ANISOTROPIC DAMPING BEHAIOR OF REINFORCED PLASTIC PARTS FOR NH SIMULATIONS Sylvain CALMELS, Sylvain Mathieu, Maxime LESUEUR e-xstream engineering Abstract Reinfrced plastic materials shw a very interesting characteristic which helps t imprve the acustic cmfrt f car passengers. Their damping behavir is much better than metals and this specific perfrmance became a very imprtant criteria t evaluate the glbal quality f vehicles. Predicting the acustic level inside a passenger cell and als utside f the car is a very difficult challenge as it depends n many parameters. The first step is therefre t be able t efficiently capture the nise generated by a single cmpnent. This is already nt a simple task when the part is made f reinfrced plastics. Predicting the acustic respnse f a cmpnent requires accurate simulatin f its vibratinal behavir, meaning its stiffness and damping. When the part is made f reinfrced plastics, the design engineer has t deal with a material fully dependent n the lcal fiber rganizatin. In such a part, the micrstructure usually shws a high degree f hetergeneity and anistrpy in terms f stiffness and vibratinal respnse. Only a material mdel based n the matrix and fiber prperties and taking int accunt the fiber rientatin distributin, thrughut the part, can accurately predict the stiffness respnse, and eventually the vibratinal respnse, f said cmpnent. This als requires a material mdel able t capture its damping behavir, itself anistrpic and dependent n the lcal definitin f the micrstructure. This paper will address the current research and develpments f e-xstream engineering regarding the predictin f reinfrced plastic material behavir applied fr frequency dmain analyses. We will demnstrate hw simulatin can be imprved, fr safety design simulatins in particular, in the autmtive industry, helping t reduce design delay, cst and weight f structures. Intrductin Over the years, the study f nise and vibratin prpagatin became cmmn practice in the autmtive industry fr assessing the acustic cmfrt f passengers. While this practice has been used fr a lng time n assemblies r parts made f metal allys, the emergence f the fiber-reinfrced plastics (FRPs) in this industry is bringing new challenges t the NH field. Indeed, predicting the acustic respnse f a given cmpnent requires accurately simulating its vibratinal behavir, i.e. its stiffness and damping. Fr parts made f FRPs, the challenge fr the design engineer is linked t dealing with a material fully dependent n a lcal fiber architecture, while shwing a high degree f hetergeneity and anistrpy, initially, in terms f stiffness. It is cmmn practice in the industry t try t circumvent such difficulties by emplying the s-called equivalent istrpic and hmgeneus material mdels inside a Finite Element Analysis (FEA). Hwever, these simplified material mdels shw n frequency dependence f Page 1
the stiffness and damping prperties and thus will fail t predict certain lcalized behavirs present in FRPs that might generate harsh vibratins, r maybe even fracture, if taken frm a vibratinal fatigue pint f view. The previus sectin illustrates ne thing: the imprtance f material mdeling and calibratin. Indeed, as referred t in sectin 1, a thrugh understanding f the viscus, i.e. strain-rate dependent, behavir f the different cnstituents is critical in building an accurate material mdel. This als implies testing the material and thus, anther questin arises: What is/are the best mechanical testing prcedure(s)? As presented in sectin 1, ur experimental data cmes frm a Dynamic Mechanical Analysis (DMA) testing prcedure. In this particular experiment, a specimen f ur studied material (PA66/GF35) was subjected t this dynamic testing in rder t extract data in terms f bth stiffness and damping. Hwever, the DMA specimen has t be f very small dimensins. In the present study they were 4x5x40mm, and thus have a high prbability f nt being representative f the materials hetergeneus micrstructure, e.g. specimens cut in the center r n the edges f an injected FRP plate. This shws us, fr instance, the imprtance f adding a quasi-static tensile test t re-calibrate the stiffness prperties given by the DMA testing prcedure. All f the previus cnsideratins are ultimately being applied t an autmtive beam subjected t a dynamic three-pint bend test in six different scenaris (see Table 1) that aim at exhibiting the influence f different assumptins n the NH analysis f a part made f FRP. ANISOTROPIC DAMPING BEHAIOR OF REINFORCED PLASTIC PARTS FOR NH SIMULATIONS Chpped fiber reinfrced plastic materials exhibit better behavir than metals regarding the