Critical Void Volume Fraction f c. at Void Coalescence for S235JR Steel at Low Initial Stress Triaxiality

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IOP Conerene Series: Materials Siene and Engineering PAPER OPEN ACCESS Critial Void Volume Fration at Void Coalesene or S235JR Steel at Low Initial Stress Triaxiality To ite this artile: Pawe

1 IOP Conerene Series: Materials Siene and Engineering PAPER OPEN ACCESS Critial Void Volume Fration at Void Coalesene or S235JR Steel at Low Initial Stress Triaxiality To ite this artile: Pawe Grzegorz Kossakowski and Wiktor Wilik 2017 IOP Con. Ser.: Mater. Si. Eng Related ontent - Considerations on stress triaxiality variation or 2P armor steel V Zihil, A Coseru, F Nede et al. - Void growth in high strength aluminium alloy single rystals: a CPFEM based study Umair Asim, M Amir Siddiq and Murat Demiral - 3D analyses o dutile ailure in metal reinored bystaggered ibres Viggo Tvergaard View the artile online or updates and enhanements. This ontent was downloaded rom IP address on 30/06/2018 at 03:37

2 Critial Void Volume Fration at Void Coalesene or S235JR Steel at Low Initial Stress Triaxiality Paweł Grzegorz Kossakowski 1, Wiktor Wiślik 1 1 Kiele University o Tehnology, Kiele, al. Tysiąleia Państwa Polskiego 7, Poland kossak@tu.kiele.pl Abstrat. The paper is onerned with the nuleation, growth and oalesene o mirodeets in the orm o voids in S235JR steel. The material is known to be one o the basi steel grades ommonly used in the onstrution industry. The theory and methods o damage mehanis were applied to determine and desribe the ailure mehanisms that our when the material undergoes deormation. Until now, engineers have generally employed the Gurson-Tvergaard- Needleman model. This material model based on damage mehanis is well suited to deine and analyze ailure proesses taking plae in the mirostruture o S235JR steel. It is partiularly important to determine the ritial void volume ration, whih is one o the basi parameters o the Gurson-Tvergaard-Needleman material model. As the ritial void volume ration reers to the ailure stage, it is determined rom the data olleted or the void oalesene phase. A ase o multi-axial stresses is onsidered taking into aount the eets o spatial stress state. In this study, the parameter o stress triaxiality η was used to desribe the ailure phenomena. Cylindrial tensile speimens with a irumerential noth were analysed to obtain low values o initial stress triaxiality (η = o the range) in order to determine the ritial void volume ration. It is essential to emphasize how unique the method applied is and how dierent it is rom the other more ommon methods involving parameter alibration, i.e. urve-itting methods. The ritial void volume ration at void oalesene was established through digital image analysis o suraes o S235JR steel, whih involved studying real, physial results obtained diretly rom the material tested. 1. Introdution Nuleation and growth o deets in the material mirostruture are the main auses whih initiate the ailure proess. Due to their relative high stiness, miro-deets orm avities, denoted as voids, during the material deormation proess. The voids evolution determines the mehanisms o material damage. This problem is very omplex due to a lot o phenomena and ators, inluding distributions o voids in the mirostruture at the initiation phase, void nuleation, anisotropy o the shape and spaing o the inlusions, hanges o void shapes during the material deormation, interations between voids and the evolution o seondary voids near oalesene. These proesses are modelled basing on dierent onepts o damage mehanis. The main problem is a high level o omplexity o partiular material models, whih limit the possibility o their pratial appliations. One o the key step whih aet the material ailure phenomena is the void oalesene, shown shematially in igure 1. Voids nuleated at inlusions and preipitations grow due to deormations o the material matrix. With a signiiant eet o loalized plasti strains, the voids link together, Content rom this work may be used under the terms o the Creative Commons Attribution 3.0 liene. Any urther distribution o this work must maintain attribution to the author(s) and the title o the work, journal itation and DOI. Published under liene by Ltd 1

