Research Article
Finite element analysis of temperature and residual stress profiles of porous cubic Ti-6Al-4V titanium alloy by electron beam melting

https://doi.org/10.1016/j.jmst.2020.01.033Get rights and content

Abstract

The temperature and stress profiles of porous cubic Ti-6Al-4V titanium alloy grids by additive manufacturing via electron beam melting (EBM) based on finite element (FE) method were investigated. Three-dimensional FE models were developed to simulate the single-layer and five-layer girds under annular and lateral scanning. The results showed that the molten pool temperature in five-layer girds was higher than that in single-layer grids owing to the larger mass and higher heat capacity. More energies accumulated by the longer scanning time for annular path than lateral path led to the higher temperature and steeper temperature gradient. The thermal stress drastically fluctuated during EBM process and the residual stress decreased with the increase of powder layer where the largest stress appeared at the first layer along the build direction. The stress under lateral scanning was slightly larger but relatively more homogeneous distribution than those under annular scanning. The stress distribution showed anisotropy and the maximum Von Mises stress occurred around the central node. The stress profiles were explained by the temperature fields and grids structure.

Introduction

Titanium alloy is widely used for the fabrication of orthopedic implant because of high mechanical strength, sound corrosion resistance, and good biocompatibility. However, the tremendous difference of elastic modulus between dense titanium alloy implants and bone creats the stress shielding phenomenon at the interface, which results in the premature failure of the implant [1]. Thus medical porous titanium alloy were developed and can be adjusted by the porosity to match the elastic modulus of bone tissue [2,3]. In addition, the three-dimensional opened networks structure would help the transportation of body fluid and nutrient, promoting the regeneration and repair of bone tissue and realizing the combined effects of structure, mechanics and bionics of porous titanium alloys [4,5]. Conventional fabrication processes, such as powder metallurgy [6], rapid prototype [7] and freeze-drying methods [8], are difficult to produce porous implants, with complex shape and desired porosity [9].

Electron beam melting (EBM) is an advanced additive manufacturing (AM) technique with the advantages of high flexible, rapid response on structure design, near net shape [10], and is an ideal choice for direct fabrication of three-dimensional parts with porous structures [11]. Significant research efforts have been required to fabricate biomedical porous titanium alloys with an emphasis on Ti-6Al-4V alloy by EBM [12,13], the relationship among microstructure, mechanical properties and EBM processing parameters [14,15], and the thermal [[16], [17], [18]] or stress behavior [[19], [20], [21]] by finite element method or other numerical simulation methods.

Luo and Zhao [22] reviewed and summarized the significance of finite element method in the connection of additive manufacturing issues such as material design, in-process monitoring and control, and process optimization. Pan et al. [23] simulated the build thickness dependent microstructure of EBM Ti-6Al-4V with thicknesses of 1 mm, 5 mm, 10 mm, 20 mm and found that cooling rates and thermal profiles during EBM process are favorable for the martensite formation and martensitic decomposition is faster in thicker samples. Huang et al. [24] investigated the effects of the linear energy density, volume shrinkage, scanning track length, hatch spacing and time interval between two neighboring tracks on the temperature distribution and molten pool dimensions. The rapid heating and cooling of EBM processes created residual stresses in as-built material, which has been predicted by theoretical modeling as well as experimentally verified. Romano et al. [25] compared the temperature distribution and melt geometry in laser and electron-beam melting processes containing titanium, stain-less steel, and aluminum powders. Vastola et al. [26] performed systematic finite element modeling of one-pass scanning to study the manufacturing parameters on the magnitude and distribution of residual stresses. Wu et al. [27] found that a reduction in residual stress is obtained by decreasing scan island size, increasing island to wall rotation to 45 deg., and increasing applied energy per unit length.

These numerical simulations of thermal or stress behaviours were mainly focused on the bulk materials during EBM of metal powders. There are limited researches on thermal and stress behaviours of porous titanium alloys during EBM. It is necessary to illustrate the complex thermo-mechanical behavior during the forming process for understanding the cyclic phase transformation and the integrated control of forming and performance. In this paper, establishment of three-dimensional finite element (FE) model of porous cubic Ti-6Al-4 V alloy during EBM based on solutions to heat transfer equations has been performed, and the thermal and stress behaviors, considering the non-linear temperature-dependent physical properties, were predicted with the aim of understanding the relationship of porous structure, process parameters and thermal or residual stress distribution.

Section snippets

Experimental

FE method framework was designed based on the ANASYS commercial software. The porous cubic FE models and electron beam scanning strategies are shown in Fig. 1. The pore size and strut of porous cubic structures are 1 mm × 1 mm and 0.2 mm, respectively. The sizes of single-layer and five-layer structures are 2.6 mm × 2.6 mm × 0.05 mm and 2.6 mm × 2.6 mm × 0.25 mm, respectively. Each layer is 0.05 mm. The substrate is 4.6 mm × 4.6 mm × 0.5 mm. The mesh size for powder bed and melt pool with

Thermal analysis

Fig. 2 shows the molten pools of porous cubic grids under annular and lateral scanning. Using the present process parameters, the width and depth of molten pool were about 211 μm, 81 μm under annular scanning and 207 μm, 72 μm under lateral scanning, respectively, which exceeds the hatching spacing (200 μm) and thickness of powder layer (50 μm). The maximum temperature can reach 2269 °C and 2197 °C under annular and lateral scanning, exceeding the melting point of the alloy. This guaranteed the

Conclusions

The temperature field and stress behaviors of porous cubic grids based on the single-layer and five-layer models have been studied. The following conclusions can be drawn:

  • (1)

    The overlaps of neighboring tracks and good metallurgical bonding of adjacent layers can be achieved by EBM parameters. The scanning time for annular path is longer than lateral path and more energies would be accumulated, leading to higher molten pool temperature under annular scanning.

  • (2)

    The higher thermal capacity of the

Acknowledgements

The work was financially supported by the Natural Science Foundation of Shandong Province, China (No. ZR2019MEM012), the Major Scientific and Technological Innovation Program of Shandong Province, China (No. 2019JZZY010325), the Key Research Program of Frontier Sciences, CAS (No. QYZDJ-SSW-JSC031-02) and the National Natural Science Foundation of China (No. 51871220).

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