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Crystallinity degree numerical calculation of construction of thermoplastic composite material
Materials Today: Proceedings xxx (xxxx) xxx
Contents lists available at ScienceDirect
Materials Today: Proceedings journal homepage: www.elsevier.com/locate/matpr
Crystallinity degree numerical calculation of construction of thermoplastic composite material Aleksandr Anoshkin, Pavel Pisarev, Yulia Pristupova ⇑ Perm National Research Polytechnic University, Komsomolsky Prospect 29, Perm 614000, Russia
a r t i c l e
i n f o
Article history: Received 15 May 2019 Received in revised form 9 July 2019 Accepted 24 July 2019 Available online xxxx Keywords: Degree of crystallinity Thermoplastic composite material Influence of the structure geometry Numerical simulation Temperature Technological processing conditions
a b s t r a c t In this work, authors formulated physical and mathematical models to calculate the crystallinity degree in the heat treatment process of a thermoplastic composite material structure made. Two structure types were considered: a layered package and a corner bracket. Computational experiments have been carried out to study the structure geometry influence on the crystallinity degree distribution in the layers under various surface cooling regimes. According to the simulation results, the temperature distribution fields and the crystallinity degree fields were identified. The temperature difference arising in the structure layers may influence the final crystallinity degree distribution and therefore the finished product quality. Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the International Conference on Modern Trends in Manufacturing Technologies and Equipment 2019.
1. Introduction In recent years there has been an increased interest in the application of thermoplastic matrices for manufacturing a wide range of products from composite materials, including critical parts of aviation equipment. World leaders in aircraft manufacturing are applying thermoplastic composite materials (TCMs) in airframe and engine designs. Use of TCMs can dramatically reduce both time and complexity of manufacturing various items, therefore, it simplifies creation of complex configuration particles, improves equipment performance, reduces the amount of assembly operations. When creating important loaded items of aviation equipment, it becomes necessary to control the process of heating and cooling the product after the structure formation. This is due to the fact that the cooling speed affects the processes of formation and development of spherulites, supramolecular formations, in a thermoplastic matrix. The thermoplastic degree of crystallinity, in turn, significantly affects thermoplastic physical and mechanical properties. With an increase in the degree of crystallinity, as a rule, the elastic modulus and material strength increase, but the ultimate deformation of elongation and fracture toughness decrease, i.e. the material becomes more durable but fragile [1–10]. In this case, the material nature and energy of destruction [11] change. ⇑ Corresponding author. E-mail address: [email protected] (Y. Pristupova).
In this regard, heat treatment of polymer items is vastly important because it provides opportunity and conditions to create items with supramolecular structures ensuring optimum durability. Or provide the structural status of the item, which has an optimal complex of strength properties [12]. Heat treatment is one of the most accessible methods for regulating the polymer structure. The main influencing factors of the heat treatment are temperature and time, so any kind of heat treatment can be represented in two coordinates: temperature T, time t. The choice of one or another type of heat treatment, the type of heat transfer agent and the duration of thermal exposure should be made taking into account the properties of the polymer material, the design and operational purpose of the item. The optimum heat treatment temperature for crystalline polyamides is the maximum crystallization rate temperature. The theoretical crystallization range is located between the melting point of the polymer and the glass transition temperature. The cooling time is determined by the required degree of crystallinity of the finished item. The less this time, the lower the degree of crystallinity. Another factor influencing the degree of crystallinity is the geometric characteristics of the structure. In this work, studies of the influence of the various shapes TCM structures geometry on the degree of crystallinity under different heat treatment conditions were carried out. The results of the research will establish a pattern between the geometric shape and the structure degree of crystallinity, as well as show the processing mode effect.
https://doi.org/10.1016/j.matpr.2019.07.683 2214-7853/Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the International Conference on Modern Trends in Manufacturing Technologies and Equipment 2019.
