Influences of multiple holes on thermal stresses in a thermoplastic composite disc

Transcription

1 Indian Jounal of Engineeing & Mateials Sciences Vol. 17, June 010, Influences of multile holes on themal stesses in a themolastic comosite disc Fauk Sen a,b, * & Metin Saye c a Deatment of Mechanical Engineeing, Univesity of Sheffield, Sheffield, United Kingdom b Deatment of Mechanical Engineeing, Aksaay Univesity, Aksaay, Tukey c Deatment of Mechanical Engineeing, Pamukkale Univesity, Denizli, Tukey Received 16 Setembe 009; acceted 4 May 010 The aim of this investigation is to obseve the influence of multile holes on themal stesses in a themolastic comosite hollow disc. Fo this uose, a themolastic comosite disc is einfoced by steel fibes as cuvilinea fo adial diection, and themal loads ae caied out fo unifom distibution at vaious temeatues. The solution is comleted in two ats that ae elastic and elastic-lastic analysis. Additionally, esidual stesses ae calculated using these analysis esults. Finite element method (FEM) is utilized fo calculation of themal stesses. Theefoe, the themal stess analysis is efomed using ANSYS finite element softwae. Due to the fact that comosite disc have diffeent themal exansions in adial and tangential diections, themal stesses ae taken lace in disc by the alied unifom themal loadings. The magnitude of the tangential stess comonents both elastic and elastic-lastic solutions is highe than that of the adial stess comonents, excet edges of multile holes. The esent study concludes that magnitudes and distibutions of themal and esidual stesses on the comosite disc ae consideably affected by inceasing the unifom temeatue loadings and existence of multile holes. Keywods: Themolastic disc, Multile holes, Residual stesses, Themal stesses, FEM The fibe einfoced comosite mateials ae widely used in many stuctual alications such as maine, automotive and aviation industies, on account of thei high stength, low weight, good fatigue life and coosion esistance. Esecially, the comosite discs ae used in automotive industy as a comosite bake disc due to thei secific advantages 1-3. Meanwhile, availability of the new, low cost, high efomance fibe einfoced lastic (FRP) stuctual comosites fo infastuctue constuction and ehabilitation has given an imetus to the develoment of a new technology in constuction industy 4. The einfoced themolastics have been extensively used in many engineeing alications due to the fact that they have high-esistance to coosion, shinking less in mould, less contaction in moist envionments and less modification in dimension. Besides, einfoced themolastic lates softened though heating ae widely used in not only avionics and sace industy but also automotive secto fo they ae oduced in unheated moulds and ae aoiate fo ecyclable mateial utilization 5. Moeove, the load-caying caacity of the einfoced discs is also much highe *Coesonding autho ( fauk.sen@deu.edu.t) than that of the taditional isotoic steel discs of the same geomety and the weight of the fome is also seveal times lowe 6,7. Some themal stess oblems fo beams, bas, cylindes and lates have been exlained by Noda et al. 8 A closed fom solution fo the stess analysis in cuvilinea othotoic disc and cylindes unde essue has been eoted by Leknitskii 9. A lot of comosite stuctues have multile holes, i.e., in, bolt etc to ovide vaious uoses. These holes may also ovide the contact fom one side of the stuctue to the othe. Howeve, the calculation of the themal stesses aound multile holes is athe difficult. In a evious study, Sen 10 estimated the elasto-lastic themal and esidual stesses in a themolastic comosite disc that was einfoced as ectilinea unde unifom temeatue effect. The designed hollow disc was not including any in o bolt hole, so the mesh geneation ocess was easie than esent study, esecially. Sen 11 also investigated the effects on themal and esidual stesses of aabolic temeatue loading in a themolastic comosite disc having a cental hole by FEM. It was einfoced by steel-fibes as unidiectional fo adial diection. The obtained esults ointed out that the

