down but also provide an early detection tool in phase of design. Finite element analysis software solves complex structures by breaking the structure into small elements. Until recently, all software’s that were out in market were either limited or capable of handling one and two dimensional problems, mainly static and small deformational problem. Researchers over years have tested and built a good numerical model that could be used to study the crash response of nonlinear and homogeneous material. Metals absorb majority of the energy under impact through progressive plastic deformation. Amount of energy absorbed in metals is associated to folding pattern it follows and modern software tool can replicate this model [31]. However, composite structures present many challenges for modeling .Finite element codes that attempt to characterize the crush/crash response of composite structure are being validated with the experimental results. The finite element analysis procedure used in this study comprised a pre-processor (PATRAN), an analysis code (LS-DYNA) and a post processor (LS-POST). The preprocessor was used to create and mesh the geometry. Once the mesh had been completed, the material and boundary condition were included in the analysis code and the system was
26
solved iteratively. Upon convergence of the analysis code, the results were viewed using a post-processor. LS-DYNA is a solver which includes both explicit and implicit finite element code, the first is mainly to analyze large deformation problem that occur in a short duration or quasi static response of inelastic solid and structure, with large time step. Implicit solver in LS–Dyna has limited capability mainly to solve structural and heat transfer problem. A well established contact algorithm is impetus for the use of Ls-Dyna in automotive industries; mainly to study the crash response in structures. Implicit and explicit methods are mainly differentiated on the condition of simulation step size, δt.
The implicit solution is
unconditionally stable for large time steps, whereas the explicit solution scheme is steady only if δt value remains smaller than δtcr of the structure being simulated. However the implicit solution method requires matrix inversion of the structural stiffness matrix, the explicit doesn’t, thus reducing the computation time and data storage space. Explicit integration method assumes a linear change in displacement over each time step, whereas the implicit function assumes a constant average acceleration over entire time step [34-36]. The software has extensive library including membrane, thin-shell, thick-shell and solid formulation. It also has cards which could simulate the crack propagation and damage in composites.
27
3.2
Classification of Loading
In an engineering world a component may be subjected to four major types of loading. Static and Fatigue, Dynamic/Rapid loading and impact or shock are types of loading. The classifications are mainly based on the loading rate or the duration to reach peak on the mechanical system. Figure 3.1 represent the load rise time on a system.
Figure 3.1 Graph showing load rise time [35] 3.2.1
Static and fatigue loading
Static loading: The loading is characterized as a constant force applied over a period, where time to reach the max stress is 3 times greater than the system fundamental period of the structure. Fatigue loading though has the cyclic loading behavior still measure the peak rise time greater than the above specified limit.
28
3.2.2
High speed or rapid loading
In this case the time requirement to reach max stress limit falls in the boundary of 1 to 3 times the system’s fundamental period. The deflection and stress level computation is complex and need both linear and nonlinear stiffness matrix
3.2.3
Impact loading
Impact loading, the load time to reach system peak stress is half the time period (Tn) of the system. In this type of loading the structure absorbs energy over the entire crushing period, thus brings the moving head to a complete stop. Impact analysis in general is a complex problem as stiffness, shape and mass of the specimen change with the contact zone. Experimental analysis carried out to study the behavior of the structure under impact condition is expensive requiring a lot of prototype and expensive equipment like cameras and digital data box. In such cases FEA turns out to be most cost efficient as the analysis are carried out on a virtual prototype in a virtual environment This not only drives the product cost down but also shortens the development phase and help in deigning a more reliable product.
29
3.3
Modeling Details of Hybrid Tube
3.3.1
Finite element model
The dimension of the hybrid tube is as shown in the Figure 3.2. The outer dimension of the square aluminum tube is 25 mm x 25 mm and the wall thickness (ta) is 1.6 mm. The Composite (tc) wrapped on the aluminum tube is 1.9 mm thick, and it varies with the number of layers used. Two layers of ± 45 o ply orientation are used for the analysis. The thickness selection was based from test conducted by Mallick [30].
Figure 3.2 Description of hybrid tube model(ta= Aluminum wall thickness, tc = Composite wall thickness, th = hybrid thickness) Hybrid tube was modeled using Patran as shown in Figure 3.3. Aluminum and Composite are modeled based on Belytschko-Tsay quadrilateral shell elements. Though shell element cannot properly simulate the delamination between the layers it’s used to minimize the computation time. According to Belytschko –Tsay [34] the given thickness is assigned to
30
both side of the shell element. On this basis the inner aluminum surface is modeled to the dimension of 23.4 mm x 23.4 mm and outer composite surface is modeled to the dimension of 26.8 mm x 26.8 mm. Inner and outer surface of the model is meshed using quadratic shell element and the size of an element is 2 mm x 2mm. The rigid loading plate is meshed coarsely using solid element as shown in Figure 3.3. Aluminum and composite material properties are defined by selecting the elements of the respective surfaces. Contact cards listed below were used for Aluminum and composite shell layers to account bondage and prevent layers interpenetration which leads to erroneous results
Figure 3.3
A FE model of Hybrid tube using Patran
The chamfer which acts as a trigger was modeled by reducing the thickness of the element as proposed by Schweizerhof [32]. The triggers were usually used to obtain progressive crushing during testing. For the chamfer angle of 45o, the height of the isosceles triangle is 21 percent greater than its base and is equal to 4.2 mm. The height of each element 31
was 2.1 mm but their thickness is different. The thickness of the top element was 0.25th and the thickness of the bottom element was 0.75 th, where th is the thickness of the hybrid tube. The first and second elemental thickness in chamfer zone was 0.875 mm and 2.625 mm. The different layers in Composite tube are modeled by defining integration point to each layer. The integration points are located evenly through the thickness. For example if the composite tube is made up of two layers and each layer is composed of one +45o lay-up and one -45o lay up then the integration point are assigned as shown in Figure 3.4.
