Mathematical and Computational Applications, Vol. 16, No. 1, pp Association for Scientific Research

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1 Matheatical and Coputational Applications, Vol. 16, No. 1, pp Association or Scientiic Research INVESTIGATION OF COATING AYER TO REDUCE THERMA STRESSES IN STEE FIBER REINFORCED AUMINUM META MATRIX COMPOSITE Fuat Okuuş Departent o Mechanical Engineering Gediz University,3530 Çankaya,İzir, Turkey okuus1953@hotail.co Abstract-In this study, by using coating layers to reduce theral stresses in the etal atrix coposites with a isatch in coeicients o theral expansions o iber and atrix is investigated. The theroelastic solutions based on a three cylinder odel are deored. It is shown that the eectiveness o the layer can be deined by the product o its coicients o theral expansions and thickness and that a copensating layer with a suiciently high coeicient o theral expansions can reduce the theral stresses in the etal atrix.. In order to veriy the results were copared with the inite eleent ethod. In this solution, 4 nodes and 44 nine-node isoparaetric eleents are used. The study is based on a three cylinder odel isolating one steel iber with a coating layer and a aluinu atrix layer. Only onotonic cooling is studied and the variation o the aterial properties with teperatures is not considered. The results have been presented in graphics. Key words: Theral stress, coating layer, stress analysis, inite eleent analysis 1.INTRODUCTION The aircrat and autootive industry is showing an increasing interest in aterials that are lighter, stronger, and ore wear resistant than conventional aterials as a eans to increase the eiciency and durability o engines. These new aterials ust retain their superior properties at higher operating teperatures to ensure that the engines eet the stringent econoic and environental requireents. ight etal alloys reinorced with steel ibers, especially aluinu based etal atrix coposites are prie candidates or such applications because they can posses properties that eet such deands. However, a theral isatch exists between the steel ibers and the aluinu atrix. The steels having a low coeicient o theral expansion (CTE and aluinu has higher values o CTE. This theral isatch induces stresses in the coposite structure when subjected to teperature change.in any investigation atrix craking has been observed ater cooling down ro processing teperature to roo teperature or brittle atrix aterials. Soe investigators have been proposed that the addition o a coating layer between the iber the atrix can reduce the tensile residual stresses in the atrix to a level which is low enough to avoid atrix craking. Due to the interest or any engineering areas (especially aircrat and autootive industry the optiization o coating layers in the design o iber reinorced etal atrix coposites received considerable attention up till now. Ghosn and Bradley [1]

2 F. Okuuş 7 have reported optiu interace properties or etal atrix coposites. Doghri and eckie [] have ade elasto-plastic analysis o interace layers or iber reinorced etal atrix coposites. Soe nuerical paraetric studies have been perored in an attept to deterine the aterial paraeters that are ost beneicial in reducing theral stresses. It has been suggested that the optiu coating layer should have a CTE between those o the atrix and iber, with low allowable odulus and a high layer thickness [3,4]. Okuuş [5]. has ade an analysis on eect o coating layer to reduce theral stresses. In the present work, sipliied elastic analysis has been perored or stainless steel iber and aluinu etal atrix coposite aterial ro re. [6]. In this study, stainless steel is used as iber aterial and aluinu is used as atrix aterial. Elastic analysis procedure is realized in two steps. Firstly, elastic analysis is perored assuing that the iber, atrix and layer aterials are isotropic and linearly elastic. In this case, the variation o aterial properties with teperature is not considered. At second, both the coating layer and the atrix are considered to be elastic-plastic and the teperature dependence o the properties o the three aterials is considered. The von Mises theory is used as a yield criterion. Theral stress analysis is carried out by using inite eleent ethod, and the residual stresses are deterined or sall deorations..mathematica FORMUATION Steel aterials are usually at least three to our ties stier than the aluinu atrix aterials. Hence, it can be assued that, E E 1 E and 1 (1 E The stress distribution in the atrix and coating layer is governed by the plane strain proble with a ixed inner radius at the iber interace. The dierential coeicients o theral expansions o atrix, iber and coating can be written as, and ( The stress distribution in the atrix is given by the plane strain solution or a thick walled cylinder subjected to an unknown internal pressure (P, a traction ree outer surace, and a teperature change T. Superiposing the solutions given in Re. [6] or an internal pressure and a teperature change gives the stress distributions in the atrix as ollow, r z (R p (R p (R /R /r /R 1 1 E 1 (R /r 1 p (3 (R /R 1 T The highest stresses in the atrix occur at the inner surace o the cylinder, r = R. The von Mises equivalent stress can be written as,

3 8 Investigation o Coating ayer to Reduce Theral Stresses in Steel Fiber r z r rz z (4 and can be calculated as 1/ C C p [3 / c 1 4(1 ] pet 1 E T (5 1 C 1 C Where C is the iber volue raction. The coating layer is subjected to a pressure in the radial direction resulting ro the contact with the atrix (6 r P The teperature change T introduces stresses in he hoop and longitudinal directions due to the constraint ro the ibers. The stresses in the hoop and longitudinal directions are equal and are the su o the stresses caused by the pressure and the theral expansion, 1 z p ET (7 1 1 The von Mises equivalent stress in the coating layer is given by ollowing equation, 1 E T (1 P (8 1 The value o P can be ound as, t(1 (1 R(1 P ET (9 1 C te (1 ( (1 1 C 1 R E 1 Where C is the iber volue raction.

