AN EXPERIMENTAL AND ANALYTICAL STUDY OF CRACK GROWTH RETARDATION IN A STRUCTURAL STEEL

Transcription

1 AN EXPERIMENTAL AND ANALYTICAL STUDY OF CRACK GROWTH RETARDATION IN A STRUCTURAL STEEL Fath Darwsh 1, Marcos Perera 1, Marcelo Lopes 1, Arnaldo Camarão 2 and Sérgo Motta 3 1 Department of Materals Scence and Metallurgy / Catholc Unversty of Ro de Janero Rua Marquês de São Vcente 225, Ro de Janero / RJ, CEP , Brazl mlopes@dcmm.puc-ro.br, marcospe@dcmm.puc-ro.br, fath@dcmm.puc-ro.br 2 GEP / ArvnMertor CVS Av. João Batsta 825, Osasco / SP, CEP , Brazl arnaldo.camarao@arvnmertor.com 3 Technology Dvson / Braslamarras Rua Eng. Fábo Goulart 40, Nteró / RJ, CEP , Brazl shamotta@braslamarras.com Abstract The purpose of the present work s to test the valdty of the Wheeler model n predctng fatgue crack growth retardaton n welded steel jonts. The fatgue data were obtaned under constant ampltude loadng cycles and crack retardaton was effectvely nduced by applyng a sngle overload at a gven crack length. Ths made t possble to detere the crack growth retardaton factor γ, whch was then related to both the current and overload plastc zone szes. The results have ndcated that the delay perod predcted by the model s n far agreement wth that expermentally observed. The exponent nvolved n the power functon, as proposed by Wheeler for the factor γ, was calculated usng the expermental data and was found to vary along the crack growth delay perod. One may thus conclude that the Wheeler formulaton could lead to mprecse predctons of the retardaton n crack growth due to overloadng. Introducton It has been known for more than four decades that overload cycles of suffcent magntude can result n a transent retardaton n the rate of fatgue crack growth at the baselne level [1]. It s also well establshed that ths retardaton s closely related to the resdual compressve stress feld nduced n the vcnty of the crack tp [2]. Followng an overload cycle, the fatgue crack starts to advance nto the overload () plastc zone and the resdual compressve stresses n an element just behnd the crack tp are relaxed. Ths contrbutes to the level of crack closure n the wake of the crack tp, thus retardng fatgue crack propagaton. As the crack exts the plastc zone, the propagaton rate s generally back agan at the baselne level correspondng to the constant ampltude (CA) loadng. The model proposed by Wheeler [3] represents an approach to explan crack growth delays caused by hgh loads. The model recognzes that new plastc zones are created nsde the large monotonc plastc zone of an overload. A crack growth retardaton factor γ, whch s related to the szes of both the cyclc and monotonc plastc zones, was then

2 ntroduced by Wheeler, makng t possble for one to predct crack growth rate wthn the delay perod, (da/dn) VA, from the expresson: (da/dn) VA = γ (da/dn) (1) CA The present study was ntated to evaluate the applcablty of the Wheeler model to predctng fatgue crack growth retardaton brought about by a sngle overload cycle appled at a gven crack length durng CA loadng of an R3 grade structural steel. As ths grade steel s largely used for fabrcatng offshore moorng chans, the study was extended to nclude flash welded chan lnks both n the as-welded and welded and heat treated condtons. Expermental The steel used for ths nvestgaton was receved n the form of hot rolled round bars of crcular cross secton wth a noal dameter of 85 mm. The steel contans, n weght percent, 0.26% C, 1.2% Cr, 1.75% Mn, 0.35% N wth the balance beng Fe and traces of mpurty elements. The crcular bars were bent n conformty wth the typcal stud lnk geometry before they were butt flash welded [4]. Followng the weldng process, a number of lnks were austentzed at C for 90 utes, water quenched and then tempered at C for 90 utes. Compact tenson (CT) specmens were machned along the L T orentaton, n accordance wth the ASTM E recommendaton [5]. The CT specmens were cut off from the welded jont as well as from the opposte sde of the lnks n both as-welded and welded and heat treated condtons. The study, therefore, was carred out contemplatng four dfferent mcrostructural condtons: as-welded jont (AW), welded and heat treated jont (WH), as-receved base metal (BM) and heat treated base metal (BH). The specmen wdth, W, and specmen thckness, B, were taken as 32 and 8 mm, respectvely and a starter notch was machned to a depth of 7 mm. The specmen surfaces were polshed and fne lnes were drawn parallel to the specmen axs n order to facltate montorng crack growth durng cyclc loadng. Fnally, the CT specmens were precracked up to a crack length of 2 mm,.e., to a total crack length-to-specmen wdth rato, a/w, of The AW and WH specmens were precraked n a way such that the crack plane always concded wth the weld plane. CA cyclc loadng was appled to the precracked specmens so as to obtan the typcal da/dn versus K curves for the four mcrostructural condtons n queston. The tests were performed at room temperature usng a servo-hydraulc machne, operated at a frequency of 20 Hz. All of the CT specmens were submtted to a tenson-tenson mode I loadng wth a maxmum load of 9 kn and a load rato R (R = K / K max ) of 0.33 and fatgue crack length was montored usng a travelng mcroscope. Overload cycles were appled manually at a/w = 0.33 under load control by ncreasng the load to the desgnated level, gong down to the mum value of 3 kn and then returnng to the CA loadng scheme. The overload rato R, defned by K / K max [6], was taken as 1.5 and 1.8, whch corresponds to sngle overload levels of 13.5 and 16.2 kn,

