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研究生： 黃國聰
Huang, Kuo-Tsung
論文名稱： 鋁-鎂合金拉伸與振動破壞特性之摩擦攪拌效應研究
Effects of Friction Stirring on Tensile and Vibration Fracture Characteristics of Al-Mg Alloys
指導教授： 陳立輝
Chen, Li-Hui
呂傳勝
Lui, Truan-Sheng
學位類別： 博士
Doctor
系所名稱： 工學院 - 材料科學及工程學系
Department of Materials Science and Engineering
論文出版年： 2008
畢業學年度： 96
語文別： 中文
論文頁數： 161
中文關鍵詞： 鋁-鎂合金 、摩擦攪拌
外文關鍵詞： Al-Mg Alloys, Friction Stirring
相關次數： 點閱：90  下載：1 
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    • 鋁-鎂合金板材是汽車、船舶與航空器常用的輕金屬，實際應用時因上述交通工具體積龐大，不可避免地遭遇板材成形與振動破壞問題。因此，本研究以固態攪拌技術，摩擦攪拌鋁-鎂合金，藉攪拌過程產生之晶粒細化提升板材強度與振動裂縫傳播阻抗。
    本論文以鋁-鎂合金為試料，研究試料經摩擦攪拌後的接合性質，並進一步探討鋁-鎂合金固溶強化、再結晶粒徑及加工前處理之拉伸及振動破壞特性的摩擦攪拌效應。本研究進行之拉伸試驗，攪拌試片之應力-伸長率曲線皆呈鋸齒狀特徵(PLC效應)的跳動，而經共振試驗得到之攪拌試片D-N曲線(偏移量與振動週期)變化可區分成兩階段：stageⅠ，試片因加工硬化，偏移量隨振動次數增加上升，裂縫於此時形成並成長；stageⅡ，裂縫已相當長，並向內部延伸，試片共振頻率開始下降，即振動台振動頻率已偏離試片之原始共振頻率。
    本研究探討5052H34經摩擦攪拌接合後產生之熱影響部對試片的影響以及攪拌區之微觀演變。橫跨整個接合部之垂直攪拌方向的拉伸試片，其拉伸斷裂處出現在熱影響區；而平行部完全取自攪拌方向(攪拌區內)之試片，其拉伸延性則因微細等軸晶粒而提升。摩擦攪拌接合後再施以振動試驗，結果顯示，攪拌區之微細等軸晶粒可得到良好接合效果。
    本研究且探討固溶鎂含量之多寡對摩擦攪拌鋁-鎂合金之影響，結果顯示，與未經攪拌之母材試料相比較，不同鎂含量之試料經摩擦攪拌，各試料之拉伸強度與延性皆可因攪拌區之晶粒細化而提升。由振動試驗之裂縫傳播行為可知，隨鎂含量增加，方位取向之滑移帶變形受抑制，裂縫轉折程度有降低傾向，較高鎂含量試片(4.3Mg-FSP)之裂縫傳播較直，部份為延晶破壞，應是鎂含量增加，β相析出所導致，而低鎂含量試片(0.5Mg-FSP)在振動過程中導入大量條紋狀變形(striation)及滑移帶，裂縫轉折程度加大。
    另外，摩擦攪拌動態再結晶粒徑對5052鋁-鎂合金之影響亦是本文探討重點。攪拌後試片皆有動態再結晶粒細化作用，攪拌區晶粒徑隨主軸轉速增加而增大(5-16μm)。由實驗之拉伸變形阻抗顯示，降伏強度隨晶粒徑增大而降低，其定量結果符合Hall-Petch 關係方程式。振動試驗結果則顯示，攪拌試片之振動壽命隨晶粒徑增大而降低，較高主軸轉速導致晶粒徑增大，出現部份滑移帶，使裂縫傳播速度增快，不利振動壽命。
    本文還探討母材前處理(退火及冷軋壓延)對摩擦攪拌5052鋁-鎂合金之影響。摩擦攪拌後，試片之拉伸均勻延性因攪拌過程之動態再結晶細晶粒而有效提升。振動試驗結果顯示，以初始偏移量為6.5mm進行振動試驗，試片振動D-N曲線之stageⅠ斜率隨軋延率增加而加大，不利振動壽命。而TEM組織解析顯示，與前退火攪拌材比較，加工前處理攪拌材其次晶粒有增大的傾向，因此，加工前處理應是振動壽命降低的主要影響因素。此外，經冷軋壓延之母材試片，因壓延過程導入大量差排交互糾結，使基地組織強化，裂縫傳播速度因而降低。
    本研究經實驗與探討後得知，鋁-鎂合金經摩擦攪拌後，攪拌區之微細等軸晶粒可提升試料之拉伸延性。再者，晶粒細化亦可使晶界面積增加，阻礙振動過程之裂縫傳播速度，提升振動壽命。本研究亦發現，試料攪拌前施予完全退火，消除其儲存能，可提升振動壽命，而加工硬化型鋁-鎂合金壓延導入大量差排交互糾結，亦可提升振動破壞阻抗。

    Al-Mg alloys are classed as a light metal, which have been widely used in automobiles, ships and aviation. However, Al-Mg alloys are prone to deformation and vibration fracture problems when they are used in the body of large vehicle, ships, etc.. This study stirs Al-Mg alloys with the solid-state friction stir technique to refine the grain size. Another aim of this study is to improve the strength and vibration fracture resistance of sheet using the technique of friction stirring.
