Simulation of progressive damage development in braided
composite tubes under axial compression
Carla J.McGregor a ,Reza Vaziri
a,*
,Anoush Poursartip a ,Xinran Xiao
b
a
Composites Group,Departments of Civil Engineering and Materials Engineering,The University of British Columbia,Vancouver,
British Columbia,Canada V6T 1Z4
b
General Motors Corporation,Rearch and Development,MC 480-106-710,30500Mound Road,Warren,MI 48090-9055,USA
Received 30June 2006;received in revid form 11October 2006;accepted 23October 2006
Abstract
A continuum damage mechanics bad model for composite materials (CODAM),which has been implemented as a ur material model in an explicit finite element code (LS-DYNA),is ud to capture the complete tensile and compressive respon of a braided com-posite material.Model parameters are related to experimentally obrved behaviour to ensure a physical basis to the model and a crack band scaling approach is ud to minimize mesh nsitivity (or lack of objectivity)of the numerical results.The predictive capability of the model is validated against the results from dynamic tube crush experiments.The damage propagation,failure morphology and energy absorption predictions correlate well with the experimental results.Ó2006Elvier Ltd.All rights rerved.电脑回车键是哪个
Keywords:A.Carbon fibre;C.Damage mechanics;C.Finite element analysis (FEA);Crashworthiness
1.Introduction
Fibre reinforced composite tubular structures are being considered as viable energy absorbing components in vehicular front rail structures.An extensive body of litera-ture indicates that stable progressive crushing and high specific energy absorption (SEA)is attainable.Energy is absorbed through a complex combination of numerous fracture mechanisms.The material is either quentially damaged on a microstructural level (fragmentation mode)or deformed into a splaying type mode of failure [1–3].Tubes reinforced with less brittle fibres,such as Kevlar,tend to fold progressively in a manner similar to that obrved in metal tubes.The actual failure behaviour of composite tubes is affected by material parameters (fibre and matrix type [4–7],fibre architecture [1,6,8,9],fibre vol-ume fraction [10]),specimen geometry [11–13],and external loading conditions [4,14,15].
Predicting the respon of the quasi-brittle tubes under axial compressive loads is difficult due to the complex nat-ure of the failure mechanisms and lack of accurate and robust predictive tools.There have been a number of attempts to simulate the crushing respon of composite tubes using finite element analysis (FEA)in conjunction with a constitutive model that simulates damage initiation,damage growth and final failure in the composite material.Typically,either a micromechanical or a macromechanical approach is adopted.
Micromechanical approaches reprent damage growth at the level of the constituents and u this i
nformation in the global model to define the overall respon of the laminate at any level of loading.Beard and Chang [16]suc-cessfully simulated the quasi-static crushing respon of braided circular and square tubes using a micromechanical model incorporated into ABAQUS (implicit version).The model calculated the overall effective material properties of a repeating unit cell (RUC)using the material properties of the individual constituents,namely the tows and the matrix,and the three-dimensional geometry of the联通流量活动
1359-835X/$-e front matter Ó2006Elvier Ltd.All rights rerved.doi:10.positesa.2006.10.007
*
Corresponding author.Tel.:+16048222800;fax:+16048226901.E-mail address:reza.vaziri@ubc.ca (R.Vaziri).
/locate/compositesa
Available online at
Composites:Part A 38(2007)
2247–2259
laminate.The model has not yet been implemented into explicit codes for dynamic analysis of crash events.
Macromechanical (or phenomenological)approaches reprent the effect of damage growth in the individual con-stituents by smearing the respon over a reprentative volume element (RVE).The efficiency and flexibility of this approach has led to its popularity [17–21].Xiao et al.[20]prented the results of a study carried out on braided com-posite tube crushing simulations using the built-in macro-mechanical material model,MAT58,in LS-DYNA.The model,bad on the work by Matzenmiller et al.[22,23],reprents the orthotropic material properties of composite laminae.The SEA and peak forces in braided tubes crushed with a plug initiator were captured well,but the SEA of non-initiated tube crushes tended to be under-pre-dicted.Morthorst and Horst [21]prented a material model incorporated into LS-DYNA to simulate failure of glass/epoxy conical shells under quasi-static crushing con-ditions.Their model focud on capturing the in-plane respon of the plies as well as accurately modelling delam-ination between layers by using both shell and solid elements.Although the model accurately predicted the crushing characteristics of glass/epoxy conical shells,the authors acknowledged that the model was fairly computa-tional intensive,requiring many parameters,most of which were determined using curve fitting methods.Additionally,although d
ifferent mesh sizes were ud in the simulations,no investigation into the effect of the changes was prented.