Figure 3.4
Integration point location in two layered composite [35]
The loading plate considered for the analysis was modeled as a rigid block mass of 100 kg and moved at constant speed of 0.1 m/s for quasi static test condition. In case of an impact problem the rigid plate was moved with an initial velocity of 7.9 m/s.
32
3.3.2
Material model
The material considered for inner tube fabrication was aluminum alloy 6063-T52, whereas one used for outer wrap was glass/epoxy reinforced composite material. The unidirectional material properties of E-glass/epoxy lamina were taken from paper[30]. MAT24 also known as a Mat_Piecewise_Linear_Plasticity is considered for the inner aluminum tube wall, this card uses the von misses flow rule. More details about this material card is referenced in Ls-Dyna Users manual. The stress-strain curve required to define failure path of the Aluminum tube is assigned via Define Curve feature. The true stress-strain characteristics of the aluminum tube material were determined by conducting tension tests on specimens of tubes [31]. The values are obtained form the graph, Figure 3.5.
Figure 3.5
True stress v/s True plastic strain curve of Aluminum tube [31]
MAT 54 damage model was used to analyze the failure mode in composite lamina wrapped on Aluminum tube. This material card features both orthotropic material properties and the [CHANG CHANG] or [Tsai Wu] failure model. This means that material behaves linearly
33
before the damage and follows nonlinearity under failure or collapse. The energy absorption mechanism of a composite laminate under collapse could be seen in one of the following failure modes; interlaminar crack propagation, fiber breakage, transverse matrix cracking, debonding of fiber matrix composition and delamination. Thin shell algorithm can analyze the first four failure modes, as it involves only the inplane stress function but the delamination and debonding failure requires a three dimensional kinematic equation and can’t be dealt with thin shell theory. The MAT 54 card is valid only for thin shell element. Laminated shell theory has to be activated in CONTROL_SHELL card in order to model the transverse shear deformation. Lamination theory was applied to correct for the assumption of a uniform constant shear strain through the thickness of the shell [36]. The material property of E-glass fiber reinforced epoxy given below in Table 3.1 is taken from literature [30].
TABLE 3.1 MATERIAL PROPERTY OF UNIDIRECTIONAL E-GLASS/EPOXY LAMINA
34
3.3.3
Failure criteria for the composite layer
Composite damage card (Mat 54/55) in Ls- dyna has the ability to use either the Tsai-Wu. or Chang –Chang based post failure model to analyze ply failures. The Tsai-Wu failure model has limited capabilities over Chang- Chang failure model; basically it doesn’t depict the micro matrix failure mode of the composite laminate under compression. This model can only be represented with thin shell elements. Also unidirectional layer material properties could be assigned for the shell element. Chang- chang modified the post failure model of the Hashin to incorporate the non linear shear stress criteria of composite. MAT 54 or Chang – chang damage model compute the tensile fiber, compressive fiber, tensile matrix and compressive matrix mode individually and then analyze the failure mechanism in composite laminate. This model also includes a post failure strength degradation regime to study the laminate behavior under each lamina collapse. According to this model, if a mode of failure in a given lamina is merely fiber breakage and matrix shears then both the transverse modulus and minor Poisson’s ratio dropped to zero, however the longitudinal modulus and shear modulus follows a weibull distribution. Additionally if the matrix degradation happens to be first cause of failure, then longitudinal and shear modulus remain unaffected, though transverse modulus and minor Poisson’s ratio value drops to zero. In this thesis I have used a Chang- Chang developed failure algorithm to study post failures in hybrid tube. The stress value from the below listed formulae determines the failure modes [35-37]. Tensile failure mode: (fiber rupture) If σ aa > 0
35
⎛σ then e = ⎜⎜ aa ⎝ Xt 2 f
2
⎛σ ⎞ ⎞ ⎟⎟ + λ ⎜⎜ ab ⎟⎟ − 1 [≥ 0 failed , < 0elastic ] ⎝ Sc ⎠ ⎠
(3.1)
Where λ is a weighting factor for the shear term in tensile fiber mode and ranges from 0-1. E a = Eb = G ab = ν ab = ν ba = 0, after lamina failure by fiber rupture.
