Cross wedge rolling (CWR), an innovative metal forming process for manufacturing axial symmetrical stepped shafts/axles, is gaining high popularity in industries such as the automotive, high-speed railway, aerospace and nuclear reactor. CWR is advantageous in many aspects such as high productivity, high material utilisation and low energy consumption, compared to the conventional forging processes such as press forging or machining [1, 2]. The material utilisation of CWR can reach 0.8–0.98 [3]. New CWR related technologies are being developed quickly. For example, Ji et al. [4] experimentally verified the capability of producing hollow parts by using CWR with mandrels. Zheng et al. [5] and Pater et al. [6] produced shafts with non-circular cross-section or normal/skew teeth using CWR, respectively. Bulzak et al. [7] compared the ball pins manufactured in hot and warm temperature. CWR products with corrugated surface were produced [8]. The composite CWR shafts made by 42CrMo and Q235 was studied in terms of deformation characteristics and effects of process parameters [9, 10]. The new technologies drive the market demand in CWR expanding sharply.
Central cracking, the formation of cavities in the central region of CWR products along the axial direction, is a critical problem impeding its further development in safety-critical industries such as the aerospace industry and nuclear industry. Central cracking has been observed and investigated in a wide range of materials, e.g., steels, aluminium, titanium and plasticine. For example, Li et al. [11] and Li and Lovell [12] discovered the central crack morphologies in pure aluminium and considered the tensile and shear stresses contributed to the central crack formation. Yang et al. [13] investigated the central crack evolution in C45 steels on a microscopic scale and attributed the central crack formation to the tensile and shear stresses. The effects of shear stress cycle and the first principal stress were emphasized in generating internal voids by experiments and simulations in multi-wedge CWR by Zhou et al. [14]. Pater et al. [15, 16] revealed that the central crack mechanism in C45 steels involved void formation and shear fracture by numerically analysing the stress triaxiality (the ratio of mean stress over the von Mises stress) range. Zhou et al. [17] confirmed the dominant role of the maximum shear stress in central crack formation by investigating the stress states on the plasticine workpiece under different central crack conditions. It is well known that the fracture mechanisms vary with the material property, such as ductility. For instance, the fracture mode of steel transitions from brittle to ductile with the increase of temperature due to improved ductility [18]. However, little research has been conducted to reveal the underlying multiple central crack mechanisms. Thus, it is necessary to identify the multiple central crack mechanisms in order to build a robust unified physic-based damage model.
Central cracking micromechanics has been researched recently. Experimentally, Yang et al. [13] observed the voids nucleated around the inclusions, grew, coalesced and led to final fracture. Zhou et al. [19] quantitively validated the critical effect of inclusions on central cracking. Pater et al. [16] clarified the co-existing fracture mechanisms, void formation and shear fracture, by analysing the stress triaxiality. However, these micromechanics understandings have not been involved in existing central cracking predictive models. Thus, it is necessary to introduce micromechanics into the central crack model to achieve high prediction accuracy based on sufficient physical meanings.
Many damage models and fracture criteria have been introduced and applied to predict the central cracks for manufacturing crack-free products. Li and Lovell [20] suggested that the equivalent plastic strain was an accurate criterion by comparing the stress/strain states in pure aluminium samples produced by using two die geometries. The phenomenological damage models for ductile fracture, such as Cockcroft and Latham (C&L) model, normalised C&L model and Oyane model, are extensively applied in predicting central cracking with high accuracy to some degrees. A density change model was applied to clarify the forming windows to prevent central cracks [21]. Recently, Pater et al. [16] proposed a damage model considering the fracture mechanisms, void formation and shear fracture, achieving high accuracy in C45 steel at the elevated temperature. Zhou et al. [22] proposed a physics-based fracture criterion capable of predicting the central cracks in 27 groups of CWR tests on pure aluminium AA1100 with different die geometries. However, these models have never been validated by different materials, which exhibit different fracture mechanisms.
Meanwhile, great progress has been witnessed in developing physics-based damage models for predicting shear dominant ductile fracture. Smith et al. [23] expanded the application of the Rice and Tracey model into the low or negative triaxiality stress states by involving the void shrinking mechanism. Zhu and Engelhardt [24] introduced a new term of shear ratio into the R&T model to describe the damage caused by shear effects. Bao and Wierzbicki [25] found that the fracture locus varies with triaxiality significantly based on experiments under various stress states. Xue and Wierzbicki [26] (X&W) modified the plastic strain criterion by considering triaxiality and Lode parameters, covering the whole range of stress states and accounting for the material ductility. Bai and Wierzbicki [27] converted the conventional Mohr-Coulomb criterion to the space of the triaxiality, Lode angle parameter and equivalent von Mises stress, enabling to predict fracture nucleation in a much wider range of stress states. However, little progress has been seen on the fracture under non-proportional loadings on the onset of ductile fracture. Bai [28] found the importance of non-linear loading paths on ductile fracture onset and modified the accumulation low of damage considering non-proportional loading histories. Benzerga et al. [29] also demonstrated the significance of the loading path on the fracture strain by conducting unit cell computations. Faleskog and Barsoum [30] noticed a decrease in ductility during the stress triaxiality interval [0, 0.33] by conducting tension–torsion experiments. Papasidero et al. [31] conducted tension–torsion experiments on tubular specimens and validated that a Hosford-Coulomb based non-linear damage law can describe the effect of non-proportional loadings on fracture strain. The above models show advances in predicting shear dominated ductile fracture under non-proportional loadings. Therefore, it is worth testing whether their robustness in predicting central cracking in CWR.
Model materials such as plasticine are widely used in physically simulating metal forming processes. Chijiiwa et al. [32] and Wong et al. [33] experimentally revealed their similarities to metals in terms of constitutive behaviours, frictional behaviours and fracture features. The softness of the model materials enables laboratory-scale reproduction to be achieved, whereby the tools can be rapidly 3D printed. Wójcik et al. [34] built the physical CWR model with 3D printed dies. Zhou et al. [35, 36] approved the feasibility of differential velocity sideways extrusion using plasticine and conducted the geometrical parametrical study. Physical models have been applied to study the CWR since 1984, when the internal defects were simulated in a rotary side-compression test with plasticine by Danno and Tanaka [37]. Fu and Dean [38] investigated the necking and twisting by using plasticine. Recently, Wójcik and Pater [39] and Wójcik et al. [34] achieved high similarities between the commercial plasticine and hot steels (1150°C) in terms of mechanical properties and defect features in CWR. Besides the temperature, the composition in plasticine is also adjustable for achieving desired mechanical properties of the modelled materials. Hawryluk et al. [40] compared the mechanical properties of plasticine with different compositions. Zhou et al. [17] designed the novel plasticine/flour composites to build the CWR billets and investigated the underlying central crack mechanism under various stress states. Thus, using model materials is reasonable to investigate the multiple fracture mechanisms and criteria in CWR.
This work aims to reveal the multiple central crack mechanisms, build a unified physics-based fracture criterion, and examine their accuracy in different materials. The multiple fracture mechanisms will be investigated using newly designed plasticine/flour composites with a lab-scale CWR machine. The fracture criterion for both the high and low ductility material will be proposed considering the multiple fracture mechanisms such as the central crack in pure aluminium at room temperature and in the hot steels at elevated temperature. Its robustness will be compared with ten existing damage models and validated by CWR tests in various materials.