perfrmances targeted fr NH needs in the autmtive industry. Carmakers d nt chse these multi-phases materials slely fr light-weighting purpses when it cmes t designing parts fr this particular type f perfrmance. There are already vehicles available which utilize this characteristic in under the hd areas, like engine munts r engine cvers, where the high damping prvided by reinfrced plastics helps reduce the nise in the passenger cell. Hwever, accurately predicting the behavir f such parts and its effect n the nise level heard by passengers still remains a huge challenge due t the fact that, as well as fr stiffness and failure, the lcal damping behavir and its dependency n the frequency are clsely linked t the lcal rientatin f fibers induced by the manufacturing prcess. This paper addresses e-xstream Engineering s secnd step in building a methd and a numerical wrkflw dedicated t the accurate predictin f shrt fiber reinfrced plastic behavir frm the materiel engineering level t the structural level. The presentatin is decmpsed int fur main sectins: 1. Material engineering Calibratin f a multi-scale viscelastic material mdels frm DMA test data Observatins n stiffness anistrpy and frequency dependency Observatins n damping anistrpy and frequency dependency 2. Structural engineering: applicatin n the frequency respnse f a rf frnt beam. Page 2
Initial mdel : hmgeneus istrpic stiffness hmgeneus istrpic frequency dependent damping 1 st step : effect f a lcal anistrpic stiffness mdel 2 nd step : effect f a lcal anistrpic stiffness and damping mdel K & D calculated at 1Hz K & D calculated at 300Hz 3 rd step : effect f a lcal anistrpic and frequency dependent stiffness and damping mdel 4 th step : effect f the manufacturing prcess 3. Summary Material Engineering: characterizatin f the anistrpic and frequency dependent damping behavir f a SFRP The cnstitutive mdeling f the frequency respnse f shrt fiber reinfrced plymer cmpsites is achieved by mean-field hmgenizatin, which derives cmpsite prperties thrugh the frequency dependency f its cnstituents. Material mdelling is dne using tensile tests and dynamic mechanical analysis (DMA) experimental data retrieved frm A. Launay [1]. These tests were cnducted n a shrt glass fiber reinfrced plyamide. The material f study is a plyamide 66 cntaining 35 wt% f shrt glass fibers, prvided by DuPnt de Nemurs (DuPnt TM Zytel 70G35 HSLX). This material is currently emplyed fr autmtive applicatins. ISO 527 tensile tests were carried ut n this material at varius strain rates. A DMA was perfrmed t study the cmpsites viscelastic respnse at lw strains, with a sweep frm 1 t 500Hz. Tw relative humidity (RH) states were tested. In this paper, nly the RH50 material is cnsidered due t it being mre dissipative, and thus mre sensitive t frequency excitatin. Mean-field hmgenizatin As cmpsite prperties depend n material micrstructure, including fiber amunt and rientatin, they are adequately mdeled frm micrmechanics. In particular, mean-field hmgenizatin cmbines the prperties f the underlying cnstituents f a multi-phase material, allwing riginal hetergeneus material t be represented by an equivalent hmgeneus ne. Implemented in the Digimat sftware [2], this technlgy has prven effective fr a brad range f materials. Fr the studied SFRP, we represent the matrix material as istrpic viscelastic, the fiber material as istrpic elastic and accunt fr the lcal fiber rientatin. Mean-field hmgenizatin prvides access t per-phase prperties, thus enabling a finer interpretatin f simulatin results as it distinguishes the matrix frm the fiber behavir. Mean-field hmgenizatin als prvides an avenue t investigate the rigin f experimental variability f cmpsite prperties by revealing their sensitivity t micrmechanical parameters. Page 3
Experimental DMA data In DMA, a sinusidal displacement signal is impsed, at an angular frequency ω. The testing device recrds the amplitude as well as the phase lag f the lad. This enables, in the frame f the viscelastic thery (see ISO 6721-1), t evaluate the strage mdulus E!, the lss mdulus E!!, and the lss factr tanδ. The strage mdulus represents the elastic part and measures the stred energy while the lss mdulus represents the viscus part and measures the dissipated energy. As fr the lss factr, it is the rati between dissipated and stred energies. The DMA was cnducted at rm temperature at frequencies ranging frm 1 t 500 Hz [1]. The samples, f dimensin 4x5x40mm 3, were cut frm the hmgeneus area f an injectin mlded ISO527 tensile specimen. Experimental data recrded is pltted in figure 1. An expected increase in stiffness with the