The definite lack of numerical models capable of truly and efficiently capturing the crushing respon of compos-ite tubular structures with physically bad model parame-ters prompted an investigation into the effectiveness of CODAM,a physics-bad macromechanical constitutive model [24–26],at predicting the behaviour of the struc-tures.The constitutive model is modified and enhanced to capture the compressive respon of composites and implemented as a ur material model in the general pur-po,explicit non-linear finite element analysis code,LS-DYNA.The main objective of the current study is to simulate the damage propagation and SEA in braided com-posite tubes subjected to axial compression.A supplemen-tary goal is to study the nsitivity of the tube crushing analysis to variations in the model parameters.2.Experiments
The braided composite tubes were tested at the General Motors Corporation drop tower facility [20],and were
宝宝拉绿色大便made of one,two or four layers of a [0/±30]braid of Forta-fil #55680k carbon fibre tows in an Hetron 922resin (an epoxy vinyl ester),with an overall fibre volume fraction of 45%and nominal thickness
of 2.3,4.9and 8.1mm.The density of the material was reported to be 1.23,1.25,and 1.36g/cm 3,for the single ply,double ply,and four ply tubes,respectively.The average mechanical properties of the resin and fibre are listed in Table 1[27].The quality of the material was generally fair to poor,with warped sur-faces,resin-rich regions,poor tow distribution/alignment,and dry and poorly bonded tows,but reprents the antic-ipated quality for the in-rvice structure.It is worth noting that the same issues that lead to high material variability may promote desirable energy absorption capabilities through a multitude of damage mechanisms that defeat the impact,resulting in lower peak load levels and less cat-astrophic failures than tho attained in defect free tubes.The tubes were approximately 360mm in length and had nominal outside dimensions of 55mm ·55mm.The leading edges of all the tubes were chamfered at a 45°angle.In tubes tested with an additional external initiator,a metal plug was inrted into the bottom of the tube.The specimens were attached to a weight of 140kg and dropped from a height of 2.54m,resulting in an impact velocity of about 7.1m/s and impact energy of approximately 3.53kJ.The tubes split into very indistinct fronds with tearing concentrated at the corners.Transver tensile fracture was obrved between and within the tows.Away from the corners,the main failure mechanism was obrved to be delamination (in multi-ply lay-ups)followed by bending of the parated material either inwards or outwards.Force-displacement profiles were produced from each test.The main details of the tube crushing tests are s
ummarized in Table 2where it can be en that the SEA increas as the number of plies increas.Additionally,in the single ply tubes,the SEA is about 50%higher in tubes crushed
Table 1
Average mechanical properties of the Fortafil #566carbon fibre and the Hetron 922resin [27]Constituent Modulus (GPa)Shear modulus (GPa)Tensile strength (MPa)Compressive strength (MPa)Shear strength (MPa)Tensile elongation at break (%)Resin 3.2 1.388311436 3.8Fibre
231
–
3800
–
–
1.6
Table 2
Summary of the main results of the tube crushing tests performed by General Motors Corporation on the [0/±30]n braided tubes (Fortafil #55680k carbon fibre tows in a Hetron 922resin)Tube
configuration Peak force (kN)Crush
distance (mm)Energy
absorbed (J)SEA (J/g)1ply with plug 16.72402153151ply without plug 50.725633902238.72583720242ply without plug 74.175********.7822808284ply without plug
107.8
43
2724
30
2248 C.J.McGregor et al./Composites:Part A 38(2007)2247–2259
without the initiator plug,due primarily to more wide-spread damage development(e Sections5.1.1and5.1.2 for illustrations of the crush morphologies of tubes tested with and without the plug initiator).
3.Constitutive model
The continuum damage mechanics bad model for composite materials,COmposite DAMage(CODAM) [24–26]was further developed and ud to simulate damage propagation in the braided composite tubes.The model is a physically-bad macromechanical material model that reprents the constitutive behaviour of polymer composite laminates through both the elastic(pre-failure)and post-initial failure regimes.The mechanical conquences of
matrix cracking,fibre breakage,and delamination(main failure mechanisms in tension),and kinking and kink band broadening,in conjunction with matrix cracking and delamination(main failure mechanisms in compression), are reprented in the model.
