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Experimental investigation on the yield loci of PA66
Polymer Testing 51 (2016) 148e150
Contents lists available at ScienceDirect
Polymer Testing journal homepage: www.elsevier.com/locate/polytest
Short communication: test method
Experimental investigation on the yield loci of PA66 Tao Jin a, b, Zhiwei Zhou c, Xuefeng Shu a, b, *, Zhihua Wang a, b, Guiying Wu d, Longmao Zhao a, b a
Institute of Applied Mechanics and Biomedical Engineering, Taiyuan University of Technology, Taiyuan 030024, China Shanxi Key Laboratory of Material Strength and Structural Impact, Taiyuan 030024, China c State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, 730000, China d Department of Mechanics, Taiyuan University of Technology, Taiyuan 030024, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 January 2016 Accepted 6 March 2016 Available online 10 March 2016
Compression, tensile and mixed compression/shear tests were performed on PA66 by using a universal material testing machine in order to identify the experimental yield loci of PA66. For the mixed compression/shear tests, instead of using a complex loading device, SCS (shear-compression specimens) were used to generate the additional shear stresses. Then, the mechanical behavior of materials under complex stress states can be obtained for further analysis. Results show that the experimental yield loci of PA66 obtained by the test method proposed in the present paper agree well with the theoretical model based on three stresses invariant, which indicates the reliability of the test method. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Polymers Elastic properties Shear-compression specimen Yield surface Test method
1. Introduction Semi-crystalline polymers are widely used as structural components in manufacturing industry for their ease of moulding and ability to be recycled [1]. Such components always suffer in a complex environment during service. Therefore, the mechanical behavior of materials under different stress states should be understood to be helpful to the material manufacturing and design. Recently, Zhou [2] investigated the failure behavior of PMMA under different loading conditions by applying a complex loading device which consisted of a short cylindrical bars system with beveled ends and a sleeve made of Teflon to apply the combined shear-compression on cubic samples. Similarity, Jin et al. [3] studied the PMMA mechanical response under mixed shear-compression based on specific sample geometries and found that the mechanical behavior of PMMA is sensitive to the introduction of shear stress, whereas the stress state of the specimen during test is not uniform, which may result in some uncertain errors. Given this situation, a shear-compression specimen (SCS) which consists of a short cylinder into which two slots have been machined
* Corresponding author. Institute of Applied Mechanics and Biomedical Engineering, Taiyuan University of Technology, Taiyuan 030024, China. Tel./fax: þ86 351 6014455. E-mail address: [email protected] (X. Shu). http://dx.doi.org/10.1016/j.polymertesting.2016.03.007 0142-9418/© 2016 Elsevier Ltd. All rights reserved.
at a certain angle to the longitudinal axis [4] could be introduced to investigate the material's yield behavior. In addition, the stress and strain fields in the gage section of SCS are uniform, which has been verified by Rittel [4]. Therefore, there will be at least two advantages of a simple loading device and uniform stress state if the SCS is applied in the investigation of the yield loci of materials. Hence, the major aim of this paper is to present a new test method to identify the yield loci of PA66. 2. Experimental procedure The material tested in this investigation was PA66. A commercial grade of the material was purchased from a supplier under the trade name, ERTALON® 66 SA. According to the supplier, the PA66 had density, melting temperature and thermal decomposition temperature of 1.14 g/cm3, 260 C and >350 C, respectively. In order to study the yield loci of PA66, semi-products (round rods) of PA 66 with diameter of 12 mm were cut and machined into special specimens with shape and size shown in Fig. 1. A cylinder specimen, a dumbbell specimen and SCS with two slots machined at different angles a (15 , 30 , 45 and 50 ) to the longitudinal axis were used in the tests with the purpose of obtaining the compression behavior, tensile behavior and combined shear-compression behavior of PA66. A universal testing machine (CMT5105A, SANS, Shenzhen, PRC) with a 100 kN load cell was used for the mechanical tests. In
T. Jin et al. / Polymer Testing 51 (2016) 148e150
149
Fig. 1. Schematic of PA66 specimens.
