共振条件下的裂纹梁振动与裂纹扩展耦合分析 *

Coupling Analysis of Vibration and Crack Propagation for a Cracked Beam at Resonant State

关键词:  呼吸裂纹  耦合分析  共振响应  接触有限元  裂纹扩展  Campbell图

Key words:  Breathing crack  Coupling analysis  Resonant response  Contact FEM  Crack propagation  Campbell diagram

摘要:

为了对裂纹静子叶片在共振激励下的损伤容限寿命潜力进行初步探索，采用接触有限元法研究了共振状态下裂纹梁的振动与疲劳裂纹扩展的耦合问题。裂纹梁采用二维平面应力单元离散，接触模型模拟呼吸裂纹开合过程中的弯曲刚度变化。振动分析中，分别使用解析法预估和瞬态响应扫频计算得到系统一阶共振频率。断裂力学参量在有限元法中使用线弹性断裂力学方法进行求解。耦合分析中，模拟了耦合现象中的两个典型问题——裂纹止裂和失稳扩展，通过在共振激励下扫描裂纹长度计算应力强度因子曲线，通过该曲线与断裂韧度、裂纹扩展门槛值对比判断裂纹扩展的稳定性、计算裂纹扩展寿命。最后使用耦合分析结论基于Campbell图对假设静子叶片进行了定性的共振分析。

Abstract:

As an exploration of damage tolerance lifetime analysis for a cracked stator blade，coupling effect of vibration and fatigue crack propagation for a cracked beam was studied by using contact FEM. Cracked beam is discretized by 2-D plane elements and stiffness changes of breathing crack during opening and closing process are described by contact model. The first resonant frequency was calculated by analytical method and transient response frequency sweeping. Linear fracture mechanics theory was used to calculate the stress intensity factor in vibration analysis. Two numerical examples were calculated to investigate coupling effects at resonant state: crack arrest problem and crack unstable propagation problem. The stability of crack propagation was predicted and crack propagation lifetime was calculated. Based on the Campbell diagram，the judgment of resonance was analyzed according to the conclusions from the numerical tests.