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Studies on Rheological Behaviors of Bismaleimide Resin System for Resin Transfer Molding
V ol. 15 N o . 3 CHIN ES E J OU RN A L O F A ER O N A U T ICS A ugust 2002
Studies on Rheological Behaviors of Bismaleimide Resin System for Resin Transfer Molding L U Yao , DUAN Yue-x in, L IANG Zhi-y ong ( School of M aterial S cience & E ngineering, Beij ing Univer sity of A eronautics and A st ronautics, Beij i ng 100083, China ) Abstract: T he r heolog ical behav io r o f bismaleimide resin fo r r esin transfer molding ( R T M ) w as studied with DSC analy sis and visco sity ex perim ents. A r heo log ical model based on the dual-A r rhenius equation w as est ablished and used to simulate the r heolog ical behavior o f t he r esin . T he model pr edictions deter mined fro m the dual-A r rhenius equatio n w er e in g oo d ag reem ent w it h ex perim ental da ta. T he pro cessing w indow of the r esin sy st em can be w ell deter mined based on the developed mo del . T he r heolog ical mo del is impor tant for pr ocessing simulation and quality contr ol of RT M pr ocessing for hig h per for mance co mposites . Key words: compo sites; RT M ; bism aleimide resin; r heolog ical models; cur ing reactio n kinetics 双 马来酰亚胺树脂化学流变特性研究 . 路遥, 段跃新, 梁志勇 . 中国航空学报( 英文版) , 2002, 15 ( 3) : 181- 185. 摘 要: 在粘 度实验的基础上, 根据双 阿累尼乌斯 方程对用 于 RT M 工 艺的双马来 酰亚胺树 脂体 系 的化学流变特性进行了研究, 建立了树脂体 系的流变模型。通过 DSC 热分析实验研究树脂体系 的 固化反应规律, 验证了双阿累尼乌斯模型。研究表明, 模型与实验结果具有良好的一 致性。模型 可 揭示树脂体系在不 同工艺条件下的粘 度变化规律, 定量预报 RT M 工艺树脂的低 粘度平台 工艺 窗 口, 为 合理制定 RT M 工艺 参数、 保 证产品质 量和实现 工艺参 数的全 局优化 提供必要 的科学 依 据。 关 键词: 复合材料; R T M 工艺; 双马树脂; 流变模型; 固化 反应动力学 文 章编号: 1000-9361( 2002) 03-0181-05 中图分类号: T B 332 文献标识码: A
T he RT M process has been recog nized as a very high pot ent ial process f or adv anced compos-
it y ar ea can be def ined precisely . Hence , one can o pt imize t he RT M pro cess par am et ers and improve
ites m anuf act uring, and has been w idely used in many industr y f ields such as aero space , mobile and
t he qualit y o f the product s .
civil archit ect ure . T he RT M pro cess must depend on t he special low viscosit y resin, whose rheolog ical behavior co nt ains a low v isco sit y area meet ing t he demand o f t he RT M . T his means , the viscosi-
[ 3]
QY8911-4 BMI resin is a suit able resin f or RT M . In o rder t o optim ize the RT M process param et ers and improv e t he qualit y of t he product s , t he chemorheolog ical behav io r of t he QY8911-4
ty of t he r esin sho uld maint ain 50-200cP w hen in-
BM I resin is st udied, it s rheolog ical model is es[ 4-8] t abl ished , and a pro cessing w indo w is predicted
ject ed in molding f or complet e fill and fiber w et -
.
ting
[ 1, 2 ]
.
T heref ore,
t hr oug h est ablishing t he chemor heolog y m odel o f t he resin -v isco sit y f unctio n about t em perat ure and t ime ( o r cure degree ) ,
1 Viscosity Ex periment QY8911-4 BM I resin is pr epared f or det ermi-
t he resin viscosit y at any t em perat ur e and t im e( or
natio n of v isco sit y. Viscosit y det erminations are
cure deg ree) can be calculated, and t he l ow viscos-
carried out at dynam ic t em perat ur es and select ed
Received date: 2002-03-20; Revision recei ved dat e: 2002-03-21 Foundati on it ems: N at ional N at ural Science Foundat ion of C hina( 59833110) and N at ional Defence Foun dat ion( 00j00. 5. 3. hk 0144) A rt icl e U R L: ht t p: / / ww w . hk xb. net. cn/ cja/ 2002/ 03/ 0181/
LU Y ao , D U A N Y ue -xin, LIA N G Zhi-yong
・ 182・
2 Dual A rrhenius M odel
t em perat ures, using NDJ-1 r ot ating v isco meter, according t o GB 7193. 1. 1. 1 Vi scosity at heating condition T he v isco sit y curve of QY8911-4 BMI resin is show n as F ig . 1.