    The base materials used in this study were Al-Mg alloys, which were friction stirred to investigate the joining properties. Moreover, the effect of solution strengthening, recrystallized grain size and pre-strain in the stir zones of FSP (friction stir process) were examined. The stress-strain curve indicated that all friction stirred specimens had the characteristic of serrated yielding resulting from the Portevin-LeChatelier (PL) effect. In addition, the resonant vibration characteristics of the friction stirred specimens can be identified from their D-N curves (deflection amplitude vs. number of vibration cycles) which can be generalized into two stages. An increase in work hardening raises the effective elastic modulus in the stageⅠregion, and the deflection amplitude then increases due to the decrease in damping capacity. For vibration cycles beyond this stageⅠregion, there is a drastic decrease in deflection amplitude which can be designated as stage Ⅱ, which results from the inward propagation of major cracks and the deviation of the actual vibration frequency from the resonant frequency.
    Experimental results show that the effect of the microstructure feature on the heat affected zone and the stir zone of FSW (friction stir welding) 5052H34, the FSW specimen which was cut from joining line of transversal stirring direction where the microstructural imhomogeneity appeared suffered to tensile fracturing in the heat affected zone. Besides, the FSW specimen which was cut totally from the stir zone of longitudinal stirring direction where the dynamic recrystallization grains appeared possessed better ductility resulting from the grain refinement. The vibration data which had V notches cut on the stir zone showed that the stir zone had joined well because of the microstructural refinement.
    According to the result of Mg content on friction stirred Al-Mg alloys, the grains of the parent plate which are refined through FSP are effective in enhancing tensile strength and elongation of materials. From crack propagation results, as Mg content increases, slip bands in the vicinity of the main crack are suppressed, which is reflected in the crack tortuosity data. Meanwhile, an intergranular crack propagation feature can be recognized in the specimen of higher Mg content (4.3Mg-FSP), and it is reasonable to suggest that the precipitation of β phase plays an important role in the reduction of vibration fracture resistance. However, when the lower Mg content specimen (0.5Mg-FSP) suffers from resonant vibration with maximum deflection, the deformation of striations and slip bands in the vicinity of the main crack raise the crack tortuosity.
