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Project titleCreation of a distributed facility for dynamic testing of structural polymer composites

AffiliationAutonomous Non-Profit Organization for Higher Education "Skolkovo Institute of Science and Technology",

Research area 09 - ENGINEERING SCIENCES, 09-101 - Durability, viability, and disintegration of materials and structures

KeywordsPolymer composites, anisotropy, high strain rate, material model, strength criterion, shock compressibility, adiabatic heating.

Annotation
For the effective design of promising structures made of polymer composite materials (PCMs) operating in a wide range of strain rates, constitutive relationships and strength criteria are required that establish a relationship between loading conditions and the limiting states of materials. The development and verification of these relationships and criteria in the range of strain rates 0.001-100000 1/s requires a large amount of experimental data on the mechanical behavior of PCM. However, the anisotropy and inhomogeneity of the PCM structure significantly complicate the experimental methods for studying of high strain rate response of this class of materials. It is urgent to solve the scientific problem of obtaining reliable experimental dependences of the mechanical characteristics and deformation curves of PCMs on the strain rate in the range 0.001-100000 1/s at various stress-strain states. The solution to this problem, in turn, requires a theoretical justification and the creation, based on traditional methods of testing isotropic materials, of a complex of dynamic testing procedures for structural PCM. Such traditional methods include, for example, drop tests, split Hopkinson pressure bar (SHPB), plate impact, electric explosion of a conductor, etc. In view of the variety and specificity of dynamic test methods, the solution of the scientific problem under consideration requires the combined efforts of various research groups specializing in various types of dynamic tests, modeling the processes of dynamic deformation and fracture of PCM, and technologies for manufacturing of PCM samples. To solve this scientific problem, a research group will be created within the framework of the project, consisting of employees of the Center for Design, Manufacturing and Materials of the Skolkovo Institute of Science and Technology (Skoltech), the Laboratory of "Dynamic Testing of Materials" of the Research Institute of Mechanics of Nizhny Novgorod State University by N.I. Lobachevsky (Research Institute of Mechanics, NNSU) and the Research Center "Dynamics" of the St. Petersburg State University (Research Center "Dynamics"). The scientific novelty of the problem under consideration lies in the creation and theoretical justification of complementary methods for dynamic testing of PCM and obtaining new experimental data necessary for constructing reliable dependences of the mechanical characteristics and deformation curves of PCM on the parameters of anisotropy and strain rate in the range 0.001-100000 1/s at various stress deformed states. Based on the obtained experimental data, a new concept of modeling the effects of the PCM loading rate will be implemented by presenting the elastic characteristics as functions of the strain rate, and the strength criterion as a function of the strain rate and the rate of damage to the medium. Within the framework of the project, a theoretical and experimental analysis of the effects of nonlinearity of the PCM deformation process will be carried out: nonlinearity due to plastic deformation and damage accumulation under static loading; nonlinearity due to the effect of strain rate and damage accumulation rate; nonlinearity due to adiabatic heating and shock compressibility. Based on the results of experimental studies of PCM in a wide range of deformation rates, the models will be calibrated and their applicability will be shown for solving engineering problems of dynamic deformation and fracture of structures made of composite materials.

Expected results
The first main result of the project will be theoretically substantiated methods of high-speed and shock-wave tests of structural PCM. The use of these techniques and modified experimental setups will provide experimental data on the high strain rate responce of PCM in the range 0.001-100000 1/s for various stress-strain states. Methods of dynamic testing of PCM, created on the basis of Skoltech, Research Institute of Mechanics of NNSU and Research Center "Dynamics", will be combined into a system of complementary tests that implement the intersection of the attainable strain rate ranges. At present, there is no such associated system of dynamic testing of PCM, due to the fact that the leading national and international laboratories, as a rule, specialize in a certain method of dynamic testing, which provides a narrow range of PCM strain rates and stress-strain states. The second main result of the project will be the experimental dependencies of the mechanical properties of PCM and strain curves on the strain rate, anisotropy parameters and stress-strain state in the range of strain rates 0.001-100000 1 / s. Despite the development of methods for dynamic testing of PCM, such dependencies in the specified range of deformation rates for a given material are currently absent. Based on these experimental dependencies, the third main result of the project will be obtained - the constitutive models and strength criteria have been built and verified, establishing the relationship between the limiting states of PCM with the strain rate, anisotropy parameters and the type of stress-strain state. The obtained results of the project are of key importance for the effective solution of the problems of creating promising structures made of PCM in the aerospace (blades of jet engines of aircraft, elements of structures of spacecraft), automotive (shock dampers, structural elements) and the military applications.

