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Determination of residual welding stresses in load bearing structures made of welded hollow sections/Liekamuju itempiu nustatymas apkrovas perimanciose konstrukcijose, pagamintose is suvirintu vamzdiniu profiliu/Paliekoso metinasanas spriegumu noteiksana nesosa konstrukcija no slegta proila metinatam dalam/Keevitamise jaavpinge maaramine koormust kandvates keevitatud ooneskonstruktsioonides.

1. Introduction

Recently more and more hollow sections from structural steel are used as the main load bearing structures for bridges. Using those profiles makes structures light weighted, saves materials and empowers to build well-balanced and economic bridges.

Most popular standard profiles between hollow sections are square and rectangular tubes. Exploitation of steel bridges proves that highest risks of failure occur in welded joints. Local expansion and shrinkage during the welding process generates local stresses and deformations in welded joints and heat-affected zone.

Residual stresses summarize together with external loads and minimize load-bearing abilities as well as originate brittle-plastic fracture due to specificity of the structure geometry.

The effect of welding process to load bearing abilities in thin-walled cylinders was described in previous studies (Cheng, Finnie 1986). Curvature of welded joints was described in studies (Teng et al. 2002). Residual stresses of welding were analyzed by (Jang et al. 2001). Finite element (FE) modeling methodology was described by Kiselev (1998), MeflBegeB (2001), Grigorjeva et al. (2008) and Ziari et al. (2007).

However, welded joints in square tubes are studied like simply welded plates due to the specific geometry. Comparable studies were made by Wimpory et al. (2003) and Makhenko et al. (2006).

FE modeling was chosen for residual welding stresses in square profile tube butt joints. As described later, this method allows changing tube profile, welded joint geometry, welding sequence, and material properties. This enables detailed evaluation of technological process and joint geometry.

2. Finite element model

Calculations were made in two stages. During stage 1 nonstationary task was solved. Here, the temperature field around welding area during and after the welding process was calculated. In stage 2 the strength calculations of welded joint determining stresses during the welding and residual stresses after the joint cooled down to room temperature were made.

For calculating temperature field the FE model consisting from 19824 SOLID70 type finite elements (98932 nodes) was developed. FE model of welded joint split to elements, and fragment of welded joint are shown in Fig. 1.

Thermal calculations were performed in 20 steps. First 19 steps were the simulation of welding process and the last step--cooling after final welding step. Welding sequence was simulated according to Fig. 2.

Each side of the tube was heated in four steps, and a welding period for one side made 12 s. Strength analysis was proportionately performed in 20 steps, respectively determining movements, deformations, and stresses. After the last step, temperature in all nodes was computed equal to 25[degrees]C.

While using FE method the calculated results were highly dependent on how exactly mechanical properties of the material were described. This is extremely important as these properties vary in the calculated range of temperatures. Using catalogues, those properties were found for pure materials, or their main alloys. Solving this model, mechanical properties of structural steel S355 J2 were needed in range of temperatures from 20[degrees]C to 1500[degrees]C (steel melting point).

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

Mechanical properties of structural steel S355 J2 were taken from Eurocode 3. Thermal conductivity, specific heat, and enthalpy reliance on temperature are shown respectively in Figs 3-5.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Structural steel S355 J2 stress and strain dependence results were taken from the tests implemented by Outinen et al. (2001) and shown in Fig. 6.

[FIGURE 6 OMITTED]

Fig. 7 shows Young's module for steel S355 J2 reliance on temperature. Poisson's ratio of main steel in full thermal ranges is taken equal to 0.3 and is the same as in welded joint.

[FIGURE 7 OMITTED]

3. Thermal fields of welded joints

Intermediate process of thermal field calculations takes the main part of calculations. FE formulation is presented below for describing variable thermal processes. Thermal balance equation of FE is as follows:

[[K.sup.e]]{[T.sup.e]} = {[S.sup.e][infinity]} + {[P.sup.e]} + {[P.sup.e]} {[Q.sup.e]}, (1)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

is thermal conductivity matrix for the element.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is vector of temperature in element nodes, (3)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

is thermal power vector for the element caused by convection.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

is thermal power vector for the element caused by volumetric heat sources.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

is thermal power vector for the element received from nearby elements.

Eq (1) describes stationary (constant in time) thermal conductivity process. Solving this equation yields temperature settlement during the long period on various nodes of the element, as conditions of heat source and heat exchange with surroundings are determined.

This process flow in time is described by non-stationary equation for thermal conductivity. It is necessary to know two more physical constants for the material: specific heat, and density.

In Eq (1), additional members are filled as caused by element heat capacity. We admit beam temperature is non-stationary and in any of its cross-sections x vary with speed:

[partial derivative]T(x)/[partial derivative]t = [??](x) (7).

This process is possible as any small segment of the beam length dx additionally is supported by heat power proportionally of beam part capacity Adx, and temperature decreasing speed T(x).

Heat power applied to whole beam is equal to:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8).

This heat power is distributed to nodes of discrete element:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

And described as matrix:

[[C.sup.c]] [[[??].sup.e]} + [[K.sup.e]] {[T.sup.e]} = {[S.sup.e][infinity]} + {[P.sup.e]} + {[Q.sup.e]}, (10)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is heat capacity matrix for the element.

