Computers and Structures

Transcription

1 Computers and Structures 118 (2013) Contents lsts avalable at ScVerse ScenceDrect Computers and Structures journal homepage: Materal plastc propertes characterzaton by couplng expermental and numercal analyss of small punch beam tests Xngguo Zhou, Wenke Pan, Donald Mackenze Department of Mechancal Engneerng, Unversty of Strathclyde, Glasgow, UK artcle nfo abstract Artcle hstory: Receved 25 June 2012 Accepted 2 July 2012 Avalable onlne 31 July 2012 Keywords: Small punch beam test Plastc propertes characterzaton Genetc algorthm nte element analyss A novel small punch beam testng (SPBT) system consstng of a top de, a bottom de and a flat punch wth sem-crcular cross-secton head has been desgned and tested. The specmen s a small beam wth rectangular cross-secton. Ths SPBT method has the advantage over conventonal tensle testng for much less materal requred for testng and also over the tradtonal small punch testng because not only less materal requred but also hgh accuracy to make the punch head. Through couplng the numercal modellng and expermental results, genetc algorthm has been employed to successfully characterze the materal plastc propertes. Ó 2012 Elsever Ltd. All rghts reserved. 1. Introducton The small punch testng (SPT) technque was developed to characterze materal propertes n the late 1970s [1]. In the test, a cylndrcal punch wth a hemsphercal head deforms a thn dsc shape specmen, whch s clamped between two co-axal hollow cylndrcal des. The thckness of the sample can be as small as 0.5 mm or 0.25 mm and the dameter s about 6 to 10 mm. Comparson of SPT results wth conventonal tensle testng (CTT) method s very encouragng. To date, materal propertes that have been evaluated by SPT nclude elastc modulus, plastc deformaton propertes such as yeld stress and tensle strength [1 5], creep propertes [6 8] and fracture propertes [9 11], etc. Several natonal assocatons have consdered or are currently nvestgatng testng standards for SPT. The Japan Atomc Energy Research Insttute has produced practce recommendatons for small punch (SP) testng of metallc Materals n 1988 [12]. CEN publshed Small Punch Test Method for Metallc Materals Part A: A Code of Practce for Small Punch Creep n 2005 [13] and Part B: A Code of Practce for Small Punch Testng for Tensle and racture Behavor n 2006 [14]. The Amercan Socety for Testng and Materals has ssued a standard test method for small punch testng of ultra-hgh molecular weght polyethene used n surgcal mplants n 2008 [15]. The progress [16] of standardzaton of small punch test n Chna was reported n One practcal advantage of SPT over conventonal tensle testng s that the specmen sze s relatvely small and therefore only Correspondng author. E-mal address: wenke.pan@strath.ac.uk (W. Pan). small quantty of materal s requred for testng. Ths s partcularly useful when testng materal from operatng plants for lfe extenson programs, as the small amount of materal requred can often be removed from the surface of components wthout plant shutdown and ntrusve welded repars are not requred afterwards. One dsadvantage of SPT s the dffculty and expense of manufacturng the 2.5 mm dameter hem-sphercal head punch to the requred dmensonal accuracy. To overcome ths problem, an alternatve Small Punch Plane Stran (SPPS) test system wth a cylndrcal punch contact surface and rectangular test specmen was proposed [17]. Ths has been successfully used to characterze materal s plastc propertes, wth Ramberg Osgood consttutve relatonshp employed. Recently, nstead of usng rectangular specmens, Sehgal et. al [18] used mnature samples for ther punch tests. The yeld strength and fracture toughness of de steel D3 and Chromum steel H11 were evaluated and compared wth the values obtaned from standard tests. Ther smulated load-dsplacement curves were n good agreement wth the results obtaned expermentally, however, as the dstance between the lower des s just a lttle bt larger than the thckness of the specmen the deformaton n the specmen s qute complex. To characterze materal propertes usng the small punch testng method, tral and error methods, a genetc algorthm method [17] and neural network method [19], etc. have all been used. In ths paper, a small punch testng system based on a small beam shape specmen and punch smlar to that of SPPS s presented. Materal propertes are evaluated from the deformaton through comparson wth mult-lnear stran hardenng nte Element analyss of specmen deformaton and a genetc algorthm utlzng a cost functon based on the relatve dfference between the /$ - see front matter Ó 2012 Elsever Ltd. All rghts reserved.