CJA
In t he case of isot hermal cur e, the viscosity , w hich is aff ect ed by t ime and temper ature, can be descr ibed into the dual Arrhenius m odel g iv en by
[ 3]
ln ( T , t ) = ln
∞
+ E /(RT ) +
k ∞tex p[ E k / ( R T ) ] w here
( 1)
and k ∞ are the Arrhenius preex po nent ial f act or s, respectively , w hile E and E k are respect ively t he act ivat io n energies f or t he f low and t he ∞
curing react ion. R is an ideal g as const ant . T he model can be simpl if ied lnA = ln ∞ + E / ( RT )
( 2)
lnB = lnk ∞ + E k / ( RT )
( 3)
Fo r QY 8911-4 BMI resin , it s viscosit y will descend w ith the heating condit ion . On t he ot her hand, it w ill ascend because o f r esin cross-linking.
So t he model can be described as ln ( T , t) = lnA + B t
( 4)
During heat ing t he r esin, viscosit y descending is pr im ary at low er t emperat ures; o therw ise ascend-
t ure are sho wn as F ig. 3.
ig . 1 V isco sity -temper ature curv e of BM I r esin system
T he curves of ln -t at t he isot herm al t empera-
ing is primary at higher t em perat ur es. T he viscosity will be a minim um when t he t w o ef f ect s keep balance . QY 8911-4 BMI resin w ill be m elt ed at 80℃. So viscosit y measurement begins at 80℃. Viscosit y maintains under 800cP bet w een 80℃ and 140℃. T herefo re, isot herm al v isco sit y measurement is select ed in t he rang e of 90-140℃. 1. 2 Isothermal viscosity measurement According to t he dynam ic viscosit y curv e, isot hermal v isco sit y measur em ent s ar e carried out at 90℃, 126℃ and 135℃. T he curv es of isot her mal viscosit y are show n as Fig . 2. T he viscosit y changing rat e is improved w it h t im e and temperature .
Fig. 3 ln vs t cur ves at isother mal temper atur e
Acco rding t o Fig . 3, t he m odel par am et ers l nA and B can be calculat ed ; t he result s are present ed in T abl e 1. Table 1 Parameters of the viscosity model T emperat ure/ ℃
l nA
B
90
5. 97
0. 008
126
4. 43
0. 039
135
3. 44
0. 060
T he cur ves of lnA -1/ T and lnB -1/ T are present ed in F ig . 4 and F ig . 5 respect ively . Acco rding to F ig . 4 and F ig . 5, o ne can obt ain t he f ollo wing relat ion about t he parameters l nA and lnB l nA = - 14. 91 + 7603/ T F ig . 2 I so therm al v iscosity -time cur ves
( 5)
lnB = 12. 98 - 6465/ T ( 6) No te t hat t he tim e unit should be chang ed
St udies on R heological Behaviors of Bism al eimide Resin Sys tem f or R es in T ransf er M ol ding
A ugus t 2002
・ 183・
m ade in American Rheom et ric Scient if ic Com pany is used in t his st udy . T he resin samples are scanned at dif ferent heat ing rat es as 5℃/ min, 10℃/ min and 20℃/ min. And t he result s are show n in Fig . 6.
Fig. 4 lnA v s 1/ T o f the dual-A rr henius equatio n
Fig . 6 Dy namic DSC curv es at var io us heating ra tes
3. 2 Data analysis T he Kissing er funct ion is perf orm ed t o describe the curing react ion kinetics of t he t hermalset r esin. T he relation betw een t he t em perat ure at m aximum rate o f t he DSC curv e and the const ant
Fig . 5 lnB vs 1/ T of t he dual-A rr henius equa tio n
fr om m inut e t o second, and the rheo logical model of QY8911-4 BM I resin can be present ed as ln = - 14. 91 + 7603/ T + t ex p( 17. 07 - 6465/ T )
ln ( 7)
Fo r nonisot hermal cure, w here t he resin t em perat ur e hist ory is g iven by T = f ( t ) , t he viscosit y can be present ed as an int eg ral f orm ation as 7603 ln = - 14. 91 + + T ( t) t 6465 exp 17. 07 dt 0 T ( t)
∫
[ 12]
heating rat e is show n as fo llow s T 2m
= ( lnA + lnR - lnE) -
E RT m
( 9)
w here is the co nst ant heat ing rat e ; T m is t em perat ur e at max im um rat e; A is preex ponential f act or , and E is the act ivat io n energ y of t he curing reaction . 2 Acco rding to Eq . ( 9) , plot ln ( / T m ) vs 1/ T m as F ig. 7. T he slope is - E/ R , and t he int ercept is
( 8)
l nA + l nR - lnE.
