STRESS ANALYSIS OF EXTERNAL FIXATOR BASED ON STAINLESS STEEL AND COMPOSITE MATERIAL

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1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 1, January 2017, pp , Article ID: IJMET_08_01_021 Available online at ISSN Print: and ISSN Online: IAEME Publication STRESS ANALYSIS OF EXTERNAL FIXATOR BASED ON STAINLESS STEEL AND COMPOSITE MATERIAL Nedim Pervan, Elmedin Mešić, Mirsad Čolić Faculty of Mechanical Engineering, Department of Mechanical Design, University of Sarajevo, Sarajevo, Bosnia and Herzegovina ABSTRACT This paper describes the stress analysis of devices for external fixation based on composite materials and stainless steel, which was performed numerically in the software CATIA V5 and which results are verified experimentally. The aim of this paper is to explore the possibility of introducing composite materials in the construction of the connecting rod fixator comparing values of displacement, principal and von Mises stresses at characteristic points structure. We investigated constructional performance of external fixator with a connecting rod formed from composite materials, and other components of external fixator formed from stainless steel. CAD model of external fixator was made in the software system CATIA V5. Also, in the same software was conducted structural analysis of external fixator under axial compression, and results were compared with experimental test. Finally, in concluding observations, we noted some advantages and disadvantages of the application of composite materials at the external fixator. Key words: stress analysis, composite materials, external fixation, structural analysis, experimental testing. Cite this Article: Nedim Pervan, Elmedin Mešić and Mirsad Čolić. Stress Analysis of External Fixator Based on Stainless Steel and Composite Material. International Journal of Mechanical Engineering and Technology, 8(1), 2017, pp INTRODUCTION It is known that in the world today looking for new, artificially created, materials which will be an adequate substitute for traditional metallic materials. Some of these materials are composite materials which conquering new markets so that the quantity and the possibility of their use is constantly growing. Today in orthopedic surgery in the preparation of the external fixation devices are commonly used biocompatible materials. They are those materials which exhibit good characteristics in contact with cells, tissues or body fluids. Namely, now in orthopedic surgery for making fixator are used primarily stainless steels, super alloys based on cobalt, titanium and its alloys, and less frequently composite materials. One of the main reasons why composite materials are less frequent in the development of external fixation devices is their insufficient research in this area. The aim of this paper is development a prototype of external fixator Sarafix based on stainless steel and composite materials, which should show the positive and negative effects of the introduction of composite materials in the fixator Sarafix editor@iaeme.com

2 Nedim Pervan, Elmedin Mešić and Mirsad Čolić Sarafix external fixation system represents a unilateral, biplanar external fixator which belongs to a group of modular fixators with one-half pins (Figure 1). [1] Figure 1 Sarafix fixator (configuration B50) and fixator components (1-connecting rod, 2-carrier connector, 3- connector, 4-half-pin) 2. GENERAL DESIGN CONCEPT AND THEORETICAL BACKGROUND The Sarafix External fixator system is a pin based external fixator meaning that the main function of healing the damaged bone structure is carried out by pins. This design approach implies a simple construction consisting of a main, primary carrier (trunk) which is supporting the secondary carrier. Configuration of fixator which will be analyzed in this paper is configuration B with the designation 4+4, meaning it consists out of four half-pins that are applied in the proximal and distal section of the bone. It is mainly applied on the lower leg and upper extremities. Table 1 Mechanical properties of materials: Symbol Carbon epoxy Normal Young Modulus E11, Ex, ER 138 GPa Transverse Young Modulus E22, Ey, ET 5 GPa Longitudinal Young Modulus E33, Ez, EL 138 GPa Poisson Ratio in XY plane ν12, νrt, νx'y' 0,3 Poisson Ratio in XZ plane ν13, νrl, νx'z' 0,27 Poisson Ratio in YZ plane ν23, νtl, νy'z' 0,2 Shear Modulus in XY plane G12, GRT, Gx'y' 6 GPa Shear Modulus in XZ plane G13, GRL, Gx'z' 5 GPa Shear Modulus in YZ plane G23, GTL, Gy'z' 5 GPa Longitudinal Tensile Stress x t 1720 MPa Materials Stainless steel X30Cr13 215GPa 0,29 83 GPa Yield strength σ v =650 MPa Density ρ 1500 kg/m kg/m 3 All components of the original configuration Sarafix external fixation system are made of stainless steel while the components of prototype Sarafix external fixation system which will be analyzed in this paper are made of stainless steel and composite materials. During the testing of fixator Sarafix, composite materials will be applied to the connecting rod of fixators. The other components of fixator Sarafix are made of stainless steel. Composite materials which will be used, consists of a combination of carbon fibers editor@iaeme.com

