Composite model 131: Ply types 1 and 7 calibration

Transcription

1 Composte model 3: Ply types and 7 calbraton Model calbraton Composte Global Ply model 3 for elastc, damage and falre PAM-CRASH materal model 3 s for mlt-layered composte shell elements. Wthn ths model dfferent ply types can be sed for dfferent fbre renforcements and damage laws. Ths docment covers the ESI composte Global Ply damage law for:. Ply type for n-drectonal compostes (shell elements only).. Ply type 7 for woven type compostes (shell elements only). The Global Ply law s not avalable for sold elements. Problem descrpton Otlne Analyss type(s): Applcaton of the Global Ply composte damage model to a sngle element nder varos loadngs Explct Element type(s): Applcable to shell elements (materal model 3) Materals law(s): PAM-CRASH materal model 3 (composte ply types and 7). Fbre and matrx are calbrated for: ) Orthotropc elastcty ) Orthotropc fbre and matrx damage wth falre Model optons: Key reslts: Prepared by: Date: Bondary condtons, Imposed velocty loads, Composte materals Otpts for compostes (fbre stresses and strans, matrx damage, fbre orentatons ) Anthony Pckett, ESI GmbH/Insttte for Arcra Desgn, Stttgart September

2 Composte model 3: Ply types and 7 calbraton Backgrond nformaton Pre-processor, Solver and Post-processor sed: Vsal-Crash PAM: To assgn materal, loadng, constrant and control data. Analyss (PAM-CRASH Explct): To perform the explct Fnte Element analyss. Vsal-Vewer: To evalate reslts for contor plots, stresses and strans, etc. Pror knowledge for the exercse It s assmed the ser has some knowledge of Vsal-Crash PAM and PAM-CRASH. Problem data and descrpton Unts: kn, mm, kg, ms Descrpton: Sngle shell element mm * mm and mm thck Loadng: Imposed constant velocty at mm/msec (draton of stdy msec) total dsplacement mm and stran. (= %) Loadng cases: 4 3 y x Case : Axal fbre Case : Transverse matrx Case 3: Shear loadng Materal: The materal to be analysed s a hgh performance balanced woven fabrc composte. The data s presented from mechancal testng n the exercse. Sppled datasets All completed datasets are sppled. The man am s to demonstrate the strategy for model calbraton whch s done here sng the shell element (materal model 3, ply type ). Calbraton for orthotropc elastc propertes: Fbre drecton n tenson Fbre drecton n compresson Shear loadng Calbraton for damage, plastcty and falre: Fbre drecton n tenson (fbre falre) Fbre drecton n compresson (fbre falre) Shear loadng (elasto-plastc shear) Shear loadng (elasto-plastc shear) Shear loadng (elasto-plastc shear) Cyclc loadng (elasto-plastc shear) Ply_TensonX_Elastc.pc Ply_CompressonX_Elastc.pc Ply_ShearXY_Elastc.pc Ply_TensonX_ElastcFbreFalre.pc Ply_CompressonX_ElastcFbreFalre.pc Ply_ShearXY_ElastcDamageFalre_Opton_Plastc.pc Ply_ShearXY_ElastcDamageFalre_Opton_Plastc.pc Ply_ShearXY_ElastcDamageFalre_Opton3_Plastc.pc Ply_ShearXY_ElastcDamageFalre_Opton3_Plastc_Cyclc.pc

