Stress Analysis of Functionally Graded Material Plate with Cut-out

Transcription

1 International Journal o Advanced Mechanical Engineering. ISSN Volume 4, Number 5 (4), pp Reearch India Publication Stre Analyi o Functionally Graded Material Plate with Cut-out Ankitkumar B. Makwana, Khuhbu C. Panchal, Anih H. Gandhi 3 P. G Student Mechanical Engineering Department (CAD/CAM) SVMIT Bharuch, Guarat. Mechanical Engineering Department, SVMIT, Bharuch, Guarat. 3 C. K. P. C. E. T., Surat, Guarat. Abtract In tructure and machine component, operation like cut-out o dierent hape or opening are acilitated. The total area o tructure are reduce due to thee cut-out, which become the tre rier or particular tructure and it work a weakening agent or the tructure or machine. Dierent hape o cut-out generate dierent eect o tre concentration, which directly eect on the lie o the Structure/machine component. The tre ield around uch cut-out mut be known under dierent loading condition. Here an attempt i made to obtain generalized olution or determining the tre concentration around circular hole, the hape which ha minimum eect o tre concentration, in compoite ininite plate ubected to arbitrary uniaxial, biaxial and uniorm preure loading at ininity uing Mukhelihvili complex variable method. General olution are obtained with MATLAB coding and compared with an FEA tool. Keyword: Functionally Graded Material (FGM), Circular Cut-out, Complex Variable method, Stre Concentration Factor Introduction Functionally Graded material (FGM) i the cla o compoite material, in which two or more than two material are compoite a per the unction or application o the material where it i going be ued. The compoition o the material i in continuouly graded orm. There i no material in nature which ha good trength with brittlene. A material with good thermal reitance (like ceramic) having brittlene which can ace the temperature reitance but, it cannot ace the high mechanical loading. On the other ide, the material with good toughne and trength

2 496 Ankitkumar B. Makwana, Khuhbu C. Panchal, Anih H. Gandhi (like metal) i with good ductility, which can ace the mechanical loading condition but or temperature reitance it i not uitable. In thi cae we can orm a compoite material which will participate a a metal at one ide and a a ceramic at another ide. In thi cae the FGM compoed will be tranormed rom ceramic to metal rom one end to another end in continuouly graded orm. So FGM i a compoite material which i made up o two or more than two material combination with deired phyical and chemical propertie []. The mot common unctionally graded material are made o ceramic/metal non homogeneou tructure, in which ceramic provide good thermal reitance and metal role a a uperior toughne and hardne. V. G. Ukadgaonker, Vyara Kakhandki [] checked the eect o dierent hape o cut-out and irregular hape o hole. General olution or determining the tre ield around circular hole in ininite orthotropic plate ubected to internal preure were obtained by D S Sharma, Panchal Khuhbu, and Patel Nirav [3], uing Mukhelivili complex variable ormulation in. D. V. Kubair, B. Bhanuchandra [4] numerically invetigated the eect o the material property in homogeneity on the tre concentration actor (SCF) due to a circular hole in unctionally graded panel. Mohammad Abedi and GH. Rahimi [5] introduced analytical olution o tre ditribution around circular cutout in orthotropic unctionally Graded Compoite (FGC) plate. Type o FGM () According to the tructure, two type, one i continuouly tructured FGM and another i dicontinue (Layered) FGM. () According to proce o manuacturing, one type i Thin FGM and another type i Bulk FGM. Thin FGM are manuactured with dierent method like Phyical Vapor Depoition (PVD), Chemical Vapor Depoition (CVD), Sel propagating High temperature Synthei (SHS) method etc. While the Bulk FGM are manuactured by the method like, Powder Metallurgical Technique, Centriugal Cating method, Solid Free Foam technique, etc. For current tudy we concentrate on bulk FGM only, o three main manuacturing technique are decribed briely. In powder Metallurgy method or making bulk gm, baic tep are weighing and mixing o powder, tacking and ramming o premixed powder, and inally intering. In Centriugal method, gravitational orce i ued through pinning o the mould to orm continuou bulk gm. By the change in mould pinning peed and change in denity o powder material o metal will produce continuouly graded tructure. A limitation o the method i that, the gradient o material cannot be tolerated a per requirement, becaue it depend naturally. Solid Free Foam Fabrication method i a method in which irt the modeling o the part i done, then converting the modeled ile in. tl (tandard triangulation language) ile. Now lice o the. tl ile model in to two dimenional cro ection. The next tep i component building, and inally removal o unneceary part & inihing. Generally in olid ree oam abrication method, laer baed method are ued. Like, laer cladding baed method, elective laer intering (SLS), 3D printing method, Selective laer melting (SLM) etc. Thi method or manuacturing gm i mot advantageou becaue it work at high peed production,

