Theoretical study on the strength of steel elements with notches under cyclic loadings

这项工作包括实验研究和理论研究。第一部分对带缺口的结构钢试件进行了疲劳试验。在试验前，通过超载对试样施加不同程度的预紧力。验证了预拉伸对疲劳强度的影响。只要预紧适度，就有利于提高疲劳强度。当过载强度一定时，缺口处应力集中越高，疲劳强度越大。预张力过大也会导致疲劳强度下降。裂纹扩展观察表明，预张力主要控制疲劳断裂的第一阶段，即裂纹萌生阶段。第二部分通过弹塑性分析对这一现象进行了理论和定量研究。由于应力集中点周围不可避免会产生很大的变形，因此采用有限变形弹塑性理论。假定塑性流动遵循J2规律，并结合各向同性-运动硬化。采用有限元法对控制微分方程进行了数值求解。数值计算表明，预压缩会在应力集中点附近产生残余应力。弹塑性分析表明，从残余应力的角度来看，预紧力与疲劳强度之间看似复杂的关系是很容易理解的。在本工作中采用的假设范围内，残余应力不会随着小循环载荷而消失。因此，断裂力学的方法可以毫无困难地应用于这种现象。

This work consists of experimental and theoretical investigation. In the first part, fatigue tests were carried out for the structural steel specimen with notches. Various magnitude of prestraining was applied by overloads to the specimen before the test. It is confirmed that the prestraining affects the fatigue strength. As long as the prestraining is moderate, it works in favor of fatigue strength. When the magnitude of overloads is fixed, the higher stress concentration at notches results in larger fatigue strength. It is also true, however, fatigue strength degrades with too large prestraining, Observation of crack propagation revealed that the prestraining controls mainly the first stage of fatigue fracture, or the stage of crack initiation. In the second part, this phenomenon was studied theoretically and quantitatively by elasto-plastic analysis. Since very large deformations are inevitable around stress concentrator, the theory of elasto-plasticity at finite deformation was employed. It is assumed that plastic flow is governed by the J2 rule with combined isotropic-kinematic hardening. Governing differential equations were solved numerically by an FEM. It was numerically shown that prestraining causes the residual stresses in the neighborhood of stress concentrators. The elasto- plastic analysis indicated that the seemingly complex relation between the prestraining and the fatigue strength was easily understood in view of such residual stresses. Within the assumptions employed in this work, the residual stresses do not disappear with small cyclic loadings. Therefore, the method of fracture mechanics can be applied to the phenomenon without any difficulty.