2 158 INDIAN J. ENG. MATER. SCI., JUNE 010 magnitude of themal and esidual stesses wee consideably affected inceasing of aabolic temeatue loadings. Moeove, Sen et al. 1 efomed elastic-lastic stess analysis of steel fibe einfoced themolastic comosite disc, cuvilinealy. The themal loading was alied as aabolic temeatue distibution duing the elastic and elastic-lastic solutions. It was comleted both analytically and numeically using FORTRAN and ANSYS ogams, esectively. Accoding to obtained esults these two solutions to be in good ageement. You et al. 13 also imoved a numeical method fo the analysis of defomations and stesses in the elastic-lastic otating discs with abitay coss-sections of continuously vaying thicknesses and abitay vaiable density made of nonlinea stain-hadening mateials. Sayman et al. 14 caied out an elastic-lastic themal stess analysis on themolastic comosite disc einfoced cuvilinealy with steel fibes unde unifom temeatue distibution. The solution was efomed numeically via a ogam develoed using FORTRAN. Sen and Aldas 15 have also investigated the effects of inceasing linea temeatue loadings on the themal stesses occuing in the disc which duing the solution diffeent linea themal loads wee selected. Besides, the themal esidual stesses wee calculated by authos using elastic and elastic-lastic solution esults via sueosition method and they eoted that the magnitudes and distibutions of the themal stesses. As a esult they eoted that the magnitudes and esidual stesses wee geatly influenced by the incease in linea temeatue load. Futhemoe, the calculation of loading and esidual stesses, and elated to stains and dislacements wee eoted fo shink fitting otating discs at elevated temeatues by Jahed and Shiazi 16. In that study, a ange of mateial behaviou was consideed including unloading descibed by an actual mateial cuve, o modeled by isotoic o kinematic hadening with a vaiable Bauschinge effect. In addition, an analytical solution fo the elastic-lastic stess distibution in otating vaiable thickness solid disks was esented by Easlan and Ocan 17. The analysis was based on Tesca s yield citeion, its associated low ule and linea stain hadening mateial behaviou. Rossit and Laua 18 investigated unsteady themal stesses caused by the esence of a hot, cental nucleus, in disc o cylindes. The temeatue field was calculated in tems of a Fouie-Bessel exansion and then, adial and tangential stesses wee evaluated analytically. The consideed oblem was of basic inteest in mechanical and naval engineeing systems. Tende et al. 19 examined esidual stesses and dimensional changes in the comession moulded glass-mat einfoced themolastic ats. A heat tansfe and cystallization model with temeatue deendent matix oeties was used to calculate inut to the subsequent themal stess analysis. Both an isotoic viscoelastic and a tansvesely isotoic elastic mateial model wee examined though finite-element calculations. Saye et al. 0 investigated themo-elastic stesses on a low-density themolastic comosite disc einfoced cuvilinealy with E-glass fibes. An analytical method was caied out to detemine themal stesses of the comosite disc having a cental hole fo both unifom and linealy changing temeatues. In the esent study, an elastic-lastic themal stess analysis was caied out on a themolastic comosite hollow disc unde vaious unifom themal loadings. The comosite disc einfoced with steel fibes as cuvilinea and it was consideed with multile holes. Finite element method was used to calculate the themal stesses. Additionally, esidual stesses wee comuted using elastic and elasticlastic solution esults. Mateials and Methods Poduction of themolastic comosite disc Mechanical oeties of the steel fibe einfoced comosite disc ae esented in Table Accoding to Sayman et al. 14 the comosite disc consists of low-density olyethylene as a themolastic matix and steel fibes as cuvilinea. Fist of all the olyethylene layes wee fabicated. The aw ganules of the olyethylene wee laced into the mold and heated by an electical esistance and the temeatue Table 1 Mechanical oeties of the cuvilinea comosite disc Modulus of elasticity fo adial diection, E (MPa) 60 Modulus of elasticity fo tangential diection, E (MPa) Shea modulus, G 1 (MPa) 75 Poisson atio, ν 0.43 Axial stength, X (MPa) 14 Tansvese stength, Y (MPa) 5.4 Shea stength, S (MPa) 3.8 Plasticity constant, K (MPa) 9 Themal exansion coefficient fo adial diection, α (1/ C) Themal exansion coefficient fo tangential diection, α (1/ C)

