Numerical analysis of the influence of material mismatching in the transition curve of welded joints
Introduction
When analysing welded joints, the heterogeneity of the joint is a key factor for understanding the fracture behaviour of any welded structure containing cracks. In any weld, at least three different materials should be considered: the weld metal, the base metal and the heat affected zone material. However, in certain situations where the crack is contained within the weld material and runs along the material’s centre-line, parallel to the weld-base material interface, and where the size of the heat affected zone is small, the effect of this zone can be considered negligible and a two material idealisation of the weld structure can be taken into account. This consists of weld material with yield stress σ0w and width 2h, which contains the crack, and base material with yield stress σ0b. Fig. 1 shows this idealisation for a short-crack bend specimen. This two material idealisation has been used, by Kirk and Dodds [1], Gordon and Wang [2], Toyoda et al. [3], Moran and Shih [4], and others. In this case, the level of material mismatching can be defined by the mismatch ratio M, in the formwith M < 1 referring to material strength undermatching, M > 1 to overmatching, and M = 1 corresponding to a homogeneous specimen of weld metal.
Using the finite element method and the slip-line field theory, Joch et al. [5], Burstow and Ainsworth [6] and Hao et al. [7] have demonstrated that material strength mismatching significantly affects both the stress and strain fields that develop around the crack tip of welded joints with the crack contained within the weld metal, even in small scale yielding conditions. In the case of overmatching the crack tip stress fields are lowered relative to those obtained in homogeneous weld material at the same load. Conversely, in the case of undermatching the stress fields are raised relative to the homogeneous reference situation. In all cases, for a certain configuration of the welded joint, the difference between the stress fields of a mismatching joint and those for the homogeneous specimen increase with load. Moreover, the higher the level of mismatching and the thinner the weld metal strip are, the more severe the former effects.
Constraint due to material mismatching has been related to constraint due to geometry by Burstow et al. [8], and Thaulow and co-workers [9] established a J–Q–M formulation for the crack tip stress fields based on that utilised for the quantification of geometrical constraint in homogeneous situations. In this three-parameter formulation, J is related to the load, Q to the geometrical constraint, and M to the material constraint. Thus, overmatching welded joints, where the weld metal is surrounded by a metal with a lower yield stress and where plasticity spreads easily, have been assimilated to low-constraint geometries. On the other hand, undermatching welded joints, where the yield stress of the surrounding material is higher than that of the weld metal and where, in consequence, the extension of plasticity is obstructed, have been assimilated to high-constraint geometries. Thus, a total constraint parameter has been defined that, from applied load, quantifies constraint due to material mismatching and to geometry for any values of the mismatch ratio M and the weld semi-width h (Betegón and Peñuelas, [10]).
On the other hand, it is known that the geometry of the specimen significantly affects the crack resistance curve. Fracture resistance is determined by the operative micro-mechanism and depends on temperature. Ferritic steels exhibit a temperature transition region from cleavage to ductile tearing. At low temperatures, the operative micro-mechanism is cleavage. However, at high temperatures, the operative micro-mechanism is ductile tearing. In a range of intermediate temperatures, known as the transition zone, fracture is initiated by ductile tearing, but final fracture is produced by a sudden cleavage failure. It has been determined not only numerically but also experimentally, that geometries with low-constraint are more resistant to both cleavage fracture and ductile tearing than geometries with high-constraint. Thus, the transition curves for the different geometries are obtained, e.g. in Amar and Pineau [11], Gao et al. [12] and Hausild et al. [13].
This paper is focussed on the study of the influence of both the base material and the weld width on the transition curve of different welded joints. Transition curves are obtained from micromechanical modelling of the fracture process. Both micro-mechanisms cleavage failure and ductile tearing have been implemented numerically. In all the mismatch cases analysed the weld metal is assumed the same, and both the base metal and the width of the weld strip are varied. Thus, different constraint conditions are obtained, for a given weld metal. In all the cases, the two material idealisation of the weld shown in Fig. 1 is considered. The weld configuration (such as V-, K-, or X-grooves) adds additional complexity. Thus, to get a meaningful insight into the mismatch effect on fracture behaviour, the weld “model”, which consists of a “well-defined (homogeneous)” weld metal and a simple weld configuration (such as a rectangular shape), would be often quite useful. Such weld model can be produced, for instant, by EB welding or by diffusion-bonding.
Section snippets
Micro-mechanical models
Cleavage fracture is described by means of the statistical model proposed by Beremin for describing the fracture of ferritic steels [14], in which the local stress is used to determine the fracture probability. Cleavage is caused by the breaking of a second phase particle, which is treated as a micro-crack. The model is based on the Weibull weakest link theory. According to this theory, the whole volume of the specimen is divided into a series of reference volumes, and the fracture of the
Parameters selection
Next, the procedure used to determine the weld and base material parameters, including the cleavage and ductile parameters, as well as the mechanical properties, will be explained.
Numerical implementation
Micromechanical models were implemented in the finite element code ABAQUS [31] by means of two user subroutines. First, the ductile fracture subroutine integrates the constitutive differential equations by an implicit procedure. The final system of equations is solved by a fifth order Runge–Kutta method with internal step control. Thus, at every instant of the load history, the actual values of the stresses, plastic strains and porosity are obtained (Peñuelas et al. [32]). These variables are
Results
The results were obtained by means of a two-stage procedure. First, for each joint configuration and each temperature, the ductile tearing process is simulated by the corresponding subroutine. Then, for each load level, the stress fields are post processed and the cleavage fracture probability is calculated.
Conclusions
In this paper the transition curves for different welded joints have been obtained numerically. In these simulations, the weld material has been kept fixed, and all the material parameters, except the yield stress, have been considered temperature-independent. On this basis, the following conclusions can be reached:
- 1.
The resistance to cleavage fracture depends on both the temperature and the configuration of the welded joint. This resistance increases with temperature. In addition, for each
Acknowledgements
The authors acknowledge the financial support of the Spanish Ministry of Science and Technology, project MAT2000-0602, the financial support of the Asturian Government (Regional Plan of I+D+I), project IB05157, and the access to ABAQUS under academic license from Hibbitt, Karlsson and Sorensen.
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