Marian Klasztorny

Determination of Complex Compliances of Fibrous Polymeric Composites

The paper presents a method for determining the complex compliances of a composite consisting of a viscoelastic isotropic matrix and unidirectional elastic monotropic fibres. These compliances represent the viscoelastic nature of a given composite material system. Elastic compliances of the composite have been derived fully analytically. Generating functions of shear/bulk viscoelasticity of the matrix have been defined by the Mittag-Leffler fractional exponential functions. This approach presents possibilities for modelling realistic shear/bulk creep of a polymer matrix. Complex compliances of the composite have been determined using the principle of elastic-viscoelastic analogy. A computer algorithm for calculating elastic and viscoelastic compliances of the composite has been formulated, programmed and tested on the selected composite material.

Constitutive Equations of Viscoelasticity and Estimation of Viscoelastic Parameters of Unidirectional Fibrous Polymeric Composites

A method for modelling viscoelastic properties of fibre reinforced polymeric composites, based on the original reinforcement theory as well as original description of viscoelasticity of the matrix [4}, is developed in the paper. The composite material consists of a viscoelastic isotropic polymer matrix and elastic monotropic fibres. In order to model arbitrary shear/bulk creep in the matrix, the Mittag-Leffler fractional exponential functions are used as the generating functions. Hence, the viscoelastic model of the polymer matrix is described with 2 elastic constants and 6 viscoelastic constants, while the elastic properties of the fibres are described with 5 well-known elastic constants. Both groups of the material constants can be estimated experimentally relatively easy. Coupled constitutive equations of linear viscoelasticity of a unidirectional fibrous polymeric composite, modeled as a homogeneous monotropic material are formulated in the study. The viscoelastic model of the composite is described using 5 elastic constants and 27 viscoelastic constants, i.e., 9 long-lasting compliance ratios, 9 retardation times, and 9 fractions defining an order of the fractional exponential functions. The elastic-viscoelastic analogy is used to predict theoretically the complex compliances of the composite [4]. An iterative optimization procedure for theoretical prediction of the viscoelastic constants of the composite is formulated, computerised and positively tested on the selected composite materials.

Effects of Operating Temperatures and Accelerated Environmental Ageing on the Mechanical Properties of a Glass-Vinylester Composite

Experimental identification of the mechanical properties of a selected glass-vinylester structural composite is developed, performed, and analysed taking into account accelerated environmental ageing and three operating temperatures (–20, 20, and 55°C) corresponding to the operating temperature range for composite footbridges in the Central Europe. The main constituents of the composite fabricated using infusion technology are a bidirectional balanced stitched E-glass fabric and a flame retardant, vinylester resin. After homogenization, the composite reinforced with one fabric forms a single lamina and is modeled as a linear elastic-brittle orthotropic material. Full sets of material constants were identified for the initial and aged composites at the selected operating temperatures. The accelerated environmental ageing of the composite was performed on 4-layer symmetric laminate platelets protected with a 300-mm-thick gelcoat layer, using an ageing chamber and a relevant ageing programme. A comparative analysis was carried out in order to determine the effects of operating temperature and accelerated environmental ageing on the material constants of the GFRP composite. It is found that the composite tested can be modeled as a linear elastic-brittle orthotropic material to the level of ~20% of its strength in each strength test. The impact of the accelerated environmental ageing and operating temperature in the range from –20 to 55°C on the elastic/strength/ultimate strain constants of the selected E-glass/vinylester composite can be significant and different for individual constants.

Application of the finite-element method to improve the quasi-exact reinforcement theory of fibrous polymeric composites

In the paper, the WL quasi-exact reinforcement theory of fibrous polymeric composites is improved. An optimum compatibility condition related to the transverse shear problem for a unit cell, which brings solutions closest to reality, is derived. This condition is formulated in the form of a linear combination of maximum radial and circumferential displacements. Optimum coefficients of this combination are determined by comparing analytical and numerical solutions for a test specimen in the form of a rectangular thin plate, which is in a plane strain state and is subject to selected loading schemes. The analytic solutions are obtained for a homogenized material by using the WL reinforcement theory. The numerical solutions are found for an actual heterogeneous composite material by using the finite-element method, and they verify the WL reinforcement theory, in particular, the admissibility of Hill’s assumption. An analysis performed for two composite materials shows that the improved WL reinforcement theory gives adequate displacement fields.

