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(C_R), 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 0.69C_R; 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.

功能梯度材料被认为是一种特殊的复合材料。通过连续改变材料的组成和结构，可以消除材料的界面和分层问题，这导致材料特性随着材料的组成和结构的变化而缓慢变化。本文采用能准确显示脆性材料力学性能的晶格弹簧模型，研究功能梯度材料在超高载荷下的裂纹扩展路径，裂纹速度和演化规律及机理。该模型使用Gusev提出的定量参数映射方法来精确求解模型的弹簧刚度系数，建立了基于格里菲斯能量平衡原理的模型的断裂准则，利用Fortran软件构造了功能梯度脆性材料的晶格弹簧模型，并进行了数值模拟，裂纹扩展路径和速度的演化。研究了超高负荷下高等级脆性材料。仿真结果表明，在超高载荷作用下，功能梯度脆性材料中高速裂纹的扩展路径分为两个阶段：单裂纹和分叉裂纹。一旦裂纹达到裂纹萌生的临界条件，它将开始裂纹并以高速生长。裂纹传播速度突然从0跃升到瑞利波速度的0.5倍以上（利用Fortran软件构造了功能梯度脆性材料的晶格弹簧模型，并进行了数值模拟，研究了超高载荷速率下功能梯度脆性材料的裂纹扩展路径和速度的演变。仿真结果表明，功能梯度脆性材料在超高加载速率作用下高速裂纹的扩展路径分为单裂纹和分叉裂纹两个阶段。一旦裂纹达到裂纹萌生的临界条件，它将开始裂纹并以高速生长。裂纹传播速度突然从0跃升到瑞利波速度的0.5倍以上（利用Fortran软件构造了功能梯度脆性材料的晶格弹簧模型，并进行了数值模拟，研究了超高载荷速率下功能梯度脆性材料的裂纹扩展路径和速度的演变。仿真结果表明，在超高载荷作用下，功能梯度脆性材料中高速裂纹的扩展路径分为两个阶段：单裂纹和分叉裂纹。一旦裂纹达到裂纹萌生的临界条件，它将开始裂纹并以高速生长。裂纹的传播速度突然从瑞利波速度的0跃升到0.5倍以上（研究了功能梯度脆性材料在超高加载速率下的裂纹扩展路径和速度的演变。仿真结果表明，功能梯度脆性材料在超高加载速率作用下高速裂纹的扩展路径分为单裂纹和分叉裂纹两个阶段。一旦裂纹达到裂纹萌生的临界条件，它将开始裂纹并以高速生长。裂纹传播速度突然从0跃升到瑞利波速度的0.5倍以上（研究了功能梯度脆性材料在超高加载速率下的裂纹扩展路径和速度的演变。仿真结果表明，功能梯度脆性材料在超高加载速率作用下高速裂纹的扩展路径分为单裂纹和分叉裂纹两个阶段。一旦裂纹达到裂纹萌生的临界条件，它将开始裂纹并以高速生长。裂纹传播速度突然从0跃升到瑞利波速度的0.5倍以上（单裂纹和分叉裂纹。一旦裂纹达到裂纹萌生的临界条件，它将开始裂纹并以高速生长。裂纹传播速度突然从0跃升到瑞利波速度的0.5倍以上（单裂纹和分叉裂纹。一旦裂纹达到裂纹萌生的临界条件，它将开始裂纹并以高速生长。裂纹传播速度突然从0跃升到瑞利波速度的0.5倍以上（C _R），然后是速度下降和恢复的过程；经过最初的急剧变化，增长速度逐渐达到了稳定的平台。此后，增长率缓慢攀升并超过0.69 C _R; 由于裂纹萌生引起的应力松弛，裂纹尖端处的最大拉应力也呈现出下降和缓慢上升的过程。通过比较发现，裂纹尖端的变化规律与裂纹扩展速率（高速增长阶段）的变化规律具有显着的相关性，这有助于揭示决定裂纹扩展速率的内部机制。研究不同载荷率下的裂纹扩展可以预测功能梯度脆性材料的裂纹扩展速度，方向和距离。