STRESS ANALYSIS And FATIGUE Of Welded Structures STRESS .
STRESS ANALYSIS and FATIGUE of welded structuresSTRESS ANALYSIS and FATIGUE of weldedstructuresA. Chattopadhyay, G. Glinka, M. El-Zein, J. Qianand R. FormasABSTRACTFatigue analyses of weldments require detailed knowledge of the stress fields in critical regions. The stressinformation is subsequently used for finding high local stresses where fatigue cracks may initiate and for calculating stress intensity factors and fatigue crack growth. The method proposed enables the determination ofthe stress concentration and the stress distribution in the weld toe region using a special shell finite elementmodelling technique. The procedure consists of a set of rules concerning the development of the finite element mesh necessary to capture the bending and membrane structural stresses. The structural stress dataobtained from the shell finite element analysis and relevant stress concentration factors are subsequentlyused to determine the peak stress and the non-linear through-thickness stress distributions. The peak stressat the weld toe is subsequently used for the determination of fatigue crack initiation life. The stress distributionand the weight function method are used for the determination of stress intensity factors and for the analysisof subsequent fatigue crack growth.IIW-Thesaurus keywords: Structural analysis; Stress distribution; Finite element analysis.21IntroductionFatigue processes originate at stress concentration points,such as the weld toe in weldments. Both the fatigue crackinitiation and propagation stages are controlled by themagnitude and the distribution of stresses in the potentialcrack plane. The peak stresses at the weld toe can becalculated using stress concentration factors, available inthe literature, and appropriate reference stresses. Thesestress concentration factors are unique for given geometry and mode of loading. However, weldments are oftensubjected to multiple loading modes, and therefore it isnot easy to define a unique nominal or reference stress.For this reason, the use of classical stress concentrationfactors is limited to simple geometry and load configurations for which they were derived. This problem can beresolved by using the hot spot or structural stress, σhs concept applied initially in the offshore structures industry [1].If the stress concentration factors, based on the hot spotstress, σhs as the reference (or nominal stress), are knownthen the shell or coarse 3D finite element mesh models[2] can be used to determine only the hot spot stress atthe weld toe and subsequently to determine the peakstress by using appropriate stress concentration factors.Unfortunately, the hot spot stress based stress concentrations factors vary for the same geometry dependingon the type of loading, i.e. such stress concentration factors are not unique for a given geometry. This is a seriousdrawback if various multiple loads are applied to the sameweldment or welded structures.The purpose of the method discussed below is to find suchan approach that would require only stress concentrationfactors independent of the load configuration and appropriate reference stresses to be used. The only parametersneeded for estimating the stress peak and the stressdistribution induced by any combination of loads are onlythe geometrically unique stress concentration factors andappropriate reference or nominal stresses.2 The nature of the stressesin the weld toe regionThe stress state at the weld toe is multi-axial in nature. Butthe plate surface is usually free of stresses, and thereforethe stress state at the weld toe is in general reduced toone non-zero shear and two in-plane normal stress components (Figure 1). Due to stress concentration at theweld toe the stress component, σyy normal to the weldtoe line is the largest in magnitude and it is predominantlyresponsible for the fatigue damage accumulation in thisregion. Therefore, it is sufficient in practice to considerfor the fatigue analysis of welded joints only the stresscomponent, i.e. its magnitude and distribution across theplate thickness.Doc. IIW-2201, recommended for publication by Commission XIII “Fatigue of Welded Components and Structure.”1106 0037 WELDING 7 8 2011.indd 214/06/11 10:35:01