3 Stress Analysis of External Fixator Based on Stainless Steel and Composite Material and epoxy resin. The bone model was designed as a cylindrical rod from wood which is separated into two parts by a distance of 50 mm representing the fracture gap that occurs during real life. Mechanical properties of materials used in the tests are given in table STRUCTURAL ANALYSIS OF EXTERNAL FIXATOR During the processes of Finite Element Analysis, the material of wooden bone models and composite connecting rod was defined as orthotropic, while the other components of the fixator Sarafix were modeled as isotropic. Figure 2 3D CAD and FEA model of the analyzed Sarafix fixator configuration During the structural analysis of the external fixator to axial compression, the bone models were supported on ball joints, while maximal axial loading force applied to the proximal bone model was F p = 600 N. Also, during the structural analysis was used of restrictions on movement in the bone models. At the proximal bone segment, the axial load applied in the form of surface forces in the direction of the z axis. These limits were established, bearing in mind the ways of reliance of bone models during the experimental tests (Figure 2). The principal stresses of the stress tensor are the distinctive values of the stress tensor, while their direction vectors are the principal directions or eigenvectors [3]. When the coordinate system is chosen to coincide with the eigenvectors of the stress tensor, the stress tensor is represented by a diagonal matrix: editor@iaeme.com

4 Nedim Pervan, Elmedin Mešić and Mirsad Čolić = () where, and are the principal stresses. During the processes of Finite Element Analysis, the values of the principal stress and von Mises stress were measured on two places at the middle of the composite connecting rod. The measuring point closer to the bone model was marked with MM- and the point on the opposite side of the composite connecting rod was marked with MM+ (Figure 3). Figure 3 Plot of the principal stresses The equivalent stress or von Mises stress is defined as: = = ( ) +( ) +( ) The von Mises stress is equivalent to the maximum distortion strain energy and it is a good indicator of the yielding of materials. By analyzing the distribution of von Mises stress fields, it can be concluded that the highest stresses on the fixator design did not occur at the measuring point. The highest von Mises stress on the Sarafix fixator occurred in the contacts between the composite connecting rod and the clamping ring. The precise information about displacement of a fracture gap, can be provided by analyzing relative displacements of end bone segments under simulated conditions of loads. Relative craniocaudal and later medial displacements (x and y direction) and axial displacements (z direction) for analyzed points were calculated as: () editor@iaeme.com

5 Stress Analysis of External Fixator Based on Stainless Steel and Composite Material () = () () ; () = () () ; () ( ) = ( ) ( ) ; where:! "(#),! "($) and! "(%) - are the relative displacements at the fracture gap in the x, y and z directions (mm), & '(#), & '($) and & '(%) - are the absolute displacements proximal at the fracture gap in the x, y and z direction (mm), & ((#), & (($) and & ((%) - are the absolute displacements distal at the fracture gap in the x, y and z direction (mm). [4] Figure 4 Plot of the Von Mises stresses editor@iaeme.com

6 Nedim Pervan, Elmedin Mešić and Mirsad Čolić Based on the values of relative displacements! ", maximal value of the resulting vector of relative displacements at the fracture gap (under the loads) is determined as: ) = ( () ) +( () ) +( ( ) ) (*) Figure 5 shows the 3D Finite Element Analysis model of the analyzed configuration Sarafix fixator after the action of maximum axial load. From Figure 5 is easy to see that displacement of proximal bone segment in the fracture is greater than displacement of distal bone segment. This might be expected, because the axial load applied to the upper part of proximal bone segment. Figure 5 Deformed structure of the Sarafix Figure 6 Translation displacement vectors under maximum axial load of points at the fracture gap The directions and intensities of deformation of each point of the structure of the system and bone models are observed in the Figure EXPERIMENTAL TESTING OF EXTERNAL FIXATOR During the experimental testing (Fig. 7), the bone models were supported on ball joints and, using the force transducer, the axial load was controlled in the range of 0 to 600 N at the rate of 5 N/s. Experimental testing of the external fixator under axial compression was performed on the universal material testing machine (Zwick GmbH & Co., Ulm, Germany, model ) using supports for holding of bone models. The composite connecting rod, due to the axial compression at the proximal segment of the bone model, is exposed to the combined loading, which consists of a combination of bending and axial compression editor@iaeme.com