3 React ion Kinetics T he curing react ion kinet ics of t he r esin is st udied by DSC analy sis [ 9-11] . In t his paper, a kinet ic model based on Kissinger funct ion is est ablished . T he paramet er s in t he kinet ic model —— pr eex ponent ial f act or and t he act ivat io n energy f or t he cur ing react io n—— are compar ed w it h the paramet ers in t he dual A rrhenius model , so the rat io nalit y of t he dual Arr henius mo del and t he physics def init io ns o f the m odel paramet er s ar e verified. 3. 1 DSC analysis Dif ferent ial Scanning Calorim et ry ( DSC )
F ig . 7 ln( / T 2m ) vs 1/ T m
T he act ivation energ y f or QY8911-4 resin sy st em is 98486J/ mo l, and t he preex ponent ial fact or is 21. 61. T he react ion order n can be det erm ined by t he peak shape f act or S of t he DSC curve. S is defined
LU Y ao , D U A N Y ue -xin, LIA N G Zhi-yong
・ 184・
as t he absolut e ratio value of t he t ang ent slopes at t he curve inflect ion point . T herefor e , n can be ob[ 13]
tained as t he fo llow ing equat io n n ≈ 1. 26S
1/ 2
( 10)
CJA
Table 2 The parameters of the two models para
dual A rr hen ius
K iss inger
Calc.
err or / %
k
17. 07
21. 61
21. 18
1. 96
E/ R
6465
11846
12594
6. 32
T he react ion o rder is 2. 076 f rom Fig . 6.
Acco rding t o the DSC analysis, one can con-
So t he cur ing react io n kinet ic model of QY 8911-4 r esin sy st em is show n as
clude t hat t he resin v isco sit y at t he low curing de-
d - 11846/ T 2. 076 = 21. 61e (1 - ) ( 11) dt Eq. 11 can be presented as an int egral f orm atio n as = 1 - [ 1 - ( 1 - 2. 076) 21. 61t e
( - 11846/ T )
1
] 1- 2. 076 ( 12)
T he cur ing degr ee v s t im e at dif ferent isot her mal temper atures is show n as Fig . 8.
g ree area can be calculat ed by t he dual Arrhenius m odel, and t he parameters in t he dual Arrhenius m odel and in cur ing react ion kinet ics have t he corresponding relation .
4 M odel Applicat ion 4. 1 Prediction of processing window T he resin viscosity at a cert ain t em perat ure and t im e can be calculat ed by t he dual Arrhenius m odel. T he v isco sit y m ap is show n as Fig . 9.
Fig . 8 Isot her mal cur ing deg ree v s time cur ves
According t o Fig . 8, the curing degr ee v s t im e show s t he linear rel at ion o n t he init ial stag e of t he curing react ion , and t he t im e maint aining the lin-
T he t em perat ures, at w hich the resin v isco sit y
ear r elat ion accords w it h t he t im e maint aining t he low v isco sit y in t he dual Arrhenius mo del. It is
is less than 800cP and t he t ime maintaining the low v isco sit y is mor e than 40 minut es, are 90℃,
cert ain t hat the assumpt io n fo r the dual Arr henius
100℃, 110℃ and 120℃. T herefo re, t he process-
model ( t he curing deg ree vs t im e show s the linear relatio n in the lo w viscosit y area ) is right .
ing w indow s o f t he QY8911-4 BM I resin sy st em
T he paramet er r elat ionship bet w een the dual Arrhenius model and t he Kissing er equat ion is present ed as the f ollo wing ex perience equation E= E
n- 1 k
and k = k
n- 1 ∞
( 13)
w here E and k are t he activ at ion energy and t he pr eex ponent ial f act or fr om t he Kissinger equat io n; E k and k ∞ are f rom t he dual Arrhenius m odel; n is
Fig . 9 V iscosity map
f or t he RT M pr ocessing are the t emper at ure range f rom 90 t o 120℃. 4. 2 Viscosity simul ation F or nonisot herm al cur e, w her e t he resin t emper at ure hist ory is given by T = f ( t) , t he v isco sit y can be present ed as t he int egral f orm ation as Eq. 8. So t he viscosit y can be simulated at t he g iven condit ion of t he t emperat ure as a funct io n o f t ime , and
T he results of t he paramet ers of t he dual Ar -
t he result s are show n in F ig . 10. T he resin is heat ed at a const ant r ate, m ain-
rhenius mo del co mpared wit h t he par am et ers o f t he Kissinger equat ion are show n in T able 2.
t ained at an assigned t emperat ure f or about 100 m inut es , and t hen heat ed again t o cure complete-
t he reactio n order .
