摘 要

本文是應用有限元素套裝軟體DEFORMTM分析壓延加工時板材於輥隙內之變形型態。研究的對象有板材非對稱壓延、板材內含空孔和介在物壓延。分析模式採用剛塑性模式，並假設壓延時輥輪為剛體，板材為等向性材料。內容可分成三部分：(1)板材非對稱壓延加工時，探討上下輥輪之周速比、半徑比、板材與輥輪界面之摩擦因子等各種壓延條件對板材於出口之曲率、壓延力之影響。由模擬得知不同輥徑比與不同周速比越大，其壓延力越小但板材出口曲率變化越大。(2)板材內含空孔之壓延過程中，模擬空孔之閉合行為、變形機制和應力應變分佈等，探討板厚壓下率、內孔尺寸大小、摩擦因子和內孔截面積等壓延條件對內孔閉合度之影響，亦討論了內孔完全閉合之臨界壓下率。由模擬得知輥輪半徑越大臨界閉合壓下率越小，這是因為大輥輪壓延時產生較大壓延應力，空孔較容易完全閉合；且空孔高度越小臨界閉合壓下率越小；因此要降低臨界壓下率，可增加輥輪半徑，以及降低孔徑－板厚比值。(3)板材內含介在物之壓延加工時，模擬介在物前後空孔發生之可能性，並且探討不同加工條件如板材厚度壓下率、介在物直徑、輥徑大小及摩擦因子等對壓延力、應力應變分佈之影響；亦討論了介在物前後不產生空孔之臨界壓下率。由模擬得知輥輪與板材之間的摩擦因子比介在物與板材之間的摩擦因子對空孔形成之影響來得大，且介在物尺寸愈大，則臨界壓下率愈小，及輥輪愈小，則臨界壓下率愈小。本文模擬之空孔和介在物之初始大小為0.1mm~2.5mm，在此尺寸範圍內其解析結果呈現穩定之趨勢變化。
最後以鋁板A1050和A6061為試片進行一系列之壓延實驗。板材內含空孔之壓延實驗中，其空孔為以微小鑽頭加工之，板材內含介在物之壓延實驗時，使用SUS HSS鋼當介在物。由模擬解析和實驗結果得知介在物前面空孔大小皆大於後面空孔大小，而且由解析值與實驗值之比較，驗證了本解析模式之適用性。這些實驗與解析結果可提供壓延加工製程設計之參考。

Abstract

Using a finite element package software DEFORMTM, this study simulated plastic deformation of the sheet at the roll-gap during sheet rolling processes. Rigid-plastic model of material is adopted. The rolls are assumed to be perfectly rigid and the sheets are isotropic. This study consists of three parts：(1) analysis of asymmetrical sheet rolling ; the effects of rolls speed ratios, roll radii ratios, friction factor ratios between sheet and rolls surface, upon the curvature of the rolled product and rolling force were systematically discussed. The larger the roll radius and the roll speed ratios are, the smaller the rolling force is and the larger the curvature of the sheet analytically. (2) Closing behavior, the deformation mechanism and stress-strain distributions around internal voids inside the sheet during sheet rolling was discussed numerically. The influences of various rolling conditions, such as the thickness reduction, the dimension of the internal void, friction factor, cross-sectional area of the void, etc., on the dimension of the void at the exit were discussed. The critical thickness reductions, over which the void would close completely, were also investigated. It is known that the critical reduction decreases with increasing roll radius. That is because the rolling pressure at the roll gap increases with increasing roll radius, accordingly, it takes smaller reductions to make the void closed completely. The critical thickness reduction decreases with increasing roll radius and decreasing voids dimension-thickness ratios. (3) The possibility of voids occurred at the front and back of the inclusion was investigated. The effects of various rolling conditions, such as the thickness reduction, the diameter of the inclusions, the roll diameter, friction factor, etc., on the generation and development of voids anticipated to occur in the front and rear of the inclusions were discussed. The critical thickness reductions under which void generation can be avoided were also examined. On the other hand, the effect of friction factor on between roll and sheet upon the void lengths in the front and rear of the inclusion is greater than that of friction factor on between inclusions and sheet. It is known that it decreases with increasing inclusions dimension, whereas the critical reduction decreases with decreasing roll radius. The analytical results showed a steady trend for 0.1mm< voids and inclusions dimension < 2.5mm.
To verify the validity of the models, a series of experiments on the sheet rolling using aluminum (A1050, A6061) sheet as specimen were carried out. The experiments on sheet rolling with an internal void inside the sheet were conducted by micro-drill. The inclusions used “SUS HSS” steel. The void length in the front of the inclusion is larger than that in the rear of the inclusion for both simulated and experimental results. The simulated results were compared with experimental results, and good agreement is found. Therefore, this numerical model using DEFORM software can offer useful knowledge for designing the pass-schedule in sheet rolling processes.

