NUMERICAL SIMULATIONS OF METAL ONTO COMPOSITES CASTING

Transcription

1 NUMERICAL SIMULATIONS OF METAL ONTO COMPOSITES CASTING E. Marklund 1, D. Mattsson 2, M. Svanberg 2 and M. Wysoki 1* 1 Swerea SICOMP AB, Box 14, SE Mölndal, Sweden 2 Swerea SICOMP AB, Box 271, SE Piteå, Sweden *maiej.wysoki@swerea.se ABSTRACT The urrent aer resents a general three dimensional finite element model for modelling thermal degradation of olymer omosites due to thermal loading. In artiular, the model is intended for modelling the thermal degradation of olymer omosites due to overasting with light alloy metals. In this work, the model is imlemented and solved using the general urose FE-akage Abaqus 6.7. The aliability of the ode to more omlex geometries was demonstrated by analysing the asting roess of a metal ring onto a omosite axle, resulting in a shrinkage fit. To sueed in manufaturing of this tye of joint, a deliate balane between thermal loadings, metal shrinkage, omosite degradation and the overall ooling must be met. The roosed subroutine together with FE-models rovides the satial distribution of these field variables, allowing for subsequent otimization of the shrinkage fit. In addition to the results resented here roer boundary onditions and material roerties affeted by the remaining resin ontent and more aurate modelling inluding effets from gas transort and ooling have to be inluded in the FEanalysis. This will be the subjet for the ontinuation of this rojet. KEYWORDS: Metal asting, multi-materials, thermal degradation, FEM 1. INTRODUCTION The tehnial ommunity of today is making inreasing demands on weight redution mainly for energy savings, artiularly in the automotive industry, but also for better rodut ergonomis, for instane in the ower tools setor. A lightweight rodut is usually rodued using lightweight materials, for instane by integrating omosites omonents into lassial metal strutures. This aroah results in a omlex multi-material rodut, where a number of different materials are ombined in one omonent. One of the biggest hallenges in roduing omlex multi-material roduts is the need of joining the different materials together. Today, suh roduts are usually rodued by the means of mehanial or adhesive joints. Unfortunately, all of the urrent joining tehniques results in a number of diffiulties. For instane, the mehanial joints are often heavy while the adhesive joints are time-onsuming to rodue and therefore exensive. In the resent work, an alternative method of joining metal and omosites is onsidered. In this method a thin metal layer is ast diretly onto the omosite omonent. Provided that the exosure time at high temerature is short enough, the olymeri material will not deomose onsiderably while the metal solidifies [1]. The joint is then formed either by geometri features, loking the two arts together, or by shrinkage fit (assuming that the metal is ast around the omosite omonent). An examle of a metal onto omosite art is resented in Fig. 1 where a arbon fibre/eoxy (CF/EP) rod is joined to a ressure die asted aluminium omonent.

2 Fig. 1. Comosite rod imbedded in ressure die asted aluminium. The method of overasting has otential to eliminate a number of rodution stes and in onsequene redue manufaturing time and therefore ost. However, the roess itself is very omlex and thus diffiult to understand. Therefore, develoment of new roduts would require extensive and ostly testing. For that reason it is attrative to relae some of the tests by numerial simulations. During the asting of melted metal onto omosites, thermal degradation of the olymer will our. Given that the exosure time is short and temerature suffiiently low this degradation may be ket to a minimum. There exist several one-dimensional models that desribe the thermal roess of degrading olymers [2-6]. However, to aount for multidimensionality of a real rodut, these models have to be develoed further and solved using numerial methods. A reditive and validated model for the thermal resonse of omosite materials will hel to minimize the number of tests required for develoment of new roduts. Realisti thermal degradation modelling will rovide the designer with the aability to demonstrate innovative, new designs using the besoken overasting tehnology, whih will minimize the initial resoures and exensive testing. The aim of this work is, therefore, to utilize a general three-dimensional finite element model to simulate the overasting roess of metal onto omosites arts. While the finite element model ermits a general reresentation of the deomosition roess and different boundary onditions, the seifi onstitutive deomosition model resented here is based on a first-order Arrhenius equation with onstant thermal and transort roerties throughout the deomosition roess. The deomosition model has been imlemented as a subroutine to the ommerial software Abaqus 6.7 in the FEM-modelling roedure. The auray of the model has been evaluated by omaring the redited temerature rofiles with those obtained from the verified ode COM_FIRE version 4. [7]. Having said that, it should be emhasized that the results resented in this aer are art of an ongoing rojet, and as suh, they may be subjeted to hanges in a future analysis. Eseially when a more reise modelling onsidering temerature/degradation deendent seifi heat aaity and thermal ondutivity in onjuntion with the gas ooling effet will be erformed. Nevertheless, we firmly believe that the thermal modelling resented herein have heled to imrove the understanding of the overasting roess.