4 F. Okuuş 9 /P 3 r z P/P Figure 1. Stresses at the inner radius o the atrix. (P = E T 3.FINITE EEMENT ANAYSIS In this work, inite eleent procedure is eployed to calculate the residual stresses and yield strength o the coposite lainates. Nine-node eleents are used with displaceent unctions.the stiness atrix o the coposite plate can be obtained by using the iniu potential energy principle. Bending and shear stiness atrices are, K b B b T D b B b da A K s B s D s B s da A Where, D b D s T A ij B ij B ij D ij k 1 A k A 55 (10

5 30 Investigation o Coating ayer to Reduce Theral Stresses in Steel Fiber ( A ij, B ij, D ij Q ij (1,z,z dz, (i, j 1,,6 ( A 44, A 55 ( Q 44, Q 55 dz. Here, D b and D s are the bending and shear parts o the aterial atrix, respectively. The ter A 45 has been neglected. Because, A 45 is negligible in coparison with A 44 and A 55. The shear correction actors are given by, k 1 k 5/6 [1]. Since, the calculated stresses do not coincide with the true stresses in a nonlinear proble, the unbalanced nodal orces and the equivalent nodal orces ust be calculated. The equivalent nodal point orces corresponding to the eleent stresses at each iteration can be calculated as ollows, {R} eq. B σ da B b σ b da + B s σ s da. Vol. -h/ -h/ T h/ When the equivalent nodal orces are known, the unbalanced nodal orces can be ound by, (1 {R} unbalanced {R} applied {R} equivalent These unbalanced nodal orces are applied or obtaining increents in the solution and ust satisy the convergence tolerance in a nonlinear analysis. Residual stresses are very iportant in theral analysis o etal atrix lainated plates. When the yield point o the lainate is exceeded, the residual stresses occur in lainate plates. The obtained residual stresses can be used to raise the yield strength o the coposite plates. In this solution, 4 nodes and 44 nine-node isoparaetric eleents are used.. In order to obtained ore accurate results at the coposite, a highly reined esh was constructed or all region. Table 1. h/ Vol. T Mechanical Properties o the iber and atrix aterials Young s odulus Theral expansion coeicient Poisson s ratio Fiber 07 GPa 11x10-6 /C Matrix 70 GPa 10.3x10-6 /C Vol. T (11

6 F. Okuuş 31 x /P 5 E / E =0,5 t / R ,1 FEM / Figure. the change o stresses in coating layer. 4. RESUTS AND DISCUSSION The stresses at the inner radius o the atrix are calculated and results are presented in igure 1. as a unction o pressure. Here, iber volue raction or steel is taken 0,5 and poisson s ratio or aluinu atrix is taken 0,5. As it is seen that a pressure at the interace causes increased tensile stresses in the axial direction that could eect atrix craking. It is also seen that the value o the critical stress or atrix, c, sets an upper liit or the principal stresses (, z, r and allowable equivalent stress, y in the atrix sets another liits on the pressure. These conditions clearly shows that an interval exist or the interace pressure so that the ailure criteria are not distrupted. Inspection o equation (9 and igure 1. shows that the von Mises equivalent stress has a iniu or an interace pressure that is close to zero. The pressure P is zero when t R (1 (1 (1 ro above equation (13 it can be obtained that the stresses in the atrix are inluenced by the paraeter t. It is seen that a coating layer o available aterials with high CTE has the ability o substantially reducing theral stresses in the atrix. Stresses in the coating layer is illustrated in igure. as a unction o the dierent diensionless paraeters. The deoration o the layer is constrained in the (13

