Keywords: concrete elements; used rubber tires; rubber aggregates; Ogden hyperelastic model. INTRODUCTION. Every year an approximated 4 million tons of ...
Section Renewable Energy Sources and Clean Technologies
NUMERICAL SIMULATION OF CONCRETE WITH RUBBER AGGREGATES Assist. Dr. Sergiu Andrei Băetu Assist. Dr. Vasile Mircea Venghiac Prof. Dr. Mihai Budescu Prof. Dr. Nicolae Ţăranu “Gheorghe Asachi” Technical University of Iasi, Romania
ABSTRACT There are many cars in the world nowadays and plenty of used rubber tires need to be disposed, with huge implications on the environment. As waste continues to accumulate and the capacity of storage spaces diminish, researchers are trying to find solutions in order to use rubber extracted from tires in constructions. The main utilization is in the composition of concrete as rubber aggregates of different dimensions mixed with the basic materials, namely cement, sand and crushed stone aggregates or gravel. Numerical simulations of some concrete elements were done in order to examine the stress distribution in concrete in which different amounts of rubber‐tire particles of several sizes were used as aggregate. The concrete element was considered in plane strain state and comparative numerical analyses using ANSYS 14 software were done between concrete without rubber aggregates and concrete with 5%, 10% and 15% rubber aggregates. The displacement on Y axis direction, linear strain εy and stresses σy and Tresca are analyzed for a uniform distributed load of 10 N/mm and for compressive displacements of 0.01mm, 0.02mm, 0.03mm, 0.04mm and 0.05mm in the Y axis direction applied at the top of the concrete elements proposed in this study. The results show that increasing the percent of rubber aggregates in concrete elements leads to low compressive strength but high deformability. Keywords: concrete elements; used rubber tires; rubber aggregates; Ogden hyperelastic model. INTRODUCTION Every year an approximated 4 million tons of natural rubber and 7 million tons of synthetic rubber are produced to make thousand different products [1]. Nowadays, rubber is a material widely used due to its good properties like strength, durability, water resistance and heat resistance and all these benefits makes it perfect for tire production. The fact is that a large percentage of rubber production goes into the automotive industry and huge deposits of used rubber tires results from it. This large quantity of used rubber provides a serious problem due to its highly polluted effluents which may pollute the environment and also may have negative effects on human health. Also, the burning of used tires causes noxious plumes of thick smoke. Therefore, these used rubber tires must be recycled. Used rubber tires are often recycled to make other items like mulch, shoes,
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bags, jewellery and coats. In addition, the civil engineering researchers found another way to recycle these wastes into the concrete composition. An elastomer is a polymer with viscoelasticity (having both viscosity and elasticity) and very weak inter-molecular forces, generally having low Young's modulus and high failure strain compared with other materials. The term, which is derived from elastic polymer, is often used interchangeably with the term rubber. Rubber can accept elastic deformations in the range 100 – 700%. These excessive deformations happens because of molecular chains and because of crossover links between these, which can modify its shape very easily. The volume change due to a state of stress is small, because the state of strain is tied of the change of molecular chains shape and results that the elastomers are almost incompressible. The stress-strain curve is extremely nonlinear and under some tensile forces, a rubber element has a small stiffness which increases while the loads are increasing [2], [3], [7]. The constitutive hyperelastic models are defined through strain energy density functions [5], [6], [7]. A series of research have developed stress-strain theoretical equations which simulates the experimental results obtained on hyperelastic materials. Money proposed a phenomenological model with two parameters based on the hypothesys of a linear relationship between stress and strain during the shear strains [7], [9]. Treloar published the neo-Hooken material model, which is based on the statistical theory with one material parameter. The neo-Hooken model proved to be a special case of the Mooney model. The strain energy functions of these two models played an important role in the hyperelastic theories development and of their applications. Rivlin modified the Mooney hyperelastic model with the purpose to obtain a general expression of the strain energy function in terms of strain invariants [7], [9]. Yeoh developed one of the most successful hyperelastic models, with the form of a third degree polynomial for the first invariant of the CauchyGreen tensor. A higher degree polynomial model with a natural logarithm form for the first invariant was proposed by Gent. In 1972, Ogden proposed a stain energy function expressed in function of principal displacements, which represents a good modality to describe the hyperelastic materials. Excelent results were obtained between Ogden equation and experimental data obtained by Treloar for natural rubber in tension till 700% [4], [7], [8], [9], [11], [12], [13]. In the Ogden model, the strain energy is expressed with the principal displacements j , j = 1, 2, 3 [7], [10]:
p (1 2 3 3) p 1 p N
W (1 , 2 , 3 )
p
p
p
where N, p , p , are materials constants. For N=3 and through material parameters fitting, the rubber behaviour can be described with high accuracy. For particular values of the material constants, the Ogden model can be reduced to the Neo-Hooken model (N = 1, α = 2) or to the Mooney-Rivlin model (N = 2, α1 = 2, α2 = -2).
