EVALUATION OF S.I.F FOR CRACK EMANATING AT 45 0 ORIENTATION FROM A HOLE IN PRESSURISED CYLINDER USING FEA

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1 EVALUATION OF S.I.F FOR CRAC EMANATING AT 45 0 ORIENTATION FROM A HOLE IN PRESSURISED CYLINDER USING FEA AASH.D.A 1, ANAND.A 2, G.V.GNANENDRA REDDY 3, SUDEV.L.J 4 1,3 Depatment of Mechanical Engineeing, S.J.C Institute of Technology, Chickaballapu, INDIA 2,4 Depatment of Mechanical Engineeing, Vidyavadhaka College of engineeing, MYSORE, INDIA Abstact- The use of factue mechanics techniques combining with Finite Element Analysis [F.E.A] in assessment of pefomance and eliability of pessue vessel stuctue is on demand.the machine elements with cylindical pofile such as cylindical shells, which ae used extensively as the stuctual configuation in aeospace and shipping industies needs to be leak poof. But duing thei sevice life, a cack may initiate on intenal/extenal bounday of cicula cylinde which influences on stess distibution in the stuctue. All flaws in a physical stuctue may not always have the same oientation elative to boundaies and mateial intefaces. In factue mechanics, Stess Intensity Facto (SIF) is an impotant citeion to evaluate the impact of cack as the magnitude of SIF detemines the popagation of cack. This pape eviews on investigation of S.I.F fo 45 0 deg abitaily oiented flaw emanating fom a hole in pessuised cylinde using Displacement Extapolation Method (DEM) in F.E.M that would aid in the detemination of the citical natue of such flaws. eywods- ( Finite Element Analysis, Factue Mechanics, Stess Intensity Facto, Displacement Extapolation Method, Linea Elastic Factue Mechanics, Stess Concentation, Cuvatue Paamete, Plane Stain, Cack Popogation,Mixed Mode Factue, Residual Stength, Cack gowth life) I. INTRODUCTION Pessue vessel and cylindical shells have been used extensively as the stuctual configuation in aeospace and shipping industies needs to be leak poof. Howeve new advancement in computes has made The use of factue mechanics techniques combining with F.E.A a pactical tool in the assessment of pessue vessels stuctues[1], especially in detemining stesses in local aeas such as penetations and sevice holes. The most likely places fo cack initiating and development of cacks ae the sevice holes. Due to the high stess concentation in this aea cacks may gow in time, leading to a loss of stength and the eduction of the lifetime of the poduct as shown in Figue1. If the stuctue is concened with diffeent loading, the cack behaviou must be assessed in ode to avoid catastophic failues. Fo this, the knowledge of the cack size, sevice stess, mateial popeties and SIF is equied [2].Hence the stuctual assessments of hallow cylindes /shell anging fom thick walled pessue vessel to thin walled pipes has to be done, that in-tun elies on availability of stess intensity facto fo factue and fatigue analysis. Thus it has been ecognized that the stess intensity facto is an impotant paamete to detemine the safety of a cacked component, but the basic pactical poblem a designe faces, is to make a decision to opt the method fo detemining stess intensity factos. It is not easy to stike a balance between the accuacy of the method, time equied to get a solution, and cost. Numeous equations fo stess intensity factos ae available in the liteatue [1 6]. These factos epesent vaious geometies and loading conditions of fundamental impotance in the pediction of stuctual failue of cacked cylindical bodies. The objective of the pesent wok is to detemine S.I.F fo 45 0 deg abitaily oiented flaw emanating fom a hole in pessuised cylinde using Displacement Extapolation Method (DEM) in F.E.M. The poposed pocedue is been validated with the available pocedue in liteatue fo a standad pactical