2 60 X. Zhou et al. / Computers and Structures 118 (2013) expermental and testng forces at the top centre of the beam. The small punch beam testng tool desgn wll be presented n the Secton 2, whle experment procedure wll be gven n Secton 3. EM modellng s presented n Secton 4, materal property characterzaton usng a genetc algorthm method n Secton 5 and results n Secton Small punch beam testng tool desgn The standard small punch test (SPT) tool employs an upper and a lower hollow cylndrcal shape de and a cylndrcal punch wth hemsphercal punch head. To avod the hgh cost and low accuracy for manufacturng hemsphercal punch head, the new desgned tool testng system shown n g. 1 has been developed. The tool conssts of top and bottom blocks, each havng a narrow through slot. The test beam specmen s located n a shallow slot perpendcular to the through slot. The punch s a rectangular bar wth a halfcylnder profle contact surface, overcomng the manufacturng dffcultes assocated wth a hemsphercal punch. The radus of the punch head s 1.25 mm and the wdth of the punch s 8 mm. The test specmen shown n g. 2 s a beam wth rectangular cross secton wth wdth of 2mm and heght of 1.6 mm. The heght of the beam s slghtly greater than the depth of the shallow slot, such that when the four fxng screws are tghtened the beam sample s fully clamped. The central part of the beam s 8 mm and an addtonal 4 mm or more of materal s ncluded at both ends to hold the beam. Chamfers wth sze 0.2 mm 45 o were created on the bottom slot to avod stress sngularty. The four screws were tghtened wth same torque usng a torque wrench to keep the top and bottom surfaces parallel. The punch s guded by the slot n the top block. The bottom block s made of two peces, makng the chamber easer to manufacture. The top and bottom blocks and punch are made of stanless steel, whle the tested specmen s alumnum AA2024 wth chemcal composton n weght percentage shown n Table 1. The specmen materal Young s modulus and Posson s rato are 73.1 GPa and 0.3, respectvely. Lubrcant was appled to the punch top surface and the sde surface to reduce the frcton between the punch and specmen and punch and the top block slot. 3. Experments The small punch beam testng tool system was ftted to a Denson Mayes materal testng machne and the force appled to the punch and the dsplacement of the machne movement were recorded. The maxmum speed of the press head was set to 1 mm per mnute; therefore, the stran rate of the specmen s small and dynamc effects are not consdered. The test was termnated when the press head dsplacement reached 0.9 mm and then the press head was released. The recorded force and dsplacement were the force appled onto the specmen and dsplacement of the central pont on the beam top surface: frcton, punch weght and the elastc deformaton of punch are assumed to be neglgble. The typcal punch force-dsplacement s shown n g. 3. The specmen ntally deformed elastcally n regon A, followed by elastc and plastc deformaton n regon B. In regon C, when large deformaton occurs, damage s accumulated wthn the specmen and the materal shows softenng behavor wth the total force decreasng. In the fnal regon D, specmen fals as the crtcal crack length s reached. 4. EM modellng 4.1. Geometry g. 2. Specmen for small punch beam test. Table 1 Chemcal composton of AA2024 n Wt.%. Component Al Mg S Cr Mn Wt.% Max 0.5 Max Component T Cu Zn e Other Wt.% Max Max 0.25 Max 0.5 Max 0.15 The am of the nvestgaton s to characterze materal plastc propertes through the comparson between numercal and expermental results. The nte Element Method model shown n g. 4 conssts of a specmen, a top block, a bottom block and a punch. g. 1. Small punch beam test tool system.