St udies on R heological Behaviors of Bism al eimide Resin Sys tem f or R es in T ransf er M ol ding
A ugus t 2002
・ 185・
1994. ) [ 2] Beckw it h S W , Craig R H . Resin t ran sf er molding , a decade of techn ology advances [ J] . SA M PE Journ al , 1998, 34( 6) : 297- 311. [ 3] G ut ow ski T G . A dvanced composit es manuf actu ring [ M ] . N ew Y ork: John W iley &Sons Inc, 1997. 393- 457. [ 4] R udd C D, Long A C , K endall K N , e t al . Liquid mol ding t echnol ogies [ M ] . London: W oodhead Pub lish ing Lt d, 1997. 23- 28. [ 5] Loos A C, Spring er G S . Curing of epox y mat rix composit es [ J ] . Journ al of composi te mat erials , 1983, 17 ( 3) : 135 -
ig . 10 Calcula ted v iscosity dur ing pr ocessing pro cedur e
167. [ 6] Hall ey P J , M ack ay M E. Chemorheology of t hermoset - an
ly. Fro m F ig. 10, o ne can get t he same t rends at
overview [ J] . Pol ymer Engin eering and Science, 1996, 36
dif ferent condit ions: At t he f irst heat ing st age, t he viscosit y dr ops cont inually , at isot hermal st ag e, t he viscosit y rises gr aduall y, and at t he second
( 5) : 593- 608. [ 7] Panag iot is I K , Ivana K P , A t t wood D avid. M odeling t he cure of a comm ercial epoxy res in f or app licat ions in res in t ransf er molding [ J ] . Polym er Int ernat ional, 1996, 41 ( 2) : 183- 191.
heat ing st age, the viscosit y dro ps mom ent ly and rises quickly t o a gel point .
[ 8] 梁志勇, 段跃 新, 林云等 . EPO N 862 环氧树脂体 系化学流变 特性研究 [ J] . 复合材料学报, 2001, 18 ( 1) : 16- 19.
Compared w ith dif ferent viscosit y curves, at
( L iang Z Y , Duan Y X , Lin Y . S t udies on rheological behav-
110℃ t he viscosity can maint ain less t han 300cP fo r 55 m inut es . So t he resin can be suit able t o manuf act ure the medium or small sized str uct ures
iors of EPO N 862 epoxy resin sys tem for res in trans fer m old-
as t he RT M processing . One can conf irm t hat t he t em perat ure at 110℃ is t he suit able injection t em perat ur e. If the part s ar e relatively larg e and t he inject ion t ime is long , t he temperatures at 90100℃ ar e t he suit able inject ion t emperat ure .
5 Conclusions QY8911-4 BM I r esin sy st em is the suit able resin f or t he RT M processing . T he dual Arr henius model can be used t o pr esent the rheo logical behav ior o f t he QY 8911-4 BMI r esin at low viscosit y ar eas. And t he model predictions are in g ood agreement wit h ex periment al dat a . T he pr ocessing w indow fo r t he RT M processing can be predicted precisely by t he dual Arrhenius mo del, and t he viscosity can be simulat ed dur ing t he processing procedure . T he rheolog ical model is import ant f or pro cessing optim ization and qualit y cont rol of RT M pr ocessing f or hig h perf orm ance com po sit es. References [ 1] 梁志勇, 段跃 新, 张佐光 . R T M 工艺 技术及 应用报 告( 技 术 鉴定报告) [ R] . 北京: 北京航空航天大学 104 教研室, 1994. ( Liang Z Y , Du an Y X , Zhan g Z G . R eport on RT M pr oces sing t echnol ogy and appl ication [ R] . Beijin g : Beijing U niversit y of A eronaut ics and A st ronaut ics 104 S taf f R oom ,
ing[ J ] . A cta M at eriae Composit ae Sin ica, 2001, 18 ( 1) : 1619. ) [ 9] Eckold C. D es ign and m anu fact ure of com pos it e st ruct ure [ M ] . N ew Y ork: M cG raw -Hill Inc, 1994. 271- 277. [ 10] K amal M R , S ou rour C. Ki net ics and t hermal charact erizat ion of t hermoset cure [ J] . Polymer Engineeri ng and S cience. 1973 ( 1) : 58- 77. [ 11] Lip shit z S D , M acosk o C W . R heological changes du ring a ur et hane net w ork polymerizat ion [ J ] . Pol ymer Engin eering and Science, 1976 ( 16) : 26- 38. [ 12] S hin D D , Hahn H T . A cons ist ent cure kinet ic model f or A S 4/ 3502 graphit e / epoxy [ J ] . Composit es Part A , 2000, 31: 991- 999. [ 13] 高家武, 高分子材料近代测试技术[ M ] . 北 京: 北京航空航天 大学出版社, 1994. 44- 45. ( G ao J W . M odern t est ing t echnol ogy on pol ymer material [ M ] . Beijin g: Beijing U n ivers ity of A eronaut ics and A st ronaut ies Pub lish ing Hou se, 1994. 44- 45. ( in Chin es e) )