The CODAM parameters required to define the com-plete in-plane orthotropic respon of the braided material were estimated using constituent properties,braid architec-ture and information recorded from coupon tests[27]. Given the large variation in the coupon specimens,it was decided to
define both upper and lower bound parameters (Table3).Bad on the failure mechanisms of the tube,ten-sion in the local y-direction(hoop direction)and compres-sion in the local x-direction(axial direction)were identified as the primary loading directions.When discussing the details of the constitutive model in the next few ctions, emphasis will be placed on the parameters that are relevant to the directions.See Ref.[28]for more detail.
3.1.Reprentative volume element
CODAM reprents damage growth in a reprentative volume element(RVE).The dimensions of the RVE have significant meaning.The height and width are equal to the characteristic height of damage(h c)in that particular direction.This characteristic height provides a measure of the inherent toughness(or brittleness)of the material(the lower the value of h c the more brittle the material).It is also related to the size of the fully developed fracture process he size of the damage zone ahead of a crack in a test configuration that leads to a stable crack growth). The size of the RVE(approximately10mm·10mm)as schematically reprented in Fig.1was estimated from the various damage heights obrved in braided specimens tested in tension and compression(Fig.2).The heights are listed in Table3as h c.The RVE thickness corresponds to the laminate thickness,allowing layer interactions in terms of damage initiation and evolution to be implici
tly taken into account while having the added benefit of making the model more computationally efficient.
3.2.Elastic material properties
The elastic moduli were bad on the upper and lower bounds measured in experimental coupon tests conducted at Lawrence Livermore National Laboratory using1-in.
(25.4mm)foil strain gauges[27].Values in the range of 33–50GPa and5.7–8GPa were measured for the local x-and y-direction,respectively.The major Poisson’s ratio ranged from1.06–1.25,with an average of1.15,and the
Table3请输入验证码
CODAM parameters for[0/±30]n braided laminate of Fortafil#55680k carbonfibre tows in a Hetron922resin(an epoxy vinyl ester) CODAM parameters Local x-direction Local y-direction
Tension Compression Tension Compression Initial elastic modulus,E0(GPa)33–5033–50 5.7–8 5.7–8
Matrix damage initiation strain,F T
mi ;F C电能计量
mi
0.006–0.0080.002–0.0030.006–0.0080.006–0.008
Matrix damage saturation strain,F T
ms ;F C
ms
0.021–0.0250.010–0.0110.021–0.0250.021–0.025
Fibre damage initiation strain,F T
fi ;F C
fi
0.006–0.0080.002–0.0030.011–0.0120.007–0.009
Fibre damage saturation strain,F T
fs ;F C
fs
0.021–0.0250.12–0.150.050–0.0600.120–0.150
Damage due to matrix damage saturation a,x ms0.550.550.550.55
Normalized modulus at matrix damage saturation a,E T
ms ;E C
ms
0.870.010.480.02
Plateau stress,r plat(MPa)–55–60–45–50
Damage height,h T
c ;h C
c
(mm)12–1511–1410–139–12
Fracture energy,G T
f ;G C
f
(kJ/m2)36–1017.3–2016–425–13
The parameters are independent of the number of plies within the laminate.
a Balance remaining is attributed to thefibres.
Tow Spacing (8-15 mm)
Braider
Axial Tows
(0˚Approximate
size of RVE
Schematic showing approximate size of
braided material.Also
tow spacing and alignment
.
C.J.McGregor et al./Composites:Part A38(2007)2247–22592249
minor Poisson’s ratio ranged from 0.198to 0.215,with an average of 0.206.The shear modulus was estimated using laminated plate theory (LPT),assuming the braid was com-pod of 3individual unidirectional laminae stacked at À30°,0°,and +30°.This resulted in an estimate of 13GPa for the shear modulus.The predicted elastic moduli values of 58and 8GPa using this approach correlated w
ell with the measured upper bound values [27],suggesting that decomposing the braid into 3individual laminae is a valid approximation.
