TREATMENT OF THERMAL AND RESIDUAL STRESSES IN THE SINTAP DEFECT ASSESSMENT PROCEDURE. R A Ainsworth (NEL) S D Smith (TWI) C S Wiesner (TWI)

Transcription

1 SNTAP/NE/018 TREATMENT OF THERMAL AND RESDUAL STRESSES N THE SNTAP DEFECT ASSESSMENT PROCEDURE R A Ainwoth (NEL S D Smith (TW C S Wiene (TW SUMMARY Within the SNTAP oject, Tak 4 i addeing themal and eidual tee. Pat of Tak 4 deal with oduction of a comendium of welding eidual tee fo a ange of weldment geometie. The othe at of Tak 4 deal with the teatment of thee eidual tee, and othe econday tee, in a defect aement aoach. Thi latte aect involve finite-element analyi, exeimental wok and an examination of the methodology fo teating themal and eidual tee. Thi note fit decibe available methodologie fo incooating themal and eidual tee in defect aement ocedue. Secondly, the methodologie ae comaed. Then numeical and exeimental eult geneated duing SNTAP ae biefly decibed and dicued in the context of thee methodologie. Finally, ecommendation ae made fo teating econday tee in the SNTAP ocedue and fo futue wok. wod\inta\929 1

2 SNTAP/NE/ NTRODUCTON Exeimental wok clealy demontate that econday tee, uch a thoe induced by temeatue gadient o the welding oce, can have a ignificant effect on the load caying caacity of a comonent containing a flaw [1]. The effect i mot onounced when tuctual eone i eentially elatic; in contat, eidual tee can have negligible effect when laticity i wideead. Thee effect have alo been demontated numeically by calculating J fo tuctue with and without eidual tee [2]. n view of the above obevation, it i imotant to oely account fo econday tee in defect aement. n thi note, available and develoing methodologie fo teating econday tee ae fit decibed in Section 2. The elationhi between the methodologie i then etablihed in Section 3. Section 4 biefly decibe the numeical and exeimental eult geneated within the SNTAP oject and dicue thee in the context of validation of the methodologie decibed in Section 2. Finally, Section 5 ovide ecommendation both fo the SNTAP ocedue and fo futue wok. 2. AVALABLE METHODOLOGES The available methodologie fo decibing combined imay and econday tee may be conideed a oviding method fo etimating J a a function of the magnitude of the econday tee and the magnitude of the imay load. The fome deendence may be aumed to lead to a value J fo econday tee acting alone; the latte deendence may be eeented a a deendence on the load atio L. n the failue aement diagam (FAD aoach, thee deendencie ae combined though a definition of the aamete K uch that failue i conceded when K =f(l, whee f(l i the function decibing the failue aement cuve which i taken a indeendent of the econday loading. n thi ection, the available methodologie ae lagely dicued in tem of the definition of K but they can equally be exeed in tem of a cack diving foce (CDF, J. 2.1 The R6 Method Within R6 [3], K i defined by K = (K + K / K mat + ρ (1 whee K, K ae the linea elatic te intenity facto fo econday and imay tee, eectively, K mat i factue toughne and ρ i a facto which cove inteaction between the imay and econday tee. Method fo calculating ρ ae given in R6 Aendix 4. The detailed aoach in that aendix i to define ρ fom whee ρ = ψ - φ (K /K -1 (2 K i elated to the value of J fo the econday loading acting alone, J, though K = E J (3 wod\inta\929 2

3 SNTAP/NE/018 with E = Young modulu, E, in lane te and E = E/(1-ν 2 in lane tain, whee ν i Poion atio. The aamete Ψ and φ ae function of L and the atio [K/(K /L ], a tabulated in R6 Aendix 4. Full detail ae et out in R6 and thee ae not dicued hee. Howeve, thee ae a numbe of featue of the aoach which ae wothy of note, a follow: Fo zeo imay load, = 0 and φ = 1 o that eqn (1-3 coeond to failue being 2 conceded when K = K o equivalently when J = K / E. mat Thee ae a numbe of otion fo calculating K in deceaing ode of comlexity: - fom eqn (3 uing a value of J calculated fom an inelatic cacked body finiteelement analyi; - inelatic analyi of the uncacked body; - fom a latic zone ize coection to K ; - when econday tee ae low comaed to the yield te and elatic follow-u i judged not to be ignificant K may imly be elaced by K. The facto i negative fo lage L value (L > 1.05 and thi can lead to negative value of when K /K i not ignificantly le than unity. Thi then coeond to mechanical te elief of the econday tee. mat Negative value of can occu even at low mechanical load if K < K. Thi geneally coeond to latic elaxation of econday tee which ae elatically in exce of the yield te. t i alo woth noting that R6 alo contain a imlified ocedue fo evaluating which coeond to etimating K ~ K and doe not allow latic elaxation of econday tee though enuing The V Facto Within the SNTAP oject, Smith[4] ha uggeted that a facto, V, may be alied to the te intenity facto, K, to account fo laticity effect. Then, K i defined by K = (VK + K /K (4 mat At zeo imay load, V ha a value V = (5 o E J /K The ocedue fo uing V ha not been et out in the ame level of detail a that in R6 fo the aamete. Howeve, thee ae a numbe of featue of the aoach which ae wothy of note, a follow: wod\inta\929 3

