* ** ** Stochastc Fnte Element Analyss for Composte Pressure Vessel Tae Kyung Hwang Young Dae Doh and Soon Il Moon Key Words : Relablty Progressve Falure Pressure Vessel Webull Functon Abstract ABAQUS ABAQUS USDFLD PATRAN (FRP (Safety Factor (Relablty (Desgn Random Varable E-mal : cass@hanmalnet TEL : (08-5 FAX : (08-9 * ** (Strength
( (Helcal (Hoop zero (Progressve Falure Mode (Relablty (In-plane shear stran ( τ γ = + α τ γ = + α τ τ ( o ( + o ( + ( G G G γ τ parameter d α o Modfed Hashn [] (( (σ > 0 (5 E = ν = 0E-8 ( E ν = 0E-8 E E G G σ α = exp[ ( ] β d 0 d σ α = exp[ ( ] β 0 E E ν α βo (Shape parameter (Scale (Edgeworth expanson method[-] (6 (Central moment τ o + α τ σ G em = ( + ( Yt S o + α S G µ ( K µ ( K F( K = φ( K φ ( K + ( /! µ ( K! µ ( K (6 τ 0 µ ( K 6 o φ ( K + ( φ ( K + + α τ / 6! µ ( K σ G e fs = ( + (σ > 0 XT S ( φ n K (k n o + α S G τ (6 o + α τ σ (7 G e fs = ( + (σ <0 ( X c S o + α S µ ( K G F( a = P( K a φ( Z φ ( Z (7 /! µ ( K X T X C Y T Y C / / S (5
s φ( Z = e ds π (8 a E( K( X Z = µ ( K Z φ ( Z = ( Z e π Z (9 Fk ( ( = P K (9 K (0 K = f( X σ j (0 (6 K ( n K E[ K( X] = K( X m + ( X Var X m = X µ ( K = E [( K ( X ] E [ K ( X ] n n n K K K X Var X m Xm X µ m X = X = X = X = ( + ( K µ ( ( µ ( X ( K = X m = X ( X µ ( X = β Γ + α µ ( X = β ( Γ + Γ + α α µ ( X = β Γ + β Γ + Γ + + β Γ + α α α α ASTM Toray (T800 0 / (goodness of ft test (Normal dstrbuton functon (Log-normal dstrbuton functon (Webull dstrbuton functon Kolmogorov Smrnov(K-S [] Maxmum lkelhood method Fg 0 o ( x µ f( x = exp[ ]: Normal dstrbuton σ π s (ln x µ f( x = exp[ ]: Log-normal ( σx π s α x α x α f( x = ( ( exp[ ( ] β β β x α F( x = exp[ ( ] β : -parameter Web µ s Cumulatve probablty of falure 09 07 05 0 0 0 Exp results Webull functon (α=57 β=08 Normal functon (µ=66 s=95 Log-normal functon (µ=768 s= 500 600 700 800 900 000 00 00 00 00 500 Longtudnal FRP Strength X T (MPa Fg Comparson of predcted cumulatve dstrbuton functons and test results for FRP 0 o tensle test Table Statstcal characterstcs of desgn random varables for T800/epoxy (Unt: MPa s ν(% Test No X T Web 08 9 8 00 8 09 07 05 0 0 0
Y T 7 79 589 9 X C 76 655 88 77 7 Y C 68 6 60 66 8 S LT 909 8 6 9 0 (s: ν: ABAQUS- STANDARD[5] PATRAN ABAQUS Fg Fg Procedure of probablstc fnte element PATRAN analyss 0 o ABAQUS (CD0R *USDFLD (Dome Fg AUTOMAT ABAQUS [6] AUTOMAT (Local element axs Fg α ϕ θ ( θ = α -ϕ (
Fg Fber trajectory at the dome of flament wound pressure vessels Surface ( (5 Table V ξ = Table Mean values of materal propertes and (x x + ( y y + ( z z ( wndng thckness (Unt: MPa {(x x ex + ( y y ex + (z z ex} E = 5 E = E = 7 06 G = G = 776 (α (6 R α = ± sn t = o t r cos α - o c c c R r cos α R: (6 (-(6 ( 50(mm 8(mm 5(mm Fg5 PATRAN 6 (CD0R 7 (Contact G = 00 ν = ν = 0 ν = 0 t = 8( mm t = 5( mm = 66 0 ( Pa o α helcal hoop 7 V m β = cos Fg Unt vector for merdan drecton = - cosγ - x R cos β e - y γ = f (r = tan ( x R + + x - y - x + sn γ = (x e y at x - y - cosγ plane + (z sn β e z (5 Fg 5 Fnte element mesh of composte pressure vessel Fg6 0 Fg7-8 Fg9-0 8(MPa 5