3 SEN & SAYER: THERMAL STRESSES IN A THERMOPLASTIC COMPOSITE DISC 159 was inceased u to 160ºC. The aw mateial was held fo 5 min unde.5 MPa essue at this temeatue, and then the temeatue was deceased to 30ºC in 3 min unde 15 MPa essue at the mentioned temeatue. Thus, a olyethylene laye with thickness of 1 mm was oduced. Steel fibes wee laced into two themolastic layes as cuvilinealy, and then the above ocesses wee alied fo eaing the comosite disc. Thus, a steel fibe einfoced cuvilinea themolastic comosite disc was obtained, and the fibe volume faction was measued as 6%. Accoding to mechanical test esults, the yield oint, the modulus of elasticity and the themal exansion coefficient of the low density themolastic ae 9.3 MPa, 170 MPa and (1/ºC), esectively. Modeling of comosite disc and bounday conditions The steel fibe einfoced cuvilinea themolastic hollow comosite disc with multile holes is illustated schematically in Fig. 1, It is seen in this figue that the dimensions of it ae modeled as inne adius a=30 mm, oute adius b=60 mm and diamete of each hole d=10 mm. In this study, finite element softwae, ANSYS 10.0, was utilized in ode to obtain the distibutions of themal elastic and elasticlastic stess comonents. Duing the modeling ocess of disc, element tye was chosen as PLANE 183 fo mesh geneation. This element tye is a highe ode -D, 8-node element. It has quadatic dislacement behaviou and is well suited to modeling iegula meshes. Additionally, this element is defined by 8 nodes having two degees of feedom at each node: tanslations in the nodal x and y diections. The element may be used as a lane element (lane stess, lane stain and genealized lane stain) o as an axisymmetic element. This element has lasticity, hyeelasticity, cee, stess stiffening, lage deflection, and lage stain caabilities. The geomety, node locations, and the coodinate system fo this element ae shown in Fig.. Othotoic mateial diections match u to the element coodinate diections 1. Accoding to this infomation, the hollow comosite disc with multile holes was modeled in ANSYS, and bounday conditions and finite element model of the disc ae shown in Fig. 3. The mesh details whee suoundings of multile holes ae also shown in this figue as K and L. It is seen in this figue that maed mesh stuctue is efeed fo the mesh geneation of the comosite disc model because of some advantages comaing to the fee mesh. It is also known, a maed mesh is limited in tems of the element shae it contains and the atten of the mesh 1,. Futhemoe, a good mesh geneation is vey imotant fo FEM solutions. If the model has multile holes, the geneation of maed mesh is vey difficult. Howeve, in this study, the maed mesh was ovided by the autho. This advantage was sulied to decease both element and node numbes. Themal stess oblem wee solved in two ats, which one of them elastic solution and othe elasticlastic solution. Afte these solutions, esidual stesses wee also calculated using sueosition method. Duing the solution, the comosite mateial was assumed to be linealy hadening, and also the mechanical oeties of disc wee assumed unchanged while temeatue was inceased. It was also desied to find out the effect on themal and esidual stesses of unifom temeatue loading in a Fig. 1 The schematic illustation of cuvilinea comosite disc with multile holes Fig. PLANE 183 element tye in ANSYS 17

4 160 INDIAN J. ENG. MATER. SCI., JUNE 010 Fig. 3 Bounday conditions and FEM model with details of the comosite disc

