Multi-scale Analyses On Quasi-brittle Propagation Of Non-ideal Cracks And Its Applications

A large of number research shows that destruction of structures is caused by local materials failing during magnitude civil structures working on.With propagation of micro-cracks and fusion of micro-holes,the whole structure losing the bearing capacity due to members was destroyed.Therefore,structure failure was a process from localization to the globe,also from meso-scale to macro-scale on research scale.Ideal cracks only were considered in traditional fracture mechanics,but real crack shape and the effect of various micro-defects on material properties were not analyzed.So,failure theory of real cracks and holes is necessary to be established under the influence of the smaller scale defects and cracks.This paper obtained the analytical solution for stress fields of non-ideal cracks front,and analyzed the influence of meso-scale defects to stress fields of macro-scale holes and propagation of non-ideal cracks.Finally,non-ideal cracks multi-scale propagation theory was established,and failure process of engineering materials with irregular holes and micro-defects was described.The research contributions are as follow:Based on least square method of complex variable function,general form of conformal mapping of non-ideal cracks was obtained,and then,using elastic mechanics method of complex variable function,the stress field of non-ideal cracks with certain aspect ratio was analyzed.When the aspect ratio was great,the first kind of non-ideal cracks front stress field could be described as ellipse,but the aspect ratio was small,it was imprecise using ellipse to simulating the first kind of non-ideal cracks.According to conformal property of mapping,the solution frame of second non-ideal cracks with a random micro-defect in an infinite plate was established.Both meso-scale and micro-scale stress fields could be solved separately by scale separation method.And then,the stress field of a non-ideal crack with multiple micro defects was solved such as that with a defect.The results show that the problem of non-ideal cracks with random defects could be solved by scale separation complex variable function method,and stresses and strains near by the micro-defects only was changed,but not away from that zone.Conformal mapping function of non-ideal cracks with semi-circles or micro-cracks was obtained by the calculation frame of stress field of both micro-defects and macro-cracks at two scales.In addition,relations of both micro and macro stress field were analyzed as the macro-crack be an ellipse and square.The results show that,micro stress fields had relation to macro stress fields,and both micro-defect and micro-cracks around the non crack increased the stress,which lead to the material cracks initiation and failure finally.Base on flat ellipse front stress fields and cohesive strength theory,using maximum tensile stress criterion,non-ideal cracks propagation criterion under the influence of all kinds of micro-defect in the plane stress case.If the micro-defects appeared on the maximum stress zone of non-ideal cracks,the existence of micro-defects decreased bearing capacity enormously,especially for micro-cracks.So,material strength was not only relation of the number of micro-defects,but also the shape of micro-defects.According to maximum tensile stress criterion,Cracks propagation direction and fracture toughness of materials containing ellipse holes with semi-circles and micro-cracks was obtained.Finally,based on multi-scale propagation theory of non-ideal cracks,the stress field near by micro-cracks in the corner of surrounding rock of tunnel was calculated,and empirical formula of the micro-crack propagation was obtained,which could provide guidance on practical engineering.