ࡱ>  ()*+,bjbjWW ==Me ]zzzz  8B z$ 0 (X X n KMMMMMM$pq  d qL <"z2X  n K R zzzzKK Kn z 4 Xf KPrediction of Failure by Using Crack Driving Force and Crack Tip Opening Displacement (CTOD) Resistance Curves of Strength Mis-match Welded Joints Nenad GUBELJAK1 and Dra~an KOZAK2 1Faculty of Mechanical Engineering University of Maribor Smetanova 17, SI-2000 Maribor Slovenia 2Strojarski fakultet u Slavonskom Brodu Sveu iliate J.J. Strossmayera u Osijeku Trg Ivane Brli Ma~urani 18, HR-35000 Slavonski Brod Hrvatska Keywords: Crack Tip Opening Displacement (CTOD), Mis-match welded joints, Crack Driving Force, CTOD-R resistance curve Klju ne rije i: Otvaranje vraka pukotine, zavareni spojevi s materijalima nejednake vrstoe, sila razvoja pukotine, CTOD-R krivulja otpornosti materijala. 1. Introduction The main task of a comparison between the experimental results of fracture behaviour and the numerically described stress-strain state is to estimate the initiation of stable and unstable crack propagation. It is reasonable to expect, that the comparison analyses depend on accurate mesh modelling and description of the mechanical properties. Usually the mechanical properties used in numerical modelling are obtained by round tensile testing. Whilst, the fracture toughness testing is performed on a three bend specimen. It is evident that a different level of constraint between these two types of testing occurred. Hence, the scatter between numerical and experimental results can be significant. It is more evident on global strength mis-match welded joints. The first passes of global strength mis-match welded joints are welded to an under-match consumable, with the aim of omitting pre-heating and reducing the cost of welded structures (1(. The filled passes are welded by over-match consumable with the purpose of ensuring a global over-match of the welded joint. The aim of this paper is to determine the initiation of stable crack growth and to predict the failure of cracked specimens made by global strength mis-match welded joint using two dimensional numerical modelling. It is necessary to determine the conditions for unstable crack propagation by considering the shape of the weld joint and the specified mechanical properties of weld metals. 2. Experimental procedure High strength low alloyed HSLA steel (with thickness of 40 mm), corresponding to the grade HT80, was used as the base metal (BM) in a quenched and tempered condition (Q+T), Table 1. Three different overmatched X-grooved multipass welded joints are studied, one with homogeneous and two with heterogeneous welds. The Flux Cored Arc Welding process (FCAW), with CO2 as a shielding gas, was used and three different consumables were selected. The first one ensured global overmatching with the weld metal denoted by WM1, and the latter two enabled a soft layer appearance in the weld metal (WM2 and WM3). An homogeneous welded joint was made by preheating using only the first consumable. Two different types of both heterogeneous welded joints were made using the other two consumables for the soft root layer, while the filler passes were made with the first consumable (2(. Three different types of global overmatched welded joint were obtained: - homogeneous weld (WM1fil+root), - overmatched welded joint with heterogeneous weld (WM1fill+WM2root) with medium strength of root layer and - overmatched welded joint with heterogeneous weld (WM1fill+WM3root) with lower strength of root passes. MaterialERp0.2Rm(oaelong.nvEMGPaMPaMPaMPa-%-J/80mm2(yWM/(yBMBase metal2097128466760.941190.09585-10(C-WM1fill21187310418330.89710.80.10733-40(C1.22WM1root2128249028010.92916.50.06550-40(C1.16WM2root2036887506670.99114.70.06162-40(C0.96WM3root2086497066290.93514.60.0587-40(C0.91 The heterogeneous welds were made with either two or four passes in the root layers. The difference between the welded joints with a