本文藉由有限單元軟體ANSYS首先針對碳纖維疊層板進行有限單元模態分析與動態分析，探討改變碳纖維疊層板中之疊層角度對結構之共振頻率與模態振型之影響，另外藉由動態分析模擬衝擊試驗(Shock test)，分析不同疊層角度之碳纖維疊層板受衝擊後，其內部的應力分佈隨時間之變化，並配合破壞準則判斷疊層板內是否有破壞產生。
在對碳纖維疊層板進行有限單元分析後，以相同方式依JEDEC規範進行印刷電路板(PCB)有限單元模型建立與其動態分析，探討PCB板在衝擊試驗後其變形與應力分佈隨時間之變化。另外建立五組不同厚度之PCB板模型探討厚度對PCB板之變形與內部應力之影響。最後使用厚度為2.6 mm之PCB板模型探討改變夾芯層材料編織玻璃纖維/環氧樹脂為編織碳纖維/環氧樹脂對PCB板結構之變形與各層應力分佈之影響。結果發現使用較厚之PCB板時可降低其在受衝擊負載後之變形與應力，而使用編織碳纖維/環氧樹脂為夾芯層時可降低PCB板之變形與銅箔層之應力，也降低PCB板受衝擊負載而破壞的機會。
本文也探討碳纖維疊層之層間剪力強度，由於脫層在碳纖維疊層中為一種破壞形式，脫層產生時會影響結構之強度。本文藉由碳纖維疊層間加入奈米碳管，並以實驗量測其層間能量釋放率為判斷層間剪力強度之依據，若奈米碳管間之空隙被環氧樹脂填滿，其能量釋放率可提升71.65%。

In this study, the modal analysis and dynamic analysis of carbon fiber laminate were carried out by using the finite element software ANSYS. The effects of changing fiber orientation in the carbon fiber laminate on the overall resonant frequency and mode shape are investigated. In addition, a shock loading was applied to the carbon fiber laminate to simulate the shock test, in order to find the time-varying stress distribution of the carbon fiber laminate with different stacking angle. The Tsai-Wu failure criteria was used to determine the failure in the laminate after subjected to a shock loading.
The PCB finite element model was build according to the JEDEC standard and the shock test for PCB was also carried out. The stress distribution and the deformation of PCB after subjected to a shock loading are discussed in this study. Five PCB finite element models with different thickness are used to discuss the thickness effect on PCB. The results show that the stress decreases in a thicker PCB, harder to deform when under a shock loading. Furthermore, for the material of core layer in PCB changing from woven E-glass/epoxy to woven carbon fiber/epoxy, the deformation of PCB and the stress in copper layer decrease significantly. Therefore by increasing the thickness of PCB or using woven carbon fiber/epoxy for core layer can improve the performance of PCB structure.
The interlaminar strength of carbon fiber laminate is also discussed. Since delamination is a major form of failure in carbon fiber laminates, it affects the strength of laminate structure. The carbon nanotubes sheet was added between the central layers in carbon fiber laminate. The energy release rate of the specimen is experimentally measured to determine the interlaminar strength of carbon fiber laminates. As a result, it was found that after adding a layer of carbon nanotubes sheet filled with epoxy into the carbon fiber laminate, the interlaminar strength of laminate was improved and a significant increase of 71.65% in energy release rate was obtained.