3 2. THEORETICAL BACKGROUND There are several mathematial models that have been develoed whih simulate the thermal resonse of materials undergoing deomosition and hemial reations and basially they are all similar in rinile. Usually they are based on heat ondution through the thikness of the struture inluding thermal effets of the organi material deomosition (the deomosition of organi substanes is an endothermi roess whih has a temorarily delaying effet of the transmission of heat through the struture). To aount for this temerature-deendent thermal deomosition an n-th order Arrhenius equation is normally utilized [5]. Following the work by Looyeh et al. [4] whih is based on the model originally roosed by Henderson et al. [2] the henomenon of energy onservation for heat transfer in a material undergoing thermal deomosition is given by the non-linear artial differential equation:x C T t 2 T ρ = k x t ρ 2 ( Q + h h ) where bold fae indiate a tensorial field variable. Q d is the heat of deomosition. h is the enthaly of the omosite and h g the generated gas enthaly. In addition to the assumtions made in their model, a further simlifying assumtion here is that the heat exhange between the deomosing omosite and the deomosition gas transorted through it is disregarded. For a fibre reinfored omosite with aligned long or ontinuous reinforement, the density ρ and seifi heat C are evaluated by the rule of mixtures as: C d ( φ) g (1) ρ = ρ fφ + ρm 1 (2) f m C ρ fφ + C ρm = ρ ( 1 φ) φ is fibre volume fration and indies f and m stands for fibre and matrix resetively. Instead of using rule of mixtures the transverse thermal ondutivity k of the omosite may be more aurately determined from the ondutivities of the fibre and matrix omonents using the well known Halin-Tsai model (3) where 1+ ξφη k = k m (4) 1 ηφ k f km 1 η = k k + ξ f m (5) ξ is a fitting arameter, but for fibres with irular ross-setion ξ = 1 an be assumed. The enthaly of the omosites and the generated gas enthaly have been assumed to be funtions of temerature only and are given by:

4 and: h h g = = T T T T C dt C g dt (6) (7) resetively. With the simlifying assumtions that the thermal and transort roerties in the omosite are onstant during the deomosition these two equations beome: and h h g ( T ) = C (8) T ( T ) g = C (9) Both density and its loss rate are alulated by the Arrhenius equation T ρ ρ ρ f = Aρ t ρ n e ( E / RT ) (1) Indies f and indiate final- and initial density resetively. A is the re-exonential fator, E is the ativation energy of deomosition, R is the gas onstant and T is temerature. Aliation of this model requires knowledge of the kineti arameters A, E and n of the resin whih generally are aquired through thermogravimetri analysis (TGA). The set of equations (1, 8-1) has been imlemented into a general FE-ode: Abaqus 6.7 as a user subroutine. 3. EXPERIMENTAL RESULTS In order to eluidate the degradation behaviour, and rovide data for the thermal degradation roess modelling, TGA exeriments were erformed in nitrogen atmoshere over temeratures ranging from 5 to 85 C using a Perkin-Elmer TGA-7 thermogravimetri analyzer. Runs were onduted at high heating rates of 1 C/min on a standard EXEL eoxy resin system. Then following the work by Looyeh et al. [4] the endothermi deomosition of the resin may be desribed by a single thermally ativated roess using an n-th order Arrhenius equation assuming no exansion of the omosite material: ρ m m m f = = Am t t m n e ( E / RT ) where m is the mass of the resin. There are several aroximate tehniques using different aroahes available for estimation of the kineti arameters A and E from TGA measurements, e.g. the Coats-Redfern method, Ozawa method and Horowitz-Metzger method just to mention a few. In this aer however, the diret non-linear regression method exlained by Slovak [8] have been utilized. This is a straightforward way of (11)