heterogeneous weld produced by two or four soft root passes (WM2root or WM3root) is only in the height of the soft root passes and not in the microstructures. The mechanical properties of the weld metal are listed in Table 1. Table 1. Mechanical properties of BM and significant regions of real welds at room temperature and testing temperature -10C. Tablica 1. Mehani ka svojstva osnovnog materijala i karakteristi nih dijelova zavarenih spojeva na temperaturi ispitivanja  10C Figure 1. Three point bending specimen (Bx2B) and measuring points (CMOD, d5). Slika 1. Epruveta za savijanje u tri to ke (Bx2B) i mjerne to ke (CMOD, d5). The single edge notched bend (SENB) specimens were used for CTOD fracture toughness testing. The specimens with the notch tip completely in the weld metal were used for the estimation of fracture behaviour of the different global mis-match microstructure metals. The geometry of SENB specimens was Bx2B (thickness x width) with B=36mm and a crack length to thickness ratio a0/W=0.5. Specimens were fatigue pre-cracked in the thickness direction using the stepwise high R-ratio SHR method (3(. In the stepwise high R-ratio technique, fatigue pre-cracking consists of two steps, each at a different fatigue stress ratio (R), in accordance with BS 7448 (4(. A single specimen method was used at a testing temperature of -10(C. The DC potential drop technique was applied for crack growth monitoring. CTOD values were directly measured with the (5 clip gauge, developed by GKSS (5(. Measuring points are marked on the specimen surface as in Figure 1. Figure 2 shows the plots load (F) vs. CTOD(d5). Since all specimens have the same crack length the curves are overlapping each other in the linear region of loading. In all specimens (except the one taken from the base metal (BM)), after some amount of stable crack growth, unstable fracture initiated, as shown in Fig. 2. This is typical fracture behaviour in the ductile-to-brittle transition region (6(. Figure 2. Experimentally obtained curves F vs. CTOD(d5) for base metal and different weld metals Slika 2. Eksperimentalno dobivena krivulja optereivanja F - CTOD(d5) za osnovni materijal i zavarene spojeve 3. Numerical procedure For the numerical modeling of specimens the two-dimensional isoparametric elements for elastic and elasto-plastic analyses are used. Actually, the stress and critical size of the hardening zone in the vicinity of the crack tip at the moment of instability are determined by the finite element method (FEM). The FEM calculations at common fracture mechanics single edge notch bend (SENB) standard Bx2B specimens (B = 36 mm) were performed, as is shown in Fig.3. An actual welded joint is rather complicated, both metallurgically and geometrically. For simplification in the following analysis the effect of the heat affected zone, residual stresses and other kinds of heterogeneity are omitted. For example, the fusion line is modeled as an interface in a bi-material system as shown in Fig. 3. Due to symmetry only one-half (hatched part) of the specimen was modeled. At the surface the specimen nodes are specified, which correspond to the measure points for d5 and CMOD as are shown in Fig. 3. The uniaxial stress-strain behaviour of specified material is described by pairs of (s-e) points, taken from an experimentally obtained s-e curve. In the case of large scale yielding (e>10 %) the single axial stress-strain behaviour is described by using the Ramberg-Osgood power low:  EMBED Equation  (1) where s0 is the reference stress, e0=s0/E is the reference strain, a is a dimensionless approximation parameter and n is the strain hardening coefficient, the values are listed in Table 1. The values of the parameters in the Romberg-Osgood power low are approximated by experimental measured data obtained from tensile testing specimens.  