Element heat capacity matrixes are collected into structure matrix according to known general rules, and non-stationary thermal balance equation is:

[C]{T}+[K]{T} = {[S.sub.[infinity]} + {P}+{Q}. (11).

Eq (11) is usually solved by numerical integration. In this study most famous FE system ANSYS is chosen for describing transitional thermal processes according to the adopted algorithm.

Algorithm for the chosen task is very similar:

--for pre-processor system, geometrical model was made in a way that was possible to change its geometry, and materials. Splitting to FE and calculating model was made;

--most suitable solver is chosen where boundary conditions are set;

--for post-processor system, received results are being analyzed.

Executed thermal calculations of intermediate processes with FE method boundary conditions are described by heat release coefficient, temperature of surrounding and primary temperature of the model. Further, a method on heat release coefficient calculation is presented. Subject of chosen model is a structural steel tube, dimensions 60x60x3 mm, with steel grade S355J2. Total heat release coefficient is calculated taking into account the forced and natural convection and radiation.

3.1. Evaluating radiation in calculations of total heat release coefficient

Radiation heat interchanges between surface of steel ([T.sub.L] = const.) and isothermal surroundings ([T.sub.a] = const.) are described in Eq (12):

[a.sub.r] = 4[[epsilon].sub.12][[sigma].sub.0][T.sup.3.sub.L], W/[m.sup.2]K. (12)

System blackness level evaluation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (13)

Radiation constant:

[[sigma].sub.0] = 5.67 x [10.sup.-8], W/[m.sup.2][K.sup.4]. (14)

Thus,

[[alpha].sub.r] = 4 x 0.14 x 5.67 x [l0.sup.-8] [T.sup.3.sub.L], W/[m.sup.2]K. (15)

Formed glass temperature decrease is assessed by the following differential equation:

-[mc.sub.p] d[T.sub.s] = [alpha]F{[T.sub.s] - [T.sub.a])dt, (16)

[K.sub.a] = [mc.sub.p]/F = 10 x 1500/200 x 0.37 x 0.37 [congruent to] 550. (17)

Thus, differential equation:

dt/550 = d[T.sub.s]/[T.sub.s] - [T.sub.a]. (18)

With integration limits:

t [right arrow] 0 / t,

[T.sub.S] [right arrow] [T.sub.L] / [T.sub.S]

is obtained

[T.sub.s] = [T.sub.a] + ([T.sub.L] - [T.sub.a] exp (- t/[K.sub.a] (19)

[T.sub.S] = [T.sub.a] + ([T.sub.L] - [T.sub.a] exp (- t/550]. (20)

Inserting [T.sub.S] instead of [T.sub.L] yields:

[[alpha].sub.r] = 3.175 x [10.sup.8][[[273 + ([T.sub.L] - 273) x exp (- t/550)].sup.3], (21)

where t--seconds; [T.sub.L]--steel melting point.

3.2. Convectional heat exchange evaluation when calculating total heat release coefficient Suppose steel plate with width varying by axis x, airflow with speed [w.sub.0] is supplied. Airflow speed on the surface of steel plate is [w.sub.x].

Then [[alpha].sub.x]x/[[lambda].sub.0] 0.332 x [P.sup.1/3.sub.r0] x [R.sup.1/2.sub.ex], (22)

where

[R.sub.ex] - [w.sub.x]x/[v.sub.o] (23)

Used known values are as follows:

0.332 [0.72 x 1/3 x 0.025/[(15 x [10.sup.-6]).sup.1/2], (13)

admitting the following

[w.sub.x] = [w.sub.0] [([r.sub.0]/x).sup.2]. (24) KXJ

Thus,

[[alpha].sub.x] = 1.86 x 1/x [([w.sub.x] x x).sup.1/2], (25)

and

[[alpha].sub.x] = 1.86 x [w.sup.1/2.sub.0] x ([d.sub.0]/2]) x 1/[x.sup.2.5], (26)

3.3. Evaluation of shield heat exchange by natural convection (caused by [DELTA]T) when calculating total heat release coefficient

Supposing [d.sub.e] is the measure that occurs from convection when surrounding environment is air, [P.sub.r] = 0.7.

[N.sub.u] = 0.429 x [Gr.sup.1/4.sub.r],

[N.sub.u] = [[alpha].sub.n] x [d.sub.e]/[[alpha].sub.0] - Nuselt number, (27)

[G.sub.r] = g x [d.sup.3.sub.e] x [beta] x [DELTA]T/[v.sup.2.sub.0] - Grasghof number, (28)

where [lambda].sub.0] = 0.025W/mK; [v.sub.0] = 15 x [10.sup.-6] [m.sup.2]/s; g = 9.81 m/[s.sup.2]; [beta] = 1/273 1/K.