Please cite this article as: A. Anoshkin, P. Pisarev and Y. Pristupova, Crystallinity degree numerical calculation of construction of thermoplastic composite material, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.683
2
A. Anoshkin et al. / Materials Today: Proceedings xxx (xxxx) xxx
2. Numerical model The research was carried out using a flat layered package and a corner bracket with a bend of layers at an angle of 30°. Both geometric models were made of six and twelve layers of TCM with a PEEK matrix. Geometrical dimensions of the layer: 800 800 0.3 mm. In the computational experiments, the calculation of the degree of crystallinity in the process of TCM structure manufacturing at different cooling rates was carried out. The processes were considered in a three-dimensional unsteady formulation, since the value of the degree of crystallinity depends on the intensity of layers heating and cooling. To carry out a numerical simulation of counting the degree of crystallinity of layered CMs with a thermoplastic matrix, two groups of geometric models were developed and constructed (Fig. 1). The mathematical formulation of the problem to be solved includes the nonstationary heat conduction equation for anisotropic bodies [13].
Cpq
2 2 2 @T @T @T @T @T ¼ k11 þ k22 þ k33 þ ðk23 þ k32 Þ @t @x @y @z @y @T @T @T @T @T þ ðk31 þ k13 Þ þ ðk12 þ k21 Þ ; @z @z @x @x @y
ð1Þ
where T(x) is the value of the temperature field; k11, k22, k33, k23, k32, k31, k13, k12, k21 are the thermal conductivity of the material in the directions x, y, z; t is time; Cp is the specific heat capacity of the material; q is the density of the material. As initial conditions, the initial value of the thermoplastic layers T(x, y, z, 0) = 375 °C was set [1–3]. The cooling mode was set using the boundary conditions of the first kind as the boundary conditions on the surfaces of structurally similar elements.
weight factor of the first and second crystallization mechanisms; Fvc1 is the value of the degree of crystallinity obtained as a result of the nucleation of crystals; Fvc2 is the value of the degree of crystallinity obtained as a result of the growth of existing crystals.
Z F v ci ¼ 1 exp C1i
Texp C2i =ðT T g þ 51:6Þ io i ðn 1Þ þ C3i =TðT mi TÞ2 ni ti i dt i ti
0
ð4Þ
Upon condition:
x1 þ x2 ¼ 1; where i ¼ 1 or 2 process
ð5Þ
where C1i is a constant coefficient of temperature-dependent preexponential coefficient (snK1); C2i is an empirical parameter related to the temperature dependence of viscosity (K); C3i is a parameter associated with free nucleation enthalpy (K3); Fvci is an integral with time expression describing the nucleation and growth of a crystal; n1 is the index of Abraham; Tmi is the crystals melting temperature; ti is the time starting from the onset of crystallization lasting till process i, (s). Integral expressions are evaluated simultaneously as a function of temperature, provided that Τ < Tmi, a crystallization cannot occur above the melt temperature for a particular mechanism. Accordingly, for each crystallization process, ti = 0 is defined as the time at which Τ = Tmi. For example, if Tm2 < Tm1, only the second equation is estimated as the temperature drops from Tm2 to Tm1. Once the temperature reaches Tm1, both equations are evaluated and integrated until the temperature drops to Tg-51.6. The constants necessary to solve Eq. (1), determined experimentally, are given in [1–3]. When developing a finite element model, a hexagonal end element SOLID90 was used (Fig. 2). The maximum element size for a
Tðx; y; z; tÞ ¼ T 10 C; where : 0 t 1707:6 s:; at 375 T 90:4 : Tðx; y; z; 1707:6Þ ¼ 90:4; Tðx; y; z; tÞ ¼ T 0:6 C; where : 0 t 28460 s:; at 375 T 90:4 : Tðx; y; z; 28460Þ ¼ 90:4;
ð2Þ
Tðx; y; z; tÞ ¼ T 60 C; where : 0 t 284 s:; at 375 T 90:4 : Tðx; y; z; 284Þ ¼ 90:4:
Relations (3)–(5) describing the value of relative crystallinity are given in [1–3]. Below is the full view of the relationships:
X v c ¼ X v c1 ðx1 F v c1 þ x2 F v c2 Þ
ð3Þ
where Xvc is the value of the relative degree of crystallinity; Xvx1 is the value of the equilibrium degree of crystallinity; x1,x2 is the
layer was taken to be 2 mm. When conducting computational experiments, the convergence in the grid was monitored. The numerical experiment was considered converged on the grid, in the case when the values of the degree of crystallinity at the control points of the structure did not change with further refinement of the finite element grid.
Fig. 1. General view of the geometric models, (a) the layered package; (b) the corner bracket with an angle of 30°.
