Inernaional Journal o Emerging Technology and Advanced Engineering Websie: www.ijeae.com (ISSN 2250-2459, ISO 9001:2008 Ceriied Journal, Volume 4, Issue 3, March 2014) Faigue Lie Predicion o a Hoop-Wrapped Composie CNG Cylinder Conaining Surace Flaw Anand Kumar Agrawal 1, Surendra Kumar 2 1 Academy o Scieniic & Innovaive Research, CSIR-CMERI, Durgapur-713209, India 2 Mechanics & Sress Analysis Deparmen, CSIR-CMERI, Duragapur-713209, India Absrac In recen years many experimenal and numerical sudies have been conduced on he aigue behaviour o CNG sorage pressure vessels. The main objecive o hese sudies is o esimae he oal aigue lie, which consiss o wo pars: i) Lie ill crack nucleaion and ii) Crack growh lie. Alhough aigue evaluaion mehods or meal cylinders are widely covered in lieraure including he ASME Boiler and Pressure Vessel Code, comprehensive approaches or aigue evaluaion o composie-reinorced pressure vessels are very ew. This paper calculaes he aigue lie ill crack nucleaion or a seel-lined hoop wrapped composie pressure vessel conaining a surace law (noch) using srain-lie approach. Firsly, saic sress analysis aking ino accoun he non-linear maerial behaviour o seel liner was perormed using inie elemen mehod o provide inpu or he aigue analysis. Then aigue analysis was carried ou by applying a cyclic pressure inside he pre-sressed cylinder using srain-lie approach, and he resuls obained by he numerical simulaions are discussed. The approach associaed wih hese calculaions can be used o sudy he eec o various maerial and geomery parameers on he aigue lie o he pressure vessel. Keywords CNG, Hoop wrapped composie cylinder, Finie elemen mehod, ANSYS, Crack nucleaion, Srain-lie approach, Faigue lie. Noaions: b Faigue srengh exponen. c Faigue duciliy exponen. e Nominal elasic srain range. 2 S Toal srain ampliude. Nominal elasic sress range. max. min E Modulus o elasiciy. Faigue duciliy coeicien. K K K K N n Cyclic srengh coeicien. Faigue srengh acor. Elasic sress concenraion acor. Faigue noch acor. No. o cycles o ailure. Cyclic srain hardening exponen. q Noch sensiiviy. Faigue srengh coeicien. m Mean sress. max Maximum sress. min Minimum sress. I. INTRODUCTION In auomobiles CNG is sored in pressure vessels a high pressure. The pressure vessels or he on-board sorage o CNG should be sae and ligh weigh. To keep he pressure vessels ligh weigh, i is reinorced wih composie maerial. The mos commonly used composie-reinorced pressure vessel is seel-lined hoop wrapped pressure vessel which is a meallic cylinder (liner) wih an overwrap o carbon ibre or ibreglass in he hoop direcion over he cylinder sidewall. CNG pressure vessels are subjeced o aigue loading which occurs as a resul o cyclic srains caused by he pressure changes due o empying and reilling. According o saisics, since 1960 abou 40% o he pressure vessel ailures are caused by aigue ailure [1]. To avoid hese ailures, proper aigue analysis and esing needs o be perormed prior o manuacuring o hese pressure vessels. Faigue evaluaion mehods or meal cylinders commonly exis in he lieraure, however very ew sudies have been repored in lieraure or aigue evaluaion o composiereinorced pressure vessels. Faigue analysis and evaluaion o composie cylinders is relaively complicaed because o heir hybrid srucure. 790
Inernaional Journal o Emerging Technology and Advanced Engineering Websie: www.ijeae.com (ISSN 2250-2459, ISO 9001:2008 Ceriied Journal, Volume 4, Issue 3, March 2014) Faigue cracks mosly iniiae a ree suraces, usually rom exernal suraces bu hey can also iniiae rom inernal suraces i he seel liner conains maerial deecs such as voids and cracked second-phase paricles. Common exernal surace deecs include geomeric noches and surace roughness. So, he research abou he aigue behaviour o seel-lined hoop-wrapped pressure vessels conaining a surace law is necessary or a more realisic assessmen o hese cylinders. The aim o his work is o carry