    In addition, dynamically recrystallized grain size of friction stirred 5052 alloy is a key, significant microstructural refinement caused by the phenomenon of dynamic recrystallization. Grain refinement could be observed at the stir zone with the average grain size varying from 5-16 μm as rotation speed increased. Based on the tensile data, the yield strength deteriorated because of the increased grain size. This can be quantitatively correlated with the Hall-Petch equation. Besides, the effect of grain size on vibration fracture characteristic shows that the vibration life of the FSP specimen decreases with increasing the rotation speed. An increase in grain size due to higher rotation speed leads to the appearance of slip bands and is detrimental to the vibration propagation resistance. As a result, the crack propagation rate speeds up.
    The experimental results regarding the prior deformation of friction stirred 5052 alloy indicate that the uniform elongation tended to increase after FSP, which was due to the microstructure being refined during dynamic recrystallization. Besides, the D-N curve of vibration shows that the slope of stageⅠincreases with increasing the prior deformation rate before FSP. However, TEM images show that the sub-grain size of the FSP specimens increase compared to the prior fully annealed FSP specimen. It is reasonable to suggest that the prior deformation of the friction stirred 5052 alloy can be regarded as one factor which reduced the vibration life. For the specimens which were not given FSP, severe dislocation tangles introduced by prior deformation raised the strength of the matrix and consequently reduced the crack propagation rate of the 5052 alloys.
