Elasto-plastic Stress Analysis of Steel Fibre Reinforced Aluminum Metal Matrix Composite Plates

Transcription

1 Elasto-plastic Stress Analysis of Steel Fibre Reinforced Aluminum Metal Matrix Composite Plates Alper Atmaca 1 - Osman Selim Türkbaş 2 - Mehmet Emin Erdin 3 - Halil Aykul 4 1 Machines Technical Program, Hitit University, Hitit Üni. Meslek Yüksekokulu Samsun Cad. No: Çorum, Türkiye, alperatmaca@hitit.edu.tr 2 Mechanical Engineering Department, Gazi University, Gazi Üni. Mühendislik Fakültesi Yükseliş Sok. No: 5 Maltepe/Ankara, Türkiye, turkbas@gazi.edu.tr 3 Mechanical Engineering Department, Hitit University, Hitit Üni. Mühendislik Fakültesi Çevre Yolu Bulvarı No: Çorum, Türkiye, eminerdin@hitit.edu.tr 4 Mechanical Engineering Department, Hitit University, Hitit Üni. Mühendislik Fakültesi Çevre Yolu Bulvarı No: Çorum, Türkiye, halilaykul@hitit.edu.tr ISSN (Print) ISSN (On-line) Keywords Composite Plates Aluminum Matrix Steel Fibre Reinforcement Elasto-plastic Stress Finite Element Analysis Abstract A numerical method for obtaining displacements and stresses in composite plates is presented. Mechanical behavior of steel fibre reinforced aluminum metal matrix composite plate is determined with elasto-plasticity. Experimental methods are used for obtaining mechanical properties of composite structure and finite element method is used for stress analysis. Stress distributions for different orientation angles are calculated using finite element analysis. Manufacturing techniques are compared. Minimal stress and yielding regions are specified. History Received 13 October 2012 / Revised 07 Jun 2013 / Accepted 09 July 2013 Article Category Citation Original Scientific Paper Atmaca A, Türkbaş O. S, Erdin E. M, Aykul H (2013) Elasto-plastic Stress Analysis of Steel Fibre Reinforced Aluminum Metal Matrix Composite Plates. Journal of Manufacturing and Industrial Engineering, 1-2(12): 12-16, doi: /mie.v12i INTRODUCTION Development of technology gained a great acceleration during the last century. Materials that are procured from nature cannot keep up with this development. Thus, new searching about materials became compulsory. To meet the material requirements of developing technology, a combined structure is developed which is formed by joining two or more different materials in macro level. This new structure which is called composite material has the superior properties of the materials which form itself. Types and area of usage of composite materials is increasing day by day. Composite plates with Aluminum metal matrix show an elasto-plastic behavior during forming operations. Elasto-plastic situation of the material is characterized as the permanent deformations on the material after elastic region is exceeded and a specific stress value is reached. Initiation of plastic deformation in a composite material is determined by the help of a yield criteria. Residual stresses occur in the material because of the deformations arising from plastic stresses [1, 2]. Daining et al. investigated the elasto-plastic stress-strain behaviours of metal matrix composite materials using finite element method [3]. Sayman investigated the elasto-plastic behaviour of simply supported stainless steel reinforced aluminum metal matrix laminated composite plates under transverse [6] and in-plane [7] loads using finite element technique. Sayman stated that composite structure increases yield strength and rigidity. Also it is stated that residual stresses can be used for enhancing mechanical properties. Özben and Arslan investigated the elastic and plastic behaviour of laminated composite plates under transverse loads using finite element method [4, 5]. Purpose of this study is to determine plastic behaviour of composite materials. To find the plastic behaviour manner of the material, finite