Biographies: LU Yao Bor n in 1977, he r eceived B. S . and M . S . fro m Beijing U niv ersity of A er onautics and A stro naut ics in 1999 and 2002 r espectiv ely . T el: ( 010) 82317127, E -mail : luyao 2000@ 263. net
Studies on Rheological Behaviors of Bismaleimide Resin System for Resin Transfer Molding L U Yao , DUAN Yue-x in, L IANG Zhi-y ong ( School of M aterial S cience & E ngineering, Beij ing Univer sity of A eronautics and A st ronautics, Beij i ng 100083, China ) Abstract: T he r heolog ical behav io r o f bismaleimide resin fo r r esin transfer molding ( R T M ) w as studied with DSC analy sis and visco sity ex perim ents. A r heo log ical model based on the dual-A r rhenius equation w as est ablished and used to simulate the r heolog ical behavior o f t he r esin . T he model pr edictions deter mined fro m the dual-A r rhenius equatio n w er e in g oo d ag reem ent w it h ex perim ental da ta. T he pro cessing w indow of the r esin sy st em can be w ell deter mined based on the developed mo del . T he r heolog ical mo del is impor tant for pr ocessing simulation and quality contr ol of RT M pr ocessing for hig h per for mance co mposites . Key words: compo sites; RT M ; bism aleimide resin; r heolog ical models; cur ing reactio n kinetics 双 马来酰亚胺树脂化学流变特性研究 . 路遥, 段跃新, 梁志勇 . 中国航空学报( 英文版) , 2002, 15 ( 3) : 181- 185. 摘 要: 在粘 度实验的基础上, 根据双 阿累尼乌斯 方程对用 于 RT M 工 艺的双马来 酰亚胺树 脂体 系 的化学流变特性进行了研究, 建立了树脂体 系的流变模型。通过 DSC 热分析实验研究树脂体系 的 固化反应规律, 验证了双阿累尼乌斯模型。研究表明, 模型与实验结果具有良好的一 致性。模型 可 揭示树脂体系在不 同工艺条件下的粘 度变化规律, 定量预报 RT M 工艺树脂的低 粘度平台 工艺 窗 口, 为 合理制定 RT M 工艺 参数、 保 证产品质 量和实现 工艺参 数的全 局优化 提供必要 的科学 依 据。 关 键词: 复合材料; R T M 工艺; 双马树脂; 流变模型; 固化 反应动力学 文 章编号: 1000-9361( 2002) 03-0181-05 中图分类号: T B 332 文献标识码: A
T he RT M process has been recog nized as a very high pot ent ial process f or adv anced compos-
it y ar ea can be def ined precisely . Hence , one can o pt imize t he RT M pro cess par am et ers and improve
ites m anuf act uring, and has been w idely used in many industr y f ields such as aero space , mobile and
t he qualit y o f the product s .
civil archit ect ure . T he RT M pro cess must depend on t he special low viscosit y resin, whose rheolog ical behavior co nt ains a low v isco sit y area meet ing t he demand o f t he RT M . T his means , the viscosi-
[ 3]
QY8911-4 BMI resin is a suit able resin f or RT M . In o rder t o optim ize the RT M process param et ers and improv e t he qualit y of t he product s , t he chemorheolog ical behav io r of t he QY8911-4
ty of t he r esin sho uld maint ain 50-200cP w hen in-
BM I resin is st udied, it s rheolog ical model is es[ 4-8] t abl ished , and a pro cessing w indo w is predicted
ject ed in molding f or complet e fill and fiber w et -
.
ting
[ 1, 2 ]
.
T heref ore,
t hr oug h est ablishing t he chemor heolog y m odel o f t he resin -v isco sit y f unctio n about t em perat ure and t ime ( o r cure degree ) ,
1 Viscosity Ex periment QY8911-4 BM I resin is pr epared f or det ermi-
t he resin viscosit y at any t em perat ur e and t im e( or
natio n of v isco sit y. Viscosit y det erminations are
cure deg ree) can be calculated, and t he l ow viscos-
carried out at dynam ic t em perat ur es and select ed
Received date: 2002-03-20; Revision recei ved dat e: 2002-03-21 Foundati on it ems: N at ional N at ural Science Foundat ion of C hina( 59833110) and N at ional Defence Foun dat ion( 00j00. 5. 3. hk 0144) A rt icl e U R L: ht t p: / / ww w . hk xb. net. cn/ cja/ 2002/ 03/ 0181/
LU Y ao , D U A N Y ue -xin, LIA N G Zhi-yong
・ 182・
2 Dual A rrhenius M odel
t em perat ures, using NDJ-1 r ot ating v isco meter, according t o GB 7193. 1. 1. 1 Vi scosity at heating condition T he v isco sit y curve of QY8911-4 BMI resin is show n as F ig . 1.
