Residual stress calculation for butt welding.

Catana, Dorin ; Popescu, Rodica ; Catana, Dorina 等

1. INTRODUCTION

The evolution of the world metal materials production enforces the implicit development of the thermal treatment technologies. Perfecting the heating methods plays an important role in both quantitative and qualitative development of the thermic treatment technologies. For welded products this evolution is critical for heating rate, process energetic threshold and for technological effects afterward. These desiderates can be achieved through improving the thermic treatment technology alongside assisting the thermic treatment by means of computer, which can be applied in the case of the butt head welding pipes. Taking into account the big quantity of steel for pipes, destined to performing the welded structures, conclusions can be drawn on the importance of the welded technologies and thermic treatment on the welded joints. The welding technologies have known a distinguished boom through the knowledge of the materials' behaviour during the welding process and afterwards, perfecting the welding procedures allowing the joints to be executed for different materials in a wide range of dimensions. The new joint technologies' economical implications are:

--reduced material expenses;

--reduced energy costs;

--isotropic and homogeneous joints.

The thermal treatment applied to butt welding pipes plays an important role because an inappropriate tension-release of the performed welding can result in consequences as to the subsequent functioning of the welded set. It is worth mentioning that most of these pipes are underground which makes it extremely difficult to locate and fix the cracks.

2. THEORETICAL CONSIDERATIONS

During the operations of welding the parts to be joined, within the products are internal tensions that equilibrate themselves within their volumes and stay integrally or partially within them, as residual tensions. The presence of the residual stresses has a sensitive bearing on the products' behaviour during the following operations of treatment and exploitation, too. As for the cause that generates them, the internal tensions are of two types (Balauca & Popescu, 2007):

--thermal tensions, due to the expansions' irregularities and contractions resulted from lack of simultaneity of the heating and cooling process in different micro-volumes of the metallic body;

--structural tensions, due to expansions' irregularities and contractions which come alongside the phase transformations that are caused by alternative heating and cooling in different micro-volumes of the metallic body. The thermal tensions turn up as a result of the cold steel hindering the deformation process; the steel is not heated by the thermic source. The thermal tensions can be assessed on the basis of Hook's law taking into account the elastic features of the steel:

[sigma](t) = [epsilon] -E([t.sub.1] - [t.sub.0]), (1)

where:

[epsilon]--specific linear deformation;

E--elasticity module;

[t.sub.1]--heated area temperature;

[t.sub.0]--cold area temperature.

The residual tensions that come during the welding process can even reach the material's flowing limit. The practical need for diminishing and removing these tensions is determined by their vicious influence in certain conditions on some exploitation properties, such as: by the tendency for fragile rupture, cracking by corrosion and exhaustion.

In view of diminishing the level of residual tensions in the welded joints, which can produce brittleness-cracking phenomena, there are some methods, but the most known is that of applying (after the welding process) the thermal tension-releasing treatment (TTD), which consists of heating to a certain temperature, keeping at that temperature and cooling.

Among the metallurgical implications of this treatment there are the following:

--restoring the deformed crystalline networks;

--rearranging the dislocations;

--blocking the sliding and limits of the grains by a fine dispersion of the stabile particles.

From analyzing the mathematical methods of the tension-releasing process, a conclusion can be drawn that this is firstly dependent on the plastic flowing speed.

The present standards take into account the experimental results, which showed that the plastic flowing speed is proportional with the value of the residual tension, but it does not reflect another phenomenon encountered in practice, such as that the plastic flowing speed increases with approaching to the flowing limit of the material (Candea & Popescu, 2007).

Here is an equation for the elastic flowing speed:

[??] = K x [sigma] / [[sigma].sub.c] - [sigma], (2)

where:

K--flowing creep rate;

[sigma]--initial residual tension;

[[sigma].sub.c]--material's flowing tension.

During the process of tensions' relaxation, the specific extension can be determined with equation (3).

[[epsilon].sub.0] = [epsilon] + [[epsilon].sub.p] (3)

Deriving the equation (3) in relation with time and taking into account equation (2), we get the differential equation of the thermal tension-releasing process (equation 4).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

All values in equation (4) are dependable on time. A possibility of resolving the equation (4) is adopting sizes E, a and K as temperature functions which in its turn are dependable on time. The functions E (t), [[sigma].sub.c](t) can be found in the product norms or they can be experimentally determined through known methods (Popescu et al., 2005).

Even if there are particular values of sizes, regression analytical functions can be calculated. The values of coefficient K can be determined using the relation (2), if the plastic flowing speed is known.

The internal tensions in different moments of the thermal tension-releasing process are given by the solutions of the differential first-degree equations. Because an analytical solution cannot be found to this equation, a numerical solution was found by using Runge-Kutta method.

Another possibility consists in solving the equation (4) through other procedure than Runge-Kutta method, this being suggested from now on. The process is divided in time intervals by pitch p (Popescu et al., 2007), and the solutions a(t) and E (t) can be written with equation (5).

