การจำแนกพฤติกรรมรีโอโลยีของวัสดุจากการทดสอบเฉือนเป็นรอบ
DOI: 10.14416/j.ind.tech.2020.12.009
คำสำคัญ:
การทดสอบแบบเฉือนเป็นรอบ; การจำแนกพฤติกรรมรีโอโลยีของวัสดุ; พิกัดอีโวล์ด; แผนภาพพิพคินบทคัดย่อ
วัตถุประสงค์ของบทความนี้ต้องการจำแนกพฤติกรรมของวัสดุ และสมบัติรีโอโลยีที่ได้จากการทดสอบแบบเฉือนเป็นรอบ (Oscillatory Shear) ซึ่งเป็นการทดสอบที่ได้รับการยอมรับในแวดวงวิชาการ ในการใช้เป็นเครื่องมือในการจำแนกวัสดุ ในบทความนี้จะใช้ตัวแปรตามประกาศสมาคมรีโอโลยีแห่งสหรัฐอเมริกา (Society of Rheology, SOR) ที่มีการแบ่งการทดสอบแบบเฉือนเป็นรอบที่ความเครียดต่ำ (Small Amplitude Oscillatory Shear, SAOS) ที่มีเลขไร้มิติไวซ์เซนเบิร์กต่ำ Wi < 1 ที่ซึ่งความเค้นเป็นฟังก์ชันเชิงเส้นกับความเครียด และการทดสอบแบบเฉือนเป็นรอบที่ความเครียดสูง (Large Amplitude Oscillatory Shear, LAOS) Wi > 1 ซึ่งความเค้นจะเขียนอยู่ในรูปของอนุกรมคำตอบของฟูริเยร์ (Fourier Series Solutions) ที่จะประกอบไปด้วยชุดคำตอบหลายชุดรวมกัน การทดสอบแบบเฉือนเป็นรอบ (Oscillatory Shear) สามารถเขียนวิเคราะห์ในรูปสมการเชิงซ้อนได้ ทำให้สะดวกในการศึกษาพฤติกรรมของพอลิเมอร์เหลวที่มีการรับแรงทางกลแบบพลวัติ (Dynamic Mechanical Load) ได้ดี และเป็นที่ยอมรับในแวดวงวิชาการ ในการทดสอบเพื่อจำแนกพฤติกรรมของวัสดุและสมบัติทางรีโอโลยีโดยใช้พิกัดอีโวล์ดบนแผนภาพพิพคิน
References
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[13] C. Saengow and A.J. Giacomin Exact Solutions for Oscillatory Shear Sweep Behaviors of Complex Fluids from Oldroyd 8-Constant Framework, Physics of Fluids, 2018, 30, 030703.
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[17] C. Kolitawong, Local Shear Stress Transduction in Sliding Plate Rheometry, Section 4.2, Ph.D. Dissertation, The University of Wisconsin-Madison, USA. 2002.
[18] J.D. Ferry, Viscoelastic properties of polymers, 2nd. ed., John Wiley & Sons, Inc., NY, USA, 1970.
[19] J.G. Nam, K. Hyun, K.H. Ahn and S.J. Lee, Phase Angle of the First Normal Stress Difference in Oscillatory Shear Flow, Korea-Australia Rheology Journal, 2010, 22(4), 247-258.
[20] C. Saengow and A.J. Giacomin, Normal Stress Differences from Oldroyd 8-Constant Framework: Exact Analytical Solution For Large-Amplitude Oscillatory Shear Flow, Physics of Fluids, 2017, 29, 121601.
[21] C. Saengow, A.J. Giacomin, C. Kolitawong Exact Analytical Solution for Large-Amplitude Oscillatory Shear Flow, Macromolecular Theory and Simulations, 2015, 24(4), 352-392.
[22] A.J. Giacomin, C Saengow, M Guay, C Kolitawong, Padé Approximants for Large-Amplitude Oscillatory Shear Flow, Rheologica Acta, 2015, 54, 679-693.