addition, a computer was used to record the displacement and load signals from the universal testing machine during the entire loading process. All tests were conducted by controlling a constant displacement rate of 0.08 mm/s. The compression stress and tensile stress were determined by dividing the applied load by the original specimen area, and the strain obtained by dividing the specimen displacement by the original specimen height. It should be pointed out that, for the SCS geometry, VURAL et al. [5] gave the state of stress at a point within the gage section as shown in Fig. 1 and can be expressed as:
s¼ t¼
P cos2 a Dt
(1-a)
P cos a sin a Dt
(1-b)
Fig. 2. Compression and tensile force-displacement curves (a), compression-shear component of SCS (b).
where s, t and P are normal/shear stress and force recorded by the test machine, respectively. Similarly, the normal strain εn and shear strain gs can be expressed as:
εn ¼
Dh cos2 a h
(2-a)
gs ¼
Dh cos a sin a h
(2-b)
w . where h ¼ cos a
3. Results and discussion Fig. 2(a) shows the compression and tensile force-displacement curves of PA66. For compression, the force increases almost linearly with displacement indicating the elastic portion, then it exhibits nonlinear increases which indicates the start of the plastic yield regime. However, the force-displacement response of PA66 under tensile loading is different from that under compression, and the main difference lies in the post-yield behavior. Strain softening was
Fig. 3. Determination of PA66 yield point.
150
T. Jin et al. / Polymer Testing 51 (2016) 148e150
Table 1 Results of yield stress under different loading conditions. Compression
Compression component/MPa Shear component/MPa s1/MPa s2/MPa
e e 0 59
Tensile
e e 48 0
SCS 15
30
45
50
52.71 14.12 3.55 56.26
41.56 23.99 10.96 51.69
26.64 26.64 16.46 43.10
23.37 27.85 18.52 41.88
is written as:
3J 27 J 2 f ¼ 2 $ 1 $ 33 32 J2 st
! þ
7ðm 1Þ 7 $I1 $m$st 8 8
(4)
where I1, J2, J3, st and m are the first invariant of stress, the second invariant of the deviatoric stress, the third invariant of the deviatoric stress, tensile strength and the ratio of compression strength and tensile strength, respectively. In addition, I1, J2 and J3 are used to characterize three basic deformation mechanisms [8] existing for polymers: dilation, pure shear and rotation, respectively. It can be observed that the experimental yield loci of PA66 obtained by the test method proposed in the present study agree well with the yield criterion, which confirms the feasibility of this approach. 4. Summary
Fig. 4. Yield loci of PA66 in the principal stress space.
observed when PA66 was under tensile load while the opposite is observed for compression. Fig. 2(b) displays the compression and shear components of SCS during compression. The compression component decreases with a while the opposite is true for the shear component. Given this phenomenon, the introduction of slots in a cylinder specimen succeeded in making changes of stress state when specimens were loaded. In order to identify the yield surface of PA66, the yield point should be defined. For most polymers, two methods (i.e. backward extrapolation and offset strain definition) methods are always used to define the yield point [6,7]. Fig. 3 shows these two methods to define the yield point of PA66 under compression, and the yield stresses obtained by two methods are nearly-identical. Given the non-linearality of the initial portion of the stress-strain curve results from contact problems between the specimen and compression plates of the test machine, offset strain definition is not suitable to define the yield point in this study. Therefore, the backward extrapolation was applied. Based on the force analysis at a point within the gage section in SCS and the definition of yield point, the compression and shear components of experimental yield point can be obtained. In addition, for a specimen under combined shear-compression loading, the principal stresses are written as:
s1 s2
s ¼ ± 2
rffiffiffiffiffiffiffiffiffiffiffi s 2 2
þ t2
(3)
where s1 and s2 are the maximum and the intermediate principal stress, respectively. It should be pointed out that, in this paper, the compression stress is negative and the tensile stress is positive. The results of yield stress under different loading conditions are listed in Table 1. Then, the experimental yield loci of PA66 were plotted in the principal stress space, as shown in Fig. 4. The yield loci found can be described by a yield criterion proposed by Ghorbel [8] which