3 respectvely, where the parameters K and K max are the overload stress ntensty factor and the CA maxmum stress ntensty factor, respectvely. Results and Dscusson Examples of the varaton of the fatgue crack growth rate da/dn wth K under CA and varable ampltude (VA) loadng are presented n Fgs 1-4. These fgures exemplfy the crack growth retardaton caused by the applcaton of a sngle overload. As expected the maxmum crack propagaton rate s reached only after a small crack length ncrement [7]. After passng ths mum, da/dn starts to ncrease and eventually returns, over some substantal further crack extenson, to the normal CA crack growth rate of the CA baselne cycles. The rato between the mum growth rate and the correspondng baselne rate, γ, s presented n Table 1, for the four mcrostructural condtons and the two overloads consdered n ths work. The fatgue crack length, a d, over whch the delay effect was detected, s also presented n the same table, together wth the correspondng overload plastc zone sze, (r ). Ths was calculated usng the followng expresson: p (r p ) = 1 K ( π σ ) 2 (2) Y where K s the stress ntensty factor calculated accordng to reference [5] and σ Y s the yeld stress, detered as 465, 500, 530 and 545MPa for the AW, WH, BM and BH condtons, respectvely. 0,001 da/dn (mm/cycle) 0,0001 0, Delta K (MPa.m 1/2 ) Wthout overloadng Wth overloadng FIGURE 1. Varaton of da/dn wth K for AW mcrostructural condton after an overload of 16,2 kn.

4 0,01 da/dn (mm/cycle) 0,001 0,0001 0, Delta K (MPa.m 1/2 ) Wthout overloadng Wth overloadng FIGURE 2. Varaton of da/dn wth K for WH mcrostructural condton after an overload of 13,5 kn. 0,01 da/dn (mm/cycle) 0,001 0,0001 0, Delta K (MPa.m 1/2 ) Wthout overloadng Wth overloadng FIGURE 3. Varaton of da/dn wth K for BM mcrostructural condton after an overload of 16,2 kn.

5 0,01 da/dn (mm/cycle) 0,001 0,0001 0, Delta K (MPa.m 1/2 ) Wthout overloadng Wth overloadng FIGURE 4. Varaton of da/dn wth K for BH mcrostructural condton after an overload of 13,5 kn. TABLE 1. Values of γ, a d and (r p ) accordng to the mcrostructural condtons. Specmen code γ d R = 1.5 R = 1.8 a / mm (r ) / mm p γ d a / mm (r ) / mm p AW WH BM BH The results presented n Table 1 ndcate that an ncrease n the overload rato R from 1.5 to 1.8 s more effectve n retardng crack growth n the welded jonts than n the base metal. Ths s clearly evdenced by comparng the values of γ assocated wth the appled overloads for each of the mcrostructural condtons n queston. The behavor of γ descrbed above s seen to be consstent wth what was reported, n a prevous work [8], on extendng the resdual fatgue lfe n these mcrostructures. The delay cycles number N was found to ncrease by a factor of about 7 for both AW and WH jonts as R was ncreased from 1.5 to 1.8. For the base metal, on the other hand, ths factor amounted to only about 1.5. Ths drastc dfference n behavor between the base metal and the welded

