Effects of Magnetic Field in Creep Behavior of Three-Phase Laminated Composite Cylindrical Shells

Document Type: Research Paper

Authors

Composite and Nanocomposite Research Laboratory, Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran.

Abstract

Due to the importance effect of magnetic field on the history of long-term radial and circumfer-ential creep strain and radial displacement for a three-phase nano-composite exposed to an internal pressure and placed uniform temperature, the present article subject has been pro-posed. Three-phase nano-composite made of single-walled carbon nano tubes (SWCNTs)/ glass fiber (GF)/vinylester used to micromechanical models in order to calculate the mechanical and thermal properties. By assuming non-linear viscoelastic based on Schapery integral model and using classical laminate theory, Prandtl-Reuss relations and Mendelson’s approximation meth-od achieved results. Distribution of the radial creep strain, circumferential creep strain and radial displacement in two states including without and with magnetic field and three tempera-ture conditions for laminated lay-ups [0/45/0/45] described for 10 years. The results indicate that the magnetic field has reduced the radial and circumferential creep strain and radial dis-placement. Furthermore, the temperature increase in the magnetic field is less effective on the increased values of creep strain and radial displacement. Finally, It has been founded that mag-netic field would reduce the creep strain of all case studies.

Keywords



 

 

Mechanics of Advanced Composite Structures 6 (2019) 51–56

 

 

 

 

 

 

Semnan University

Mechanics of Advanced Composite Structures

journal homepage: http://MACS.journals.semnan.ac.ir

 

Effects of Magnetic Field in Creep Behavior of Three-Phase Laminated Composite Cylindrical Shells

K. Hosseinpour, A.R. Ghasemi*

Composite and Nanocomposite Research Laboratory, Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, 87317-53153, Iran.

 

Paper INFO

 

ABSTRACT

Paper history:

Received 2019-01-25

Received in revised form

2019-02-15

Accepted 2019-04-26

Due to the importance effect of magnetic field on the history of long-term radial and circumferential creep strain and radial displacement for a three-phase nano-composite exposed to an internal pressure and placed uniform temperature,the present article subject has been proposed. Three-phase nano-composite made ofsingle-walled carbon nano tubes (SWCNTs)/ glass fiber (GF)/vinylester used to micromechanical models in order to calculate the mechanical and thermal properties. By assuming non-linear viscoelastic based on Schapery integral model and using classical laminate theory, Prandtl-Reuss relations and Mendelson’s approximation method achieved results. Distribution of the radial creep strain, circumferential creep strain and radial displacement in two states including without and with magnetic field and three temperature conditions for laminated lay-ups [0/45/0/45] described for 10 years. The results indicate that the magnetic field has reduced the radial and circumferential creep strain and radial displacement. Furthermore, the temperature increase in the magnetic field is less effective on the increased values of creep strain and radial displacement. Finally, It has been founded that magnetic field would reduce the creep strain of all case studies.

 

Keywords:

Thermo-magneto-mechanical loading

Three-phase composite cylinder Micromechanical model

 

© 2019 Published by Semnan University Press. All rights reserved.

 

 

  1. Introduction

In the recent years, use of the polymer composite cylinders in various industries with high temperature and pressure environments due to high mechanical strength, low weight and easy to shape increased [1,2]. Due to the time-dependent behavior of polymer matrix composites and nano-composites even at low temperatures, investigating the long-term creep behavior using the viscoelastic assumptions attracted many researchers. Zhang et al. [3] used the thermo-elasticity analysis theory to study of stress distribution in the wall of the composite cylinder. They showed that the results of the analytical method and finite element model (FEM) for multi-layer composite cylinder under the thermo-mechanical loads have acceptable agreement with each other. Time-dependent behavior of thick walled multi-layered composite cylinders made of carbon/epoxy assuming nonlinear viscoelastic Schapery’s model [4] was studied by Guedes [5]. The long-term performance of GRP after 50 years was predicted from failure pressure and time to failure through sustained internal pressure test by Yoon and Oh [6]. Due to the development of nano-industry and performed studies it was shown that the addition of nano-particles will improve the mechanical [7], thermal [8] and residual [9] properties of two-phase and three-phase nano-composites. Creep behavior of the polycarbonate reinforced by MWCNTs fiber nano-composite was studied by Zhou et al. [10]. They demonstrated that the results of experimental and Burger’s model [11] had a good agreement. Starkova et al. [12] predicted the long-term creep behavior of MWCNT/epoxy nano-composites and used the experimental work and modeling. Their results illustrated that the Schapery’s model [6] had a good agreement with their experimental results. Mohandes et al. [13] studied the influence of size dependency and volume percentage of CNTs on the mechanical behavior of the nano-composite cylinders. They used the Mori-Tanaka model [14] to obtain the thermal, mechanical and piezoelectric properties of nano-composite cylinders. In another work, Mohandes et al. [15] studied the behaviour of rotating cylinder made of composite reinforced by multi-walled carbon nanotubes (MWCNTs) subjected to mechanical loading. Ghasemi et al. [16] studied the influence of weight fraction of MWCNTs and lay-ups on the way of distribution creep strains in the wall of the MWCNTs /E-glass/vinylester three-phase nano-composites. Their results demonstrated that the addition of the MWCNT to the vinylester can reduce the absolute values of the radial and circumferential creep strains. Also, all the mechanical properties of nano-composites cylinder were obtained using micromechanical relations.

