ࡱ> "# !Oh+'0`    ( 4@HPX ssKSKSKNormalKozak38aMicrosoft Word 8.0@@@&@Nҩ]Program Files 0Microsoft Office0Templates!@h@:i+00 [B@B Normal$ a$CJ_HmHsHtH$:@: Heading 1$$@&a$6CJ<A@< Default Paragraph FontFF zaglavlje_8_L(&d p#CJ8@8 Header  p# mHsHu22 zaglavlj_8_D$a$>"> Footnote TextCJmHsHu8&@18 Footnote STATE-OF-STRESS MODELLING IN A INHOMOGENOUS SENB FRACTURE TOUGHNESS SPECIMEN Drazan KOZAK1, Franjo MATEJICEK2 and Ivo ALFIREVIC3 1 MSc, Teaching Assistant, Mechanical Eng. Faculty, HR-35000 Slavonski Brod, Croatia, E-mail: dkozak@sfsb.hr2 PhD, Full-time Professor, Mechanical Eng. Faculty, HR-35000 Slavonski Brod, Croatia, E-mail: fmatej@sfsb.hr3 PhD, Full-time Professor, Faculty of Mechanical Engineering and Naval Architecture, HR-10000 Zagreb, Croatia Abstract Single edge notch bend (SENB) fracture toughness specimen with geometric and material mismatch has been chosen to analyse the influence of assumption about stress state on the CTOD (d5) displacement. It was shown that plane strain finite element analysis is appropriate for the middle of the specimen. Also, plane stress assumption seems to be more valid for the free specimen's surface. 1 INTRODUCTION Three-dimensional (3D) elastic-plastic finite element analyses of real fracture mechanics problems demand a lot of CPU time, especially when the crack extension should be taken into consideration. So, many analyses have been confined to thick side-grooved specimens in a plane strain state or very thin specimens in a plane stress state. However, thickness by most of cracked structures lies between these two extremes, so state of stress vary from plane stress near the surface of structure to plane strain in the mid-thickness. Very detailed investigations of three-dimensional effects near a crack tip in a ductile three-point bend specimen, Narasimhan and Rosakis ten years ago are performed [1]. Their observations indicate that the plane strain field prevails in the interior of the specimen very near the crack front. Rosakis and Ravi-Chandar are shown in [2] that for distances from the crack tip exceeding about half a specimen thickness B, plane-stress conditions are approached. Analysed specimens were supposed as homogeneous. However, the problem becomes more complex, if the specimen is composed from the heterogeneous welded joint with irregular shape. Today, a lot of research is devoted to consider the effects of geometry and strength mismatch by finite element modelling [3,4,5]. In this paper, SENB specimen with heterogeneous X-welded joint different mechanical properties from the base metal has been used to assess the influence of stress state assumption on the crack tip opening displacement d5. THE FRACTURE TOUGHNESS SPECIMEN Here is chosen the Bx2B SENB specimen (thickness B=36 mm) that consists X-shaped welded joint with crack through the whole thickness of specimen (Fig. 1). The base metal of the specimen is HSLA steel with 712 MPa of yield strength and 846 MPa of ultimate strength. Two passes in the root of weld joint were performing by the electrode with 13% overmatch. The yield strength of the weld cap is 22% larger related to the base metal. EMBED Word.Picture.8 Figure 1 Bx2B SENB fracture toughness specimen STRESS STATE MODELLING Regarding the symmetry of the specimen, only of the specimen has been modelled by finite elements (Fig. 2). The finite element modelling enables the calculation of the stress components. Hence, it is possible to find out the magnitude of the stress triaxility parameter by Eq. 1.  EMBED Word.Picture.8  Figure 2 Finite element model of the of the specimen The base metal of the specimen is HSLA steel with 712 MPa of yield strength and 846 MPa of ultimate strength. Two passes in the root of weld joint were performing by the electrode with 13% overmatch. The yield strength of the weld cap is 22% larger related to the base metal. The finite element mesh consists of 28947 nodes and 6528 20-nodes elements. The first row of the elements around the crack front has the size of about 50 mm. Standard finite element packages have not the option to calculate the local stress triaxility parameter directionally. So, for this purpose special code which is operating