EMBED Word.Picture.6 Figure 3. Position of crack notch, geometry and manner of loading CTOD testing specimens by simplifying the heterogeneity of a welded joint as a bi-metal material Slika 3. Polo~aj vraka pukotine, dimenzije i na in optereivanja CTOD epruvete s pojednostavljenjem zavarenog spoja kao dvo-materijalni sistem    Figure 4. Mesh and boundary fixed supports on one half of Bx2B specimens. Slika 4. Umre~enje i nepomi ni oslonci na polovici epruvete Bx2B. The conventional small strain theory of plasticity is employed in the finite element analyses by using ANSYS 5.0 (7( software. The mesh was automatically generated with a determined radius of r=0.5 mm in first row of crack-tip elements. Figures 4 presents the mesh on one half of Bx2B specimens. In the FEM analyses the singularity at the crack tip was solved by using two-dimensional 8-nodes isoparametric crack-tip elements. These elements are essentially 4-sided elements which collapse into triangle elements with three coincident nodes at the crack tip. Using the first array of elements the crack tip stress concentration was assigned. For linear-elastic problems these nodes have the same displacements and mid nodes in the 1/4 position, because of r-1/2 strain singularity at the crack tip. In the case where large scale yielding is expected it is necessary to provide three coincident nodes at the crack tip elements, because r-1 strain singularity now exists at the crack tip. Those nodes have the ability to displace from the same start point in different directions and to model blunting in this way (8(. The use of different finite elements under condition of different singularity was suggested by Huchinson, (9( Rice and Rosengren (10(. Today their recommendations are generally accepted in the numerical modeling of fracture behaviour. For each type of weld joint one of the B x 2B specimens is used. FEM calculation was performed by the successive increase of force up to the maximum load measured by experiments for all specimens. It means that FEM solutions lie on the crack driving force curves, while the CTOD-R resistance curve was obtained by experimental CTOD testing (11(. All nodes of elements in axis x (axis of specimen symmetry) and the node in support position (y axis) were fixed. Specimens were loaded in three point bending, with a load applied at mid-span. In the elastic-plastic analyses, the manner in which the load is applied can be very important. If the load is applied to a single node, a local stress and strain concentration will occur, and the elements connected to this node will yield almost immediately (12(. A better way of applying this boundary condition might be to distribute the load over several nodes and specifying that the elements on which the load acts remain elastic, i.e. F/2=F/6+F/3 (13(, as is shown in Fig. 4. 4 Numerical analysis The fracture behaviour of specimens has been calculated by quasi-static increasing of the load up to the point of experimental instability. The stress-strain conditions at the surfaces of specimens, displacement in the characteristic points (d5, CMOD) and the maximum equivalent stress seq were calculated. In order to enable a comparability of fracture behaviour between specimens made from different weld metals and different crack depth a/W it is convenient to interpret the results with load ratio F/Fy. The yield load Fy depends on the geometry of the specimens and the types of loading (e.i. bending, tensile), crack depth and the yield stress of material. The term Fy is yield load, which is also used in ETM model (14(, for the SENB specimens  EMBED Equation  (2) where B-thickness of specimen, W-width of specimen, S-span distance between supports a/W-depth of specimens, sy is usually yield stress Rp0.2 (offset 0.2% strain in tensile plot), A=1.072 plane stress, a/W>0.02 (3.a) A=1.455 plane strain, a/W>0.296 (3.b) A=1.455-3.141((0.31-a/W)2 plan strain, a/W<0.31 (3.c) A is the approximation parameter determined by a correlation between FEM and experimental results for isotropic ferrite steels, (15(. In this case it was found that the best could be obtained if A is exactly the same as at Eq. (3.b) and (3.c) and sy equal to so from Ramberg-Osgood Eq. 1. The normalized load F/Fy is a kind of utility load level, also the named ratio of load carrying capacity. The accuracy of estimates beyond Fy depends on the accuracy of the yield load solutions. Particular problems arise when the state of stress is somewhere between plane stress and plane strain. Optimistic estimates of the load carrying capacity than can than be made if planes stress is assumed to prevail (A=1.072). A taken from Eq. (3.b) or (3.c) can be used for strain hardened elements in the plain strain state. In this case cleavage fracture occurred in the ductile-to-brittle transition region. This is the reason for the use of reference yielding stress so instead of Rp0.2 for sy.  a)  b) Figure 5. Comparison between FE calculation results and experimental results a) for F/Fy vs. CMOD and b) F/Fy vs. CTOD(d5). Slika 5. Usporedba izmeu numeri kih MKE i eksperimentalnih rezultata a) za F/Fy  CMOD te b) F/Fy  CTOD(d5) Figure 6. seq/so vs. CTOD(d5) in comparison between all weld joints Slika 6. Usporedba ovisnosti seq/so - CTOD(d5) za sva tri tipa zavarenih spojeva The mean stresses (s1, s2 and s3) are related to the Cartesian stress by Sneddons equations for sxx, syy and txy:  EMBED Equation  (4)  EMBED Equation  plain stress (4.a)  EMBED Equation  plain strain (4.b) Equivalent stress seq is determined as von Misses yield stress:  EMBED Equation  (5) The dependence of equivalent stresses seq on CTOD values up to an unstable point is shown in Figs. 6.a) and b). From the comparison between specimens made from base metal and the weld joint, it is evident that the initiation of cleavage fracture in weld joints occur when F/Fy<1. It means that the material does not achieve full load carrying capacity, as happens in base metal. This is a consequence of the high constraint caused by the bending of specimens and mainly by a narrowing of the width of the weld joint gap. Note, that cleavage initiation occurred when F/Fy<1 and at the same time as the moment of instability seq/so>1 at all weld joints. This means that the cleavage fracture occurred during the process of hardening in all welded joints. High constraint is related to lower yielding and higher hardening. The process of strain hardening (with some amount of ductile tearing) would be interrupted if the origin of the cleavage initiation (e.g. LBZ or M - A constituents) is loaded by a high enough normal syy stress component. The syy corresponds to critical stress for I mode of loading. The obtained isostress lines of equivalent stresses seq are shown in Figures 7,8,9 for WM1, WM2 and WM3 welded joint, respectively. The yielding of materials is given by a contour of equivalent stresses seq for each type of material (three types of weld metals and base metal) for reference yield load s0. The contour is the border between two colors, for example: - WM1fill (seq = s0 = 833 MPa) it is contour between red and orange color, - WM1root (seq = s0 = 801 MPa) it is contour between orange and yellow color, - WM2root (seq = s0 = 787 MPa) it is contour between yellow and green color, - WM2root (seq = s0 = 667 MPa) it is contour between green and light blue color, - base metal (seq = s0 = 676 MPa) it is contour between green and light blue color, - WM3root (seq = s0 = 629 MPa) it is contour between green and light blue color. The contour between the blue and dark blue colors corresponds to stress seq = 600 MPa. The reference yield load of base metal (s0 = 667 MPa) and weld metal (seq = s0 = 676 MPa) are similar, hence these two contours are given as one at seq = s0 = 676 MPa. From the isostresses seq at the moment of instability it is obvious that yielding is limited by the shape of the weld joint. In the case of B x 2B specimen with the weld metal WM3root (Fig. 9) the yielding zone is of the same size as in the case of another two WM1fill+root (Fig. 7) and WM1fill+WM2root (Fig. 8). This is a consequence of the carrying effect in the high strength filler region WM1fill.    