STRESS ANALYSIS and FATIGUE of welded structuresa) The overall geometryb) The stress stateat the weld toeFigure 1 – Stress state in the weld toe regionof a welded joint3 The hot spot stress and the stressconcentration factorThe nominal stress, σn in a plate without any attachmentsor notches [Figure 2 a)] would be equal to that one determined using the simple tension or/and bending stressformula. The existence of the attachment changes thestiffness in the weld toe region resulting in the stress concentration and non-linear through-thickness distributionas shown in Figure 2 b). However the nominal membraneand bending stresses, actually nonexistent in the weldedjoint, are the same as in the unwelded plate. Unfortunately,determination of meaningful nominal stress in complexwelded structures is difficult and often non-unique.Therefore the structural stress, σhs often termed as the ‘hotspot stress’, is used in some cases. The hot spot stress hasthe advantage that it accounts for the effect of the globalgeometry of the structure and the existence of the weld,but it does not account for the micro-geometrical effects[Figure 2 b)] such as the weld toe radius, r, and weld angle,Θ. Typical stress distributions in a welded connection withfillet welds are shown in Figure 2 b). These various stressa) Stress fields in an unwelded plateb) Stress fields in a plate with non-load carrying one-sidedattachment with fillet weldsFigure 2 – Stresses in unwelded and welded platedistributions are defined as follows; (A) represents theremote normal through-thickness stress distribution awayfrom the weld, (B) the actual through-thickness normalstress distribution in the weld toe plane, (C) the staticallyequivalent linearized normal stress distribution in the weldtoe plane, i.e. the stress distribution (C) yields the sameresultant force and bending moment as the actual stressdistribution (B). The linearized stress distribution (C) isindependent of the micro-geometrical weld parameterssuch as the weld radius, r, and the weld angle, Θ, contraryto the stress distribution (B) which does depend on thesefeatures. The statically equivalent linearized stress distribution (C) can be characterized by two parameters, i.e. themagnitude of the hot spot stress, σhs and the slope.The stress concentration factor and the peak stress aredependent on the magnitude and also the slope (gradient) of the linearized stress field C (Figure 3). Therefore1,a1,bV hsthe same hot spot stress (V hs), as seen in Figure 3,may ‘produce’ different stress concentration factors anddifferent peak stresses, σpeak. For this reason the hot spotstress alone is not sufficient for the determination of theload independent stress concentration factors. In order todefine a unique stress concentration factor dependent onthe geometry only both the magnitude and the gradientof the linearized (hot spot) stress must be accounted for.Therefore, Niemi [3] has proposed to decompose the linearized through-thickness stress field (Figure 3) into themuniformly distributed membrane (axial) stress field, V hsband the anti-symmetric bending stress field, V hs . This is avery useful concept because it captures the stress gradiment (V hsV hsb ) around the hot spot stress location. However,in order to determine appropriate magnitude of the peakstress, σpeak, the stress concentration for pure axial load( K tm,hs ) and pure bending load ( K tb,hs) need to be known.The advantage of using two stress concentration factorsK tm,hs and K tb,hs lies in the fact that they are independent ofthe load magnitude and are unique for a given geometry.In addition, the nominal stresses and the hot spot stressesfor pure axial loading are the same, and analogously thesame applies to bending load. Therefore the classicalFigure 3 – The effect of load configuration on throughthickness stress fields in two geometrically identicalweldments having the same hot spot stress magnitudebut different stress contributionsN 0708 2011 Vol. 55 WELDING IN THE WORLD1106 0037 WELDING 7 8 2011.indd 33Peer-reviewed Section14/06/11 10:35:02