Despite studies on creep behavior of composite cylinders, there is no article that reviews the effect of adding nano-particles, temperature loads and magnetic field to long-term creep strain distribution of the wall of the three-phase nano-composite cylinders. The main purpose of the present article is to study the effect of thermal and magneto loading on creep strains and radial displacement in the three-phase nano-composite cylinder wall.

  1. Mathematical Model

A SWCNTs/GF/Vinylester composite cylinder with the conditions having inner radius of  and outer radius of  was considered. Internal pressure in the inner wall of the cylinder is  and the cylinder was subjected to uniform distributed temperature field   and placed in a uniform magnetic field .

Prandtl-Reuss relation defined the creep strains increment in radial and circumferential direction and current stresses and also, creep constitutive model could be written as:

 

(1)

The constitutive creep model in this literature has been assumed the Schapery nonlinear viscoelastic model that results in [17]:

 

 

(2)

where  is the effective stress which is an octahedral stress:

 

(3)

Also, ,  and  are linear elastic coefficients and for GF/Vinylester are shown in Table 1 for different angles and , , ,  and are nonlinear coefficients of the Schapery constitutive model that following equations are used for the GF/vinylester [18].

 

(4)

By assumption of uniform magnetic field, the equilibrium equation for the thick walled cylinder would be the expressed as:

 

(5)

where  is Lorenz’s force and its equation is:

 

(6)

where μ is the magnetic permeability and    is the magnetic field intensity in the axial direction. Also, the considered total strain is the summation of elastic strain and creep strain, stress and strain relations would be written as:

 

(7)

where ,  and  denoted radial, circumferential and axial directions, respectively.

Table 1. Viscoelastic linear parameters of glass/vinylester [19]

90°

45°

Off-axis angle ( )

0.81

0.79

0.53

 

1.35

0.16

0.32

 

0.189

0.20

0.16

n

Also,  is the modulus matrix in cylindrical coordinate as follows:

 

(8)

where  is the Cartesian coordinate and  is the transfer matrix as:

 

(9)

 

(10)

where ,   and  is lay-up direction. Also,  is the modulus matrix in cylindrical coordinate where superscript  denoted the number of layers. Superscript  in Eq. (7) specifies the creep. Assuming axial symmetry and linear strain relation, strain-displacement relation could be written as:

 

(11)

Also with assuming constant thermal gradient in the wall of the cylinder, thermal strain relation would be written as:

 

(12)

 

Substituting radial and circumferential stresses from Eq. (7) into Eq. (5), the following differential equation containing creep strains is obtained:

 

(13)

where constant coefficients  in Eq. (13) could be summarized as follow:

   

(14)

The solution for Eq. (13) can be obtained:

 

(15)

 

 

where and  are unknown integration constants and other parameters are:

 

(16)

 

In order to calculate the unknown constant coefficients for each layer, there is a need to use boundary conditions. For the -layered composite cylinder, there are  unknown constant coefficients which include  and  used in below boundary conditions:

 

 

 

 

 

(17)

 

 

Using the expressed relations and Mendelson’s approximation method for the long period of time, the history of strains in time can be calculated [16].

