统一平面应变滑移线场理论

UNIFIED PLANE-STRAIN SLIP LINE FIELD THEORY SYSTEM

本文提出了一种基于双剪统一强度理论的统一平面应变滑移线场理论.本理论充分考虑了各种不同材料的中间主应力效应,是一种完全意义上的统一理论.各种基于其他强度理论,如Tresea,Mises和Mohr-Coulomb等的平面应变正交或非正交滑移线场理论均是本理论的特例,并且可以通过不同的加权参数b而构成一系列新的理论.本文讨论了基于刚塑性的Prandtl-Reuss假设的平面应变滑移线场理论的应用范围,证明了该假设可以由Mises屈服条件和相关联流动法则推导得出.本文还通过引入中间主应力系数m,首次提出了另外一条比刚塑性Prandtl-Reuss假设更宽的假设来反映体积可以(或不可以)压缩的材料的中间主应力,该中间主应力即是z方向的主应力.我们通过试验和弹塑性有限单元方法验证了本统一理论的正确性.本理论可以很容易地应用到众多工业领域如金属塑性成型、地基承载力预测、边坡稳定性预测等.由于双剪统一强度理论的通用性和优越性已被逐渐认识,因此,平面应变统一滑移线场理论可以应用于各种工程材料,尤其对在土木工程中广泛应用的、具有强烈中间主应力依赖性的岩土类材料,本理论会更显示出其优越性.

The Twin Shear Unified Strength Theory is extended to Plane-Strain Slip Line Field Theory. A new system of orthogonal and non-orthogonal Unified Plane-Strain Slip Line Field Theories is proposed and developed. The new theory system, which takes into account of different effects of intermediate principal stress on yield or failure of materials, is a completely unified plane-strain slid line field theory system. Various orthogonal and non-orthogonal plane-strain slip line field theories based on different strength theories, such as Tresca, Mises and Mohr-Coulomb, are special cases ( Tresca and Mohr-Coulomb) or linear approximation ( Mises ) of the proposed theory system. Besides, a system ofnew theories can be introduced by selecting different values of weighted parameter, b, of the proposed unified theory system. The paper discusses the scope of application of plane-strain slip line field theories based on the rigid-plastic Prandtl-Reuss equation and proves that the rigid plastic Prandtl-Reuss equation can be derived by Mises yield criterion and associated flow theory. The paper also proposes for the first time a broader assumption than the rigid-plastic Prandtl-Reuss equation by introducing an intermediate principal stress parameter, m.The new assumption can reflect the intermediate principal stress of plane-strain compressible and non-compressible plasticity, where the intermediate principal stress is the principal stress in z direction. Experiments based on the colour-change phenomenon and Elasto-Plastic Finite Element calculations have been used to verified the validity of the proposed theory system. Because of the advantage of Twin Shear Unified Strength Theory,the proposed theory system can be used in many engineering fields,especially for materials with obvious intermediate principal stress effect.