Figure 7. Contour of von Misess isostress seq for base metal Slika 7. Kontura von Misesove granice te enja za osnovni materijal Figure 8. Contour of isostress seq for homogeneous weld joint WM1fill+root Slika 8. Kontura von Misesove granice te enja za homogen zavareni spoj WM1fill+root  Figure 9. Contour of isostress seq at the root of heterogeneous weld joint WM1fill+WM2root Slika 9. Kontura von Misesove granice te enja u korijenu heterogenog zavarenog spoja WM1fill+WM2rootFigure 10. Contour of isostress seq at the root of heterogeneous weld joint WM1fill+WM3root Slika 10. Kontura von Misesove granice te enja u korijenu heterogenog zavarenog spoja WM1fill+WM3rootFigure 11.a) Determination of the initiation of stable crack propagation as a deviation point between experimentally and numerically (Da=0) obtained loading curves WM1fill+ root Slika 11.a) Odreivanje inicijacije stabilnog airenja pukotine kao to ke gdje dolazi do odstupanja izmeu eksperimentalne i numeri ke (Da=0) krivulje optereenja za spoj WM1fill+ root  Figure 11.b) Determination of an unstable point at the intersection of the CTOD-R resistance curve and Crack Drawing force curve for homogeneous weld joint WM1fill+root Slika 11.b) Odreivanje to ke nestabilnog loma kao sjeciata izmeu CTOD-R krive otpornosti materijala i krive sile razvoja pukotine za homogen zavaren spoj WM1fill+root  Figure 12.a) Determination of the initiation of stable crack propagation as a deviation point between experimentally and numerically (Da=0) obtained curves for heterogeneous weld joint WM1fill+WM2root Slika 12.a) Odreivanje inicijacije stabilnog airenja pukotine kao to ke gdje dolazi do odstupanja izmeu eksperimentalne i numeri ke (Da=0) krivulje optereenja za heterogeni spoj WM1fill+WM2root  Figure 12.b) Determination of an unstable point at the intersection of the CTOD-R resistance curve and Crack Drawing force curve for heterogeneous weld joint WM1fill+WM2root Slika 12.b) Odreivanje to ke nestabilnog loma kao sjeciata izmeu CTOD-R krive otpornosti materijala i krive sile razvoja pukotine za heterogen zavaren spoj WM1fill+WM2root  Figure 12.a) Determination of the initiation of stable crack propagation as a deviation point between experimentally and numerically (Da=0) obtained curves for heterogeneous weld joint WM1fill+WM2root Slika 12.a) Odreivanje inicijacije stabilnog airenja pukotine kao to ke gdje dolazi do odstupanja izmeu eksperimentalne i numeri ke (Da=0) krivulje optereenja za heterogeni spoj WM1fill+WM2root  Figure 12.b) Determination of an unstable point at the intersection of the CTOD-R resistance curve and Crack Drawing force curve for heterogeneous weld joint WM1fill+WM2root Slika 12.b) Odreivanje to ke nestabilnog loma kao sjeciata izmeu CTOD-R krive otpornosti materijala i krive sile razvoja pukotine za heterogen zavaren spoj WM1fill+WM2root Figure 13.a) Determination of the initiation of stable crack propagation as a deviation point between experimentally and numerically (Da=0) obtained curves for homogeneous weld joint WM1fill+WM3root Slika 13.a) Odreivanje inicijacije stabilnog airenja pukotine kao to ke gdje dolazi do odstupanja izmeu eksperimentalne i numeri ke (Da=0) krivulje optereenja za heterogeni spoj WM1fill+WM3root  Figure 13.b) Determination of an unstable point at the intersection of the CTOD-R resistance curve and Crack Drawing force curve for heterogeneous weld joint WM1fill+WM3root Slika 13.b) Odreivanje to ke nestabilnog loma kao sjeciata izmeu CTOD-R krivulje otpornosti