Long-term Stress Relaxation Prediction for Nylon 1010 Using Time-temperature Superposition Method†

doi:10.7503/cjcu20180685

Abstract

Abstract:

Stress relaxation behavior of plastic has great influence on its service life and safety. The master curves were generated by horizontal and vertical shifts of the short term curves of stress relaxation for Nylon 1010 at temperatures ranging from 293 K to 353 K using proposed time-temperature superposition equivalence method. The apparent activation energy was calculated from the Arrhenius plots of shift factor, and the values of activation volume and stress-assisted work were calculated from the master curves. The time-temperature superposition principle was found to be available for the stress relaxation curves. During the superposition interval of the experimental temperature from 293 K to 323 K, the apparent activation energy and stress-assisted work show a tendency to decrease gradually, which is helpful for the relaxation of the moving units in the polymer over the energy barrier. During the superposition interval of the experimental temperature from 333 K to 353 K, the apparent activation energy of different initial strain samples is about the same value of 260 kJ/mol and the stress-aided work is basically unchanged at the value of 60 MPa·nm³, which indicates that the energy barrier of the moving unit is independent of the stress effect. According to the mater curves of Nylon 1010, the relationship between stress decay and relaxation time in a long time range can be obtained under the strain of 1.0%, 2.8% and 5.1%, which provides a reference for predicting stress relaxation behavior in practical use.

Key words: Nylon 1010, Stress relaxation, Time-temperature superposition, Apparent activation energy, Activation volume, Stress-aided work

CLC Number:

O631

TrendMD:

CAI Lihai,GUO Baohua,ZHANG Cheng,XU Jun,HUANG Zhongyao. Long-term Stress Relaxation Prediction for Nylon 1010 Using Time-temperature Superposition Method^†[J]. Chem. J. Chinese Universities, 2019, 40(4): 832.

Figures/Tables 11

Fig.1 Relaxation modulus of relaxation samples under different initial strains(A) 1.0% strain; (B) 2.8% strain; (C) 5.1% strain. 293 K; 303 K; 313 K; 323 K; 333 K; 343 K; 353 K.

Fig.2 Fitting the dimension in linear expansion test of Nylon 1010

Fig.3 X-Ray diffraction patterns of Nylon 1010 samples(A) Initial; (B) 5.1% strain at 293 K; (C) 5.1% strain at 313 K; (D) 5.1% strain at 353 K.

Fig.4 Azimuthal X-ray diffraction intensity curves of Nylon 1010 samples(A) (002) reflection; (B) (100) reflection. a. Initial; b. 5.1% strain at 293 K; c. 5.1% strain at 313 K; d. 5.1% strain at 353 K.

Table 1 Crystallinity(Xc) and orientation degree(Π) of Nylon 1010 samples

Sample	ΔH/(J×g^-1)	X_c(%)	Π(%)
Initial	93.6	38.4	51.2
5.1% strain at 293 K	94.8	38.9	50.5
5.1% strain at 313 K	93.5	38.3	52.2
5.1% strain at 333 K	95.5	39.1
5.1% strain at 353 K	94.6	38.8	50.3

Fig.5 DSC curves of Nylon 1010 samples

Fig.6 Master curves of relaxation modulus for the samples in the strain of 1.0%(A), 2.8%(B) and 5.1%(C)

Fig.7 Temperature dependence of logarithm of shift factor for the samples(A) lnαT and T; (B) lnαT and T-1.

Table 2 Apparent activation energies(ΔHa) in Arrhenius plots of Fig.6

Initial strain(%)	ΔH_a/(kJ×mol^-1)	Temperature/K
1.0	596	293—323
	263	333—353
2.8	432	293—323
	259	333—353
5.1	356	293—323
	258	333—353

Fig.8 Curves of σ*Va vs. lgt(A) and σ*(B) calculated from the master curves of Fig.6

Fig.9 Master curves of relaxation samples under the initial strains of 1.0%(A), 2.8%(B), 5.1%(C) and the comparison of different strains(D)