In this paper, quasi-static loading tests were performed on PA66 specimens. The compression behavior, tensile behavior, and combined shear-compression behavior of PA66 were obtained by testing cylinder specimens, dumbbell specimens and cylinder specimens with two slots machined at different angles a (15 , 30 , 45 and 50 ) to the longitudinal axis, respectively. Results show that the experimental yield loci of PA66 obtained by the test method proposed in present paper agrees well with the theoretical model, which confirms the feasibility of this approach. Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant Nos. 11172195, and 11572214), the Natural Science Foundation of Shanxi Province (Grant No.2014011009-1), Foundation the Top Young Academic Leaders of Shanxi and Program for the homecoming foundation and Outstanding Innovative Teams of Higher Learning Institutions of Shanxi. The financial contributions are gratefully acknowledged. References [1] D.W. Holmes, J.G. Loughran, H. Suehrcke, Constitutive model for large strain deformation of semicrystalline polymers, Mech. Time-Depend. Mater. 10 (2006) 281e313. [2] Z.W. Zhou, B.Y. Su, Z.H. Wang, Z.Q. Li, X.F. Shu, L.M. Zhao, Shear-compression failure behavior of PMMA at different loading rates, Mater. Lett. 109 (2013) 151e153. [3] T. Jin, Z.W. Zhou, Z.H. Wang, G.Y. Wu, Z.G. Liu, X.F. Shu, Quasi-static failure behaviour of PMMA under combined shearecompression loading, J. Polym. Test. 42 (2015) 181e184. [4] D. Rittel, S. Lee, G. Ravichandran, A shear-compression specimen for large strain testing, Exp. Mech. 48 (2002) 58e64. [5] M. Vural, D. Rittel, G. Ravichandran, Large strain mechanical behavior of 1018 cold-rolled steel over a wide range of strain rates, Metall. Mater. Trans. A 34A (2003) 2873e2885. [6] H. Pouriayevali, S. Arabnejad, Y.B. Guo, V.P.W. Shim, A constitutive description of the rate-sensitive response of semi-crystalline polymers, Int. J. Impact. Eng. 62 (2013) 35e47. [7] R. Raghava, R.M. Caddell, G.S.Y. Yeh, The macroscopic yield behaviour of polymers, J. Mater. Sci. 8 (1973) 225e232. [8] E. Ghorbel, A viscoplastic constitutive model for polymeric materials, Int. J. Plast. 24 (2008) 2032e2058.
Contents lists available at ScienceDirect
Polymer Testing journal homepage: www.elsevier.com/locate/polytest
Short communication: test method
Experimental investigation on the yield loci of PA66 Tao Jin a, b, Zhiwei Zhou c, Xuefeng Shu a, b, *, Zhihua Wang a, b, Guiying Wu d, Longmao Zhao a, b a
Institute of Applied Mechanics and Biomedical Engineering, Taiyuan University of Technology, Taiyuan 030024, China Shanxi Key Laboratory of Material Strength and Structural Impact, Taiyuan 030024, China c State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, 730000, China d Department of Mechanics, Taiyuan University of Technology, Taiyuan 030024, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 January 2016 Accepted 6 March 2016 Available online 10 March 2016
Compression, tensile and mixed compression/shear tests were performed on PA66 by using a universal material testing machine in order to identify the experimental yield loci of PA66. For the mixed compression/shear tests, instead of using a complex loading device, SCS (shear-compression specimens) were used to generate the additional shear stresses. Then, the mechanical behavior of materials under complex stress states can be obtained for further analysis. Results show that the experimental yield loci of PA66 obtained by the test method proposed in the present paper agree well with the theoretical model based on three stresses invariant, which indicates the reliability of the test method. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Polymers Elastic properties Shear-compression specimen Yield surface Test method
1. Introduction Semi-crystalline polymers are widely used as structural components in manufacturing industry for their ease of moulding and ability to be recycled [1]. Such components always suffer in a complex environment during service. Therefore, the mechanical behavior of materials under different stress states should be understood to be helpful to the material manufacturing and design. Recently, Zhou [2] investigated the failure behavior of PMMA under different loading conditions by applying a complex loading device which consisted of a short cylindrical bars system with beveled ends and a sleeve made of Teflon to apply the combined shear-compression on cubic samples. Similarity, Jin et al. [3] studied the PMMA mechanical response under mixed shear-compression based on specific sample geometries and found that the mechanical behavior of PMMA is sensitive to the introduction of shear stress, whereas the stress state of the specimen during test is not uniform, which may result in some uncertain errors. Given this situation, a shear-compression specimen (SCS) which consists of a short cylinder into which two slots have been machined
* Corresponding author. Institute of Applied Mechanics and Biomedical Engineering, Taiyuan University of Technology, Taiyuan 030024, China. Tel./fax: þ86 351 6014455. E-mail address: [email protected] (X. Shu). http://dx.doi.org/10.1016/j.polymertesting.2016.03.007 0142-9418/© 2016 Elsevier Ltd. All rights reserved.