7 3 Investigation o Coating ayer to Reduce Theral Stresses in Steel Fiber longitudinal direction so that tensile stresses increase in the layer. The stress in the coating layer is dependent on the layer odulus (E /E and CTE, /, but the inluence o the layer thickness t /R on the stress in the coating layer is not signiicant. This result indicates that the inluence o the constrained theral expansions on the stress is ore signiicant or coating layer and it is also displayed that stress in the coating layer is weakly dependent on the interace pressure. It can be deduced ro igure. that it is ore preer to have a thick layer and a oderate high layer CTE than a thin layer and a high CTE in order to obtain stress reduction in the atrix and to prevent high tensile stresses in the coating layer. The inluence o the young s odulus (E and the CTE ( and the thickness (t on the reduction o the residual stresses in the atrix are obtained. For this purpose the iber and the atrix echanical properties are given in table 1. The iber volue raction is taken as, C R ( 38 (14 R The echanical properties o the iber and the atrix were kept constant and the range o coating layer paraeters was chosen as ollows: For E, 50 Gpa<E <500 Gpa For, 5x10-6 /C 0 < <5x10-6 /C 0 For t R, 0.03< t R <0.3 The poisson s ratio o the coating layer was kept constant =0.3. Figure 3. displays the layer CTE eect on the stresses in the atrix. In this case, young s odulus E and thickness t was kept ixed or each calculations. The results show that the atrix equivalent stress decreases considerably as increases. However as showed in igure 3., the equivalent stresses reach a iniu value (about =4 ater this iniu value they increase again with increasing. Results also show that the decrease o is ore pronounced i the ixed thickness t is high. Results pointed out that the addition o the interace coating layer does reduce the residual stresses in the atrix. Inluence o he young s odulus o the coating layer is presented in igure 4. in the case that the layer CTE and thickness t was kept ixed or each calculations. It is seen that in the range 60 GPa-00 GPa, the value o young s odulus o the layer is relatively insensitive on the atrix stresses. Ater the 00 GPa point the value o E has ore eect on atrix stresses until 450 GPa. It is shown that i is big value ro 10x10-6 /c 0 value the increase o E ay reduce the stress in the atrix. I value is sall ro 10x10-6 /C 0 value, the eect o E on the stresses has no signiicant. Inluence o the thickness on the stresses in the atrix is given in igure 5. It is seen that stresses in the atrix is decrease while the thickness o the layer is increase. In this case, E and was kept ixed or each calculations.

8 F. Okuuş 33 In all the cases the analysis it was shown that the iportant layer paraeter which aected the atrix stress is t. / re t /R = 0,0 t /R = 0,15 t /R = 0, FEM (10-6 /C Figure 3. Eect o the layer CTE on the stresses in the atrix. 5.CONCUSIONS In the present study, theral stresses analysis is carried out or cylindirical coposite aterial.metal atrix coposites reinorced with stainless steel ibers are attractive because o their high speciic stiness and strength. Advantage can be taken ro the high teperature strength o stainless steel ibers and the ductily o the aluinu etal atrix to produce a coposite with superior cobined properties. However a theral isatch exist between the iber and the atrix. This theral isatch induces stress in the coposite when subjected to teperature change. This stresses ay cause atrix craking which have been observed in any application. It has been proposed that the addition o the coating layer between the iber and the atrix can reduce the tensile residual stresses which ay prevent atrix craking. Based on this study, the ollowing results were obtained. 1. A high coating layer with a suiciently high CTE has an inluence on the reducing theral stresses in the atrix.. While using the coating layer between the atrix and the iber it should be noted that the young s odulus o the coating layer has not to be very low. 3. I young s odulus o the coating layer is taken in a certain range, the coating layer perorance is deined by the product o its CTE and thickness.

9 34 Investigation o Coating ayer to Reduce Theral Stresses in Steel Fiber 4. I the coating layer has high young s odulus, it ay create high stresses in the atrix 5. The theral isatch between the iber and the atrix has to be taken up by the coating layer. 6. The inluence o the layer properties on the axial stress in the atrix is not uch iportant. / re FEM t /R = 0,0 t /R = 0,15 t /R = 0, E /E M Figure 4. Inluence o the layer young's odulus on the stresses in the atr

10 F. Okuuş 35 / re 1.0 0, ,4 = 10 = FEM t / R Figure 5. Eect o the layer thickness on the stresses in the atrix 6.REFERENCES 1. Ghosn,.J. and A.. Bradley. Optiu Interace Properties or Metal Matrix Coposites,NASA TM-10985, Doghri, I. and F.A. eckie. Elasto-Plastic Analysis o Interace ayers or Fiber Reinorced Metal Matrix Coposites, Coposites Science and Technology, Caruso, J.J., C.C. Chais and H.C. Brown. Paraetric Studies to Deterine the Eects o Copliant ayers on Metal Matrix Coposite Systes, NASA TM , Jansson, S. and F.A. eckie. Reduction o Theral Stresses in Continuous Fiber Reinorced Metal Matrix Coposites with Interace ayers, Journal o Coposite Materials, 6 (10: , Okuuş, F. Inluence o coating layer to reduce theral stresses in cylindirically ored etal atrix coposites, ASME 14 th Reliability Stress Analysis and Failure Prevention Conerence, Vol.5,11-18, Doghri, I. and Jansson, S. and eckie, A. and eaitre, J. Optiization o Coating ayers In the Design o Ceraic Fiber Reinorced Metal Matrix Coposites, Journal o Coposite Materials, 8 (: ,1994.