3 Composte model 3: Ply types and 7 calbraton Comments concernng ply types and 7 Two ply types are avalable that se the Global ply damage law for UD and woven type compostes: Ply type s ntended for UD compostes, bt can also be sed to approxmate a woven fabrc by stackng two UD layers wth approprate fbre angles and dstrbton of mechancal propertes. Indeed, t can be advantageos for non-orthogonal renforcement (e.g. ±3 ) and cases where large ntra-ply shear strans occr. Ply type 7 s for woven fabrcs and mostly sted to orthogonal renforcement and applcatons where shear strans are small. The followng table smmarses these three cases. Opton / Ply type Representaton Comments (Ply type ) t Standard representaton for UD composte ples The woven composte s dealsed as two (Two layers of Ply type ) t E WOVEN t/ t/ E -UD E -UD stacked pled of ply type In plane and shear propertes mst be careflly dstrbted between ples Usefl for non-orthogonal renforcement and large shear loadng 3 (Ply type 7) t E WOVEN Standard representaton for woven composte ples: Ideally for orthogonal renforcement Intra-ply shear strans shold not be large Ths docment demonstrates the calbraton strategy for opton n the above table appled to a balanced woven fabrc composte. Actal tests reslts are sed n ths calbraton. The methods sed are dentcal f standard ply types or 7 are sed. Basc theory A fll descrpton of the Global ply model s gven n the orgnal reference and also n the ESI PAM- CRASH TM ser s manal. Essentally the fbre phase ses a stran based falre crtera for tenson and compresson; non-lnear (elastc) behavor s possble n compresson and s oen necessary to accont for mcro-bcklng effects n compresson. The shear behavor ses a copled damage and plastcty model that acconts for modls redcton and permanent plastc deformatons. The fbre and matrx laws are decopled, bt parameters are avalable that allow coplng of transverse and shear matrx damage. Ladevèze P, Le Dantec E, Damage Modellng of the elementary ply for lamnated compostes, Compostes Scence and Technology, Vol. 43, Isse 3, 99, pp PAM-CRASH Users manals, Engneerng Systems Internatonal, Re Saarnen, Slc 7, Rngs- Cedex, France. 3

4 Composte model 3: Ply types and 7 calbraton Part : Some basc explanaton of the npt data Typcal model loadngs and spports (e.g. for dataset Ply_TensonX_Elastc.pc) Load the dataset nto the Vsal-Crash Program (VCP) and stdy the spports and the loadng:. In Loads > Dsplacement Bondary Condton the followng defntons are fond: Node s flly constraned. Node s flly fxed, except free n the x-drecton. Node 4 s flly fxed, except free n the y-drecton.. In Loads > 3D BC nodes and 3 are loaded at constant velocty n the postve x-drecton (for tenson fbre loadng). 4 y x 3 Remark: Ths smple setp ensres the element s properly spported and has pre tenson loadng n the x-drecton wth free contracton n the y-drecton. Ply, Materal and Part data cards Note from the dataset:. The parts data contan nformaton on geometrc data sch as the reference fber orentaton. A lnk to assocated materal data (varable IMAT) s also made.. The materals cards (IMAT) contan nformaton on densty, the nmber of ples n the lamnate and the stackng seqence. Wthn ths stackng seqence nformaton on each ply, ncldng the reference ply set (parameter IDPLY), the ply thckness and a fbre orentaton angle are defned. 3. The ply cards (IDPLY) contan all ply mechancal data for stffness, damage and falre. Consderng the seqence n whch the data refers to each other ( 3) t s best to defne thngs n reverse order;.e. the ples frst, then materals and fnally parts; all three are needed. 4

5 Composte model 3: Ply types and 7 calbraton Ply cards (e.g. Ply propertes for dataset Ply_TensonX_Elastc.pc). In the ply cards yo wll fnd the mechancal, damage and falre data assgned to the ply. o IDPLY s the ply dentfcaton nmber and ITYP s the ply type ( or 7). o The mechancal data (densty, modls, shear and Poson s rato) are gven on the frst cards. Ths s then followed by falre, compresson, plastcty and stran rate data. o Note: Contrary to the PAM-CRASH B-phase model all mechancal data represents homogensed propertes. Materal cards (e.g. Materal propertes for dataset Ply_TensonX_Elastc.pc).. The nmber of ples n the lamnate are defned (NOPLY) and for each ply the assocated ply nmber (IDPLY), the ply thckness (THKPL) and fbre angle (ANGPL) are defned. Note the fbre angle s wth respect to a reference vector defned n the Parts cards (see below) and that two stacked ples are defned.. Specal otpt reslts to the.thp and.dsy fles (or.enf fle f sed) are possble sch as fber, transverse and shear stresses/strans. For ths the ply nmber n the lamnate lay-p and an axlary reference nmber for the varable to be otpt are gven. Examples of axlary reference nmbers are Ax s -3 for fbre stran, stran and shear stran, and Ax s 6-8 for correspondng fber stresses. Axlary reference nmbers are also avalable for reslts sch as fbre and matrx damage. Part cards (e.g. Part propertes for dataset Ply_TensonX_Elastc.pc).. The connecton to the assocated materal s made va the IDMAT nmber (n ths case = ).. A vector for the reference fbre drecton s defned. Here the global vector opton wth a reference vector,, (.e. the global x-drecton) s sed. For shell elements the transverse drecton s normal to the fber drecton n the element plane. 5

