High speed crack propagation characteristics of functionally graded brittle materials under ultra-high loading rate

Abstract

Functionally graded materials are considered to be a special composite material. By continuously changing the composition and structure of the material, the interface and delamination problems of the material can be eliminated, which causes the material properties to change slowly with the change of the composition and structure of the material. In this paper, a lattice spring model, which can accurately show the mechanical properties of brittle materials, is used to study the evolution law and mechanism of the crack path and crack velocity in functionally graded brittle materials under ultra-high loading rate. This model uses the quantitative parameter mapping method proposed by Gusev to solve the spring stiffness coefficient of the model accurately, and the fracture criterion of the model based on the energy balance principle of Griffith is set up, using the Fortran software construct the lattice spring model for functionally graded brittle materials and carry out the numerical simulation, the evolution of crack propagation path and velocity in functionally graded brittle materials under ultra-high loading rate is studied. The simulation results show that the propagation path of high speed cracks in functionally graded brittle materials under the action of ultra-high loading rate has two stages: single crack and bifurcation crack. Once the crack reaches the critical condition of crack initiation, it will start to crack and grow at a high speed. The crack propagation velocity suddenly jumps from 0 to more than 0.5 times the Rayleigh wave velocity(CR), followed by a process of speed decline and recovery; after the initial drastic change, the growth speed gradually reaches a stable platform. Thereafter, the growth rate slowly climbed and exceeded 0.69CR; due to the stress relaxation caused by the crack initiation, the maximum tensile stress at the crack tip also showed a process of declining and slowly rising. Through comparison, it is found that the change law of the crack tip has a significant correlation with the change law of crack growth rate (high-speed growth stage), which is helpful to reveal the internal mechanism that determines the crack growth rate. The study of crack propagation under different loading rates can predict the crack propagation speed, direction and distance in functionally graded brittle materials.