Simulation of the Dynamic Responses of Layered Polymer Composites under Plate Impact Using the DSGZ Model
Abstract
:1. Introduction
2. Numerical Simulation Methods
2.1. Time Integration Scheme of the Flow Theory
2.2. The DSGZ Models
2.3. VUMAT Implementation
2.4. Other Material Models
2.5. Impact Dynamics
3. Modeling and Simulation
4. Results and Discussion
4.1. VUMAT Subroutine Validation
4.2. Dynamic Responses of the Single-Layer Target
4.3. Dynamic Responses of the CPM Composite
4.4. Layer Sequence Effect on the Protected Target
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Zhang, X.; Xu, Y.; Zhang, X.; Wu, H.; Shen, J.; Chen, R.; Xiong, Y.; Li, J.; Guo, S. Progress on the Layer-by-Layer Assembly of Multilayered Polymer Composites: Strategy, Structural Control and Applications. Prog. Polym. Sci. 2019, 89, 76–107. [Google Scholar] [CrossRef]
- Stephen, C.; Shivamurthy, B.; Mohan, M.; Mourad, A.-H.I.; Selvam, R.; Thimmappa, B.H.S. Low Velocity Impact Behavior of Fabric Reinforced Polymer Composites—A Review. Eng. Sci. 2022, 18, 75–97. [Google Scholar] [CrossRef]
- Tasdemirci, A.; Hall, I.W.; Gama, B.A.; Guden, M. Stress Wave Propagation Effects in Two- and Three-Layered Composite Materials. J. Compos. Mater. 2004, 38, 995–1009. [Google Scholar] [CrossRef]
- Zhuang, S.; Ravichandran, G.; Grady, D.E. An Experimental Investigation of Shock Wave Propagation in Periodically Layered Composites. J. Mech. Phys. Solids 2003, 51, 245–265. [Google Scholar] [CrossRef]
- Oladele, I.O.; Omotosho, T.F.; Adediran, A.A. Polymer-Based Composites: An Indispensable Material for Present and Future Applications. Int. J. Polym. Sci. 2020, 2020, 8834518. [Google Scholar] [CrossRef]
- Agrawal, S.; Singh, K.K.; Sarkar, P. Impact Damage on Fibre-Reinforced Polymer Matrix Composite—A Review. J. Compos. Mater. 2014, 48, 317–332. [Google Scholar] [CrossRef]
- Park, R.; Jang, J. Impact Behavior of Aramid Fiber/Glass Fiber Hybrid Composites: The Effect of Stacking Sequence. Polym. Compos. 2001, 22, 80–89. [Google Scholar] [CrossRef]
- Lopes, C.S.; Camanho, P.P.; Gürdal, Z.; Maimí, P.; González, E.V. Low-Velocity Impact Damage on Dispersed Stacking Sequence Laminates. Part II: Numerical Simulations. Compos. Sci. Technol. 2009, 69, 937–947. [Google Scholar] [CrossRef]
- Mousavi, M.V.; Khoramishad, H. Investigation of Energy Absorption in Hybridized Fiber-Reinforced Polymer Composites under High-Velocity Impact Loading. Int. J. Impact Eng. 2020, 146, 103692. [Google Scholar] [CrossRef]
- Schwab, M.; Pettermann, H.E. Modelling and Simulation of Damage and Failure in Large Composite Components Subjected to Impact Loads. Compos. Struct. 2016, 158, 208–216. [Google Scholar] [CrossRef]
- Mullaoğlu, F.; Usta, F.; Türkmen, H.S.; Kazancı, Z.; Balkan, D.; Akay, E. Deformation Behavior of the Polycarbonate Plates Subjected to Impact Loading. Procedia Eng. 2016, 167, 143–150. [Google Scholar] [CrossRef]
- Zhang, W.; Tekalur, S.A.; Huynh, L. Impact Behavior and Dynamic Failure of PMMA and PC Plates. In Dynamic Behavior of Materials; Proulx, T., Ed.; Conference Proceedings of the Society for Experimental Mechanics Series; Springer: New York, NY, USA, 2011; Volume 1, pp. 93–104. ISBN 978-1-4419-8227-8. [Google Scholar]
- Antoine, G.O.; Batra, R.C. Low Speed Impact of Laminated Polymethylmethacrylate/Adhesive/Polycarbonate Plates. Compos. Struct. 2014, 116, 193–210. [Google Scholar] [CrossRef]
- Tekalur, S.A.; Shukla, A.; Shivakumar, K. Blast Resistance of Polyurea Based Layered Composite Materials. Compos. Struct. 2008, 84, 271–281. [Google Scholar] [CrossRef]