5 SEN & SAYER: THERMAL STRESSES IN A THERMOPLASTIC COMPOSITE DISC 161 themolastic comosite disc. Theefoe, alied unifom temeatue values wee chosen fom 50 to 100 C. The temeatue incement was 5 C. Mathematical Fomulation Elastic solution In this study, themal stess oblem was solved analytically in two ats. Fistly, elastic solution was caied out on the comosite disc unde selected unifom temeatue loadings. The comosite disc was assumed that it is vey thin theefoe the temeatue distibution didn t change acoss the thickness of the comosite disc and the solution was educed to a lane stess case. The stess-stain elations in a comosite disc einfoced cuvilinea can be witten as 14, du ε = = aσ + a σ d u ε = = a σ + aσ (1) whee u is the dislacement in the adial diection and a, a and a ae the comonents of the comliance matix, α and α ae the themal exansion coefficients in the adial and tangential diections, esectively. The equation of equilibium in the lane stess case fo a cuvilinea othotoic laye can be educed to the next shae, σ + σ σ = 0 () The comatibility equation is witten fom the elation between the dislacement and stains as given in Eq. (3), ε ε = ε + (3) The stess function F satisfies the equation of equilibium as, σ = σ = F df d (4) The govening stess function is witten by using the Eqs (1)-(4), d F df a +a -a F= d d dt -α +αt-αt d (5) If T is chosen as a constant value, T 0, the stess function F can be witten as, k k A F = C1 + C + (6) 1 k whee k = a / a, C 1 and C ae the integation constants and last tem is, A T ( α α ) a 0 = The stess comonents ae found as, (7) F k 1 k 1 A σ = = C1 + C + 1 k (8) df k 1 k 1 A σ = = C1k Ck + d 1 k Consequently, adial and tangential stess comonents ( σ and σ ) can be calculated fom the bounday conditions. Elastic-lastic solution Afte the themal elastic solution was comleted, the themal elastic-lastic solution was efomed on the comosite disc unde same unifom themal loadings as second at of the solution. The stain incements in the adial and tangential diections ae witten as 14, dε = a dε = a dσ + a dσ + a dσ + dε dσ + dε + α dt + α dt (9) The stain incements fo anisotoic mateials ae obtained fom the lastic otential f, f dε ij = dλ (10) σ ij

6 16 INDIAN J. ENG. MATER. SCI., JUNE 010 whee f is the otential function which is equal to the equivalent stess (σ ), λ is a scala quantity and it is equal to the equivalent lastic stain incement dε. The equivalent stess fo the Tsai-Hill citeion can be witten as 3, σ X σ = σ σ σ + (11) Y whee, X and Y ae the yield stengths of the disc in the fibe and tansvese diections, esectively. In this solution, it is assumed that the mateial hadens linealy. σ = σ o + Kε whee σ o is equal to X and K is the lasticity constant. The tangential stess can be witten in tems of the adial stess comonent. Consequently, the Tsai-Hill citeion, d σ the adial stess incement is obtained as, σ ± σ 4 dσ = X Y σ σ d (1) whee σ is the equivalent stess, which is equal to X. The lastic stain incements in the fibe and tansvese diections ae calculated fom the lastic otential, accoding to the Pandtl-Reuss equations, X σ + σ f dε = dλ = Y dε σ σ (13) f σ σ dε = dλ = dε σ σ The total stain incements ae calculated as, ε ε du = d u = = a = a σ + a σ σ + a σ + + dε dε + α dt + B + α T + B 1 (14) Whee B 1 and B ae the integation constants. B 1 and B ae found to be equal to zeo by using the elation between the elastic and lastic stain incements which ae equal at the beginning of lastic yielding. Calculation of esidual stesses To find the themal esidual stesses, it is necessay to sueose on the themal stess system. The sueosition of the elastic and elastic-lastic stesses gives the esidual stesses. Hence, the magnitudes of themal esidual stesses ae calculated using the Eq. (15) as, ( σ ) = ( σ ) ( σ ) e ( σ ) = ( σ ) ( σ ) e (15) Results and Discussion The themal stesses concentations take lace in the disc when the unifom temeatue was inceased fom 50 to 100 o C. Accodingly, the fou oints wee selected on the modeling disc since they have citical imotance in tems of themal stesses. As seen in Fig. 3, two nodes of these ae selected on inne and oute sufaces of the disc as named A and B, esectively. In addition, othe two nodes labeled as C and D which ae consideed nea the one of the multile holes. The themal elastic, lastic, esidual stess and equivalent lastic stain comonents oduced by unifom temeatue effects at selected nodes on the disc ae given in Table. It can be seen fom this table that the magnitude of themal stesses and othe comonents incease by inceasing unifom themal loads. Theefoe, the minimum values of it ae calculated at 50 C, while the maximum values ae obtained at 90 C. Themal stesses fo tangential diection ae highe than that of adial diection on nodes A, B and C, although its values fo adial diection ae bigge than that of tangential diection on node D. In addition, the maximum values of themal stesses ae obtained on node A fo tangential diection as comessive. The magnitudes of themal stesses on node B fo adial diection ae estimated extemely small if it is comaed with othe stess comonents; theefoe thei values can be neglected. These all assumtions ae also valid fo both elastic and lastic stesses. As seen clealy in Table that a lastic stain is fistly began at 55 C alied unifom temeatue on nodes A, B, and C. Namely, esidual stess comonents ae equal to zeo fo all nodes at 50 C.

