Analysis of Stress and Strain Fields in and around Inclusions of Various Shapes in a Cylindrical Specimen Loaded in Tension

Arch. Metall. Mater., Vol. 61 (2016), No 2, p. 569–576 DOI: 10.1515/amm-2016-0097 A. Neimitz*,#, U. Janus* Analysis of stress and strain fields in and around inclusions of various shapes in a cylindrical specimen loaded in tension. A numerical analysis is performed of the stress field in and around inclusions of various shapes. Inclusions both stiffer and more compliant than the metal matrix are analysed. The critical stresses required for inclusion fracture are estimated after observation of cavities and inclusions by scanning electron microscopy. Real inclusions were observed after performing uniaxial loading to different amounts of overall strain. The material tested was Hardox-400 steel. Keywords: void nucleation, inclusion fracture, critical stress. 1. Introduction Both ductile and cleavage failure processes usually initiate by the nucleation of voids or microcracks. They can originate from second-phase particles such as inclusions (e.g., manganese sulphide, MnS) and/or interstitials (e.g., carbides). This first stage is likely common to multiple types of ultimate failure. Whether the failure mechanism exhibits primarily ductile or cleavage character, depends on the levels of the hydrostatic stresses, stress triaxiality, plastic strain and other characteristics of the stress and strain fields. When the mechanical fields favour ductile failure, the nucleus grows as a void. When the opening stress is sufficiently large, the nucleus evolves into a micro-, meso- and finally macrocleavage crack. In the present paper, we concentrate on the nucleation stage only, which in itself is sufficiently complex to warrant study. The process depends on many factors, including crystallographic structure (e.g., BCC, FCC, HCP), microstructural features (e.g., the size and shape of the grains), morphology and volume fraction of the inclusions or interstitials, and the features of the stress and strain fields. Second-phase particles can either fracture or split from the metal matrix by a debonding process. Which of the two mechanisms takes place depends on the size, shape and chemical composition of the failure nucleus. The numerical analysis of the nucleation stage of failure, as presented in this paper, involves the presence of large plastic deformations. However, the ultimate failure can be either ductile or brittle in character. This type of failure is often observed in BCC materials, among them ferritic steels. The failure process is characterized by evolution through the following three stages: 1) the nucleation of voids or microcracks, 2) the growth of voids or micro-cracks to mesocracks and 3) a void’s coalescence or sudden cleavage crack jump. These processes are the subject of numerous research programs and research reports, and excellent overviews are available [1], [2], [3]. However, the nucleation stage is not as often discussed in the literature for several reasons: 1. Experimental observations are distributed across various alloys. The nucleation of micro-cracks and voids from carbides and nonmetallic inclusions in ferritic steels are less often studied. 2. All three processes: nucleation, growth, and coalescence/ cleavage jump can take place very rapidly in highstrength alloys, and it is difficult to observe the first stage of failure. 3. Voids or microcracks do not nucleate at the same time, and observations are often focused on an individual void or on a few voids only; thus, quantitative results are difficult to interpret. This process is inherently a discontinuous one, consisting of a succession of discrete nucleation events. Moreover, microscopic observations are often challenging to interpret because they depend on the quality of polishing, which can smear out the inclusions. 4. Void or microcrack nucleation is a heterogeneous process that takes place either through particle fracture or from interface debonding. Both of these processes are influenced by multiple factors. There are, however, several experimental observations accepted by most researchers investigating the nucleation process of voids and micro-cracks: 1. The nucleation process starts with the largest particles and becomes energetically less favourable as the size of the particles decreases [1], [3], [4], [5], [6], [7]. 2. Larger particles fracture more often than smaller ones. The latter become the kernels of nucleation through the process of debonding from the metal matrix. This can be attributed to the higher likelihood that a larger particle will contain a submicron defect [4]. 3. A soft matrix favours particle debonding, whereas a hard matrix favours particle cracking. *  Kielce University of Technology,Faculty of Mechatronics and Machine Design, 1000 Lecia P.P. 7 Av.,25-314 Kielce, Poland   Corresponding author: # 570 4. 5. The shape of the particle may determine the mode of nucleation. For example, an oblong particle oriented along the loading direction is more prone to fracture than the same particle oriented perpendicular to the loading direction. In the latter case, nucleation by interface debonding is more likely. Cleavage microcracks and voids are progressively nucleated under the influence of plastic deformation. Some authors claim that the nucleation process arises from the heterogeneity of plastic deformation in the so-called slip-induced process. Other claim that plastic deformation must necessarily accumulate sufficiently at the interface (whose physical interpretation is debateable) to raise the stress above a critical strength level. Inclusions within metals are generally inhomogeneously present in various shapes, sizes and clusters through the material. Shabrov and Needleman [8] addressed inclusion failure, though their treatment assumed only square inclusion shapes and they analysed the debonding process only. In their study the cohesive model along the inclusion surface was used. The shape, size, morphology of inclusions and stress triaxiality levels were the parameters of the model. Although the analysis consisted of a relatively simple inclusion model, it enabled several interesting qualitative conclusions concerning void nucleation. Among them were: 1) low triaxiality requires more extensive plastic straining, 2) smaller inclusions require higher values of void nucleation strain than larger inclusions, and 3) clustering has a significant effect on debonding strain and stress. For this simple inclusion model, the strain at debonding varied from 0.5% to 9%. In turn, the effective stress σ e was ( where σ 0 recorded within the range of is the yield stress. In an additional paper by Shabrov et al. [9], experimental results obtained from 4340 steel were presented along with the results of finite element analysis. In this case, the fracture of titanium-nitride particles was observed. This process took place over a narrow loading range corresponding to the weighted sum of the hydrostatic tension σ h and the effective stress σ e (1) Argon and Im [10] were probably the f (...truncated)