ou he aigue analysis o a noched seel-lined hoop wrapped pressure vessel using srain-lie approach in order o calculae he aigue lie ill crack nucleaion. The approach adoped here is as ollows: Firsly, saic sress analysis aking ino accoun he non-linear maerial behaviour o seel liner was perormed using inie elemen mehod. The sress resuls obained by saic sress analysis ac as inpu or he aigue analysis. Subsequenly, he aigue analysis is carried ou by applying a cyclic pressure inside he pre-sressed cylinder and aigue lie ill crack nucleaion is calculaed. I is expeced ha he resuls o presen analysis will provide he designers wih a valuable knowledge ha may be used in a more realisic aigue assessmen o composie CNG cylinders conaining laws. This paper is organized ino 5 Secions including his secion. Secion II presens he exising work on he aigue analysis o pressure vessels. Secion III describes he proposed mehodology or aigue evaluaion o composie cylinders while Secion IV presens he resuls o he analysis and discusses he perinen poins regarding he resuls. Finally, Secion V gives he conclusion and menions urher scope o work. II. LITERATURE SURVEY The various sandards do speciy he requiremens o be me during he manuacure o pressure vessels o sore gases. However, he means used o mee hese requiremens are unspeciied in hese sandards. For example ISO 11439:2000 code [2] neiher provides design ormulae nor liss permissible sresses or srains, bu requires he adequacy o he design o be esablished by appropriae calculaions and demonsraed by esing o show ha cylinders are capable o consisenly passing he maerials, design qualiicaion, producion and bach ess speciied in his sandard. Mackerle [3, 4] presened a bibliographical review o he Finie Elemen Mehods (FEMs) applied or he analysis o pressure vessel srucures/componens and piping rom he heoreical as well as pracical poins o view. As menioned earlier, pressure vessels or on-board sorage o CNG are subjeced o aigue caused by pressure changes due o reilling and empying. Two major ypes o mehodologies are available or aigue lie predicion. One approach is based on he maerial aigue-lie curves (sress-lie and srain-lie models) and a damage accumulaion rule. The oher approach is based on he racure mechanics and crack growh analysis. Yaxin e al. [1] emphasized he imporance o aigue analysis o CNG sorage pressure vessels and carried ou a sress analysis ollowed by a aigue analysis using sress-lie approach or an unnoched meal cylinder wih he aid o ANSYS soware. Alhough, aigue evaluaion mehods or meal cylinders are included in Secion VIII, Division 3 o he ASME Boiler and Pressure Vessel Code [5], bu very ew approaches have been repored in lieraure or aigue evaluaion o composie-reinorced pressure vessels due o heir hybrid srucure and complex sress behaviour. Su and Bhuyan [6] modelled a seel-lined hoop-wrapped cylinder wih inernal axial semi-ellipical cracks in he cylindrical porion cenre o seel-liner by inie elemen mehod, and calculaed sress inensiy acor and crack mouh opening displacemen. Tarakcioglu e al. [7] sudied experimenally he aigue behaviour o ilamen wound composie pipes made o E-glass/epoxy, under alernaing inernal pressure and esed under open ended condiions. Chen and Pan [8] invesigaed he racure behavior o compressed naural gas (CNG) cylinder wih hoop wrapped composie layer or he axial crack a he inner surace. The sress inensiy acors along he crack ron were obained or dieren crack proiles using inie elemen mehod, and he eecs o cylinder geomery, hoop wrapped layer hickness and propery disribuions o he composie layer on he sress inensiy acor were discussed. Their numerical resuls showed ha he hoop wrapped composie cylinder can lower he sress inensiy acor value grealy and ensure he sae use o pressure vessels conaining deecs in service. The above papers dealing wih analysis o composie reinorced pressure vessels mainly ocus on racure behavior o hese vessels. However, a comprehensive analysis o composie cylinder or aigue lie predicion using srain-lie approach is no repored in he open lieraure and hus is he opic o he curren sudy. Furher, eec o he sress concenraion on aigue lie predicion is an imporan issue in aigue reliabiliy evaluaion and has been invesigaed in he presen work. 791
