FINITE ELEMENT ANALYSIS OF THE THERMAL RESIDUAL STRESSES OF PRECIPITATE FORMED DURING THE WELDING PROCESS

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3^ème Conférence Internationale sur

le Soudage, le CND et l’Industrie des Matériaux et Alliages (IC-WNDT-MI’12) Oran du 26 au 28 Novembre 2012.

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FINITE ELEMENT ANALYSIS OF THE THERMAL RESIDUAL STRESSES OF PRECIPITATE FORMED DURING THE WELDING

PROCESS

Hamida Fekirini¹, Boualem Serier ¹, Farida Bouafia^{1, 2} et Sidi Ahmed Bouafia²

1: LMPM, Mechanical Engineering Department, University of Sidi Bel Abbes, BP 89, Cite Arbi Ben M’Hidi, Sidi Bel Abbes 22000, Algeria

2: Institute of Science and Technology, University of Ain Temouchent, BP 284 RP, Ain Temouchent, 46000, Algeria.

E-mail address: fe_hamida@yahoo.fr

Abstract:

In the present work the finite element method is used to analyze the distribution and the level of residual stress induced in a matrix by the phenomena of precipitation Fe2C compounds resulting from the process of welding. The effect of temperature and the interaction between precipitates on the residual stress level were highlighted.

Keywords : Weld, Defect, Precipitate, Contrainte résiduelle.

1 Introduction

The carbon is one of the most important alloying elements in iron and steel, which is a solid solution in austenite and ferrite or forms carbide with other elements. The types and quantities of carbide have a decisive effect on mechanical properties, deformation behavior and many other properties of steel. The Fe2C carbide, which is identified as epsilon (ε)-carbide by Jack [1] with a hexagonal crystal structure, precipitates in tempered steels. It has also been shown afterwards that the Fe2C forming in tempered martensite has an orthorhombic structure isomorphous with the transition metal carbides of the M2C type [2], which is designated as eta (η)-carbide. Although the cold deformation becomes one of the study focuses on high carbon steels, the investigation on the properties of metastable carbide Fe2C is far from sufficient. Cementite dissolution due to pearlite cold deformation occurs [3–5] as well as metastable carbide Fe2C is observed during dissolution of the pearlite [6].

In certain steel welded parts, the solid-state austenite–martensite transformation during cooling has a significant influence on the residual stresses and distortion. In the welding process, it is important to study the distribution and the level of residual stress induced in a matrix by the phenomena of precipitation Fe2C compounds resulting from the process of welding. The precipitate characteristics influence welds metal microstructure development, especially the formation of high toughness acicular ferrite phase.

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2 Finite element model

In this study, a three-dimensional finite element analysis was developed. The figure 1a shows the complete geometry of the model, one goes study the symmetry (Fig.2b), and it is the one half of the complete model selected as the analysis model in order to reduce the calculation time, the x-y plane is a symmetry plane, with UZ = 0 (Fig.2b).

Figure 1 : Geometry of complete model with precipitate, (b) symmetry of model, (c) model of precipitate-precipitate interaction, (d) Finite element mesh of model, (e) Finite element mesh of

precipitate- precipitate interaction

The finite-element computations was performed, using commercial FE software package ABAQUS [7].

The thermal cycle used for calculation consists of an increase of temperature at 720^oC and a cooling to the Matrix

(a)

(e) (d)

Matrix Precipita

te

(b) (c)

x

y z

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http://www.csc.dz/ic-wndt-mi12/index.php 25 ambient temperature 20^oCwith constant speed.

Medium carbon steel (S45C), is selected in this study, it was defined as elastic–plastic material. The behaviour of the precipitate is considered as an isotropic elastic material. The precipitate is assumed to be elastic.

3 Results and discussion

3.1

Residual Stress analysis

The objective of this study is to numerically analyze by the finite element method the distribution and the level of the stresses thermal origin induced in the matrix by the mechanism of precipitation Fe2C compounds resulting from the process of welding. The intensity of these stresses is directly related to the variation in temperature due to cooling.

Von-Mises equivalence and normal residual stress (σvm , σxx , σyy , σzz) obtained for ΔT=700^oC and Ψ=50μm is given in figure 2 . The higher stresses are located at the vicinity of the interface matrix and precipitate. Far from the interface, the matrix is completely released of these stresses.