excitatin frequency rise is seen n the measured data. Hwever, n clear dissipative peak appears in the frequency range, making the identificatin f a characteristic time difficult. Figure 1: DMA in tensile mde. Frequency sweep at rm temperature n RH50 material Frequency-dependent material mdeling The studied material is cmpsed f tw phases: the shrt glass fiber inclusins and the plyamide 66 matrix. The shrt glass fiber material is mdeled by an istrpic elastic material. A linear istrpic viscelastic mdel is defined using a 4 term Prny series fr the plyamide 66 matrix. A linear viscelastic cnstitutive mdel is defined as: σ t = G t : ε 0 + G t τ : ε!" τ dτ With ε 0 = lim!! ε t and G t = 2G! t I!"# + K! t 1 1 The integral equatin represents the memry effect. This means that the stress σ t at time > 0 depends n all the strain histry up t that time, i.e., σ t depends n ε s, s t. G t are the relaxatin mduli which, in the istrpic case, are represented by time-dependent shear and bulk mduli G! t and K! t, respectively. That leads us t intrduce the istrpic viscelasticity as a Prny series f the shear mdulus G t and f the bulk mdulus K t, which are defined in the fllwing way: Page 4
G! t = G! 1 w! 1 e!!!!!!! Where G! is defined as the initial shear mdulus (at t = 0) and τ! s and w! s are the characteristic times and assciated weights f the Prny series. Thse are the parameters needed t define the deviatric part f the cnstitutive behavir. The same equatins can be derived with the bulk mdulus K! t instead f the shear mdulus G! t t represent the vlumetric behavir. With the bjective f a calibratin frm DMA data, the expressin f the shear and bulk mduli can be derived as a functin f angular frequency instead f time. A cmplex dynamic mdulus is then btained: G! ω = G!!! ω + ig!!! ω w!! G! ω = G! G! 1 + ω!! τ! G!! w! ωτ!! ω = G! 1 + ω!! τ!!!! Where prime and duble prime symbls define, respectively, the strage and lss mduli. The same equatins can be written with the bulk mdulus. Frm a micrstructural pint f view, the shrt glass fibers are treated as inclusins distributed inside a matrix. They have an aspect rati f 30 and are cnsidered t be mainly riented alng the lading directin. An rientatin tensr a!" is defined t capture the rientatin distributin f the shrt glass fibers [3]. A strng alignment f the fibers alng the lading directin is chsen:!!!!! a = 0.85 0 0 0 0.13 0 0 0 0.02 A reverse engineering is then run t fit the frequency dependent material behavir based n the DMA data. The nly phase being reverse engineered is the viscelastic matrix: the instantaneus bulk and shear mduli, as well as the relaxatin times and weight f each f the Prny series. Because the frequency dependence f the Yung s mdulus is ur nly available input, a simplificatin was in rder. This simplificatin assumes that the bulk and shear relaxatin times and weights are identical. This leads t assuming a cnstant Pissn s rati ver all frequencies. Hwever, it is wrth nting that, while ften assumed cnstant in harmnic calculatins, the Pissn s rati cmmnly decreases with increasing frequency. The resulting mdel, as well as experimental data, is pltted in figure 2. Page 5
Figure 2: DMA in tensile mde. Frequency sweep at rm temperature n RH50 material and calibrated material mdel. Once identified, the resulting material and micrstructure can be used t predict the frequency respnse in ther lading directins r shrt fiber distributins. Respnses in the transverse directin and with a perfectly randm fiber rientatin are detailed in figure 3. (a) Figure 3: Strage mdulus and lss factr predictins as a functin f frequency: in the lngitudinal (L) and transverse (T) directins (a) and with randm fiber rientatin (b) (b) Experimental tensile data crrelatin It is knwn that DMA tests prvide meaningful infrmatin n a physical level, but nn harmnic calculatins based n the calibrated mdel shuld nt be relied n a priri. The weak lcal strains (0.1%) and the limited experimental frequency range may nt be representative f the true lading cnditins r f the underlying physics f the plymer under study. Cmparisn with tensile test data wuld cnfirm the cnsistency f the material mdel. Static tensin tests were perfrmed with stress lading rates spanning fur rders f magnitude, frm 2.5 t 2500 MPa/s [2]. Influence f the stress rate n the stiffness is visible frm the very beginning f the lading n these tensile specimens. The evlutin f the surface temperature during lading crrbrates the influence f the stress rate n the dissipative effects frm the very beginning f the lading. This clearly highlights shrt-term viscelastic Page 6
