Simulation of temperature and stress distributions in functionally graded materials synthesized by a spark plasma sintering process

Abstract

A coupled electrical–thermal–mechanical finite element model is established to systematically investigate the temperature and stress distributions in a functionally graded material (FGM) based on Ti and TiB during a spark plasma sintering (SPS) process. The simulation results indicate that a stable axial temperature gradient in the specimen can be achieved using a die with an area-changing cross-section in the SPS process, thereby providing a beneficial condition for FGM sintering. The stress and the stress gradient are high at the bottom of the specimen, possibly leading to microstructural heterogeneity and cracks among adjacent layers. The simulation results also suggest that the temperature and stress gradient increase as the heating rate increases. The corresponding SPS experiments verified the simulation results and proved the superiority of the specially designed die.

Introduction

Functionally graded materials (FGMs) are inhomogeneous composite materials in which the structure or composition changes continuously or stepwise as a function of position. The mechanical properties also vary gradually as functions of the variation of structure and composition [1], [2], [3], [4]. FGMs have attracted considerable attention, due to their unique performance, sophisticated designation and great potential in engineering applications. Recently, FGMs based on titanium boride (TiB) and titanium (Ti) systems have been studied by researchers [5], [6]. Because TiB exhibits high hardness, a high melting point, high electrical conductivity, good thermal shock resistance and chemical inertness [7], [8], FGMs with a composition that changes from Ti to TiB along the axial direction of the specimen have many potential applications, particularly in the defence field [9], [10], [11], [12]. Because the theoretical sintering temperature of a certain layer in the FGM composed of Ti and TiB increases with the increasing content of the ceramic phase (TiB) [13], FGMs with excellent mechanical properties can be achieved only if they are sintered in a graded temperature field.

Spark plasma sintering (SPS) is a recently developed consolidation method that allows the compacted powders to be sintered at a low temperature with a short heating, holding and cooling time [14], [15], [16], [17], [18], [19], [20]. These characteristics effectively prohibit the grain growth of materials during the sintering process. Moreover, the spark discharged in the SPS process can easily puncture the oxide film on the surface of the ceramic particles. Therefore, the SPS process is considered to be suitable for the fabrication of hard-to-sinter materials, including most ceramics, amorphous materials and nanocrystalline materials [21], [22], [23], [24], [25], [26], [27], [28]. Additionally, in the SPS process, Joule heat generated by a direct current is the main heating source on which a die with an area-changing cross-section can be designed. Accordingly, an axial graded temperature field may be produced in the die during the SPS process, due to the different heat-generation rates [29]. Thus, the SPS process can be used to synthesize FGMs. However, the temperature and stress distributions in the specimen and die are complex, due to the special sintering mechanism [30], [31], [32], [33], resulting in a significant obstacle to designing a die with a reasonable structure for synthesizing FGMs with good mechanical properties.

In recent years, many researchers have studied temperature and stress distributions during the SPS process using a numerical simulation method. Anselmi-Tamburini et al. [30] studied the current distributions in two sample materials, specifically, alumina and copper, using CFD-ACE+ software. These researchers’ results showed that the current distribution was determined by the electrical conductivity of the specimen, and the temperature distribution was closely related to the current distribution. Wang and Fu [31] calculated the temperature differences between the die surface and the sample by a one-dimensional Fourier equation and noted that the temperature difference was related to the heating rate. Zavaliangos et al. [32] applied ABAQUS to investigate the temperature evolution during the SPS process using a specimen composed of graphite, silicon and lithium silicate. It was proved that a linear correlation existed between the die surface and inside temperatures. Introducing a dynamical FE model, Räthel et al. [33] compared the temperature difference in silicon nitride samples by varying the die geometries, and the temperature distribution was found to be greatly influenced by tool geometry. Wang et al. [34] applied COMSOL software and studied the stress distribution in Al₂O₃ samples and in the entire setup. These researchers showed that only the vertical stress had a significant magnitude. Muňozet and Anselmi-Tamburini [35] developed a model in ANSYS code and found that the stress distribution depended on the difference in thermal expansion between the specimen and its surrounding. Using graphite dummies with different geometries, Vanmeensel et al. [36] discovered that the thermal and electrical contact resistances between the die and the specimen had a significant influence on the temperature field. Maizza et al. [37] compared literature involving contact resistances and studied the contact multiphysics using a moving mesh/moving boundary technique.

However, only homogeneous specimens and hollow cylinder dies were involved in the abovementioned work. To date, few numerical simulations have been carried out on the sintering process of FGMs through SPS. The present study aims to systematically understand the SPS process for fabricating FGMs with a numerical simulation method. As a result, rational design of specimen compositions and die structures can be achieved, and the mechanical properties of the FGMs can be improved.