Thus,

[[alpha].sub.n] = [[lambda].sub.0] x 0.429 x [(g x [beta]/[v.sup.2.sub.0]).sup.1/4 x [([DELTA]T).sup.1/4] x [d.sup.1/4.sub.e]. (29)

Therefore,

[[alpha].sub.n] = 1.206[[([T.sub.L] - 273])exp(- t/550)].sup.1/4][d.sup.1/4.sub.e]. (30)

As shown, total heat release coefficient evaluating natural and forced convection and radiation is described:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (31)

Considering that Eq (31) has several variable values (time, coordinates, airflow speed) with the help of MATLAB software package ruling program for calculations of total heat release coefficient on various places of the model, according to the surrounding conditions and the forced cooling conditions in certain period was made.

3.4. Thermal fields of defect-free welded joints

Thermal fields of welded tube butt joint were calculated in three cooling modes: intensive, average and slow. Highest differences in temperatures were noticed as intensive temperature decrease in welded joint was performed.

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

[FIGURE 12 OMITTED]

[FIGURE 13 OMITTED]

4. Residual stresses calculation results

In this section, results of welding residual stresses in defect-free tube butt joint are presented. Fig. 14 shows positions of coordinate axes regarding to welded joint geometry.

[FIGURE 14 OMITTED]

[FIGURE 15 OMITTED]

[FIGURE 16 OMITTED]

[FIGURE 17 OMITTED]

[FIGURE 18 OMITTED]

[FIGURE 19 OMITTED]

4. Conclusions

Using FE method, the distribution of temperatures in the various points of welding area was obtained. The process was described in a time flow. Total heat release process was calculated taking into account forced and natural convection and radiation. That enabled calculating heat release coefficient in various points of the model.

During calculations, different cooling modes were used: intensive, average and slow. Highest differences of temperatures were noticed when intensive cooling of welded joint was performed.

Welding residual stresses were calculated after joint welding process and cooling down to room temperature. The highest values of residual stresses were found on corners of tube butt joints. That shows high-risk areas in such kind of welded joints.

doi: 10.3846/bjrbe.2010.08

Received 17 August 2008; accepted 7 January 2010

References

Cheng, W.; Finnie, I. 1986. Measurement of Residual Hoop Stresses in Cylinders Using the Compliance Method, Journal of Engineering Materials and Technology 108(2): 87-92. doi:10.1115/1.3225864

Grigorjeva, T.; Juozapaitis, A.; Kamaitis, Z.; Paeglitis, A. 2008. Finite Element Modeling for Static Behavior Analysis of Suspension Bridges with Varying Rigidity of Main Cables, he Baltic Journal of Road and Bridge Engineering 3(3): 121-128. doi:10.3846/1822-427X.2008.3.121-128

Jang, G. B.; Kim, H. K.; Kang, S. S. 2001. Effect of Root Opening on Mechanical Properties, Deformation and Residual Stress of Weldments, Welding Journal 80(3):80-89.

Kiselev, S. N.; Kiselev, A. S.; Kurkin, A.; Aladinskii, V. V.; Makhenko, V. O. 1999. Current Aspects of Computer Modelling Thermal and Deformation Stresses and Structure Formation in Welding and Related Technologies, Welding International 13(4): 314-322. doi:10.1080/09507119909447387

Makhenko, V. I.; Pochynok, V. E. 2006. Strength Calculation of Welded Joints with Crack-Like Imperfections. Kiev: E. O. Paton Electric Welding Institute. 266 p. ISBN 966-8872-02-9.

Outinen, J.; Kaitila, O.; Makelainen, P. 2001. High- temperature Testing of Structural Steel and Modelling of Structures at Fire Temperatures. Research Report. Helsinki University of Technology.

Teng, T.-L.; Fung, Ch.-P.; Chang, P.-H. 2002. Effect of Weld Geometry and Residual Stresses of Fatique in Butt-welded Joints, International Journal of Pressure Vessels and Piping 79 (1): 467-482. doi:10.1016/S0308-0161(02)00060-1

Wimpory, R. C.; May, P. S.; O'Dowd, N. P.; Webster, G. A.; Smith, D. J.; Kingston, E. 2003. Measurement of Residual Stresses in T-Plate Weldments, Journal of Strain Analysis for Engineering Design 38(4): 349-365. doi:10.1243/03093240360692931

Ziari, H.; Keymanesh, M.-R.; Khabiri, M. M. 2007. Finite-Element Modelling of Crack Sealant Flexible Pavement, he Baltic Journal of Road and Bridge Engineering 2(2): 89-93.

[TEXT NOT REPRODUCIBLE IN ASCII], C. B. 2001. [TEXT NOT REPRODUCIBLE IN ASCII] Medvedev, S. V Computer modeling of residual welding deformations beside technological designing of welding constructions], [TEXT NOT REPRODUCIBLE IN ASCII] [Welding production] 8: 10-17.

Antanas Ziliukas (1), Andrius Surantas (2)

(1,2) Kaunas University of Technology, Strength and Fracture Mechanics Centre, Kestucio g. 27, 44025 Kaunas, Lithuania E-mails: (1) antanas.ziliukas@ktu.lt; (1) andrius.surantas@gmail.com
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Author:Ziliukas, Antanas; Surantas, Andrius
Publication:The Baltic Journal of Road and Bridge Engineering
Article Type:Report
Geographic Code:4EXLT
Date:Mar 1, 2010
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