目錄
摘要 I
Abstract II
致謝 IV
目錄 V
圖表目錄 VIII
第一章 緒論 1
1.1 研究動機 2
1.2文獻回顧 3
1.3 研究主題 5
第二章 實驗方法與分析 7
2.1 複合材料 7
2.1.1 碳纖維/環氧樹脂預浸材 7
2.1.2 奈米碳管 7
2.2 實驗儀器設備 8
2.2.1 熱壓機 8
2.2.2 鑽石切割機 9
2.2.3 拉伸試驗機 9
2.2.4 應變規與訊號擷取盒 9
2.2.5電子天秤 10
2.2.6 熱風循環式烤箱 10
2.2.7 機械攪拌機 10
2.2.8 真空烘箱與真空幫浦 10
2.2.9超音波粉碎儀 10
2.2.10 場發射掃描式電子顯微鏡 11
2.3 試片製作 11
2.3.1 碳纖維/環氧樹脂試片製作 11
2.3.2 含裂縫碳纖維/環氧樹脂試片製作 12
2.3.3 奈米碳管薄片製作 12
2.3.4 含裂縫碳纖維/奈米碳管/環氧樹脂試片製作 13
2.4 材料參數測量 14
2.4.1 試片尺寸 14
2.4.2 軸向楊氏模數(E_11)與柏松比(v_12)量測 15
2.4.3側向楊氏模數(E_22)量測 16
2.4.4剪力模數(G_12)量測 16
2.4.5 能量釋放率之 ENF實驗與計算 16
2.5數據分析 18
2.5.1 Chauvenet’s準則 18
2.5.2 最小平方法 19
第三章 有限單元分析 20
3.1有限單元簡介 20
3.2有限單元原理 21
3.3碳纖維疊層板之有限單元模型 23
3.3.1 單元選用 23
3.3.2材料參數設定 24
3.3.3碳纖維疊層板之幾何尺寸 26
3.4碳纖維疊層板之模態分析 26
3.5碳纖維疊層板掉落試驗之衝擊分析 27
3.6 Tsai-Wu破壞準則 28
3.7 PCB板掉落試驗之衝擊分析之有限單元模型 29
3.7.1 PCB板模型之幾何尺寸 29
3.7.2 PCB之材料參數 30
3.7.3 PCB衝擊動態分析之有限單元模型與邊界條件 30
3.7.4 PCB有限單元模型之收斂性分析 30
3.8 最大畸變能準則 31
3.9 最大主應力準則 31
第四章 結果與討論 32
4.1疊層角度對碳纖維疊層板共振頻率之影響 32
4.1.1彎曲模態(Bending mode) 32
4.1.2扭轉模態(Torsion mode) 33
4.1.3其他模態(Other mode) 33
4.2碳纖維疊層板掉落衝擊變形分佈 33
4.3碳纖維疊層板掉衝擊後應力分佈 34
4.4衝擊後疊層板之破壞判定 34
4.5 PCB板衝擊分析結果 35
4.5.1標準尺寸PCB板受衝擊後之分析結果 35
4.5.2厚度對PCB板之影響 36
4.5.3 改變PCB板夾芯層材料之分析結果 37
4.6疊層板能量釋放率 38
4.6.1碳纖維疊層板之能量釋放率 38
4.6.2含奈米碳管碳纖維疊層板之能量釋放率 38
4.6.3含奈米碳管碳纖維疊層板改良製程後之能量釋放率 39
第五章 結論 41
參考文獻 43
圖表 49

圖表目錄
表3.1 碳纖維疊層之強度 49
表3.2 銅箔之材料參數 49
表3.3 編織玻璃纖維/環氧樹脂之材料參數 49
表3.4 編織碳纖維/環氧樹脂之材料參數 49
表3.5 PCB板之收斂性分析結果 50
表4.1 疊層角度在各模態共振頻率值 50
表4.2 碳纖維疊層板固定端中點之各層應力 51
表4.3 碳纖維疊層板中央之各層應力 52
表4.4 不同厚度PCB板之模擬結果 53
表4.5 PCB板不同材料知破壞強度 53
表4.6 不同夾芯層材料PCB板分析結果 53
圖2.1 熱壓機 54
圖2.2 鑽石切割機 54
圖2.3 拉伸試驗機 55
圖2.4 應變規 55
圖2.5 訊號擷取盒 56
圖2.6 電子天秤 56
圖2.7 熱風循環式烤箱 57
圖2.8 機械攪拌器機 57
圖2.9 真空烘箱 58
圖2.10真空幫浦 58
圖2.11超音波粉碎儀 59
圖2.12場發射掃描式電子顯微鏡 59