References 50

[1]	Tobolsky A. V., J. Appl.Phys., 1956, 27(7), 673—685
[2]	Dotsenko V. I., Phys. Status Solidi B, 1979, 93(1), 11—43
[3]	Kubat J., Nilsson L. A., Rigdahl M., Mater. Sci.Eng.,1982, 53(2), 199—208
[4]	Kubat J., Nilsson L. A., Mater. Sci.Eng.,1982, 52(3), 223—228
[5]	Kubat J., Rigdahl M., Selden R., J. Appl. Polym.Sci.,1976, 20(10), 2799—2809
[6]	Lu Y., Yang W., Zhang K., Yang M. B., Polym.Test.,2010, 29(7), 866—871
[7]	Mohomane S., Djokovic V., Thomas S., Luyt A. S., Polym.Test.,2011, 30(5), 585—593
[8]	Hejlova A., Blahovec J., Polym. Eng.Sci.,2015, 55(3), 624—633
[9]	Razavi-Nouri M., Iran. J. Chem.Eng., 2012, 9(1), 60—69
[10]	Bagley R. L., Torvik P., J.Rheol.,1983, 27(3), 201—210
[11]	Dobreva A., Gutzow I., Schmelzer J., J. Non-Cryst.Solids,1997, 209(3), 257—263
[12]	Fancey K. S., J. Mater.Sci., 2005, 40(18), 4827—4831
[13]	Ghosh A., Das S., Banerjee D., Indian J. Fibre Text. Res.,2013, 38(4), 375—379
[14]	Koeller R. C., J. Appl.Mech., 1984, 51(2), 299—307
[15]	Chen Y., Chen H. S., Kang Y. G., Chem. J. Chinese Universities,2006, 27(11), 2160—2163
	(陈艳, 陈宏善, 康永刚. 高等学校化学学报, 2006, 27(11), 2160—2163)
[16]	Chen H. S., Li M. M., Kang Y. G., Zhang S. L., Chem. J. Chinese Universities,2008, 29(6), 1271—1275
	(陈宏善, 李明明, 康永刚, 张素玲. 高等学校化学学报, 2008, 29(6), 1271—1275)
[17]	Kubat J., Nilsson L. A., Rigdahl M., Mater. Sci.Eng.,1983, 61(3), 267—274
[18]	Kubat J., Selden R., Rigdahl M., J. Appl. Polym.Sci.,1978, 22(6), 1715—1723
[19]	Shaw M.T., Macknight W. J., Introduction to Polymer Viscoelasticity(3rd Ed.), Translated by Li Y. N., East China University of Science and Technology Press, Shanghai, 2012, 117—121
	(李怡宁[译]李怡宁[译]. 聚合物黏弹性引论(第三版), 上海: 华东理工大学出版社, 2012, 82—98)
[20]	Zeng H. M., Chen H. M., Chem. J. Chinese Universities,1986, 7(12), 1140—1145
	(曾汉民, 陈海宁. 高等学校化学学报, 1986, 7(12), 1140—1145)
[21]	Lv Y.F., Yang X. Z., Zhu S. N., Li X. K.,Acta Chim. Sin., 1983, (6), 525—533
	(吕亚非, 杨小震, 朱善农, 李相魁. 化学学报, 1983, (6), 525—533)
[22]	Yang X.Z., Hu S. R., Lv Y. F., Zhu S. N., Li X. K.,Polym. Commun., 1985, (3), 202—206
	(杨小震, 胡世如, 吕亚非, 朱善农, 李相魁. 高分子通讯, 1985, (3), 202—206)
[23]	Mo Z.S., Zhang H. F., Meng Q. B., Xue X. F., Zhang L. H.,Acta Polym. Sin., 1990, (6), 655—660
	(莫志深, 张宏放, 孟庆波, 薛小芙, 张利华. 高分子学报, 1990, (6), 655—660)
[24]	Fu S. R., Zhang G., Tan Q., Yang Y., J. Therm.Anal.,1993, 40(2), 689—695
[25]	Feng J. H., Mo Z. S., Chen D. L., Chinese J. Polym.Sci.,1990, 8(1), 61—68
[26]	Zhu C. S., Li X. D., Pu S. T., Chem. J. Chinese Universities,1991, 12(12), 1677—1680