Compressive Fiber mode: (Fiber buckling or kinking) If σ aa < 0
⎛σ Then e = ⎜⎜ aa ⎝ Xc 2 c
2
⎞ ⎟⎟ − 1 ⎠
[≥ 0 failed , < 0elastic ]
(3.2)
E a = ν ab = ν ba = 0 after lamina failure by fiber buckling or kinking
Tensile matrix mode: (matrix cracking under transverse tension and in-plane shear) If σ bb > 0 ⎛σ Then e = ⎜⎜ bb ⎝ Yt 2 m
2
2
⎞ ⎛σ ⎞ ⎟⎟ + λ ⎜⎜ ab ⎟⎟ − 1 [≥ 0 failed , < 0elastic ] ⎠ ⎝ Sc ⎠
(3.3)
Eb =ν ba = G ab =0 after lamina failure by matrix cracking
Compressive matrix mode: (matrix cracking under transverse compression and in plane shear)
If σ bb < 0 ⎛σ Then e = ⎜⎜ bb ⎝ 2S c 2 d
2 ⎞ ⎡⎛ Yc ⎟⎟ + ⎢⎜⎜ ⎠ ⎢⎣⎝ 2 S c
2 2 ⎤σ ⎞ ⎛ σ ab ⎞ bb ⎟⎟ − 1⎥ ⎟⎟ [≥ 0 failed , < 0elastic ] + ⎜⎜ Y S ⎥ ⎠ ⎦ c ⎝ c ⎠
36
(3.4)
Eb =ν ba =ν ab = G ab =0 after lamina failure by matrix cracking In equation (3.1) to (3.4) σ aa and σ bb are the stresses in the direction of the fiber and normal to fiber. σ ab , represents the shear stress in lamina plane. Where, Xt and Xc = tensile and compressive strengths in the fiber direction, respectively Yt and Yc = tensile and compressive strengths in the matrix direction, respectively Sc = shear strength Ea and Eb = Module in the longitudinal and transverse directions, respectively Each lamina properties are checked to determine its failure characteristic by using above equation .When the lamina fails, the post-failure conditions are applied to that lamina and a ply-discount method is applied to determine its subsequent contribution to the laminate’s load carrying capacity and failure. In addition to the stress-related failure criteria represented in above equation, maximum strain limits were specified for fiber tension and fiber compression using DFAILT and DFAILC parameters in material model 54. Figure 3.6 shows an example of the usefulness of these parameters. For example, a given material considered for analysis has a material property of 800Mpa in longitudinal direction and if its DEFAILT value if set to Zero, then under tension the fiber breaks when the stress in fiber direction exceeds its longitudinal strength number. The failure strain in the above example will be around 2.7%, and could also be set to .024 , then the stress limit stays same till it reaches (0.027 + 0.024) = 0.051 or 5.1%. The lamina behaves as a linear-brittle material in first case, and in the second case; the lamina behaves as an elastic-perfectly plastic material. 37
The degradation in nominal strength due to the diffusive crack formation in the crash front and the delamination of the stacks of lamina is taken into account by considering few parameters in enhanced composite damage card like FBRT, YCFAC and TFAIL. FBRT and YCFAC account for reduction in tensile and compressive strengths in the fiber direction, respectively, after compressive failure of the matrix.
Figure 3.6
3.3.4
Stress-strain curve of unidirectional E-Glass/Epoxy composite material with DFAILT =0.0 and 0.024 [35]
Contact modeling
Contact algorithm that were used for the analysis are listed below
CONTACT_AUTOMATIC_NODES_TO_SURFACE (CANTS)
38
This LS-Dyna card simulated the interaction between the aluminum tube and the composite over wrap in case there was no bonding between them or after the bond had failed. CANTS interface card was also used between the rigid plate and the hybrid tube. The coefficient of friction considered for this type of contact is 0.25.
CONTACT_AUTOMATIC_SINGLE_SURFACE (CASS)
This card is used to avoid the interpenetration of the successive folds in hybrid tube.
CONTACT_TIEBREAK_NODES_ONLY (CTNO)
This contact algorithm is used to simulate the bonding between the composite and aluminum tube. This contact algorithm accounts for both normal and shear forces at the interface. The normal and shear force considered for the analysis was assumed to be equal. The tiebreak criterion in this algorithm is given by the following equation.
⎛ fn ⎜⎜ ⎝ Pn
2
2
⎞ ⎛ fs ⎞ ⎟⎟ + ⎜⎜ ⎟⎟ ≥ 1.0 ⎠ ⎝ Ps ⎠
Where f n = normal force at the interface f s =shear force at the interface Pn =Maximum normal force at bond failure Ps = Maximum Shear force at bond failure
39
(3.5)
CHAPTER 4 RESULTS AND DISCUSSION
4.1
Validation of FE Hybrid Model
Mallick [30] studied the crush resistance of both circular and square hybrid tubes. The tube considered for the study was E-glass fiber/epoxy composite prepreg wrapped on square aluminum alloy 6063-T52 tube. The hybrid tube was tested on Interlaken servo press with load capacity of 330 KN. The speed at which the tube was tested was 12.7 mm/min. The number of layers considered for the study was 1,2,3,4 with ply orientation ±450 to tube axis. In this research work, LS-Dyna solver was used to simulate the behavior of the hybrid tube under quasi-static test condition to that of experimental test. The tube considered for validation was 2 layers of E-glass/epoxy composite prepregs wrapped on square Aluminum tube. In this model, the fiber orientation was at an angle of ± 45 0 to the tube axis. The following assumptions where made for this model [31].
The bond failure limit between the aluminum and composite wall was assumed 150 N.
The coefficient of friction between Aluminum and composite was assumed to be 0.25.