目 錄

摘要………………………………………………………………………………….………...I
Abstract……………………………………………………………….……….. II
目錄………………………………………………………………………………………….IV
圖表目錄…………………………………………………………………………...….…..VII
符號說明…………………………………………………………………...………....….....XI
第一章 緒論………………………………………………………………………………...1
1- 1前言……………………………………………………………………………………1
1- 2壓延製程簡介…………………………………………………………………………2
1- 3介在物 (inclusions)的形成…………………………………………………………...2
1- 4空孔(voids)的形成…………………………………………………………………….3
1- 5有限元素套裝軟體之簡介……………………………………………………………3
1- 6塑性加工解析法………………………………………………………………………4
1-6-1 切片法…………………………………………………………………………….5
1-6-2 滑移線場法……………………………………………………………………….5
1-6-3 極限解析法……………………………………………………………………….5
1-6-3-1 上界限法……………………………………………………………………...5
1-6-3-2 下界限法……………………………………………………………………...6
1-6-4 有限元素法……………………………………………………………………….6
1-7 文獻回顧……………………………………………………………………………...6
1-7-1 板材非對稱壓延………………………………………………………………….6
1-7-2板材內含空孔壓延………………………………………………………………..8
1-7-3板材內含介在物壓延……………………………………………………………..8
1-8 研究目的……………………………………………………………………………...9
1-9 論文架構…………………………………………………………………………….10
第二章 有限元素法與塑性力學之介紹……………………………………………..11
2-1 有限元素法簡介…………………………………………………………………….11
2-2 金屬之降伏條件………………………………………………………………….…12
2-3 材料的塑性法則與性質…………………………………………………………….13
2-3-1 塑性流動法則…………………………………………………………………...13
2-3-2 應變硬化、等效應力及等效應變……………………………………………...14
2-4 剛塑性有限元素法………………………………………………………………….16
2-4-1 剛塑性有限元素法的基礎……………………………………………………...17
2-4-2 方程式的線性化………………………………………………………………...18
2-5 邊界條件…………………………………………………………………………….19
2-6 剛性區域的處理…………………………………………………………………….20
第三章 DEFORM有限元素軟體介紹……………………………………….……..21
3-1 DEFORM 之架構及模組之功能…………………………………………….……...21
3-2 DEFORM之解析模式……………………………………………………………….23
3-3 DEFORM之材料模式……………………………………………………………….23
3-4 摩擦條件…………………………….………………………………...…………….23
3-5 迭代法(Iteration methods) …………………………………………………………..24
第四章 板材壓延加工之模擬解析…………………………………………………...26
4-1板材非對稱壓延之模擬解析……………………………………………………......26
4-2板材內含空孔壓延之模擬解析……………………………………………………..27
4-3板材內含介在物壓延之模擬解析…………………………………………………..29
第五章 模擬解析之結果與討論………………………………………………………59
5-1板材非對稱壓延之探討……………………………………………………………...59
5-2板材內含空孔壓延之探討…………………………………………………………..60
5-2-1長方形空孔………………………………………………………….……………60
5-2-2圓形空孔…………………………………………………………………………61
5-3板材內含介在物壓延之探討………………………………………………………...62
5-3-1圓形介在物………………………………………………………………………62
5-3-2長方形介在物……………………………………………………………………63
第六章 板材壓延加工之實驗分析…………………………………………………...99
6-1 單軸拉伸試驗……………………………………………..…………...…...……….99
6-1-1加工硬化指數n值及強度係數K值之求法………………………..………….99
6-1-2拉伸試驗速度…………………………………………………………………..100
6-1-3萬能材料試驗機………………………………………………………..………101
6-2單軸壓縮試驗………………………………………………………………...…….101
6-3 環壓縮試驗………………………………………………………………………...102
6-4 壓延實驗…………………………………………………………………………...102
6-4-1實驗設備……………………………………………………………………..…102
6-4-2 實驗設備之校正…………………………………………………….………... 103
6-4-2-1 荷重計(Load cell)之校正………………………………………….……... 103
6-4-2-2 資料擷取系統之校正………………………………………… ..………. 103
6-4-3試片準備………………………………………………………………………. 103
6-4-4實驗步驟……………………………………………………………………..…103
6-5板材非對稱壓延實驗之分析…………………………………………….……….104
6-6板材內含空孔壓延實驗之分析……………………………………………….….105
6-7板材內含介在物壓延實驗之分析……………..…………………………….….105
第七章 結論與建議…………………………………………………………………….126
7-1 研究成果之概要…………………………………………………………………...126
7-1-1板材非對稱壓延………………………………………………………………..126
7-1-2板材內含空孔之壓延…………………………………………………………..127
7-1-3板材內含介在物之壓延………………………………………………………..127
7-2 未來研究方向……………………………………………………………………...128
7-2-1異形材壓延…………………………………………………………….………..128
7-2-2多道次壓延……………………………………..………………………………128
7-2-3粉末多孔性金屬壓延………………………………….……………………….129
參考文獻…………………………………………………………………………….…….130

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