**1. Introduction**

Porous Ti3SiC2 [1–5], as a new type of porous intermetallic compound with MAX phase, has the performance advantages of porous metals and ceramics, such as excellent environmental corrosion resistivity [1], high temperature stability [2] as well as good thermal shock resistance and machining performance [3]. In addition, porous Ti3SiC2 prepared by reactive synthesis of elemental powders [6–8] also shows a good open-pore structure and pore-structure stability [1,2].

Compared with dense material, the mechanical strength of porous material decreases significantly [9–11]. The mechanical model [8,12], microstructure [8] and the effect of porosity on mechanical properties [12,13] of porous Ti3SiC2 have been investigated, which is classified as a kinking nonlinear elastic solid [14,15]. The strength and stiffness of porous Ti3SiC2 decrease with increasing the porosity [12]. In the case of porous MAX phases prepared with space holder with the size of several hundred microns [4,5,13], it was found that the porosity and the pore type were the main factors influencing the elastic properties [13]. On the other hand, porous Ti3SiC2, due to its unique pore structure and material properties, can be well applied in biological separation [16], chemical filtration and hydrometallurgy [1], etc., where the mechanical properties of porous materials should meet the requirements of the working conditions [3]. The pore size is an important pore structure parameter determining the filtration accuracy, and its influence on mechanical properties is an important design basis for porous materials in the filtration application. To the best of our knowledge, investigations on the effect of pore size of porous Ti3SiC2 on its strength and stiffness have not been reported so far.

Currently, the relationship between porosity and strength of porous materials can be simulated by the Barsen equation [17]. The Hall–Petch equation can be used to reveal the relation between the strength or hardness and the grain size of single phase material [18–20] or composite material [21–23]. In this work, a series of porous Ti3SiC2 compounds with di fferent pore sizes and approximately the same porosities and phase purities were prepared by the reactive synthesis of elemental powders through a pressure less sintering process. The Hall–Petch relationship between the pore size and the bending strength was studied, and the e ffect of pore size on the flexural modulus of porous Ti3SiC2 was discussed.
