关键词: 孔隙, 分形, 数值试验, 抗压强度, 损伤, 应力集中

Abstract: Four types of porous material models with different pore distribution patterns are established, and their fractal dimensions of pore distribution (FDPD) are calculated based on both the range and concentration of their pore locations. Then biaxial numerical experiments are conducted to obtain the compressive strength of samples with identical intact strength and different pore distributions and porosities. The results indicate that the failure modes of samples with small porosity or high FDPD conform to the law of 45° angle of rupture, while other samples with low FDPD show asymmetric rupture in oblique section; for samples with identical porosity, the higher the FDPD is, the greater the compressive strength is; the theoretical relationship between sample porosity and its compressive strength proposed demonstrates that the higher the FDPD is, the slower the rate of strength declining with the growth of porosity is; and according to the prediction for compressive strength using damage model, the predicting result is more accurate for porous materials when their FDPD is high, while its accuracy gradually decreases as the FDPD becomes lower. The laws above can be attribute to the fact that a drop in FDPD will lead to more irregular distribution of pores, thus the accumulation of stress concentration in turn will more likely to trigger irregular and easy failures.

Key words: pore, fractal, numerical test, compressive strength, damage, stress concentration