NUMERICAL SIMULATION OF CRACK PROPAGATION IN ELECTRON BEAM WELDED JOINTS. University of Stuttgart, D Stuttgart, Germany

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1 NUMERICAL SIMULATION OF CRACK PROPAGATION IN ELECTRON BEAM WELDED JOINTS H. Y. Tu 1, Y. Rudnik 2, S. Schmauder 1, U. Weber 1, V. Ploshikhin 2 1 Institute for Materials Testing, Materials Science and Strength of Materials (IMWF) University of Stuttgart, D Stuttgart, Germany 2 Neue Materialien Bayreuth GmbH, D Bayreuth, Germany ABSTRACT In this paper, the ductile fracture behaviour of an electron beam welded steel S355 joint is studied experimentally and numerically. The hardness is measured across the steel welded joint in order to identify the different weld regions. Mechanical properties are obtained from tensile test results of unnotched round bars extracted from the base material (BM) and flat specimens extracted from the BM, the fusion zone (FZ) and the heat affect zone (HAZ), respectively. These local mechanical properties are used as model input. In this article, round specimens gotten from BM and C(T) specimens extracted from different weld regions are studied numerically. Finite element calculations about ductile fracture of smooth round bars and notched bars are performed in order to determine the Rousselier parameters. The same Rousselier parameters set is used to predict crack growth of C(T) specimens numerically. For C(T) specimens, the initial crack is located in the BM and in the FZ separately. The Rousselier model is used to predict ductile crack growth in the base material and in the electron beam welded joint. The numerical results are presented in terms of force vs. Crack Opening Displacement (COD) as well as fracture resistance J R curves. KEYWORDS Electron beam welding, crack propagation, Rousselier model, FEM INTRODUCTION Nowadays advanced welding techniques, such as electron beam welding (EBW) and friction stir welding (FSW), are used widely in transportation and aircraft industries. As the welded joints are used more and more in practice, the fracture mechanism of welded joints have been focused on because the properties of welded joints influence the mechanical behaviour of welded constructions and structures. In order to predict the serving life of the welded structures, numerical technique is used to study fracture behaviour of the welded joint. The typical welded joint can be divided into three different weld regions, i.e. the fusion zone (FZ) in which the fusion process has taken place, the heat affected zone (HAZ) which is an intermediate region and the base material (BM) which has not been affected during the welding process. However, if the crack is located in the FZ and runs along the material centre line, the size of the HAZ is small enough; the effect of HAZ can be neglected [1]. In this article, the influence of the HAZ on the fracture behaviour of the welded joint is ignored. Despite different welding techniques can produce similar joints, this work focus on the EBW joint. In ductile material, failure can be described by void initiation, growth and coalescence. The first damage model on these phenomena was proposed by McClintock and Rice [2, 3], the porous damage model was developed by Gurson [4], later revised by Tvergaard and Needleman [5, 6]. Similar to the GTN model, another damage model was developed by - 1 -