7 SEN & SAYER: THERMAL STRESSES IN A THERMOPLASTIC COMPOSITE DISC 163 Table Themal elastic, lastic, esidual stess and equivalent lastic stain comonents at selected nodes on the comosite disc T o ( o C) Node Elastic stess (MPa) Plastic stess (MPa) Residual stess (MPa) Eqv. Plastic Stain ( 10-6 ) (σ ) e (σ ) e (σ ) (σ ) (σ ) (σ ) ε eqv A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D The maximum value of esidual stesses is obtained fo tangential diection on node A at 90 C as MPa fo tangential diection. In othe wods, the highest value of esidual stesses is ceated on the inne suface of the disc as tensile fom fo tangential diection. The magnitudes of esidual stesses on node D fo tangential diection ae equal to zeo unde all themal loadings. Meanwhile, the values of equivalent lastic stains ae also calculated fo only node B fom 55 to 90 C. The maximum value of it is estimated as at 90 C, wheeas it is equal to zeo on all othe selected nodes and alied unifom temeatues. Themal elastic and lastic stess distibutions utilizing stess contous fo adial and tangential diections fo diffeent alied themal loadings ae given in Figs 4 and 5, esectively. It is mentioned eviously, themal stesses at 50 C ae calculated as only elastic fom, since this themal load does not oduce any lastic stain on the comosite disc. Theefoe, stess contous ae lotted as elastic fom fo 50 C in Fig. 4. Themal stesses fo tangential diection ae highe than that of adial diection both elastic and lastic solutions as seen in Figues 4 and 5. These diffeences of themal stess esults between adial and tangential diections fo elastic solution ae bigge than that of lastic solution esults. Fo instance, the maximum values of elastic stesses fo adial and tangential diections ae calculated as and MPa at 90 C, esectively.

8 164 INDIAN J. ENG. MATER. SCI., JUNE 010 Fig. 4 The distibutions of themal elastic stesses fo diffeent themal loadings (MPa) Nevetheless, the maximum values of lastic comessive stesses fo adial and tangential diections ae obtained as MPa and MPa at 90 C, esectively. Fo tangential diection, themal stesses on the inne and oute sufaces ae obtained as comessive and tensile foms, esectively. Besides, the magnitudes of comessive stesses ae highe than that of tensile stesses both adial and tangential diections. It is also seen in Figs 4 and 5, multile holes caused stess concentations aound itself. These concentations ae clealy seen fo adial diection. Additionally, the maximum values of comessive stesses occu nea the multile holes fo adial diection. This means that stess concentations ae ceated by esence of multile holes in the disc. Meanwhile, it is known that holes ae necessay in many comosite stuctues including discs fo some

9 SEN & SAYER: THERMAL STRESSES IN A THERMOPLASTIC COMPOSITE DISC 165 Fig. 5 The distibutions of themal lastic stesses fo diffeent themal loadings (MPa) uoses such as in, bolt and ivet alications. Consequently, in actice the numbe of multile holes and thei sizes must be consideed to avoid fom a weakest constuction by the constucte. The effects of unifom temeatue loads on esidual stesses on selected nodes fo adial and tangential diections ae shown in Fig. 6. This figue oints out that the magnitude of esidual stess comonents fo tangential diection is highe than that of adial diection. The value of esidual stesses on node A ae extemely bigge than that of othe nodes both adial and tangential diections, esecially. Its foms ae comessive and tensile on node A fo adial and tangential diections, esectively. On the othe hand the maximum values of esidual stesses ae come into being on the inne suface of the disc. It is mentioned eviously, the magnitudes of esidual stesses ae equal to zeo both adial and tangential diections at 50 C. Othe imotant node is seemed as node D since highe values of esidual stesses ae obtained on this node fo adial diection. Biefly, the

10 166 INDIAN J. ENG. MATER. SCI., JUNE 010 Fig. 6 The effect of unifom temeatue loads on esidual stesses on selected nodes