[23] F.B. Hildebrand, Advanced calculus for applications, Chapter 10, 2nd ed., Prantice-Hall, Inc., NJ, USA. 1976.
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[25] [ ] A.J. Giacomin and R.B. Bird, Erratum: Official Nomenclature of The Society of Rheology: -’’, Journal of Rheology, 2011, 55(4), 921-923.
[26] G. Marin, Oscillatory Rheometry, Chapter 1, Rheological Measurement, 2nd ed., Chapman and Hall, London & New York, 1998, p.3-46.
[27] A.C. Pipkin, Lectures in Viscoelastic Theory, Springer-Verlag, NY, USA, 1972.
[28] N. Eiamnipon, P. Nimdum, J. Renard and C. Kolitawong, (2012) Low Velocity Impact Responses and Impact-Induced Damages on Steel Cord-Rubber Composite, ECCM-15th European Conference on Composite Materials, Proceedings, 1-6.
[29] R.H. Ewoldt, A.E. Hosoi and G.H. McKinley, New Measures for Characterizing Nonlinear Viscoelasticity in Large Amplitude Oscillatory Shear, Journol of Rheology, 2008, 52, 1427.
[30] R.H. Ewoldt, P. Winter, J. Maxey and G.H. McKinley, Large Amplitude Oscillatory Shear of Pseudoplastic and Elastoviscoplastic Materials, Rheologica Acta, 2010, 49, 191-212.
[31] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series No. 55, U.S. Govt. Printing Office, Washington, D.C, USA, 1964, p.776.
[32] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 9th printing, Dover, NY, USA, 1972, p.776.
[2] S. Wangchai, C. Kolitawong, and A. Chaikittiratna, Finite Element Simulation for Heat Built-up in Vulcanized Natural Rubber Subjected to Dynamic Load, The Journal of King Mongkut’s University of Technology North Bangkok, 2008, 18(3), 49-61. (in Thai).
[3] S. Wangchai, C. Kolitawong, and A. Chaikittiratna, Finite Element Analysis of Heat Generation in Particle Filled Natural rubber Valcanizates During Cyclic Deformation, The Journal of King Mongkut’s University of Technology North Bangkok, 2011, 21(1), 754-762. (in Thai).
[4] I.M. Ward and J. Sweeney, An Introduction to The Mechanical Properties of Solid Polymers, Chapter 7, 2nd ed., John Wiley & Sons, Ltd., West Sussex, UK, 2004.
[5] W. Gleißle, Rate- or Stress-Controlled Rheometry, Chapter 12, Rheological Measurement, 2nd ed., Chapman and Hall, London & New York, USA, 1998, p.357-391.
[6] K.S. Cho, Viscoelasticity of Polymers: Theory and Numerical Algorithms, Section 2.3, Chapter 5 and Chapter 11, Springer Series in Materials Science Vol. 241, Springer, Dordrecht. 2016.
[7] C. Saengow, A.J. Giacomin, P.H. Gilbert and C. Kolitawong, Reflections on Inflections, Korea-Australia Rheology Journal, 2015, 27(4), 267-285.
[8] Ad Hoc Committee on Official Nomenclature and Symbols, Official Symbols and Nomenclature of the Society of Rheology, Journal of Rheology, 2013, 57, 1047.
[9] J.M. Dealy, Official Nomenclature for Material Functions Describing the Response of a Viscoelastic Fluid to Various Shearing and Extensional Deformations, Journal of Rheology, 1984, 28, 181.
[10] J.M. Dealy, Official Nomenclature for Material Functions Describing the Response of a Viscoelastic Fluid to Various Shearing and Extensional Deformations, Journal of Rheology, 1995, 39, 253.
[11] R.J. Poole, The Deborah and Weissenberg Numbers, The British Society of Rheology, Rheology Bulletin, 2012, 53(2), 32-39.
[12] C. Saengow, A.J. Giacomin, and C. Kolitawong, Exact Analytical Solution for Large-Amplitude Oscillatory Shear Flow From Oldroyd 8-Constant Framework: Shear Stress, Physics of Fluids, 2017, 29(4), 043101.