6 Composte model 3: Ply types and 7 calbraton Part : Determnaton of orthotropc elastc and falre propertes from test measrements In ths exercse test reslts are frst presented from whch the necessary materal propertes for stffness and falre are extracted. The model and npt data are then valdated sng a sngle element test case. For the woven fabrc composte the tests needed to extract data are:. Tenson test on specmens elastc and falre propertes. Compresson test on specmens elastc and falre propertes 3a. Shear elastc propertes (Tenson test on a ±45 specmen) 3b. Shear damage propertes (Cyclc tenson test on a ±45 specmen) 3c. Shear plastcty propertes (Cyclc tenson test on a ±45 specmen). Tenson test on specmens: Elastc and falre propertes For test copons loaded n the drecton (=9 drecton for a balanced woven fabrc composte) are shown. For a smple copon: L = and L L = T by defnton = E E t L t L = L (Mpa) sample 9 sample3 8 sample5 7 sample ,,4,6,8,,,4 There s some scatter n the test data; bt reasonable averages for stffness and falre data are smmarsed n the table below. Property Vale t E Tensle elastc modls (fbre drecton) 67.5 GPa Tensle falre stress (fbre drecton) 88 MPa Tensle falre stran (fbre drecton) - ntaton.3 Tensle falre stran (fbre drecton) - ltmate.3 d Assmed ltmate damage (fbre drecton). 6

7 Composte model 3: Ply types and 7 calbraton. Compresson test on specmens: Elastc and falre propertes C E In ths case s gven by the ntal slope of the compresson stress-stran crve (dashed lne); e.g. C E 4 /.575 GPa = 69. GPa. (Mpa) smlaton All other falre data s estmated and gven n the table below. Property Vale t E Compresson elastc modls (fbre drecton) 69. GPa Compresson falre stress (fbre drecton) 65 MPa Compresson falre stran (fbre drecton) - ntaton.4 Compresson falre stran (fbre drecton) - ltmate.5 d Ultmate compresson damage (fbre drecton). A frther sefl parameter n compresson s the correctve parameter (γ) to help approxmate the nonlnear compresson crve (de to fbre crmp and mcro-bcklng). Ths s gven by,. Performng ths comptaton abot an arbtrary pont ( e.g. stran =.8) gves γ =.7 3a. Shear elastc propertes (Tenson test on a ±45 specmen) For the elastc shear data the ntal (ndamaged) porton of the tensle loaded cyclc shear test s sed; an example for the woven fabrc s gven below. The stress-stran relatons n the fbre frame are defned as follow: = and L / = L T G o s gven by the ntal slope of the shear stress ( ) verss the engneerng shear stran ( ). 7

8 Composte model 3: Ply types and 7 calbraton (GPa) (GPa) G,,4,6,8.75. The ntal shear modls s defned as the ntal slope of the test crve (rememberng that engneerng shear stran mst be sed (γ = ), G o = / = 6 / (*.75) = 4. GPa. 3b. Shear damage propertes (cyclc tenson test on a ±45 specmen) The prevos cyclc shear test for tensle loadng of a ±45 copon s sed to extract damage evolton, plastcty and fnal shear falre data. Shear damage s gven by the change n slope of the cyclc modls G and plastcty by the growth n p and each loadng cycle. G O G Fve loadng cycles have been performed on the copon as shown n the next crve. Note that ths fgre shows test reslts wth, and wthot, takng accont of changes n cross sectonal area n the comptaton of. If these changes can be measred drng testng and nclded then the model calbraton wll be more accrate. The crve wth secton varaton s sed here. 8