  1. Micro-Mechanical Model

Three-phase nano-composite laminate was formed to the combination of isotropic matrix (vinylester resin), carbon nanotubes (SWCNTs) and fibers (E-Glass). It is assumed that SWCTs are homogeneously distributed in the matrix without the presence of air voids and have the same mechanical and thermal properties and are isotropic. The effective mechanical and thermal properties of the three-phase SWCNTPC multi-layered cylinder can be predicted according to Halpin–Tsai [20] and Schapery relations [21], respectively. Young’s moduli, shear moduli, Poisson’s ratio and the coefficient of thermal expansion are as follow:

 

(18)

 

(19)

 

(20)

 

 

(21)

 

(22)

 

(23)

where , , ,  and  are elastic and  shear modulus,   Poisson’s ratio, volume fraction and coefficient of thermal expansion (CTE) of the fiber, respectively. Also , , ,  and  are elastic and  shear moduli,  Poisson’s ratio, volume fraction and coefficient of thermal expansion of the SWCNTs/vinylester Two-phase nano-composite, respectively and are presented as below:

 

(24)

 

(25)

 

(26)

 

(27)

     

where  and  are the elastic moduli of the SWCNTs and the matrix, respectively and  and  are the orientation factor and aspect ratio, respectively. Also  and  are the CTE of the SWCNTs and matrix, respectively. For nano-composite with two-phase (MWCCNTs/vinylester) and no trapped air, volume fraction of the SWCNTs is obtained as [22]:

 

(28)

where  and  are the density of the SWCNTs and matrix, respectively, and  is the weight fraction of SWCNTs.

For the mentioned conditions, a composite cylinder made of SWCNTs/GF/vinylester with elastic properties for each one is shown in the Table 2.

  1. Numerical Results and Discussion

The results discussed in the present section are based on the material properties, geometry, loading condition and introduced in previous section and Tables 1 and 2 as well. Effect of temperature and magnetic field on creep strains and radial displacement after 10 years are discussed in the three-phase nano-composite cylinder with  weight fraction of SWCNTs is considered and distribution of creep strains and radial displacement in the wall of three-phase nano-composite cylinder with lay-up [0/45/0/45] for a period of 10 years is plotted. Fig. 2 demonstrated the distribution of radial creep strains with and without the magnetic field. As it is shown in the presence of a magnetic field, the creep strain for every thermal loading is lower in magnitude. Also, Fig. 3 demonstrated that an increase in temperature, increases the radial creep strain and the increased creep strain in a magnetic field is lower without magnetic field.

Variation of circumferential creep strain in the wall of three-phase nano-composite cylinder demonstrated in Fig. 3. Values of circumferential decreased in each layer with increased dimensionless ratio of the radius. Also, values of circumferential creep strain in the same temperature and with magnetic field is lower than without magnetic field.

Table 2. Material properties of SWCNTs/GF/vinylester three-phase composites

Nano-filler [23]

Fiber

Polymer matrix

Property

SWCNT

E-glass

Vinylester

640

71.78

4.99

Young's modulus ( )

0.33

0.25

0.3

Poisson’s ratio ( )

3.45

5

62.46

CTE ( )

 

0.66-

34

Volume fraction (%)

 

a

 

b

Fig. 2. Radial creep strain of the nano-composite cylinder with lay-up [0/45/0/45] (a) without and (b) with the effect of magnetic field.

 

a

 

b

Fig. 3. Circumferential creep strain of the nano-composite cylinder with lay-up [0/45/0/45] (a) without and (b) with the effect of magnetic field.

Fig.s 4-a and 4-b illustrated the distribution radial displacement in the wall of three-phase nano-composite cylinder in two state of without and with the magnetic field, respectively. Fig. 4 demonstrated that with rising the temperatures, radial displacement increased. Also, radial displacement with magnetic field are lower than that of without magnetic field.

  1. Conclusions

Creep response of a three-phase nano-composite cylinder made of SWCNTs /E-glass/vinylester with 4.5% weight fraction subjected to thermal, mechanical and magnetic loads has been investigated. Effects of operating temperature, magnetic field and lay-up on radial and circumferential creep strains and radial displacements are also studied. The magnetic field is reduced the radial and circumferential creep strain and radial displacement. An increase in temperature would increase the radial and circumferential creep strain and radial displacement. Furthermore, the temperature increase in the magnetic field is less effective on the values of creep strain and radial displacement.

References

[1]      HollaWay LC. A review of the present and future utilisation of FRP composites in the civil infrastructure with reference to their important in-service properties. Const Build Mater 2010; 24: 2419-2445.

[2]      Watkins RK, Anderson LR. Struct mech buried pipes. CRC Press LLC;2000.

 

a

 

b

Fig. 4. Radial displacement of the nano-composite cylinder with lay-up [0/45/0/45] (a) without and (b) with the effect of magnetic field.

