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Activate the row by clicking on any of its cells. GcGdGtot=. Choose any available row and enter the required parameters.6. Explanation of symbolseysyGCGdk0smaxhaEa;If nonzero, the Limiting Maximum Stress Approach is chosen.0G 1. TheoryLoading / Unloading ConditionElastic loading and unloading..Elastic-plastic loading and elastic unloading.&Elastic-plastic loading and unloading.[%][MPa][mm][GPa][N][deg][J/m2]Input parameters:Output parameters:)Young's modulus of the peel arm material.Thickness of the peel arm. Thickness of the adhesive layer.)Young's modulus of the adhesive material.Average peel force. Peel angle.1Nondimensional maximum curvature of the peel arm.One of the three cases:Maximum Stress^Maximum, limiting stress. If zero (or blank), the Linear-Elastic Stiffness Approach is chosen.2S[1. Kinloch AJ, Lau CC, Williams JG, International Journal of Fracture (1994), 66, pp 45-70.$Ex2. Georgiou I, Hadavinia H, Ivankovic A, Kinloch AJ, Tropsa V, Williams JG, The Journal of Adhesion (2003), 79, pp 1-27.Lc1The theory has been also published in two papers:3. Calculating a single case5. TipsShortcut key: CTRL + AShortcut key: CTRL + Z Importantoto the adhesion of packaging laminates, from the Department of Mechanical Engineering, º£½ÇÉçÇø.& 4. Calculating a series of cases}The theory behind the calculations was outlined in the PhD thesis by C. C. Lau (1993), entitled A fracture mechanics approach`g. The program will calculate the cases one by one, from the first downward, until a blank row is found.T]8. Enter the parameters for all cases in successive rows.(7-. Activate the first row (top) of the series. 2. Choosing the approachH. Click the button 'Compute a single case' or press the keys 'CTRL + A'.)>FL. Click the button 'Compute a series of cases' of press the keys 'CTRL + Z'.-BJx. The sheet can be scrolled up and down for more rows, and it is not necessary to follow a sequence when entering cases.GtotGinfsmax (o)smax (o)GtotAdhesive fracture energy.Plastic work in bending.Total input energy.Gd / G4 (If both sy and ey are given, only sy is considered)   #$%gPower law n of the peel arm material. If nonzero, the power-law model is chosen (a must be left blank).  QReBilinear a of the peel arm material. If nonzero, the bilinear model is chosen (n must be left blank).  