element based elasto-plastic stress analysis is executed using ANSYS packaged computer software. Composite material is manufactured. Tensile and shear tests are carried out to obtain necessary data for elasto-plastic stress analysis. Besides, composite material is manufactured using two different methods which are hot pressing method and resiny method. Composite plate properties and quality is corresponded in terms of manufacturing method. This study is constituted from three stages. First of all, a metal matrix composite plate is obtained. Matrix material of the composite structure is aluminum plate and reinforcement material is steel fibre. Steel fibres are placed on the matrix in only one axis. To procure a bond between matrix and fibre hot pressing or epoxy resin is used. Composite structure is subjected to heat treatment for an hour in 80 C for gelling and hardening of epoxy resin. Resiny manufacturing method is simpler than hot pressing method. In this method, high affinity of aluminum to oxygen does not engender a disadvantage. After the manufacturing of composite plate, simple tensile and shear tests are performed to achieve engineering constants and mechanical properties of the composite structure. It is seen that, tensile strength of composite material increases with the increasing fibre ratio. From the performed mechanical tests, it is understood that has no contribution on the strength of composite material but it is a very good adhesive indeed. In the final stage, elasto-plastic finite element based stress analyses are executed using ANSYS computer packaged software. In the finite element analyses, elasto-plastic stress values are calculated for (0/90 ) 2 symmetrical cross reinforced and (15/- 15 ) 2, (30/-30 ) 2, (45/-45 ) 2 symmetrical angular reinforced laminated aluminum metal matrix composite plates. In symmetrical laminated plates, plate is simply supported from all of the sides to prevent them to move in x and y directions. Tsai- Hill Theory is used as a yield criteria in the analyses /mie.v12i

2 Elasto-plastic Stress Analysis of Steel Fibre Reinforced Aluminum Metal Matrix Composite Plates Atmaca A, Türkbaş OS, Erdin ME, Aykul H COMPOSITE STRUCTURE Two 5083 series aluminum plates are prepared in the dimensions of standard tensile test sample. Chemical composition and mechanical properties of aluminum is given in Table 1 and Table 2 respectively. Table 1 Chemical composition of 5083 series aluminum Element Cu Mg Mn Fe Si % Mass < Element Zn Ni Cr Ti % Mass <0.20 < <0.10 Table 2 Mechanical properties of 5083 series aluminum Property X [MPa] Y [MPa] E [GPa] Value Property G [GPa] δ 5 [%] ρ [kg/dm 3 ] Value 26 30~ Paksoy resin is prepared by mixing components A and B in a container for approximately 3 minutes and applied on the aluminum plate. Resin composition and properties is given in Table 3. Table 3 Epoxy resin composition and properties Component Number 2 (A & B) Massive Mixture Ratio (A/B) 50/50 Volumetric Mixture Ratio (A/B) 50/50 Mixture Density [gr/cm3], at 20 o C 1.5 Mixture Life [min.], 200 gr. at 20 o C 60~100 Overall Hardening Time [week], at 23 o C 1 EXPERIMENTAL STUDY Tensile and shear tests of composite structure is performed for finding necessary mechanical properties of composite material for elasto-plastic stress analysis. Tests are performed in Hitit University Engineering Faculty Laboratories with 100 kn computer controlled Shimadzu Autograph Universal Testing Machine. The samples for tensile tests are prepared according to TS 138 EN standards. Thickness of the obtained composite structure is more than 3 mm. Thus, the gauge length is calculated with below equation; L o = 5.65(S o ) 1/2, (1) where Lo is initial gauge length of the sample, So is initial crosssectional area and 5.65 is a coefficient related with the