通过面积转换,修正了有限变形条件下的分形维数,并证明在应变小于10%的条件下,面积变化对分形维数的影响很小。通过蠕变试验,采集了聚甲基丙烯酸甲酯（PMMA）在不同应力和不同时间下的蠕变银纹图像,并用盒维法计算了其分形维数。试验证明,蠕变银纹引发的应力阈值随时间的增长呈指数关系降低,并最终趋于常数;蠕变银纹的分形维数与应力呈线性关系,与时间呈指数关系;在达到应力阈值的瞬间,能产生大量银纹,导致银纹的分形维数产生阶跃。根据实验结果,建立了蠕变银纹的分形维数与应力、时间的关系式。
The modified fractal dimension was imposed by the area transformation under the condition of finite deformation. It proved that the area deformation has little influence on the fractal dimension if the strain is less than 20%. The fractal dimensions of crazing images with different tensile stresses and acting time obtained by creep testing of PMMA were calculated by box-counting method. In the test the critical stress of crazing initiation decreases in exponential form with the creep time and tends to be constant at last. The fractal dimensions of creep crazes increases linearly with the tensile stress and in exponential form with the creep time. As the tensile stress is greater than the critical, a mass of crazes are formed instantaneously, which makes a step change in the fractal dimension of crazes. On the base of the testing results, the relation among the fractal dimension, tensile stress and creep time is obtained.
参考文献
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