7 Stress Analysis of External Fixator Based on Stainless Steel and Composite Material Tensometric measurement equipment was used to obtain the maximum positive and negative principal strain on the opposite sides of the composite connecting rod. In such a manner, strain gauge measured the maximum positive principal strain at the measuring point (SG+) on the basis of which was determined by the value of the largest principal stress (Fig. 8). Figure 7 Experimental setup for tensometric testing The strain gauges were connected in two Wheatstone half-bridge configuration, with two strain gauges, which are connected with the DMC system via two built-in DMVamplifiers. The strain, registered by Wheatstone half-bridge with active strain gauge (SG+ and SG-) and compensation strain gauge (SGc+ and SGc-), is given by the relation [2,5,6]: U U A ε (+) = 4 k E where: k is gauge factor, U A bridge output voltage, U E excitation voltage (bridge input). Compensating strain gauges are used to compensate the effect of temperature on the measurement and they are of the same type as the active ones. They were placed on the plate that is tied to a composite connecting rod, near the active strain gauges. The plate and connecting rod are made from the same composite material. In this way, it is possible to determine the intensity of the dominant principal stresses at the measuring points. Displacement of points at the fracture gap is measured with a digital high-speed camera. The camera was set in such a position so it could cover the end of the proximal and distal bone segment. (Fig.9) editor@iaeme.com

8 Nedim Pervan, Elmedin Mešić and Mirsad Čolić Figure 8. Arrangement of strain gauges on Figure 9. Experimental setup for measuring composite connecting rod displacement of points at the fracture gap A scheme of the experimental setup for measuring displacement of points at the fracture gap is shown in Figure 10. Figure 10 Experimental setup scheme: 1 Camera; 2 Specialised camera stand; 3 External Fixator; 4 Testing machine; 5,6 supporting table; 7 Computer (additional light source is not shown) The load process is simulated with a testing machine from 0 N to 600 N, and during that time were made recordings of displacement bone models with high-speed camera. Recordings of displacements bone models were processed in the software, and the results are shown in Figure editor@iaeme.com

9 Stress Analysis of External Fixator Based on Stainless Steel and Composite Material a) b) Figure 11 Evaluation of proximal and distal segment displacements; a) F=0 N; b) F=600N 5. RESULTS In order to achieve a direct comparison of results of the Finite Element Analysis and experimental testing, all parameters of geometry, materials, loads, restrains on the FEA model are set according to experimental settings. Tables 2 show the intensities of principal and von Mises stresses generated at the measuring points in the case of maximum axial compression force. The value of the maximum principal stress ( ) at the MM+ was significantly higher than the other two principal stresses ( and ) so they are not shown in the table 2. Likewise, the value of the minimum principal stress ( ) at the MM- was significantly higher than the other two principal stresses ( and ) which are also not shown in the table 2. On the basis of the relation (2) which calculates the value of von Mises stress at the measurement points, von Mises stresses have the same value as the maximum principal stresses. Table 2 Values of principal and von Mises stresses at the measuring points: Method Principal stresses (MPa) von Mises stresses (MPa) MM+ MM- MM+ MMσ1 σ3 σvm σvm FEA Exp editor@iaeme.com