Please cite this article as: A. Anoshkin, P. Pisarev and Y. Pristupova, Crystallinity degree numerical calculation of construction of thermoplastic composite material, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.683
A. Anoshkin et al. / Materials Today: Proceedings xxx (xxxx) xxx
3
Fig. 2. General view of the finite element model (a) the layered package; (b) the corner bracket.
As a solution method, the finite element method is chosen. The numerical model is implemented in the ANSYS Workbench software package.
3. Results and discussions
Fig. 3. Scheme of the location of control points for: (a) the layered package; (b) the bracket.
As the results of computational experiments the temperature distribution fields in the sample layers were obtained. For a more detailed analysis of the temperature distribution in the structures under consideration, epures were constructed. The layout of epures going through the control points along the thickness of the structure is presented in Fig. 3.
Fig. 4. Dependence of temperature values on the structure height: (a, b, c) the layered package; (d, e, f) the corner bracket at times t = 360 s, 3600 s, 60 s.
Please cite this article as: A. Anoshkin, P. Pisarev and Y. Pristupova, Crystallinity degree numerical calculation of construction of thermoplastic composite material, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.683
4
A. Anoshkin et al. / Materials Today: Proceedings xxx (xxxx) xxx
Fig. 5. Dependence of the values of the degree of crystallinity on the structure height: (a, b, c) the layered packet; (d, e, f) the corner bracket at characteristic moments.
Fig. 6. The dependence of the average value of the degree of crystallinity on the temperature in: (a) the layered package; (b) the corner bracket.
Please cite this article as: A. Anoshkin, P. Pisarev and Y. Pristupova, Crystallinity degree numerical calculation of construction of thermoplastic composite material, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.683
A. Anoshkin et al. / Materials Today: Proceedings xxx (xxxx) xxx
Figs. 4, 5 shows the graphs of the distribution of temperatures and crystallinity values at the control points. Analysis of the results obtained revealed a temperature difference between the extreme and central layers of the package of 2° during the entire simulation time at the surface cooling rate V = 60 °C/min. For the bracket, the maximum temperature difference is 10° at the same cooling rate. A comparative analysis of the obtained dependences revealed a five times increase in temperature difference for the corner bracket. When considering the results presented in Fig. 5, it was found that at cooling rates V = 0.6 °C/min, V = 10 °C/min, the layered packet has a uniform distribution of the degree of crystallinity. Moreover, for the bracket, the degree of crystallinity is observed to be non-uniform at cooling rates V = 10 °C/min, V = 60 °C/min. The graphs of the dependences of the average value of the degree of crystallinity in the temperature range are based on the obtained temperature distribution in the layers of the structure. Fig. 6 shows the dependences of the degree of crystallinity at surface cooling rates of V = 0.6 °C/min, V = 10 °C/min, V = 60 °C/min. Analysis of the results presented in Fig. 6 revealed that a decrease in the cooling rate of the layered packet promotes an increase in the degree of crystallinity. It has been determined that the range of a uniform value of the degree of crystallinity increases with decreasing the layered packet surface cooling rate. Fig. 6 shows the difference of the degree of crystallinity in the sample for the considered cooling rates at a temperature T = 285 °C. Comparative analysis has been carried out of the dependences of the effect of sample thickness on the uniformity of the degree of crystallinity distribution in the sample volume. 4. Conclusion In this research, physical and mathematical models were formulated for calculating the structure degree of crystallinity in the process of surfaces cooling. A numerical study of the structure geometry influence on the degree of crystallinity was carried out. Temperature distribution fields and the degree of crystallinity values were obtained for a flat layered sample and a corner bracket sample with an angle of 30°, both made of TCM with a PEEK matrix. The results of the research showed that when the cooling rate is above V = 10 °C/min, a variation in the degree of crystallinity appears in the corner bracket sample. According to the simulation
5