5 determining the kineti arameters and may be onveniently imlemented in any numerial omuting environment, suh as MATLAB for instane. The basi idea is first to relae the derivatives in Eq. (11) by finite differenes. This is reasonable if the time ste is hosen small enough and if we assume that the TGA urve is omosed of very small linear segments in whih the reation rate is onstant. Then Eq. (11) turns into the following reurrene relation: n mi 1 m f ( E / RTi 1 m = ) 1 i mi Am e ( ti ti 1) (12) m Slovak also exanded Eq. (12) for allowing to deal with several arallel roesses. Here it is assumed that a single thermally ativated roess will suffie to desribe the deomosition behaviour of the eoxy resin. Therefore, no exansion of exression (12) is neessary and the omlexity of the Abaqus subroutine rogramming will be ket lower. The arameters A and E are determined by diret testing and sreening of suitable values through a range of values with hosen auray. For eah ombination of A and E the residual sum of squares (RSS) is alulated omaring theoretially determined masses in individual oints to the orresonding exerimental oints. The A and E ombination giving the minimum RSS is then regarded as the best fit. Fig. 2 shows TGA urves at a onstant heating rate of 1 C/se for two eoxy seimens and their average fitted urve using the first order Arrhenius exression (n = 1). Mass remaining (%) EP1 EP2 Average fitted urve A = (1/se) E = (J/mole) Temerature ( C) Fig. 2. TGA-urves for two eoxy seimens and their average fitted urve. It is evident from Fig. 2 that a single thermally ativated roess using the first order Arrhenius equation does not give a erfet fit to exerimental data in this ase. The model annot ature the behaviour of the urves in the beginning and in the end of the deomosition. This also addresses an imortant issue when dealing with modelling of the thermal degradation of thermoset olymers. Beause there is no lear hysial meaning of the kineti arameters and the reation order of a thermal degradation roess for thermoset resins. The thermal degradation is attributed both to the gaseous roduts emission and to

6 the hemial sission of the network bonding without gas emission and olymer weight loss [9]. Several roesses an be oerating at the same time, eah having its own kineti arameters. Therefore the kineti arameters obtained here should be regarded as aarent values for these arallel roesses. 4. NUMERICAL RESULTS AND DISCUSSION 4.1. Abaqus subroutine rogramming and validation against COM_FIRE The ommerial FE-rogram Abaqus 6.7 have been used in onjuntion with user defined subroutines written in Fortran-ode in order to model the thermal degradation roblem. The subroutine USDFLD is used to alulate the remaining resin ontent (RRC) and redefine a field variable reresenting RRC whih sets the density of the omosite through the deendenies ommand in the Abaqus inut file. Here it is assumed that the density of the laminate follows a linear relationshi between the virgin material and the fully degraded material. The subroutine HETVAL is used to aount for heat of deomosition and enthaly hange due to degradation. The auray of the rogrammed subroutine has been evaluated by omaring the redited temerature rofile and RRC of a degrading material with values obtained from the verified ode COM_FIRE. The studied ase was a 1-D roblem using tyial roerties for a glass fibre vinyl-ester (GF/VE) laminate with V =.6. The geometry was.5 mm in height and 25 mm in thikness. 5 4-node linear f diffusive heat transfer elements (DC2D4) were used through the thikness. The model was first heked against alulations in Exel assuming adiabati and isothermal onditions, resetively. Then followed a omarison to COM_FIRE where the initial ondition was set to 2 C in the whole omosite. A onstant temerature of 7 C was alied at one end and all other boundaries were insulated. Results obtained using Abaqus seem to be in aordane to those obtained with COM_FIRE, as an be seen in Fig. 3. There is a slight temerature differene, but the RRC shows a very good math Temerature ( C) ABAQUS COM_FIRE RRC (-) ABAQUS COM_FIRE Time (se) Time (se) Fig. 3. Temerature variation and RRC for the GF/VE laminate 5 mm from the heated end. The auray of the model has also been verified against COM_FIRE using two different models in 1-D ase (not shown here): with and without gas transort and ooling. The omarison revealed a relatively small differene between the two ases.