CJA
In t he case of isot hermal cur e, the viscosity , w hich is aff ect ed by t ime and temper ature, can be descr ibed into the dual Arrhenius m odel g iv en by
[ 3]
ln ( T , t ) = ln
∞
+ E /(RT ) +
k ∞tex p[ E k / ( R T ) ] w here
( 1)
and k ∞ are the Arrhenius preex po nent ial f act or s, respectively , w hile E and E k are respect ively t he act ivat io n energies f or t he f low and t he ∞
curing react ion. R is an ideal g as const ant . T he model can be simpl if ied lnA = ln ∞ + E / ( RT )
( 2)
lnB = lnk ∞ + E k / ( RT )
( 3)
Fo r QY 8911-4 BMI resin , it s viscosit y will descend w ith the heating condit ion . On t he ot her hand, it w ill ascend because o f r esin cross-linking.
So t he model can be described as ln ( T , t) = lnA + B t
( 4)
During heat ing t he r esin, viscosit y descending is pr im ary at low er t emperat ures; o therw ise ascend-
t ure are sho wn as F ig. 3.
ig . 1 V isco sity -temper ature curv e of BM I r esin system
T he curves of ln -t at t he isot herm al t empera-
ing is primary at higher t em perat ur es. T he viscosity will be a minim um when t he t w o ef f ect s keep balance . QY 8911-4 BMI resin w ill be m elt ed at 80℃. So viscosit y measurement begins at 80℃. Viscosit y maintains under 800cP bet w een 80℃ and 140℃. T herefo re, isot herm al v isco sit y measurement is select ed in t he rang e of 90-140℃. 1. 2 Isothermal viscosity measurement According to t he dynam ic viscosit y curv e, isot hermal v isco sit y measur em ent s ar e carried out at 90℃, 126℃ and 135℃. T he curv es of isot her mal viscosit y are show n as Fig . 2. T he viscosit y changing rat e is improved w it h t im e and temperature .
Fig. 3 ln vs t cur ves at isother mal temper atur e
Acco rding t o Fig . 3, t he m odel par am et ers l nA and B can be calculat ed ; t he result s are present ed in T abl e 1. Table 1 Parameters of the viscosity model T emperat ure/ ℃
l nA
B
90
5. 97
0. 008
126
4. 43
0. 039
135
3. 44
0. 060
T he cur ves of lnA -1/ T and lnB -1/ T are present ed in F ig . 4 and F ig . 5 respect ively . Acco rding to F ig . 4 and F ig . 5, o ne can obt ain t he f ollo wing relat ion about t he parameters l nA and lnB l nA = - 14. 91 + 7603/ T F ig . 2 I so therm al v iscosity -time cur ves
( 5)
lnB = 12. 98 - 6465/ T ( 6) No te t hat t he tim e unit should be chang ed
St udies on R heological Behaviors of Bism al eimide Resin Sys tem f or R es in T ransf er M ol ding
A ugus t 2002
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m ade in American Rheom et ric Scient if ic Com pany is used in t his st udy . T he resin samples are scanned at dif ferent heat ing rat es as 5℃/ min, 10℃/ min and 20℃/ min. And t he result s are show n in Fig . 6.
Fig. 4 lnA v s 1/ T o f the dual-A rr henius equatio n
Fig . 6 Dy namic DSC curv es at var io us heating ra tes
3. 2 Data analysis T he Kissing er funct ion is perf orm ed t o describe the curing react ion kinetics of t he t hermalset r esin. T he relation betw een t he t em perat ure at m aximum rate o f t he DSC curv e and the const ant
Fig . 5 lnB vs 1/ T of t he dual-A rr henius equa tio n
fr om m inut e t o second, and the rheo logical model of QY8911-4 BM I resin can be present ed as ln = - 14. 91 + 7603/ T + t ex p( 17. 07 - 6465/ T )
ln ( 7)
Fo r nonisot hermal cure, w here t he resin t em perat ur e hist ory is g iven by T = f ( t ) , t he viscosit y can be present ed as an int eg ral f orm ation as 7603 ln = - 14. 91 + + T ( t) t 6465 exp 17. 07 dt 0 T ( t)
∫
[ 12]
heating rat e is show n as fo llow s T 2m
= ( lnA + lnR - lnE) -
E RT m
( 9)
w here is the co nst ant heat ing rat e ; T m is t em perat ur e at max im um rat e; A is preex ponential f act or , and E is the act ivat io n energ y of t he curing reaction . 2 Acco rding to Eq . ( 9) , plot ln ( / T m ) vs 1/ T m as F ig. 7. T he slope is - E/ R , and t he int ercept is
( 8)
l nA + l nR - lnE.
