Theoretical Investigations On The Micro-toughening Mechanisms Of Crack-bridging In Biological Composites

Many biological materials,such as nacre,bones,teeth,spruce,cellulose nanopaper,etc.,have excellent mechanical properties of both high strength and toughness.Among the many factors that contribute to its excellent mechanical properties,crackbridging is considered to be a significant toughening mechanism.In most of the current scientific researches,only the bridging situation of the mode I crack caused by the bridging fiber perpendicular to the crack surface is considered.In fact,the fibers in the crack-bridging zone may be inclined at a certain angle with respect to the crack surface,resulting in the mixed mode of crack tip even under pure mode I loading in the far field.Based on the one-dimensional multi-scale crack-bridging model,this paper introduces three mixed mode functions to express the hybrid critical matrix crack growth energy release rate under the mode I loading condition,and combines the condition of fibers pulled out from the matrix.Under the critical conditions,the mode I stress intensity factor and flaw size in the critical state are calculated.This model can quantitatively calculate the crack-bridging toughening effect of fiber-reinforced composite materials,and can be used to guide the synthesis and design optimization of biomimetic fiber composite materials.Nacre and nacre-like composite materials have high strength and high toughness due to the optimal interlocking angles.In order to quantify the toughening effect of the interlocking angles,in this paper,we have established a mode I crack-bridging model of nacre with interlocking interface.The effects of the interlocking angle on the toughening effect of the crack-bridging are explored,and the interlocking angle for the optimal toughening effect is obtained.Theoretical analysis gives the expression of the critical interlocking angle for a given aspect ratio,and the predicted results agree with the actual situation in nacre.Based on this model,we calculated the effect of the interlocking angle on the bridging behavior and fracture toughness at different aspect ratios.The results show that the toughening effect of the interlocking angle is significant at a large aspect ratio.Theoretical calculations reveal two mechanisms for the toughening of the interlocking structure for the first time,that is,the existence of the interlocking angle can significantly increase cohesion stress of crack-bridging,and it can also increase the fracture toughness by increasing the elastic modulus.A quantitative comparison between the related calculation results and the experimental observation results of nacre has proved the correctness of this model.This kind of crackbridging model provides a theoretical analysis method for guiding the design of the nacre-like materials with interlocking interface,and has important guiding significance.In order to compare the toughening effects of crack-bridging and modulus inhomogeneity,first,for the situation that the crack in the interface layer model is completely located in a homogeneous material,the shielding coefficient of the stress intensity factor that varies with the modulus ratio is calculated.By using the mode I crack-bridging model,the shielding coefficient of the stress intensity factor for a fully bridging crack gradually in a steady state is calculated.By comparing the shielding coefficients of the two mechanisms,it is found that as the modulus ratio increases,the shielding coefficient tends to be stable.The crack-bridging mechanism has a more significant shielding effect on the stress intensity factor of crack tip.