with stress components has to be written and implemented into ANSY 5.6 [7]. The variation of the stress triaxility parameter in the ligament of the specimen for the maximum load from experiment is presented in the Fig. 3. Two curves are depicting the changing of the stress triaxility. One is on the ligament's front (surface of specimen) and the other is on the ligament's back (mid-thickness section). It is evident that constraint effects are more in presence in the middle of the specimen. The surrounding material here limits the yielding near the crack tip. The peak of the stress triaxility parameter is some displaced from the crack tip, because similar behaviour shows the crack opening stress distribution. On the end of the ligament, the constraint effect is little increased. This is a consequence of the concentrated load acting. Hydrostatic stress is always less than effective stress, so we can say that out-of-plane constraint is not significant in this case. One can conclude that plane stress state is much closer to the reality, if two-dimensional finite element modelling is needed.  EMBED Word.Picture.8  Figure 3 The stress triaxility parameter variation 4 CONCLUSIONS The local stress triaxility as a measure of the out-of-plane constraint for heterogeneous fracture toughness specimen has been investigated. It is shown that effect of yielding constraint is more significant in the middle plane of the specimen than on the specimen's surfaces. However, hydrostatic stress for both analysed planes is less than equivalent stress. This could be understood as neglected effect of yielding constraint through the thickness in this case. Namely, according to the references, for the parameter of stress triaxility greater than 2,5, it is reasonable to suppose significant out-of-plane constraint and plane strain stress state. Acknowledgement This investigation is financially supported by Ministry of Science and Technology of Republic of Croatia through the project 152-504. 5 REFERENCES [1] Narasimhan, R., Rosakis, A. J., Three-Dimensional Effects Near a Crack Tip in a Ductile Three-Point Bend Specimen: Part I - A Numerical Investigation, Journal of Applied Mechanics, Vol. 57, 1990, pp. 607-617 [2] Rosakis, A. J. and Ravi-Chandar, K., On Crack-Tip Stress State: An Experimental Evaluation of Three-Dimensional Effects, Int. Journal of Solids and Structures, Vol. 22, No. 2, 1986, pp. 121-134 [3] Lin, G., Meng, X.-G., Cornec, A. and Schwalbe, K.-H., The effect of strength mis-match on mechanical performance of weld joints, International Journal of Fracture 96, 1999, pp. 37-54 [4] Thaulow, C., Ranestad, ., Hauge, M., Zhang, Z., Toyoda, M. and Minami, F., FE calculations of stress fields from cracks located at the fusion line of weldments, Engineering Fracture Mechanics, Vol. 57, No. 6, 1997, pp. 637-651 [5] Quintino, L. and Vilaa, P., Numerical analysis of weld strength mismatch effect on crack propagation, IIW Doc. 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Initial crack length is equal 35,8 mm. During the testing force F, load line displacement LLD, CTOD (d5), crack mouth opening displacemenck Driving Force Curve and Crack Tip Opening Displacement (CTOD) Resistance Curve, Strojarstvo 42 (3,4), 2000, 85-101 crack tip opening displacement plane an in the middleThe weld width in the root is about 5 mm and on the face 28 mm. Initial crack length is equal 35,8 mm. During the testing force F, load line displacement LLD, CTOD (d5), crack mouth opening displacement CMOD and crack extension a were recorded. Every section plane of the specimen is composing from the different percent of base metal rto X-shape of welded joint. Therefore, the mid-thickness plane is just imaginary the plane of the specimen's s.Assuming the plane strain state for the plane in the middle, Gubeljak et al in 6 obtained conservative finite element results, but on the safe side. However, aforementioned characteristic displacements are measuring on the surface side of the specimen. OGubeljak, N., Kozak, D. and Matejicek, F., Prediction of Strength Mis-match Welded Joints Failure by Using of Crack Driving Force Curve and Crack Tip Opening Displacement (CTOD) Resistance Curve, Strojarstvo 42 (3,4), 2000, 85-101 ՜.