Inernaional Journal o Emerging Technology and Advanced Engineering Websie: www.ijeae.com (ISSN 2250-2459, ISO 9001:2008 Ceriied Journal, Volume 4, Issue 3, March 2014) III. PROPOSED METHODOLOGY In manuacuring o pressure vessels, sress concenraion poins (noches) are unavoidable. Mos o he imes crack nucleae rom regions o high sress concenraion or deecs, hereore when aigue analysis is perormed o make he lie predicions, he presence o noches mus be modeled. Due o he presence o inelasic sresses a noch roo, srain-lie approach is suiable or aigue analysis because i considers noch sresses and srains explicily. Applicaion o he srain-lie approach involves wo seps [9]: 1. Deerminaion o local(noch) sresses and srains 2. Lie predicion using he local sresses and srains, based on he srain-lie equaion. I nominal elasic sress range is given, urher calculaions or local sress and srain range can be done eiher by: (a)experimenal mehod, (b)finie elemen mehod or (c)analyical Model. Ou o hese hree mehods, Finie Elemen Mehod is used here. A. Applicaion o Finie elemen mehod To calculae lie ill crack nucleaion using modiied srain-lie equaion (Eq. 1), he oal srain (elasic + plasic) is he required inpu. Bu, perorming Finie Elemen analysis o deermine he oal response can be expensive, especially i he nominal response o he srucure is elasic. So, an acceped approach is o assume a nominally elasic response and hen make use o Neuber s equaion or cyclic load (Eq. 2) o relae local sress/srain o nominal sress/srain a a sress concenraion locaion [10]. m b c 2N 2 N...(1) 2 E Equaion (1) is he modiied srain-lie equaion wih eec o mean sress considered using Morrow's heory. K e S...(2) 2 Equaion (2) is he Neuber s relaion or cyclic loading. 1 n...(3) 2 2E 2K Equaion (3) is he cyclic srain equaion or Ramberg Osgood relaionship. Simulaneously solving equaion (2) along wih equaion (3), we can calculae he local sress/srains (including plasic response) given only elasic inpu. Noe ha his calculaion is nonlinear and is solved via ieraive mehods. ANSYS aigue uses a value o 1 or K, assuming ha he mesh is reined enough o capure any sress concenraion eecs. For K equal o 1, K also will be equal o 1 irrespecive o he value o q rom Eq. 4. K 1 q K 1...(4) Figure 1 shows he seps ollowed in he complee analysis. Finie elemen soware ANSYS 14.0 [11] was used or he above Finie Elemen analysis. Following are some deails o his analysis in ANSYS: Creae he geomery Mesh he geomery Assign maerial properies Apply boundary condiions and load seps Perorm saic sress analysis Faigue Analysis using ANSYS aigue ool Analysis o resuls Fig.1. Seps adoped in he analysis Model: The analysis uilizes he geomerical and loading symmeries in he circumerenial (angenial) direcion. 792
Inernaional Journal o Emerging Technology and Advanced Engineering Websie: www.ijeae.com (ISSN 2250-2459, ISO 9001:2008 Ceriied Journal, Volume 4, Issue 3, March 2014) Furher, symmery abou he mid-plane perpendicular o he axis o revoluion o he cylinder was assumed. Thus, only a quarer o he cylinder as shown in Figure 2 needs o be modeled hereby reducing he compuaional expenses. Wih reerence o he igure, he major dimensions are as ollows: inernal radius o he liner (R)=164.5 mm; lengh o he cylindrical porion o he vessel (2h)=705 mm; hickness o he liner ()=4.8 mm; hickness o he composie wrap ( c )=3.5 mm; noch deph (a) = 0.2 and noch widh (b) = 0.2. The quarer model o he seel-lined hoop wrapped pressure vessel was meshed wih hreedimensional 10 noded erahedral elemens, he mesh near he edge o he noch was ine enough o capure he seep srain gradien. TABLE