results, it can be said that the temperature difference arising in the structure layers can influence the final distribution of the degree of crystallinity in the cooling process. The following features of the research can be distinguished: for a flat layered packet the surface cooling mode does not have a significant effect on the dispersion of the degree of crystallinity; for the corner bracket it was revealed that the temperature difference arising from an inadequate cooling mode led to a variation in the degree of crystallinity; the epure of the average degree of crystallinity value versus temperature is similar for the two structures under consideration, but there are differences for the temperatures T = 315 °C, 275 °C, 185 °C. At the next stages of the research it is planned to conduct a more detailed study of the dependence of the degree of crystallinity on various thicknesses and angles of the structure. It is also planned to conduct a study of the degree of crystallinity effect on the structure mechanical characteristics in various operating conditions. Acknowledgments The work was carried out with the financial support of the state represented by the Ministry of Education and Science of Russia, the unique identifier of the project RFMEFI57717X0261. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
W.E. Lawrence, J.C. Seferis, J.W.J.R. Gillespie, Polym. Compos. 2 (1992) 8696. C.N. Velisaris, J.C. Seferis, Polym. Eng. Sci. 9 (1988) 1322. C.N. Velisaris, J.C. Seferis, Polym. Eng. Sci. 22 (1986) 15741581. Y. Lee, R.S. Porter, Polym. Eng. Sci. 26 (1986) 633–639. M.C. Li, J.J. Wu, A.C. Loos, J. Morton, J. Compos. Mater. 31 (1997) 212–243. V.V. Lapshin, Foundations of thermoplastics processing by injection molding, Chemistry, Moscow (1974) (in Russian). T.J. Chapman Jr., J.W. Gillespie, R.B. Pipes, E. Manson, J.C. Seferis, J. Compos. Mater. 26 (1990) 616643. N.A. Trufanov, O.Yu. Smetannikov, T.G. Zavyalova, Mat. Modeling. 7 (2000) 45– 50 (in Russian). John J. Tierney, J.W. Gillespie Jr., Compos. A Appl. Sci. Manuf. 35 (2004) 547– 558. B.N. Fedulov, A.A. Saonov, M.M. Kantor, S.V. Lomov, Compos. Nanostruc. 2 (2017) 102–122 (in Russian). I.N. Fedorova, Effect of Polymerization and Heat Treatment on the Properties of Caprolon, TSNIITS, Khabarovsk, 1971 (in Russian). A.A. Tager, Physicochemistry of polymers, Chemistry, Moscow (1978) (in Russian). G. Karslow, D. Eger, Thermal conductivity of solids, Science, Moscow (1964) (in Russian).
Please cite this article as: A. Anoshkin, P. Pisarev and Y. Pristupova, Crystallinity degree numerical calculation of construction of thermoplastic composite material, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.683
Contents lists available at ScienceDirect
Materials Today: Proceedings journal homepage: www.elsevier.com/locate/matpr
Crystallinity degree numerical calculation of construction of thermoplastic composite material Aleksandr Anoshkin, Pavel Pisarev, Yulia Pristupova ⇑ Perm National Research Polytechnic University, Komsomolsky Prospect 29, Perm 614000, Russia
a r t i c l e
i n f o
Article history: Received 15 May 2019 Received in revised form 9 July 2019 Accepted 24 July 2019 Available online xxxx Keywords: Degree of crystallinity Thermoplastic composite material Influence of the structure geometry Numerical simulation Temperature Technological processing conditions
a b s t r a c t In this work, authors formulated physical and mathematical models to calculate the crystallinity degree in the heat treatment process of a thermoplastic composite material structure made. Two structure types were considered: a layered package and a corner bracket. Computational experiments have been carried out to study the structure geometry influence on the crystallinity degree distribution in the layers under various surface cooling regimes. According to the simulation results, the temperature distribution fields and the crystallinity degree fields were identified. The temperature difference arising in the structure layers may influence the final crystallinity degree distribution and therefore the finished product quality. Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the International Conference on Modern Trends in Manufacturing Technologies and Equipment 2019.
1. Introduction In recent years there has been an increased interest in the application of thermoplastic matrices for manufacturing a wide range of products from composite materials, including critical parts of aviation equipment. World leaders in aircraft manufacturing are applying thermoplastic composite materials (TCMs) in airframe and engine designs. Use of TCMs can dramatically reduce both time and complexity of manufacturing various items, therefore, it simplifies creation of complex configuration particles, improves equipment performance, reduces the amount of assembly operations. When creating important loaded items of aviation equipment, it becomes necessary to control the process of heating and cooling the product after the structure formation. This is due to the fact that the cooling speed affects the processes of formation and development of spherulites, supramolecular formations, in a thermoplastic matrix. The thermoplastic degree of crystallinity, in turn, significantly affects thermoplastic physical and mechanical properties. With an increase in the degree of crystallinity, as a rule, the elastic modulus and material strength increase, but the ultimate deformation of elongation and fracture toughness decrease, i.e. the material becomes more durable but fragile [1–10]. In this case, the material nature and energy of destruction [11] change. ⇑ Corresponding author. E-mail address: [email protected] (Y. Pristupova).
