3-D FINITE ELEMENT ANALYSIS OF THE EFFECT OF PORE SIZE AND FORM ON STRESS CONCENTRATION FACTOR IN SPOT WELDS

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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, http://www.csc.dz/ic-wndt-mi12/index.php 108

3-D FINITE ELEMENT ANALYSIS OF THE EFFECT OF PORE SIZE AND FORM ON STRESS CONCENTRATION FACTOR IN SPOT WELDS

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: [email protected]

Abstract:

The work presented in this paper utilises a numerical analysis for the computation of stress concentration factor generated by the presence in the weld nugget of a pore formed during the welding process. Welded structure containing porosity is subjected to uniaxial tensile stress. The effects of geometrical parameters of the pore and the interaction pore-defect on the stress concentration factor variation have been analysed.

Keywords: Finite Element Method, Stress Concentration Factor, Defect, Porosity, Spot weld, Steel.

1 Introduction

As it well known, the process of assembly by welding led to the creation of micro-structural heterogeneities zones. Generally these zones can be discontinuities macroscopic geometrical (macro- geometry of the weld nugget) or/and geometrical or metallurgical defects. At the origins of stress concentration, these regions are favourable sites where fatigue cracks can initiates and propagate. In agreement with many authors, fatigue and fracture, are the most critical failure mode of resistance-welded joints [1–3]. Hence, it is up of importance to study the stresses distribution around these zones.

Usually a weld is imperfect, containing inclusions, porosities, cavities, etc [4]. Fatigue cracks can initiate from these defects and propagate from a subcritical size to critical size [5]. In addition catastrophic fracture is due to the unstable propagation of a crack form a pre-existing defect [6].

Porosity is an important factor responsible of mechanical properties reduction. Liu et al. [7] stated that the influence of porosity in the weld metal is similar to that in sintered steels, where porosity caused reduction of toughness, ductility, yield and ultimate strength limits.

The objective of this study is numerically analysis, by FEM, stress concentration factors generated by the presence of welding-induced porosities in the weld nugget. The investigation has been extended to the effect of porosity size and form.

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2 Finite element model

In this investigation, a 3-dimensional finite element analysis has been conducted to simulate the distribution of stresses and the stress concentration factors around porosities in a weld nugget. The finite- element computations was performed using commercial FE software package ABAQUS [8].

Figure 1 : (a) A 2-D schematic view of a welded joint with porosity, (b) Geometry of complete model in a 3-D, (c) Geometry of one half of the complete model in 3-D, boundary condition and loading

condition, (d) Finite element mesh.

Figure 1a gives a schematic view of the welded nugget with porosity. Due to the symmetry of the geometry and the use of isotropic material properties, the model was reduced to only half of the system (Fig.1c) in order to reduce the calculation time. Hence, the boundary conditions, must be such that the symmetry is retained. The material sample selected for this study was steel, considered as elastic material.

The precision of numerical computation is strongly related to the quality of the mesh around the porosity,

(a) (c)

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Upper sheet

Lower sheet Nugget

Porosity

Y X

Z Porosity

UZ=0

(b)

P

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le Soudage, le CND et l’Industrie des Matériaux et Alliages (IC-WNDT-MI’12) Oran du 26 au 28 Novembre 2012, http://www.csc.dz/ic-wndt-mi12/index.php 110 a 4-node linear tetrahedron (C3D4) finite elements are used for the model. The finite element model is shown in Fig. 1d, with 47965 elements, and it has a fine grid in the porosity. Welded structure containing porosity is subjected to uniaxial mechanical loading (Fig.1c).

3 Results and discussion

3.1

Strain and Stress analysis

Figure 2 presents the distribution of equivalent and normal stresses in matrix and porosity for a mechanical loading of 100MPa. The analysis of the stress field, clearly indicate that whatever its direction the stresses takes their higher levels around the porosity and decreases to a low level in the matrix.

Figure 2 : Equivalent and normal stresses distribution (P=100Mpa, Øp=50μm)

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3.2

Effect of porosity size

The influence of the porosity size (diameter) on the variation of the stress concentration factor has been investigated hereafter. The structure is subjected to a load of traction of 100 MPa, with the assumption of a spherical porosity.

The variation of the stress concentration factor according to the porosity size is represented in figure 3.

As seen, the stress concentration factor increases proportionally with the increase of the porosity size to reach the maximum value for the biggest size.

Figure 3: Variation of stress concentration factor according to the porosity size (P=100MPa).

3.3

Effect of porosity form

The previous investigations were developed with the assumption of a spherical porosity. In this part of the study, the effect of the porosity form on stress distribution and stress concentration factors has been highlighted. Hence, the investigations were performed for shuttle-shaped porosities, with two radiuses (x and y). Moreover, since it has been reported from anterior results that S22 is the most important stress;

only this later was considered in this study.

