塑流模式彈塑性材料受預應力及溫升之三次歪扭降伏超面演化

Abstract

一個應變控制的軸向-扭轉模型已經在ASCE《工程力學雜誌》2022年: J. Eng. Mech., 2022, 148(6): 04022027中發表。該模型稍微調整以適用於應力控制實驗。

這篇論文旨在使用無速率依賴的彈塑性流動材料模型推導閉合正解並通過與Phillips和他的合作者在五十年前獲得的眾所周知的應力控制實驗數據進行擬合，以最佳化出重要的材料常數。該模型除了需要楊氏模量和剪切模量外，還需要8個材料常數。軸向-扭轉模型具有不斷演化的三次歪扭降伏超面，該超面與兩個Mises超球體相結合，此球體的特徵是在塑性相位中正交性Poincare群元素的內部對稱性。與應力空間中的每個Mises超球體相關聯的是一個混合指數型Armstrong-Frederick的正交性塑性流動規則，該規則結合了二次各向同性指數規則和走動學規則。

通過對該材料進行應變表面的軸向-扭向應力控制實驗，可以優化和擬合相應的唯一參數組合。然後，通過將該唯一參數集合和任何應力輸入閉合正解中，本文可以預測在任何施加的應力下該材料的應力狀態和塑性行為等重要信息。

溫度層面，本研究將利用閉合正解來擬合材料在預應力和溫度上產生的降伏面，並與Phillips的實驗數據進行比較，以驗證本文中所提出的模型的可行性。

A strain-controlled axial-torsional model has been published in ASCE Journal of Engineering Mechanics 2022: J. Eng. Mech., 2022, 148(6): 04022027. The model is mildly adjusted to be suitable also for stress-controlled experiments.

This thesis aims to derive closed-form solutions using a rate-independent flow elastoplastic material model and optimize important parameters through fitting with the well-known stressed-controlled experimental data of Phillips and his collaborators obtained five decades ago. The model needs a total of 8 material constants in addition to Young's modulus and shear modulus. The axial-torsional model features an evolving cubic distortional yield hypersurface, which is articulated with two Mises hyperspheres, characteristic of internal symmetry of two elements of the projective proper orthochronous Poincare group in the plastic phase. Associated with each Mises hypersphere in stress space is a normality plastic flow rule of mixed-exp-AF, referring to a combined isotropic-kinematic rule of hardening-softening, which combines the isotropic exponential rule of degree 2 and the kinematic rule of Armstrong-Frederick.

By conducting yield surface axial-torsional stress-controlled experiments on the material, the corresponding unique parameter combination can be optimized and fitted. Then, by inputting this unique parameter set and any stress into the closed-form solution, this paper can predict important information such as the stress state and plastic behavior of the material under any applied stress.

Our investigation is executed at room and at elevated temperatures.