軸扭環三次降伏面演化之實驗與幾何分析

Abstract

本文延續本實驗室過往進行之降伏面實驗與理論研究，探討鋁合金6061在軸扭環 (σzz − σzθ − σθθ) 三向應力空間中降伏面演化現象。設計多種預應變路徑，使同一試棒經過多組預加載路徑而產生連續的塑性行為，藉此觀察路徑效應對塑性行為之影響，並利用探尋應力空間中不同截面之降伏點，搭配三次多項式之擬合方法，以建立三向應力空間中的降伏面。本研究中亦針對Liu與Hong [5] 提出之三次多項式之擬合方法進行檢討，除了簡化標準式中的參數以及修改了座標變換關係中在射影變換步驟的錯誤外，更進一步拆解成相似、仿射及射影三個變換關係，使標準式中的參數更具幾何性質，有效減少擬合過程中的人為主觀判斷，且擬合結果也明顯更貼近實驗點扭曲趨勢。釐清擬合方法中參數的幾何性質也有助於對擬合結果的討論，本文由修正之擬合方法重新擬合張睿成 [15] 的實驗資料，加上本次設計之路徑，就不同路徑分類進行演化行為之探討。另外也藉由準確的擬合結果，在不變量架構下分析降伏面函數的可能形式。

Continued to the past research and experiments in MSV lab, the evolution of yield surface in three dimensional axial-torsional-hoop stress space for alloy Al 6061 was studied in this thesis. Thin-walled tubes were conducted to multiple pre-loading paths in order to produce successive plastic behavior. By probing yield points on the planes of constant hoop stresses, the yield surfaces in three dimensional stress space were build up using a cubic polynomial fitting method. The fitting method firstly proposed by Liu & Hong [5] was modified to reduce the number of required parameters, the errors in projective transformation and to decompose the transformation into three successive stages: similar, affine and projective transformation matrix. The modificated fitting method helps clarify the parameters in the yield function and effectively eliminate subjective judgement during the fitting process. The fitting results were observed closer to the yield point data. The geometric properties of the parameters are also beneficial for discussion of the fitting results. In this thesis, the experimental data by Ruei-Cheng Chang [15] were refitted using the modified fitting method, and compared to the paths designed here for exploring the plastic behavior under different pre-loading paths. In addition, the possible forms of the yield functions were analyzed in the structure of invariants by using accurate fitting results.