Formation Mechanism And Evolution Laws Of Fracture Spacing In Layered Materials

As a common phenomenon in nature and engineering materials,fracture spacing mainly displays two-dimensional parallel fractures and three-dimensional polygonal fractures in layered materials.It widely exists in layered structures of different materials,different scales,and various geometric shapes,involving a wide range of fields.Although there are certain differences in crack patterns,they have obvious similarities.In fields such as geotechnical engineering,either interlaminar cracks or surface cracks would affect the structural safety and service life of the project to some extent and pose a hidden safety hazard.Therefore,this regular fracture issue has aroused extensive concern from scientists and scholars.However,there are still limitations in the understanding of its formation and mechanism due to the complexity of its formation factors.This research is mainly carried out focusing on fracture spacing phenomenon in layered materials by numerical methods.The evolution process and formation mechanism of fracture spacing on various geometric surfaces are discussed based on the finite element code Realistic Failure Process Analysis system(RFPA).The whole failure process from fracture initiation to saturation of fracture spacing under quasi-static loading in three-dimensional layered models of various geometries is elaborated.The effects of fractured layer thickness,flat dimensions,and surface curvature on crack pattern and spacing are studied by means of quantitative statistics.Based on the stress transformation analysis during the crack evolution process of the flat and cylindrical surface,the occurrence and development law of the fracture spacing is revealed.The main results are summarized as follows:1.Numerically reproduce the whole progressive failure process of fracture spacing on flat,cylindrical,and spherical surfaces.The evolution processes of fracture spacing on three various surfaces under quasi-static loads share the same regularities,beginning with failures at low strength region,ending with layer separation of overlay and substrate.Both on flat and cylindrical surfaces show a transition of various fracture patterns through changing strain ratio in different directions,while on the spherical surface,only polygonal fractures emerge.2.Through the rearrangement of the surface elements by a program,the three-dimensional cylinder is displayed as the two-dimensional plane.Based on the analysis of the surface saturated cracks network by the quantitative statistical method,the fractured layer thickness has a significant influence on the crack density that the crack density decreases with the increase of the thickness.Besides,the surface curvature shows a modest effect on the crack density that the crack density increases with its increase,whereas the curvature reaches a large value,the generation of cracks will be limited.Furthermore,the distribution of saturated cracks has statistical similarity at different dimensions,and so does the distribution of corresponding fracture polygons.3.Although the loading conditions are different,the stress distributions in the plane and the curved surface are equivalent,and the crack evolution process follows a similar stress mechanism.The process of tensile and compressive stress transformation occurs with crack insertion,which is the main reason for fracture saturation.In the process of crack insertion,the crack spacing shows a negative exponential relationship with the tensile strain along the layer.Furthermore,layer separation is a key process of fracture saturation,which is caused by tensile failure due to the large load at the interface.And it would lead to the transformation of tensile and compressive stress fields as well,and the tensile stress peak value position shift,thus affecting the crack inserting position.