	(朱诚身, 李修道, 李华光, 蒲帅天. 高等学校化学学报, 1991, 12s(12), 1677—1680)
[27]	Zhu C. S., Mo Z. S., Mou Z. C., Chem. J. Chinese Universities,1992, 13(6), 864—866
	(朱诚身, 莫志深, 牟忠诚. 高等学校化学学报, 1992, 13(6), 864—866)
[28]	Mo Z. S., Meng Q. B., Feng J. H., Zhang H. F., Chen D. L., Polym.Int.,1993, 32(1), 53—60
[29]	Zeng H. M., Chen H. N., Chem. J. Chinese Universities,1986, 7(9), 851—856
	(曾汉民, 陈海宁. 高等学校化学学报,1986, 7(9), 851—856)
[30]	Zhu C. S., Chen Y., Yang G. P., Wang Y. W., Wang J. W., Mo Z. S., Chem. J. Chinese Universities,1996, 17(5), 805—807
	(朱诚身, 陈玉, 杨桂萍, 王友文, 王经武, 莫志深. 高等学校化学学报, 1996, 17(5), 805—807)
[31]	Wang J. K., Zhao G. S., Zhou Y. C., Chem. J. Chinese Universities,2011, 32(5), 1225—1230
	(王继库, 赵国升, 周云春. 高等学校化学学报, 2011, 32(5), 1225—1230)
[32]	Lu H. B., Zhang X. Y., Zhang H., J. Appl.Phys.,2006, 100(054104), 1—7
[33]	Lu H. B., Zhang X. Y., J. Macromol. Sci. Part B,2006, 45(5), 933—944
[34]	Cai L.H., Zhang C., Guo B. H., Xu J., Huang Z. Y.,Acta Polym. Sin., 2016, (3), 382—390
	(蔡利海, 张诚, 郭宝华, 徐军, 黄忠耀. 高分子学报, 2016, (3), 382—390)
[35]	Cai L. H., Qi Z. G., Xu J., Guo B. H., Huang Z. Y., Chinese Chem.Lett.,2017, 28(5), 949—954
[36]	Ferry J. D., J. Am. Chem.Soc., 1950, 72(8), 3746—3752
[37]	Nagamatsu K., Kolloid Z., 1960, 172(2), 141—162
[38]	Nagamatsu K., Yoshitomi T., J. Colloid Sci.,1959, 14(4), 377—384
[39]	Yoshitomi T., Nagamatsu K., Kosiyama K., J. Appl. Polym.Sci.,1958, 27(115), 335—347
[40]	Nagamatsu K., Yoshitomi T., Takemoto T., J. Colloid Sci.,1958, 13(3), 257—265
[41]	Williams M. L., Bender M. F., J. Appl.Phys.,1965, 36(10), 3044—3049
[42]	Murayama T., Dumbleton J. H., Williams M. L., J. Macromol. Sci., Part B,1967, 1(1), 1—14
[43]	Tajvidi M., Falk R. H., Hermanson J. C., J. Appl. Polym.Sci.,2005, 97(5), 1995—2004
[44]	Nakano T., Mech. Time-Depend Mater., 2013, 17(3), 439—447
[45]	Zhang J., Jiang H., Jiang C., Kang G., Lu F., Polym.Test.,2015, 44(7), 8—14
[46]	Van Krevelen D.W., Nijenhuis K. T., Properties of Polymers(4th Ed.), Science Press, Beijing, 2010, 89—101
[47]	Mo Z.S., Zhang H. F., Zhang J. D., Structure of Crystalline Polymers by X-Ray Diffraction(2nd Ed.), Science Press, Beijing, 2003, 234
	(莫志深, 张宏放, 张吉东. 晶态聚合物结构和X射线衍射(第2版), 北京: 科学出版社, 2003, 234)
[48]	Gupta V., Rao D. R., J. Appl. Polym.Sci.,1992, 45(2), 253—263
[49]	William M., Landel R., Ferry J., J. Am. Chem.Soc.,1955, 77(14), 3701—3707
[50]	Brostow W., Corneliussen R.D., Failure of Plastics, Hanser Press, New York, 1986, 60—83