[13] C. Saengow and A.J. Giacomin Exact Solutions for Oscillatory Shear Sweep Behaviors of Complex Fluids from Oldroyd 8-Constant Framework, Physics of Fluids, 2018, 30, 030703.
[14] P. Poungthong, C. Saengow, A.J. Giacomin, C. Kolitawong, D.M. Merger, and M. Wilhelm, Padé Approximation for Normal Stress Differences in Large-Amplitude Oscillatory Shear Flow, Physics of Fluids, 2018, 30(4), 040910.
[15] J.M. Dealy, and K.F. Wissbrun, Melt Rheology and its Role in Plastics Processing: Theory and Applications, Section 5.7, Van Nostrand Reinhold, New York. 1990.
[16] A.J. Giacomin and J.M. Dealy, Using large-amplitude oscillatory shear, Chapter 11, Rheological Measurement, 2nd ed., Chapman and Hall, London & New York, 1998, p.327-356.
[17] C. Kolitawong, Local Shear Stress Transduction in Sliding Plate Rheometry, Section 4.2, Ph.D. Dissertation, The University of Wisconsin-Madison, USA. 2002.
[18] J.D. Ferry, Viscoelastic properties of polymers, 2nd. ed., John Wiley & Sons, Inc., NY, USA, 1970.
[19] J.G. Nam, K. Hyun, K.H. Ahn and S.J. Lee, Phase Angle of the First Normal Stress Difference in Oscillatory Shear Flow, Korea-Australia Rheology Journal, 2010, 22(4), 247-258.
[20] C. Saengow and A.J. Giacomin, Normal Stress Differences from Oldroyd 8-Constant Framework: Exact Analytical Solution For Large-Amplitude Oscillatory Shear Flow, Physics of Fluids, 2017, 29, 121601.
[21] C. Saengow, A.J. Giacomin, C. Kolitawong Exact Analytical Solution for Large-Amplitude Oscillatory Shear Flow, Macromolecular Theory and Simulations, 2015, 24(4), 352-392.
[22] A.J. Giacomin, C Saengow, M Guay, C Kolitawong, Padé Approximants for Large-Amplitude Oscillatory Shear Flow, Rheologica Acta, 2015, 54, 679-693.
[23] F.B. Hildebrand, Advanced calculus for applications, Chapter 10, 2nd ed., Prantice-Hall, Inc., NJ, USA. 1976.
[24] F.A. Morrison, Understanding Rheology, Section 5.2.2.6, Oxford University Press, NY, USA, 2001.
[25] [ ] A.J. Giacomin and R.B. Bird, Erratum: Official Nomenclature of The Society of Rheology: -’’, Journal of Rheology, 2011, 55(4), 921-923.
[26] G. Marin, Oscillatory Rheometry, Chapter 1, Rheological Measurement, 2nd ed., Chapman and Hall, London & New York, 1998, p.3-46.
[27] A.C. Pipkin, Lectures in Viscoelastic Theory, Springer-Verlag, NY, USA, 1972.
[28] N. Eiamnipon, P. Nimdum, J. Renard and C. Kolitawong, (2012) Low Velocity Impact Responses and Impact-Induced Damages on Steel Cord-Rubber Composite, ECCM-15th European Conference on Composite Materials, Proceedings, 1-6.
[29] R.H. Ewoldt, A.E. Hosoi and G.H. McKinley, New Measures for Characterizing Nonlinear Viscoelasticity in Large Amplitude Oscillatory Shear, Journol of Rheology, 2008, 52, 1427.
[30] R.H. Ewoldt, P. Winter, J. Maxey and G.H. McKinley, Large Amplitude Oscillatory Shear of Pseudoplastic and Elastoviscoplastic Materials, Rheologica Acta, 2010, 49, 191-212.
[31] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series No. 55, U.S. Govt. Printing Office, Washington, D.C, USA, 1964, p.776.
[32] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 9th printing, Dover, NY, USA, 1972, p.776.
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