10 Nedim Pervan, Elmedin Mešić and Mirsad Čolić Table 3 Displacement of points at the fracture gap Method Displacement of proximal bone segment (mm) Displacement of distal bone segment (mm) Dp(x) Dp(y) Dp(z) Dd(x) Dd(y) Dd(z) FEA 5,76 0,07-5,38 5,81-0,09 0,38 Exp. 6, ,76 5,92-0,41 Tables 3 shows the values of displacement of points at the fracture gap for two different methods. The resulting vector of relative displacements at the fracture gap is determined by relation (4) and amounts to 5,76 mm. Figure 12 shows the axial displacement at the point of load for two different methods, and where can be seen good agreement between Finite Element Analysis and experimental measurement. Figure 12 Diagram of the axial displacement at the point of load 6. CONCLUSION The conducted research has shown that there is a linear dependence between the loads and stresses generated on the composite connecting rod, as a result of the absence of large displacement and plastic deformation of the fixator components. Comparing the results of Finite Element Analysis and experimental testing of the principal stresses and displacement at the measuring points reveals their good agreement and argues that the solutions obtained by FEA were verified. We can notice that the deviation results values of principal stresses obtained by FEA method compared to the results of experimental tests, ranging up to 4%, which is very good, because it is a very demanding construction. The maximum values of von Mises and maximum principal stress at the measuring points is respectively,- = 232MPa and = 270MPa and they are lower than the longitudinal tensile stress of the material of the fixator connecting rod (, = 1720MPa). As for the results of displacement, we can notice that the deviation results values of displacement obtained by FEA method compared to the results of experimental tests, ranging up to 7%. Interfragmentary displacements parallel to the fracture surfaces, lead to the appearance of pseudo-arthrosis instead of fracture healing. For these reasons, it is necessary to control interfragmentary displacements, especially to minimize transverse (shearing) displacements of bone ends at the fracture gap. Application of composite materials in the construction of fixation enabled the invisible to x-rays of those components, which facilitates the postoperative patient treatment. Also, the application of composite materials has been reduced weight and stress in the construction of fixation editor@iaeme.com

11 Stress Analysis of External Fixator Based on Stainless Steel and Composite Material For analyzed configuration of fixator reducing stress on the composite connecting rod is approximately 44% compared to the original configuration of fixator which all components are made of stainless steel. Also, for the same configuration of fixator we have increase of displacements bone models amounting to 30%. During the experimental testing was observed local kneading of the fixator connecting rod in contact with the clamping ring which is manifested in the form of holes on the surface of the fixator connecting rod, due to the high value of surface pressure. Also the occurrence of kneading shows performed structural analysis. The solution to this problem can be found in increasing the contact area between the connecting rod and the clamping ring. REFERENCES [1] Mesic, E. Development of an integrated CAD/KBE system for design/redesign of external bone fixation devices, University of Sarajevo, Faculty of Mechanical Engineering, [2] Basic, H. Mechanical Engineering Measurements, Faculty of Mechanical Engineering, University of Sarajevo, Sarajevo, [3] Zienkiewicz, O.Z., Taylor, R.L. and Zhu, J.Z. The Finite Element Method: Its Basis and Fundamentals, 6th ed., Butterworth-Heinemann, Oxford, [4] Mesic, E. Research of Mechanical Stability of the Sarafix External Fixation System, University of Sarajevo, Faculty of Mechanical Engineering, [5] Mesic, E., Avdic, V., Pervan, N. Numerical and experimental stress analysis of an external fixation system, Folia Medica Facultatis Medicinae Universitatis Saraeviensis, Vol.50, No.1, 2015, pp [6] Mesic, E., Pervan, N., Repcic, N., Muminovic, A. Research of Influential Constructional Parameters on the Stability of the Fixator Sarafix, Annals of DAAAM for 2012 & Proceedings of the 23 rd International DAAAM Symposium, ISBN ISSN , Vienna, Austria, 2012, pp [7] Manish Saini, Rahul sharma, Abhinav, Gurupreet Singh, Prabhat Mangla and Er. Amit Sethi. Optimizations of Machining Parameter in Wire EDM for 316l Stainless Steel by Using Taguchi Method, Anova, and Grey Analysis. International Journal of Mechanical Engineering and Technology (IJMET), 7(2), 2016, pp [8] Pervan, N., Mesic, E., Čolić, M., Avdić, V. Stiffness Analysis of the Sarafix External Fixator based on Stainless Steel and Composite Material, TEM Journal - Technology, Education, Management, Informatics, Vol. 4, No. 4, 2015, pp [9] K. Sunil Kumar, Dr. B. Nagalingeswara Raju, J. Arulmani and P. Amirthalingam, Design and Structural Analysis of Liquified Cryogenic Tank under Seismic and Operating Loading. International Journal of Mechanical Engineering and Technology (IJMET), 7(6), 2016, pp [10] Pervan, N., Mesic, E., Čolić, M., Avdić, V. Stiffness Analysis of the Sarafix External Fixator of Composite Material, TEM Journal - Technology, Education, Management, Informatics, Vol. 5, No. 1, 2016, pp editor@iaeme.com