3 X. Zhou et al. / Computers and Structures 118 (2013) rffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff r ¼ 1 2 ½ðr 1 r 2 Þ 2 þðr 2 r 3 Þ 2 þðr 3 r 1 Þ 2 Š where r 1, r 2 and r 3 are the prncple stresses Boundary condtons and loadng ð1þ g. 3. Typcal small punch testng force vs. dsplacement curve. Both top block and bottom blocks were fully constraned. The punch s assumed to be a rgd body and a reference pont assgned to t n ABAQUS, such that only ths reference pont s requred to be constraned. The three rotaton degrees of freedom and the two translaton degrees of freedom wthn the horzontal plane were set to 0. The load appled to the specmen was replaced by vertcal dsplacement control of the punch. The reacton force from the ABAQUS model correspondng to ths constrant corresponds to the force appled to the specmen Contact and frcton coeffcent The ABAQUS/mplct fnte element code was used for the smulaton. The steel punch s treated as a rgd body as t s sgnfcantly stffer than the alumnum test specmen. The top and bottom blocks were modelled as elastc bodes. The length between the two nner surfaces of the bottom block s 8mm and the wdth and the heght of the beam cross secton are 1.6 mm and 2 mm, respectvely Materal model g. 4. EM geometrcal model. As the specmen s alumnum AA2024-T3, an oxde layer was formed on ts surface when t was exposed to the atmosphere. As ths oxde layer s very thn, ts nfluence on the mechancal propertes of specmen was not consdered. The mult-lnear stran hardenng materal model shown n g. 5 was used n the ABAQUS numercal smulaton, wth S1, S2 and S3 representng the ntal yeld stress, proof stress (at 0.2% plastc stran) and ultmate tensle strength, respectvely. The materal wll yeld and plastc deformaton occurs when von Mses stress reaches the yeld surface, whch s assumed to be a functon of equvalent plastc stran. The von Mses stress r s represented as Contact between the punch head and specmen top surface, specmen and top block and specmen and bottom block were consdered n the ABAQUS model. The nfluence of the frcton coeffcent on the punch force versus the top surface mddle pont dsplacement was nvestgated. As lubrcant was appled to punch top, the frcton coeffcent was assumed to be zero, whle the frcton coeffcent between the top block and specmen, bottom block and specmen were fnally set at 0.3. The default penalty formulaton n ABAQUS/Standard mplct codes was appled Mesh convergence The ABAQUS three dmensonal brck element C3D20R wth reduced ntegraton was used n the analyss. our dscretsaton cases, as shown n g. 6(a) to (d), were nvestgated. The mesh used n characterzaton of materal propertes by the Genetc Algorthm method was selected by consderng the CPU requrements and the accuracy of the analyses, as reported n Secton Materal propertes characterzaton usng genetc algorthm method The Genetc Algorthm (GA) [20] optmzaton method s based on a smple natural rule: survval of the fttest. The ftter creatures wll have more chances to survve and to produce off-sprng. The GA method s appled to characterze the materal nonlnear plastc parameters. The am s to use the GA to search for the best values for a set of materal parameters by comparng the fnte element and expermental results. The total dsplacement s dscretzed unformly nto n segments; therefore, wthout consderng the ntal pont, there are n values of dsplacement u ( =1,2,...,n) and ther correspondng force values are ( =1,2,...,n). However, as the expermental and fnte element method results may not fall exactly at the dscretzed dsplacement pont, a lnear nterpolaton method s used to obtan the correspondng force value. Shown n g. 7, assumng u falls wthn the expermental or fnte element method consecutve ponts u j and u j+1, the force correspondng to u can be calculated as ¼ j þ u u j u jþ1 u j ð jþ1 j Þ ð2þ g. 5. Materal stress vs. plastc stran relatonshp. A flow chart of a general GA optmzaton procedure s gven n g. 8. Eq. (3) shows the formulaton of the objectve functon U, whch s defned as the square root of the average of the summaton of the square of the relatve dfference between the expermental and numercal results. The ftness s smply chosen as the nverse of the objectve functon,.e. f ¼ 1 U