3 React ion Kinetics T he curing react ion kinet ics of t he r esin is st udied by DSC analy sis [ 9-11] . In t his paper, a kinet ic model based on Kissinger funct ion is est ablished . T he paramet er s in t he kinet ic model —— pr eex ponent ial f act or and t he act ivat io n energy f or t he cur ing react io n—— are compar ed w it h the paramet ers in t he dual A rrhenius model , so the rat io nalit y of t he dual Arr henius mo del and t he physics def init io ns o f the m odel paramet er s ar e verified. 3. 1 DSC analysis Dif ferent ial Scanning Calorim et ry ( DSC )
F ig . 7 ln( / T 2m ) vs 1/ T m
T he act ivation energ y f or QY8911-4 resin sy st em is 98486J/ mo l, and t he preex ponent ial fact or is 21. 61. T he react ion order n can be det erm ined by t he peak shape f act or S of t he DSC curve. S is defined
LU Y ao , D U A N Y ue -xin, LIA N G Zhi-yong
・ 184・
as t he absolut e ratio value of t he t ang ent slopes at t he curve inflect ion point . T herefor e , n can be ob[ 13]
tained as t he fo llow ing equat io n n ≈ 1. 26S
1/ 2
( 10)
CJA
Table 2 The parameters of the two models para
dual A rr hen ius
K iss inger
Calc.
err or / %
k
17. 07
21. 61
21. 18
1. 96
E/ R
6465
11846
12594
6. 32
T he react ion o rder is 2. 076 f rom Fig . 6.
Acco rding t o the DSC analysis, one can con-
So t he cur ing react io n kinet ic model of QY 8911-4 r esin sy st em is show n as
clude t hat t he resin v isco sit y at t he low curing de-
d - 11846/ T 2. 076 = 21. 61e (1 - ) ( 11) dt Eq. 11 can be presented as an int egral f orm atio n as = 1 - [ 1 - ( 1 - 2. 076) 21. 61t e
( - 11846/ T )
1
] 1- 2. 076 ( 12)
T he cur ing degr ee v s t im e at dif ferent isot her mal temper atures is show n as Fig . 8.
g ree area can be calculat ed by t he dual Arrhenius m odel, and t he parameters in t he dual Arrhenius m odel and in cur ing react ion kinet ics have t he corresponding relation .
4 M odel Applicat ion 4. 1 Prediction of processing window T he resin viscosity at a cert ain t em perat ure and t im e can be calculat ed by t he dual Arrhenius m odel. T he v isco sit y m ap is show n as Fig . 9.
Fig . 8 Isot her mal cur ing deg ree v s time cur ves
According t o Fig . 8, the curing degr ee v s t im e show s t he linear rel at ion o n t he init ial stag e of t he curing react ion , and t he t im e maint aining the lin-
T he t em perat ures, at w hich the resin v isco sit y
ear r elat ion accords w it h t he t im e maint aining t he low v isco sit y in t he dual Arrhenius mo del. It is
is less than 800cP and t he t ime maintaining the low v isco sit y is mor e than 40 minut es, are 90℃,
cert ain t hat the assumpt io n fo r the dual Arr henius
100℃, 110℃ and 120℃. T herefo re, t he process-
model ( t he curing deg ree vs t im e show s the linear relatio n in the lo w viscosit y area ) is right .
ing w indow s o f t he QY8911-4 BM I resin sy st em
T he paramet er r elat ionship bet w een the dual Arrhenius model and t he Kissing er equat ion is present ed as the f ollo wing ex perience equation E= E
n- 1 k
and k = k
n- 1 ∞
( 13)
w here E and k are t he activ at ion energy and t he pr eex ponent ial f act or fr om t he Kissinger equat io n; E k and k ∞ are f rom t he dual Arrhenius m odel; n is
Fig . 9 V iscosity map
f or t he RT M pr ocessing are the t emper at ure range f rom 90 t o 120℃. 4. 2 Viscosity simul ation F or nonisot herm al cur e, w her e t he resin t emper at ure hist ory is given by T = f ( t) , t he v isco sit y can be present ed as t he int egral f orm ation as Eq. 8. So t he viscosit y can be simulated at t he g iven condit ion of t he t emperat ure as a funct io n o f t ime , and
T he results of t he paramet ers of t he dual Ar -
t he result s are show n in F ig . 10. T he resin is heat ed at a const ant r ate, m ain-
rhenius mo del co mpared wit h t he par am et ers o f t he Kissinger equat ion are show n in T able 2.
t ained at an assigned t emperat ure f or about 100 m inut es , and t hen heat ed again t o cure complete-
t he reactio n order .
