考虑尺寸效应的厚壁圆筒统一塑性极限解

为了扩大传统厚壁圆筒塑性极限理论的应用范围,基于俞茂宏统一屈服准则和应变梯度塑性理论,对由拉压强度相等的线性硬化材料组成的受内压厚壁圆筒进行塑性极限分析,得到考虑尺寸效应的厚壁圆筒统一塑性极限解.该统一解可以适用于各种拉压强度相等的材料,现有相应的传统解均为它的特例.利用得到的统一解,分析圆筒塑性极限荷载的尺寸效应.结果表明,当厚壁圆筒的特征尺寸为μm量级时,塑性极限荷载有显著的尺寸效应.研究厚壁圆筒塑性极限荷载和材料硬化程度的关系,发现塑性极限荷载随着材料的硬化程度增加而增大.

Unified plastic limit solution for thick-walled cylinder with size effect

In order to expand the application of the classical plastic limit theory for thick-walled cylinder, a plastic limit analysis was conducted by using the unified yield criterion and a strain gradient plasticity theory for an internally pressurized thick walled cylinder of elastic linear-hardening plastic material with the same tension-compression strength. A unified plastic limit solution with size effect was derived in a closed form, which was adapted to various materials with the same tension-compression strength, and the classical plasticity solution can be recovered as a special case of it. The size effect of strain-hardening level on the load-carrying capacity was analyzed based on the unified solution. Results showed that the size effect was significant as the characteristic length was in the level of micrometer. The relationship between the plastic limit loading and the material hardening level was analyzed. Results showed that the plastic limit loading increased with the increase of hardening level.