In this regard, heat treatment of polymer items is vastly important because it provides opportunity and conditions to create items with supramolecular structures ensuring optimum durability. Or provide the structural status of the item, which has an optimal complex of strength properties [12]. Heat treatment is one of the most accessible methods for regulating the polymer structure. The main influencing factors of the heat treatment are temperature and time, so any kind of heat treatment can be represented in two coordinates: temperature T, time t. The choice of one or another type of heat treatment, the type of heat transfer agent and the duration of thermal exposure should be made taking into account the properties of the polymer material, the design and operational purpose of the item. The optimum heat treatment temperature for crystalline polyamides is the maximum crystallization rate temperature. The theoretical crystallization range is located between the melting point of the polymer and the glass transition temperature. The cooling time is determined by the required degree of crystallinity of the finished item. The less this time, the lower the degree of crystallinity. Another factor influencing the degree of crystallinity is the geometric characteristics of the structure. In this work, studies of the influence of the various shapes TCM structures geometry on the degree of crystallinity under different heat treatment conditions were carried out. The results of the research will establish a pattern between the geometric shape and the structure degree of crystallinity, as well as show the processing mode effect.
https://doi.org/10.1016/j.matpr.2019.07.683 2214-7853/Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the International Conference on Modern Trends in Manufacturing Technologies and Equipment 2019.
Please cite this article as: A. Anoshkin, P. Pisarev and Y. Pristupova, Crystallinity degree numerical calculation of construction of thermoplastic composite material, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.683
2
A. Anoshkin et al. / Materials Today: Proceedings xxx (xxxx) xxx
2. Numerical model The research was carried out using a flat layered package and a corner bracket with a bend of layers at an angle of 30°. Both geometric models were made of six and twelve layers of TCM with a PEEK matrix. Geometrical dimensions of the layer: 800 800 0.3 mm. In the computational experiments, the calculation of the degree of crystallinity in the process of TCM structure manufacturing at different cooling rates was carried out. The processes were considered in a three-dimensional unsteady formulation, since the value of the degree of crystallinity depends on the intensity of layers heating and cooling. To carry out a numerical simulation of counting the degree of crystallinity of layered CMs with a thermoplastic matrix, two groups of geometric models were developed and constructed (Fig. 1). The mathematical formulation of the problem to be solved includes the nonstationary heat conduction equation for anisotropic bodies [13].
Cpq
2 2 2 @T @T @T @T @T ¼ k11 þ k22 þ k33 þ ðk23 þ k32 Þ @t @x @y @z @y @T @T @T @T @T þ ðk31 þ k13 Þ þ ðk12 þ k21 Þ ; @z @z @x @x @y
ð1Þ
where T(x) is the value of the temperature field; k11, k22, k33, k23, k32, k31, k13, k12, k21 are the thermal conductivity of the material in the directions x, y, z; t is time; Cp is the specific heat capacity of the material; q is the density of the material. As initial conditions, the initial value of the thermoplastic layers T(x, y, z, 0) = 375 °C was set [1–3]. The cooling mode was set using the boundary conditions of the first kind as the boundary conditions on the surfaces of structurally similar elements.
weight factor of the first and second crystallization mechanisms; Fvc1 is the value of the degree of crystallinity obtained as a result of the nucleation of crystals; Fvc2 is the value of the degree of crystallinity obtained as a result of the growth of existing crystals.