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NUMERICAL SIMULATION OF SOME CONCRETE ELEMENTS WITH VARIOUS PERCENTS OF RUBBER AGGREGATES The numerical simulations was done with finite element ANSYS 14. There are some hypothesis for the hyperelastic models from ANSYS software such as (ANSYS 14, 2013): the material is isotropic, isotermal and elastic (the termal dilatation is isotropic and the strains are fully recoverable); the material is fully or almost incompressible. The finite element Plane 183 is used to simulate the elastomers in this software. Plane 183 finite element is a higher order 2-D element with 8-node or 6-node. Plane183 has quadratic displacement behavior and is well suited to modeling irregular meshes. This element is defined by 8 nodes or 6-nodes, having two degrees of freedom at each node: translations in the nodal x and y directions. This element may be used as a plane element (plane stress, plane strain and generalized plane strain) or as an axisymmetric element. This element has plasticity, hyperelasticity, creep, stress stiffening, large deflection and large strain capabilities. It also has mixed formulation capability for simulating deformations of nearly incompressible elastoplastic materials and fully incompressible hyperelastic materials (ANSYS 14, 2013). In the simulations presented in this paper the finite element has the following properties (ANSYS 14, 2013): the finite element shape is quadrilateral, the finite element behaviour is in plane strain state and the finite element formulation is mixed U/P. In the numerical simulation of concrete elements with rubber aggregates, the material properties for the matrices, stone aggregates and rubber aggregates were defined separately in the finite element software ANSYS. The matrices properties used in the numerical simulations are: the Young's modulus of elasticity is E = 20000 N/mm2 and Poisson's ratio, ν = 0.2. The properties of stone aggregates used in the numerical simulations are: the Young's modulus of elasticity is E = 50000 N/mm2 and Poisson's ratio, ν = 0.2. The properties of rubber aggregates used in the numerical simulations are: the Young's modulus of elasticity is E = 3 N/mm2 and Poisson's ratio, ν = 0.49967. The properties of the Ogden hyperelastic model are: μ1 = 0.62, a1 = 1.3, μ2 = 0.00118, a2 = 5, μ3 = -0.00981, a3 = -2, d1 = 6.9306E-005, d2 = 0, d3 = 0. The concrete elements studied are shown in Fig. 1 - 4 and the rubber aggregates percent was varied from 0% to 15%, namely in Fig. 1 is shown a concrete element without rubber aggregates, in Fig. 2 is shown a concrete element with 5% rubber aggregates, in Fig. 3 is shown a concrete element with 10% rubber aggregates and in Fig. 4 is shown a concrete element with 15% rubber aggregates. All the concrete elements considered in this study were simulated in plane strain state. The shape and orientation of stone and rubber aggregates from the concrete element simulated numerical in ANSYS software was copied exactly from a concrete element tested in laboratory. The finite element mesh of the concrete element with rubber aggregates can be seen in Fig. 5. There are approximately 30000 finite elements Plane 183, with different properties for stone aggregates, rubber aggregates and for matrices. The finite elements that simulate each different component of concrete are perfectly connected in nodes.
