Effects of Forming Pores on Mechanical Property of Zr₇₀Cu₃₀ Metallic Glass

Abstract

Effects of forming pores in Zr₇₀Cu₃₀ metallic glass on the deformation behaviour is investigated through molecular dynamics simulations. The formation of pores leads to only a small reduction in strength, but dramatically enhanced plasticity in compression. The large plasticity of glass is attributed to the large effective free space induced by forming pores. It can also promote formation of crystalline phases in the amorphous matrix during deformation. Simulation reproduces the images of the evolution of pores in the metallic glass. The simulation results are in good agreement with experimental results.

Keywords:
pores; metallic glass; mechanical property; molecular dynamic simulation

1 Introduction

Bulk metallic glasses (BMGs) have several superior mechanical properties, including large elastic limits, high strengths, high hardness, and high corrosion resistance¹. However, their applications are limited by falling catastrophically on one dominant shear upon uniaxial load at room temperature^2,3. To alleviate this problem, many studies have been done recently to enhance their plasticity^4-10 by various methods such as introduction of a second phase, introduction of shear bands, and control of free volume.

With low density and special structures imparting high plasticity, foams based on BMGs have attracted much attention^11,12. The foams can be fabricated by using different methos such as mixing the melt with hydrated B₂O₃ in BMGs¹³, or holding it under pressurized hydrogen¹⁴; or by infiltration of the melt between packed crystals of NaCl salts which can then be leached out in water or acid solution¹⁵. It has been shown that dispersing pores in metallig glasses can greatly improve their plasticity. However, the reason why the pores can improve plasticity is not clear on the atomic scale.

In this study, we remove Cu atoms from Zr₇₀Cu₃₀ MG via molecular dynamics simulations in order to form pores. Molecular dynamics simulations can efficiently achieve the process on the atomic scale. It was found that the forming pores can improve the glass plasticity significantly during uniaxial compression test.

2 Theoretical Model and Calculation Details

We introduce pores in Zr₇₀Cu₃₀ MG by removing Cu atoms. ZrCu was discovered to be a binary bulk MG¹⁶. Since binary alloys are easier to model than alloys which with more elements, it makes ZrCu an attractive MG to study theoretically. The simulations are carried out using the embedded atom method (EAM) potential¹⁷ supplied in LAMMPS. The dimension of the model structures used in the calculations are 27.5 nm × 5.5 nm × 55 nm, respectively in x, y and z direction, the structures contain approximately 500 000 atoms. We first equilibrated these models with 3D periodic boundary conditions (PBCs) at 2000K, which is above the melting point of these amorphous alloys, for 1 ns. The models were then cooled at an MD cooling rate of 1 K/ps to 50 K at zero external pressure (NPT ensemble, i.e., constant number, constant pressure, and constant temperature).

In order to distinguish the original Zr₇₀Cu₃₀, we adopt Zr₇₀ to stand for processed sample. Afterward, a constant and uniaxial strain rate of 1×10^–7 fs^–1 is used at the temperature of 50 K by moving the rigid atoms at one end along the z axis, while keeping the rigid atoms at the other end unchanged. It is worth mentioning that we take the low temperature (50 K) as simulation temperature to highlight the material responses upon mechanical activation and prevent the annihilation of free volume by thermal activations¹⁸.

3 Result and Discussion

3.1 Pair distribution function

To confirm the glassy nature, we adopt pair distribution function (PDF) to describe the structure. Figure 1a shows the PDF of Zr₇₀ and Zr₇₀Cu₃₀ specimen. It is obviously observed that the structure of the specimen is unaffected by the removing Cu atoms, keeping the amorphous structure suggested by splitting in the second peak of the PDF. Figure 1b shows various proportions of voronoi polyhedron (VP) coordination number, which are around Zr. It can be seen that they satisfy the Gaussian distribution, and the main VP coordination number of Zr₇₀ is 11, while that of Zr₇₀Cu₃₀ is 14, indicating the bigger free space in Zr₇₀ specimen.

Figure 1
(a) The PDF of Zr₇₀ MG. (b) Various proportions of voronoi polyhedron (VP) coordination number, which are around Zr.

3.2 Effective free space

In order to further characterizing the increased free space, we calculated the content of each VP, whose content is more than 5%, and the corresponding volume of VP, as shown in Table 1. In order to be more comparable, we propose a parameter:

$V_e=\frac{1}{N}{\displaystyle \sum }_{i=1}^N{V}_i\times P_i$ (1)

where V_e stands for the effective free space, N stands for the total types of VP, V_i is the volume of polyhedra type i, P_i is the content of polyhedra type i. The V_e of Zr₇₀ is 2.16, while that of Zr₇₀Cu₃₀ is 1.71. We can see that after forming pores, the effective free space gets larger, and atoms have more free volume. Compared with that of the original Zr₇₀Cu₃₀ MG, about 26.3% extra free space is introduced by forming pores.

Table 1
The content of each voronoi polyhedron (VP), and the corresponding volume of VP.