- McShane, G.J.; Stewart, C.; Aronson, M.T.; Wadley, H.N.G.; Fleck, N.A.; Deshpande, V.S. Dynamic Rupture of Polymer–Metal Bilayer Plates. Int. J. Solids Struct. 2008, 45, 4407–4426. [Google Scholar] [CrossRef]
- Stergiou, T.; Baxevanakis, K.P.; Roy, A.; Sazhenkov, N.A.; Nikhamkin, S.M.; Silberschmidt, V.V. Impact of Polyurea-Coated Metallic Targets: Computational Framework. Compos. Struct. 2021, 267, 113893. [Google Scholar] [CrossRef]
- Amini, M.R.; Simon, J.; Nemat-Nasser, S. Numerical Modeling of Effect of Polyurea on Response of Steel Plates to Impulsive Loads in Direct Pressure-Pulse Experiments. Mech. Mater. 2010, 42, 615–627. [Google Scholar] [CrossRef]
- Chu, D.; Li, Z.; Yao, K.; Wang, Y.; Tian, R.; Zhuang, Z.; Liu, Z. Studying the Strengthening Mechanism and Thickness Effect of Elastomer Coating on the Ballistic-Resistance of the Polyurea-Coated Steel Plate. Int. J. Impact Eng. 2022, 163, 104181. [Google Scholar] [CrossRef]
- Jerabek, M.; Major, Z.; Lang, R.W. Uniaxial Compression Testing of Polymeric Materials. Polym. Test. 2010, 29, 302–309. [Google Scholar] [CrossRef]
- Lin, P.; Cheng, S.; Wang, S.-Q. Strain Hardening During Uniaxial Compression of Polymer Glasses. ACS Macro Lett. 2014, 3, 784–787. [Google Scholar] [CrossRef] [PubMed]
- Richeton, J.; Ahzi, S.; Vecchio, K.S.; Jiang, F.C.; Adharapurapu, R.R. Influence of Temperature and Strain Rate on the Mechanical Behavior of Three Amorphous Polymers: Characterization and Modeling of the Compressive Yield Stress. Int. J. Solids Struct. 2006, 43, 2318–2335. [Google Scholar] [CrossRef]
- G’sell, C.; Jonas, J.J. Determination of the Plastic Behaviour of Solid Polymers at Constant True Strain Rate. J. Mater. Sci. 1979, 14, 583–591. [Google Scholar] [CrossRef]
- Duan, Y.; Saigal, A.; Greif, R.; Zimmerman, M.A. A Uniform Phenomenological Constitutive Model for Glassy and Semicrystalline Polymers. Polym. Eng. Sci. 2001, 41, 1322–1328. [Google Scholar] [CrossRef]
- Wang, J.; Xu, Y.; Zhang, W. Finite Element Simulation of PMMA Aircraft Windshield against Bird Strike by Using a Rate and Temperature Dependent Nonlinear Viscoelastic Constitutive Model. Compos. Struct. 2014, 108, 21–30. [Google Scholar] [CrossRef]
- Zhu, H.; Ou, H.; Popov, A. A New Phenomenological Constitutive Model for Thermoplastics. Mech. Mater. 2021, 157, 103817. [Google Scholar] [CrossRef]
- Ferreira, B.P.; Carvalho Alves, A.F.; Andrade Pires, F.M. An Efficient Finite Strain Constitutive Model for Amorphous Thermoplastics: Fully Implicit Computational Implementation and Optimization-Based Parameter Calibration. Comput. Struct. 2023, 281, 107007. [Google Scholar] [CrossRef]
- Xiang, Y.; Zhong, D.; Rudykh, S.; Zhou, H.; Qu, S.; Yang, W. A Review of Physically Based and Thermodynamically Based Constitutive Models for Soft Materials. J. Appl. Mech. 2020, 87, 110801. [Google Scholar] [CrossRef]
- Ling, S.; Wu, Z.; Mei, J. Comparison and Review of Classical and Machine Learning-Based Constitutive Models for Polymers Used in Aeronautical Thermoplastic Composites. Rev. Adv. Mater. Sci. 2023, 62, 20230107. [Google Scholar] [CrossRef]
- Duodu, E.A.; Gu, J.N.; Shang, Z.; Ding, W.; Tang, S. Damage Induced by High-Velocity Impact on Composite Structures Using Finite Element Simulation. Iran. J. Sci. Technol. Trans. Mech. Eng. 2017, 41, 97–107. [Google Scholar] [CrossRef]
- Achour, N.; Chatzigeorgiou, G.; Meraghni, F.; Chemisky, Y.; Fitoussi, J. Implicit Implementation and Consistent Tangent Modulus of a Viscoplastic Model for Polymers. Int. J. Mech. Sci. 2015, 103, 297–305. [Google Scholar] [CrossRef]
