Stress-state dependency of ductile fracture in an extruded magnesium alloy and its underlying mechanisms

Highlights

• Fracture strain of Mg alloy is found to be insensitive to stress states of differently notched compressive specimens.

• Fracture strain of Mg alloy decreases with increasing stress triaxiality in the range covered by smooth and differently notched tensile specimens.

• Unconventional stress-state dependency of ductile fracture is explained by fracture mechanisms in various deformations.

• Two-component fracture model is successfully applied to describe fracture strains of Mg alloy in a wide range of stress states.

Abstract

A comprehensive investigation into the ductile fracture of an extruded magnesium alloy at various stress states is conducted. Tension tests of the smooth and differently notched round specimens, plane strain tension as well as shear tests are carried out to obtain the medium to high stress triaxialities. Additionally, new types of notched round specimens are proposed for compression tests, by which the negative stress triaxialities are realized. In all notched round specimens of the magnesium alloy, ductile fracture is found to initiate from the notch root rather than the inner center of specimen, which is different from some relevant reports on aluminum alloy and steel. Based on a hybrid experimental-numerical procedure, fracture strains and the corresponding loading paths in all tests are obtained. It is found that the fracture strain of magnesium alloy decreases monotonically with increasing stress triaxiality in the range covered by the smooth round and plane strain specimens, while it is less sensitive to the stress states covered by the notched compressive specimens. Besides, the fracture occurring at various compressive states is dominated by shear mode, and the ductility is slightly better than that at the shear state. Despite that the fracture strain of magnesium alloy varies unconventionally in a wide range of stress triaxialities, it is accurately described by the two-component DF2014 fracture model. Furthermore, the fracture mechanisms of magnesium alloy in various deformations are explored by fractographic analysis, and the important roles played by second phase particles and deformation twins in the variation of fracture strain are revealed.

Introduction

Exhibiting a combination of high specific strength, good machinability, and being environmentally friendly, magnesium alloys are promising to serve as structural products in industries where lightweight design is vital (Nie et al., 2020). However, magnesium alloys have relatively poor formability at room temperature due to their hexagonal close-packed (HCP) crystal structure and the consequently limited number of active slip systems. The ductile fracture prone to occur during deformation has become a big challenge for engineering applications of magnesium alloy. In this context, a comprehensive study on the deformation and the ductile fracture of magnesium alloys at various stress states is indispensable. This demands both elaborately tailor-designed experiments and effective modeling strategies.

It is well established that fracture behaviors of metallic materials are dictated by the stress state, which can be uniquely determined by stress triaxiality and Lode parameter. Investigations on the stress-state dependency of ductile fracture in magnesium alloy sheets were reported, e.g., Abedini et al. (2018) studied the fracture behaviors of ZEK100 sheet in proportional and non-proportional cases; Habib et al. (2019) investigated the fracture behaviors of ZEK100 sheet at different stress states and strain rates; Jia and Bai (2016) conducted a research on the fracture behaviors of AZ31B sheet under various loading conditions; Lee et al. (2018) examined the fracture limits of AZ31 and ZE10 sheets under various stress states. In these reports, notched plate specimens were frequently used for tensile fracture tests. As the notch acuity changes, local stress states at the specimen center vary between uniaxial tension and plane strain tension. Although widely used, these tests are restricted to plane stress states.

To study the fracture behaviors at triaxial stress states, notched round specimens were almost exclusively used. Specific to magnesium alloys, tension experiments of the smooth and differently notched round specimens were conducted to explore the triaxiality effect on room-temperature ductility of hot-rolled AZ31 (Kondori and Benzerga, 2014) and WE43 (Kondori and Benzerga, 2015) plates. It was shown that as stress triaxiality increases, fracture strains of these two magnesium alloys first increase to a maximum and then decrease in varying degrees. The authors (Kondori and Benzerga, 2014, 2015) attributed this trend to fracture mode transition associated with the activating deformation mechanisms, second phase particles and grain-boundary precipitates, etc. Motivated by the experiments of Kondori and Benzerga (2014), Selvarajou et al. (2016, 2017) quantified the distributions of stress triaxiality and the evolutions of relative activities of key deformation mechanisms in smooth and notched round specimens through crystal plasticity FE simulations. Although modeling of the mechanism-based failure was not attempted in their work, some fundamental understanding of ductile fracture in magnesium alloy was inspired. One advantage of using the notched round specimens for tension tests is that stress triaxialities generated at the notch area increase as the notch gets sharper. This renders notched round specimen ideal for the investigation of ductile fracture at high stress triaxialities. Another advantage is that plastic deformations are localized at the notch area, and ductile fracture can be expected to initiate there. Nevertheless, the exact site of fracture initiation is somewhat ambiguous. Typically, ductile fracture initiates from the inner center of the notched round specimen in tension tests of aluminum alloys (Bao and Wierzbicki, 2004) and steels (Benzerga et al., 2004a, b), while in tension tests of AZ31 magnesium alloy, fracture initiation was reported to occur near the notch root rather than the inner center when the notch is severe (Kondori, 2015, 2018).