    To sum up the above-mentioned results about friction stirred Al-Mg alloys, the grain refinement in the stir zone can improve the tensile elongation. In addition, the smaller grains possessed a greater area fraction of grain boundaries which decreased the crack propagation rate during vibration. Meanwhile, the prior fully annealed the FSP specimen has a better vibration life, which can be attributed to a decrease in stored strain energy. However, prior rolling of the work-hardened Al-Mg alloys introduced a large number of retained dislocation tangles and improved the crack propagation resistance.

    總目錄 中文摘要 I 英文摘要 III 誌謝 VI 總目錄 VII 表目錄 XII 圖目錄 XIII 第一章 前言 1 第二章 文獻回顧 5 2-1 金屬材料之摩擦攪拌與相關效應 6 2-1-1 摩擦攪拌接合 6 2-1-2 摩擦攪拌之熱效應 6 2-1-3 摩擦攪拌工具頭之旋轉效應 8 2-1-4 摩擦攪拌後組織演變對織構之影響 9 2-1-5 摩擦攪拌製程之應用 10 2-2 回復與再結晶 12 2-2-1 回復 12 2-2-2 再結晶 13 2-2-3 攪拌區動態再結晶行為之研究現況 15 2-3 振動狀態與裂縫傳播行為 17 2-3-1 共振頻率 18 2-3-2 阻尼的影響 18 2-3-3 試片之裂縫傳播行為 19 2-4 鋁-鎂合金之特性 20 2-4-1 固溶強化效應 20 2-4-2 加工硬化效應 21 2-5 研究架構 22 第三章 實驗方法 31 3-1 摩擦攪拌試料、微觀組織及微硬度分佈 31 3-2 拉伸試驗 32 3-3 振動試驗設備及流程 33 3-3-1 決定共振頻率 34 3-3-2 共振試驗 34 3-3-3 振動變形破壞阻抗之意義 35 3-4 振動試片裂縫傳播行為之觀察 36 第四章 摩擦攪拌熱影響部及攪拌接合對5052 鋁-鎂合金拉伸與振動破壞特性之影響 44 4-1 前言 44 4-2 實驗方法提要 45 4-3 實驗結果 46 4-3-1 微觀組織特徵及微硬度 46 4-3-2 拉伸性質 47 4-3-3 振動破壞行為與特徵 48 4-4 討論 49 4-5 結論 51 第五章 鎂固溶效應對摩擦攪拌Al-Mg合金之拉伸及振動破壞特性之影響 64 5-1 前言 64 5-2 實驗方法提要 64 5-3 實驗結果 65 5-3-1 微觀組織特徵及微硬度 65 5-3-2 不同Mg含量試料之拉伸性質 66 5-3-3 不同Mg含量試料之振動破壞阻抗 66 5-4 討論 69 5-5 結論 70 第六章 摩擦攪拌動態再結晶粒徑對5052鋁-鎂合金拉伸與振動破壞特性之探討 82 6-1 前言 82 6-2 實驗方法提要 83 6-3 實驗結果 84 6-3-1 主軸轉速與動態再結晶粒徑及微硬度分佈之間關係 84 6-3-2 不同主軸轉速試料之拉伸性質 85 6-3-3 不同主軸轉速試料之振動破壞阻抗 86 6-4 討論 87 6-5 結論 90 第七章 前處理對摩擦攪拌之5052鋁-鎂合金拉伸及振動破壞特性之影響 102 7-1 前言 102 7-2 實驗方法提要 102 7-3 實驗結果 104 7-3-1 前(退火)處理對摩擦攪拌試料之拉伸及振動破壞特性影響 104 7-3-1-1 微觀組織 104 7-3-1-2 拉伸性質 105 7-3-1-3 振動破壞阻抗與裂縫傳播特徵 105 7-3-2 冷軋壓延前處理對摩擦攪拌試料之拉伸及振動破壞特性影響 107 7-3-2-1 微觀組織 107 7-3-2-2 拉伸性質 108 7-3-2-3 振動破壞阻抗與裂縫傳播特徵 108 7-4 討論 111 7-5 結論 114 第八章 Al-Mg合金變形破壞行為之摩擦攪拌效應檢討 137 8-1 前言 137 8-2 5052鋁-鎂合金之動態再結晶粒均勻變形特性 137 8-3 拉伸應變硬化指數與振動D-N曲線的關係 139 8-4 摩擦攪拌晶粒細化對振動裂縫傳播之影響 140 第九章 總結論 147 第十章 參考文獻 150 表目錄 表4-1 5052鋁-鎂合金試料之化學成分(wt%) 53 表5-1 不同鎂含量試料之化學組成(wt%) 72 表5-2 摩擦攪拌試片與母材之拉伸性質及平均晶粒徑(d) 72 表5-3 不同鎂含量攪拌試片之裂縫轉折程度 72 表6-1 主軸轉速效應對拉伸特性及平均晶粒徑 92 表6-2 主軸轉速效應對裂縫轉折程度的影響 92 表7-1前(退火)處理試料之平均晶粒徑及拉伸性質 116 表7-2 前(退火)熱處理試料之振動壽命 116 