- Nahar, C.; Sanariya, S.; Gurrala, P.K. Numerical Simulation of Polymers at Low and Moderate Strain Rates. Mater. Today Proc. 2021, 44, 696–700. [Google Scholar] [CrossRef]
- Yu, M.-H. Elasto-Plastic Constitutive Relations. In Generalized Plasticity; Springer: Berlin/Heidelberg, Germany, 2006; pp. 122–153. ISBN 978-3-540-25127-9. [Google Scholar]
- Borja, R.I. J2 Plasticity. In Plasticity; Springer: Berlin/Heidelberg, Germany, 2013; pp. 31–58. ISBN 978-3-642-38546-9. [Google Scholar]
- Taylor, G.I.; Quinney, H. The Latent Energy Remaining in a Metal after Cold Working. Proc. R. Soc. Lond. Ser. Contain. Pap. Math. Phys. Character 1934, 143, 307–326. [Google Scholar] [CrossRef]
- Wilkins, M.L. Calculation of Elastic-Plastic Flow; University of California-Lawrence Radiation Laboratory: Livermore, CA, USA, 1963. [Google Scholar]
- Maenchen, G.; Sack, S. The Tensor Code; University of California-Lawrence Radiation Laboratory: Livermore, CA, USA, 1963. [Google Scholar]
- Simo, J.C.; Hughes, T.J.R. Computational Inelasticity; Interdisciplinary Applied Mathematics; Springer: New York, NY, USA, 1998; Volume 7, ISBN 978-0-387-97520-7. [Google Scholar]
- Dunne, F.; Petrinic, N. Introduction to Computational Plasticity; Oxford University Press: Oxford, UK, 2005; ISBN 978-0-19-856826-1. [Google Scholar]
- Zaera, R.; Fernández-Sáez, J. An Implicit Consistent Algorithm for the Integration of Thermoviscoplastic Constitutive Equations in Adiabatic Conditions and Finite Deformations. Int. J. Solids Struct. 2006, 43, 1594–1612. [Google Scholar] [CrossRef]
- Ming, L.; Pantalé, O. An Efficient and Robust VUMAT Implementation of Elastoplastic Constitutive Laws in Abaqus/Explicit Finite Element Code. Mech. Ind. 2018, 19, 308. [Google Scholar] [CrossRef]
- Ypma, T.J. Historical Development of the Newton–Raphson Method. SIAM Rev. 1995, 37, 531–551. [Google Scholar] [CrossRef]
- Neto, M.A.; Ambrósio, J.A.C.; Leal, R.P. Sensitivity Analysis of Flexible Multibody Systems Using Composite Materials Components. Int. J. Numer. Methods Eng. 2009, 77, 386–413. [Google Scholar] [CrossRef]
- Johnson, G.R.; Cook, W.H. A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates, and High Temperatures. In Proceedings of the 7th International Symposium on Ballistics, The Hague, The Netherlands, 19–21 April 1983; Volume 21, pp. 541–547. [Google Scholar]
- Terselius, B.; Gedde, U.W.; Jansson, J.F. Failure of Plastics: With 51 Tables; Brostow, W., Corneliussen, R.D., Society of Plastics Engineers, Eds.; Hanser: München, Germany; Vienna, Austria; New York, NY, USA, 1986; ISBN 978-0-02-947510-2. [Google Scholar]
- Brooks, J.W. Processing Wrought Nickel and Titanium Superalloys. In Proceedings of the Conference Organized in Celebration of the 75th Anniversary of the Swedish Society for Material Technology—Thermo-Mechanical Processing: Theory, Modelling and Practice, Stockholm, Sweden, 4–6 September 1996. [Google Scholar]
- Duan, Y.; Saigal, A.; Greif, R.; Zimmerman, M.A. Analysis of Multiaxial Impact Behavior of Polymers. Polym. Eng. Sci. 2002, 42, 395–402. [Google Scholar] [CrossRef]
- Dar, U.A.; Zhang, W. Polymer Based Aerospace Structures under High Velocity Impact Applications; Experimental, Constitutive and Finite Element Analysis. J. Mech. Sci. Technol. 2015, 29, 4259–4265. [Google Scholar] [CrossRef]
- High-Velocity Impact of a Ceramic Target—SIMULIA User Assistance 2023. Available online: https://help.3ds.com/2023/english/dssimulia_established/simacaeexarefmap/simaexa-c-impactceramictarget.htm?contextscope=all (accessed on 10 January 2024).