4 62 X. Zhou et al. / Computers and Structures 118 (2013) (a) (b) (c) (d) g. 6. EM model wth dfferent mesh sze near the beam center: (a) 0.4 mm, (b) 0.3 mm, (c) 0.2 mm and (d) 0.15 mm. vffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff! u1 X n cal exp 2 U ¼ t n exp ¼1 j + 1 j u u j u j + 1 g. 7. dsplacements and ther correspondng forces. where exp and cal are the expermental and fnte element method punch forces correspondng to the th dsplacement u. or ths case, the lnear nterpolaton method was used. u ð3þ Smaller values of the objectve functon correspond to the larger values of the ftness. The general GA procedure conssts of ntalzaton, selecton, crossover and mutaton, wth a hgher ftness seed havng more chance to be selected and one of the fttest offsprng at each generaton always beng kept. The GA procedure stops when the convergence crteron s satsfed. One example of selecton, cross over and mutaton from generaton 0 to generaton 1 of the GA method, s descrbed as follows. As the materal propertes to be characterzed are S1, S2 and S3, the range of ther values are set at start. or ntalzaton, S1, S2 and S3 are randomly assgned an nteger from 0 to 255. At the start, chromosomes wth the ntegers from 0 to 255 are represented as 8- dgt bnary strngs. At teraton 0, there are 20 seeds for each set of S1, S2 and S3, and each seed can be lnearly mapped to the parameters S1, S2 and S3 used n the E models, as shown n g. 9. These 20 seeds are ranked accordng to the objectve functon value calculated from the correspondng E analyss: the seed wth the smallest objectve functon ranks frst, whle the seed wth the largest objectve functon ranks last. The selecton operator s to delete the last seed for preparaton of the next procedure cross over. The cross over procedure randomly selects a par of seeds from seed numbers 1 to 18 and exchanges ther genes at a random poston. Ths procedure s contnued untl all seeds from seed Φ < Φ 0 g. 8. low chart of the genetc algorthm.

5 X. Zhou et al. / Computers and Structures 118 (2013) g. 9. Mappng parameters from ntegers to real. Punch force, N Expermental results Numercal results orce, N Dsplacement, mm g. 11. Comparson between experment and EM numercal force vs. dsplacement results. and S3 respectvely and the newly generated seed s numbered as new seeds for the next teraton are then prepared. 6. Results 6.1. Expermental results Dsplacement, mm g. 10. The two experment force vs. dsplacement results. Two tests were performed and the test results are shown n g. 10. Due to the accuracy of the testng machne, the testng results fluctuate. However, from ths fgure, t can be seen clearly that the test results are qute consstent. In ths paper, we am to present a novel desgn and a GA method to characterze materal plastc parameters; therefore, only the specmen 2 results were used for ths purpose. To make the comparson easer, the average expermental results were compared wth EM results. Table 2 Comparson of punch force at dfferent mesh sze. Case Mesh sze (mm) orce appled onto specmen (N) Relatve dfference to the fnest mesh (case 4)% NA Table 3 Influence of frcton coeffcent on the punch force at top surface mddle pont dsplacement of 0.85 mm. rcton coeffcent Punch force, N Table 4 Objectve functon U vares wth teraton number. Iteraton No Objectve functon U number 1 to 18 are selected and crossed-over, gvng new seeds numbered from 1 to 18. nally, three seeds from 0 to 18 are randomly selected and mutated at random postons to obtan S1, S nte element results g. 6(a) to (d) show the meshes wth element sze of 0.4 mm, 0.3 mm, 0.2 mm and 0.15 mm for the central part of the beam. Table 2 dsplays the punch force correspondng to punch vertcal dsplacement of 0.9 mm under dfferent element sze. The relatve dfference of the reacton force to the fnest mesh s also shown n ths table. rom ths table, t can be concluded that the model wth mesh sze of 0.2 mm, g. 6(c), gves a good balance between accuracy and CPU tme and the results reported here were based on ths mesh. To nvestgate the nfluence of the frcton coeffcent on the punch force-dsplacement curve, dfferent frcton