10th International DAAAM Baltic Conference "INDUSTRIAL ENGINEERING - 12-13 May 2015, Tallinn, Estonia COMPARISON OF NUMERICAL SIMULATION AND EXPERIMENT OF A FLEXIBLE COMPOSITE CONNECTING ROD Sedláček, F.; Lašová, V.; Kottner R. & Bernardin P. Abstract: The work deals with a comparison of numerical simulations and experimental tests of a flexible composite connecting rod in order to create an appropriate computational model for predicting the strength and stiffness. For the numerical simulation were used finite element analysis in the software Siemens NX 10 and SIMULIA Abaqus 6.14. Experimental specimens with different geometry were exposed to quasi-static loading. Zwick/Roell Z050 testing machine was used for tensile tests. Key words: flexible, composite connecting rod, FEM analysis 1. INTRODUCTION Composite materials have an ever greater range of applications in industrial practice. Today, commonly used construction materials in aviation and aerospace engineering, are increasingly used in the automotive and railway industries. One possible application is in flexible elements, for which the main factor is strain energy, which could be simply described by the equation; U = σ2 ρρ From which clearly follows that the material with a lower modulus of elasticity E and density ρ, will have a relatively higher strain energy U. And the composite materials fulfil this property excellently (composite materials have high strength with low weight compared with conventional steel, up to 80%). Other positive properties of composite materials are water resistance, high fatigue strength, resistance to corrosion, higher natural frequency, low friction, etc. However, the use of composite materials has many negative aspects, which include in particular complicated design and difficult manufacturing, which are mainly caused by orthotropic (or anisotropic) properties of the material. The objective of this work is to design and verify potential applicability of composite materials in for example a flexible joint. It has the task of transferring tensile/compressive loads as well as bending and torsion. It is not such a problem to propose fundamental (functional) areas for this element, but the part that is used to connect to subsequent components and this paper focuses on this area. It specifically focuses on the integrated types of joints of glass fibre. Integrated joints are already addressed in several papers [ 4, 5, 6 ]. However, they are targeted at the use of carbon fibre joints. 2. EXPERIMENTAL TESTS A simplified element was created for possible design verification using numerical simulations, specifically the wrapping loops. E-glass fibres (Aeroglass 2400 TEX) and epoxy resin (LH298 + hardener H512) as were chosen the material. The
experimental samples were wound on a special form in two versions (16pcs with seven threads a 16pcs with four threads of the fibreglass). Experimental tensile tests were carried out by quasi-static load (0.5 mm/sec) on the Zwick/Roell Z050 machine. The samples were attached according to verified methods [ 4, 5 ] where one side eyes were tightly attached using special jaws and the other side free fastening was used. The results can be seen on the charts. // Fig.3 measured wrapping loops Fig.1 results of the experiment wrapping loops with seven threads of fibres E-Glass fibre + epoxy resin (H512+LH298) V f [-] 0.73 V m [-] 0.27 E 1 [MPa] 52640 E 2 [MPa] 8576.16 E 3 [MPa] 8576.16 G 12 [MPa] 1986.75 G 23 [MPa] 1986.75 G 13 [MPa] 3264.20 ν 12 [-] 0.295 ν 23 [-] 0.31366 ν 13 [-] 0.295 X T [MPa] 2000 X C [MPa] 1033 Y T [MPa] 315 Y C [MPa] 51 Z T [MPa] 315 Z C [MPa] 51 S or S 12 [MPa] 48 S 13 [MPa] 42 S 23 [MPa] 48 Tab.1 Mechanical properties of tested composites 3. NUMERICAL SIMULATION Fig.2 results of the experiment wrapping loops with four threads of fibres Numerical simulation was performed on the three-dimensional model by using finite element software Siemens NX 10 (with solver NX Nastran 10) and SIMULIA Abaqus 6.14.