3 reating the avities. Due to onsiderable size o suh void ormation, this proess leads inally to the material rature. Figure 1. Sheme o the void oalesene The knowledge about damage mehanisms taking plae in the material mirostruture is very important, rom sientii as well as pratial point o view. By using several damage models now it is possible to model the ailure proesses and perorm numerial analysis. There are a lot o engineering omputer programs that allow to simulate the material ailure and struture ollapse. Basi problem is onneted with material onstants neessary or appliation o material models based on the damage mehanis. There is a lak o onstants or many strutural materials, inluding strutural steels used in engineering. This study is onerned with determination o one o the Gurson-Tvergaard-Needleman (GTN) material model parameters. This model is based on damage mehanis and allows to deine and analyse ailure proesses observed in many kinds o materials. The ritial void volume ration, whih is one o the basi GTN parameters, is onsidered in the study. It is determined or one o the basi strutural steel grade, S235JR, ommonly used in ivil engineering. The ritial void volume ration at void oalesene is established in the ase o low initial stress triaxiality. To this end, the digital image method was applied, whih involved studying real, physial results obtained diretly rom the material tested. 2. Critial void volume ration at void oalesene History o material models whih attempt to desribe ailure phenomena taking plae in the mirostruture and link them with the materials response is dated bak to the mid-twentieth entury [1]. They have been developed until today [2-10], as well as ombinations o dierent methods, eg. [11]. Quite an advaned onept was proposed in 1977 by Gurson [2], who modiied original Huber- Mises-Henky hypothesis. Gurson introdued to the yield potential untion the material damage parameter in the orm o void volume ration [2]. As the eet, he took into onsideration the inluene o the number o mirodeets on the material strength. Original Gurson material model was modiied and developed later during several years. In order to desribe the hanges in stress state taking plae during deormation due to void nuleation and growth, original Gurson yield potential was modiied by Tvergaard and Needleman [12, 13]. They redeined void volume ration parameter aording to the ollowing untion [13]: * 1/ q1 F where: ritial void volume ration orresponding to the onset o void oalesene, F ritial void volume ration orresponding to the material ailure, q 1 Tvergaard s oeiient. or or (1) 2

4 It allowed to desribe the phenomena observed in the material or the range o deormation when the value o is higher than ritial parameter. Critial void volume ration orresponds to the onset o void oalesene. Together with Tvergaard s oeiient q 1 and ritial void volume ration F whih orresponds to the material ailure, ritial void volume ration aet value o atual void volume ration *, whih desribes the ailure proesses taking plae in the material. Critial void volume ration is treated as a material onstant, whih as riterion parameter determines material rupture. 3. Sope o analysis The researh onerns the experimental determination o the ritial void volume ration at void oalesene or S235JR steel. The ase o low initial stress triaxiality η is onsidered. The investigations inlude the tensile tests o ylindrial speimens with a irumerential noth, whih allowed to obtain low initial value o η = The void oalesene phase was onsidered during the experiments in order to determine the ritial void volume ration. The material obtained rom tensile speimens were used at digital image analysis o suraes o S235JR steel. The proedure involved studying real, physial results obtained diretly rom the material tested. 4. Tested material Due to sientii as well as pratial sope o the study, one o the ommon strutural steel, S235JR, used in ivil engineering was hosen or analysis. This is a mild, low-arbon steel grade, used or strutural elements o building, bridges and others. Requirements or hemial omposition o S235JR steel is desribed in [14]. Aording that, the maximum ontent o elements is: C = 0.14 %, Mn = 0.54 %, Si = 0.17 %, P = %, S = %, Cu = 0.29 %, Cr = 0.12 %, Ni = 0.12 %, Mo = 0.03 %, V = % and N = 0.01 %. For tested steel, large amounts o impurities, i.e. inlusions and seond-phase partiles, were observed in the mirostruture. Basi mehanial properties o S235JR steel were determined by perorming standard tensile tests aording to [15]. The speimens in the orm o round bars were used. The number o the test was n = 8 speimens. The geometri parameters o speimens were: nominal diameter d = 10 mm, the gauge length l 0 = 50 mm and the initial ross-setional area S 0 = 78.5 mm 2. Mehanial properties o tested S235JR steel obtained or the signiiane level o 0.05 are listed in Table 1. Table 1. Mehanial properties o tested S235JR steel. Yield stress R 0.2 [MPa] Tensile strength R m [MPa] Perentage elongation A t [%] Value Standard deviation Comparing with standard requirements [14], tested material was haraterised by better mehanial properties then it is required. 5. Tensile tests Tensile tests were the irst stage o investigations. In order to take into aount the eets o spatial stress state, a ase o multi-axial stresses was onsidered. The spatial stress state was desribed by using stress triaxiality η parameter, whih is deined: m (2) e 3

where: σ m = (σ 1 + σ 2 + σ 3 )/3 hydrostati stress (with σ 1, σ 2,σ 3 being the prinipal stresses), 1 2 2 2 1 2 2 3 1 eetive stress aording to the Huber-Mises-Henky.