The folding patterns were in close proximity to what was seen in test lab. Tube was simulated for the quasi-static test condition by considering a loading plate of mass 100kg moving at a constant speed of 0.1m/s. Figure 4.1(b) shows the pictorial representation of progressive crushing of hybrid tube. Below are few listed assumptions that were made to interpret the quasi –static loading condition in Dyna run. [34]. 40
The ratio of kinetic energy and internal energy was less than 5%.
The ratio of hourglass energy to internal energy was less than 10%.
The ratio of internal energy to the output energy was between 0.9 and 1.0.
(a) Figure 4.1
(b) The progressive crushing of hybrid tube. a) Experimental test tube [30] (b) FE model
The load displacement curve of numerical model showed comparable results to that of experimental test. From the Figure 4.3 it can be seen that the crush initiation force was close to that of experimental results, but the mean crush load was higher by 1.5% and the reason for that is no bonding strength considered for the analysis. Based on this results parametric studies where conducted for different condition. The energy absorption capability found by calculating area under the load displacement curve of FE hybrid model is 1931 J and that of experimental test tube is 1754 J. A 10% variation in result is observed which is within acceptable limits.
41
Crush pattern of hybrid tube at different time step could be observed in Figure 4.2. The impact condition considered for the analysis is quasi static. The folding initiation force was reduced by implementing trigger mechanism.
Figure 4.2
Crush pattern of hybrid tube under quasi-static condition
42
50
Num erical
45
Experim ental [30]
40
Force (kn)
35 30 25 20 15 10 5 0 0
10
20
30
40
50
60
70
80
Displacement(mm)
Figure 4.3
Comparison of load displacement curve of experimental and numerical mode tube
The Al alloy and composite tube of wall thickness 2.2 mm and 2.5 mm was considered for analysis and it showed a lower energy absorption capacity when compared to the hybrid tube as shown in Figure 4.5. The three structures considered were of equal weight. Crush pattern of aluminum, composite and hybrid tube are as shown in Figure 4.4. Increase in composite tube thickness increases the energy absorption to some extent but shows the tendency of brittleness and may fail catastrophically. Better energy absorption and a progressive crushing could be achieved using hybrid tube.
(a)
(b)
(c)
Figure 4.4 Crush pattern of (a) Composite tube (b) Aluminum tube (c) Hybrid tube 43
Al Tube- 2.2mm 40
Gl/Epoxy Tube- 2.5mm Hybrid Tube
35
Force (Kn)
30 25 20 15 10 5 0 0
15
30
45
60
75
90
Displacement (mm)
Figure 4.5
Comparison of load displacement curve of AL and GL/epoxy tube with hybrid tube
Composite tube (GL/Epoxy) of thickness 2.7 mm was considered for analysis and it was observed that as the thickness of composite material increases the failure pattern changes as shown in Figure 4.6(a). A rise in peak to mean crush force was observed in Figure 4.6(b) and this was mainly due to fiber and matrix breakage.
45 GL/Epoxy-2.7mm
40
Force (Kn)
35 30 25 20 15 10 5 0 0
15
30
45
60
75
90
Displacement (mm)
(a) Figure 4.6
(b) (a) Crush pattern of GL/Epoxy tube (b) Load displacement of GL/Epoxy tube of wall thickness 2.7mm
44
4.2
Parametric study of hybrid tube
Following are some the parameters which were considered for studying the behavior of hybrid tube. 4.2.1
Effect of ply orientation
The Energy absorption of hybrid tube under quasi-static condition increases with the orientation angle as shown in Table 4.1. For hybrid tube with ply orientation ± 15 o the peak, crush initiation force is high when compared to other ply orientation. Delamination and debonding away from the metal is observed during compression .This mechanism may greatly reduce the Energy absorption, because the composite layer no longer contribute to the energy absorption during crushing mode. Under impact, the energy absorption capacity of the hybrid tube increases to approximately 12% more than of quasi-static loading. The reason for this may be strain rate effect. The load displacement curve of different ply orientation under quasi-static and impact load is as shown in Figure 4.7 and Figure 4.8. An ideal crashworthy structure used in a car has to meet two requirements. Absorb the kinetic energy of the car and to dissipate this energy over a time frame to avoid any critical injuries to passengers. So while analyzing the specimen’s one needs to note down both magnitude of energy that is capable of absorbing and length of time over which this energy is absorbed. Figure 4.9 shows the crush pattern and the time to crush a length of 65mm of hybrid tube.