2 Rousselier which involves less model parameters [7]. After solving fracture problems of different homogeneous materials [8, 9], scientists are trying to use damage models studying the fracture problems of complex structures. Recent works have confirmed the GTN model can be successfully used to study the fracture behaviour of laser-hybrid welds [10-13], however, whether the Rousselier model can be used to solve the problem of electron beam welded joint is unknown. In this article, EBW joints are studied experimentally and numerically. For the numerical simulation of EBW joints, only two material phases (BM and FZ) are considered here for simplicity of finite element model. THE DAMAGE MODEL In damage mechanics, ductile fracture is described by void initiation, void growth and void coalescence. In the frame of continuum damage mechanics a model for porous metal plasticity is presented by G. Rousselier [7]. This model yields material instability (localization of deformation and damage in a plane) and can be used to predict ductile fracture of plane and cracked structures in the frame of a local approach to fracture [14]. In the Rousselier model, damage is defined by the variation of the void volume fraction. Rousselier suggested in the case of a damaged material that the yield surface had to be corrected as follows: eq Df K 1 f m exp( (1 f K ) ) R( p) 0 where σ eq is the von Mises equivalent stress, σ m is the hydrostatic stress, f is void volume fraction (initial value f 0 ), σ K and D are material constants, and R(p) is yield stress of the material. The initial void volume fraction, f 0, depends on the volume fraction of non-metallic inclusions, like sulphides and oxides, as explained, e.g., by Schmauder [9]. In the framework of damage models, it is assumed that a crack propagates from void to void. This can be simulated by the finite element model that the crack growths from integration point to integration point. For a rectangular finite element with reduced integration, the distance between integration points is equal to half of the element size. Due to this, the half of the element size corresponds to the mean distance between voids (l c ). In this work, crack propagation is assumed to occur at a void volume fraction of f f =60% according to internal report of GKSS [15]. Details of the numerical procedure of the crack propagation are given in Uhlmann s report [16]. From these explanations it can be seen that the initial void volume fraction f 0 and the mean void distance l c are microstructure parameters for the Rousselier model. In this article the determination of these two parameters is given for steel S355 BM. The calibration of these Rousselier parameters are performed on notched round specimens by numerical technique. The same Rousselier parameters are applied for the welded joint. The simulation works are performed on ABAQUS platform with the Rousselier model as a user subroutine (UMAT) [17]. (1) MATERIALS AND EXPERIMENTAL ANALYSIS Low-alloyed construction steel S355 is chosen as BM, which is often used for steel constructions. After the electron beam welding process, a butt joint is obtained from two S355 plates with the thickness of 60 mm. The chemical components are measured by spectrometric analysis on 5 random points on the material surface, of which the mean values are shown in Table 1. The basic mechanical properties of the BM obtained from tensile tests of unnotched round specimens are shown in Table

3 Steel C Si Mn P S Cr Mo Ni Al Co S <0.005 < Table 1: Chemical composition of the investigated steel, mass contents in % Steel R e (MPa) R m (MPa) Ag A Young s Modulus (MPa) S Table 2: Mechanical properties of S355 base material In order to identify the different weld regions, especially the FZ and the HAZ, the hardness is measured at three different test locations across the welded joint, namely at the weld root, middle-section and top part of the joints as shown in Fig. 1. Every 1mm a measurement is performed using the Vickers method (HV5). The hardness profile across the welded joint is shown in Fig. 1. Fig. 1: Hardness profile of the EBW joint at different positions Due the narrowness of the FZ and HAZ, flat tensile specimens extracted along the weld line from different weld regions are tested in order to get the local mechanical properties. Previous work has proven flat specimens exhibit similar stress-strain curves to that of standard round tensile specimens [18]. The comparison of these stress-strain curves are shown in Fig. 2. Fig. 2: Comparison of the stress-strain curves of base material obtained by testing standard round and flat tensile specimen - 3 -

4 The flat specimens are manufactured by an electrical discharge machining (EDM) in order to avoid the process influence. The local stress-strain curves from different weld regions are shown in Fig. 3. They show the strong inhomogeneity and the data scatter within the different regions. Fig. 3: Stress-strain curves obtained from tensile tests results of flat tensile specimens taken from different weld regions of S355 electron beam welded joint The fracture surfaces of notched round specimens extracted from the BM show typical honeycomb structures as observed in Fig. 4(a)-(b). The fracture surfaces show typical ductile fracture characteristics, large voids are next to smaller voids [12]. This indicates that the fracture of the BM is controlled by void growth and void coalescence during deformation. (a) (b) Fig. 4: (a)-(b) Fracture surface for S355 BM with different magnifications RESULTS AND DISCUSSION As mentioned in the previous section, l c and f 0 are the relevant Rousselier parameters. Before using the Rousselier model in a FE simulation, these parameters must be fixed. Notched round specimens with 4 mm notch radius obtained from the BM are used to calibrate these parameters. According to the metallographic pictures, not shown at here, the voids are not equidistantly distributed but are locally clustered. As experimental information for l c is not reliable, typical l c values (l c =0.05 mm, l c =0.1 mm) which influence the slope of force vs