effects with a large characteristic scale time f abut 1s. This rder f relaxatin time cannt be calibrated frm the DMA cnducted, as frequencies belw 1 Hz wuld be necessary. As a result, the previusly calibrated data cannt fully represent the time respnse f the material. Hwever, in rder t validate the identified viscelastic mdel, the lwest stress rate tensile test can be used as a cmparisn. In this case, where the lading rate is lw, ne can expect the shrt term viscelastic effects t be verridden s that they d nt impact and stiffen the initial behavir. The cmparisn between the experimental tensile tests perfrmed at 2.5 MPa/s and the numerical mdel predictin is shwn in figure 4. The first percent f strain lading shws a gd crrelatin between the DMA calibrated mdel and the lw stress rate tensile test, validating the cnsistency f the reverse engineered behavir. Figure 4: Experimental/numerical cmparisn f initial stiffness at 2.5MPa/s Structural engineering: applicatin n the frequency respnse f a rf frnt beam The previus sectin has driven the prcess f creatin f a multi-scale visc-elastic material mdel fr a PA66GF35 grade capable f capturing the macrscpic behaviral dependency t lcal fiber rientatin and frequency. This mdel has been validated thrugh cmparisn with experimental data and is nw applicable at the structural level. In this 2nd sectin, we will bserve the effect f each level f accuracy available in this mdel n a frequency respnse analysis perfrmed n an injected rf frnt beam. The fllwing test matrix will be cvered: Page 7
Gates Psitining Hmgeneus istrpic stiffness Hmgeneus istrpic damping Fiber rientatin dependent stiffness Fiber rientatin dependent damping Frequency dependent stiffness Frequency dependent damping Reference Mdel 1 Mdel 2 Mdel 3 Mdel 4 Mdel 5 N 1 N 1 N 1 N 1 N 2 (calculated at 1Hz) (calculated at 1Hz) Table 1: Test matrix (calculated at 300Hz) (calculated at 300Hz) Reference mdel and ladcase descriptin The chsen cmpnent is a rf frnt beam (see figure 5). This cmpnent has an imprtant influence n the NH behavir f the passenger cell due t its rle in cnstraining the rf, an imprtant panel whse vibratins can cause undesired nise in the vehicle, as well as hlding several accessries, like the sunshields. This cmpnent is, currently, mstly made with Rf Frnt Beam in shell elements Figure 5: Chsen cmpnent fr the structural applicatin is a rf frnt beam meshed in shell elements Page 8
steel in, hwever it culd be dne using reinfrced plastic materials. That is the scpe f the exercise prpsed here, regarding its vibratinal behavir. The reference mdel has been defined using an istrpic and hmgeneus stiffness and damping mdel. The istrpic E-mdulus has been defined using the cmmnly used rati f 0.6, applied n the measured axial E-mdulus f the cmpsite, here, 7705 MPa. On the damping side, a hmgeneus value f 0.03 has been applied n the verall mdel. Table 2 belw summarizes this reference mdel apprach: Mdel E-mdulus Pissn s rati Damping Density Reference 4623MPa 0.35 0.03 1.4125e-09T/mm3 Table 2: Reference mdeling apprach The ladcase applied is a 3 pint bending frequency respnse case as shwn in figure 6 belw: Figure 6: Ladcase descriptin fr a driving pint frequency respnse case 0-300Hz Mdel 1 5: Injectin simulatins t predict fiber rientatin distributins Mdels 1 thrugh 5 will be defined using a multi-scale visc-elastic material mdel capable f capturing the macrscpic behaviral dependency t fiber rientatin, bth fr stiffness and damping. This infers that the FE mdel must cntain the fiber rientatin distributin thrughut the part, thus allwing us t take int accunt the material s hetergeneity, due t the manufacturing prcess, in the FEA s predictin. Tw injectin simulatins have been perfrmed in rder t get tw different fiber rientatin fields, as shwn in figure 7. This will allw us t quantify the effect f using different parameters fr the injectin prcess n the cmpnents behavir. We can bserve that sme lcal differences in the fiber rientatin rganizatin appear, especially arund the tw hles clse t the beam s extremities. Fiber rientatins in the middle f the beam lk similar acrss the tw prcesses. Mdel 1 4 will use fiber rientatin field N 1 Page 9
Mdel 5 will use fiber rientatin field N 2. Field N 1 Field N 2 Figure 7: 2 different fiber rientatin distributins frm 2 different set f gate psitining in Injectin Prcess Results n Mdel 1: Effect f a lcal anistrpic stiffness mdel The material mdel used in mdel 1 is an elastic material mdel. This mdel is capable f capturing lcal stiffness dependency t fiber rientatin and takes it int accunt in a FEA. This has been used in cmbinatin with the fiber rientatin Field 1 shwn previusly. Figure 8 shws the range f behavirs which will be used lcally in the FEA, depending n the lcal fiber rientatin infrmatin available in each finite element. isible behavirs will be applied n each material directin fr each fiber rientatin tensr cefficient in rder t reprduce the lcal anistrpy due t lcal fiber rientatins. Page 10
