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建立了4组不同孔隙分布形式的多孔材料模型,在考虑孔隙分布范围和密度的基础上计算其孔隙分布分形维数,并利用假三维数值试验的方法获得了相同初始强度、不同孔隙度和孔隙分布形式试样的抗压强度。数值试验结果表明,除了孔隙度较小和孔隙分布分维数较大的试样破坏形式基本满足45°??/2破裂角的规律以外,该分维数较小的试样均呈现出不对称的斜截面破坏;在孔隙度相同的情况下,该分维数越大,样品的抗压强度越高;通过推导假三维情况下材料孔隙度与抗压强度的理论关系发现,该分维数越大,样组的抗压强度随孔隙度增大而衰减的速率越慢;根据损伤力学模型对试样的抗压强度进行预测分析发现,当样组的该分维数较大时,该模型能够较准确地预测多孔材料的抗压强度,而当样组的该分维数逐渐减小时,损伤力学模型的精度也逐渐降低。上述规律是由孔隙分布分维数越小、孔隙分布越不均匀、试样中应力集中的累积效应越显著的原因而造成的。
Four groups of porous material models with different pore distributions were established. Based on the distribution range and density of pores, the fractal dimension of pore distribution was calculated, and the same initial strength, different porosity and porosity The compressive strength of the sample in the form of distribution. The numerical results show that except for the samples with smaller porosity and larger fractal dimension of fracture distribution, the failure modes of fracture specimens basically meet the rule of 45 ° / / 2 fracture angle, The symmetry of the oblique cross-section failure; in the case of the same porosity, the larger the fractal dimension, the higher the compressive strength of the sample; by deducing the pseudo-three-dimensional case of material porosity and compressive strength of the theoretical relationship found that the fractal dimension The larger the number is, the slower the compressive strength declines with the increase of porosity. According to the damage mechanics model, the compressive strength of the sample is predicted and analyzed. When the fractal dimension of the sample group is larger, The model can predict the compressive strength of porous materials more accurately, and the accuracy of the damage mechanics model gradually decreases when the fractal dimension of the sample decreases. The above law is caused by the smaller fractal dimension of pore distribution, the more uneven pore distribution, and the more significant the cumulative effect of stress concentration in the sample.