碳纤维/环氧树脂预浸料固化动力学建模研究

高腾龙; 余建虎; 许英杰

doi:10.13433/j.cnki.1003-8728.20200430

碳纤维/环氧树脂预浸料固化动力学建模研究

doi: 10.13433/j.cnki.1003-8728.20200430

1.
中国飞行试验研究院, 西安 710089
2.
西北工业大学机电学院, 西安 710072

详细信息

作者简介:
高腾龙(1993-), 工程师, 硕士, 研究方向为飞行载荷与强度研究, gao.tl@foxmail.com

中图分类号: TB332
计量
- 文章访问数: 93
- HTML全文浏览量: 231
- PDF下载量: 35
- 被引次数: 0
出版历程
- 收稿日期: 2019-08-12
- 刊出日期: 2022-07-25

Dynamic Modeling of Curing Process of Carbon/Epoxy Prepreg

1.
Chinese Flight Test Establishment, Xi′an 710089, China
2.
School of Mechanical Engineering, Northwestern Polytechnical University, Xi′an 710072, China

摘要

摘要: 采用动态及等温的差示扫描量热法(DSC)对碳纤维/环氧树脂预浸料体系的固化过程进行了研究，分别建立了预浸料的玻璃化转变温度方程和固化动力学方程。通过n级反应动力学模型、自催化模型以及改进后的Kamal模型3种方法对预浸料体系固化动力学方程进行建模和对比，并通过等温DSC试验数据对模型进行验证。最终结果表明，预浸料的固化过程可以分为两个子反应，改进后的Kamal模型能够更为准确的描述该固化过程，拟合数据与动态和等温试验数据均能很好的吻合。
- 动力学模型 /
- 差示扫描量热法 /
- 碳纤维/环氧树脂预浸料 /
- 固化度 /
- 固化动力学方程
Abstract: In this paper, the dynamic models for carbon/epoxy prepreg system was studied by nonisothermal and isothermal differential scanning calorimetry (DSC). The glass transition temperature (T_g) was firstly determined with DSC analysis as a function of curing degree of the samples. Subsequently, three kinetics mechanism equations consist of nth order reaction model, autocatalytic model as well as modified Kamal model were used to describe the curing process under dynamic condition. The modified Kamal model was finally adopted in view of the existence of two reactions in DSC curve. In addition, the prediction of modified Kamal model shows highly in accordance with the experimental via isothermal scans.
- dynamic model /
- differential scanning calorimetry (DSC) /
- carbon/epoxy prepreg /
- degree of cure /
- curing kinetics model

HTML全文

图 1 DSC差示扫描量热仪

下载: 全尺寸图片幻灯片

图 2 预浸料在20 ℃/min升温速率下DSC试验曲线

下载: 全尺寸图片幻灯片

图 3 等温DSC试验曲线

下载: 全尺寸图片幻灯片

图 4 不同升温速率下的DSC试验曲线

下载: 全尺寸图片幻灯片

图 5 玻璃化温度随固化度变化试验点及拟合曲线

下载: 全尺寸图片幻灯片

图 6 n级反应动力学模型ln(β/²T_p)-1/T_p关系图

下载: 全尺寸图片幻灯片

图 7 ln(dα/dt)+E/RT和ln(1-α)关系图

下载: 全尺寸图片幻灯片

图 8 10 ℃/min下n级反应动力学模型与试验数据对比

下载: 全尺寸图片幻灯片

图 9 动态DSC试验固化度随温度变化曲线

下载: 全尺寸图片幻灯片

图 10 自催化模型拟合曲线与试验数据对比

下载: 全尺寸图片幻灯片

图 11 升温速率为10 ℃/min时的分峰结果

下载: 全尺寸图片幻灯片

图 12 固化度与反应速率的关系

下载: 全尺寸图片幻灯片

图 13 Kamal模型中两子反应的ln(β/T_p²)-1/T_p关系图

下载: 全尺寸图片幻灯片

图 14 改进的Kamal模型拟合曲线与试验数据对比

下载: 全尺寸图片幻灯片

图 15 3种模型拟合曲线与试验数据对比

下载: 全尺寸图片幻灯片

图 16 模型等温固化预测与试验结果对比

下载: 全尺寸图片幻灯片

表 1 不同升温速率下的特征温度值

升温速率β/(℃·min^-1)	1	3	5	10	15	20
T_i/℃	141.2	166.0	177.6	190.3	200.7	208.4
T_p/℃	178.9	206.1	220.5	242.3	269.7	277.4
T_f/℃	244.6	265.6	278.9	297.1	308.6	316.2