Figure 8: Range f stiffness behavirs captured lcally by the multi-scale elastic mdel. Damping mdeling is the same as the reference mdel: - istrpic hmgeneus mdal damping = 0.03 Figure 9 shws the cmparisn between the predictin f dynamic respnses btained with the reference mdel and mdel 1 (Lcal anis K). The usage f this multi-scale stiffness mdel directly influences the predictin f excited frequencies, in this case, with gaps between 4% and 7%. As the damping mdeling apprach is the same, there is a very negligible impact n the acceleratin peak predictins. Page 11
Shifts in frequencies 4% t 7% Negligible effect n maximum peaks Figure 9: The usage f a fiber rientatin dependent stiffness shifts the predictin f excited frequencies cmpared t an istrpic and hmgeneus stiffness mdel. Results n Mdel 2: Effect f a lcal K & D calculated at 1Hz Mdel 2 has been defined using the multi-scale visc-elastic material mdel calibrated in the material engineering sectin, in cmbinatin with fiber rientatin field N 1. Hence, in this case, bth the stiffness and the damping behavir take int accunt the anistrpic behavir f the material as a functin f lcal fiber rientatins. N frequency dependency is mdeled here. Anistrpic stiffness and damping has been calculated at 1Hz and used fr the cmplete frequency range 0-300Hz in the FEA. Figure 10 shws a cmparisn between the reference result and the mdel 2 (Lcal K&D 1Hz) result in terms f dynamic stiffness bserved at the excitatin pint. The usage f lcal anistrpic stiffness calculated at 1Hz here exhibits a higher influence n the excited frequency predictins. The gap with the reference has increased frm 7% t 15%. Mrever, the mdel 2 apprach als has an influence n the mdal density f the structure and predicts nly ne peak fr the first excited frequency instead f tw. The lcal anistrpic damping mdel here, with data calculated at 1Hz, shws nnnegligible differences cmpared t the reference fr the predictin f the 1 st maximum acceleratin peak. The gap here is 28%, which culd highly influence the final design f such a part. Page 12
1 peak instead f 2 Higher shifts in frequencies 15% Effect n maximum peaks with data calculated at 1Hz: 28% Figure 10: The usage f a fiber rientatin dependent damping shws nn negligible differences with the reference when cnsidering the predictin f maximum acceleratin peaks. Results n Mdel 3: Effect f lcal K & D calculated at 300Hz The material mdel used fr mdel 3 is the same as mdel 2, but the stiffness and damping data have been calculated at 300Hz instead f 1Hz. The fiber rientatin distributin cnsidered is still field 1. Figure 11 shws the cmparisn f results between the reference and mdel 3 (Lcal K&D 300Hz). The predictin f the structure s dynamic stiffness is nw cmpletely different, depending n the mdeling apprach. The difference in terms f frequency fr the 2 nd peak is 32%, and in terms f the acceleratin peak, the gap reaches 71%. Mrever, the high frequency behavir is cmpletely different with a very distinctive level f acceleratin, due t the frequency dependency f bth stiffness and damping. The difference likely seems due t the frequency dependency f stiffness but shuld be cnfirmed by further investigatin. Page 13
Higher shifts in frequencies 33% High effect n maximum peaks with data calculated at 1Hz: 71% ery different respnse at high frequencies Figure 11: the frequency dependence f bth stiffness and damping highly influence the predictin f FEA. Results n Mdel 4: Effect f lcal K & D including frequency dependency The material mdel used fr mdel 4 is the same as mdel 2 and 3 but here stiffness and damping exhibit a frequency dependency, in additin t their fiber rientatin dependency. The fiber rientatin distributin cnsidered is still field 1. Figure 12 shws the cmparisn f results between the reference, mdel 3 (Lcal K&D 300Hz) and mdel 4 (Lcal K&D freq dep). At first, ne interesting bservatin which pps up is that mdel 3 and 4 shw very clse results. During the material calibratin wrk, it has been bserved n measured data that the frequency dependence f bth stiffness and damping decrease quickly starting frm 100Hz. This means stiffness and damping are varying slwly while the frequency is increasing t 300Hz. Hence wrking with fixed data at 300Hz r with a full frequency