VP index of Zr70	Percent %	Volume (A3)	VP index of Zr70Cu30	Percent %	Volume (A3)
(0,2,8,1)	8.87	29.38	(0,1,10,2)	7.69	21.73
(0,3,6,2)	6.20	29.76	(0,1,10,3)	5.53	21.91
(0,3,6,3)	6.67	29.91	(0,2,8,4)	9.77	22.17
(0,4,4,2)	6.17	31.02	(0,3,6,4)	9.54	22.06
(0,4,4,3)	8.07	30.32	(0,3,6,5)	6.21	22.41

3.3 Stress-strain curves

Figure 2 presents the compressive stress-strain curves for Zr₇₀ and Zr₇₀Cu₃₀ MGs. Compressive stress-strain curves are strongly affected by forming pores. For Zr₇₀Cu₃₀ MG, the stress reaches 1.5 GPa and then suddenly drops. The sudden drops are caused by the formation of shear bands (SBs). However, for Zr₇₀ MG, the curve does not appear sudden drop. The results demonstrate that the deformability and stability of samples produced with forming pores is significantly enhanced as compared to original samples, and it has been achieved without much degradation of strength.

Figure 2
The compressive stress-strain curves for Zr₇₀ and Zr₇₀Cu₃₀ MGs.

3.4 Atomic shear strain

To better understand the mechanism of improved plasticity, systems compressed by 7% strain with atoms colored by the local value of the deviatoric shear strain η_i^Misses, corresponding to Zr₇₀ and Zr₇₀Cu₃₀ MGs were observed in Figure 3 ¹⁹. The forming porosity force the proliferation of shear bands (SBs) below the overall failure stress. Not only the quantity of SBs in (b) is more than that in (a) but also the distribution of SBs in (b) is more scattered than that in (a). Figure 3a shows the directions of the SBs are mainly 45° and 135°, while the directions of SBs in (b) are not very clear. The multishear-band pattern is usually observed in the multiaxial stress state such as that in the indentation or notched samples²⁰. In the present study, it is realized that the deformation proceeds under the uniaxial stress mode. These differences suggest that after forming porosity, amount of SBs generate at these locations in the following uniaxial compression deformation process. The shear-band pattern is affected by the pores acting as stress concentrators. It was found that the shear bands branch and highly intersect with each other in the sample prepared by forming porosity. The high density of shear bands with the extensive interaction and branch of shear bands is closed related with plasticity enhancement, reflecting the good deforming ability of Zr₇₀ MG. In contrast, the Zr₇₀Cu₃₀ MG is easy to form strain location in the compressive deformation process. With increasing strain, two major SBs penetrates the system, as shown in (a). Importantly, the simulation result is in very good agreement with the experimental results^21,22. Wang et al.²¹ explained multiplication shear band formation resulting from forming porosity contributes to the improved plasticity. The difference is obviously at the composition, deformation temperature and straining conditions. However, the fact that forming porosity which prevents stress localization is well agreed between the experiment and simulation. As a result, the initiation and propagation of a major SB that cause catastrophic shear fracture will be avoided.

Figure 3
Systems compressed by 7% strain with atoms colored by the local value of the deviatoric shear strain η_i^Misses, corresponding to (a) Zr₇₀Cu₃₀ and (b) Zr₇₀ MGs .

In all, the large effective free space could be induced by forming pores. The nucleation of multiple shear bands owes to the large amount of randomly distributed free space, together with the branch and interaction of the shear bands, directly results in the enhancement of plastic deformation. The large amount of free space also leads to the increase of the mobility of atoms. The high mobility of atoms due to the large amount of free space remits the shear local deformation.

3.5 Common neighbor analysis

Figure 4 shows the common neighbor analysis (CNA) for Zr₇₀ and Zr₇₀Cu₃₀ MGs when strain is 7%. We can easily see that there formed the FCC and HCP crystals in Zr₇₀ MG. One of the effective approaches for enhancing plasticity is the fabrication of materials consisting of an amorphous matrix with one or more crystalline phases^23-25. In the process of deformation, grain nucleates and mergers induced by stress. It is analogical to crystallization by annealing. The main difference is the external cause, meaning the stress and temperature. Pores formed by removing Cu atoms are stress concentrators, and this forces atoms around pores generating crystallization. The second phase induced by porosity can effectively stabilize against the shear localization and propagation of critical shear bands upon loading.

Figure 4
The CNA structure analysis for (a) Zr₇₀Cu₃₀ and (b) Zr₇₀ MGs when strain is 7%.

4 Conclusions

The effect of forming pores on the plasticity of Zr₇₀Cu₃₀ metallic glasses was studied. Simulation reproduces the images of the evolution of pores in the metallic glass. Our results indicate that forming porosity in Zr₇₀Cu₃₀ metallic glasses can enhance the glass plasticity significantly. The enhancement of plasticity is attributed to large amount of randomly distributed free space. And it can also promote forming crystalline phases in amorphous matrix. The simulation results are in good agreement with experimental results.

Acknowledgements

We thank Shaopeng Pan from Peking University for helpful program analysis. This work was supported by the National Basic Research Program of China (2013CB733000) and the National Natural Science Foundation of China (51271161 and 51271162).

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Publication Dates

• Publication in this collection
  17 Nov 2015
• Date of issue
  Nov 2015

History

• Received
  09 Sept 2014
• Reviewed
  30 Sept 2015