含沟槽轴对称杆疲劳寿命的损伤力学闭合解

 首先建立了工程中常见的含环形沟槽轴对称杆的一个损伤力学守恒积分。利用此积分的守恒性与小范围损伤的条件，证明了在应力集中点有损伤时之应变比能等于无损伤时之应变比能。然后根据以损伤驱动力表示的损伤演化方程，通过分离变量积分获得疲劳裂纹形成寿命的闭合解。根据以上分析与结论，利用一种应力集中系数为K-T1试件的实验中值S-N曲线及相应数据确定了一种材料的疲劳演化参数，从而推出同样材料的其他应力集中系数为K-T2试件的中值S-N曲线。该项研究的应用可以大大地节约疲劳试验的机时与费用。

Closed Form Solution of Damage Mechanics to Predict the Fatigue Life of Axially Symmetric Bars with Grooves

A conservative integral of axially symmetric bars with grooves in damage mechanics is established for the first time. By means of the path independent property of this integral and the condition of small scale dam age, it is proved that the specific strain energy with damage is equal to that without damage at the point of stress concentration. Afterwards, based on the damage evolution equations expressed by the damage driving force, a closed form solution to determine the fatigue crack formation life is obtained by the integration method of separating variables. According to the above analysis, the experimental data and median S-N curve of one kind of specimen with stress concentration coefficient KT1 , are used to determine the fatigue damage evolution parameters of this kind of specimen, and then the median S-N curve of another kind of specimen made of the same material with different stress concentration coefficient KT2 is deduced. This research achievement can be used to reduce the time and the cost of fatigue test evidently.