Figure 2: Von-Mises equivalence and normal residual stress distribution for ΔT=700^oC and Ψ=50μm.

σxx

σyy σzz

Path σvm

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http://www.csc.dz/ic-wndt-mi12/index.php 26 3.2

Effect of temperature

The temperature is a fundamental parameter for the junction of materials. It determines the quality of the interface of the parts assembled by welding and other techniques. It is at the origin of the induced residual stresses after their cooling. Indeed, it determines the level of these stresses in a material macroscopically homogeneous and from the microscopic point of view the distribution of the internal stresses in the vicinity close to the interface matrix-precipitate. The residual stresses were computed along a path schematized in Fig. 1. The results obtained are illustrated in figure 3. These last show the variation of the normal, equivalent and tangential stresses according to the variation in temperature.

On figure 3a is illustrates the effect of the variation in temperature on the intensity of the equivalent stress of Von Mises. This figure shows that the level of this stress reaches its maximum with the interface precipitate-matrix then decrease surface towards the core of the defect and in the matrix far from the interface. This behavior is accentuated by the variation in temperature. Indeed, the level of this stress increases with the increase in this gradient. A structure matrix-precipitate carried at high temperatures induced the much more intense of stresses.

The analysis of the figure 3b shows that the matrix and the precipitate are in compression. The level of these stresses (σxx) believes with the increase in the variation in temperature. These stresses are strongly localised at the interface precipitate-matrix. Far from the interface, the matrix is completely released of these stresses. In the precipitate, their intensity decrease interface towards the heart. The distribution of these normal stresses is perfectly symmetrical on both sides precipitate in the matrix and the precipitate.

The internal stresses σyy put the matrix in tension and the precipitate in compression whose intensity believes with the increase in temperature. The amplitude of these stresses is comparable with that resulting from the axis xx. Their distribution is symmetrical in the matrix and the precipitate. Indeed, their effect is cancelled in the matrix far from the interface and decrease interface towards the centre of gravity of the precipitate (Fig.3c). In the heart of this defect the level of the normal stress remains high, this is due to its size.

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http://www.csc.dz/ic-wndt-mi12/index.php 27 Figure 3: Variation of equivalent and normal residual stresses according to a temperature for Ψ=50μm.

The internal stresses σzz compress at the same time the matrix and the precipitate (Fig.3d). The distribution of these stresses in these two elements differs from that of the stresses σxx. Indeed, they are intensively localised with the interface of these components. Their amplitudes decrease abruptly in the matrix and the precipitate for tending towards zero values. Compared to the normal stresses σxx, the two components are completely released residual stresses in the vicinity very close to the interface. The level of these stresses is higher than that induces in σyy. Indeed, in the matrix close to the interface and in the heart of the precipitate, the normal stresses σyy are completely released (Fig.3d).They are strongly concentrated in the vicinity close to the interface.

(a) (b)

(c) (d)

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

-400 -300 -200 -100 0 100

Normal residual stress yy(MPa)

Normalize distance

T= 700 ^OC

T= 500 ^OC

T= 300 ^OC

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

-600 -400 -200 0

Normal residual stresszz(MPa)

Normalize distance

T= 700 ^OC

T= 500 ^OC

T= 300 ^OC

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

0 100 200 300 400

Von mises residual stressvm(MPa)

Normalize distance

T= 700 ^OC

T= 500 ^OC

T= 300 ^OC

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

0 -100 -200 -300 -400 -500

Normal residual stressxx(MPa)

Normalize distance

T= 700 ^OC

T= 500 ^OC

T= 300 ^OC

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http://www.csc.dz/ic-wndt-mi12/index.php 28 3.3

Effect of precipitate-precipitate interaction

One studied the effect of the two precipitates interaction on the level of the internal stresses induced in the matrix.. The residual stresses were computed along a distance d schematized in Fig. 1c. The higher stresses are located at the vicinity of the interface matrix-precipitates. The analysis of the figure 7a shows that the stress equivalent in matrix, increase progressively when the distance between the two precipitates decreases. These stresses are strongly localised in the matrix at the close vicinity to precipitate. The decrease of the distance between precipitates involves an increase on the stress level leading almost to a homogeneous distribution of internal stresses.

