传统疲劳经验公式的损伤力学解释

一般认为传统的疲劳方程为一经验公式,无法解释其力学含义.采用损伤力学方法研究梁的弯曲疲劳问题,分别以初始无损伤时的应力幅值和损伤材料的有效应力(或有效应变)幅值作为损伤演化的控制量,推导出相互等价的疲劳裂纹形成寿命的工程封闭公式.发现二者均与传统的疲劳经验公式等价,表明传统的疲劳方程可由损伤理论导出,从而赋予传统的疲劳经验公式损伤力学意义下的解释.

Damage Mechanical Interpretation of Classical Fatigue Empirical Formula

It is thought that the classical fatigue equation is empirical and its mechanical implications are unknown. In this paper the authors study the fatigue failure of beam-bending by means of damage mechanics. The amplitudes of initial undamaged stress and effective stress are used as controlling variations of damage development respectively to obtain the engineering closed solutions of fatigue crack initiation life which are equivalent to one another. The two closed solutions are also equivalent to those of the classical fatigue empirical formula. This is shown clearly that the classical fatigue empirical formula can be derived from the damage mechanical theory and its mechanical implications can be obtained consequently.