[sigma](t) = [sigma](I) - [sigma] (I - 1) / p; E(t) = E(I) - E(I - 1) / p (5)

By replacing equation (5) with equation (4) and performing the calculations, a second-degree equation results, such as:

A x [[sigma].sup.2] (I) - B x [sigma] (I) + C = 0 (6)

where:

A = E(I) / E(I - 1) B = [[sigma].sub.c](I) x E(I - 1) / E(I) + [sigma] (I - 1) + K(I) x E(I) x p C = [[sigma].sub.c](I) x [sigma] (I - 1) (7)

All values from equation (6) and (7) are known. The material characteristics E, [[sigma].sub.c] and K have known functions during the whole process, and the tensions only turn up with the value [sigma](I-1), which is known from the previous calculation step. On the basis of the pattern suggested, there have been determined the expressions of the material's characteristics according to temperature (see table 1), only for the heating phase during the thermal treatment process, applied to a steel brand OLC45 (0.45 %C). By comparing the accuracy of the two methods, table 2 shows the tension's values at the end of heating cycle (Balauca et al., 2005).

The flowing stress's values at different temperatures can be obtained from the function ac(t) presented in table 1. Following the calculation, the flowing stress's values are: ac(20)=365.99 MPa, [[sigma].sub.c] (200)=329.73 MPa, [[sigma].sub.c] (400)=249.05 MPa, and [[sigma].sub.c] (600)=177.8 MPa.

3. CONCLUSIONS

As a result of pipe's butt welding, internal tension within the material will appear but critical tensions from butt seam are increased with 34.44% over steel yield limit. After applying the tension-releasing thermal treatment (TTD), the butt seam diminishes with 35. 6% in comparison to the flowing limit, the measurements performed on the internal tensions highlighting the efficiency of the local thermic treatment.

The theoretical and experimental researches performed establish the mathematical equations of the elasticity module and flowing limit after tension releasing. Also the mathematical equation for creep rate was established. Based on determined equations, thermal treatment parameters can be established in order to avoid cracks in welded joint while operating.

By using the same procedure these characteristics can be determined for any kind of material.

4. REFERENCES

Balauca, I.; Ploscariu, C. & Tont, F. (2005). Final heat treatment for welded joints in piping, Proceedings of International Conference on Materials Science and Engineering, pp. 135-138, ISBN 973-635-454-7, University Transylvania, 02.2005, University Transylvania, Brasov

Balauca, I. & Popescu, R. (2007). Contribution to establishing the reliability of ash delivery piping in steam power plants, Proceedings of International Conference on Materials Science and Engineering, Catana, D., pp. 279-282, ISSN 1223-9631, University Transylvania, 02-2007, Supplement of Bulletin of Transilvania University of Brasov, Brasov

Candea, V. & Popescu, R. (2007). The mechanism of fissuring in welded joints, Bulletin of Polytechnic Institute of Jassy, Vol. LIII, No. 4, 05.2007, pp. 111-114, ISSN 1453-1690

Popescu, R.; Candea, V. & Balauca, I. (2005). The influence of allied elements on steels used in steam power plants, Bulletin of Polytechnic Institute of Jassy, Vol. LIII, No. 4, 05.2007, pp. 341-344, ISSN 1453-1690

Popescu, R.; Balauca, I. & Medan, R. (2007). Methods for determining the reability of service pipes for transporting cinder in power plants, Bulletin of Polytechnic lnstitute of Jassy, Vol. LIII, No. 4, 05.2007, pp. 337-340, ISSN 1453-1690

Table 1. Material characteristics according to temperature.

E(t)= [A.sub.1] * [t.sup.3] [A.sub.1] = -1.584559 * [10.sub.-4]
+ [B.sub.1] * [t.sup.2] [B.sub.1] = 3.042152 * [10.sub.-3]
+ [D.sub.1] [C.sub.1] = -32.70786
 [D.sub.1] = 210654

[[sigma].sub.c](t) = [A.sub.2] = 9.949638 * [10.sub.-7]
[A.sub.2] * [t.sup.3] + [B.sub.2] = -1.112616 * [10.sub.-3]
[B.sub.2] * [t.sup.2] + [C.sub.2] = -6.420578 * [10.sub.-3]
[D.sub.2] [D.sub.2] = 366,56

K(t) = [K.sub.min] + [K.sub.min] = [10.sub.-7]
[A.sub.3][eXp([B.sub.3] * t) [A.sub.3] = 2.895451 * [10.sub.-9]
- 1] + [C.sub.3] * t [B.sub.3] = 1.303368 * [10.sub.-2]
 [C.sub.3] = 6.363989 * [10.sub.-2]

Table 2. Stress values at the end of heating cycle.

[t.sub.0] [t.sub.max] Time P [MPa] Final stress [MPa]
[[degrees] [[degrees] [h] R-K Eq. (6)
 C] C]

 20 300 3 1000 100 93.6733 93.6731
 10 93.5363 93.5361
 600 3 100 200 148.0739 147.9977
 3 1000 148.074 148.0658
 10 143.3567 143.3380