5 Fg 8 (MPa (MPa Fg 8 Contour for the dstrbuton of fber stress 500 500 50 Hoop 50 000 000 750 750 Fber stress (MPa 500 50 000 750 Helcal 500 50 000 750 500 500 50 50 0 00 5 50 75 00 5 50 75 00 5 50 Y-Axs (mm Fg 9 The dstrbuton of fber stress for helcal and hoop layer P=8(MPa 0 50 50 Helcal Fg 6 Confguraton of deformed shape (x 0 Transverse stress (MPa 050 9 750 6 50 Hoop 050 9 750 6 50 50 50 00 5 50 75 00 5 50 75 00 5 50 Y-Axs (mm Fg 0 The dstrbuton of transverse stress for helcal and hoop layer P=8(MPa Fg 7 Contour for the dstrbuton of resultant deformaton 6 Fg 9
/ Fg 50% 5(MPa Fg5 8 50% ~08(MPa 50% 97(MPa 76(MPa Stran (% Hoop stran (% 0 Hoop stran Axal stran 5 50 75 5 50 75 5 50 Pressure (MPa Fg Dstrbuton of the hoop and axal stran predcted by FEA 8 6 0 Expermental results (ASTEB-0/-05/-06/-07/-08/-/-/-/- Present analyss -0-00 0 00 800 00 600 000 00 800 00 600 Pressure (ps Fg Comparson of FEA results and test data for the hoop stran of cylnder 0 8 6 0-0 0% Fg [7] % Fg 05~55(MPa 5(MPa 0(MPa 8(MPa % 86(MPa 07% Cumulatve probablty of falure 09 07 05 0 0 0 Matrx crackng n helcal layer Fber falure n hoop ples Matrx crackng n hoop ples 0 6 9 5 8 7 0 Pressure (MPa Fg Cumulatve dstrbuton functon of probablty of falure for matrx and fber falure Cumulatve probablty of falure 09 07 05 0 0 0 Probablstc FEA Analytcal method (Average bound -0-0 8 9 0 5 6 7 8 Pressure (MPa Fg Comparson of FEA and analytcal method for the cumulatve probablty of falure of composte pressure vessel 09 07 05 0 0 0 09 07 05 0 0 0 7
Burst pressure (MPa 50 5 75 50 t helcal =8(mm t hoop =5 (mm Strength rato= 50 5 75 50 technques J of structural engneerngvol0 98 pp707-7 (5 H Karlsson and Sorensen ABAQUS User s Manual Ver6 (6 TK Hwang and HK Km The development of FEA program to analyss the composte motor case wth ABAQUS ADD Report MSDC-5-990008 (7 TK Hwang CS Hong and C G Km Probablstc Deformaton and Strength Predcton for a Flament Wound Pressure vessel Compostes Part B: Engneerng 00 0 0 6 7 8 9 0 5 Number of pressure vessel Fg 5 The dstrbuton of expermental burst pressure for eght pressure vessels 5 ( KY Chang S Lu and Fu-kuo chang Damage tolerance of lamnated compostes contanng an open hole and subjected to tensle loadngs Journal of composte materals Vol5 99 pp7-00 ( R C Wetherhold Relablty calculaton for strength of a fbrous composte under mult-axal loadng J of composte materals Vol5 98 pp0-8 ( T P Phlppds and D J Lekou Probablstc falure predcton for FRP compostes Compostes scence and technology Vol58 998 pp97-98 ( A B Haldar Practcal structural relablty 8