5 diameter reduction curves after the fracture point are used, q.v. Schmauder [9]. For different l c values, f 0 varies in order to achieve the same fracture point according to the experimental force vs. diameter reduction curves, as shown in Fig. 5 and Fig. 6. When l c =0.05 mm, the good agreement is achieved under f 0 =0.0006; when l c =0.1 mm, the good agreement is achieved under f 0 = The comparison with the experiment show that the best agreement for the numerical force vs. diameter reduction curves is obtained for the parameter set l c =0.1 mm, f 0 = The same parameter set is used to study the fracture extension in the BM and in the welded joint. Fig. 5: Comparison of experimental and calculated force vs. diameter reduction curves (l c =0.05 mm) Fig. 6: Comparison of experimental and calculated force vs. diameter reduction curves (l c =0.1 mm) In order to study the ductile fracture behavior of homogenous BM and electron beam welded joint, standard compact tension specimens (CT25) are chosen. The specimens according to ESIS P2/92 have a thickness of B=25mm with 20% side groove, a width of W=50mm [19], the original fatigue length is a 0 =26.69 mm. For C(T) specimens extracted from BM, the initial crack locates in the BM. For C(T) specimens extracted from the welded joint, - 5 -

6 the initial crack locates in the centre of the FZ which coincides with the centre of the C(T) specimen. Because the structure shows symmetry with respect to the crack plane, only half of the C(T) specimen is modeled, both for the BM and the welded joint. Loading is defined by a described displacement on the loading point. The dimensions of C(T) specimens and boundary conditions are shown in Fig. 7. The simulation results in terms of force vs. Crack Opening Displacement (COD) as well as fracture resistance J R curves are shown in Fig. 8 and Fig. 9 separately. Crack propagation can be assumed to occur straightly due to the symmetry of the geometry in contrast to experimental observations where slight unsymmetry lead to crack deviation from the fusion zone to the base material. The difference between the two F-COD curves is due to the strength difference of BM and FZ material. The detailed differences of the F-COD curves give rise to the observed preferred crack propagation in the fused material. There is no big difference regarding the crack initiation values between BM with J i = N/mm and BM-FZ with J i = N/mm. However, the BM shows higher crack resistance values with increasing crack growth compared to the welded joint. (a) (b) Fig. 7 (a) Dimensions of C(T) specimen (CT25), (b) mesh and boundary conditions Fig. 8: Numerical predicted Force vs. opening displacement curves for different C(T) structure (where BM is base material, FZ is fusion zone) - 6 -

7 Fig. 9: Numerical predicted J-Integral vs. crack growth a curves for different C(T) structure (where BM is base material, FZ is fusion zone) SUMMARY Experimental and numerical techniques have been used to analyze the fracture behavior of electron beam welded S355 which is widely used in industry fields. The Rousselier damage model is used to simulate crack growth and crack coalescence during the fracture process. Local mechanical properties of different weld regions are derived from flat tensile specimens who are manufactured from these regions. This stress-strain information is used as model input. The critical Rousselier parameter set (l c, f 0 ) is determined by numerical adjustment of simulation and experiment, which is performed on notched round specimens. The same parameter set is used to study the fracture behavior of base material as well as welded joints. All the simulations are performed on the ABAQUS platform with the Rousselier model as a user-subroutine. In order to study the crack propagation behavior of homogenous BM and electron beam welded joints, C(T) specimens with symmetric crack geometries are used for the numerical calculation. Unsymmetric crack geometries with crack deviations into the base material as well as different initial crack lengths are under investigation. The simulation results are shown in terms of force vs. Crack Opening Displacement (COD) as well as fracture resistance J R curves. Compared with the BM, the BM-FZ structure shows a stronger behavior. It is shown that the BM-FZ weld shows slightly lower crack growth resistance. In summary the Rousselier damage model can be used to predict crack growth in EBW joints. It provides a numerical method and valuable tool to analyze the damage behavior of electron beam welded joints. However, the obtained results have to be confirmed experimentally in the future

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