poblem of detemining SIF of longitudinal cacks in a pessuized cylinde. The validated pocedue futhe foms the basis fo a detailed eseach on assessing the impact of SIF in a pessuized vessel. Fig.1: Lage cack fomed in thin pessuized cylind II. FRACTURE MECHANICS Factue mechanics involves a study of the pesence of the cacks on oveall popeties and behaviou of the engineeing component. The pocess of factue may be initiated at defect locations like mico-cacks, voids, and the cavities at the gain boundaies. These defects can lead to the fomation of a cack due to the uptue and disentanglement of molecules, uptue of atomic bonds o dislocation slip [3]. Cacked body can be subjected to thee modes of loads as shown in Figue 2. In some Intenational Jounal of Applied Reseach in Mechanical Engineeing (IJARME) ISSN: , Volume-3, Issue-1,

2 Evaluation of S.I.F fo Cack Emanating at 45 0 Oientation Fom a Hole in Pessuised Cylinde Using FEA cases, body may expeience combination of the thee modes: 1. Opening mode: The pincipal load is applied nomal to the cack sufaces, which tends to open the cack. This is also efeed as Mode I loading (Figue 2a). 2. In-plane shea mode: This mode coesponds to inplane shea loading which tends to slide One cack suface with espect to the othe. This is also efeed as Mode II loading (Figue2b). 3. Out-of-plane shea mode: This is the teaing and antiplane shea mode whee the cack sufaces move elative to one anothe and paallel to the leading edge of the cack (Figue 2c). The Stess Intensity Facto (SIF) is one the most impotant paametes in factue mechanics analysis. It defines the stess field close to the cack tip and povides fundamental infomation of how the cack is going to popagate. In this study, a typical and pactical point matching technique, called Displacement Extapolation Method (DEM) is chosen fo the numeical analysis method. Plane stain assumption is valid fo vey thinwalled stuctues; the evaluation of S.I.F ( I ) by Displacement Extapolation Method (DEM) is as discussed bellow. The stess intensity factos at a cack fo a linea elastic factue mechanics analysis may be computed using the CALC command. The analysis uses a fit of the nodal displacements in the vicinity of the cack. The actual displacements at and nea a cack fo linea elastic mateials ae 11 u + (1 + k ) 2 G 2 π 1 v + (1 + k ) 4 G 2 π 2 + G 2 π (1) (2) w 111 (3) Whee: u, v, w displacements in a local Catesian coodinate system as shown in figue 3, θ coodinates in a local cylindical coodinate system as shown in figue 3. G shea modulus ν In Plane Stess (4) 1 + v 3-4ν In Plane stain...(5) Poisson's atio Fo Mode-1, SIF at cack tip is expessed as 2 4G ΔV k 1 π (6) Whee Δv, is the motion of one cack face with espect to the othe. At points J and. if, let appoach zeo V lim 0 u lim 0 w lim 0 Theefoe A B C 4GA 1 2π k 2GB 1 2π k GC 2π 111 2(1 + k) III. METHODOLOGY.. (7)..(8)..(9)..(10) Fig. 2: Thee modes of loading that can be applied to a cack Fig. 3: Nodes Used fo the Appoximate Cack-Tip Displacements fo Full cack Model The objective of this wok is to detemine SIF fo a 45 0 deg abitaily oiented cack emanating fom a hole in a pessuized cylinde as shown in figue 4. The objective is achieved by developing a model of a cylinde with hole and a though cack using CATIA V5 softwae. The CATIA model is impoted to ANSYS.The FE model is meshed using 8-node quadilateal doubly cuved SHELL 93 elements in the pe-pocesso of the ANSYS softwae. A shell with a longitudinal cack was meshed using thee diffeent mesh densities. Mainly, the aea aound the impefection was modeled with a fine mesh. As a pat of the finite element wok, a mesh sensitivity Study was conducted. Futhe, the cack tip singula elements wee ceated using SCON command. Fo this model thee ae 36 singula elements aound the cack tip and the adius of the fist ow elements is Δa (Whee Δa a/100).the model is then Intenational Jounal of Applied Reseach in Mechanical Engineeing (IJARME) ISSN: , Volume-3, Issue-1,