9 Composte model 3: Ply types and 7 calbraton 6 4 sample3 sample3 wth cross secton varaton (GPa) 8 6 4,,4,6,8,,,4,6 At each cycle the stffness loss s charactersed by the shear modls redcton. The degree of shear damage d s gven by the relatonshp: d G = G Shear modls and damage vales for every cycle are smmarsed n the table below; agan sng engneerng shear stran (γ = ) to calclate the G vales, cycle Shear modls G d Ths model ses the term Y to defne how damage s progressng (t s the change of stored elastc energy wth damage). The stored energy for a ply s, E D e = : ν = E E + + E ( d + G ( d Consderng only stored energy for shear () the conjgate qantty Y s + ) E ) Y δ E = δ d D = G ( d ) From e = Y G o = G ( ) ( d ) A smlar expresson to Y cold be developed for UD ples where damage wll occr n the nrenforced transverse drecton; however ths s not needed here for the woven fabrc. The conjgate force qantty at each cycle () s therefore gven by, 9

10 Composte model 3: Ply types and 7 calbraton Y e = G ( ). From the cyclc test crve and the above expresson, e cycle Y.E E E E E E-.873 It s now possble to plot the evolton of Y wth damage d. cycle Y d The damage s ntally lnear (for small strans and then ncreases rapdly close to falre), as shown n the adjacent plot. Several optons are avalable n PAM-CRASH to characterse damage evolton; for example, an exponental fncton, a crve fncton and the followng (orgnal) lnear damage fncton, Y = YC d + Y, where Yo s the ntal constant and Yc s the slope of the lnear fncton. A frther parameter YR s sed to specfy falre (Yo, Yc and YR are data npt vales for PAM-CRASH shear damage evolton and falre). Two examples to try and the lnear fncton to the test crve are shown n the graph wth data n the table below; clearly ths s not accrate. For ths dctle matrx the exponental or crve fncton methods wold be better. Y (Gpa^.5) Y verss d 6 ponts approx 4 ponts approx y =.464x +.4 y =.4x d Y O Y C Y R Ln. Fncton Ln. Fncton Crve fncton Usng the data ponts n the table above.88

11 Composte model 3: Ply types and 7 calbraton 3c. Shear plastcty propertes (Cyclc tenson test on a ±45 specmen) The nelastc deformaton s descrbed by a plastcty law whch coples transverse () and shear () strans only. The plastc stran p j s the measre of effectve plastc stran and the term R s sed to determne how the vale of d affects the yeld stress n each cycle. In ths model the terms effectve stress and effectve stran are ntrodced as measres of actal materal stress and stran carred by the damaged materal. The damage (mcro-crackng) redces the effectve area of the load carryng materal casng effectve materal stress to be rased and effectve materal stran to be lowered. Note ths termnology s not the same as Von Mses effectve stress and stran whch s commonly sed n plastcty n the lteratre. The term p j and R are calclated n the followng eqatons: p R = P j p p = p ( d ) = j = p = d R R, j nmber of cyclc loads = β ( P ) j m (Eq.) where P s the plastc stran at each cycle, as shown on fgre below. The followng table gves the plastc stran measred from the cyclc shear test crve and the damage term whch are sed to calclate p. Accordng to Eqatons a plot of -d verss P allows the (p ) vales to be fond by ntegraton for each cycle. The vales for (P j ) are then compted from smmaton of these vales. The followng crve and table smmarse reslts of ths ntegraton and the smmaton. (GPa) sample3 sample3 wth cross secton varaton,,4,6,8,,,4,6 cycle p - d 7.4E E E E E-.5838

12 Composte model 3: Ply types and 7 calbraton, p,8 -d,6,4 p 3 p 4 p 5,,5,,5, plast Cycle p P j R (MPa) Fnally, a crve tng exercse s performed to the PAM-CRASH exponental plastcty fncton (wth parameters β and m) to the R verss P crve. Ths has prodced the followng reslts wth the ntal plastcty yeld stress Ro = MPa.,3,5, R (MPa),5,,5 R =.566 ( P j ).7986Pj expermental gor power law,,4,6,8,, P j P