Experimental validation of numerical modelling of the bridge-track-moving train system

A new methodology of physical and FE modelling and simulation of bridge–track –moving train (BTT) systems has been developed with the use of commercial CAE systems. A methodology is related to composite (steel-concrete) bridges, ballasted tracks and high-speed trains. In the methodology, Altair HyperMesh, LS-DYNA, LS-PrePost and HyperView software was applied. The methodology is based on homogenization of reinforced concrete (RC) platform slab, RAIL_TRACK and RAIL_TRAIN LS-Dyna’s modules for simulating the moving train–track interaction, non-linear modelling of rail fastenings and crushed stone ballast, application of cylindrical and revolute constrained joints and discrete springs and dampers for modelling suspensions in rail-vehicles. For experimental validation of numerical modelling and simulation of BTT systems, the KNI 140070 composite viaduct and the EuroCity EC 114 train moving at 160 km/h have been selected. The experimental setup contained Keyence LK-G 157 system (CCD laser displacement sensors), PULSE system (acceleration sensors), and PHANTOM v12 high-speed camera. According to the experiment plan, selected vertical displacements and vertical and horizontal accelerations vs. time were measured. The simulated time-histories of displacements and accelerations have been compared to respective experimental diagrams. The results have proved that the validation is positive.

Constitutive Modelling of Resins in the Compliance Domain

A rheological HWKK/H model for resins is developed taking into consideration the up-to-date analyses of experimental results. Constitutive compliance equations of linear are formulated for this model in the shear/bulk form, which describes, among other things, the first-rank reversible isothermal creep. The shear (distorsional) deformations are simulated with three independent stress history functions of fractional and normal exponential types. The volume deformations are simulated as perfectly elastic. The model is described by two elastic and six viscoelastic constants, namely three long-term creep coefficients and three retardation times.The constitutive compliance equations of viscoealsticity for resins are also formulated in the coupled form. Formulae for converting the constants of shear/bulk (uncoupled) viscoelasticity into the constants of coupled viscoelasticity are given too.An algorithm for identifying the material constants, based on the creep of uniaxially tensioned bar samples, is formulated in a way that gives unique results. The material constants are fiund for Epidian 53 epoxy and Polimal 109 polyester resins. The creep processes, simulated based on the experimental data, are presented graphically for both the resins examined.

Modelling and simulation of crash tests of N2-W4-A category safety road barrier in horizontal concave arc

ABSTRACT The paper examines a road safety barrier of a N2-W4-A class, with a B-type guide bar, located on a road bend of a 150 m radius and shaped as a horizontal concave arc. In order to ensure accepting the TB11 and TB32 standard crash tests, a composite/foam/rubber overlay is designed, combined with the guide bar with screw connectors spaced by 2 m. The study develops a methodology for numerical modelling and simulation of unmodified (a straight barrier) and modified (a curved barrier) crash tests, without and with the overlay, including deformable joints with limited load capacities, contact with friction, tire pressure, posts embedded in deformable subsoil, gravity load and damping. The TB11- and TB32-simulated crash tests are conducted for the four above-mentioned barrier systems. It has been proved that the barrier with the overlay provides approval for the standard crash tests on road bends.

The inverse problem in the reinforcement theory of fibre-reinforced composites

The inverse problem in Wilczynskis reinforcement theory of fibre-reinforced composites (Wilczynski AP. A basic theory of reinforcement for unidirectional fibrous composites. Comp Sci Technol, 1990;38:327–337; Wilczynski AP, Lewinski J. Predicting the properties of unidirectional fibrous composites with monotropic reinforcement. Comp Sci Technol, 1995;55:139–143) has been solved fully analytically. This problem is understood as determination of the elastic constants of monotropic fibres, having the elastic constants of the isotropic matrix and the elastic constants of the homogenised monotropic composite material, measured experimentally. The analytical solution of the inverse problem has been computerised and positively tested, for both theoretical and experimental data related to the selected polyethylene/epoxy composite.