Annotation of the results obtained in 2023
1. Methods of dynamic testing of polymer composite materials based on modifications have been created and tested - drop tower method: schemes of tensile and compression tests in the range of deformation rates of 50-200 1/s; - split Hopkinson pressure bar method (SHPB): test schemes for compression and radial expansion of a cylindrical sample by an internal hydrostatic pressure pulse in the range of deformation rates 200 – 1000 1/s; - method of electric explosion of a conductor: test scheme for radial expansion of a cylindrical sample by a shock wave pulse of internal pressure, deformation rate up to 20000 1/s. 2. Experimental stress – strain – strain rate curves and the dependence of the strength of unidirectional carbon fiber plastics on the strain rate for tension, compression and shear in the direction along and across reinforcing fibers at strain rates up to 10000 1/s are obtained. These dependences are determined based on the results of dynamic and shock wave tests using modifications of the drop tower method, SHPB and the electric explosion of the conductor. 3. The heat release process during quasi-static deformation of structural carbon fiber plastics were studied. The correlation of changes in thermodynamic and mechanical parameters at various stages of the development of material damage were identified. Analysis of the results of studies of heat release during quasi-static tension shows that changes in thermodynamic and mechanical parameters during deformation of polymer composites are interrelated with changes in the stages of the deformation process. The correlation of these changes is especially clearly observed at the nonlinear stage of the deformation process and is determined by the influence of the anharmonicity of the forces of interparticle interaction, which apparently manifests itself both on the molecular and meso scales of the microstructure of materials. That is, the anharmonicity of the interaction potentials determines the transient nonlinear stage of deformation of materials and activation of structural transformation processes. Concretization of the latent energy requires further research and detailing of the process at various stages of deformation, taking into account micromechanisms and their contribution to the temperature dependence and the thermodynamic function of the material state. 4. A model of deformation and fracture of carbon fiber is constructed and calibrated, describing the effects of anisotropy and deformation rates in the range 0.001-1000 1/ c. The model parameters were determined on the basis of experimental stress–strain deformation curves obtained for unidirectional carbon fiber plastics at deformation rates of 0.001...1000 1/s. The model is verified based on the results of experimental studies and modeling of the process of dynamic shrinkage of tubular samples under axial compression under dynamic testing conditions using a vertical drop tower and a direct impact method based on a Hopkinson measuring bar for different orientations of material layers in the samples. The model of high-speed hardening is implemented in a finite element solver and modeling of the process of dynamic shrinkage of tubular samples under axial compression is performed under the conditions of these dynamic tests for the orientations of the material layers of 90, +-45 and +-30 degrees relative to the axis of the samples. 5. Modifications of the method of plane-wave shock experiment based on the method of plate collision and plate loading by a short pulse initiated by an electric explosion of foil at the end of a short waveguide rod were created. These modifications made it possible to determine the values of the deflection strength of carbon reinforced polymers 45-55 MPa at a deformation rate of ~ 50000 1/s.