45
2 layers- (+/-45)deg 4 layers-90deg
55
2 layers-(+/-15)deg
50
2 layers-(0/90)deg
45
2 layers- (90/0)deg
Force (Kn)
40 35 30 25 20 15 10 5 0 0
10
20
30
40
50
60
70
80
Displacement (mm)
Figure 4.7
Load displacement response of hybrid tube under quasi-static loading
TABLE 4.1 EFFECT OF PLY ORIENTATION UNDER QUASI STATIC LOADING Mean Crush Force Pm (KN) 27.75
Energy absorption capacity (Joule)
2 layers ( ±15° )
Peak Crush Force Pa (KN) 51.15
2 layers ( ±45° )
37.05
29.71
1931
4 layers ( 90° )
34.53
26.04
1692
2 layers ( 0 / 90° )
45.29
32.96
2143
40.92
31.67
2059
Ply Orientation
°
2 layers ( 90 / 0 )
46
1804
2 layers (+/-15)deg
80
2 layers (+/-45)deg
70
4 layers-90deg 2 layers-(90/0)deg
Force (Kn)
60 50 40 30 20 10 0 0
15
30
45
60
75
90
Displacement (mm)
Figure 4.8
Load displacement response of hybrid tube under impact loading
TABLE 4.2 EFFECT OF PLY ORIENTATION UNDER IMPACT LOADING Mean Crush Force Pm (KN) 32.93
Energy absorption capacity (Joule)
2 layers ( ±15° )
Peak Crush Force Pa (KN) 71.84
2 layers ( ±45° )
52.2
34.47
2241
4 layers ( 90° )
39.42
30.29
1969
2 layers ( 90 / 0° )
51.15
34.16
2221
Ply Orientation
47
2141
Figure 4.9 4.2.2
Crush Pattern and time duration to deform a length of 65 mm
Effect of adhesive
Hybrid tube simulations were run to investigate the effect of adhesive on the load displacement response under impact load (crush speed 7.9 mps). The model was also analyzed without adhesives. Since the bond strength was not known, the values selected were 150 N, 250 N and 750 N to represent weak, medium and strong failure bond strength. Figure 4.10 and Figure 4.11 shows the load displacement response of hybrid tube with ± 45 o and
48
(90 o / 0 o ) ply orientation. The peak crush force at 250 N bond failure strength was almost equal to that of 150 N bond failure strength. However there was a slight variation in mean crush force. With 750 N bond failure strength the load displacement response was much lower as seen in Figure 4.10.
Bond Strength-150N Bond Strength-250N Bond strength-750N No-bond
60 50
Force (Kn)
40 30 20 10 0 0
15
30
45
60
75
90
Displace me nt (mm)
Effect of adhesive strength on the force displacement response of ±45o hybrid tube
Figure 4.10
70
Bond Strength- 750N Bond-Strength -250N
60
Bond-Strength-150N No-Bond
Force(KN)
50 40 30 20 10 0 0
15
30
45
60
75
90
Displacement(mm)
Figure 4.11
Effect of adhesive strength on the force displacement response of hybrid (90 / 0) degree tube
49
4.2.3
Effect of crush speed
The Figure 4.12 and Figure 4.13 show the load displacement response of the hybrid tube with ply orientation ± 45 o and 90 o / 0 o under varying crush speed. The peak and valley location of load displacement response of hybrid tube crushed at a speed of 7.9 mps 15 mps and 30 mps varied slightly. The bond failure strength considered for the analysis was 150 N.
Crush speed-7.9mps Crush speed-15mps
60
Crush speed-30mps
Force (Kn)
50 40 30 20 10 0 0
10
20
30
40
50
60
70
80
Displace me nt (mm)
Figure 4.12
o Effect of crush speed on load displacement response of ±45 hybrid tube with bond strength of 150 N
70
Crush Speed -7.9mps Crush Speed-15mps
60
Crush Speed-30mps
Force (kn)
50 40 30 20 10 0 0
15
30
45 60 Displacement (mm)
75
90
Figure 4.13 Effect of crush speed on load displacement response of 90 o / 0 o hybrid tube with bond strength of 150 N 50
4.2.4
Effect of trigger mechanism
The trigger mechanism allows the tube to buckle locally and to deform in a progressive manner. Although the location of the trigger influences the folding pattern, the size and shape of the initiator control the peak crush load. Because after local buckling, a maximum portion of the axial load is supported by the corners, in order to effectively cripple a beam with square cross section, the corners of the beam must be deformed. In this work, two types of trigger were considered. One, chamfer at the end of the tube and second is introduction of sectional bead at particular distance form the end. The chamfer is modeled by progressively reducing the thickness at the chamfer zone. However, the sectional bead is modeled as shown in Figure 4.14. The load Displacement response of hybrid tube with different trigger mechanism is as sown in Figure 4.15. Though the initial folding force of tube with sectional bead is high, the mean crush force is almost identical to the tube with 45 0 chamfer. Hybrid tube without a trigger mechanism shows a high folding force, which is not desirable for crashworthy structure.
Figure 4.14
FE model of different trigger geometry
51
Chamfer Bead
60
No-Trigger
Force (Kn)
50 40 30 20 10 0 0
15
30
45
60
75
90
Displaceme nt (mm)
Figure 4.15
Load displacement curve of hybrid tube with different trigger geometry
The folding initiation force was lower for the tube with chamfer trigger geometry and the adhesive between the Al tubes and composite over-wrap helped to achieve a defined crush pattern.
4.2.5
Effect of impact angle
Hybrid tube with an impact angle of 15, 30, and 90 deg to rigid wall was considered for the analysis. The Figure 4.16 shows the crush pattern of these tubes. It was observed that even though the tube was impacted with an angle it showed better energy absorption capability than the aluminum and composite tube. Figure 4.17 shows the load displacement curve of hybrid tubes impacted at 15 mps. It was observed that there was not much difference in load displacement curve of 15 deg and 30 deg impact angles.