at a certain angle to the longitudinal axis [4] could be introduced to investigate the material's yield behavior. In addition, the stress and strain fields in the gage section of SCS are uniform, which has been verified by Rittel [4]. Therefore, there will be at least two advantages of a simple loading device and uniform stress state if the SCS is applied in the investigation of the yield loci of materials. Hence, the major aim of this paper is to present a new test method to identify the yield loci of PA66. 2. Experimental procedure The material tested in this investigation was PA66. A commercial grade of the material was purchased from a supplier under the trade name, ERTALON® 66 SA. According to the supplier, the PA66 had density, melting temperature and thermal decomposition temperature of 1.14 g/cm3, 260 C and >350 C, respectively. In order to study the yield loci of PA66, semi-products (round rods) of PA 66 with diameter of 12 mm were cut and machined into special specimens with shape and size shown in Fig. 1. A cylinder specimen, a dumbbell specimen and SCS with two slots machined at different angles a (15 , 30 , 45 and 50 ) to the longitudinal axis were used in the tests with the purpose of obtaining the compression behavior, tensile behavior and combined shear-compression behavior of PA66. A universal testing machine (CMT5105A, SANS, Shenzhen, PRC) with a 100 kN load cell was used for the mechanical tests. In
T. Jin et al. / Polymer Testing 51 (2016) 148e150
149
Fig. 1. Schematic of PA66 specimens.
addition, a computer was used to record the displacement and load signals from the universal testing machine during the entire loading process. All tests were conducted by controlling a constant displacement rate of 0.08 mm/s. The compression stress and tensile stress were determined by dividing the applied load by the original specimen area, and the strain obtained by dividing the specimen displacement by the original specimen height. It should be pointed out that, for the SCS geometry, VURAL et al. [5] gave the state of stress at a point within the gage section as shown in Fig. 1 and can be expressed as:
s¼ t¼
P cos2 a Dt
(1-a)
P cos a sin a Dt
(1-b)
Fig. 2. Compression and tensile force-displacement curves (a), compression-shear component of SCS (b).
where s, t and P are normal/shear stress and force recorded by the test machine, respectively. Similarly, the normal strain εn and shear strain gs can be expressed as:
εn ¼
Dh cos2 a h
(2-a)
gs ¼
Dh cos a sin a h
(2-b)
w . where h ¼ cos a
3. Results and discussion Fig. 2(a) shows the compression and tensile force-displacement curves of PA66. For compression, the force increases almost linearly with displacement indicating the elastic portion, then it exhibits nonlinear increases which indicates the start of the plastic yield regime. However, the force-displacement response of PA66 under tensile loading is different from that under compression, and the main difference lies in the post-yield behavior. Strain softening was
Fig. 3. Determination of PA66 yield point.
150
T. Jin et al. / Polymer Testing 51 (2016) 148e150
Table 1 Results of yield stress under different loading conditions. Compression
Compression component/MPa Shear component/MPa s1/MPa s2/MPa
e e 0 59
Tensile
e e 48 0
SCS 15
30
45
50
52.71 14.12 3.55 56.26
41.56 23.99 10.96 51.69
26.64 26.64 16.46 43.10
23.37 27.85 18.52 41.88
is written as:
3J 27 J 2 f ¼ 2 $ 1 $ 33 32 J2 st
! þ
7ðm 1Þ 7 $I1 $m$st 8 8
(4)
where I1, J2, J3, st and m are the first invariant of stress, the second invariant of the deviatoric stress, the third invariant of the deviatoric stress, tensile strength and the ratio of compression strength and tensile strength, respectively. In addition, I1, J2 and J3 are used to characterize three basic deformation mechanisms [8] existing for polymers: dilation, pure shear and rotation, respectively. It can be observed that the experimental yield loci of PA66 obtained by the test method proposed in the present study agree well with the yield criterion, which confirms the feasibility of this approach. 4. Summary
Fig. 4. Yield loci of PA66 in the principal stress space.