Z F v ci ¼ 1 exp C1i
Texp C2i =ðT T g þ 51:6Þ io i ðn 1Þ þ C3i =TðT mi TÞ2 ni ti i dt i ti
0
ð4Þ
Upon condition:
x1 þ x2 ¼ 1; where i ¼ 1 or 2 process
ð5Þ
where C1i is a constant coefficient of temperature-dependent preexponential coefficient (snK1); C2i is an empirical parameter related to the temperature dependence of viscosity (K); C3i is a parameter associated with free nucleation enthalpy (K3); Fvci is an integral with time expression describing the nucleation and growth of a crystal; n1 is the index of Abraham; Tmi is the crystals melting temperature; ti is the time starting from the onset of crystallization lasting till process i, (s). Integral expressions are evaluated simultaneously as a function of temperature, provided that Τ < Tmi, a crystallization cannot occur above the melt temperature for a particular mechanism. Accordingly, for each crystallization process, ti = 0 is defined as the time at which Τ = Tmi. For example, if Tm2 < Tm1, only the second equation is estimated as the temperature drops from Tm2 to Tm1. Once the temperature reaches Tm1, both equations are evaluated and integrated until the temperature drops to Tg-51.6. The constants necessary to solve Eq. (1), determined experimentally, are given in [1–3]. When developing a finite element model, a hexagonal end element SOLID90 was used (Fig. 2). The maximum element size for a
Tðx; y; z; tÞ ¼ T 10 C; where : 0 t 1707:6 s:; at 375 T 90:4 : Tðx; y; z; 1707:6Þ ¼ 90:4; Tðx; y; z; tÞ ¼ T 0:6 C; where : 0 t 28460 s:; at 375 T 90:4 : Tðx; y; z; 28460Þ ¼ 90:4;
ð2Þ
Tðx; y; z; tÞ ¼ T 60 C; where : 0 t 284 s:; at 375 T 90:4 : Tðx; y; z; 284Þ ¼ 90:4:
Relations (3)–(5) describing the value of relative crystallinity are given in [1–3]. Below is the full view of the relationships:
X v c ¼ X v c1 ðx1 F v c1 þ x2 F v c2 Þ
ð3Þ
where Xvc is the value of the relative degree of crystallinity; Xvx1 is the value of the equilibrium degree of crystallinity; x1,x2 is the
layer was taken to be 2 mm. When conducting computational experiments, the convergence in the grid was monitored. The numerical experiment was considered converged on the grid, in the case when the values of the degree of crystallinity at the control points of the structure did not change with further refinement of the finite element grid.
Fig. 1. General view of the geometric models, (a) the layered package; (b) the corner bracket with an angle of 30°.
Please cite this article as: A. Anoshkin, P. Pisarev and Y. Pristupova, Crystallinity degree numerical calculation of construction of thermoplastic composite material, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.683
A. Anoshkin et al. / Materials Today: Proceedings xxx (xxxx) xxx
3
Fig. 2. General view of the finite element model (a) the layered package; (b) the corner bracket.
As a solution method, the finite element method is chosen. The numerical model is implemented in the ANSYS Workbench software package.
3. Results and discussions
Fig. 3. Scheme of the location of control points for: (a) the layered package; (b) the bracket.
As the results of computational experiments the temperature distribution fields in the sample layers were obtained. For a more detailed analysis of the temperature distribution in the structures under consideration, epures were constructed. The layout of epures going through the control points along the thickness of the structure is presented in Fig. 3.
Fig. 4. Dependence of temperature values on the structure height: (a, b, c) the layered package; (d, e, f) the corner bracket at times t = 360 s, 3600 s, 60 s.
Please cite this article as: A. Anoshkin, P. Pisarev and Y. Pristupova, Crystallinity degree numerical calculation of construction of thermoplastic composite material, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.683
4
A. Anoshkin et al. / Materials Today: Proceedings xxx (xxxx) xxx
Fig. 5. Dependence of the values of the degree of crystallinity on the structure height: (a, b, c) the layered packet; (d, e, f) the corner bracket at characteristic moments.
Fig. 6. The dependence of the average value of the degree of crystallinity on the temperature in: (a) the layered package; (b) the corner bracket.
