Influence of grain size distribution on the Hall–Petch relationship of welded structural steel
Introduction
New lightweight solutions are needed to improve the energy efficiency of steel structures. Further development of the steel structures requires the utilisation of new materials and advanced production technology. In this development work, one of the fundamental issues is to understand the relation between microstructural quantities and material properties. This is especially challenging for advanced joining methods such as laser welding, where the properties of the narrow joint differ significantly from those of the base material [1], [2], [3], [4], [5].
In general, the mechanical properties of metallic materials have shown to correlate with the microstructural dimensions, most commonly with the average grain size. Based on the work of Hall [6] and Petch [7], a relationship was found between grain size and the mechanical properties of steel. For yield strength the relationship is formulated:where is the lattice friction stress required to move individual dislocations, k is a material-dependent constant known as the Hall–Petch slope, and d is the average grain size [8]. The work of Hall and Petch was focused on the lower yield point and the cleavage fracture stress of mild steel, respectively. Since then, the Hall–Petch relationship has been applied to a large variety of materials and material properties, such as hardness, stress–strain properties and fatigue [9], [10], [11], [12], [13], [14], [15]. As the Hall–Petch relationship is related to the measure of grain size, the correct definition of the effective grain size is crucial. Typically the average grain size is used to describe the microstructure [16], but its suitability for heterogeneous microstructures is questionable. Several investigations [8], [16], [17], [18], [19], [20], [21] have shown that the grain size distribution has an effect on the mechanical properties. For example, Berbenni et al. [20] showed that for a given average grain size, broadening of the grain size dispersion reduces the strength of the material.
To consider the influence of grain size distribution, Kurzydlowski [22] proposed an alternative approach, where the strength of different grain sizes was estimated by applying a weighting factor equal to the volume of the grains. This approach was further developed by Raeisinia and Sinclair [23]. They proposed a new geometric grain size parameter, the representative grain size, which eliminates the influence of grain size distribution on the Hall–Petch relationship. The fundamental assumptions of this approach are that all grains have the same shape and that the grain size distribution is log-normal. The same assumptions have been used in various numerical simulations of fictitious grain size distributions [16], [24], [25], [26], [27]. However, the previous studies [8], [16], [17], [18], [19], [20], [21], [24], [27] are focused on single phase base materials and do not cover heterogeneous weld metals.
The objective is to study the grain size distribution of weld metals and its influence on the Hall–Petch relationship. Furthermore, methods for the characterisation of the grain size distribution are extended to be applicable for weld metal microstructures. The microstructures of nine structural steel weld metals and two base materials are characterised using electron backscatter diffraction (EBSD) and optical microscopy. Because of the narrow welds, micro-indentation is applied for mechanical testing. Based on the experimental results, a modified Hall–Petch relationship is introduced for the strength prediction of heterogeneous microstructures. The study utilises stereological methods for estimating the volume fraction of grains from their surface area fractions. The investigation is limited to the transverse cross-sections of the material and thus the effects caused by grain shape three-dimensionality are omitted.
Section snippets
Definitions
Based on the role of grain boundaries as an effective barrier to the movement of dislocations, the grain size dependence of yield strength can be explained by the pile-up of dislocations at grain boundaries [6]. The pile-up causes an additional stress, which allows the deformation to be transmitted to the next grain. The additional stress is in relation to the number of dislocations in a pile-up, which is limited by the length of the slip band that can be identified with the average grain
Test specimens
To investigate the grain size distribution and its influence on the Hall–Petch relationship, various material microstructures are examined. In addition to structural steel, the weld metals (WM) of conventional arc (CV), laser (LA), and laser-hybrid (HY) welded joints are included in the test series. The weld metals represent complex microstructures with a large variety of grain size distributions. Table 1 lists specimen nomenclature with the corresponding joint type and welding method.
Microstructure and grain size distribution
Weld metals have complex microstructures with a large variation in grain size in comparison to base material. The complexity of the weld metal microstructures can be seen from the grain boundary enhanced optical micrographs in Fig. 3 and the inverse pole figure (IPF) maps in Fig. 4. Furthermore, the weld metals have visibly broader grain size distributions. In addition to the grain size distribution, differences were also found in the microstructural constituents. The base material BM.1 in Fig.
Discussion
The grain size distribution and its influence on the mechanical properties of welded structural steel were investigated experimentally. The base materials and weld metals were found to have distinct differences in the complexity of the microstructure and consequently in the grain size distribution. Conventional characterisation methods were compared to the proposed volume-weighted approach and the applicability of different grain size parameters was evaluated based on the Hall–Petch
Conclusions
In this paper, the influence of grain size distribution on the Hall–Petch relationship was investigated experimentally for heterogeneous microstructures. Grain size measurements carried out for structural steel weld metals revealed a large variety of grain size distributions that were noticeably broader than those of the base material due to differences in the phase contents. Therefore, the distributions need to be characterised in addition to the average grain size. Because of the large
Acknowledgements
The research is related to “Fatigue of Steel Sandwich Panels” (FASA), a Finnish Academy of Science project under Grant Agreement no. 261286. The financial support is gratefully appreciated.
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