52
(a)
(b)
Figure 4.16
(c)
Crush pattern of hybrid tube impacted at an angle to tube axis (a) 90 Deg
(b) 30 deg
(c) 15 deg
Impact Angle-15deg
60
Impact Angle -30deg Impact Angle-90deg
50
Force (KN)
40 30 20 10 0 0
15
30
45
60
75
90
Displacement (mm)
Figure 4.17
Load displacement curve of Hybrid tube with different impact angle
53
CHAPTER 5 CONCLUSION AND FUTURE WORK 5.1
Conclusions
A LS-Dyna based numerical model was put together to simulate the quasi–static axial crushing of aluminum-composite hybrid tube. The simulation correlated well with the experimental data and several other models generated to do a parametric study. Among them where the chamfer angles, trigger mechanism, crush speed and contact between the aluminum tube and the composite over-wrap. The study showed that the axial crush performance of the square hybrid tube can be improved using the E-glass fiber/epoxy overwrap. The axial crush parameters that improve significantly by using composite over-wrap are the maximum load, mean load and the crush energy absorption. The specific energy also increases by small amount. The model was also analyzed for impact load condition. The results showed that the energy absorption capability of the hybrid tube increases by 12% and performance can be optimized by parameters like material type, lay-up sequence, number of layers in the over-wrap, etc. The following observations where made form the FE Model.
The hybrid tube has energy absorption capability better than either Al tube or composite tube.
The progressive crushing behavior can be observed in hybrid tube.
The energy absorption capability increases with the increase in orientation angle for both quasi-static and impact loading condition.
54
The 45 deg lay up sequence has better energy absorption capability when compared to other fiber orientation.
A 12% increase in energy absorption is observed under impact loading of hybrid tube.
Trigger mechanism plays an important role in reducing the peak force.
The folding initiation force was lower with adhesive between the Al tube and composite over-wrap than without adhesive; however the higher the bond strength the lower was the initiation force and mean crush force
5.2
Recommendations for Future work
Further analysis should be carried out to determine the effect of number of plies over wrapped on square metal tube. Experimental testing and finite element analysis could be carried out to study the occupant injury criteria when hybrid tubes are used as crash absorbing structure in front rail of an automobile or as sub floor beams of helicopter. Analysis can also be carried out to observe the effect of length to breadth ratio of the hybrid tube. An attempt to simulate the debonding failure of hybrid tube is encouraging. A study on procedures like rigid wall planar moving force instead of boundary prescribed motion would be required to confirm whether the procedure has any effect on the crush behavior of the FE models. More studies are required to justify the use of parameters used in damage model.
55
REFERENCE
56
LIST OF REFRENCES
1.
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2.
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Abdel H., Newaz G.M., “Influence of Crush Mechanisms on Energy Absorption of PMC Square Tubes”, Sage Publication, Vol. 2 (2001) p160-174.
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8.
Hamada H., Ramakrishna S., Maekawa Z., Nakamura M., “Energy Absorption Behavior of Hybrid Composite Tubes”, Proc. 10th Annual ASM/ESD Advanced Composite Conference, Michigan, USA, (Nov. 1994) p. 511-522.
9.
Berry J. P., “Energy Absorption and Failure Mechanisms of Axially Crushed GRP Tubes”, Ph.D., Thesis, University of Liverpool, UK, (1984)
10.
Ramakrishna S., Hamada H., Maekawa Z., Sato H., “Energy Absorption Behavior of Carbon Fiber Reinforced Thermoplastic Composite Tubes”, Journal of Thermoplastic Comp. Material, Vol. 8 (July 1995) p. 323-344.
11.
Hong W. S., Zin-Min W., Zhi-Min X., Xing-Wen D., “Axial Impact Behavior and Energy Absorption Efficiency of Composite Wrapped Metal Tubes”, Int. J. of Impact Eng., Vol. 24 (2000) 385-401.
12.
Shin K.C, Lee J.J., Kim K. H., Song M.C., “Axial crush and bending collapse of an aluminum/GFR hybrid square tube and its energy absorption capability”, Composite Structures, Vol. 57 (2002) p 279–287.
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Schmueser D. W., Wickliffe L. E., “Impact Energy Absorption of Continuous Fiber Composite Tubes”, J. Eng. Mat. Trans., Vol. 72 (1987) p. 72-77.
14.
Berry J., Hull D., “Effect of Speed on Progressive Crushing of Epoxy-Glass Cloth Tubes”, 3rd Conf. Mech. Prop. High Rates of Strain, Oxford, 1984 p-463 470.
15.
Farley G.L., “The Effects of Crushing Speed on the Energy Absorption Capability of Composite Material”, NASA Tech Mem. (1987) p. 89-122.
16.
Thornton, P.H., “The crush behavior of pultruded tubes at high strain rate”, J. Composite materials, Vol. 24 (1990) p. 594-615.
17.
Farley G.L. “The Effects of Crushing Speed on the Energy Absorption Capability of Composite Tubes”, J. Composite Materials, vol.25 (1991) p. 1314-1329.
18.
Langseth M., Hopperstad O.S., “Static and Dynamic Axial crushing of Square Thin Walled Aluminum extrusions”, Int. J. of Impact Eng. (1996) 949-968.
19.
Thornton P. H., “Energy Absorption in Composite Structures,” Journal of Composite Materials, Vol. 13(1979), p. 247-263.