13 Composte model 3: Ply types and 7 calbraton Part 3: Smmary of the Global Ply dataset for elastc, damage, plastcty and falre For the prpose of ths calbraton a total ply thckness of.mm s assmed meanng that each ply n the stacked approxmaton s.5mm (Make sre the tre vale s sed n any real composte). In order to compensate for the halved ply thckness n ths dealsed model: Doble the modls for tenson and compresson modls. Use nchanged shear modls (and shear damage/plastcty) for each ply. Use a low modls (say GPa) for the transverse drecton (to mnmse nteracton effects). Note: Any modfcatons to ply modl wll correspondngly modfy the stress levels; however, damage and falre s always controlled by stran and therefore the approach (to treat a woven compostes as two stacked UD ples) s vald. The followng table smmarses the data so far for each ply (thckness =.5mm) n the dealsed woven compostes. Inplane Tenson Inplane Compresson t E c = (*67.5)=35 GPa E = t E =. GPa = fc ν =.33 = fc =.3 = (*69,)=38 GPa γ fc =.3 = d =. d. Table : Inplane stffness/falre data For the shear the followng data/optons were determned (to be sed for each ply): Stffness G O = 4. GPa Damage Yo Yc YR Ln. Fncton Ln. Fncton Crve fncton Usng the Y-d data ponts.89 Plastcty R =.566 ( P j ).7986Pj R = MPa, β =.7986, m =.566 Table : Shear stffness, damage and plastcty data 3

14 Composte model 3: Ply types and 7 calbraton Part 4: Checkng the npt wth smlaton reslts Smlaton reslts Fbre tenson (elastc wthot and wth falre) Usng dataset: Ply_TensonX_ElastcFbre.pc (for no falre) Ply_TensonX_ElastcFbreFalre.pc (for fbre falre) Postve x-velocty s appled to nodes,3 (.mm/sec) (= Case, Pg ).. Fbre tenson (for the falre case) The shell element tme hstory plot Comp. Ax4 (fbre stress) aganst Ax (fbre stran) s plotted for the fbre drecton ply. For a stran of. the correspondng fbre drecton stress s.35gpa; note:. Ths stress s ( correctly) doble that of the test vale (7N/mm at. stran) snce the eqvalent ply thckness s half of the tre woven ply. The dfference s de to the small contrbton from the transverse drecton n the second ply; calbraton cold be done to correct ths.. The falre data =.3, =.3 and d = 4 3 y x. s mposed. In ths case tensle fbre falre s ntated at the reqred.3% stran and fll damage occrs (d=.). 3. If a resdal damage s reqred se d<.. E.g. for d=.3 only 3% of damage occrs (Edamage =.7 * Eo) and the stress wll reman constant aer ths damage state s reached. Reslts: fbre compresson Usng dataset: Ply_CompressonX_ElastcFbre.pc (for no falre) Ply_CompressonX_ElastcFbreFalre.pc (for fbre falre) Negatve x-velocty (=-.mm/sec) s appled to nodes,3.. Fbre compresson (for the falre case) The nonlnear form of the compresson fbre stress (Ax 4) verss fbre stran (Ax ) s evdent de to the factor γ =.7. Stress n the fbre ply (x-drecton) s approxmately twce the test vale de to the prevosly mentoned reason; for example, at fbre stran.9, the smlaton stress s.kn compared to test.54kn. fc fc The falre data =., =. fc and d =. s mposed. Falre s ntated and completed, as expected, wth total damage de to d=.. 4