[3]      Zhang Q, Wang ZW, Tang CY, Hu DP, Liu PQ, Xia LZ. Analytical solution of the thermo-mechanical stresses in a multilayered composite pressure vessel considering the influence of the closed ends. Int J Press Vess and Pip2012; 98: 102-110.

[4]      Papanicolaou GC, Zaoutsos SP, Kontou EA. Fiber orientation dependence of continuous carbon/epoxy composites nonlinear viscoelastic behavior. Comp Sci Technol 2004;64: 2535-2545.

[5]    Guedes RM. Nonlinear viscoelastic analysis of thick-Walled cylindrical composite pipes. Int J Mech Sci 2010; 52: 1064-1073.

[6]    Yoon SH, Oh JO. Prediction of long term performance for GRP pipes under sustained internal pressure. Compos Struct 2015; 134: 185–189.

[7]      Hadavand BS, Javid KM, Gharagozlou M. Mechanical properties of multiwalled carbon nanotube/epoxy polysulfide nanocomposite. Mat Des 2013; 50:62-67.

[8]      Shokrieh MM, Daneshvar A, Akbari S. Reduction of thermal residual stresses of laminated polymer composites by addition of carbon nanotubes. Mater Des 2014; 53: 209-216.

[9]    Ghasemi AR, Fesharaki M M, Mohandes M. Three-phase micromechanical analysis of residual stresses in reinforced fiber by carbon nanotubes. J Comp Mater 2016; 51(12), 1783-1794.

[10]Zhou YX, Wu PX, Cheng ZY, Ingram J, Jeelani S. Improvement in electrical, thermal and mechanical properties of epoxy by filling carbon nanotube. Expe Poly Let 2008; 2(1): 40–48.

[11]Papanicolaou GC, Xepapadaki AG and Tagaris GD. Effect of thermal shock cycling on the creep behavior of glass-epoxy composite. Comp Struc 2009; 88: 436-442.

[12]  Starkova O, Buschhorn ST, Mannov E, Schulte K, Aniskevich A. Creep and recovery of epoxy/MWCNT nanocomposites. Comp Part A 2012; 43: 1212–1218.

[13]  Mohandes M, Ghasemi AR. Modified couple stress theory and finite strain assumption for nonlinear free vibration and bending of micro/nanolaminated composite Euler–Bernoulli beam under thermal loading. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 2017; 231(21):4044-56.

[14]  Mori T, Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall Mater 1973; 21: 571- 574.

[15]  Mohandes M, Ghasemi AR. A new approach to reinforce the fiber of nanocomposite reinforced by CNTs to analyze free vibration of hybrid laminated cylindrical shell using beam modal function method. European Journal of Mechanics-A/Solids 2019, 1; 73: 224-34.

[16]   Ghasemi AR, Hosseinpour K, Mohandes M. Modelling creep behavior of carbon-nanotubes/fiber/polymer composite cylinders. Part N:  J Nanomater Nanoeng Nanosys 2018; 232(2–3), 49–58.

[17] Muddasani M, Sawant S, Muliana A. Thermo-viscoelastic responses of multilayered polymer composite experimental and numerical studies. Comp Struc 2010; 92: 2641-2652.

[18]  Sawant S, Muliana A, A thermo-mechanical viscoelastic analysis of orthotropic materials. Compos Struct 2008; 83: 61-72.

[19]  Muliana A, Nair A, Khan KA, Wagner S. Characterization of thermo-mechanical and long term behaviors of multi-layered composite materials. Comp Sci Technol2006; 66: 2907-2924.

[20]Halpin JC, Kardos JL. The Halpin-Tsai equations: a review. Poly Eng Sci 1976; 16(5): 344-352.

[21]  Schapery RA. Thermal expansion coefficients of composite materials based on energy principles. J Comp Materl 1986; 2(3): 380-404.

[22]  Ghasemi AR, Mohammadi MM, Mohandes M. The role of carbon nanofibers on thermo-mechanical properties of polymer matrix composites and their effect on reduction of residual stresses”. Compos Part B 2015; 77: 1-9.

[23]  Rafiee M, Liu XF, He XQ, Kitipornchai S. Geometrically nonlinear free vibration of shear deformable carbon nanotube/fiber/polymer multiscale laminated composite plates. J Sound Vib 2014; 333(14): 3236–3251.

 

 

[1]      HollaWay LC. A review of the present and future utilisation of FRP composites in the civil infrastructure with reference to their important in-service properties. Const Build Mater 2010; 24: 2419-2445.