coeffcents between upper de and specmen and lower de and specmen were assgned to the E model. The smulaton results are shown n Table 3, from whch t can be seen that the punch force ncreases wth ncreasng of frcton coeffcent. By comparng these results, t s found that the maxmum relatve dfference s less than 4.5%. In ths paper, frcton coeffcent of 0.3 s used GA method results Table 4 shows the hstory of evoluton of the mnmum objectve functon U of generaton varyng wth teraton number. At the begnnng of the GA procedure, all seeds are randomly generated and the lowest objectve functon value s The bnary strng for the best seed s [ ], [ ] and [ ] and ther correspondng S1, S2 and S3 values are MPa, MPa and MPa. rom Table 4, t can be seen that gener-

6 64 X. Zhou et al. / Computers and Structures 118 (2013) (a) (b) (c) g. 12. The von Mses stress contours of the specmen at dfferent top surface mddle pont dsplacement: (a) mm, (b) 0.5 mm and (c) 0.89 mm. ally the mnmum value of the objectve functon decreases as the teraton number ncreases. The value of the mnmum objectve functon wll eventually reach a certan value, leadng to the convergence of the GA. In ths paper, after evoluton of 20 generatons, the mnmum U reaches The bnary strngs for ths generaton are [ ], [ ] and [ ] and ther correspondng S1, S2 and S3 values are MPa, MPa and 509 MPa respectvely. The ultmate tensle strength s very close to the 496 MPa report n Ref. [21]. Comparson of the expermental and fnte element punch force-dsplacement curves s shown n g. 11, from whch t can be seen that the predcted results are n good agreement the expermental results. After obtanng the materal plastc parameters, the EM smulaton results produced usng the optmal parameters values were re-nvestgated. g. 12(a) to (c) show the stress contours at the top surface mddle pont dsplacement of mm, 0.5 mm and 0.89 mm, respectvely. rom g. 12(a), t can be seen that apart from the contact pont between punch and specmen, the maxmum stress was less than the 0.2% proof stress and the hgh stresses occurred n elements close to the mddle ponts of the top and bottom surfaces. Ths shows the beam deformaton behavour. By checkng the punch force versus specmen top surface mddle pont dsplacement, t s found that ths stage corresponds to lnear elastc deformaton n the specmen. Wth hgher punch force appled onto the specmen, the maxmum von Mses stress exceeded the yeld stress and plastc deformaton developed n the specmen. rom g. 12(b) and (c), t s clear that the locaton of hgh stress n the elements expanded from the mddle ponts of the top and bottom surfaces to the centre of the specmen and the areas near the bottom support regons also have hgh stresses. 7. Conclusons and future work Based on the above results, t s concluded that: (1) The novel small punch beam testng tool system presented has an advantage over conventonal tensle testng n that much less sample materal s requred. It also has an advantage over the semsphercal head small punch test, as the cylndrcal shape punch head s much easer to manufacture wth hgh accuracy and low cost. (2) As the test specmen are smaller than the conventonal SPT specmen, the same amount of materal removed from an n-servce component could make more specmens, or, to produce same number of specmens wll requre less materal to be removed from components. (3) The small punch beam testng results are consstent, makng the testng method a sutable canddate method for materal property characterzaton. (4) The GA method has been successfully used to characterze the materal plastc parameters. The calculated punch force dsplacement results are n good agreement wth expermental results. or future work, beam specmens wll be tested to falure and characterzaton of materal damage parameters wll be nvestgated. If ths can be acheved t would enable numercal estmaton of materal fracture toughness. The beam dmensons could also be further reduced to thckness of 0.5 mm, wdth of around 1 mm and length of 6 to 8 mm. Ths wll requre less materal compared to the beam specmens used n ths research. Other methods, such as the neural network method, wll also be used to characterze materal property parameters.