Publications

1. Fedorenko, A., Sudenkov, Y., Konev, S., Sergeichev, I. Exploding wire method for the characterization of dynamic tensile strength of composite materials International Journal of Impact Engineering, Volume 180, October 2023, 104704 (year - 2023) https://doi.org/10.1016/j.ijimpeng.2023.104704

2. Kirill Minchenkov, Sergey Gusev, Artem Sulimov, Omar Alajarmeh, Ivan Sergeichev, Alexander Safonov Experimental and numerical analyses of the thermoplastic pultrusion of large structural profiles Materials & Design, Volume 232, 112149 (year - 2023) https://doi.org/10.1016/j.matdes.2023.112149

3. Simonov A.P.; Sergeichev I.V On alternative strain rate analysis for direct impact method International Journal of Impact Engineering, 104835 (year - 2023) https://doi.org/10.1016/j.ijimpeng.2023.104835

Annotation of the results obtained in 2021
During 2021, the following results were obtained. A group of the Skolkovo Institute of Science and Technology (hereinafter referred to as Skoltech) has developed tooling and carried out technological experiments on the production of epoxy-based CFRP specimens using flat and cylindrical winding methods. To conduct shock-wave tests by the method of electric explosion of a conductor, the specimens were made by the methods of circular and spiral winding on plexiglass rods. Thermoplastic composite specimens randomly reinforced with short glass fibers were manufactured by technology of casting (infusion). To obtain the reference values of the composite characteristics for subsequent experimental and theoretical analysis of the effect of the strain rate on the strength of the composites, the Skoltech group performed a set of quasi-static tests of the thermoplastic composites and the unidirectional carbon-fiber reinforced plastics. As a result, stress-strain diagrams, elastic and strength characteristics in tension, compression and shear in the directions of the principal axes of anisotropy were obtained. These results were used to develop and verify the theoretical material model with properties that depend on the type of stress state and strain rate. To analyze the dynamic strength of the composites in the range of deformation rates of ~ 100 1/s, the Skoltech group developed a test procedure based on a vertical drop tower technique. Because of impact testing of the unidirectional carbon plastics specimens for impact compression, linear strain - time dependencies were obtained, which makes it possible with good reliability to consider the strain rate to be practically constant until the initiation of the failure process. In the laboratory of Dynamic testing of materials of the Research Institute of Mechanics of the Nizhny Novgorod University named after N.I. Lobachevsky, the modification of the experimental setup was developed for testing of composite specimens using the split Hopkinson bar method, and an experimental analysis of the processes of high strain rate and failure was carried out when implementing various loading schemes for the unidirectional carbon plastics specimens under dynamic compression. The group of the Research Center "Dynamics" of St. Petersburg State University developed a method of shock-wave tests of composites based on the method of electric explosion of a conductor and carried out a series of tests of cylindrical specimens of carbon plastics with circular and spiral winding of layers. Because of the tests, on the basis of the obtained interferograms of the speed of the free surface, the corresponding stress were determined at various energies of the explosion of the conductors. Experimental studies have shown that the most reliable data on the critical failure stresses of cylindrical composite shells can be obtained using the method of laser interferometry. In the course of the research, the difficulties of applying reflective coatings on the surface of the cylindrical composite specimens were overcome, and methods for aligning the components of the laser interferometry system when measuring the speed of the surfaces of cylindrical specimens were developed. To take into account the effect of the strain rate and the type of stress-strain state on the behavior of the composites with different reinforcement schemes, based on the analysis of the results of experimental studies obtained during the first year, the Skoltech group developed the theoretical models of deformation and damage evolution, taking into account the strain rate hardening, and also performed the numerical modeling of high strain rate processes of the composite specimens. The composite material models with parameters determined based on the results of static and dynamic tests for tension, compression and shear were implemented in the ABAQUS finite element solver. To verify the model, three-point bending tests of composite samples were carried out. To substantiate the choice of the shape and size of unidirectional composite specimens applicable to the both static and dynamic compression tests, finite element modeling of the process of high-speed deformation of specimens with fiber orientation of 0, 45 and 90 degrees relative to the direction of propagation of the loading pulse in the SHPB system was performed. Because of modeling high strain rate of unidirectional CFRP specimens, stress distributions in the gauge length of the specimens and damage parameters at different times were obtained, as well as stress, impulses directly in the gauge length of the specimens and stress impulses calculated based on the transmitted pulse using the Kolsky formulas. The obtained results confirmed the applicability of the shapes and sizes of the specimens and the loading schemes proposed by the research team for dynamic tests of the UD fiber reinforced composites.