STRESS ANALYSIS and FATIGUE of welded structuresbstress concentration K tm,hs and K t ,hs factors based on thenominal stress can be used. The peak stress, σpeak, necessary for the prediction of fatigue crack initiation can befinally determined as the sum of the membrane and purebending load contribution.V peakV hsm K tm,hs V hsb K tb,hsnoting that the definition of the classical nominal stressaround point B (Figure 4) is very vague in this case.In the case of shell finite element analysis the linearizedthrough-thickness stress is the final result of the analysisand can be easily extracted from the final output data.(1)Thus, in order to determine the peak stress, σpeak, thembaxial and bending hot spot stresses V hsand V hsrespecmtively and appropriate stress concentration factors K t ,hsband K t ,hs must be known. Therefore, it may be informative at this moment to clarify the difference between thelinearized stress field and the classical nominal stressand various stress concentration factor definitions usedin practice. The difference between the classical nominalstress and the original hot spot stress definition lies in thembfact that the hot spot stresses V hsand V hsare uniquelydefined at any point along the weld toe (Figure 4). Theycan be determined by linearization of the through-thickness stress below the point on the weld toe line where thepeak stress needs to be determined.The relationships between the actual through-thicknessbmand V hsstress distribution and hot spot stresses V hsare given by Equations (2) and (3) respectively and theyrepresent the average membrane and bending stresscontributions.4 Stress concentration factorsfor fillet weldsThe hot spot stresses under pure axial and pure bendingmloads are the same as the nominal stresses (V hsV nm andbbV hs V n ) and therefore the classical stress concentrationfactors can be used in Equation (1). Extensive literaturesearch was carried out [4-7] for this reason and severalstress concentration factor solutions were compared witheach other and verified using in-house finite elementdata. The most universal were the stress concentrationfactors supplied by Japanese researchers [7] and theyare discussed below. The generic geometrical configurations used for producing these stress concentration factors were the T-butt and cruciform welded joints shown in(Figure 5) and (Figure 6) respectively.04mV hs³t V x , y 0 dxt(2)0bV hs6 ³V x, y0 xdxtt2(3)Definitions and the method of determination of stressesV hsm and V hsb at points A and B (Figure 4) on the weldtoe line are the same and the stress concentration factorsK tm,hs and K tb,hs at those points are also the same if theweld geometry and dimensions are the same. Therefore,in order to determine the peak stress σpeak, at point A or Bthe same stress concentration factors K tm,hs and K tb,hs canbe used when correctly associated with the hot spot memmbbrane V hsand bending V hsstresses at those points. WorthFigure 4 – The actual through-thickness stress distributionsalong the weld toe line and the linearized staticallyequivalent stress fields1106 0037 WELDING 7 8 2011.indd 4Figure 5 – Geometry and dimensions of a T-butt weldedjoint subjected to axial and bending loadFigure 6 – Geometry and dimensions of a cruciform weldedjoint subjected to axial and bending load14/06/11 10:35:03
STRESS ANALYSIS and FATIGUE of welded structures– Stress concentration factor near one-sided fillet weldunder axial load (Figure 5, point A)Kmt ,hs§1 exp 0.94 1 §1 exp 0.45S 0.65W · ªº «»2h ¹h1u«u »(4)WW · « 2.8 § · 2 r » «» t ¹¼2h ¹ – Stress concentration factor near one-sided fillet weldunder bending load (Figure 5, point A).§W ·1 exp 0.94 2h ¹§ 2t p2r · K tb,hs 1 u 1.9 tanh u§W · t 2h t ¹1 exp 0.45S 2h ¹ 4 ºª § 2h ·0.25 º ª§ r·« » « 0.13 0.65 1 »«t t¹ »tanh « ¹ » u «1»r »«»§ r ·3« 1 t » « » ¼ « t ¹¼V hsb(5)W (t 2h) 0.3 (tp 2hp )Equations (4) and (5) are semi-empirical in nature andhave been derived using analytical solutions for stressconcentrations at corners supplemented by extensivefinite element stress concentration database. Their application was verified for a range of geometrical configurations limited to 0.02 r/t 0.16 and 30 Θ 60 .Similar expressions have also been derived for stress concentration factors in cruciform welded joints [7] and theyapply in general to weldments with two symmetric filletwelds placed on both sides of the load carrying plate.