圖2.13熱壓炭纖維疊層之上下模、鋁片、脫模布及模具擺設示 意圖 60
圖2.14熱壓製成碳纖維/環氧樹脂疊層試片之溫度控制圖 60
圖2.15 ENF試片圖 61
圖2.16奈米碳管薄片烘乾時之堆疊示意圖 61
圖2.17和裂縫之奈米碳管/碳纖維試片疊層示意圖 62
圖2.18熱壓製成奈米碳管/碳纖維/環氧樹脂疊層試片之溫度控制圖 62
圖2.19拉伸試片之尺寸 63
圖2.20碳纖維/環氧樹脂疊層試片之軸向應力-應變關係圖 64
圖2.21碳纖維/環氧樹脂疊層試片之軸向應力-橫向應變關係圖 64
圖2.22碳纖維/環氧樹脂疊層試片之橫向應力-應變關係圖 65
圖2.23裂縫受力模式 65
圖2.24 ENF實驗示意圖 66
圖2.25 ENF實驗圖 66
圖3.1 SOLIDSHELL190單元示意圖 67
圖3.2 碳纖維疊層板幾何尺寸示意圖 67
圖3.3 碳纖維疊層板排列示意圖 67
圖3.4 碳纖維疊層板有限單元模型邊界示意圖 68
圖3.5 加速度負載與時間關係圖 68
圖3.6 PCB板幾何尺寸示意圖 69
圖3.7 標準厚度之8層PCB板示意圖 69
圖3.8 探討厚度影響之PCB板示意圖 70
圖3.9 PCB板衝擊動態分析之有限單元模型圖 70
圖3.10 PCB板衝擊動態分析之邊界條件示意圖 71
圖3.11 PCB板有限單元模型單元數與最大應力關係圖 71
圖4.1 碳纖維疊層板彎曲模態振型圖及共振頻率與疊層角度關係圖 72
圖4.2 碳纖維疊層板扭轉模態振型圖及共振頻率與疊層角度關係圖 73
圖4.3 碳纖維疊層板其他模態振型圖及共振頻率與疊層角度關係圖 74
圖4.4 [(0°)_12]碳纖維疊層板之變形分佈圖 75
圖4.5 [(0°)_2/(±60°)_2 ]_s碳纖維疊層板之變形分佈圖 75
圖4.6 t=0.5ms,[(0°)_2/(±60°)_2 ]_s 碳纖維疊層板各層von Mises stress 分佈圖 76
圖4.7 t=0.5ms,[(0°)_2/(±60°)_2 ]_s 碳纖維疊層板各層σ_x分佈圖 77
圖4.8 t=0.5ms,[(0°)_2/(±60°)_2 ]_s 碳纖維疊層板各層σ_y分佈圖 78
圖4.9 t=35ms,[(0°)2/(±60°)2]s碳纖維疊層板各層von Mises stress 分佈圖 79
圖4.10 t=35ms,[(0°)_2/(±60°)_2 ]_s 碳纖維疊層板各層σ_x分佈圖 80
圖4.11 t=35ms,[(0°)_2/(±60°)_2 ]_s 碳纖維疊層板各層σ_y分佈圖 81
圖4.12 t=26.375ms,[(0°)_2/(±60°)_2 ]_s碳纖維疊層板Tsai-Wu index分佈圖 82
圖4.13 t=22.925ms,[(0°)12] 碳纖維疊層板Tsai-Wu index分佈圖 82
圖4.14 PCB板中央之z方向位移隨時間變化圖 83
圖4.15 PCB板在t=1.98ms之z方向位移隨分佈圖 83
圖4.16 PCB板中央夾芯層之最大von Mises應力隨時間變化圖 84
圖4.17 PCB板中點之各層主應力變化圖 84
圖4.18 PCB於達最大位移時之位移分佈圖 85
圖4.19 PCB於達最大主應力時之應力分佈圖 85
圖4.20 ENF實驗之負載與位移曲線圖 86
圖4.21 ENF實驗後試片之破壞情形 86
圖4.22 碳纖維疊層板斷裂面 86
圖4.23 碳纖維/環氧樹脂疊層板斷裂面SEM圖 87
圖4.24 奈米碳管薄片 88
圖4.25含奈米碳管之碳纖維疊層板斷裂面 88
圖4.26含奈米碳管碳纖維/環氧樹脂疊層板斷裂面SEM圖 89
圖4.27不同材料於ENF試驗中之負載與位移曲線圖 91
圖4.28含奈米碳管碳纖維疊層板ENF實驗後之破壞情形 91

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