materijala i krivulje sile razvoja pukotine za heterogen zavaren spoj WM1fill+WM3root 4. Discussion The comparison between numerically and experimentally obtained values of CTOD as a fracture toughness parameter is shown in Figures 11, 12, 13 for specimens WM1fill+root, WM1fill+WM2root and WM1fill+WM3root, respectively. Figures 11.a), 12.a) and 13.a) represent numerically obtained loading curves for different crack lengths (a0+Da). A prediction of the initiation of stable crack propagation is possible to recognize at the range where the array of experimental data started to deviate from the loading curve for Da=0. The experimental loading curve intersects several numerical loading curves with different crack extensions, as in Da=0,25 mm, Da=0.5 mm etc. However, too large a yielding and hardening zone can be obtained if the nodes on the crack tip are not released. The initiation of stable crack growth can be determined as the deviation between experimentally and numerically obtained curves because in both cases the yielding and hardening zone at the crack tip has been taken in the account. From the CTOD(d5) loading curve it is evident that the initiation of stable crack growth has started at the significant lower values for CTOD(d5) than in the case of the CTOD-R resistance curve, in the all types of weld joints. If these CTOD(d5) values is to be accepted as the relevant allowed value for crack tip opening displacement then the safe approach to the assessment of carry loading capacity has been ensured. The comparison between the numerically obtained crack driving force and the experimentally obtained CTOD-R curves enables a determination of the unstability point on CTOD-R curve, at an intersection between those curves, as is shown in Figures 11.b), 12.b) and 13.c) for specimens WM1fill+root, WM1fill+WM2root and WM1fill+WM3root, respectively. It is evident that unstable point always lies above intersection point of the crack driving force and CTOD-R curves. It means that the numerically obtained values of the fracture toughness parameter CTOD are always lower than the experimentally obtained ones. Therefore, the numerically calculated size of the yielding and hardening zone is always lower than the experimentally obtained ones. Since, the size of yielding zone affects the initiation of stable/unstable crack growth it means that two-dimensional numerical modelling in plane strain mode enables a safer approach to the prediction of the failure of strength mis-match welded joints. 6. Conclusions Two-dimensional numerical modelling by using plane stain mesh elements enables a safer prediction of the failure by using crack drawing force and crack tip opening displacement resistance curves of strength mis-match welded joints. The numerically and experimentally obtained results are comparable in spite of any rough estimation of the mechanical properties of the specified regions of welded joint (root and filled part) and the simplification of the mesh modelling. Therefore, the mesh modelling of a section of a specimen at the narrowest region of the welded joint can be used as a critical region for the fracture behaviour of a whole specimen. Therefore the size and mechanical properties of the root region of the weld joint has a dominant influence on fracture behaviour. In the case when strength mis-match is higher than the weld joint is susceptible to unstable fracture behaviour, since yielding occurred under a lower load level. (1( Denys, Provisional Definitive Statement on the Significance of Over and Undermatching Weld Metal Strength IIW Doc. X 1222-91, Commission X, The Hague 1991 (2( Gubeljak, The effect of strength mis-match on welded joint fracture behaviour dissertation. Faculty of Mech. Eng. Maribor, 1998 IX (3( Koak, Seifert, Yao and Lampe Comparison of fatigue pre-cracking methods for fracture toughness testing of weldments: Local Compression and Step-Wise High Ratio Conference Welding-90. (4( BS 7448, Fracture mechanics toughness test, Part 1 published in 1991, Part 2 -Sixth Draft: Method for Determination of KIC, Critical CTOD and Critical J Values of Welds in Metallic Materials TWI Abingdon Hall Cambridge, December 1995 (5( GKSS, Displacement Gauge System for Applications in Fracture Mechanics, Patent Publication, Geesthacht (6( Vojvodi -Gvardjan i , Ule , A~man, Fracture Toughness of Fine Grained Micro-Alloyed Steels at Nil Ductility Temperature and Transition Range, Journal de Physique III, Vol. 3, Nov. 1993, pp. 105-108. (7( ANSYS/ED 5.0, Manual guide, 1995. (8( LA`, PLANI KA VACEK and ZAVADIL, Experimental and Numerical Determination of Critical Load for Cracks Surrounded by a Zone of Large Plastic Deformations, 13th Danubia-Adria Symposium, Rajecke Teplice Slovakia, Sept. 26-28, 1996, pp. 51-52. (9( HUTCHINSON, Singular Behaviour at the End of a Tensile Crack Tip in a Hardening Material, Journal of the Mechanics and Physics of Solids, Vol. 16, 1968, pp.13-31. (10( Rice and Rosengren, Plane Strain Deformation near a Crack Tip in a Power Law Hardening Material, Journal of the Mechanics and Physics of Solids, Vol. 16, 1968, pp.1-12 (11( GUBELJAK, Dolo evanje CTOD-R odpornostnih krivulj trdnostno heterogenih zvarnih spojev , to be published in Varilna tehnika Ljubljana, 1999 (12( PLANI KA, LA` and VACEK, Contribution to a Behaviour of a Crack in the Region of Brittle Fracture, Acta Mechanica Slovaca, Vol. 2, 1998, pp. 23-26. (13( Anderson, Fracture Mechanics Fundamentals and Applications, Second edition 1994 (14( Schwalbe, Zerbst , Brocks, Cornec, Heerens and Amsutz, The ETM Method for Assessing the Significance of Crack-Like Defects in Engineering Structures, Comprising the Versions ETM 95/1 and ETM 95/2, Geesthacht, August 1996, Draft for comments, (15( Royer, Tissot, Pelissier-Tanon, le Poac and Miannay, J-integral determination and analysis for small test specimens and their unsefulness for estimating fracture toughness, ASTM STP 668, pp. 334-357, 1979. PAGE 6 PAGE 7 Prediction of failure of fracture toughness specimen is possible to estimate by using crack driving force and CTOD-R resistance curve of material. Accuracy of determination points on curve of crack driving force depends from numerical model and description of mechanical properties. The appropriate of numerical model is possible to determine by comparison between numerical and experimental results for displacements on surface of specimen. Initiation of stable crack propagation can be determinate by deviation between numerically and experimentally obtained fracture behaviour curves. The intersection point between curve of crack driving force and CTOD-R resistance curve gives the critical values of CTOD and crack extension, where the instability can be expected. The unstable fracture behaviour depends on hardening ability of weld metal and its volume in the weld joint. Predvianje nestabilnog loma kod zavarenih spojeva nejednake vrstoe pomou krivulje sile razvoja pukotine i krivulje otpornosti materijala Predvianje nestabilnog ponaaanja lomnomehani ke epruvete je mogue ocijeniti pomou krivulje sile razvoja pukotine i krivulje otpornosti materijala. Precizno odreivanje to aka na krivulji sile razvoja pukotine zavisi od numeri kog modela i to nog opisa mehani kih svojstava materijala u modelu. Primjerenost numeri kog modela je mogue odrediti iz usporedbe izmeu numeri kih i eksperimentalnih rezultata za karakteristi ne pomake na povraini epruvete. Rezultati su pokazali da se podru je inicijacije stabilnog airenja pukotine mo~e odrediti kao po etak odstupanja izmeu eksperimentalno i numeri ki dobivene krivulje lomnog ponaaanja. To ka presijecanja krivulje sile razvoja pukotine i krivulje otpornosti materijala predstavlja kriti nu vrijednost otvaranja vraka pukotine i prirasta pukotine kod koje dolazi do nestabilnosti. Nestabilno lomno ponaaanje je uvjetovano deformacijskom sposobnoau materijala i njegovom koli inom u zavarenom spoju. W=2B=72 a CMOD B=36 4(W F d5 Numerically modelled part of specimen Numeri no modeliran dio epruvete  EMBED EditorImage  Crack tip Vraak pukotine Measured points: CTOD(d5) Mjerne to ke: 4 2.5 CMOD Unfractured ligament Neslomljen ligament Load F Sila 72 144 crack pukotina Width of root `irina korjena x y Zavar 2.5 mm Fusion line Linija spajanja 8. 