– Stress concentration factor for a cruciform joint subjected to an axial load (Figure 6, point A).K tm,hsW · 2h ¹ª«1u 2.2 «« 2.8 § WW · « t2h ¹ºh»u »r»·2 »¼¹The linear through-thickness stress field is naturallyembedded in as the property of most basic shell finiteelements. The output stresses are the stress components12and V hs(Figure 7) acting on each side of the plateV hsthickness. Therefore the determination of the membraneand bending hot spot stresses requires only simple postprocessing as shown below.V hsmwhere§1 exp 0.94 1 §1 exp 0.45S 5 The shell finite element model12V hs V hs(8)212V hs V hs(9)2Unfortunately, such a simple finite element model as thatone shown in Figure 7 b) is not capable of supplying sufficiently accurate stresses in the weld toe region. This isdue to the fact that the critical cross-section in the actualwelded joint is located at the weld toe (sections A and B,Figure 7) being away from the mid-planes intersection. In12and V hsand theaddition, the magnitude of stresses V hsresultant slope of the linear stress field depend on the distance from point ‘O’ [Figure 7 b)] and the size of the shellelement. The shell stresses in the weld toe region dependstrongly on the local stiffness of the joint and, therefore,they are sensitive to how the weld stiffness is accountedfor in the finite element shell model. It is important to modelthe weldment and any welded structure in such a way thatmbthe hot spot shell membrane V hsand bending stress V hsincritical cross-sections [Figure 7 b)] are the same as thosewhich would be determined from the linearization of theactual 3D stress fields, obtained analytically or from finemesh 3D finite element model [Figure 7 a)] of the joint. Inother words the shell model of the weld needs to be alsoincluded.5Fayard, Bignonnet and Dang Van [8] have proposed ashell finite element model with rigid bars simulating the0.65(6)– Stress concentration factor for cruciform joint subjected to bending load (Figure 6, point A).§W ·1 exp 0.94 2h ¹§ 2t p2r · u tanh u1K tben,n§W · t 2h t ¹1 exp 0.45S 2h ¹ 4 ºª § 2h ·0.25 º ª§ r·« » « 0.13 0.65 1 »«t t¹ »tanh « ¹ » u «1»r »«3 1r«»§ ·«»t ¼ « » t ¹ ¼(7)whereW (t 4h) 0.3(tp 2hp)Equations (6) and (7) are also empirical in nature andhave been derived using extensive finite element stressdata. The range of application for these expressions is:r/t 0.1-0.2, h/t 0.5-1.2, Θ 30 -80 .a) Welded joint and stress distributionsin critical cross-sectionsb) Shell finite element model and resultant stressdistributionsFigure 7 – A welded joint and its simple shell finiteelement modelN 0708 2011 Vol. 55 WELDING IN THE WORLD1106 0037 WELDING 7 8 2011.indd 5Peer-reviewed Section14/06/11 10:35:07
STRESS ANALYSIS and FATIGUE of welded structuresweld. They have also formulated a set of rules concerningthe finite element meshing in order to capture correctlythe properties of the linear stress field. However, usingshell elements and rigid bars was found not very convenient in practice. Therefore, a new model involving onlyshell elements of the same type in the entire structurewas proposed.There are two important issues concerning the shell FEmodelling of welded joints namely: the simulation of thelocal weld stiffness and the location of the stress reference point where the stress corresponding to the actualweld toe position is to be determined. Therefore, the shellfinite element model has to be constructed in such a waythat the location of the stress reference point coincideswith the actual position of the weld toe (Figure 7).In order to assure that the global effects of the jointgeometry and the weld are adequately modelled, a setof rules have been formulated concerning the construction of appropriate finite element shell model as shown inFigure 8. The meshing principles of the model are illustrated using as an example a T-welded joint. The followingsteps need to be carried out while creating appropriateshell finite element mesh.6a. Connect the mid-thickness plate planes[Figure 8 a) and 8 b)], and add one layer (blue)of inclined shell elements representing theweld.b. The first and the second row of elementsadjacent to the theoretical intersection lineof mid-thickness planes must be of the size(tp h)/4 in the ‘x’ direction for elements inthe main plate and (t h)/4 in the ‘y’ directionfor elements in the attachment. The shell elements simulating the weld are subsequentlyattached to each plate in the middle of theweld leg length and they are spanning the firsttwo rows of elements in each plate. The thickness of the shell elements simulating the weldis recommended to be equal to the thicknessof the thinner plate being connected by theweld (i.e. either t or tp whichever is less). Allshell elements simulating the weld are of thesame thickness.All shell elements in the weld region have thesame dimension in the z direction and it isequal or less than the half weld leg length, i.e.