observed when PA66 was under tensile load while the opposite is observed for compression. Fig. 2(b) displays the compression and shear components of SCS during compression. The compression component decreases with a while the opposite is true for the shear component. Given this phenomenon, the introduction of slots in a cylinder specimen succeeded in making changes of stress state when specimens were loaded. In order to identify the yield surface of PA66, the yield point should be defined. For most polymers, two methods (i.e. backward extrapolation and offset strain definition) methods are always used to define the yield point [6,7]. Fig. 3 shows these two methods to define the yield point of PA66 under compression, and the yield stresses obtained by two methods are nearly-identical. Given the non-linearality of the initial portion of the stress-strain curve results from contact problems between the specimen and compression plates of the test machine, offset strain definition is not suitable to define the yield point in this study. Therefore, the backward extrapolation was applied. Based on the force analysis at a point within the gage section in SCS and the definition of yield point, the compression and shear components of experimental yield point can be obtained. In addition, for a specimen under combined shear-compression loading, the principal stresses are written as:
s1 s2
s ¼ ± 2
rffiffiffiffiffiffiffiffiffiffiffi s 2 2
þ t2
(3)
where s1 and s2 are the maximum and the intermediate principal stress, respectively. It should be pointed out that, in this paper, the compression stress is negative and the tensile stress is positive. The results of yield stress under different loading conditions are listed in Table 1. Then, the experimental yield loci of PA66 were plotted in the principal stress space, as shown in Fig. 4. The yield loci found can be described by a yield criterion proposed by Ghorbel [8] which
In this paper, quasi-static loading tests were performed on PA66 specimens. The compression behavior, tensile behavior, and combined shear-compression behavior of PA66 were obtained by testing cylinder specimens, dumbbell specimens and cylinder specimens with two slots machined at different angles a (15 , 30 , 45 and 50 ) to the longitudinal axis, respectively. Results show that the experimental yield loci of PA66 obtained by the test method proposed in present paper agrees well with the theoretical model, which confirms the feasibility of this approach. Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant Nos. 11172195, and 11572214), the Natural Science Foundation of Shanxi Province (Grant No.2014011009-1), Foundation the Top Young Academic Leaders of Shanxi and Program for the homecoming foundation and Outstanding Innovative Teams of Higher Learning Institutions of Shanxi. The financial contributions are gratefully acknowledged. References [1] D.W. Holmes, J.G. Loughran, H. Suehrcke, Constitutive model for large strain deformation of semicrystalline polymers, Mech. Time-Depend. Mater. 10 (2006) 281e313. [2] Z.W. Zhou, B.Y. Su, Z.H. Wang, Z.Q. Li, X.F. Shu, L.M. Zhao, Shear-compression failure behavior of PMMA at different loading rates, Mater. Lett. 109 (2013) 151e153. [3] T. Jin, Z.W. Zhou, Z.H. Wang, G.Y. Wu, Z.G. Liu, X.F. Shu, Quasi-static failure behaviour of PMMA under combined shearecompression loading, J. Polym. Test. 42 (2015) 181e184. [4] D. Rittel, S. Lee, G. Ravichandran, A shear-compression specimen for large strain testing, Exp. Mech. 48 (2002) 58e64. [5] M. Vural, D. Rittel, G. Ravichandran, Large strain mechanical behavior of 1018 cold-rolled steel over a wide range of strain rates, Metall. Mater. Trans. A 34A (2003) 2873e2885. [6] H. Pouriayevali, S. Arabnejad, Y.B. Guo, V.P.W. Shim, A constitutive description of the rate-sensitive response of semi-crystalline polymers, Int. J. Impact. Eng. 62 (2013) 35e47. [7] R. Raghava, R.M. Caddell, G.S.Y. Yeh, The macroscopic yield behaviour of polymers, J. Mater. Sci. 8 (1973) 225e232. [8] E. Ghorbel, A viscoplastic constitutive model for polymeric materials, Int. J. Plast. 24 (2008) 2032e2058.