下载: 导出CSV

表 2 不同升温速率下的总反应热量

升温速率β/(℃·min^-1)	1	3	5	10	15	20
ΔH₀/(J·g^-1)	118.6	129.8	111.2	106.1	132.5	123.3

下载: 导出CSV

表 3 不同固化度下材料的玻璃化温度和残余热量

固化度α	残余热量/(J·g^-1)	玻璃化温度/℃	玻璃化温度/K
0	120.250	1.98	275.13
0.466	64.230	70.50	343.65
0.653	41.570	100.40	373.55
0.841	19.060	139.00	412.15
0.927	8.812	158.40	431.55
0.997	0.416	181.00	454.15

下载: 导出CSV

表 4 自催化模型动力学参数拟合结果

β/(℃·min^-1)	1	3	5	10	15	20
A	622.4	717.27	757.18	907.57	964.55	1 089
m	0.212 2	0.182 6	0.179 4	0.199 2	0.198	0.219 1
n	1.136 3	0.957 2	0.871 1	0.805 1	0.751 8	0.739 1

下载: 导出CSV

表 5 不同升温速率下的峰值温度

β/(℃·min^-1)	1	3	5	10	15	20
峰值1/℃	178.9	206.9	220.5	239.8	257.7	267.2
峰值2/℃	198.8	228.7	240.7	254.9	269.7	277.4

下载: 导出CSV

表 6 改进的Kamal模型参数拟合结果

β/(℃·min^-1)	1	3	5	10	15	20
A₁(×10³s^-1)	6.913	6.997	6.866	5.822	4.620	4.927
A₂(×10⁵s^-1)	3.175	3.380	3.657	3.941	3.994	4.135
m	0.648	0.633	0.667	0.641	0.583	0.658
n₁	2.885	2.926	2.987	2.999	3.011	3.003
n₂	0.821	0.769	0.773	0.763	0.749	0.736

下载: 导出CSV

表 7 固化动力学模型对等温固化反应的预测

温度/℃	时间/min	残余热量/(J·g^-1)	总热量/(J·g^-1)	预测α	测量α
120	360	64.23	120.25	0.453	0.466
140	240	41.57	120.25	0.647	0.654
160	180	19.06	120.25	0.787	0.841
180	120	8.812	120.25	0.888	0.927
200	120	0.416	120.25	0.993	0.997

下载: 导出CSV

参考文献(25)