NUMERICAL MODELLING AND DESIGN OF ALFC SHIELD LOADED BY 20 MM FSP FRAGMENT

The study develops numerical modelling and design of the ALFC shield loaded by the 20 mm 54 g FSP fragment moving at impact velocity of 1800 m/s (fragmentation simulation of IED devices), used to protect 5 mm-thick Armox 500T steel plate. The ALFC shield is composed of the ALF energy-absorbing subsystem and a 99.7% Al 2O3 alumina ceramic layer. The ALF subsystem is designed to absorb blast wave impact energy induced by explosive materials up to 10 kg TNT. The ceramic layer is aimed at stopping FSP fragments. The 5 mm-thick Armox 500T steel plate reflects the body bottom segment of a light armoured vehicle. The main purpose of the study is to determine the minimum thickness of the ceramic layer at which the 5 mm-thick Armox 500T steel plate is fully protected from perforation. The ALF subsystem has the following layered structure: Al2024 aluminium alloy plate, SCACS hybrid laminate plate, ALPORAS aluminium foam, SCACS hybrid laminate plate. The layers are joined with Soudaseal 2K chemoset glue. SCACS hybrid laminate contains the following components: VE 11-M modified vinylester resin (matrix), SWR800 glass S plain weave fabric, Tenax HTA40 6K carbon plain weave fabric, Kevlar 49 T 968 aramid plain weave fabric. The total thickness of the ALF shield amounts to 76 mm. In the numerical modelling, the aluminium alloy plate and Armox 500T steel plate are working in the elasto-plastic range according to Johnson–Cook model. The 99.7% Al 2O3 alumina ceramic is working in elasto-short range according to JH-2 Johnson–Holmquist model. The simulations correspond to large displacements, large deformations and contact among all the components of the system. In FE mesh, the 8-node 24 DOF hexahedral finite elements with single integration point have been used. Additional failure criteria governing ad-hoc erosion of finite elements have been applied. The FEM modelling, simulation and postprocessing have been carried out using Catia, HyperMesh, LS-DYNA and LS-PrePost systems. The simulation results are presented in the form of displacement – perforation contours and the FSP final deformation for both the FSP–shield–plate and the FSP–plate systems. It has been pointed out that 18 mm-thick ceramic layer protects the LAV body bottom plate from perforation.

NUMERICAL MODELLING AND VALIDATION OF 12.7 MM FSP IMPACT INTO ALFC SHIELD - ARMOX 500T STEEL PLATE SYSTEM

The study develops a methodology for numerical modelling and simulation of a 12.7 mm 13.4 g FSP fragment impact into the ALFC shield – ARMOX 500T steel plate system. The ALFC shield is composed of the ALF energyabsorbing subsystem and a 10 mm-thick 99,7% Al 2O3 alumina ceramic layer. The ALF subsystem is designed to absorb blast wave impact energy induced by explosive materials up to 10 kg TNT. The ceramic layer is designed to stop fragments from IED explosion. The 5 mm-thick Armox 500T steel plate constitutes the body bottom segment of a light armoured vehicle. The ALF subsystem has the following layered structure: Al2024 aluminium alloy plate, SCACS hybrid laminate plate, ALPORAS aluminium foam, SCACS hybrid laminate plate. The layers are joined with Soudaseal 2K chemoset glue. SCACS hybrid laminate contains the following components: VE 11-M modified vinylester resin (matrix), SWR800 S-glass plain weave fabric, Tenax HTA40 6K carbon plain weave fabric, Kevlar 49 T 968 aramid plain weave fabric. The total thickness of the ALFC shield amounts to 90 mm. Proof ground tests of a 12.7 mm 13.4 g FSP fragment impact into the ALFC shield – ARMOX 500T steel plate system have been performed at impact velocity 715 m/s and used for experimental validation of numerical modelling and simulation. In the numerical modelling, the aluminium alloy plate and Armox 500T steel plate are working in the elasto-plastic range according to Johnson–Cook model. The 99.7% Al 2O3 alumina ceramic is working in elasto-short range according to JH-2 Johnson–Holmquist model. The simulations correspond to large displacements, large deformations and potential contact among all the components of the system. In FE mesh, the 8-node 24 DOF hexahedral finite elements with single integration point have been used. Failure criteria governing ad-hoc erosion of finite elements have been applied. The FEM modelling, simulation and postprocessing have been carried out using Catia, HyperMesh, LS-DYNA and LS-PrePost systems. The simulation results in the form of displacement/penetration contours and the FSP final deformation have been compared with the experimental results.