OPx. The Linear-Elastic Stiffness Approach is a more standard option; it yields a single characteristic fracture parameter,'.There is an option from two types of analysis:.l. The Limiting Maximum Stress Approach is a cohesive zone analysis; it describes the fracture process by two&K(If the Limiting Maximum Stress Approach was chosen, then smax (o) = smax) (:;BEFI+ 'Maximum Stress' in the appropriate cell.3Theory by A.J. Kinloch, C.C. Lau and J.G. Williams.)Program by L.F. Kawashita and D.R. Moore.a.kinloch@imperial.ac.ukPeel Arm Propertiesq0#theta0q0Root rotation. Conditionj necessary to define the value of smax precisely. To conduct this analysis, enter a nonzero value for the#"$'U\m the fracture energy Gc. To conduct this analysis, input the data but leave the 'Maximum Stress' cell blank.!gl{. This spreadsheet accepts the same 'drag-and-drop' and 'auto-complete' functions available in standard Excel spreadsheets.SYield stress of the peel arm material. If sy is given, then ey need not be defined.*+,<=>SYield strain of the peel arm material. If ey is given, then sy need not be defined.*+,<=>K(For an elastic-perfectly plastic peel arm, leave both n and a cells blank)78=>$Width of the peel arm and bond line.YInput energy corrected for stored strain energy and tensile dissipations on the peel arm..Calculated maximum stress for the damage zone.€Further considerations of the plasticity of the peel arm during peel fracture have suggested that a zero constraint approach is }an appropriate description of the peel arm. This is based on two further papers; one on modelling and one on experimentation:]4. Kawashita LF, Moore DR, Williams JG, Journal of Material Science (2005), 40, pp 4541-4548.(Dr3. Williams JG, Hadavina H, Cotterell B, International Journal of Solids and Structures (2005), 42 , pp 4927-4946.)W^_nThis program is an alternative to the previous version of the ICPeel, which was placed on the Website in 2003.>%D 8This previous version is now called "ICPeel (Historic)".BTo request copies of those, please contact Prof. A. J. Kinloch on:02006 Kinloch, Williams, º£½ÇÉçÇø.R0'emaxemaxR0(3Maximum bending strain in the peel arm at the root.0Radius of curvature of the peel arm at the root.;(If both n and a are given, an error message will be shown)  n parameters, the fracture energy Gc and the maximum stress for the damage zone, smax. 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-------------------------------ÿÿà --> block 1ø * ¬ ($r 'L  & ¬¬'Jà --> block 2 *  &  'Pà--> blocks 3, 4, 5 P¬ œ L J P¬ 'H DeàBilinear model L J P¬¬ $ ¬¬ P   $ 'HdÿÿÀàPower law model L J¬ " P¬ "  "¬ " ¬ "  'HkÿÿHà:Pre-calculate the criterion for choosing f1(k0) and f2(k0) DœàBilinear model¬¬ $ ¬¬ $ '6dÿÿ°àPower law model¬¬¬ " '6kÿÿpà --> block 6¬'N H'<àOChoosing approach ------------------------------------------------------------- FœàOLINEAR STIFFNESS approach -----------------------------------------------------à --> block 7¬'2à --> block 8A@và --> block 9 H N '<àSets output value of smax¬´V-²­? , ¬ & . ´à?