20.
Farley G. L. “Effect of Specimen Geometry on the Energy Absorption Capability of Composite Materials”, Journal of Composite Materials, Vol. 20(July 1986) p. 390400.
21.
Farley G. L., Jones, Robert M., “Crushing Characteristics of Composite Tubes with Near-Elliptical Cross Section,” Journal of Composite Materials, Vol. 26 (1992) p.1741-1751.
22.
McCarthy, Wiggenraad J.F., “Finite Element Modeling of Crash Response of Aerospace Sub-Floor Structure”, National Aerospace Laboratory, Netherlands.
23.
Thuis H., Metz V. H., “The Influence of Trigger Configurations and Laminate LayUp on the Failure Mode of Composite Crush Cylinders,” Composite Structures, Vol. 25, p. 37-43.
24.
Sigalas I., Kumosa M., Hull D., “Trigger Mechanisms in Energy-Absorbing Glass Cloth/Epoxy Tubes”, Composite Science and Technology, Vol. 40 (1991) pp. 265287.
25.
Mamalis A. G., Yuan Y. B., Viegelahn G. L., “Collapse of Thin Wall Composite Sections Subjected to High Speed Axial Loading”, Int. J. of Vehicle Design, Vol. 13 (1992) p. 564–579.
58
26.
Wierzbicki T., Bhat S.U., Abramowicz W., Brodkin D., “A Two Folding Elements Model of Progressive Crushing of Tubes”, Int. J. Solids Struct., Vol. 29 (1992) p 3269-88.
27.
Wierzbicki T., Bhat S.U., “A Moving Hinge Solution for Axi-Symmetric Crushing of Tubes”, Int. J. Mech. Science, Vol. 28 (1986) p. 135-151.
28.
Hanefi E.H, Wierzbicki T., “Axial Resistance and Energy Absorption of Externally Reinforced Metal Tubes”, Composites Part-B, Vol.270 (1996) p. 387-94.
29.
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30.
Babbage, J and Mallick, P K. ‘Axial Crush Resistance of Aluminum Composite Hybrid Tubes’, Proceedings of 17th Annual Technical Conference of the American Society for Composites, (2002) p 70.
31.
El-Hage H., Mallick P. K., Zamani H., “A Numerical Study on the Quasi-static axial crush characteristics of square aluminum tubes with chamfering and other triggering mechanisms”, I. J. Crash Vol. 10 (2005) p. 183–195.
32.
Schweizerhof K., Weimar K., Münz T., Rottner T., “Crashworthiness analysis with enhanced composite material models in LS DYNA-3D: Merits and Limits”, 5th International LS-DYNA Users Conference, (1998).
33.
Ramakrishna S., Hamada H., “Energy absorption characteristic of crashworthy structural composite materials”, Key engineering material, Vol. 141-143(1998) p.585-620.
34.
Schultz M. R,. “Energy absorption capacity of graphite-epoxy composite”, M.S. Thesis, Virginia Polytechnic Institute and State University, Virginia, (1998).
35.
Vivek. M,. “Energy absorption characteristic of stitched corrugated sandwich panels”, M.S. Thesis, Wichita State University, Wichita, (2005).
36.
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37.
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59
APPENDIX SAMPLE KEY FILE
*KEYWORD *CONTROL_BULK_VISCOSITY 1.5 0.06 *CONTROL_CONTACT 0.1 0 2 0 1 1 0 0 10 0 4 *CONTROL_COUPLING 1 1 1 0 *CONTROL_CPU 0 *CONTROL_DYNAMIC_RELAXATION 250 0.001 0.995 1e+30 0.9 *CONTROL_ENERGY 1 2 1 1 *CONTROL_HOURGLASS 1 0.1 *CONTROL_OUTPUT 0 3 0 0 0 *CONTROL_SHELL 20 2 -1 0 2 2 *CONTROL_TERMINATION 20 0 0 0 0 *CONTROL_TIMESTEP 0 0.7 0 0 0
1 1
0.04
0
0 1
$$ CARDS FOR GENERATING FORCE, DISPLACEMENT OUTPUTS
*DATABASE_BINARY_D3PLOT 0.1 *DATABASE_MATSUM 0.1 *DATABASE_NODFOR 0.1 *DATABASE_RBDOUT 0.1 *DATABASE_RCFORC 0.1
60
$$ Square Tube with Chamfer Part: Aluminum Tube