11 SEN & SAYER: THERMAL STRESSES IN A THERMOPLASTIC COMPOSITE DISC 167 Fig. 7 The distibutions of equivalent lastic stains fo diffeent themal loadings esence of any multile holes oduces esidual stesses on the comosite disc. The distibutions of equivalent lastic stains with colo contous fo 70 and 90 C ae shown in Fig. 7. It is seen clealy that the distibutions and magnitudes of equivalent lastic stains ae enlaged elated to inceasing of unifom themal loads. The values of it ae obtained as zeo at oute suface of the disc and aound the multile holes both 70 and 90 C, while the maximum value is calculated as on the inne suface of the disc at 90 C. Conclusions Accoding to the elastic and elastic-lastic themal stess analyses esults of the cuvilinea steel fibe einfoced themolastic comosite disc with multile holes utilizing FEM, the following conclusions can be dawn: (iv) The magnitude of tangential stess comonents ae highe than that of adial stess comonents both inne and oute sufaces of the disc. (v) The maximum values of themal stesses fo adial diection ae obtained edges of the multile holes. (vi) The multile holes cause stess concentations on the disc. (vii) Because of the causing stess concentations, the designe must be selected numbe of multile holes and its size to avoid fom weakest stuctue in actice. (viii) Themal esidual stesses ae obtained on the disc due to unifom temeatue loadings. The maximum values of esidual stesses ae oduced on the inne suface of the disc. (ix) Residual stesses ae also oduced fom the existence of the multile holes on the disc. (i) (ii) (iii) Themal and esidual stesses occued in the disc unde unifom temeatue loads, due to the fact that diffeent themal exansion coefficients in incial mateial diections. In the disc, lastic flow stats both edges of multile holes and inne suface of the disc at 55 o C, initially. Plastic yielding exands, if the unifom temeatue load is bigge than eve. Refeences 1 Im K H, Hsu D K & Jeong H, Comosites: Pt B, 31 (000) Yuan Y D, Zhang F K & Zhou W C, J Cental South Univ Technol, 1(4) (005) Stadle Z, Knel K & Kosmac T, Fiction behavio of sinteed metallic bake ads on a C/C SiC comosite bake disc, J Eu Ceam Soc, 7 (007) Haddad Y M, Advanced multilayeed and fibe-einfoced comosites (Kluwe Academic Publishes, Nethelands), 1998.

12 168 INDIAN J. ENG. MATER. SCI., JUNE Aslan N & Celik M, J Reinfoced Plastics Comos, 0 (001) Nemiovskii Y V & Yankovskii A P, Mech Comos Mate, 38 (00) Çallıoğlu H, J Reinfoced Plastics Comos, 3 (004) Noda N, Hetnaski R B & Tanigawa Y, Themal stesses, (Lastan Cooation, New Yok), Leknitskii S G, Theoy of elasticity of an anisotoic body (Mi Publishes, Moscow), Sen F, J Reinfoced Plastics Comos, 5 (006) Sen F, J Reinfoced Plastics Comos, 7 (008) Sen F, Pekbey Y & Sayman O, Indian J Eng Mate Sci, 14 (007) You L H, Tang Y Y, Zhang J J & Zheng C Y, Int J Solids Stuct, 37 (000) Sayman O, Yanginci S & Saye M, J Reinfoced Plastics Comos, 4 (005) Sen F & Aldas K, Adv Eng Softwae, 40 (009) Jahed H & Shiazi R, Int J Pessue Vessel Piing, 78 (001) Easlan A N & Ocan Y, Int J Mech Sci, 44 (00) Rossit C A & Laua P A A, Ocean Eng, 7 (000) Tende A, Astöm B T & Nilsson G, Comosites Pt A, 31, (000) Saye M, Tocu M, Bektas N B & Taakcila A R, Sci Eng Comos Mate, 1 (005) Release 10.0, Documentation fo ANSYS ANSYS, Inc. Moaveni S, Finite element analysis: Theoy and alication with ANSYS (Peason Education. Inc. New Jesey, USA), Jones R M, Mechanics of comosite mateials, (Taylo & Fancis Inc., USA), 1999.