6 γ ECF15 jonts has been attrbuted to the fact that fatgue crack propagaton n the jonts occurs along a natural path represented by the weld plane [8]. Further, the marked mprovement n the fatgue behavor of the welded jonts, upon ncreasng the ntensty of overloadng, has been assocated wth crack growth retardaton mechansms, whch become ncreasngly operatve at hgher overloads. Mechansms such as crack bluntng [9], stran hardenng of the materal wthn the plastc zone [10] and crack surface asperty [11] seem to have ther effcency mproved by ncreasng the ntensty of overloadng, partcularly for the welded jonts. Accordng to the Wheeler model [3], the retardaton factor γ s assumed to be a power functon of the rato r p, / λ, where r p, s the current plastc zone sze correspondng to a gven crack length a and λ the dstance between the crack tp and the edge of the plastc zone. Thus s expressed as: γ m = (r p, / λ ) (3) where the exponent m s an emprcal constant dependent on the type of the VA load hstory. The current plastc zone sze r can be calculated from the expresson below: p, where crack length r = p, K max 1 K ( max 2 ) (4) π σ Y s the maxmum stress ntensty factor correspondng to the CA loadng for a a. For ths crack length, λ s gven by the expresson: λ = + (r ) - a (5) a0 p where a 0 s the crack length at whch the overload was appled. As the crack propagates through the delay zone, r p, becomes larger whereas λ gets smaller. As a result, γ wll ncrease gradually from ts mum value γ to a maxmum value of unty as the far edge of the current plastc zone starts to ext the plastc zone and the delay effect would thus be gone. Wth ths n d, one can estmate a d from: = + (r ) - ( + r ) (6) a d a0 p a p, where a s the crack length necessary for the current plastc zone to reach the far edge of the plastc zone. a d The values estmated from the above relaton are lsted n Table 2 n comparson wth the values detered from the expermental data. One can conclude from ths comparson that the delay perod measured expermentally agrees farly well wth the correspondng a d value estmated from equaton (6) for each of the mcrostructural condtons consdered n ths study.

7 TABLE 2. Values of a d, a d and m accordng to the mcrostructural condtons. Specmen code R = 1.5 R = 1.8 a d / mm / mm m ad / mm / mm m a d a d AW ± ± 0.4 WH ± 0.3 BM ± ± 0.2 BH ± 0.1 An expermental value of γ, correspondng to a gven crack length wthn the delay zone, a d, can be used to estmate the exponent m by substtutng n equaton (3) the approprate r and λ values calculated, respectvely, from equatons (4) and (5). The p, value of m thus obtaned was found to vary wth the crack length, gvng rse to a consderable degree of scatter as can be verfed from Table 2. The use of the average m values lsted n ths table may lead ntally to overestmatng the retardaton factor γ, and as crack propagaton proceeds, the value of γ would tend to be underestmated. These observatons appear, as ponted out by Schjve [7], to corroborate the lmtatons of the Wheeler model n predctng the crack growth behavor under VA loadng. a a Conclusons From what s presented above, the followng conclusons can be drawn: The extent of the fatgue crack growth retardaton perod predcted by the Wheeler model agrees farly well wth the expermental observatons made on flash welded steel jonts as well as on the base metal. An ncrease n the ntensty of overloadng results n a more effectve crack growth retardaton as evdenced by an observed decrease n the mum propagaton rate, wth the effect beng more pronounced for the welded jonts than for the base materal. The form of the power functon proposed by Wheeler for the retardaton factor mples n dfferent values of the exponent m as calculated from the expermental data. A sngle value of that exponent would therefore lead to mprecse estmates of the crack propagaton rate along the delay perod. References 1. Schvje, J., Fatgue Crack Propagaton n Lght Alloy Sheet Materals and Structures, Natonal Luchtvaart Laboratorum, Report No.MP-195, 1960.

8 2. McEvly, A.J. and Ishhara, S., In Proceedngs of the Fatgue 2001 SAE Brazl - Internatonal Conference on Fatgue, edted by P.M. Pmenta, L.C. Rcardo and A.F. Camarão, SAE Brazl, São Paulo, 2001, Wheeler, O.E., J. Basc Eng., vol. 94, , ABS, Gude for Certfcaton of Offshore Moorng Chans, ABS, New York, USA, ASTM, Standard Test Method for Measurements of Fatgue Crack Growth Rates, ASTM, Warrendale, USA, Decoopman, X., Imad, A., Abdelazz, N.M. and Mesmacque, G., In Proceedngs of the 12 th Bennal Conference on Fracture - ECF 12, edted by M.W. Brown, E.R.de los Ros and K.J. Mller, EMAS, Cradley Heath, 1998, Schjve, J., Fatgue of Structures and Materals, Kluwer Academc Publshers, Dordrecht, The Netherlands, Lopes, M.R., Perera, M.V., Darwsh, F.A. and Camarão, A.F., In Proceedngs of the Eghth Internatonal Fatgue Congress - Fatgue 2002, edted by A.F. Blom, EMAS, Cradley Heath, 2002, Hammouda, M.M.I., Ahmad, S.S.E., Sherbn, A.S. and Sallam, H.E.M., Fatgue Fract. Engng, Mater. Struct., vol. 22, , Knott, J.F., Metal Sc., vol. 11, , Suresh, S., Engng. Fract. Mech., vol. 18, , 1983.