3 Evaluation of S.I.F fo Cack Emanating at 45 0 Oientation Fom a Hole in Pessuised Cylinde Using FEA solved (Static Analysis) by subjecting it to an intenal pessue of 1MPa load with appopiate bounday conditions. Then the SIF is evaluated in geneal postpocesso by using CALC command. The geomety of the meshed test model with cack tip singula elements in ANSYS 12 is as shown in the Figue 5.The mateial consideed is 304 steel (ASME). The mateial is assumed to be linea elastic with young s modulus of 2.5GPa and poisons atio f1( α) ( x x 0.07x ) a x ( Rt) The half cack length was vaied fom 20mm to mm.The maximum cack length in a given dimensions of cylindical shell was detemined using cuvatue paamete β [11] a 4 β 12(1 ν 2 ). (12) Rt if β 8 fo longitudinal cacks, thickness of the cylindical shell is 10mm and adius of the cylindical shell is 1000mm then the maximum cack length fo given set of cylindical shell dimension is mm. The values of mode 1 SIF fom the pocedue explained in the pevious section is also detemined fo the same poblem using FEA in ANSYS. Table 1 shows the values of SIF obtained by the theoetical and FEM. Fig.6: Longitudinal cack in intenally pessuized cylinde Fig.4: Geomety of model Whee, D Diamete of the hole (20mm), a Half Cack length mm σapplied hoop stess (P/t) P Intenal pessue 1MPa tthickness of the cylindical shell 10mm Table 1: Mode-1 S.I.F ( I ) Using FEA and theoetical I (Theo) fo diffeent Half Cack lengths (a) Fig. 5: (a) Finite Element Model with Bounday Condition (b) Meshed Finite Element Model (c) Zoomed View of Cack Tip Singula Elements IV. RESULTS AND DISCUSSION The Figue 6 shows a pessuized cylindical shell with vaying longitudinal cack length. The theoitical fomulae involved in the detemination of mode 1 SIF of the cack is given below [3]. Mode I S.I.F ( I ) is given by I (Theo) σ πa. f1( α ).(11) Whee Fig.7: vaiation of theoetical and FEA values of S.I.F Vs cack length in Pessuized cylinde Intenational Jounal of Applied Reseach in Mechanical Engineeing (IJARME) ISSN: , Volume-3, Issue-1,

4 Evaluation of S.I.F fo Cack Emanating at 45 0 Oientation Fom a Hole in Pessuised Cylinde Using FEA Figue 7 shows the vaiation of theoetical and simulated FEA SIF values fo vaious longitudinal cack length in pessuized cylinde. Fom the Figue it is indicated that the esults which wee obtained by using FEM ae in good ageement with theoetical equation fo a longitudinal though cack emanating in intenally pessuized cylindical shell The aveage pecentage of eo between the FEA and theoetical SIF values is 1.53%, which is negligible. Thus the poposed methodology to detemine the Mode- 1 S.I.F fo longitudinal cacks in pessuized cylindical shell is validated against a standad pocedue elucidated in liteatue [3]. The above pocedue is used fo Detemination of SIF fo a Cack Emanating at 45 0 oientation fom a Hole in a Pessuized cylinde the test models containing a though 45 0 cack emanating fom a hole is meshed unde plane stain condition it is intenally pessuized and espective SIF s ae calculated by vaying half cack length(a). 