4 SNTAP/NE/018 Fo zeo imay load, eqn(4-5 coeond to failue being conceded when 2 J = K mat/e o equivalently when K = K mat. The otion develoed in R6 fo etimating ince V =. o K/K K could equally be ued to etimate V o The facto V become le than unity fo lage L value coeonding to mechanical te elief of the econday tee. The atio V/V o i elatively inenitive to the magnitude of econday tee uggeting that a imlified ocedue fo etimating V could be develoed (ee Section 3 below. 3. COMPARSON OF and V METHODS A eview of technique fo teating eidual tee ha ecently been oduced by Smith [5]. Thi comaed the latet aoache in R6, a decibed in Section 2.1, with ealie method fo etimating and ecommended incluion of the ecent R6 method in eviion to PD6493 (now BS7910. Theoe, in thi ection attention i concentated on a comaion of the method in Section 2.1 with the V facto aoach of Section 2.2. n ode to make thi comaion, the backgound to eqn (2 i fit et out and thi then enable a elationhi between V and to be deived in Section 3.1. Then ome numeical eult fo V and ome imlified etimate of V ae eented in Section 3.2. Finally, the eult of thi ection ae biefly ummaied in Section Deivation of Paamete ρ and V The backgound to eqn (2 i et out in [6,7]. n [6], the combined effect of imay and econday tee i eeented by a eence te,,, fo the total loading. The value of J fo the combined loading i then 2 J = [ σ /f( σ Y ] πa/e (6 whee a ha dimenion of length and i defined by whee K 1 2 = σ ( πa (7 σ (8 = L σ Y Fo econday tee acting alone, the value of J i aumed to be given by J a obtained fom K by eqn (3. Following eqn (6, a eence te, σ fo the econday loading may then be obtained by olving σ /f( σ Y = V K /( πa o 1 2 = K /( πa 1 2 (9 wod\inta\929 4

5 SNTAP/NE/018 n [6], a method i eented fo deiving in tem of σ and σ. Thi lead to a value of J though eqn (6 o equivalently may be ued to deive in eqn (1 o V in eqn (4 uch that failue within the FAD method at K = f(l i conitent with that uing a CDF, 2 J = K /E. Thu, combining eqn (1,6,7,9 lead to mat f( σ Y K ( σ Y ρ = f(l - L + (10 ( σ Y K f( σ Y o combining eqn (4,6,7,9 give V V σ f(l f( σ L f( σ Y Y = - (11 o σ f( σ Y σ Y Equation (10 i identical to eqn (2 with ψ = f(l - f( σ ( σ Y L Y ( σ + f( σ Y Y (12 and f( σ φ = ( σ y y ( σ f( σ y y (13 a et out in [7]. Value of and φ have been obtained fom [6] leading to the table in R6 [3]. With thee aamete, eqn (11 can be imly exeed V/V o = 1+ ψ/ φ (14 t i aaent that the R6 aoach of Section 2.1 can be equally exeed a the V facto method of Section 2.2 ovided V i defined by eqn (14. Thi equie identical infomation to that in R6: value of K to define V o = K /K and the aamete φ and which ae function of L and (K L /K. 3.2 Numeical and Simlified Etimate of V Some limit to V may be deived. Fit, if laticity effect ae aumed to be negligible o that the failue aement cuve i flat (i.e. f (L ~1, then eone i elatic o that σ = σ + σ and V/V o = 1. Secondly, fo econday loading acting alone, =0 and φ = 1 o that again V=V o. Finally, fo lage value of L (>1.05, i negative o that V/ V o <1, coeonding to mechanical te elief. At intemediate value of L ome numeical eult ae hown in Figue 1; thee have been evaluated uing the value of φ and ψ in R6. Note, thee value ae baed on the R6 Otion 1 failue aement cuve, but ae not exected to be aticulaly enitive to the hae of that wod\inta\929 5