thickness of the tensile sample. A special apparatus is used in tests for preventing shear between matrix and fibres. A snapshot from the shear testing operation is seen in Figure 2 and graphical output of the tensile testing is seen in Figure 3. Steel fibres of 150 mm length are placed on resiny aluminum plates. Mechanical properties of steel fibre are given in Table 4. Table 4 Mechanical properties of steel fibre Property X [MPa] Y [MPa] E [GPa] ρ [kg/dm 3 ] Value Figure 2 A snapshot from shear testing operation Some more resin is applied on steel fibres and the other aluminum plate is placed on them. Plates are slightly compressed by hand to avoid pores on structure. After heat treatment as mentioned above, resin is hardened and bond is procured between aluminum matrix and steel fibres. A manufactured sample of composite plate is seen in Figure 1. Figure 3 Graphical output of the tensile testing Necessary mechanical properties of composite material for elasto-plastic stress analysis is obtained from the results of tensile tests as given in Table 5. Figure 1 A sample of manufactured composite plate 13

3 Atmaca A, Türkbaş OS, Erdin ME, Aykul H Elasto-plastic Stress Analysis of Steel Fibre Reinforced Aluminum Metal Matrix Composite Plates Table 5 Mechanical properties of composite material Property X [MPa] Y [MPa] S [MPa] Value Property k [MPa] n [-] ν 12 [-] Value Property G 12 [GPa] E 1 [GPa] E 2 [GPa] Value ELASTO-PLASTIC STRESS ANALYSIS Elasto-plastic stress analysis are executed in Hitit University Engineering Faculty using ANSYS packaged software. A four laminated plate of 50x50x3.2 mm dimensions is modelled in which thickness of each plate is 0.8 mm. the model is simply supported to prevent motion in x and y axes. The model is subjected to a pressure of 10 MPa as shown in Figure 4. where F indicates forces in nodal points. Finally, stress values are calculatede from the equation σ = D.B.q (8) In this equation, stress matrix (σ) is obtained in the form of [σ x σ y σ z ] T. These stresses are replaced in the Tsai-Hill equivalent stress equation which is given below. (9) If the equivalent stress is less than the yield strength (X), elasticity limit is not exceeded and plastic analysis is not necessary. If the equivalent stress is more than the yield strength (X), stresses are calculated from Ludwig Equation which is given below. (10) where σ o is the yield strength of the material, K is the strength coefficient and n is the strain hardening exponent. Figure 4 Finite element model of the elasto-plastic stress analysis problem Stress distribution on finite element composite model is seen in Figure 5. The solution procedure for above mentioned mechanical problem will be described step by step thereinafter. The model is divided into elements of finite number. Direct Stiffness Matrix (D) of all elements and the whole model is found. D - [ - ] (2) In this equation, E; is the elasticity modulus and ν; is the poissons ratio. Stress-Displacement Matrix (B) is found for all elements. [ ] (3) In this equation, superscript e indicates element and = - (4) where J is the Jacobean Matrix. Figure 5 Stress distribution on finite element model Stress variation from the side of composite plate to the center is seen in Figure 6. [ ] (5) Rigidity Matrix is found for all elements. Then Overall Rigidity Matrix is constituted by combining Element Rigidity Matrices. Displacements are calculated from the equation F = k.q (7) (6) /mie.v12i