[1]	DING A X, LI S X, WANG J H, et al. A new path-dependent constitutive model predicting cure-induced distortions in composite structures[J]. Composites Part A: Applied Science and Manufacturing, 2017, 95: 183-196 doi: 10.1016/j.compositesa.2016.11.032
[2]	MAHNKEN R, DAMMANN C. A three-scale framework for fibre-reinforced-polymer curing part I: microscopic modeling and mesoscopic effective properties[J]. International Journal of Solids and Structures, 2016, 100-101: 341-355 doi: 10.1016/j.ijsolstr.2016.09.003
[3]	YUAN Z Y, WANG Y J, PENG X Q, et al. An analytical model on through-thickness stresses and warpage of composite laminates due to tool-part interaction[J]. Composites Part B: Engineering, 2016, 91: 408-413 doi: 10.1016/j.compositesb.2016.01.016
[4]	ZHANG G M, WANG J H, NI A Q. Process-induced stress and deformation of variable-stiffness composite cylinders during curing[J]. Materials, 2019, 12(2): 259 doi: 10.3390/ma12020259
[5]	SHAH D B, PATEL K M, PATEL A I, et al. Experimental investigation on spring-back deformation during autoclave curing of parabolic antenna reflectors[J]. Composites Part A: Applied Science and Manufacturing, 2018, 115: 134-146 doi: 10.1016/j.compositesa.2018.09.017
[6]	STARK W. Investigation of the curing behaviour of carbon fibre epoxy prepreg by dynamic mechanical analysis DMA[J]. Polymer Testing, 2013, 32(2): 231-239 doi: 10.1016/j.polymertesting.2012.11.004
[7]	VAN ASSCHE G, VAN HEMELRIJCK A, RAHIER H, et al. Modulated differential scanning calorimetry: isothermal cure and vitrification of thermosetting systems[J]. Thermochimica Acta, 1995, 268: 121-142 doi: 10.1016/0040-6031(95)02693-2
[8]	ZHENG T, WANG X D, LU C R, et al. Studies on curing kinetics and tensile properties of silica-filled phenolic amine/epoxy resin nanocomposite[J]. Polymers, 2019, 11(4): 680 doi: 10.3390/polym11040680
[9]	CHAIWAN P, KAEWKITTINARONG A, PUMCHUSAK J. Nonisothermal curing kinetics of solid resole by differential scanning calorimetry[J]. Thermochimica Acta, 2019, 675: 119-126 doi: 10.1016/j.tca.2019.03.023
[10]	LIU Z F, XIAO J Y, BAI S X, et al. Study on phenomenological curing model of epoxy resin for prediction of degree of cure[J]. Journal of Thermal Analysis and Calorimetry, 2012, 109(3): 1555-1561 doi: 10.1007/s10973-011-2070-z
[11]	FLORES H A, FASCE L A, RICCARDI C C. On the cure kinetics modeling of epoxy-anhydride systems used in glass reinforced pipe production[J]. Thermochimica Acta, 2013, 573: 1-9 doi: 10.1016/j.tca.2013.09.004
[12]	廖栋, 颜春, 潘利剑, 等. 非等温DSC法研究苯并恶嗪树脂固化反应动力学[J]. 热固性树脂, 2011, 26(1): 1-5 https://www.cnki.com.cn/Article/CJFDTOTAL-RGXS201101002.htm LIAO D, YAN C, PAN L J, et al. Study on curing kinetics of benzoxazine resin using non-isothermal DSC method[J]. Thermosetting Resin, 2011, 26(1): 1-5 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-RGXS201101002.htm
[13]	ZHOU T L, WANG X, LIU X H, et al. Influence of multi-walled carbon nanotubes on the cure behavior of epoxy-imidazole system[J]. Carbon, 2009, 47(4): 1112-1118 doi: 10.1016/j.carbon.2008.12.039
[14]	YANG K, GU M Y, JIN Y P. Cure behavior and thermal stability analysis of multiwalled carbon nanotube/epoxy resin nanocomposites[J]. Journal of Applied Polymer Science, 2008, 110(5): 2980-2988 doi: 10.1002/app.28898
[15]	SHIN D D, HAHN H T. A consistent cure kinetic model for AS4/3502 graphite/epoxy[J]. Composites Part A: Applied Science and Manufacturing, 2000, 31(9): 991-999 doi: 10.1016/S1359-835X(00)00011-7
[16]	KIM Y K, WHITE S R. Process-induced stress relaxation analysis of AS4/3501-6 laminate[J]. Journal of Reinforced Plastics and Composites, 1997, 16(1): 2-16 doi: 10.1177/073168449701600102
[17]	VAFAYAN M, BEHESHTY M H, GHOREISHY M H R, et al. The prediction capability of the kinetic models extracted from isothermal data in non-isothermal conditions for an epoxy prepreg[J]. Journal of Composite Materials, 2014, 48(9): 1039-1048 doi: 10.1177/0021998313482020
[18]	吴晓青, 李嘉禄, 康庄, 等世. TDE-85环氧树脂固化动力学的DSC和DMA研究[J]. 固体火箭技术, 2007, 30(3): 264-268 doi: 10.3969/j.issn.1006-2793.2007.03.020 WU X Q, LI J L, KANG Z, et al. Study on curing kinetics of TDE-85 epoxy resin by means of DSC and DMA[J]. Journal of Solid Rocket Technology, 2007, 30(3): 264-268 (in Chinese) doi: 10.3969/j.issn.1006-2793.2007.03.020
[19]	D'ELIA R, DUSSERRE G, DEL CONFETTO S, et al. Cure kinetics of a polysilazane system: experimental characterization and numerical modelling[J]. European Polymer Journal, 2016, 76: 40-52 doi: 10.1016/j.eurpolymj.2016.01.025
[20]	SIDDIQUI A O, SUDHER P, MURTHY B V S R. Cure kinetics modeling of cyanate-ester resin system[J]. Thermochimica Acta, 2013, 554: 8-14 doi: 10.1016/j.tca.2012.12.009
[21]	HESEKAMP D, BROECKER H C, PAHL M H. Chemo-rheology of cross-linking polymers[J]. Chemical Engineering Technology, 1998, 21(2): 149-153 doi: 10.1002/(SICI)1521-4125(199802)21:2<149::AID-CEAT149>3.0.CO;2-P
[22]	KISSINGER H E. Reaction kinetics in differential thermal analysis[J]. Analytical Chemistry, 1957, 29(11): 1702-1706 doi: 10.1021/ac60131a045
[23]	OZAWA T. Kinetic analysis of derivative curves in thermal analysis[J]. Journal of Thermal Analysis, 1970, 2(3): 301-324 doi: 10.1007/BF01911411
[24]	SULTANIA M, RAI J S P, SRIVASTAVA D. Modeling and simulation of curing kinetics for the cardanol-based vinyl ester resin by means of non-isothermal DSC measurements[J]. Materials Chemistry and Physics, 2012, 132(1): 180-186 doi: 10.1016/j.matchemphys.2011.11.022
[25]	SUN L F, PANG S S, STERLING A M, et al. Dynamic modeling of curing process of epoxy prepreg[J]. Journal of Applied Polymer Science, 2002, 86(8): 1911-1923 doi: 10.1002/app.11146