The study reviewed above mainly concerned the ductile fracture at positive stress triaxialities. By comparison, ductile fracture at negative stress triaxialities has received fewer research efforts. One important reason might be that ductile fracture in metals is generally the result of the nucleation, growth and coalescence of micro-voids (Shang et al., 2020), and a compressive state would probably impede such processes. Whereas, there is growing experimental evidence that ductile fracture can occur even at very low stress triaxialities due to the evolution of micro-cracks (Khan and Liu, 2012; Brünig et al., 2018). The fact is that microscopic fracture mechanisms vary at different stress states, and this leads to diverse macroscopic fracture behaviors (Pineau et al., 2016). For the magnesium alloy with a limited ductility at room temperature, ductile fracture at both positive and negative stress triaxialities merit serious attention.

Cylindrical specimens are conventionally used for compression tests. These tests are easy to implement but have the following limitations in the characterization of ductile fracture. On the one hand, compression results are highly sensitive to friction conditions between the specimen and platen, which is unfavorable for obtaining reliable experimental data. On the other hand, ductile fracture generally initiates at the equatorial bulging area of the cylindrical specimen, where the deformation has experienced a transition from compression to shear. This means that using cylindrical specimen is insufficient to study the ductile fracture at low negative stress triaxialities.

By modification of the cylindrical specimen, some novel specimens were proposed. For example, the cylindrical specimen with a spherical recess at the equatorial area (Kubík et al., 2016) and that with a non-prismatic notch along the length (Kubík et al., 2018) were adopted. Such modifications provide the exact fracture initiation site with an average stress triaxiality lower than −1/3. However, due to the ‘eccentric’ geometry of the specimen, obvious distortion appears during compressive loading and stress triaxiality at the fracture initiation site changes enormously as well. Additionally, specimens with only one certain geometry were adopted and no method to change or control the generated stress triaxiality was introduced. To achieve various negative stress triaxialities, some biaxially loaded specimens were proposed. Brünig et al. (2018) designed new cruciform specimen with a notch at its center and loaded it in vertical and horizontal directions concurrently. The vertical load leads to shear deformation and the horizontal load superimposes tensile or compressive deformation in the notched part. By applying a vertical and horizontal load ratio of 1: −8, the cruciform specimen fractured at a stress triaxiality low to −0.56. In the same vein, Gerke et al. (2017) designed double symmetric H-specimen with four notched regions and loaded it in two dimensions. With different loading ratios, stress triaxialities in the range of (−0.6, 0.8) were obtained. Although such biaxially loaded specimens appear to be versatile, the specimen processing is cumbersome and a special biaxial testing machine is needed. Actually, negative stress triaxialities can be realized in a notched round specimen under the compressive condition according to the Bridgman formula (Bridgman, 1952). However, unlike notched tensile specimens, notched compressive specimens are seldom reported. Bao and Wierzbicki (2004) used the notched round specimen for compression tests to study the fracture behaviors of 2024-T351 aluminum alloy. In their study, only one type of notched round specimen was adopted, and it was designed mainly to eliminate the friction effect during compression. Moreover, stress triaxiality at the fracture initiation site of the designed specimen gets closer to zero as deformation increases, which resembles the situation in compression tests of the cylindrical specimen. It seems that to date there have not been satisfactory specimens for fracture tests in the negative stress triaxiality regime.

Experiments aside, ductile fracture modeling is another important subject, since fracture tests at a lot of stress states are not achievable. In this respect, some advanced phenomenological fracture models, e.g. MMC model by Bai and Wierzbicki (2010), DF2014 model by Lou et al. (2014), and HC model by Mohr and Marcadet (2015), work well by taking both accuracy and efficiency into consideration. Previously, we proposed a new framework for establishing multi-component fracture models, and the established two-component DF2014 model was shown to have higher accuracy than the single-component counterpart when applied to describe the fracture strains in a wide range of stress triaxialities (Li and Fang, 2018). In phenomenological models, a damage index is defined as the integral of a stress-state function along strain path. Ductile fracture is assumed to occur when the damage index reaches a critical value. To obtain the accurate stress and strain fields during deformation, a hybrid experimental-numerical procedure is always exploited (Dunand and Mohr, 2010; Papasidero et al., 2014, 2015). In this procedure, the plasticity model employed in numerical simulations is of great importance for successful implementation of the fracture model.

In the present work, ductile fracture of an extruded magnesium alloy at both positive and negative stress triaxialities is investigated experimentally and numerically. Differently notched round specimens are used for tensile fracture tests, spanning a wide range of positive stress triaxialities. To realize negative stress triaxialities, new types of notched round specimens are proposed for compressive fracture tests. The new specimens are designed to have different notch radii, hence the triaxiality effect in the range of compressive states can be characterized quantitatively. What is worth mentioning is that during all fracture tests of notched round specimens, the loading process is successfully stopped at the onset of macroscopic crack, which facilitates the correct location of the fracture initiation site. In conjunction with the plasticity model based on Yoon2014 function (Yoon et al., 2014), FE simulations of all fracture tests are performed. The obtained experimental and numerical data are utilized to calibrate both the single- and two-component DF2014 fracture models. After that, a comparison of the description results between these two models is performed. Finally, the fractured surfaces of various specimens are detected and analyzed by scanning electron microscopy (SEM), to shed some light on the fracture mechanisms of magnesium alloy at different stress states.