+,D՜.+,0 hp  SFSBitl6 k   Title 6> _PID_GUIDAN{F5772D48-43A5-11D0-9336-00C0DFE8465A}0TemplatesA,@:i+00/C [4@4Normal $ CJmH4@4 Heading 1$@&5mH << Heading 2$@& 5mH DD Heading 3$$@& 6;CJmH 88 Heading 4$@& 5CJmH HH Heading 5$$@& 5;CJ mH <A@<Default Paragraph FontFF zaglavlje_8_L(&d p#CJ0@0Header  p#mH00 zaglavlj_8_D$6@"6 Footnote TextCJmH8&@18Footnote ReferenceH*0 B0Footer  p#mH8Z@R8 Plain TextCJOJQJmH&)@a& Page Number: :Index 18 5CJ.B@. Body Text5mH 6P@6 Body Text 2$5mH 0"0Caption $ mH(U@( Hyperlink>*B*8Y8 Document Map-D OJQJH(HfH{ W X q || |||||@|| |nMDno"(87Qo!#9" UnknownKozakX m o :::l,2$+jGnR9@0(   B S  ? _1048330532 _1048330648 _1048341907 _1048342335 _1048342473 _1048343003 _1048424220 _1048424773 _1048424825 _1048424896 _1048426927 _1048427142 _1048427401 _1048429173 _1048521223 _910121029 _910121444 _910121551 _1048344764 _1048346716 _1048349799 _1048427414 _1048429601 _910094653 _910095004 _910095059 _910110356 _1048349041 _1048349230 _1048427853 _1048429689 _1048429823m m m m m m m m m m m m m m m @@@@@@@@@ @ @ @ @ @@@@@@@@@@@@@@@@@@@m m m m m m m m m m m m m m m ]csv=G$0zE K KozakC:\CLANCI\Steyr.docKozakC:\CLANCI\Steyr.docKozakC:\CLANCI\Steyr.docKozakC:\CLANCI\Steyr.docKozakC:\CLANCI\Steyr.docKozakC:\CLANCI\Steyr.docKozakC:\CLANCI\Steyr.docKozakC:\CLANCI\Steyr.docKozak.C:\WINDOWS\TEMP\AutoRecovery save of Steyr.asdKozak.C:\WINDOWS\TEMP\AutoRecovery save of Steyr.asdnP|$}T^`o(.^`.L^`L.f f ^f `.6 6 ^6 `.L^`L.^`.^`.vLv^v`L.hho(nP$}@uV6H*C$Eƀb'     ) L    : D F V W m n o     $ = L Z a b c r v  ./8GV*0@11h11J1>h10@1Jh1Lh1Nh1@01Ph11 @1lh1h1h1i1F @1:i1Ji1Ri1bi1ni1ti1i1i1i1i1i1"j16j1:j0l"@0n"@1Zj1\j0"@1^j1j1j1j1j1k14#@1k1F#@1k1Lk1jk1k1k1k1k1k1k1k1k1P#@1k1^#@QR& !"6"7"8"9"H CJUVmH 5CJH*5CJOJQJ 56CJ5CJ56!t CMOD and crack extension a were recorded. Every section plane of the specimen is composing from the different percent of base metal rto X-shape of welded joint. Therefore, the mid-thickness plane is just imaginary the plane of the specimen's s.Assuming the plane strain state for the plane in the middle, Gubeljak et al in 6 obtained conservative finite element results, but on the safe side. However, aforementioned characteristic displacements are measuring on the surface side of the specimen. This plane OGubeljak, N., Kozak, D. and Matejicek, F., Prediction of Strength Mis-match Welded Joints Failure by Using of Crack Driving Force Curve and Crack Tip Opening Displacement (CTOD) Resistance Curve, Strojarstvo 42 (3,4), 2000, 85-101  [4@4Normal $ CJmH4@4 Heading 1$@&5mH << Heading 2$@& 5mH DD Heading 3$$@& 6;CJmH 88 Heading 4$@& 5CJmH HH Heading 5$$@& 5;CJ mH <A@<Default Paragraph FontFF zaglavlje_8_L(&d p#CJ0@0Header  p#mH00 zaglavlj_8_D$6@"6 Footnote TextCJmH8&@18Footnote ReferenceH*0 B0Footer  p#mH8Z@R8 Plain TextCJOJQJmH&)@a& Page Number: :Index 18 5CJ.B@. 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Initial crack length is equal 35,8 mm. During the testing force F, load line displacement LLD, CTOD (d5), crack mouth opening displacement CMOD and crack extension a were recorded. Every section plane of the specimen is composing from the different percent of base metal rto X-shape of welded joint. Therefore, the mid-thickness plane is just imaginary the plane of the specimen's s.Assuming the plane strain state for the plane in the middle, Gubeljak et al in 6 obtained conservative finite element results, but on the safe side. However, aforementioned characteristic displacements are measuring on the surface side of the specimen. This plane i plane stress i WB800 OGubeljak, N., Kozak, D. and Matejicek, F., Prediction of Strength Mis-match Welded Joints Failure by Using of Crack Driving Force Curve and Crack Tip Opening Displacement (CTOD) Resistance Curve, Strojarstvo 42 (3,4), 2000, 85-101  [4@4Normal $ CJmH4@4 Heading 1$@&5mH << Heading 2$@& 5mH DD Heading 3$$@& 6;CJmH 88 Heading 4$@& 5CJmH HH Heading 5$$@& 5;CJ mH <A@<Default Paragraph FontFF zaglavlje_8_L(&d p#CJ0@0Header  p#mH00 zaglavlj_8_D$6@"6 Footnote TextCJmH8&@18Footnote ReferenceH*0 B0Footer  p#mH8Z@R8 Plain TextCJOJQJmH&)@a& Page Number: :Index 18 5CJ.B@. 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