5 where: σ m = (σ 1 + σ 2 + σ 3 )/3 hydrostati stress (with σ 1, σ 2,σ 3 being the prinipal stresses), eetive stress aording to the Huber-Mises-Henky. e 3 2 Experiments were perormed with ylindrial tensile speimens with a irumerential noth, as shown in igure 2. The geometri parameters o speimens were: nominal diameter D = 14 mm, the noth radius R = 7.0 mm. It allowed to obtain very low value o stress triaxiality parameter η = Speimens were subjeted to the stati tension in a multi-axial stress ase. Figure 2. Geometry o ylindrial tensile speimens with a irumerential noth and view o the tensile test in multi-axial stress ase The main onept o the investigations was determination o the phase o void oalesene. Basing on the results o own researh [16-18], the stress-strain urves and the time o rapid void growth was analysed in detail. It was established, that the moment o void oalesene initiation was observed as the stage ater exeeding the maximum ore during the tensile tests. Basing on these observations, the ore riterion was applied or deteting the void oalesene time. Aording that, the void oalesene was determined when ore was about 5 % lower than maximum ore reorded during the tensile test. Sheme o that riterion or one o speimens tested is shown in igure 3. Figure 3. Criterion or determination the time o void oalesene or S235JR steel 4

6 Experiments were stopped when above riterion was met. Then speimens were taken out rom testing mahine and used or urther analysis. This way the mirostruture o S235JR steel in the void oalesene phase was obtained, and ould be used or experimental determination o ritial void volume ration. 6. Methodology or the parameter assessment Speimens subjeted to the loading desribed above were prepared to mirosopi investigations. The area around the noth was ut out (igure 4). The obtained ragment o the speimen was then ut along the longitudinal axis, abraded and polished. Figure 4. Surae o the noth ross setion hosen or mirosopi examination In order to ailitate the implementation o mirosopi images the sample was embedded in the resin. The sample used in mirosopi investigations is presented in igure 5. Figure 5. Metallographi speimen used in mirosopi investigations The next stage involved mirosopi observations. Sanning eletron mirosope (SEM) Quanta FEG 250 was used. The photographs were made at the magniiation o 1000x. The photographs were divided into three groups, depending on the analysed area (sample axis, area around the noth surae, area between the entre and the edge o the sample igure 6). 5

Figure 6. Regions o sample surae under mirosopi examination Figure 7 presents an example o steel mirostruture in the area adjaent to the sample edge.

7 Figure 6. Regions o sample surae under mirosopi examination Figure 7 presents an example o steel mirostruture in the area adjaent to the sample edge. Darker areas represent voids and inlusions embedded in the matrix (grey areas). Two merged voids are learly visible on the right side o the photograph. Figure 7. An exemplary mirosopi photograph o the sample surae (magniiation 1000x) Assessment o ritial void volume ration required a detailed quantitative image analysis. Basing on the greysale riterion the image binarization was perormed and thus dark areas, representing voids and other disontinuities were deleted. The proedure was perormed or 30 photographs. Binary photograph rom igure 7 is shown in igure 8. 6

Figure 8. Mirosopi photograph o the sample (igure 7) ater binarization The inal stage involved alulation o trimmed areas (voids) ration in the area o the entire image.

8 Figure 8. Mirosopi photograph o the sample (igure 7) ater binarization The inal stage involved alulation o trimmed areas (voids) ration in the area o the entire image. The obtained value was interpreted as the parameter. It is worth noting that the proedure desribed above made it possible to alulate superiial, not volume ration o voids. 7. Results and disussions The value o obtained in the present study was 1.64%. This is deined as the mean ratio o voids area on the surae mirophotograph to the area o the whole analysed surae. The parameter alulated in the present study is notieably lower than the value o 6% desribed in the literature [19]. As desribed in [20] the value o depends on the stress state triaxiality ratio and inreases with inreasing. The samples analysed in the present study were subjeted to low stress state triaxiality ratio (0.556) and thus is onsidered to be relatively low. The inal issue was alulation o void volume (not superiial) ration. A sheme o two spheres was adopted (igure 9) the smaller sphere represents generalized void embedded in matrix. It was assumed that the relation o small and large sphere ross setion areas was equal to superiial ration alulated or the samples experimentally (1.64%). Figure 9. Sheme adopted or void volume ration assessment 7