II PROPERTIES OF CARBON/EPOXY COMPOSITE (CARBON FIBRE T- 700/EPOXY RESIN (LY556 & HY5200)) [13] Propery Value Longiudinal ensile modulus 160 GPa Major Poisson s raio 0.1987 Transverse ensile modulus 8GPa In-plane shear modulus 5 GPa Longiudinal ensile srengh 1500 MPa Transverse ensile srengh 14 MPa In-plane shear srengh 70 MPa TABLE III Srain-Lie Parameers or Liner Maerial [12] Propery Value Faigue srengh coeiciens 1481MPa Faigue srengh exponen -0.112 Faigue duciliy coeicien 11.431 Faigue duciliy exponen -1.02 Cyclic srengh coeicien 789 MPa Cyclic srain hardening exponen 0.054 Fig. 2. Geomery o he quarer model Maerial properies: The maerial properies which are used in he analysis are aken rom lieraure. Table I, II and III lis all he relevan properies. TABLE I PROPERTIES OF LINER MATERIAL (LOW ALLOY STEEL) [12] Propery Value Densiy 7700 kg/m 3 Young's Modulus 207 GPa Poisson's Raio 0.32 Yield Srengh 860 MPa Tensile Srengh 965 MPa Tangen Modulus (bilinear 920 MPa sress-srain curve) 793 Boundary condiions: Boundary condiions applied here are ricionless suppor and displacemen boundary condiion. Fricionless suppor prevens one or more aces rom moving or deorming in he normal direcion. The surace body is ree o move, roae, and deorm angenial o he ace. The ricionless suppor is equivalen o a symmery condiion when applied o a la surace body [11]. Here ricionless suppor was applied o model symmeric consrain condiion in he circumerenial direcion and a consrained displacemen in he axial direcion was applied on he mid-plane perpendicular o his direcion o he cylinder. Load: Hoop-wrapped cylinder generaes residual sress via an auoreage process, and hence he inie elemen sress analysis should be conduced irs o deermine limis o auoreage pressure beore he design pressure can be applied, which is an ieraive process. Once auoreage pressure is calculaed, subsequen non-linear sress analysis need o be perormed using loads divided ino our seps as shown in Figure 3. In sep 1 auoreage pressure calculaed o be 42 MPa was applied, which was ollowed by sep 2 in which he load was released o zero. In sep 3 working pressure o 20 MPa was applied and inally in sep 4 pressure was raised o he es pressure o 30 MPa. Assuming he environmenal eecs o be absen, he aigue load can be made independen o requency and wave orm. Thus, aigue load can be applied in a sinusoidal orm as shown in Figure 4.
Inernaional Journal o Emerging Technology and Advanced Engineering Websie: www.ijeae.com (ISSN 2250-2459, ISO 9001:2008 Ceriied Journal, Volume 4, Issue 3, March 2014) Fig. 3. Applied load seps Faigue lie was ound o be minimum in he viciniy o he noch and esimaed o be above 21000 cycles. This value is he minimum prediced lie o he cylinder in erms o he number o cycles, aer which a macroscopic crack may iniiae a he locaion where his minimum occurs. In Figure 7, aigue lie is shown a a speciic value o aigue srengh acor, K o be 0.9. Faigue srengh acor (or Faigue srengh reducion acor) is a modiicaion acor o accoun or he dierences beween he componen in service and he es specimen. I reduces he aigue srengh and mus be less han one. Variaion o aigue lie or a noched cylinder wih aigue srengh acor was also obained as depiced in Figure 8. I mus be poined ou ha he resuls shown here are speciic o geomeric dimensions o he pressure vessel, and noch shape and size. The value o lie ill crack nucleaion and he exac locaion o he minimum lie may change wih changes in geomeric dimensions and noch parameers. Fig. 4. Applied aigue load. IV. RESULTS AND DISCUSSION Saic sress analysis prediced sress disribuion in he cylinder a dieren seps o loading. A load sep 2, he analysis prediced dieren residual sress disribuions due o auoreaging. The residual sress in he circumerenial direcion is ploed in Figure 5 which indicaes ha considerable compressive residual sress is generaed in he liner which is expeced o improve aigue resisance o he liner. As expeced, he composie hoop wrap experiences a lile ensile residual sress. The von-mises sress disribuion a he 4h loading sep o es pressure is depiced in Figure 6. The maximum value o von-mises sress a any poin in he liner is well below he yield srengh o he liner maerial. The resul o aigue analysis o he liner in Figure 7 shows ha aigue lie ill crack nucleaion orms a considerable par o he oal aigue lie in he absence o an iniial macroscopic crack. Fig. 5. Residual sress disribuion (in Pascal) in he cylinder a zero pressure aer auoreage. 794