‘h/2’ or less.c. The shell elements in the third row simulating the main plate should have the size equalto the half weld leg length ‘h/2’ in the ‘x’ and‘z’ directions and the same ‘h/2’ dimensionin the ‘y’ and ‘z’ directions for elements in theattachment plate [Figure 8 b)]. The choice ofsuch element dimensions enables to locatethe reference points A at the nodal points ofelements from the third row. The location ofa) Side view of a T-joint with single fillet weldb) The shell finite element modelc) Superposition of the actual welded joint and its shell finite element modelFigure 8 – Rules for constructing the shell finite element mesh of a welded T-joint1106 0037 WELDING 7 8 2011.indd 614/06/11 10:35:08
STRESS ANALYSIS and FATIGUE of welded structuresthe reference point A must coincide with thephysical position of the weld toe. Thus stressesat the reference point A are the same as thenodal stresses and they can be extractedwithout any interpolation or additional postprocessing.d. The dimension ‘z’ of the first two rows of elements adjacent to the intersection of platemid-thickness planes is dictated by the smallest element in the region, i.e. it should not begreater than half of the weld leg length ‘h/2’. Itmeans that the first and the second row of elements in the main plate [Figure 8 b)] have thedimension of [(h/4 tp/4) h/2]. The first tworows of elements in the attachment countedfrom the mid-plane intersection should havethe size of [(h/4 t/4) h/2]. The elementsin the third row are (h/2 h/2) in size. Thespacing in the ‘z’ direction might need to besmaller than half of the weld leg length ‘h/2’while modelling corners of non-circular tubesor weld ends around gusset plates.5.1 Determination of the peak stressat the weld toeIn order to determine the peak stress σpeak at the weld toemit is necessary to determine the membrane V hsand bendbing V hs stress from the shell finite element model usingEquations (8-9). Then the stress concentration factorsK tm,hs and K tb,hs for tension and bending need to be calculated from Equations (4-5) or (6-7) by using actual dimensions of the weld. The peak stress σpeak can be finally calculated from Equation (1).
Θ. Typical stress distributions in a welded connection with fi llet welds are shown in Figure 2 b). These various stress a) The overall geometry b) The stress state at the weld toe Figure 1 – Stress state in the weld toe region of a welded joint a) Stress fi elds in an unwelded plate b) Stress fi elds in a plate with non-load carrying one .
Application of ASME Fatigue Code: 3-F.1 ASME Smooth Bar Fatigue Curves Alternative Effective Stress vs Fatigue Cycles (S-N Curve) With your weld quality level assessed and an accurate FEA stress number, one can use the ASME fatigue curve to calculate the number of Fatigue Cycles. In our prior example, the fatigue stress could be 25.5 ksi or as .
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contribute to fatigue risk. A pre-implementation study shall consider the following: implementing a survey of personnel on fatigue and fatigue-management strategies analyzing exposure to fatigue risk on work schedules (e.g., bio mathematical fatigue modeling)
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1. Stress-Strain Data 10 2. Mohr Coulomb Strength Criteria and 11 Stress Paths 3. Effect of Different Stress Paths 13 4. Stress-Strain Data for Different Stress 1, Paths and the Hyperbolic Stress-Strain Relationship 5. Water Content versus Log Stress 16 6. Review 17 B. CIU Tests 18 1. Stress-Strain Data 18 2.
2D Stress Tensor x z xx xx zz zz xz xz zx zx. Lithostatic stress/ hydrostatic stress Lithostatic stress Tectonic stress Fluid Pressure-Hydrostatic-Hydrodynamic Lithostatic Stress Due to load of overburden Magnitude of stress components is the same in all
fatigue (endurance) limit, ferrous and titanium alloys. This value is the maximum stress which can be applied over an infinite number of cycles. The fatigue limit for steel is typically 35 to 60% of the tensile strength of the material. Fatigue strength. is a term applied for nonferrous metals and alloys (Al, Cu, Mg) which do not have a fatigue .
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