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Fig. 1. Concrete element without rubber aggregates
Fig. 2. Concrete element with 5% rubber aggregates
Fig. 3. Concrete element with 10% rubber aggregates
Fig. 4. Concrete element with 15% rubber aggregates
The concrete elements are fully restrained at the base and imposed vertical displacements are set at the top of it. A comparative analysis was done between the proposed concrete elements with various percents of rubber aggregates for incremental imposed displacements of 0.01mm, 0.02mm, 0.03mm, 0.04mm and 0.05mm in Y axis directions and the normal stress distribution σy was extracted and analyzed. Also, the Tresca stress distribution was extracted and analyzed for a displacement of 0.05mm in Y axis directions.
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Fig. 5. The finite element mesh of the concrete element with rubber aggregates
It can be seen in Fig. 6 that the increasing of percent of the rubber aggregates leads to an increase of normal stress σy in concrete zones where there are agglomerations of stone aggregates. These results show that the concrete elements with high percent of rubber aggregates have low compressive strength. For instance, for a concrete characteristic strength of 25 N/mm2, the concrete element without rubber aggregates fails at a displacement of 0.05 mm, the concrete element with 5% rubber aggregates fails at a displacement of 0.03 mm, the concrete element with 10% rubber aggregates fails at a displacement of 0.027 mm and the concrete element with 15% rubber aggregates fails at a displacement of 0.02 mm.
Fig. 6. Variation of maximum normal stress σy with vertical displacement for concrete elements with no rubber aggregates, 5% rubber aggregates, 10% rubber aggregates and 15% rubber aggregates
Also, the stress distributions on the surface of the proposed concrete elements have similar pattern for each imposed displacements and also for each percent of rubber aggregates. For instance, at a displacement of 0.04mm in the direction of Y axis (Fig. 710), the maximum values of the normal stress σy in the concrete element without rubber 349
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aggregates reach the value of 20 N/mm2 on the zones with agglomerations of stone aggregates and between 10 and 15 N/mm2 on the matrices zone. For the same displacement, the values of normal stresses σy in the concrete element with 5% rubber aggregates are almost 30 N/mm2 on the zones with agglomerations of stone aggregates. Increasing the percent of rubber aggregates to 10% and then to 15% in the concrete element results the increasing of normal stresses σy to 33 N/mm2 and respectively to 35 N/mm2.
Fig. 7. The distribution of the normal stresses σy in the concrete element without rubber aggregates for a displacement of 0.04 mm in the Y axis direction
Fig. 8. The distribution of the normal stresses σy in the concrete element with 5% rubber aggregates for a displacement of 0.04 mm in the Y axis direction
Fig. 9. The distribution of the normal stresses σy in the concrete element with 10% rubber aggregates for a displacement of 0.04 mm in the Y axis direction
Fig. 10. The distribution of the normal stresses σy in the concrete element with 15% rubber aggregates for a displacement of 0.04 mm in the Y axis direction
Also, in Fig. 11 and 12 were ploted the distribution of Tresca stresses in the concrete element without rubber aggregates and with 15% rubber aggregates for a displacement of 0.05 mm in the Y axis direction. These results show similar results as in the percedent 350
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stresses distributions, namely that the maximum stresses develop in the zones with agglomerations of stone aggregates and very low stresses develop in zones with agglomerations of rubber aggregates.