¬  <¬ &´à?'RàSMAXIMUM STRESS approach -----------------------------------------------------------dÿÿØ·'B Bô <'>à --> block 7¬'2à solve_ko_smax (0.01)A@x´ü©ñÒMbP?A@xà --> block 8A@và --> block 9 H N '<à--> Gc convergence criterion < > '@ @¬ œ·'Bkÿÿ¨à--> End of loopóÿÿˆàSets output value of smax T'RkÿÿXàSOutput parameters -----------------------------------------------------------------A@zš|è£pà † \¶Gc$€!‚$~(„¶ \¶Gc$€!‚+~£|XoÿÿP–è·'Ь'4´ _ B': Šô 2 4 '2¬  2´š™™™™™É?¬  <¬ &´à? T ´à?'0 2 6œ 2¬¬'XdÿÿØ Dœ¬¬ $¬¬ $ ¬ 2¬¬¬ $ ¬ $¬ ¬¬ $  2 ¬¬¬ $ ¬¬ $¬ ¬¬ $  2 ¬¬ $ ¬¬ $¬  'XdÿÿȬ¬ "  2¬ " ¬¬ " ¬¬ " "¬ ¬ "  2¬¬ " ¬  ¬¬¬ " ¬¬ " ¬ "¬ ¬¬ "¬ " ¬¬ " ¬ " ¬¬ " "¬  2 ¬¬¬ " ¬ "  2¬ " 'XkÿÿHkÿÿ@ L¬ ($r ¬ ( 0 $r  J X '8à-Checking if k0 must be increased or decreased 8¬ œ ˆ'4 8¬ e ˆ'4dÿÿ€·'Škÿÿpà(Checking if convergence has been reached 8'8 8 :œ·'Šdÿÿ 8':kÿÿóÿÿøiÿÿð–H·'Ь'4´´�ÙyCxêD': Šô 2 4 '2¬  2´š™™™™™É?´V-²­? , ¬ & . ´à? ´à?'0 2 6œ 2¬¬'Xdÿÿh Dœ¬¬ $¬¬ $ ¬ 2¬¬¬ $ ¬ $¬ ¬¬ $  2 ¬¬¬ $ ¬¬ $¬ ¬¬ $  2 ¬¬ $ ¬¬ $¬  'XdÿÿX¬¬ "  2¬ " ¬¬ " ¬¬ " "¬ ¬ "  2¬¬ " ¬  ¬¬¬ " ¬¬ " ¬ "¬ ¬¬ "¬ " ¬¬ " ¬ " ¬¬ " "¬  2 ¬¬¬ " ¬ "  2¬ " 'XkÿÿØ kÿÿÐ L¬ ($r ¬ ( 0 $r  J X '8à-Checking if k0 must be increased or decreased 8¬ œ ˆ'4 8¬ e ˆ'4dÿÿ ·'Škÿÿ à(Checking if convergence has been reached 8'8 8':kóÿÿˆ iÿÿ€ –¨à )Equivalent to block 8 in ICPeel flowchart 2¬œ¬'^¬'Ndÿÿ 2 6œ¬'^ Dœ¬ $  2¬¬¬¬ 2 ¬ 'Vdÿÿ¸ 2¬¬¬ "¬ " ¬ "  2¬ "  ¬¬¬ " ¬ "  2 ¬ " ¬ "  'Vkÿÿ dÿÿ ¬'^ Dœ¬¬ $¬ $ ¬ $¬ ¬¬  2¬¬¬ $ ¬ $¬ ¬¬ $  2 ¬¬ $ ¬¬¬ $  2¬¬ $¬¬ $  ¬¬ $ ¬  ¬ $ ¬¬ $¬ $  ¬¬ $ ¬  'Vdÿÿ˜¬¬ " ¬ "  2¬ " ¬¬ " ¬¬ " "¬ ¬ "  2¬¬ " ¬  ¬¬¬¬¬ " ¬ " ¬ "¬ ¬ " ¬¬¬ " ¬ " ¬¬ " "¬ ¬¬¬ " ¬ "   2 ¬¬¬ " ¬ "  2¬ " ¬ " ¬ "  'VkÿÿÈkÿÿÀ J V'Nkÿÿ¨iÿÿ –èà)Read and check input values¶'d¬¬$Œ'Z \¶E$€!‚$~­Êš;' \¶sy$€!‚$~­@B' \¶ey$€!‚$~¬d'  \¶n$€!‚$~'" \¶Alpha$€!‚$~'$ \¶h$€!‚$~¬è'& \¶b$€!‚$~¬è' \¶ha$€!‚$~¬è', \¶Ea$€!‚$~­Êš;'. \¶P$€!‚$~'* \¶Theta$€!‚$~ Z¬´'( \¶smax_i$€!‚$~­@B'T¶ \¶Ginf$€!‚+~¶ \¶Gtot$€!‚+~¶ \¶Gd$€!‚+~¶ \¶Gc$€!‚+~¶ \¶ Correction$€!‚+~¶ \¶smax_o$€!‚+~¶ \¶k0$€!‚+~¶ \¶theta0$€!‚+~¶ \¶ Condition$€!‚+~ † \¶Gc$€!‚$~(„¶ Processing... \¶Gc$€!‚+~àChecking input values ¬œ d¶elastic modulus - 'd¬'kÿÿ€  '   '  ' kÿÿ�·'D¬'"kÿÿ  &¬œ d¶peel arm thickness - 'dkÿÿ` ¬œ d¶specimen width - 'dkÿÿ(¬'. d¶adhesive modulus - 'dkÿÿ€ *¬œ d¶ peel force - 'dkÿÿH (¬ (¬´ œ d¶ peel angle - 'dkÿÿàSet approaches T¬œ·'Fdÿÿз'FkÿÿÀàChecking errorsdà Errors found·'n¶ Errors: d'd·'nkÿÿ0iÿÿ(–(à! Write results Ž \¶Gc$€!‚$~(„ < \¶Gc$€!‚+~ N \¶Gd$€!‚+~ H \¶Gtot$€!‚+~ L \¶Ginf$€!‚+~¬d N L \¶ Correction$€!‚+~ R­@B \¶smax_o$€!‚+~ 0¬´ Z \¶theta0$€!‚+~ 2 \¶k0$€!‚+~ ^ \¶ Condition$€!