Inernaional Journal o Emerging Technology and Advanced Engineering Websie: www.ijeae.com (ISSN 2250-2459, ISO 9001:2008 Ceriied Journal, Volume 4, Issue 3, March 2014) Figure 8. Variaion o lie ill crack nucleaion wih aigue srengh acor. Fig. 6. von-mises sress disribuion (in Pascal) in he liner a es pressure o 30 MPa. Fig. 7. Lie disribuion (in No. o load cycles) due o a pressure range beween zero and es pressure or K = 0.9. V. CONCLUSION & FURTHER SCOPE A non-linear inie elemen sress analysis o a hoopwrapped composie pressure vessel was perormed ollowed by a aigue analysis using srain-lie approach. Faigue lie o he cylinder ill crack nucleaion was prediced in he presence o a possible surace law presen in i and he variaion o aigue lie wih aigue srengh acor was calculaed. Alhough he prediced resuls are or a paricular se o maerial properies, geomeric dimensions, load range and noch shape; he approach associaed is general and can accoun or changes in he above parameers. Thus, by ollowing he proposed approach, he eecs o above parameers on aigue lie ill crack nucleaion can be sudied. These resuls can be useul in speciying he sae service lie o hoop-wrapped composie pressure vessels. REFERENCES [1] Yaxin, Z., Junge, D., Chuanmei, S., Faigue analysis or CNG sorage gas pressure vessel based on ANSYS. Advanced Maerials Research, Vols. 33-37 (2008), pp 109-114. [2] ISO 11439:2000: Gas cylinders - High pressure cylinders or he onboard sorage o naural gas as a uel or auomoive vehicles. Firs Ediion, 2000. [3] Mackerle, J., Finie elemens in he analysis o pressure vessels and piping a bibliography (1976 1996). Inernaional Journal o Pressure Vessels and Piping, Vol. 69 (1996), Issue 3, pp. 279 339. [4] Mackerle, J., Finie Elemens in he Analysis o Pressure Vessels and Piping, an Addendum: a Bibliography (1998-2001). Inernaional Journal o Pressure Vessels and Piping, Vol. 79 (2002), pp. 1-26. 795
Inernaional Journal o Emerging Technology and Advanced Engineering Websie: www.ijeae.com (ISSN 2250-2459, ISO 9001:2008 Ceriied Journal, Volume 4, Issue 3, March 2014) [5] ASME, ASME Boiler and Pressure Vessel Code, Secion VIII, Division 3 : Alernaive Rules or Consrucion o High-Pressure Vessels, The American Sociey o Mechanical Engineers, 2004 [6] Su, B., Bhuyan, G. S., Eec o composie wrapping on he racure behavior o he seel-lined hoop-wrapped cylinders. Inernaional Journal o Pressure Vessels and Piping, Vol. 75 (1998), pp. 931 937. [7] Tarakcıoglu, N., Gemi. L., Yapıcı, A., Faigue ailure behaviour o glass/epoxy ±55 ilamen wound pipes under inernal pressure. Composies Science and Technology, Vol. 65, 2005, pp. 703-708. [8] Chen, J., Pan, H., Sress inensiy acor o semi-ellipical surace crack in a cylinder wih hoop wrapped composie layer, Inernaional Journal o Pressure Vessels and Piping, Vol. 110 (2013), pp. 77 81. [9] Sephens, R. I., Faemi, A., Sephens, R. R., Fuchs, H.O., Meal Faigue in Engineering. John Wiley & Sons, Inc., 2001. [10] Raymond L. Browell, P.E., Al Hancq, Predicing Faigue Lie wih ANSYS Workbench. Inernaional ANSYS Conerence May 2-4, 2006. [11] ANSYS Workbench, Version 14.0, User's Manual. [12] Kumar, S., Basu-Mandal, P., Mukherjee, S., Design o ligh-weigh composie cylinders or sorage o compressed naural gas or mobile applicaions, Projec Repor, No. SSP097812, Sponsor: GAIL (India) Ld., May 2013. [13] ASM Handbook, Faigue & Fracure,Vol.19, page-972 796