3.1. FE model of wrapping loop The meshes were created by brick elements CHEXA8 type (C3D8 in Abaqus) with 8 nodes. Subsequently, the elements were assigned to the appropriate orientation of material (see Fig. 4). The model was calculated as a symmetrical solution by transverse plane (YZ) with appropriate removal of degrees of freedom. The load was applied in the form of displacement of a pin according to the values obtained from experimental measurements. Fig.4 FE model, including a material orientation of the elements 3.2. Results of the numerical simulation From the results of the individual components of normal stresses (L, T, T') and shear stress (LT, TT', LT') follows that the most critical is the index 3 (T ) and 6 (LT ), see Fig. 5 and 6. // Fig.5 stress values in the direction T (loop with seven threads of the fibres) // Fig.6 stress values in the direction LT (loop with seven threads of the fibres) Subsequently, the failure indexes from individual components of stresses were evaluated. Strength criterion 'Maximum stress' for the first approach was chosen. According to this theory, failure occurs if any component of stress has reached the ultimate strength of the material [ 7 ]. Failure indexes for individual directions of this strength criterion are listed in Table 2. Where σ L (σ T, σ T' ) is normal stress in longitudinal (transverse) direction; X T (Y T, Z T ) is in Longitudinal tensile strength (transverse) direction; X C (Y C, Z C ) is compressive strength in longitudinal (transverse) direction; τ LT (τ TT', τ LT' ) is shear stresses in LT (TT' or LT') plane and S LT (S TT', S LT' ) is shear strength in LT (TT' or LT') plane. Failure indexes F L F T F T Maximum stress criterion σ L /X T if σ L > 0 σ L /X C if σ L < 0 σ T /Y T if σ T > 0 σ T /Y C if σ T < 0 σ T /Z T if σ T > 0 σ T /Z C if σ T < 0 F LT τ LT / S LT F TT F LT τ TT /S TT τ LT /S LT Tab.2 Failure indexes of Maximum stress criterion
the LaRC04 #2 mode (matrix failure, if σ T < 0, σ L 0): τ T FF M = S T η T σ n + σ L P M τ L + S L η L σ n + σ L P M 2 2 1 And parameter P F for LaRC04 #03 mode (fibre failure, if σ L > 0): Fig.7 Failure index in the direction T (Maximum stress criterion) Fig.8 Failure index in the direction LT (Maximum stress criterion) By using this strength criterion, the results of FI indexes do not correspond to values obtained by experimental tests. Therefore strength criterion LaRC04 (Laminates and Reinforced Composites/Langley Research Centre invented in 2004 [ 8 ]) was used. LaRC04 is an interactive strength criterion for long fibre unidirectional composites. It is derived for the three-dimensional stress state and has incorporated therein correction for the nonlinear behaviour of the composite in shear area. For the modes LaRC04 #02 and LaRC04 #03 this strength criterion was modified, according to [ 5, 6 ]. The modification assumes that the strength of the matrix at loading pressure in the direction transverse to the fibre is also dependent on the tension in the direction of the fibers σ L. However the stress σ L causes hardening of the matrix. Further were used the adjusting parameters, parameter P M for FF F = σ L X T + X T 1 P F Y C + X T σ P T P F + X T M where τ T and τ L are stresses in the plain of the failure, S T is the transverse shear strength and S L is the longitudinal shear strength and η T and η L are coefficients of the friction. The failure criterion and the values of the adjusting parameters P F and P M were investigated using the comparison of the experiments and corresponding numerical simulations including results of previous works [ 3, 4, 5 ]. Fig.9 Mesh of the FE model with divide of cross-section