dependent mdel will have a lw influence in this case. Glbally, the cmparisn with the reference is similar t what has been bserved previusly n mdel 3 (Lcal K&D 300Hz). Gaps between mdel 3 and 4 are nt negligible, but the reader culd cnsider it lw, cmpared t the level f cmplexity required t accunt fr a full frequency dependent mdel. The pint here is that it s difficult t knw in advance which frequencies will be excited. In this case, the 1 st peak appears at frequencies clse t this saturatin state. If this happened at 30Hz r 50Hz, the influence f using, r nt using, a full frequency dependent mdel wuld be higher. Hence, accunting fr this aspect f the mdel behavir can be seen as a way t be mre rbust frm the very first calculatin n the predictin s level f quality. Page 14
Lw effect f full frequency dependency cmpared t mdel data calculated at 300Hz Figure 12: In this case, accunting fr a full frequency dependence des nt change significantly the predictin. Results n Mdel 5: Effect f the manufacturing prcess The aim f this last sensitivity study is t bserve the influence that the manufacturing prcess parameters culd have n the final perfrmance f a part. We have applied the same material mdel as mdel 4, accunting fr the full frequency and fiber rientatin dependency n bth stiffness and damping, but with a different fiber rientatin field crrespnding t different gate psitining chices. Fr this mdel, the fiber rientatin distributin cnsidered is field 2. Figure 13 shws the cmparisn f results between mdel 4 (Lcal K&D freq dep) and mdel 5 (Lcal K&D freq dep 2). The glbal shape f the behavir remains the same between the structure with field 1 r field 2, but sme slight differences can be bserved n the predictin f the excited frequencies and maximum acceleratin peaks with gaps, respectively, f 6% and 5%. This is f curse lw cmpared t the previus gaps bserved between the mdels, but here, the tpic is slightly different as we are nt trying t cnsider which mechanical parameters shuld be captured crrectly by the material mdel, but hw much the manufacturing prcess culd influence the final design f a part. Hence, in this case, 5% difference in the mechanical behavir f a structure can drive us t ptimize the design and ptentially save mass n it. Page 15
Shift in frequency 6% Effect n maximum peaks: 5% Figure 13: The manufacturing prcess influences the final part s behavir and becme a parameter t be cnsidered during design iteratins. Summary In cnclusin, this paper has demnstrated a prcedure t calibrate a viscelastic material mdel capable f capturing bth fiber rientatin and frequency dependency f stiffness and damping in a FEA. Once the material mdel has been defined, a sensitivity study was perfrmed, at a structural level, n a frequency respnse analysis f a beam which allwed us t identify the first rder material specificities t capture in FEA in rder t be accurate. Material engineering level DMA test data are required t characterize the material s vibratinal behavir in the desired range f frequencies, accrding t the targeted final applicatin Quasi static tensile data are required t calibrate the material s stiffness The micrstructure in tested cupns is necessary t accurately calibrate a fiber rientatin dependent material mdel Final mdels exhibit anistrpic stiffness and damping behavir as a functin f fiber rientatin and frequency Structural engineering level Capture, fr NH needs, the anistrpic and hetergeneus stiffness and damping behavir f reinfrced plastic materials driven by the fiber rientatin field thrughut a part induced by the manufacturing prcess Frequency dependency f stiffness and damping have a very imprtant influence n the FEA predictin. A full frequency dependent mdel is recmmended as it s impssible t knw, in advance, the frequencies where maximum acceleratin peaks will appear. Page 16
This paper has addressed the mst advanced material mdeling apprach available tday fr NH applicatins f reinfrced plastic materials and has demnstrated the interest t use a multi-scale visc-elastic material mdel. The influence f such a mdel n the predictins f FEA culd help NH and Fatigue CAE teams t better predict the vibratinal behavirs f parts t be designed and drive t save weight in better ptimized final designs. Bibligraphy 1. A. Launay et Al., " Cyclic behavir f shrt glass fiber reinfrced plyamide fr fatigue life predictin f autmtive cmpnents", Prcedia Eng, 2:901 10. 2. e-xstream engineering, "Digimat Users' Manual Release 2016.1", 2016. 3. Advani, S., Tucker III, C., 1987. The Use f Tensrs t Describe and Predict Fiber Orientatin in Shrt Fiber Cmpsites. J. Rhel., 31:751 Page 17