20 40 60 80 100 120 140 160 180 200

1,6 1,8 2,0 2,2 2,4 2,6

Stress concentration factor (K t )

Porosity size (m) Porosity size

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Figure 4: Stress distribution for different porosity form(x/y ratio)

Figure 5: Variation of stress concentration factors according to the porosity form (x/y ratio).

x/y = 1 x/y = 2 x/y = 4 x/y = 8

0 1 2 3 4 5 6 7 8 9

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

x/y Ratio

x y

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le Soudage, le CND et l’Industrie des Matériaux et Alliages (IC-WNDT-MI’12) Oran du 26 au 28 Novembre 2012, http://www.csc.dz/ic-wndt-mi12/index.php 113 Figure 4 shows the distribution of normal stresses S22 in matrix (weld nugget) and porosity for a mechanical loading of 100MPa and different x/y ratios. In this case the x is maintained in the same value and y was varied (i.e. the variation were proceed according to y axis), in order to have four x/y ratios (x/y

= 1, 2, 4 and 8). It is clear from the obtained results that distribution of normal stresses in matrix (weld nugget) varies with the porosity shape. It can be also seen that there is a stress concentration in the pointed porosities-corners for all forms. In the others sides the matrix is completely released of these stresses. Figure 5 presents the effect of the geometrical form of the porosity (ratio x/y which changes along the y axis) on the stress concentration factor. From this plot it can be shown that as far as the spherical porosity is concerned, the stress concentration factor remains a high level. When the porosity becomes more and more acute, the stress concentration factor decrease rapidly and becomes lower.

Figure 4 : Stress distribution for different porosity form(y/x ratio)

y/x = 1 y/x = 2 y/x = 4 y/x = 8

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le Soudage, le CND et l’Industrie des Matériaux et Alliages (IC-WNDT-MI’12) Oran du 26 au 28 Novembre 2012, http://www.csc.dz/ic-wndt-mi12/index.php 114 Figure 7: Variation of stress concentration factors according to the porosity form (y/x ratio) . In the other hand normal residual stress S22 according to y/x ratio is given in figure 6. In this case the porosity changes in form were developed according to x-direction, and y radius was kept constant. As previous analysis the results indicate that is a stress concentration in the pointed porosities-corners for all forms, and decreases more and more in the weld nugget.

Figure 7 illustrates the variation of the stress concentration factor according to the porosity form according to y/x variation. As it can be seen from the figure, the plot of the evolution of Kt has the same behaviour to that obtained in the precedent case (i.e. according to x/y variation), with of the same intensity. A circular porosity led to high stress concentrations; consequently this type of defect can represent a great risk of damage of the welding joint.

4 Conclusion

In the present work 3-dimensional finite element method was used to investigate the effects of process- induced porosities in the general behaviour of welded nugget. Geometrical parameters such as size and shape of the porosity were the variables of this study. The principal results of the simulations are summarized as follows:

- The higher stresses are located at the vicinity of the interface between matrix and pore. Far from the interface the matrix is completely free of these stresses.

- Based in the assumption of a spherical porosity, the distribution of stresses reveals a concentration around the porosity, mainly in y-direction (S22). Thus, a crack can be initiated from this point, which presents a real risk of failure of the structure.

- The stress concentration factor is sensible to the porosity size. It has been observed that Kt becomes more and more intense proportionally to the diameter of the porosity.

0 1 2 3 4 5 6 7 8 9

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

y/x Ratio

x y

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le Soudage, le CND et l’Industrie des Matériaux et Alliages (IC-WNDT-MI’12) Oran du 26 au 28 Novembre 2012, http://www.csc.dz/ic-wndt-mi12/index.php 115 - As far as the spherical defect is concerned, the normal stress according to y-direction takes a high level.

When the defect becomes angular, this concentration increases rapidly and becomes more and more low.

Thus, the acute porosities are less dangerous compared to those spherical.

Références

[1] Fricke W. Fatigue analysis of welded joints: state of development. Marine Structures, Vol. 16 (2003), pp: 185-200.

[2] Zhang Y, Taylor D: Sheet thickness effect of spot welds based on crack propagation. Engineering Fracture Mechanics, (2000), Vol. 67, pp: 55-63.

[3] Kang H, Barkey ME, Lee Y: Evaluation of multiaxial spot welds fatigue parameters for proportional loading. International journal of fatigue (2000), Vol. 22, pp: 691-702.

[4] E Ergun; Aslantas. K ; Tasgetiren. S ; Topcu. M: Fracture analysis of resistance welded Lshaped and straight sheets. Materials and Design (2006), Vol. 27, pp: 2-9.

[5] Maddox S.J: Recent advances in the fatigue assessment of weld imperfections. Welding Journal (1993); Vol. 72; pp: 42-52.

[6] E.E .Gdoutos: Fracture mechanics an introduction (solid mechanics and its applications), volume 14.

[7] S. Liu, A.M. Pope and R. Daemen: Welding consumables and weldability. International Workshop on Underwater Welding of Marine Structures Louisiana, USA (1994), pp. 321–350.

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