6 SNTAP/NE/018 cuve ince it ha aleady been noted that V/V o = 1 fo a hoizontal failue aement cuve. t can be een that V/V o inceae with inceaing L initially but only at modet ate. t i alo inenitive to the magnitude of the econday te, aticulaly fo L >0.9. Thi ugget that a imle aoximate aoach could be develoed a an altenative to eqn (14. Fo examle, Figue 1 include two aoximation V/V o = 1.25, L 0.9 V/V o = L 0.9 < L 1.4 (15 V/V o = 0.4 L > 1.4 V/V o = L L 0.8 V/V o = L 0.8 < L 1.4 (16 V/V o = 0.4 L > 1.4 Equation (15 bound the olution fo K /(K / L 2 and ue a contant value fo low L, imila to the aoximate method cuently in R6 which ue a contant value of ρ in thi egion. The lateau value could clealy be made a function of the magnitude of the econday te. Equation (16 ue a linea fit at low L and bound the olution fo K /(K / L 5. At value of L geate than 0.9, equation (15 and (16 ae identical and alo coeond to the imle ue of ρ = 0 in R6 fo L = At highe value of L, equation (14-16 coeond to mechanical te elief of the econday tee. The value of 0.4 ued fo L > 1.4 in eqn (15 and (16 i imly a bounding value to the numeical eult but in actice, full mechanical te elief (i.e. V = 0 ha been obeved exeimentally [1]. Clealy the aoximate aoache of eqn (15 and (16 could be ined baed on exeimental and finite-element data. Such data ae dicued in Section Summay of Comaion of ρ and V Method n ummay, it ha been hown that the and V aoache can be made fully comatible. Each method equie an etimate of the value of J due to econday loading acting alone: in R6 thi i exeed in tem of an effective te intenity facto K ; with the V aoach thi i exeed in tem of an initial value V o. Subequently, o V/ V o deend on the value of L and the magnitude of the econday tee a exeed in tem of the facto (K L /K. Table cuently in R6 can be ued to evaluate and V/ V o. Numeical eult fo V/V o ugget that thi atio i elatively inenitive to the magnitude of the econday te o that it may be oible to develo imle bounding cuve fo V/V o a a function of L. 4. VALDATON OF METHODOLOGES With SNTAP Tak 4, exeimental data have been geneated at AEA Technology in tet with and without eidual tee[1]. Thee coveed aluminium late tet with though cack and A533B teel late with uface cack. Analye of the aluminium late uing the detailed R6 aoach decibed in Section 2.1 geneally gave conevative undeetimate of alied load value fo vaiou amount of cack extenion. Thi geneal conevatim i wod\inta\929 6