7 4.2. FE-analysis of a CF/EP rod in ast aluminium After verifiation of the subroutine in 1-D ase a CF/EP omosite rod was modelled using axisymmetri (DCAX4) elements. The material roerties used in the modelling roedure are shown in Table 1. The values for density, seifi heat and transverse thermal ondutivity for the laminate were alulated using Eq. (2-4). The heat of deomosition Q d whih is also needed in the modelling is assumed to be 234 kj/kg based on a value resented in literature [2]. However, it is ointed out that heat transmission through the omosite is rather sensitive to this (in our ase) unknown assumed arameter. Table 1. Assumed material roerties for the CF/EP laminate Material ρ [kg/m 3 ] k [W/mK] C [J/kgK] C g [J/kgK] RRC f [-] Carbon fibre Eoxy resin Laminate In the following simulation a number of simlifiations have been made, i.e. seifi heat is assumed to be onstant throughout the analysis whereas it is atually known to vary with both temerature and amount of degraded material. Thermal ondutivity is assumed to be unaffeted by temerature inrease and level of degradation. In reality a orous har layer will form on the omosite surfae and at as an insulator. Here the arbon fibres are also assumed to be inert, whereas being an organi material, they too are rone to degrade at high temeratures. Furthermore, the omosite is modelled as an isotroi material having only one value for thermal ondutivity. A more thorough analysis should also inlude the anisotroi nature of the material and thus allowing for at least two values for thermal ondutivities (transversely isotroi). In the ontinuation of this ongoing rojet these issues will be addressed in a more reise modelling roedure. The omosite rod surrounded by ast aluminium and the alied boundary onditions on the axisymmetri FE-modelled art is illustrated by Fig. 4. In the analysis 4 elements in thikness (radial) diretion was used. The temerature variation on the omosite boundary has been modelled earlier [1]. Here the nodal temerature on the surfae of the rod was onstrained to follow the temerature rofile of the aluminium shown in Fig. 4. This imlies very effiient heat transfer between the aluminium and the omosite, whih robably is more effiient than in reality. In order to later on imrove the model the heat transfer between the aluminium and omosite will be modelled using a onvetion boundary ondition with a tailored onvetion film oeffiient. Fig. 4 shows that the temerature rofile on the omosite boundary quikly delines from 76 C down to about 11 C in no more than five seonds. Obviously this behaviour will be related to the thikness of the aluminium overasting omonent and the steel asting mould.

8 Al Temerature ( C) Temerature variation on the omosite boundary (T b ) Time (s) T b Axisym T b 8 mm Insulating Fig. 4. Illustration showing the omosite rod surrounded by ast aluminium and the FE-modelled art with boundary onditions. The results of the simulation an be seen in Fig Fig. 5 and 6 shows temerature and RRC of the uer right orner of the axisymmetri modelled art resetively. In these figures the horizontal view is over the whole radius (4 mm). a) b) Fig. 5. (a) Temerature distribution in the omosite after.5 se and (b) after 1 se. Fig. 6. RRC distribution in the omosite after 3 se.