‚+~iÿÿxÿÿÿÿp·'D "¬ $¬ eÿÿÿÿ˜#·'D "¬ $¬ e "¬ $¬eÿÿÿÿ8# "¬ $¬œà8If both n and a are zero, a power-law n=0 mode is chosenÿÿÿÿ$àChoosing stress-strain modelÿÿÿÿ€#àPeel arm thickness ¬ ¬œ ¬ ¬e ¬ ¬ eÿÿÿÿÐ#ÿÿÿÿØ# ¬ ¬ eà"2If both sy and ey are given, only sy is consideredÿÿÿÿ$à Yield pointÿÿÿÿð# ,¬œàNo bondline considerationÿÿÿÿ($ .¬eà*Bondline consideration but invalid modulusÿÿÿÿ0$ d¶œà No errors foundÿÿÿÿ@$à Wend&à k0 = k0 + 0.001à k0 = k0 - 0.001ÿÿÿÿˆ#ÿÿÿÿÀ$ÿÿÿÿ%ÿÿÿÿH%ÿÿÿÿX%ÿÿÿÿ€%ÿÿÿÿp%ÿÿÿÿp%ÿÿÿÿ`%ÿÿÿÿp%à End If·'ŠdPÿÿÿÿØ$ÿÿÿÿ8&ÿÿÿÿX&ÿÿÿÿH&ÿÿÿÿh&ÿÿÿÿX&]ò¬'Πά 'ÎÿÿÿÿP&ÿÿÿÿp&ÿÿÿÿ¸&ÿÿÿÿÐ&ÿÿÿÿø&à Elseÿÿ„'Kÿÿÿÿ'à+ If k0_error < precision * 1000 Then"c"à k0_converged = True"à! prev_error = k0_error 8 :œ>~$ÿÿÿÿ'ÿÿÿÿø&ÿÿÿÿ ÿÿÿÿ('ÿÿÿÿø&ÿÿÿÿ'ÿÿÿÿ8'ÿÿÿÿ 'àsolve_k0_linear (1)ÿÿ'ÿÿÿÿè&ÿÿÿÿ'ÿÿÿÿh'ÿÿÿÿH'ÿÿÿÿˆ'ÿÿÿÿˆ'àsolve_k0_linear (0.1)�Â#ÿÿÿÿp'´ü©ñÒMbP?A@tear (0ÿÿÿÿˆ'ÿÿÿÿ¸'ÿÿÿÿ¨'àu While theta >= 2 * ey * 6 * k0 ^ 3 / (1 + 5 * k0 ^ 2) * (0.2 + (0.058 + ha * E / 3 / h / Ea) ^ 0.5) ^ 0.5<Â#ÿÿÿÿ¨'ÿÿÿÿð' d \¶Gc$€!‚+~#ÿÿÿÿð' 0 ( œ`W$kÿÿ˜' d¶Could not converge k0 'daÇ#ÿÿÿÿ€'k d¶œFÿÿÿÿ(šp8(ÿÿÿÿ8(ÿÿÿÿ8( d¶yield point - 'dng cÿÿÿÿH(ÿÿÿÿX(ÿÿÿÿx( d¶work-hardening coefficient - 'dH(ÿÿÿÿ€(ÿÿÿÿ`(ÿÿÿÿ€(ÿÿÿÿ€(àsolve_k0_linear (0.01)ÿÿÿÿp(ÿÿÿÿx(ÿÿÿÿ°( d¶-tensile stress greater than ultimate stress - 'dXÿÿÿÿH( "¬ $¬eÿÿÿÿè(šp)ÿÿÿÿø(à1 Cells(activeRow, Range("k0").Column).Activateà) MsgBox ("No. of iterations: " & iter)ÿÿÿÿð(à solve_ko_smax (1)à solve_ko_smax (0.1)ÿÿÿÿ)ÿÿÿÿ8ÿÿÿÿ ÿÿÿÿ¨ &¬  2¬è \¶R0$€!‚+~ÿÿÿÿ°'ÿÿÿÿð'ÿÿÿÿh(ÿÿÿÿˆ( 2 ¬d \¶emax$€!‚+~ÿÿÿÿP(ÿÿÿÿ·Attribute VB_Name = "Module1" Dim E, sy, e n, a, h, b@, thetP E"0 As Double„�k0, k0_inccri`terioTerror, prØev_ Gg?' ious_ gc2_converged½ilin eanƒ_app roach�9Bo olean ^gt@ot, gb�gEdg€#chi€�maxo€f1,H f2—]Pi— activeRowD, Vdit‚�m˜ode€¾�No€Integer PñšMsgÑ„f�·‰> Sub ICPeel_Fast() 'Programmer: Luiz Kawashita 28.1ð1.03Á Á‡†,€ŽA‚/Cell.rowBRead and check input @valuesEI€f Not r@ ƒ@†Às The„_��GoTo E�?*H@l>E@IfBStart c@alculaMs accordi ng toD8 f lowch� ---> bloM@-1ÁA"g0@9P / b * (1 - Cos(}B½)@N�ƒ\A‰€ E€ hÀey ^ ê2À 2Ed'GÆ�£”†/ h€ EÀeyK$s 3, p4, 5&ÀPA<ü 1ÈNÃA�®€€/~+°€$� À$g#Eèlse€ n àx ,~a"2ÅMF+ "tensile stress gà:€|€…an ÀultimaÀ�„Þ-„Œa´<ÊbÄv’l'B¥fl°(ÉÄ +Ã8a)@":Ò2c#))À.ag#¡##£á'Pow€er law ÿZ(Á nC @B(@+¬ na €+ 7-£?ä§ #E^áÂte-…^eÁ± &ª fo"r`noosA`f1�(k0)âpf2Aÿà £À=ÿ*�¥í`¶ç n=à[db€)/Ã*¡aÛ c?(e(7. ^á „ .nKnÈ�gk6dgd;áX¦c ÁBå 'CþhD%Á\„ˆC4¡à+�ÌÃi 8LINEAR STIFFNðESS ßá(‹Ö7åÁka—0áybÁ= ð�5Wfha<ÂM >ãpL*Œ 6à+À^ 3 2‚*52b40.2Aq50.058€h>aàQLñM"^ ð0.5) 0`|ñK @+`00ðW'ÃU qWend‡ è=e-eUÙ5'sàolve_0&ã %Ǥ*ß0.1ÿØïð Þð0ð *f8)¶<_Gû ÷9mùge,€hg�S€ets outfvà of sŠyñúo01` ojà×rKÑl /‚hÆÑÑ'MAXIMUúMÐ,R¯,o+sS£C³10Ÿ�À Fþa kÓ73,á…Ù]çÑè¤Àgc7ú 5ÿÑ1Ñ¢'È415$œo_û%ÿ (&ÿ"$¡5t&5_&ÿŒP&á ß&šš&ÑÏÝ&15”Gcq«B¶ønce×hƒëbƒ¡ÐAbs(Ð-²¿ÿ4½¤6; Tf»ŽÉ ñ‰!Tru„ÈEit5‡ 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