9 Basing on geometri relationships the ratio o void volume to the volume o the whole material sample was alulated. The void volume ration obtained using this proedure was 0.2%. As reported in [10] initial void volume ration 0 or unloaded S235JR steel was 0.17%, but this value was determined using standard proedure or porosity determination, whih is based on alulations o pores area. 8. Conlusions GTN model is oten disussed to be eetive in analyses o strutural members operating in plasti range, under pre-ailure onditions. Lak o the model parameters or typial engineering materials severely limits the possibility o pratial appliation. Typial proedures or GTN parameters assessment involve only numerial analyses and itting urve proedure. Consideration o atual hanges in the struture o the material has reeived little attention so ar. Researh presented in this artile is an attempt to assess ritial void volume ration by the experimental proedure, taking into aount eet o low stress state triaxiality ratio (η = 0.556). The inal result was = 1.64 %, whih is onsiderably lower than typially used in the GTN model [19]. Comparative analysis o and initial porosity 0 indiates that in the stress range rom 0 to the material strength the voids growth is a relatively slight proess. Inrease in avities volume shortly beore ailure is a ar more intense proess [21]. Reerenes [1] L. M. Kahanov, Time o the rupture proess under reep onditions, Izvestiya Akademii Nauk SSSR, Otdelenie Tekhniheskikh Nauk, 8, pp , [2] A. L. Gurson, Continuum theory o dutile rupture by void nuleation and growth: Part I Yield riteria and low rules or porous dutile media, Journal o Engineering Materials and Tehnology (ASME), 99, pp. 2 15, [3] P. Suquet, Plastiité et homogénéisation, Dissertation: Thèse d Etat: Sienes Mathématiques (Méanique théorique): Paris 6, Université Pierre et Marie Curie, Paris, [4] J. P. Cordebois, F. Sidoro, Endommanegament Anisotrope En Élastiité et Plastiité, Journal de Méanique Théorique et Appliquée, Numero Spéial, pp , [5] J. Lemaitre, A ontinuous damage mehanis model or dutile rature, Journal o Engineering Materials and Tehnology, 107, pp , [6] J. Murzewski, Brittle and dutile damage o stohastially homogeneous solids, International Journal o Damage Mehanis, 1, pp , [7] S. F. Taher, M. H. Baluh, A. H. Al-Gadhib, Towards a anonial elastoplasti damage model, Engineering Frature Mehanis, 48, pp , [8] K. Nahshon, J.W. Huthinson, Modiiation o the Gurson Model or shear ailure, European Journal o Mehanis A/Solids, 27, pp. 1 17, [9] P. G. Kossakowski, An analysis o the Tvergaard parameters at low initial stress triaxiality or S235JR steel, Polish Maritime Researh, 21, pp , [10] P. G. Kossakowski, Mirostrutural ailure riteria or S235JR steel subjeted to spatial stress states, Arhives o Civil and Mehanial Engineering, 15, pp , [11] P. G. Kossakowski, Stress Modiied Critial Strain riterion or S235JR steel at low initial stress triaxiality, Journal o Theoretial and Applied Mehanis, 52, pp , [12] V. Tvergaard, "Inluene o voids on shear band instabilities under plane strain onditions", International Journal o Frature, 17, pp , [13] V. Tvergaard, A. Needleman, Analysis o the up-one rature in a round tensile bar, Ata Metallurgia, 32, pp , [14] PN-EN :2007 Hot-rolled strutural steel. Part 2 Tehnial delivery onditions or nonalloy strutural steels. [15] PN-EN :2004 Metalli materials Tensile testing Part 1: Method o test at ambient temperature. 8

10 [16] P. G. Kossakowski, W. Wiślik, Experimental determination and appliation o ritial void volume ration or S235JR steel subjeted to multi-axial stress state, in: T. Łodygowski, J. Rakowski, P. Litewka (Eds.), Reent Advanes in Computational Mehanis, CRC Press/Balkema, London, pp , [17] W. Wiślik, Numerial determination o ritial void nuleation strain in the Gurson- Tvergaard-Needleman porous material model or low stress state triaxiality ratio, Proeedings o METAL 2014: 23rd International Conerene on Metallurgy and Materials, Brno, pp , [18] P. G. Kossakowski, W. Wiślik, Eet o ritial void volume ration F on results o dutile rature simulation or S235JR steel under multi-axial stress states, Key Engineering Materials Frature and Fatigue o Materials and Strutures, 598, pp , [19] A. B. Rihelsen, V. Tvergaard, "Dilatant plastiity or upper bound estimates or porous dutile solids", Ata Metallurgia et Materialia, 42, 8, pp , [20] W. Wislik, "Experimental and numerial determination and analysis o Gurson-Tvergaard- Needleman model parameters or S355 steel in omplex stress states" (in Polish), dotoral dissertation, Kiele University o Tehnology, Poland, [21] W. Wislik, Experimental determination o ritial void volume ration F or the Gurson Tvergaard Needleman (GTN) model, Proedia Strutural Integrity, 2, pp ,

Arch. Metall. Mater. 62 (2017), 1,

Arch. Metall. Mater. 62 (2017), 1, Arh. Metall. Mater. 6 (017), 1, 167-17 DOI: 10.1515/amm-017-003 P.G. KOSSAKOWSKI* # EXPERIMENTAL DETERMINATION OF THE VOID VOLUME FRACTION FOR S35JR STEEL AT FAILURE IN THE RANGE OF HIGH STRESS TRIAXIALITIES