- Mie, G. Zur Kinetischen Theorie Der Einatomigen Körper. Ann. Phys. 1903, 316, 657–697. [Google Scholar] [CrossRef]
- Grüneisen, E. Theorie Des Festen Zustandes Einatomiger Elemente. Ann. Phys. 1912, 344, 257–306. [Google Scholar] [CrossRef]
- Zhang, H.; Shukla, M.K.; Rajendran, A.M.; Jiang, S. Simulations of Single and Double Shock Experiments Using Generalized Interpolation Material Point Method with a Noise Control Strategy. Comput. Part. Mech. 2023, 10, 1795–1809. [Google Scholar] [CrossRef]
- Johnson, G.R.; Holmquist, T.J. An Improved Computational Constitutive Model for Brittle Materials. AIP Conf. Proc. 1994, 309, 981–984. [Google Scholar]
- Johnson, G.R.; Holmquist, T.J. Response of Boron Carbide Subjected to Large Strains, High Strain Rates, and High Pressures. J. Appl. Phys. 1999, 85, 8060–8073. [Google Scholar] [CrossRef]
- Ramezani, M.; Ripin, Z.M.; Ahmad, R. Numerical Simulation of Sheet Stamping Process Using Flexible Punch. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 2009, 223, 829–840. [Google Scholar] [CrossRef]
- Ramezani, M.; Ripin, Z.M.; Ahmad, R. Plastic Bulging of Sheet Metals at High Strain Rates. Int. J. Adv. Manuf. Technol. 2010, 48, 847–858. [Google Scholar] [CrossRef]
- Mooney, M. A Theory of Large Elastic Deformation. J. Appl. Phys. 1940, 11, 582–592. [Google Scholar] [CrossRef]
- Doman, D.A.; Cronin, D.S.; Salisbury, C.P. Characterization of Polyurethane Rubber at High Deformation Rates. Exp. Mech. 2006, 46, 367–376. [Google Scholar] [CrossRef]
- Mohotti, D.; Ali, M.; Ngo, T.; Lu, J.; Mendis, P. Strain Rate Dependent Constitutive Model for Predicting the Material Behaviour of Polyurea under High Strain Rate Tensile Loading. Mater. Des. 2014, 53, 830–837. [Google Scholar] [CrossRef]
- Graff, K.F. Wave Motion in Elastic Solids; Dover Publications: New York, NY, USA, 1991; ISBN 978-0-486-66745-4. [Google Scholar]
- Duan, Y.; Saigal, A.; Greif, R.; Zimmerman, M.A. Impact Behavior and Modeling of Engineering Polymers. Polym. Eng. Sci. 2003, 43, 112–124. [Google Scholar] [CrossRef]
- El-Qoubaa, Z.; Colard, L.; Matadi Boumbimba, R.; Rusinek, A. Experimental Study and Modelling of Poly (Methyl Methacrylate) and Polycarbonate Compressive Behavior from Low to High Strain Rates. J. Dyn. Behav. Mater. 2018, 4, 179–189. [Google Scholar] [CrossRef]
- Grujicic, M.; Bell, W.C.; Pandurangan, B.; He, T. Blast-Wave Impact-Mitigation Capability of Polyurea When Used as Helmet Suspension-Pad Material. Mater. Des. 2010, 31, 4050–4065. [Google Scholar] [CrossRef]
- Derakhshani, S.M.; Schott, D.L.; Lodewijks, G. Micro–Macro Properties of Quartz Sand: Experimental Investigation and DEM Simulation. Powder Technol. 2015, 269, 127–138. [Google Scholar] [CrossRef]
- Johnson, J.N. Dynamic Fracture and Spallation in Ductile Solids. J. Appl. Phys. 1981, 52, 2812–2825. [Google Scholar] [CrossRef]
- Yaziv, D.; Bless, S.J.; Rosenberg, Z. Study of Spall and Recompaction of Ceramics Using a Double-impact Technique. J. Appl. Phys. 1985, 58, 3415–3418. [Google Scholar] [CrossRef]