Publications

1. Ivan Sergeichev, Boris Fedulov, Alexey Fedorenko, Konstantin Zershchikov, Evgeny Lomakin, Iskander Akhatov Constitutive material model for the design and virtual testing of pressure vessel service equipment manufactured from thermoplastic fiber-reinforced polymer composites International Journal of Pressure Vessels and Piping, 193 (2021) 104475 (year - 2021) https://doi.org/10.1016/j.ijpvp.2021.104475

Annotation of the results obtained in 2022
During the second year of research, the project carried out work aimed at developing experimental methods for studying high-speed deformation of polymer composite materials (PCM) and obtaining new data on the speed dependences of strength and elastic characteristics. In accordance with certain requirements for shapes and sizes, the Skoltech group carried out work on the manufacture of PCM samples using flat and cylindrical winding technologies. Initial components (polymer binders, carbon reinforcing fibers), promising for the manufacture of aerospace and automotive structures, were used for the manufacture of PCM samples. Based on the developed schemes of dynamic loading of samples, experimental equipment was made. Using the developed equipment, the research groups of Skoltech, the Research Institute of Mechanics of the National Research University and the Research Center "Dynamics" carried out dynamic tests of PCM samples and tested the developed loading schemes. The Skoltech group has developed a methodology for conducting tensile testing of carbon fiber in the range of deformation rates of 10-100 1/s on the basis of a vertical copra and obtained test results of carbon fiber samples, see the file with additional materials. The Skoltech research group has completed experimental studies of the processes of dynamic deformation and destruction of unidirectional carbon fiber samples during compression in the direction along and across reinforcing fibers in the deformation rate range of 10-100 1/s using a vertical copra. A group of the NSU Mechanics Research Institute together with the Skoltech group completed tests of unidirectional carbon fiber samples under compression in the direction along and across reinforcing fibers in the deformation rate range of 100-700 1/s using a modification of the Hopkinson split rod method developed within the framework of the project. Based on the results obtained, the article "Strain-rate dependence of unidirectional filament wound composite under compression" was prepared, accepted in 2023 for publication in the journal "Computer Modeling in Engineering & Sciences" (Scopus, Q2, Impact factor 2.027). The Dynamics Research Center group, together with the Skoltech group, completed tensile tests of carbon fiber samples using the method of electric explosion of a conductor. The Skoltech group modeled the process of shock-wave loading of the sample and showed the correctness of the assumptions implemented in the experimental methodology for determining the dynamic strength of the samples under study. Based on the results obtained, an article "Wire explosion method for characterization of dynamic tensile strength of composite materials" was prepared, sent to the journal "International Journal of Impact Engineering" (Scopus/WoS, Q1, Impact factor 4.592), see the file with additional materials. The Skoltech group has proposed a scheme for dynamic loading of ring samples of PCM by an internal pressure pulse. This scheme has been adapted to tests in the Hopkinson split rod system. Numerical simulation of the proposed loading scheme was performed and tests of carbon fiber samples with annular and spiral (± 45°) winding layers were carried out. As a result, the characteristics of the strength and elasticity of the material under tension with a deformation rate of ~ 103 1/s are obtained. The proposed loading scheme ensures the uniformity of the stress-strain state of the working area of the sample, which allows you to correctly construct a dynamic diagram of the deformation of the PCM, see the file with additional materials. To analyze the specific characteristics of energy absorption, tests for dynamic axial compression of tubular carbon fiber samples with various schemes of winding layers using a vertical copra (Skoltech) and the direct impact method (NSU Mechanics Research Institute) were performed. The analysis of the influence of loading conditions on the energy intensity of the destruction of samples was performed, see the file with additional materials. The Skoltech group has proposed and theoretically justified an alternative procedure for processing primary data when conducting tests according to the direct impact scheme (Drahan-Hauser scheme). The proposed procedure makes it possible to correctly construct a dynamic deformation diagram and a history of deformation rate changes for a wide range of polymers, metals and alloys, excluding the assumption of the classical direct impact method about the constancy of the striker velocity during the deformation of the sample. Based on the results obtained, the article "On alternative strain rate analysis for direct impact method" was prepared for publication in the journal "Experimental Mechanics" (Scopus/WoS, Q1, Impact factor 2.794), see the file with additional materials. The Dynamics Research Center group has developed a method for measuring the temperature of samples during static and cyclic in the range of deformation rates 0.001-0.01 1/ using the ThermaCAM SC 3000 infrared camera with a shooting frequency of 50 Hz. The developed technique was tested during tests of carbon fiber samples, as well as samples of M1 copper, VT6 titanium alloy and D16 aluminum alloy in the direction along and across the direction of the rolled product. According to the test results, an article was published by Sudienkov Yu.V., Smirnov I.V., Zimin B.A. Influence of metal texture and loading rate on heat release under quasi-static tension (2022) Journal of Physics: Conference Series, 2231 (1), art. no. 012009, DOI: 10.1088/1742-6596/2231/1/012009. The Skoltech group has developed and verified a model for the development of fatigue damage, which phenomenologically takes into account changes in the stiffness and residual strength of the PCM layer in accordance with experimental diagrams of constant service life (constant life diagram). The results obtained indicate the sufficiency of using S-N curves for layers with fiber orientation in the direction of 0°, 45° and 90° relative to the direction of application of the load to identify the model. The model was verified using fatigue curves (S-N curves) for orientations of 10°, 15° and 30°. The applicability of the model for predicting the fatigue life of layered PCM with arbitrary laying of layers was shown. The model is implemented in the finite element complex ABAQUS in the form of a user subroutine. Based on the results obtained, an article was published by Elkin, A.; Gaibel, V.; Dzhurinsky, D.; Sergeichev, I. A Multiaxial Fatigue Damage Model Based on Constant Life Diagrams for Polymer Fiber-Reinforced Laminates. Polymers 2022, 14, 4985. https://doi.org/10.3390/polym14224985 (Scopus/WoS, Q1, Impact factor 4.967). The Skoltech group has constructed and calibrated a model of deformation and fracture of carbon fiber, describing the effects of anisotropy and deformation rates in the range 0.001-1000 1/ c, see the file with additional materials.