7 X. Zhou et al. / Computers and Structures 118 (2013) Acknowledgements The author Xngguo Zhou would lke to thank the fnancal support by Scottsh Overseas Research Student Awards Scheme and Unversty of Strathclyde. References [1] Manahan MP, Argon AS, Harlng OK. The development of mnnaturzed dsk bend test for the determnaton of postrradaton mechancal propertes. Journal of Nuclear Materals 1981;103&104: [2] Egan Patrck, Whelan Maurce P, Lakestan ereydoun, Connelly Mchael J. Small punch test: an approach to csolve the nverse problem by deformaton shaper and fnte element optmzaton. Comput Mater Sc 2007;40:33 9. [3] Isseln J, Iost A, Golek J, Najjar D, Bgerelle M. Assessment of the conbsttutve law by nverse methodology: small punch test and hardness. J Nucl Mater 2006;352: [4] Steven M, oulds Jude R, Jewett Charles W, Srvastav Sanjeev, Eddn Avram A. Valdaton of a small punch testng technque to characterze the mechancal behavour of ultra-hgh-molecular-weght polyethylene. Bomaterals 1997;18: [5] Karthk V, Vsweswaran P, Vjayraghavan A, Kasvswanathan KV, Raj Baldev. Tensle-shear correlatons obtaned from shear punch test technque usng a modfed expermental approach. J Nucl Mater 2009;393(3): [6] Mlcka Karel, Dobes erdonand. Small punch testng of P91 steel. Int J Pressure Vessels Ppng 2006;83: [7] Kobayash Ken-ch, Tabuch Masaak, Stratford Gavn C. Creep Rupture lfe of weldng components n P92 errtc steel usng small punch creep test. Metal J 2010;LXIII:54 8. [8] Blagoeva DT, Hurst RC. Applcaton of the CEN (European Commttee for Standardzaton) small punch creep testng code of practce to a representatve repar welded P91 ppe. Mater Sc Eng 2009;A : [9] Mao X, Takahash H. Development of a further-mnaturzed specmen of 3 mm dameter for tem dsk small punch tests. J. Nucl Mater 1987;150: [10] oulds J, Vswanathan R. Small punch testng for determnng the materal toughness of low alloy steel components n servce. J Eng Mater Technol 1994;116(4):457. [11] L Yngzh, Hurst Roger, Matocha Karel, Czek Peter, Blagoeva Darna. New approach to determne fracture toughness from the small punch test. Metal J 2010;LXIII: [12] Takahash H, Shoj T, Mao X, Hamaguch Y, Msawa T, Sato M Oku T, Kodara T, ukaya, K Nsh H, Suzuk M. Recommended practce for small punch (SP) testng of metallc Materals, JAERI-M; September 1988: [13] CEN, Small punch test method for metallc materals. Part A: A Code of Practce for Small Punch Creep, [14] CEN, Small punch test method for metallc materals. Part B: A Code of Practce for Small Punch Testng for Tensle and racture Behavor, [15] ASTM (2008) Standard test method for small punch testng of ultrahgh molecular weght polyethylene used n surgcal mplants. [16] Guan Ka-shu, Wang Zh-wen, Xu Tong, Shou B-nan. Development of small punch test n Chna. Czech Metal J 2010;LXIII. [17] Pan W, Boyle Jm, Ramlan Mohd, Dun Crag, Ismal Mohd, Hakoda Kenj. Selected for Czech Metallurgcal Journal 2010; LXIII: [18] Sehgal DK, Husan A, Pandey RK. The Rectangular Shaped Mnature Specmen to study the Mechancal Behavor of Materals. In: 2nd nternatonal conference on Mechancal and electroncs engneerng (ICMEE), vol. 1, Kyoto, 2010; [19] Abendroth M, Kuna M. Determnaton of deformaton and falure propertes of ductle materals by means of the small punch test and neural networks. Comput Mater Sc 2003;28: [20] Castro C, Antono CAC, Sousa LC. Optmsaton of shape and process parameters n metal forgng usng genetc algorthms. J Mater Process Technol 2004;146: [21] [accessed ].