[2]      Watkins RK, Anderson LR. Struct mech buried pipes. CRC Press LLC;2000.

[3]      Zhang Q, Wang ZW, Tang CY, Hu DP, Liu PQ, Xia LZ. Analytical solution of the thermo-mechanical stresses in a multilayered composite pressure vessel considering the influence of the closed ends. Int J Press Vess and Pip2012; 98: 102-110.

[4]      Papanicolaou GC, Zaoutsos SP, Kontou EA. Fiber orientation dependence of continuous carbon/epoxy composites nonlinear viscoelastic behavior. Comp Sci Technol 2004;64: 2535-2545.

[5]    Guedes RM. Nonlinear viscoelastic analysis of thick-Walled cylindrical composite pipes. Int J Mech Sci 2010; 52: 1064-1073.

[6]    Yoon SH, Oh JO. Prediction of long term performance for GRP pipes under sustained internal pressure. Compos Struct 2015; 134: 185–189.

[7]      Hadavand BS, Javid KM, Gharagozlou M. Mechanical properties of multiwalled carbon nanotube/epoxy polysulfide nanocomposite. Mat Des 2013; 50:62-67.

[8]      Shokrieh MM, Daneshvar A, Akbari S. Reduction of thermal residual stresses of laminated polymer composites by addition of carbon nanotubes. Mater Des 2014; 53: 209-216.

[9]    Ghasemi AR, Fesharaki M M, Mohandes M. Three-phase micromechanical analysis of residual stresses in reinforced fiber by carbon nanotubes. J Comp Mater 2016; 51(12), 1783-1794.

[10]Zhou YX, Wu PX, Cheng ZY, Ingram J, Jeelani S. Improvement in electrical, thermal and mechanical properties of epoxy by filling carbon nanotube. Expe Poly Let 2008; 2(1): 40–48.

[11]Papanicolaou GC, Xepapadaki AG and Tagaris GD. Effect of thermal shock cycling on the creep behavior of glass-epoxy composite. Comp Struc 2009; 88: 436-442.

[12]  Starkova O, Buschhorn ST, Mannov E, Schulte K, Aniskevich A. Creep and recovery of epoxy/MWCNT nanocomposites. Comp Part A 2012; 43: 1212–1218.

[13]  Mohandes M, Ghasemi AR. Modified couple stress theory and finite strain assumption for nonlinear free vibration and bending of micro/nanolaminated composite Euler–Bernoulli beam under thermal loading. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 2017; 231(21):4044-56.

[14]  Mori T, Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall Mater 1973; 21: 571- 574.

[15]  Mohandes M, Ghasemi AR. A new approach to reinforce the fiber of nanocomposite reinforced by CNTs to analyze free vibration of hybrid laminated cylindrical shell using beam modal function method. European Journal of Mechanics-A/Solids 2019, 1; 73: 224-34.

[16]   Ghasemi AR, Hosseinpour K, Mohandes M. Modelling creep behavior of carbon-nanotubes/fiber/polymer composite cylinders. Part N:  J Nanomater Nanoeng Nanosys 2018; 232(2–3), 49–58.

[17] Muddasani M, Sawant S, Muliana A. Thermo-viscoelastic responses of multilayered polymer composite experimental and numerical studies. Comp Struc 2010; 92: 2641-2652.

[18]  Sawant S, Muliana A, A thermo-mechanical viscoelastic analysis of orthotropic materials. Compos Struct 2008; 83: 61-72.

[19]  Muliana A, Nair A, Khan KA, Wagner S. Characterization of thermo-mechanical and long term behaviors of multi-layered composite materials. Comp Sci Technol2006; 66: 2907-2924.

[20]Halpin JC, Kardos JL. The Halpin-Tsai equations: a review. Poly Eng Sci 1976; 16(5): 344-352.

[21]  Schapery RA. Thermal expansion coefficients of composite materials based on energy principles. J Comp Materl 1986; 2(3): 380-404.

[22]  Ghasemi AR, Mohammadi MM, Mohandes M. The role of carbon nanofibers on thermo-mechanical properties of polymer matrix composites and their effect on reduction of residual stresses”. Compos Part B 2015; 77: 1-9.

[23]  Rafiee M, Liu XF, He XQ, Kitipornchai S. Geometrically nonlinear free vibration of shear deformable carbon nanotube/fiber/polymer multiscale laminated composite plates. J Sound Vib 2014; 333(14): 3236–3251.