- Hawkins, M.C.; Thomas, S.A.; Fensin, S.J.; Jones, D.R.; Hixson, R.S. Spall and Subsequent Recompaction of Copper under Shock Loading. J. Appl. Phys. 2020, 128, 045902. [Google Scholar] [CrossRef]
- Armanios, E.; Bucinell, R.; Wilson, D.; Chandra, N.; Chen, X.; Rajendran, A. The Effect of Material Heterogeneity on the Shock Response of Layered Systems in Plate Impact Tests. J. Compos. Technol. Res. 2002, 24, 232. [Google Scholar] [CrossRef]
(MPa·sm) | (sm) | (K) | |||||||
---|---|---|---|---|---|---|---|---|---|
PC_1 a | 28.4 | 0.0 | 0.49 | 4.02 | 0.03 | 5.8 | 415 | 6.8 | 0.038 |
PMMA_1 b | 3.9 | 0.0 | 1.91 | 1.49 | 0.0029 | 11.0 | 1191 | 11.7 | 0.064 |
PA-12 c | 3.083 | 0.0 | 0.415 | 2.687 | 3.0 | 200.0 | 870 | 6.6 | 0.01 |
ABS d | 17.85 | 0.4 | 1.83 | 0.2 | 0.06 | 5 | 306 | 50 | 0.044 |
PBT e | 24.5 | 0.0 | 0.32 | 0.12 | 0.1 | 6 | 140 | 200 | 0.058 |
PC/ABS | 19.85 | 0.0 | −1.324 | 1.984 | 0.021 | 3.58 | 232 | 22.26 | 0.0854 |
(MPa·sm) | (sm) | (K) | |||||||
PC_2 f | 8.97 | 1.127 | −0.161 | 1.35 | 0.007 | 100 | 465 | 65 | 0.093 |
PMMA_2 g | 2.7 | 1.582 | −0.76 | 2.443 | 0.03 | 20 | 800 | 18 | 0.138 |
(kg·m−3) | (GPa) | (MPa) | ||||
---|---|---|---|---|---|---|
OFHC-Cu | 8960 | 44.7 | 90 | 292 | 0.31 | 0.025 |
Steel-4340 | 7830 | 25.9 | 792 | 510 | 0.26 | 0.014 |
Al-6061 | 2700 | 77.5 | 290 | 204 | 0.35 | 0.011 |
(s−1) | (K) | (m·s−1) | ||||
1.09 | 1.0 | 1356 | 3933 | 1.49 | 1.0 | |
1.03 | 1.0 | 1793 | 5350 | 1.34 | 2.0 | |
1.34 | 1.0 | 858 | 4578 | 1.33 | 1.67 |
(kg·m−3) | (GPa) | |||||
---|---|---|---|---|---|---|
SiC | 3251 | 193 | 0.96 | 0.65 | 0.35 | 1.0 |
(s−1) | (GPa) | (GPa) | (GPa) | HEL (GPa) | ||
0.009 | 1.0 | 0.75 | 12.2 | 1.3 | 11.7 | |
(GPa) | ||||||
5.13 | 1.0 | 0.48 | 0.48 | 1.2 | 0.0 | |
FS | IDamage | (GPa) | (GPa) | (GPa) | ||
0.2 | 0 | 220 | 361 | 0 |
PU elastomer | 77.69 | −37.66 | 0.000251 |
(GPa) | (m·s−1) | |||
---|---|---|---|---|
Bone | 2.664 | 1850 | 0.94 | 0.0 |
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Zhang, H.; Rajendran, A.M.; Shukla, M.K.; Nouranian, S.; Al-Ostaz, A.; Larson, S.; Jiang, S. Simulation of the Dynamic Responses of Layered Polymer Composites under Plate Impact Using the DSGZ Model. J. Compos. Sci. 2024, 8, 159. https://doi.org/10.3390/jcs8050159
Zhang H, Rajendran AM, Shukla MK, Nouranian S, Al-Ostaz A, Larson S, Jiang S. Simulation of the Dynamic Responses of Layered Polymer Composites under Plate Impact Using the DSGZ Model. Journal of Composites Science. 2024; 8(5):159. https://doi.org/10.3390/jcs8050159
Chicago/Turabian StyleZhang, Huadian, Arunachalam M. Rajendran, Manoj K. Shukla, Sasan Nouranian, Ahmed Al-Ostaz, Steven Larson, and Shan Jiang. 2024. "Simulation of the Dynamic Responses of Layered Polymer Composites under Plate Impact Using the DSGZ Model" Journal of Composites Science 8, no. 5: 159. https://doi.org/10.3390/jcs8050159
APA StyleZhang, H., Rajendran, A. M., Shukla, M. K., Nouranian, S., Al-Ostaz, A., Larson, S., & Jiang, S. (2024). Simulation of the Dynamic Responses of Layered Polymer Composites under Plate Impact Using the DSGZ Model. Journal of Composites Science, 8(5), 159. https://doi.org/10.3390/jcs8050159