Analysis of the cup-cone fracture in a round tensile bar. Acta Metall. 32 (1984), pp.157-169. [7] G. Rousselier. Ductile fracture models and their potential in local ...
NUMERICAL SIMULATION OF CRACK PROPAGATION IN ELECTRON BEAM WELDED JOINTS
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H. Y. Tu1, Y. Rudnik2, S. Schmauder1, U. Weber1, V. Ploshikhin2 Institute for Materials Testing, Materials Science and Strength of Materials (IMWF) University of Stuttgart, D-70569 Stuttgart, Germany 2 Neue Materialien Bayreuth GmbH, D-95448 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 JR 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
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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
1 f
Df K exp(
m
K (1 f )
) R( p) 0
(1)
where σeq is the von Mises equivalent stress, σm is the hydrostatic stress, f is void volume fraction (initial value f0) , σK and D are material constants, and R(p) is yield stress of the material. The initial void volume fraction, f0, 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 (lc). 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 f0 and the mean void distance lc 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].
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 2.
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Steel
C
Si
Mn
P
S
Cr
Mo
Ni
Al
Co
S355 0.198 0.260 1.386 0.026 0.013 0.020