3.3.Progressive damage properties
Damage development within the RVE is dependent on the strain state.In CODAM,the strain state is defined by an effective strain function (F )written in the following general form:
The constants,K ,L ,M ,S ,T ,and U are ud here to
define the relative contribution of each strain component to the driving force for damage growth.
For the ca of the tube crushing simulations,strain interactions were ignored,such that F x ¼j e x j F y ¼j e y j F z ¼j e z j
ð2Þ
Damage growth laws are defined at the constituent level (fibre and matrix),and subquently ud to define the overall damage growth law for the RVE.The overall dam-age state,as indicated by 3damage parameters (x x ,x y ,and x z ),can then be monitored throughout the loading history.To prevent lf-healing of the material,damage parameters
are non-decreasing functions that range from 0(indicating no damage)to 1(indicating complete damage).The fibre and matrix damage initiation and saturation values depend on the constituent properties,fibre architecture,manufac-turing and material quality,and direction of loading.
In the local x -direction,when under compression (pri-mary mode of loading in this direction),the initiation of damage in the matrix and fibre is linked to the initiation of kinking in the axial tows.Due to the significant waviness of the axial tows (caud by the braided architecture)and the poor interfacial bond,kinking is assumed to initiate fairly early.Matrix and fibre damage initiation values between 0.2%and 0.3%are thus assumed.Experimentally,nonlinearities in the stress–strain respon were noticed at approximately this level of strain [27].The damage satura-tion values are the most difficult model parameters to esti-mate and thus were lected such that peak stress and RVE specific energy absorption values were within reasonable
ranges.Matrix damage is assumed to saturate before fibre damage at effective strain values between 1.0%and 1.1%.To account for the ability of fibres to bend significantly (either in the kink band or in the buckled tows)before strains reach a level that caus failure,damage saturation values in the range of 12–15%strain are assumed.Given the difficulties in determining the parameters,it is note-worthy that nsitivity studies conducted in this work (e Section 5.3)showed t
hat the parameters do not signifi-cantly affect the overall simulation results.Fig.3a shows schematically the assumed damage growth law in the local x -direction of the RVE under applied compressive strains.In the local y -direction,when under tension (primary mode of loading in this direction),matrix damage initiation strains are assumed to range from 0.6%to 0.8%.Theoret-ically,one would expect matrix damage to initiate at
自学练字
or
Fig.2.Examples of compressive damage heights obrved in (a)the local y -direction of [0/±30]2carbon/vinyl ester panels [27]and (b)the local x -direction,(c)the local y -direction and (d)45°from the local x -direction of [0/±60]2carbon/vinyl ester panels.
F i ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffie x i 2þe y i 2þe z i 2Àe x i e y i Àe y i e z i Àe z i e x i þ
e xy i 2þe yz i 2þe zx
i
2
s i ¼x ;y ;and z
ð1Þ
2250 C.J.McGregor et al./Composites:Part A 38(2007)2247–2259
near the elongation at break of the resin,which was reported to be3.8%.Smaller values were chon to repre-nt the poor quality of the laminate.Studies conducted on similar braided composite material noted that at strain values between0.3%and0.4%,audible popping sounds were heard in most tensile tests,which corresponded to the initiation of cracks oriented parallel to the off-axis tows [
29].The formation of micro-cracks in the directions will lead to rotation of thefibres bridging the crack as they gradually align themlves with the loading direction[30]. Eventually,fibres will begin to fracture.The exact initia-tion of damage in thefibres is hard to predict without detailed experimental testing,and thus strain values rang-ing from1.1%to1.2%(approximately twice the matrix damage initiation strain)are assumed.Matrix damage sat-uration values were assumed to vary between2.1%and 2.5%,slightly smaller than values that were ud to model the tensile behaviour of a quasi-isotropic carbon/epoxy laminate in a previous study involving CODAM[26].Fibre damage was assumed to saturate at a higher level of RVE effective strains(between5%and6%)to account for the fibre bridging mechanism.In coupon specimens,a signifi-cant post-peak stress obrved in this direction was attrib-uted to the load borne by the tows that bridged the fracture zone[27].Fig.4a shows schematically the assumed damage growth law in the local y-direction of the RVE under applied tensile loading.
高中自我介绍3.4.Progressive modulus degradation
Damage growth is reprented by a progressive degrada-tion of the RVE normalized elastic moduli(ratio of
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C.J.McGregor et al./Composites:Part A38(2007)2247–22592251