15 Composte model 3: Ply types and 7 calbraton Transverse drecton (= Case, Pg ) Snce ths composte has a balanced fabrc the second ply transverse drecton wll have the same propertes as the fbre drecton calbrated above. Ths s assred n the dataset sng layers for the model wth dentcal propertes for layer (n the ) and layer (n the 9 ). Shear (for the elastc case sng dataset - Ply_ShearXY_Elastc.pc) The sngle element test case s loaded n the postve x and negatve y drectons to mpose pre shear loadng (= Case 3, Pg ). The fbre drectons are set to ±45 wth respect to the x-drecton. A tme hstory plot of shear stress (Ax6) aganst shear stran (Ax3) s shown. At.75 shear stran the shear stress s 6MPa; whch corresponds to the vale of the ntal slope of the expermental shear stress verss shear stran crve. Shear (for the damage wth falre pls plastcty) Shear damage can be treated sng the lnear damage fncton, an exponental fncton or the crve fncton; ltmate shear falre s specfed by the vale of YR. The prevos table for shear damage evolton and falre s repeated below wth the three optons (,, 3) evalated here to compte shear damage. In each case the prevosly determned plastcty data s sed. Shear damage data Plastcty data Opton Damage fncton Yo Yc YR Ro β m Ln. Fncton MPa Ln. Fncton Crve fncton sng the data ponts n the Y-D table The three sppled datasets for the above cases are:. Ply_ShearXY_ElastcDamageFalre_Opton_Plastc.pc. Ply_ShearXY_ElastcDamageFalre_Opton_Plastc.pc 3. Ply_ShearXY_ElastcDamageFalre_Opton3_Plastc.pc Usng the lnear shear fncton (optons and ): For some sem-brttle materals the lnear may be satsfactory; bt n ths case the s poor, especally to descrbe the rapd damage growth at large shear strans. The followng crves llstrate the poor of the lnear fncton to the test (damage) crve and the correspondngly poor correlaton of the sngle element analyss to the test shear stressstran crve. 5

16 Composte model 3: Ply types and 7 calbraton Y (Gpa^.5) Y verss d 6 ponts approx 4 ponts approx y =.464x +.4 y =.4x d (GPa),4,,,8,6,4 expermental 4 ponts lnear law, 6 ponts lnear law,,4,6,8,,,4,6 Usng the crve shear fncton (opton 3) In PAM-CRASH (verson V8+) exponental and crve descrptons for shear and transverse damage evolton are avalable. In the Opton 3 dataset the Lnear parameters for Yo, Yo are removed and the varable ISH s set to. A crve descrpton of Y aganst d s sed wth the prevosly determned data (note the, start pont) n an axlary crve; set ths crve nmber to the parameter ICURV n the ply data. The ltmate shear stran parameter YR s set to.89. From the reslts a plot of shear stress (Ax 6) aganst shear stran (Ax 3) shows a good agreement wth the test crve for both shape and falre; althogh some mprovements sng more data ponts cold help to smooth the shape, especally at shear stran.4. Cyclc shear loadng Usng shear damage (opton 3) and the dataset Ply_ShearXY_ElastcDamageFalre_Opton3 _Plastc_Cyclc.pc The adjacent plot shows cyclc (velocty) loadng of the sngle element test case. The change n slope of the nloadng crve represents damaged shear modls. Also, the nelastc (permanent) plastc strans are evdent. 6

17 Composte model 3: Ply types and 7 calbraton Part 5: Alternatve optons for damage and falre Damage crve fnctons Dfferent methods can be sed to defne the form of the damage fnctons; namely, Lnear, Exponental or Crve. For most compostes an exponental or Crve fncton wll be needed to reasonably descrbe the damage fncton evolton. Spermposed falre crtera For fbre and matrx damage the Global ply model has so far been sed. However, t s also possble to spermpose a classcal falre crtera sch as Tsa-W, Max. stress, etc. Set IFAIL_INP= and choose the falre crtera wth flag FAILTYP. Dependng on the selected falre crtera addtonal falre nformaton s reqred. If the state of stress or stran reaches the falre crtera the element wll be elmnated (for FAILDAM = ). In the materals cards the IFAIL opton mst also be set. Part 6: Specfc nformaton for woven renforcement (Mat 3 ply type 7) The data shown s typcal nformaton for ply type 7. Some ponts to note are:. The strctre and general nformaton reqred s smlar to ply type.. The two man fbre drectons are assmed to be orthogonal. 3. Tenson and compresson nformaton s provded for the man fbre drecton (E, Ec) and the second fbre drecton (E, Ec). 4. For tenson fbre falre drvng force vales YIIC, Y and YR are sed, for compresson YIIcC, Yc and YcR are sed. Note that crrently ths nformaton s appled to both renforcement drectons, so strctly the fabrc shold be balanced (.e. E = E and Ec = Ec). 5. Stran rate can be appled. 7