9 It is evident from Fig. 6 that due to the relatively short exosure time only a small ortion of the omosite will be thermally degraded. The most ritial art will be the orner and therefore, Fig. 7 shows RRC and temerature distribution along a 1 mm ath drawn diagonally down from the uer right orner. It is onluded that aroximately.8 mm along this ath the material integrity will be totally unaffeted by the alied thermal load. Further it an be seen that the temerature wave is travelling very fast through the material. After only.5 seonds at 1 mm along the ath the temerature is about 345 C. However, this is not totally unexeted due to the rather rude assumtions regarding the thermal roerties of the omosite/al interfae as mentioned earlier. RRC (-) Temerature ( C) se.5 se 1 se a) b) Distane from orner (mm) Distane from orner (mm) Fig. 7. (a) Final RRC (after 3 se) and (b) temerature distribution along the diagonal ath for three different time instants. 5. CONCLUSIONS Modelling the thermal degradation of omosites used for metal overasting has two major benefits. First, it seeds u the design roess and, thereby, redues the ost of using this kind of manufaturing roess. Seond, it imroves the knowledge of how these materials behave when exosed to elevated temeratures during overasting. The objetive of this work was to develo and investigate the aliability of the finite element method to analyse the thermal behaviour of olymer omosite materials when exosed to metal melt. Basi onets of the henomena ourring in the material exosed to the melted metal were desribed. The aliability of user defined subroutines develoed during this study in onjuntion with the ommerial finite element rogram Abaqus 6.7 was demonstrated for thermal resonse of an axisymmetri omosite omonent overasted with aluminium. The model was verified against Exel alulations and the validated ode COM_FIRE. The redited temeratures and degree of degradation were found to agree well with the results obtained using COM_FIRE. The auray of the model was also verified against COM_FIRE using two different models in 1-D ase: with and without gas transort and ooling. The omarison reveals a relatively small differene between the two ases. We therefore onlude that the roosed FE-model is able to simulate metal overasting for a large range of tyial omosites omonents. As a result, this will allow for reditions of the shrinkage fit for these omonents and in onsequene their mehanial erformane. However, it is emhasized that the FE-model have to be validated against asting exeriments and fators imortant for the overasting roess,

10 suh as roer boundary onditions between the aluminium and the omosite, and material roerties affeted by the remaining resin ontent have to be inluded in the FEmodel. The key fators are those that determine heat transmission through the roteting har layer, namely the endothermi deomosition effet, mentioned earlier, assisted by the low thermal ondutivity of the fibrous reinforement after the resin has been removed. Finally, by using the finite element method, a wide range of geometries of omosite omonents may onveniently be studied with little hange to the subroutine omuter ode. Work on a more aurate three-dimensional model inluding effets from gas transort and ooling is ongoing. ACKNOWLEDGEMENTS The work resented in this aer has been funded in art by VINNOVA in the rojet CASTCOMP (rojet no. P ) under ontrat number REFERENCES 1. Qviker A., Jansson N., Metal over Comosite Casting, Master Thesis, Deartment of Aeronautial and Vehile Engineering, Division of Lightweight Strutures, Royal Institute of Tehnology KTH, Stokholm, Sweden Henderson J.B., Wiebelt J.A., Tant M.R., A model for the thermal resonse of olymer omosite materials with exerimental verifiation, Journal of Comosite Materials, 1985;19(6): Henderson J.B., Wieek T.E., A mathematial model to redit the thermal resonse of deomosing, exanding olymer omosites, Journal of Comosite Materials, 1987;21(4): Looyeh M.R.E., Bettess P., and Gibson A.G., A one-dimensional finite element simulation for the fire-erformane of GRP anels for offshore strutures, International Journal of Numerial Methods for Heat & Fluid Flow, 1997;7(6): Dodds N., Gibson A.G., Dewhurst D., Davies J.M., Fire behaviour of omosite laminates, Comosites Part A: Alied Siene and Manufaturing, 2;31(7): Gibson A.G., Wright P.N.H., Wu Y.-S., Mouritz A.P., Mathys Z., Gardiner C.P., The integrity of olymer omosites during and after fire, Journal of Comosite Materials, 24;38(15): Wu Y.-S., User s guide to the rogram COM_FIRE: v4.1, CCME Shool of Mehanial and System Engineering, University of Newastle, Newastle uon Tyne, Slovak V., Determination of kineti arameters by diret non-linear regression from TG urves, Thermohimia Ata, 21;372: Regnier N., Guibe C., Methodology for multistage degradation of olyimide olymer, Polymer Degradation and Stability, 1997;55(2):