Figure 4: Vaiation of equivalent and normal residual stresses according to precipitate-precipitate inter- distance for ΔT=700°C and Ψ=50μm.

-0,08 -0,06 -0,04 -0,02 00,00 0,02 0,04 0,06 0,08 -100

-200 -300 -400 -500 -600

xx(MPa)

d(mm)

d1=50 m d2=100 m d3=150 m

-0,08 -0,06 -0,04 -0,02 0,00 0,02 0,04 0,06 0,08

-200 -150 -100 -50 0 50 100

yy(MPa) d(mm)

d1=50 m d2=100 m d3=150 m

-0,08 -0,06 -0,04 -0,02 0,00 0,02 0,04 0,06 0,08

-250 -200 -150 -100 -50 0 50 100

zz(MPa)

d(mm) d1=50 m d2=100 m d3=150 m -0,08 -0,06 -0,04 -0,02 0,00 0,02 0,04 0,06 0,08

0 50 100 150 200 250 300 350

VM(MPa)

d(mm)

d1=50 m d2=100 m d3=150 m

(a) (b)

(c) (d)

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http://www.csc.dz/ic-wndt-mi12/index.php 29 The normal stresses σxx induced in the matrix are all the more significant as the precipitates are close one to the other (Fig.4b). Indeed, a reduction in the inter-distance of three times involves an intensification of the stress σxx, analyzed halfway of the precipitates, of approximately ten times. This stress increases the amplitude of this zone towards the interface with the precipitate. In this zone the internal stresses vary very little with the inter-distance precipitate-precipitate. This shows clearly that a bringing together of the precipitates, formed after the process of welding, generates in the matrix a strong intensification of the internal stresses. The latter put it in compression. Far from these defects, the matrix is completely released of these stresses (Fig.4b).

On the figure 4c is represents the variation of the normal residual stress σyy according to the inter- distance precipitate-precipitate. In the matrix between the two precipitates, this stress very strongly grows with the reduction in the distance separating them. Its amplitude intensifies practically approximately twelve times. The most significant stresses are localised in the vicinity close to the interface precipitate- matrix. They put in this zone the matrix in compression and the halfway between the precipitates in traction. It is completely released when these two volume defects are far one from the other. Their effect of interaction tends to disappear. Compared to the stresses σxx, their level is relatively low.

The induced internal stress σzz in the matrix according to the inter-distance defect-defect is illustrated in the figure 4d. The behavior of these stresses according to this distance is comparable with that resulting from the σyy with lower levels. The level of the tangential residual stresses seems not very depend on the inter-distance precipitate- precipitate (Fig.4d).

4 Conclusion

The results obtained numerically by the finite element method show that:

-The precipitate Fe2C in the steel matrix resulting from a process of welding generates normal and tangential residual stresses whose level reach its maximum value with the interface matrix-precipitate. Far from this interface the matrix is completely released of these stresses.

-The level of the internal normal and tangential stresses induced in the matrix and the precipitate grows with the increase in the variation in temperature during cooling;

-The amplitude of the internal normal stresses induced in the steel matrix is closely related to the inter- distance precipitate-precipitate. A bringing together of these precipitates involves a strong intensification of the induced residual stresses according to three directions xx, yy,and zz;

-The internal stresses of shearing depend very little on the inter-distance precipitate- precipitate;

Références

[1] K.H. Jack, J. Iron Steel Inst., London 169 (1951) 26.

[2] Y. Hirotsu, S. Nagakura, Acta Metall. 20 (1972) 645.

[3] J. Languillaume, G. Kapelski, B. Baudelet, Acta Mater. 45 (1997) 1201.

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http://www.csc.dz/ic-wndt-mi12/index.php 30 [4] K. Hono, M. Ohuma, M. Murayama, Scripta Mater. 44 (2001) 977.

[5] V.G. Gavriljuk, Mate. Sci. Eng. A 345 (2003) 81.

[6] V.A. Shabashov, L.G. Korshunov, A.G. Mukoseev, Mater. Sci. Eng. A 346 (2003) 196.

[7] ABAQUS, User’s Manual, 6.5, Hibbit, Karlsson & Sorensen Inc.F.