Publications

1. Aleksandr Elkin, Viktor Gaibel, Dmitry Dzhurinskiy, Ivan Sergeichev A Multiaxial Fatigue Damage Model Based on Constant Life Diagrams for Polymer Fiber-Reinforced Laminates Polymers, 4985, 14, 1-14 (year - 2022) https://doi.org/10.3390/polym14224985

2. Anastasiia Moskaleva, Sergey Gusev, Stepan Konev, Ivan Sergeichev, Alexander Safonov, Enrique Hernandez-Montes Composite freeform shell structures: design, construction and testing Composite Structures, Volume 306, 116603 (year - 2023) https://doi.org/10.1016/j.compstruct.2022.116603

3. Konev,Stepan; Eremeev,Victor; Hamid M. Sedighi; Igumnov,Leonid; Bragov,Anatoly; Konstantinov,Aleksandr; Kuanyshova,Ayaulym;Sergeichev,Ivan Strain-rate dependency of unidirectional filament wound composite under compression Computer Modeling in Engineering & Sciences, 137(3), 2149-2161 (year - 2023) https://doi.org/10.32604/cmes.2023.028179

4. Sudienkov Yu. V., Smirnov I.V., Zimin B. A. Infuence of metal texture and loading rate on heat release under quasi-static tension Journal of Physics: Conference Series. IOP Publishing Ltd., 2231, 012009, 1-9 (year - 2022) https://doi.org/10.1088/1742-6596/2231/1/012009