7 SNTAP/NE/018 hown in Fig 2, taken fom [1], whee the exeimental data can be comaed to the R6 Otion 1 failue aement cuve. t i woth emaking that the R6 analye ae conitent with the econday tee having a educed effect with inceaing alied load. Thi i hown gahically in Fig 3, again fom [1], whee the atio of the load caying caacity of a late without eidual te to that of a late with eidual te i lotted a a function of the value of L at factue in the late with eidual te. The obevation fom the aluminium exeiment wee geneally confimed in the A533B tet but in thoe tet, R6 aement ignificantly undeetimated the exeimental failue load. Thi wa attibuted to the effect of cack ti containt fo the uface cack. The eult in [1] wee alo aeed in tem of the V aamete of Section 2.2. A the V and aoache can be made fully conitent, not uiingly the exeimental data wee alo conevatively aeed with the V method. Finite-element eult fo combined imay and econday tee have been geneated within SNTAP Tak 4 by SAQ[2]. Thee eult howed a aid deceae in the elative contibution to J of eidual tee, comaed to imay tee, fo high value of L. Comaion with R6 ediction, exeed in tem of a cack diving foce J, howed R6 to be conevative although the degee of conevatim wa deendent on the value of limit load ued to deive L. A the R6 analye wee conevative, it follow that the V aoach of Section 2.2 would alo be conevative, although the finite-element eult have not been oceed in thi way. Finite-element eult fo late with unde-, ove- and even-matched weld have alo been oduced by TW[4]. The eult fo V ae hown in Fig 4 which i imila to Fig 1 although educing to a value le than 0.1 fo L > Thu the eult again uot the method of Section 3.2, with V etimated a deicted in Fig 1. Fo the ovematched cae the eult ugget that the method of Section 3.2 may be ove-conevative. Outide SNTAP, validation of the R6 aoach ha been efomed [7]. A the V aoach can be made fully comatible with the aoach, Section 3, thi may alo be taken a validation of the V aoach. Howeve, it hould be ecognied that, aat fom analyi of exeimental data in [1], thee i little exeience with the ue of V. The choice of method deend lagely on eae of ue. n view of eqn(14, eaate table fo ψ and φ would not be equied fo the V aoach; intead a ingle table fo V/V o could be deived. Howeve, it hould be ecognied that while the aamete ha been hown to be inenitive to the hae of the failue aement cuve, i.e. that ψ and φ ae not enitive, it emain to be demontated that the atio ψ/φ i alo inenitive to the detail of the failue aement cuve. Note, thi i moe imotant at high value of L (> 1.05, ince at lowe L, failue aement cuve outide R6 Otion 1 ae exected to lead to value of V/V o cloe to unity than thoe in Figue 1, a dicued in Section 3.2. Thu, it eem udent to adot the R6 aoach of Section 2.1 within the SNTAP ocedue but to note that the V aoach i an altenative develoing methodology. Thi and othe ecommendation ae et out in Section 5 below. 5. RECOMMENDATONS On the bai of the eview and analyi decibed above, the following ecommendation ae made: wod\inta\929 7

8 SNTAP/NE/018 (a The SNTAP ocedue hould adot the R6 definition of K given in Section 2.1 with allowance fo elaxation of econday tee due to laticity being included though the otential fo ρ to become negative. (b (c (d (e The SNTAP ocedue hould mention the V aoach of Section 2.2 a an altenative develoing method and be witten in a manne which enable V and V o to be eadily evaluated though thei elationhi with the aamete K, φ and which ae defined in R6. The calculation leading to V/V o in Figue 1 hould be eeated fo diffeent hae of failue aement cuve, including the cuve in the SNTAP ocedue. Finite-element eult geneated within SNTAP, and elewhee, hould be comaed with the theoetical etimate of V/V o fom (c. The otential fo develoment of a imle bounding cuve fo V/V o a a function of L, o a table of value, hould be conideed on the bai of the eult of (c and (d. 6. REFERENCES 1. C C Fance, J K Shale and C Wignall, Exeimental ogamme to ae the influence of eidual tee on factue behaviou ummay eot, AEA Technology Reot AEAT-4236 ( P Delfin, Sattai-Fa and B Bicktad, Effect of themal and weld-induced eidual tee on the J-integal and CTOD in elatic-latic factue analye, SAQ Reot SNTAP/SAQ/03 ( Aement of the ntegity of Stuctue containing Defect, Nuclea Electic Pocedue R/H/R6; Aendix 4 Evaluation of K ( S D Smith, Comaion of the PD6493:1991 Rho( facto with FEA eult, TW Reot SNTAP/TW/1-2 ( S D Smith, A eview of tuctual aement technique fo yield tength mimatch and welding eidual tee, TW Reot 638/1998 ( R A Ainwoth, The teatment of themal and eidual tee in factue aement, Engng Fact Mech 24, ( D G Hooton and P J Budden, R6 develoment in the teatment of econday tee, ASME PVP Volume 304, (1995. wod\inta\929 8

9 SNTAP/NE/018 Figue 1 Numeical Reult fo V/V o fom Equation(14 and the R6 Table fo ψ and φ, and the Aoximation of Equation (15 and (16. wod\inta\929 9

10 SNTAP/NE/018 Figue 2 Aluminium Reidual Ste Tet Aeed uing the R6 Aoach of Section 2.1 and Comaed to the R6 Otion 1 Failue Aement Cuve, fom [1] wod\inta\929 10

11 SNTAP/NE/018 Figue 3 Ratio of Load Caying Caacitie of Plate with and without Reidual Stee a a function of L fo Aluminium Tet, fom [1]. The line ae imle fit Bounding the Data wod\inta\929 11

12 SNTAP/NE/018 Figue 4 Comaion of Equation (15 and (16 with Numeical Reult fom [4] fo Unde-, Even-, and Ove-matched Plate. wod\inta\929 12