Fig. 11. The distribution of Tresca stresses in the concrete element without rubber aggregates for a displacement of 0.05 mm in the Y axis direction
Fig. 12. The distribution of Tresca stresses in the concrete element with 15% rubber aggregates for a displacement of 0.05 mm in the Y axis direction
In the final part of the study, were analyzed the displacement in Y axis direction and the linear strains εy, for a uniform distributed load of 10 N/mm applied at the top of the concrete elements proposed in this study. The results show that for the concrete element without rubber aggregates the maximum displacement in the Y axis direction is 0.032 mm and the linear strains εy in matrices is 0.0009 and in the zones with agglomerations of stone aggregates is 0.0001. The fact is that in the concrete elements with rubber aggregates the displacements and linear strains εy increase a lot for the same applied load at the top. For the concrete element with 5% rubber aggregates, the maximum displacement in the Y axis direction is 0.039 mm and the linear strains εy in the zones with agglomerations of rubber aggregates is 0.003 and in the zones with agglomerations of stone aggregates is 0.0002. Also, in the case of the concrete element with 10% rubber aggregates, the maximum displacement in the Y axis direction is 0.0437 mm and the linear strains εy in the zones with agglomerations of rubber aggregates is 0.0031 and in the zones with agglomerations of stone aggregates is 0.00032. Moreover, the concrete element with 15% rubber aggregates, the maximum displacement in the Y axis direction is 0.052 mm and the linear strains εy in the zones with agglomerations of rubber aggregates is 0.0048 and in the zones with agglomerations of stone aggregates is 0.0004. CONCLUSIONS Some numerical simulations of concrete elements with different percents of rubber aggregates were done in order to examine the stress distribution in the matrices, also in the zones with agglomerations of rubber aggregates and in the zones with agglomerations of stone aggregates. The results from numerical analyses using ANSYS 14 software were the displacement on Y axis direction, linear strain εy and stresses σy and Tresca, for a 351
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uniform distributed load of 10 N/mm and respectively for compressive displacements of 0.01mm, 0.02mm, 0.03mm, 0.04mm and 0.05mm in the Y axis direction applied at the top of the concrete elements proposed in this study. The results show that increasing the percent of rubber aggregates in concrete element leads to low compressive strength but high deformability. This type of concrete with rubber aggregates may have many utilizations in constructions field, such as to create elements with capacity to resist impact loads. Also, in seismic areas, ductile infill walls can be constructed in the frame buildings using this special concrete. Another utilisation can be in industrial buildings in order to isolate and to absorb the vibrations produced by the heavy machines. REFERENCES [1] [2] [3]
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http://www.polymer-search.com/rubber.html Muhammad, B. (2012), Technology, Properties and Application of NRL Elastomers, Publisher InTech. Berselli, G., Vertechy, R., Pellicciari, M., Vassura, G. (2011), Rapid Prototyping Technology - Principles and Functional Requirements, Hyperelastic Modeling of RubberLike Photopolymers for Additive Manufacturing Processes, ISBN 978-953-307-970-7, Publisher InTech. http://ansys.net/ansys/papers/nonlinear/conflong_hyperel.pdf Brodersen, B. (2004), Ogden type materials in non-linear continuum mechanics, Technische Universitat Braunschweig, Institut fur Angewandte Mechanik, Mat.- Nr. 2569716, Germany. Amin, A., Wiraguna, S., Okui Z. 2006, Hyperelasticity Model for Finite Element Analysis of Natural and High Damping Rubbers in Compression and Shear, Journal of engineering mechanics © ASCE, 132 (1), pp. 54 - 64. Mills, N. (2007), Polymer Foams Handbook, Elsevier, Oxford. Briody, C., Duignan, B., Jerrams, S., Tiernan, J. (2012), The Implementation of a Viscohyperelastic Numerical Material Model for Simulating the Behaviour of Polymer Foam Materials, Journal of Computational Material Science, in press. Ali, A., Hosseini, M., Sahari, B.B. (2010), A Review of Constitutive Models for RubberLike Materials, American J. of Engineering and Applied Sciences 3 (1), pp. 232-239. Souza Neto, E.A., Peric, D., Owen, D.R.J. (2008), Computational Methods for Plasticity: Theory and Applications, John Wiley & Sons Ltd, ISBN 978-0-470-69452-7. Ogden, R.W. (2001), Nonlinear elasticity, Cambridge University Press, Cambridge. Yeoh O.H. (1993), Some forms of the strain energy function for rubber, Rubber Chem. Technol, 66, pp. 754–771. Ihueze, C.C., Mgbemena, C.O. (2014), Modeling Hyperelastic Behavior of Natural Rubber/ Organomodified Kaolin Composites Oleochemically Derived from Tea Seed Oils for Automobile Tire Side Walls Application, Journal of Scientific Research & Reports, 3(19). ANSYS 14 Structural Analysis Guide, 2013.