For numerical simulation of the matrix it is considered that it is already broken (if the failure of the matrix occurred before the failure of the fibres according LaRC04 # 2). For each geometry the cross-section was divided at an angle α in the place where according LaRC04 #2; FI M = 1 = FI Mmax. Between the separate parts and base part the contact of the type "touching" (without considering the friction) was defined (see Fig.9). In the chart (Fig. 10) is possible to see comparing experimental data with numerical analysis using a modified strength criterion LaRC04 (for the most critical modes LaRC04 #02 and LaRC04 #03) and strength criterion Maximum stress (for the most critical index in direction T ). Fig.10 comparison of experimental data with numerical analysis 4. CONCLUSION By using numerical simulation with the comparison of the resulting data from the experimental tests significant mismatch using the strength criterion 'Maximum stress' was revealed. Subsequently a modified strength criterion LaRC04 was used. By using this strength criterion the maximum difference of 27% was created to conformity compared with the experiments. These data are the basis for further research in the area of integrated joints of glass fibre and we are still working on further experimental tests that provide more accurate results for a modified strength criterion LaRC04. 5. ACKNOWLEDGEMENTS This paper is based upon work sponsored by project RTI - Regional Technological Institute reg. no. CZ.1.05/2.1.00/03.0093 and TAČR TA project TE01020075. 6. REFERENCES [1] Krishan K. Chawla, Composite materials; Science and Engineering, 3rd Edition. Springer, New York, 2012. [2] Laš, V.: Mechanika kompozitních materiálů. Západočeská univerzita v Plzni, Plzeň, 2. vydání, 2008. [3] Kottner, R., Krystek, J., Zemčík, R., Lomberský, J., Hynek, R. Strength Analysis of Carbon Fiber-reinforced Plastic Coupling for Tensile and Compressive Loading Transmission. Collection of Technical Papers - Structures, Structural Dynamics and Materials Conference, 2011, roč. 2011-1982, č. April 2011, s. 1-12. ISSN: 0273-4508 [4] Kottner, R., Bek, L., Krystek, J., Kroupa, T., Lašová V. Failure analysis of pin joint of carbon/epoxy composite plate. Advanced Materials Research, 2012, roč. 634-638, č. 1, s. 2796-2799. ISSN: 1662-8985 [5] Krystek, J., Kottner, R., Load capacity prediction of carbon or glass fibre reinforced plastic part of wrapped pin joint. Materiali in Tehnologije, 2015, roč. 49, č. 6. ISSN: 1580-2949 [6] Kottner R., Spojování kompozitních a kovových strojních částí z hlediska tuhosti a pevnosti. Západočeská univerzita v Plzni, Disertační práce, Plzeň, 2007
[7] Vasiliev Valery V., Morozov Evgeny V.: Advanced Mechanics of Composite Materials and Structural elements, 3rd Edition. ISBN: 978-0-08-098231-1, Elsevier, Oxford, 2013. [8] Pinho, S. T., Dávila, C. G., Camanho, P. P., Iannucci, L., Robinson, P., Failure Models and Criteria for FRP Under In- Plane or Three-Dimensional Stress States Including Shear Non-Linearity. Research report, NASA/TM-2005-213530, NASA Langley Research Center, 2005, 69 p. 7. ADDITIONAL DATA ABOUT AUTHORS Ing. František Sedláček*; Department of Machine Design, Faculty of Mechanical Engineering, RTI - Regional Technological Institute, University of West Bohemia; Univerzitní 8, 306 14, Czech Republic, fsedlace@kks.zcu.cz doc. Ing. Václava Lašová, Ph.D.; Department of Machine Design, Faculty of Mechanical Engineering, University of West Bohemia; Univerzitní 8, 306 14, Czech Republic, lasova@kks.zcu.cz Ing. Radek Kottner, Ph.D.; NTIS - New Technologies for the Information Society; University of West Bohemia, Univerzitní 8, 306 14, Czech Republic, kottner@kme.zcu.cz Ing. Petr Bernardin; Department of Machine Design, Faculty of Mechanical Engineering, University of West Bohemia; Univerzitní 8, 306 14, Czech Republic, berny@kks.zcu.cz * Corresponding Author