Please cite this article as: A. Anoshkin, P. Pisarev and Y. Pristupova, Crystallinity degree numerical calculation of construction of thermoplastic composite material, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.683
A. Anoshkin et al. / Materials Today: Proceedings xxx (xxxx) xxx
Figs. 4, 5 shows the graphs of the distribution of temperatures and crystallinity values at the control points. Analysis of the results obtained revealed a temperature difference between the extreme and central layers of the package of 2° during the entire simulation time at the surface cooling rate V = 60 °C/min. For the bracket, the maximum temperature difference is 10° at the same cooling rate. A comparative analysis of the obtained dependences revealed a five times increase in temperature difference for the corner bracket. When considering the results presented in Fig. 5, it was found that at cooling rates V = 0.6 °C/min, V = 10 °C/min, the layered packet has a uniform distribution of the degree of crystallinity. Moreover, for the bracket, the degree of crystallinity is observed to be non-uniform at cooling rates V = 10 °C/min, V = 60 °C/min. The graphs of the dependences of the average value of the degree of crystallinity in the temperature range are based on the obtained temperature distribution in the layers of the structure. Fig. 6 shows the dependences of the degree of crystallinity at surface cooling rates of V = 0.6 °C/min, V = 10 °C/min, V = 60 °C/min. Analysis of the results presented in Fig. 6 revealed that a decrease in the cooling rate of the layered packet promotes an increase in the degree of crystallinity. It has been determined that the range of a uniform value of the degree of crystallinity increases with decreasing the layered packet surface cooling rate. Fig. 6 shows the difference of the degree of crystallinity in the sample for the considered cooling rates at a temperature T = 285 °C. Comparative analysis has been carried out of the dependences of the effect of sample thickness on the uniformity of the degree of crystallinity distribution in the sample volume. 4. Conclusion In this research, physical and mathematical models were formulated for calculating the structure degree of crystallinity in the process of surfaces cooling. A numerical study of the structure geometry influence on the degree of crystallinity was carried out. Temperature distribution fields and the degree of crystallinity values were obtained for a flat layered sample and a corner bracket sample with an angle of 30°, both made of TCM with a PEEK matrix. The results of the research showed that when the cooling rate is above V = 10 °C/min, a variation in the degree of crystallinity appears in the corner bracket sample. According to the simulation
5
results, it can be said that the temperature difference arising in the structure layers can influence the final distribution of the degree of crystallinity in the cooling process. The following features of the research can be distinguished: for a flat layered packet the surface cooling mode does not have a significant effect on the dispersion of the degree of crystallinity; for the corner bracket it was revealed that the temperature difference arising from an inadequate cooling mode led to a variation in the degree of crystallinity; the epure of the average degree of crystallinity value versus temperature is similar for the two structures under consideration, but there are differences for the temperatures T = 315 °C, 275 °C, 185 °C. At the next stages of the research it is planned to conduct a more detailed study of the dependence of the degree of crystallinity on various thicknesses and angles of the structure. It is also planned to conduct a study of the degree of crystallinity effect on the structure mechanical characteristics in various operating conditions. Acknowledgments The work was carried out with the financial support of the state represented by the Ministry of Education and Science of Russia, the unique identifier of the project RFMEFI57717X0261. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
W.E. Lawrence, J.C. Seferis, J.W.J.R. Gillespie, Polym. Compos. 2 (1992) 8696. C.N. Velisaris, J.C. Seferis, Polym. Eng. Sci. 9 (1988) 1322. C.N. Velisaris, J.C. Seferis, Polym. Eng. Sci. 22 (1986) 15741581. Y. Lee, R.S. Porter, Polym. Eng. Sci. 26 (1986) 633–639. M.C. Li, J.J. Wu, A.C. Loos, J. Morton, J. Compos. Mater. 31 (1997) 212–243. V.V. Lapshin, Foundations of thermoplastics processing by injection molding, Chemistry, Moscow (1974) (in Russian). T.J. Chapman Jr., J.W. Gillespie, R.B. Pipes, E. Manson, J.C. Seferis, J. Compos. Mater. 26 (1990) 616643. N.A. Trufanov, O.Yu. Smetannikov, T.G. Zavyalova, Mat. Modeling. 7 (2000) 45– 50 (in Russian). John J. Tierney, J.W. Gillespie Jr., Compos. A Appl. Sci. Manuf. 35 (2004) 547– 558. B.N. Fedulov, A.A. Saonov, M.M. Kantor, S.V. Lomov, Compos. Nanostruc. 2 (2017) 102–122 (in Russian). I.N. Fedorova, Effect of Polymerization and Heat Treatment on the Properties of Caprolon, TSNIITS, Khabarovsk, 1971 (in Russian). A.A. Tager, Physicochemistry of polymers, Chemistry, Moscow (1978) (in Russian). G. Karslow, D. Eger, Thermal conductivity of solids, Science, Moscow (1964) (in Russian).
Please cite this article as: A. Anoshkin, P. Pisarev and Y. Pristupova, Crystallinity degree numerical calculation of construction of thermoplastic composite material, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.683