*PART iso1 1 1 1 0 0 0 *SECTION_SHELL 1 2 4 0.5 0.5 0.5 0.5 *ELEMENT_SHELL 1 1 1 2 55 54 53 1 54 55 108 107 105 1 107 108 161 160 157 1 160 161 214 213 209 1 213 214 267 266 405 1 1538 1539 1592 1591 1457 1 1591 1592 1645 1644 1509 1 1644 1645 1155 1166 2071 1 1168 1167 2323 2312 2072 1 2312 2323 2324 2313 2073 1 2313 2324 2325 2314 2074 1 2314 2325 2326 2315 2075 1 2315 2326 2327 2316 2076 1 2316 2327 2328 2317 2077 1 2317 2328 2329 2318 2078 1 2318 2329 2330 2319 2079 1 2319 2330 2331 2320 2080 1 2320 2331 531 532 *PART iso2 2 2 1 0 0 *SECTION_SHELL 2 2 4 1.4 1.4 1.4 1.4 *ELEMENT_SHELL 2 2 2 3 56 55 54 2 55 56 109 108 106 2 108 109 162 161 158 2 161 162 215 214 210 2 214 215 268 267 262 2 267 268 321 320 314 2 320 321 374 373
0
0
61
0
366 2 373 374 427 426 418 2 426 427 480 479 470 2 479 480 533 532 1021 2 3 2 1146 1135 1022 2 1135 1146 1147 1136 1023 2 1136 1147 1148 1137 2067 2 2306 2317 2318 2307 2068 2 2307 2318 2319 2308 2069 2 2308 2319 2320 2309 2070 2 2309 2320 532 533 *PART iso3 3 3 1 0 0 *SECTION_SHELL 3 2 4 1.6 1.6 1.6 1.6 *ELEMENT_SHELL 3 3 3 4 57 56 4 3 4 5 58 57 5 3 5 6 59 58 6 3 6 7 60 59 7 3 7 8 61 60 8 3 8 9 62 61 2055 3 2293 2304 2305 2056 3 2294 2305 2306 2057 3 2295 2306 2307 2058 3 2296 2307 2308 2059 3 2297 2308 2309 2060 3 2298 2309 533
0 0
2294 2295 2296 2297 2298 534
Part: GL/Epoxy Tube
*PART prop1 4 4 2 0 *SECTION_SHELL 4 10 4 0.5 0.5 0.5 0.5 90 90 90 90 *INTEGRATION_SHELL 4 4 0 -0.75 0.25 1 -0.25 0.25 1
0
0 -4
0 1
62
0
0.25 0.25 1 0.75 0.25 1 *ELEMENT_SHELL 2756 4 3356 3357 2808 4 3409 3410 2860 4 3462 3463 2912 4 3515 3516 2964 4 3568 3569 3016 4 3621 3622 3068 4 3674 3675 3120 4 3727 3728 *PART prop2 5 5 2 0 *SECTION_SHELL 5 10 4 1.2 1.2 1.2 1.2 90 90 90 90 *INTEGRATION_SHELL 5 4 0 -0.75 0.25 1 -0.25 0.25 1 0.25 0.25 5 0.75 0.25 1 *ELEMENT_SHELL 2757 5 3357 3358 2809 5 3410 3411 2861 5 3463 3464 2913 5 3516 3517 2965 5 3569 3570 3017 5 3622 3623 3069 5 3675 3676 3121 5 3728 3729 *PART prop3 6 6 2 0 *SECTION_SHELL 6 10 4 1.9 1.9 1.9 1.9 90 90 90 90 *INTEGRATION_SHELL 6 4 0 -0.75 0.25 1 -0.25 0.25 1
3410 3463 3516 3569 3622 3675 3728 3781
3409 3462 3515 3568 3621 3674 3727 3780
0
0 -5
3411 3464 3517 3570 3623 3676 3729 3782
3410 3463 3516 3569 3622 3675 3728 3781
0
0 -6
63
0.25 0.75
0.25 0.25
1 1
*ELEMENT_SHELL 2758 6 3358 2759 6 3359 2760 6 3360 2761 6 3361 2762 6 3362 2763 6 3363 2764 6 3364
3359 3360 3361 3362 3363 3364 3365
*PART Rigid 7 7 3 *SECTION_SOLID 7 1
3412 3413 3414 3415 3416 3417 3418
3411 3412 3413 3414 3415 3416 3417
0
0
0
2332 2333 2334 2336 2337
2333 2334 2335 2337 2338
2399 2401 2403 2405 2406
0
*ELEMENT_SOLID 2081 7 2337 2082 7 2338 2083 7 2339 2084 7 2341 2085 7 2342
2336 2337 2338 2340 2341
0
2396 2399 2401 2404 2405
2397 2398 2400 2396 2399
$$ Material Cards Check LS-Dyna User Manual for Explanation Material: GL/Epoxy
*MAT_ENHANCED_COMPOSITE_DAMAGE 2, 1.8e-06, 30.9, 8.3, 0.086 2.8, 3.00, 2.8 0.1,0,1,4 0.480, 0.798, 0.140, 0.040, 0.070, 54 Material: Steel
*MAT_RIGID 3 4.0e-03 1, 5, 7
207
0.3
0
*MAT_PIECEWISE_LINEAR_PLASTICITY
64
1, 2.6e-6, 69 0.33, 0.160,,, 0 0,0,1,0
$$ Contact cards check key word manual for explanation
*CONTACT_AUTOMATIC_NODES_TO_SURFACE 15, 7, 2, 3 0.25 *CONTACT_AUTOMATIC_NODES_TO_SURFACE 16, 17, 2, 2 0.25 *CONTACT_AUTOMATIC_SINGLE_SURFACE 16, 2 0.25 *CONTACT_AUTOMATIC_SINGLE_SURFACE 17, 2 0.25 *BOUNDARY_PRESCRIBED_MOTION_RIGID 71021 *DEFINE_CURVE 2, 1 1 0 0 1 0.1 5 0.1 10 0.1 15 0.1 20 0.1
65