4 Elasto-plastic Stress Analysis of Steel Fibre Reinforced Aluminum Metal Matrix Composite Plates Atmaca A, Türkbaş OS, Erdin ME, Aykul H Figure 6 Stress variation on composite plate CONCLUSION AND RESULTS Elasto-plastic stress analyses results for all symmetry and orientation situations in critical nodes (A, B, C, D and E which are seen in Figure 5) are given in Table 6. Conclusions from the performed analyses are listed below: Resin has no effect on strength of the composite structure. Density of resin is low and has no negative effect on weight of the composite structure. In resiny method fibres do not penetrate into matrix, thus thickness is more in resiny method than hot pressing method. Resiny method is simpler and cheaper than hot pressing method. In hot pressing method, structures of fibre and matrix materials change and their strength values decrease because of high temperatures. In hot pressing method, oxidation is an important problem. In resiny method, temperature strength is limited by the decomposition temperature of the resin which is 250 C for the Paksoy resin used in this study. In symmetrical orientation, maximal stress occured in (0/90 ) 2 reinforcement angle and minimal stress occured in (0/15 ) 2 reinforcement angle. In antisymmetric orientation, maximal stress occured in (15/-15 ) 2 reinforcement angle and minimal stress occured in (0/90 ) 2 reinforcement angle. In antisymmetric orientation, minimal plastic region occured in (15/-15 ) 2 reinforcement angle. In symmetrical orientation, minimal plastic region occured in (0/15 ) 2 reinforcement angle. In symmetrical orientation, yielding occurred only in the central region In antisymmetric orientation, yielding occured in central region and corners. REFERENCES [1] Mendelson A (1968) Plasticity Theory and Application. The Macmillan Company, New York. [2] Owen D R J, Hinton E (1980) Finite Elements in Plasticity. Pineridge Press Limited, Swansea. [3] Daining F, Hang Q, Shangdong T (1996) Elastic and Plastic Properties of Metal-Matrix Composites: Geometrical Effects of Particles. Computational Materials Science, 6: [4] Özben T, Arslan N (2009) Expansion of Plastic Zone and Residual Stresses in the Thermoplastic-Matrix Laminated Plates ([0 /θ ] 2) with a Rectangular Hole Subjected to Transverse Uniformly Distributed Load Expansion. Computational Materials Science, 44 (3): Table 6 Results of the elasto-plastic stress analyses Yönlenme Açilari NODLAR σ x σ y xy yz xz A 798,82 652,96 0, ,618E-03-0,257E-04 (0 /90 ) 2 (0 /15 ) 2 (0 /30 ) 2 (0 /45 ) 2 B 95,410 32,477-0, ,275E-01-6,1401 C 94,785 31,997 0, ,284E-01 6,1766 D 373,15 427,36 0, ,411-0,185E-01 E 372,77 425,63 40,319-23,078-1,2013 A 739,60 613,37-0, ,351E-03 0,106E-05 B 82,581 27,985 1,5870-0,137E-01 4,2004 C 81,470 27,332 1,3112 0,140E-01-4,2147 D 337,62 382,94 0, ,561 0,11310 E 336,48 381,48 36,406-18,277-0,83006 A 788,71 653,45-1,5662-0,385E-03 0,497E-04 B 86,628 28,145 2,3317-0, ,2489 C 86, ,055 2,0120 0, ,7455 D 357,55 406,47 0, ,987 0,1439 E 356,25 404,76 38,519-20,654-0,9118 A 336,97 380,86 1, ,495 0,281E-01 B 82,023 30,188 1,8827-0, ,6779 C 8,933 28,587 1,6850 0, ,2235 D 336,97 380,86 1, ,495 0,283E-01 E -361,15-359,78-43,817 17,249 1,

5 Atmaca A, Türkbaş OS, Erdin ME, Aykul H Elasto-plastic Stress Analysis of Steel Fibre Reinforced Aluminum Metal Matrix Composite Plates [5] Özben T, Arslan N (2010) FEM Analysis Laminated Composite Plate with Rectangular Hole and Various Elastic Modulus under Transverse Loads. Applied Mathematical Modeling, 34 (7): [6] Sayman O (1998) Elasto-plastic Stress Analysis in Stainless Steel Fiber Reinforced Aluminium Metal Matrix Laminated Plates Loaded Transversely. Composite Structures, 43: [7] Sayman O, Akbulut H, Meriç C (2000) Elasto-plastic Stress Analysis of Aluminium Metal Matrix Composite Laminated Plates under Inplane Loading. Computers & Structures, 75 (1): LIST OF USED SYMBOLS F Force [N] σ, X, Y Stress [MPa] τ, S Shear stress [MPa] E Modulus od elasticity [GPa] G Modulus of shear [GPa] L Length [mm] q Unknown displacement vector [mm] x, y Displacement [mm] k Stiffness matrix [-] n Strain hardening exponential [-] ν Poissons ratio [-] /mie.v12i