3 Stre Analyi o Functionally Graded Material Plate with Cut-out 497 le energy intenive, maximum material utilization, lexibility in modeling becaue we can directly convert the model rom cad otware, and complex hape ormulation i alo become eay by olid ree oam abrication method. Limitation o thi method i that the rough urace inihing. [] COMPLEX VARIABLE FORMULATION [] An FGM plate with circular hole i conidered under generalized plane tre condition. The plate i aumed under tre in XY plane o here the value o tre or Z axi will become zero, o, and z xz yz. Stre contour or FGM plate with circular cut-out under dierent loading condition (e. g. Uniaxial, Biaxial and Uniorm preure around hole) are tudied. The area external to a given hole, in Z- plane i mapped conormably to the area outide the unit circle in ζ plane uing ollowing mapping unction. N N R k m k z ( ) a mk b k k k Where, a, b i ; =,. Eq. () i Depending on the value o mk dierent hape can be mapped outide the unit circle and by applying boundary condition the tree i derived. p x co p y co p xy in Eq. () and explain uniaxial and biaxial loading condition, repectively. GENERAL SOLUTION FOR UNIFORM PRESSURE AROUND THE HOLE [3] For the cae o uniorm preure p around hole, the reultant tre X n, Y n on the hole boundary are given by dy dx X n p co( n, x) p, Y n p co( n, y) p Eq. (3) d d Where n i the poitive direction o the outward normal to the hole boundary. The tre boundary condition are given by Ynd cont. px, X n d cont. py, Eq. (4)

4 498 Ankitkumar B. Makwana, Khuhbu C. Panchal, Anih H. Gandhi The tre unction are obtained uing thee boundary condition (, ) into Schwarz ormula: ( ) 4( ( ) 4( i i ) ) ( ( t dt ) t t t dt ) t t Eq. (5) The tre unction and their derivative obtained are given bellow, ipr a ipr a ( ) (, ( ) ) ( ) ipr a ipr a '( ) (, ' ) Eq. (6) Put thee value in tre equation, x ' z ' ' z ' ' z Re z Re z y xy ' Re z Eq. (7) Reult and dicuion Figure : - Contruction o FGM plate [6] Meaurement o tre a per generalized method, we can check with mathematical coding in MATLAB Ra, and compare it with FEA otware tool (ANSYS ).

5 Stre Analyi o Functionally Graded Material Plate with Cut-out 499 Figure : - Stre contour o Steel and FGM plate under Uniaxial and Biaxial Loading condition Figure 3: - Stre contour o FGM plate under uniorm preure on hole boundary CONCLUSION In thi paper reult or main three loading condition i. e. Uniaxial, Biaxial and Uniorm preure on hole boundary or Steel and Nickel baed FGM material plate with circular cut-out are tudied. The reult with mathematical ormulation in MATLAB Ra are compared with FEA (Finite Element Analyi) reult in ANSYS.. The comparion conclude that the work Simulation reult in ANSYS and mathematical reult in MATLAB are nearer and give atiactory reult. The Reult obtained in thi reearch work i baed on caled modeling o obect and o by taking dierent cale actor (a per condition) we can check the eect o tre concentration eect.

6 5 Ankitkumar B. Makwana, Khuhbu C. Panchal, Anih H. Gandhi REFERENCES [] D. K. Jha, Tarun Kant, R. K. Singh, A critical review o recent reearch on unctionally graded plate, Compoite Structure 96 (3) [] V. G. Ukadgaonker, D. K. N. Rao, A general olution or tree around hole in ymmetric laminate under inplane loading, Compoite Structure 49 () [3] D S Sharma, Panchal Khuhbu, Patel Nirav, A General Solution or the Stree around Internally Preurized Circular hole in Symmetric Laminate, Intitute o Technology, Nirma Univerity, Ahmedabad 38 48, 8- December,. [4] D. V. Kubair, B. Bhanuchandra, Stre concentration actor due to a circular hole in unctionally graded panel under uniaxial tenion, International Journal o Mechanical Science 5 (8) [5] Mohammad Abedi, GH. Rahimi, Stre analyi o orthotropic FGC plate with a circular cutout uing complex variable method. [6] Ahmet Polat, Ozkan Sarikaya, Erdal Celik, Eect o poroity on thermal loading o unctionally graded YO3 ZrOyNiCoCrAlY coating, Material and Deign 3 ()