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F. zzzz   F.0-46+Dʇ !+ Root EntryD F@I6+Dʇ AData  WordDocumentFObjectPool ཀ@m!   z "#{|}~ObjInfoOle10Native@B.dOle10ItemName1TableM      !"#$%&'()*+,-./0123456789:;<=>?@ABEMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~D SummaryInformation(E,DocumentSummaryInformation8CompObjGj0TableCL    !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~_1042043550HRF@"Dʇ@"DʇOle PIC QTLMETA CompObjSVfObjInfoOle10NativeUWEquation Native Y \bjbjWW =Ke ]zzz  +++8+|, $-.(0.0.F.  $t1e Wd 1zz0.F.wd-"&z20. F. zzzz   F.0-4@;iʇ !+ Root EntryD F@I@;iʇ AData WordDocumentFObjectPool ཀ@m!SummaryInformation(E,DocumentSummaryInformation8CompObjGj0TableC"      !"#$%&'()*+,-./0123456789:;<=>?@ABEIKJ   z $"#%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxy{|}~ObjInfoOle10Native@B.dOle10ItemName1TableM&      !"#$%/0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~_1042043550HRF iʇ iʇOle PIC QTLMETA CompObjSVfObjInfoOle10NativeUWEquation Native     !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Ole10Native9Equation Native =_988907067-P FD Ole @_1042043569JF[ȇ[ȇOle PIC ILLMETA SummaryInformation(DocumentSummaryInformation8_988907087F𽀤Ole !Prediction of Failure by Using Crack Driving Force and Crack Tip Opening Displacement (CTOD) Resistance Curves of Strength Mis-match Welded JointsredNenad GubeljakaenaNormaluKozaku11aMicrosoft Word 8.0r@n @0] @@~HRʇS՜.+,D՜.+, hp  0Laboratorij za strojne elemente in konstrukcije*f  Prediction of Failure by Using Crack Driving Force and Crack Tip Opening Displacement (CTOD) Resistance Curves of Strength Mis-match Welded Joints Title 6> _PID_GUIDAN{FDA11205-0C68-11D3-A678-0080489F4499}  FMicrosoft Word Document MSWordDocWord.Document.89qԘhyIPI  0 = 0 + 0 () 1/n ee 0 =ss 0 +ass 0 () 1 JFUlead Image Editor Image EditorImage EditorImage9q 0 0 490 256Oh+'04@Xdt     -HOle10Native9Equation Native =_988907067-P FD Ole @_1042043569JF[ȇ[ȇOle PIC ILLMETA SummaryInformation(DocumentSummaryInformation8_988907087F𽀤Ole !Prediction of Failure by Using Crack Driving Force and Crack Tip Opening Displacement (CTOD) Resistance Curves of Strength Mis-match Welded JointsredNenad GubeljakaenaNormaluKozaku10aMicrosoft Word 8.0r@(- @0] @@8.ʇS՜.+,D՜.+, hp  0Laboratorij za strojne elemente in konstrukcije*f  Prediction of Failure by Using Crack Driving Force and Crack Tip Opening Displacement (CTOD) Resistance Curves of Strength Mis-match Welded Joints Title 6> _PID_GUIDAN{FDA11205-0C68-11D3-A678-0080489F4499}  FMicrosoft Word Document MSWordDocWord.Document.89qԘhyIPI  0 = 0 + 0 () 1/n ee 0 =ss 0 +ass 0 () 1 JFUlead Image Editor Image EditorImage EditorImage9q 0 0 490 256Oh+'04@Xdt     -ԘhyIPI  0 = 0 + 0 () 1/n ee 0 =ss 0 +ass 0 () 1/n FMicrosoft Equation 3.0 DS Equation Equation.39q <F  .1  @ &  & MathType "-} }}M}}M} Symbol- 2 e 2 /e 2 s 2 Os 2 pa 2 s 2 Os Times New Roman Cyr2- 2 i0p 2 iv0p 2 iv 0p 2 1pSymbol- 2 = 2 m+Fences- 2 F 2 H 2 >G 2 & I 2 & K 2 >& J Times New Roman Cyr2- 2 M /> Times New Roman Cyr2- 2 np & "System-ssssL <ԘhyIPI  0 = 0 + 0 () 1/n ee 0 =ss 0 +ass 0 () 1/n FMicrosoft Equation 3.0 DS Equation Equation.39q <F  .1  @ &  & MathType "-} }}M}}M} Symbol- 2 e 2 /e 2 s 2 Os 2 pa 2 s 2 Os Times New Roman Cyr2- 2 i0p 2 iv0p 2 iv 0p 2 1pSymbol- 2 = 2 m+Fences- 2 F 2 H 2 >G 2 & I 2 & K 2 >& J Times New Roman Cyr2- 2 M /> Times New Roman Cyr2- 2 np & "System-ssssL <