St udies on R heological Behaviors of Bism al eimide Resin Sys tem f or R es in T ransf er M ol ding
A ugus t 2002
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1994. ) [ 2] Beckw it h S W , Craig R H . Resin t ran sf er molding , a decade of techn ology advances [ J] . SA M PE Journ al , 1998, 34( 6) : 297- 311. [ 3] G ut ow ski T G . A dvanced composit es manuf actu ring [ M ] . N ew Y ork: John W iley &Sons Inc, 1997. 393- 457. [ 4] R udd C D, Long A C , K endall K N , e t al . Liquid mol ding t echnol ogies [ M ] . London: W oodhead Pub lish ing Lt d, 1997. 23- 28. [ 5] Loos A C, Spring er G S . Curing of epox y mat rix composit es [ J ] . Journ al of composi te mat erials , 1983, 17 ( 3) : 135 -
ig . 10 Calcula ted v iscosity dur ing pr ocessing pro cedur e
167. [ 6] Hall ey P J , M ack ay M E. Chemorheology of t hermoset - an
ly. Fro m F ig. 10, o ne can get t he same t rends at
overview [ J] . Pol ymer Engin eering and Science, 1996, 36
dif ferent condit ions: At t he f irst heat ing st age, t he viscosit y dr ops cont inually , at isot hermal st ag e, t he viscosit y rises gr aduall y, and at t he second
( 5) : 593- 608. [ 7] Panag iot is I K , Ivana K P , A t t wood D avid. M odeling t he cure of a comm ercial epoxy res in f or app licat ions in res in t ransf er molding [ J ] . Polym er Int ernat ional, 1996, 41 ( 2) : 183- 191.
heat ing st age, the viscosit y dro ps mom ent ly and rises quickly t o a gel point .
[ 8] 梁志勇, 段跃 新, 林云等 . EPO N 862 环氧树脂体 系化学流变 特性研究 [ J] . 复合材料学报, 2001, 18 ( 1) : 16- 19.
Compared w ith dif ferent viscosit y curves, at
( L iang Z Y , Duan Y X , Lin Y . S t udies on rheological behav-
110℃ t he viscosity can maint ain less t han 300cP fo r 55 m inut es . So t he resin can be suit able t o manuf act ure the medium or small sized str uct ures
iors of EPO N 862 epoxy resin sys tem for res in trans fer m old-
as t he RT M processing . One can conf irm t hat t he t em perat ure at 110℃ is t he suit able injection t em perat ur e. If the part s ar e relatively larg e and t he inject ion t ime is long , t he temperatures at 90100℃ ar e t he suit able inject ion t emperat ure .
5 Conclusions QY8911-4 BM I r esin sy st em is the suit able resin f or t he RT M processing . T he dual Arr henius model can be used t o pr esent the rheo logical behav ior o f t he QY 8911-4 BMI r esin at low viscosit y ar eas. And t he model predictions are in g ood agreement wit h ex periment al dat a . T he pr ocessing w indow fo r t he RT M processing can be predicted precisely by t he dual Arrhenius mo del, and t he viscosity can be simulat ed dur ing t he processing procedure . T he rheolog ical model is import ant f or pro cessing optim ization and qualit y cont rol of RT M pr ocessing f or hig h perf orm ance com po sit es. References [ 1] 梁志勇, 段跃 新, 张佐光 . R T M 工艺 技术及 应用报 告( 技 术 鉴定报告) [ R] . 北京: 北京航空航天大学 104 教研室, 1994. ( Liang Z Y , Du an Y X , Zhan g Z G . R eport on RT M pr oces sing t echnol ogy and appl ication [ R] . Beijin g : Beijing U niversit y of A eronaut ics and A st ronaut ics 104 S taf f R oom ,
ing[ J ] . A cta M at eriae Composit ae Sin ica, 2001, 18 ( 1) : 1619. ) [ 9] Eckold C. D es ign and m anu fact ure of com pos it e st ruct ure [ M ] . N ew Y ork: M cG raw -Hill Inc, 1994. 271- 277. [ 10] K amal M R , S ou rour C. Ki net ics and t hermal charact erizat ion of t hermoset cure [ J] . Polymer Engineeri ng and S cience. 1973 ( 1) : 58- 77. [ 11] Lip shit z S D , M acosk o C W . R heological changes du ring a ur et hane net w ork polymerizat ion [ J ] . Pol ymer Engin eering and Science, 1976 ( 16) : 26- 38. [ 12] S hin D D , Hahn H T . A cons ist ent cure kinet ic model f or A S 4/ 3502 graphit e / epoxy [ J ] . Composit es Part A , 2000, 31: 991- 999. [ 13] 高家武, 高分子材料近代测试技术[ M ] . 北 京: 北京航空航天 大学出版社, 1994. 44- 45. ( G ao J W . M odern t est ing t echnol ogy on pol ymer material [ M ] . Beijin g: Beijing U n ivers ity of A eronaut ics and A st ronaut ies Pub lish ing Hou se, 1994. 44- 45. ( in Chin es e) )
Biographies: LU Yao Bor n in 1977, he r eceived B. S . and M . S . fro m Beijing U niv ersity of A er onautics and A stro naut ics in 1999 and 2002 r espectiv ely . T el: ( 010) 82317127, E -mail : luyao 2000@ 263. net