0( Theo) σ πa eff.. The specimen gaphs ae plotted to vaiation of nomalized Stess Intensity Facto s ( I / O ), ( II / O ), ( III / O ) with espect to (a/d) atio is as shown in Figue 8(a),8(b),8(c) espectively. Fig.8(a): Vaiation of nomalized S.I.F ( I / 0 ) fo a cack emanating fom cicula hole in pessuized cylinde Vs a/d Fig.8 (b): Vaiation of nomalized S.I.F ( II / 0 ) fo a cack emanating fom cicula hole in pessuized cylinde Vs a/d The values of I, II, & III with espect to (a/d) is as shown in table 2. It is obseved that I & II (opening mode and in-plane sheaing mode) have equal contibution fo cack popagation. The specimen gaphs 8(a) & 8(b) shows that the Mode-I S.I.F ( I ) & Mode-II S.I.F ( II ) inceases steadily as cack gows. The value of Mode-III S.I.F ( III ) is vey small compaed to Mode- I ( I ) & Mode-II ( II ).The Mode-III S.I.F ( III ) has negligible contibution fo cack popagation compaed to Mode-I & Mode-II. Theefoe fo 45 0 oiented cack in intenally pessuized cylinde the Mode-I S.I.F ( I ) & Mode-II S.I.F ( II ) ae dominant and have equal contibution fo cack popagation. Table 2: The nomalized Stess Intensity Facto ( I / O ) with espect to a/d atio Fig.8(c): Vaiation of nomalized S.I.F ( III / 0 ) fo a cack emanating fom cicula hole in pessuized cylinde Vs a/d CONCLUSION The poblem of detemining SIF fo a 45 0 deg abitaily oiented cack emanating fom a hole in a pessuized cylinde is of pime impotance in damage toleance analysis. In the pesent study ANSYS12, unified FEA softwae is chosen. It has the equied pe-pocessing capabilities fo finite element modeling and analysis of cacked shell stuctues as Demonstated in this pape. The poposed methodology to detemine SIF by DEM in FEM is validated with the standad pocedue available in liteatue. The vaiation of nomalized S.I.F ( I / O ),( II / O ),( III / O ) with espect to a/d atio is used to obtain the chaacteistic cuves of SIF which depends only on the geometical facto and its vaiation within the Intenational Jounal of Applied Reseach in Mechanical Engineeing (IJARME) ISSN: , Volume-3, Issue-1,

5 Evaluation of S.I.F fo Cack Emanating at 45 0 Oientation Fom a Hole in Pessuised Cylinde Using FEA given domain (a/d) ae plotted sepaately. It is obseved that fo, 45 0 oiented cack in intenally pessuized cylinde the Mode-I S.I.F ( I ) & Mode-II S.I.F ( II ) ae dominant and have equal contibution fo cack popagation. The pesented stess intensity factos in this pape ae essential to pedict (1) Mixed mode factue unde static, dynamic and sustained loads (2) Residual stength (3) Cack gowth life unde cyclic loading conditions. Howeve thee is a clea need to veify the pedictions using expeimental investigations, but the method used in this pape can be utilized fo calculating the stess intensity facto fo many othe loading cases and many values of the cack length. This povides impotant infomation fo subsequent studies, especially fo fatigue loads, whee stess intensity facto is necessay fo the cack gowth ate detemination. REFERENCES [1] Heckman david: Finite element analysis of pessue vessels, MBARI 1998 [2] A.Anand,L.J.Sudev,H.V.Laakshminaayana Detemination of SIF fo a Cack Emanating Fom a Rivet Hole in a Plate using Displacement Extapolation Method Jounal of Applied Sciences 12(10) 2012,pp [3] D.Dinesh Babu, Theoitical and Finite Element Analysis of High Pessue Components IOSR Jounal of Engineeing 3(2)2013,pp [4] T.L.Andeson Factue mechanics-fundamentals and Applications published by Taylo and Fancis goup [5] Gustavo V. Guinea, Jaime Planas and Manuel Elices, I Evaluation by the Displacement Extapolation Technique, Engineeing Factue Mechanics 66 (2000), pp [6] Miloud Souiyah, A. Muchta,2009, Finite Element Analysis of the Cack Popagation fo Solid Mateials Ameican Jounal of Applied Sciences 6 (7), pp [7] Caig A. Bawell, Loenz.,A Study of Failue in Small Pessuized Cylindical Shells Containing a Cack., NASA/CR [8] Agne alsson and Jan Backlund, 1978, Summay of SIF Design Gaphs fo Cacks Emanating Fom Cicula Holes Intenational Jounal of Factue, Vol. 14, No. 6 [9] Richad D. Young Non-linea local bending esponse and bulging factos fo longitudinal and cicumfeential cacks in pessuised cylindical shells Intenational Jounal of Applied Reseach in Mechanical Engineeing (IJARME) ISSN: , Volume-3, Issue-1,