表7-3 不同條件冷軋壓延率攪拌材之平均晶粒徑 116 表7-4 加工前處理母材及攪拌材之拉伸性質 117 表7-5 加工前處理母材及攪拌材之振動壽命 117 圖目錄 圖2-1 摩擦攪拌銲接合示意圖(參考文獻[31-32]) 23 圖2-2 材料受塑性變形所產生的回復五階段示意圖[62] 24 圖2-3 動態再結晶與差排密度之關係圖[62] 25 圖2-4 不連續動態再結晶階段示意圖：(a)動態再結晶在晶界處成核起始；(b)、(c)由晶粒形成的項鍊狀結構；(d)完全再結晶形成示意圖[62] 26 圖2-5 懸臂梁加末端荷重的振動系統：(L：懸臂梁長度、E：彈性係數、M：懸臂梁重量、m：末端重物的重量及I：慣性矩) 27 圖2-6 振動裂縫傳播手繪示意圖 28 圖2-7 Al-Mg合金二元相圖[84] 29 圖2-8 本研究之實驗架構圖 30 圖3-1 摩擦攪拌主軸幾何形狀示意圖 37 圖3-2 摩擦攪拌製程(FSP)示意圖 37 圖3-3 攪拌試片完成後之巨觀觀察：(a)完整圖；(b)局部放大圖 38 圖3-4 平行攪拌方向之拉伸試片取樣示意圖 39 圖3-5 振動測試機台示意圖 40 圖3-6 振動試片之幾何形狀及尺寸：(a)半圓形切槽；(b) V形切槽 41 圖3-7 共振頻率與偏移量之關係 42 圖3-8 鋁-鎂合金D-N曲線相對位置之共振頻率變化：(a)5052鋁-鎂合金初始偏移量6.5mm之D-N曲線，(b)相對應A-E各點之共振動頻率 43 圖4-1 拉伸試片截切示意圖：(a) FSW試料；(b) FSP試料 54 圖4-2 攪拌接合試片(H34-FSW)沿攪拌方向橫截面金相照片(距上表面1.6 mm)：(a)-(e) 顯示“A” “B” “C” “D”和“E”相關位置 (A：SZ區；B：AS之TMAZ；C：RS之TMAZ；D：HAZ；E：BM) 55 圖4-3 H34試料摩擦攪拌方向橫截面中心之微硬度分佈曲線 (距上表面1.6mm處) 56 圖4-4 H34摩擦攪拌(FSW及FSP)前後之拉伸應力-伸長率曲線(圖中各試片代號T及L分別表示拉伸方向垂直及平行於攪拌方向) 57 圖4-5 5052H34摩擦攪拌接合試片拉伸試驗斷裂位置 57 圖4-6 5052鋁-鎂合金偏移量與振動週期數之D-N曲線(初始偏移量為6.5mm)：(a)半圓形切槽；(b)Ｖ形切槽 58 圖4-7 半圓型切槽振動試片初始偏移量為6.5mm之stageⅠ階段裂縫傳播行為之光學顯微組織(虛線箭頭指示裂縫傳播方向)：(a) H34；(b) H34-FSW攪拌區裂紋；(c) H34-FSW熱影響區裂紋 59 圖4-8 V形切槽振動試片初始偏移量為6.5mm之D-N曲線stageⅠ階段裂縫傳播之SEM照片(箭頭指示裂縫傳播方向)：(a) H34-FSW；(b) H34 (裂縫偶爾延slip bands傳播) 60 圖4-9 初始偏移量為6.5mm之D-N曲線stageⅠ階段試片經腐蝕後裂縫傳播光學顯微組織(V形切槽)：(a) H34-FSW；(b) H34 (箭頭指示為裂縫傳播方向) 61 圖4-10 TEM明視野照片：(a) H34母材；(b) H34-FSW之攪拌區 62 圖4-11 H34試料延攪拌方向攪拌區橫截面之光學顯微組織(距上表面1.6 mm)：(a) FSW；(b) FSP 63 圖5-1不同鎂含量試片光學顯微組織(攪拌試片距表面1.6mm)：(a) 2.5 Mg；(b) 2.5Mg-FSP；(c) 4.3Mg-FSP；(d) 0.5Mg-FSP (攪拌試片取自攪拌方向之橫截面，未攪拌母材取自壓延方向之橫截面) 73 圖5-2 不同鎂含量試片攪拌區橫截面中心線之微硬度曲線圖(距上表面1.6mm。水平虛線為未攪拌母材) 74 圖5-3 不同鎂含量試片之應力-伸長率之關係 75 圖5-4 不同鎂含量試片偏移量與振動週期數曲線：(a)加速度1.1G；(b)初始偏移量6.5 mm 76 圖5-5 不同鎂含量試片之D-N曲線stageⅠ週期數關係(初始偏移量為6.5mm) 77 圖5-6 不同鎂含量攪拌試片初始偏移量為6.5mm之振動破斷面SEM顯微組織：(a) 4.3Mg-FSP；(b) 2.5Mg-FSP；(c) 0.5Mg-FSP 78 圖5-7 不同鎂含量攪拌試片裂縫傳播行為之光學顯微組織(初始偏移量為6.5mm之stageⅠ階段)：(a) 4.3Mg-FSP；(b) 2.5Mg-FSP；(c) 0.5Mg-FSP；(d) 0.5Mg-FSP (最大偏移量) 79 圖5-8 不同鎂含量攪拌試片裂縫傳播特徵SEM顯微組織(初始偏移量為6.5mm之stageⅠ階段)：(a) 4.3Mg-FSP；(b) 2.5Mg-FSP；(c) 0.5Mg-FSP；(d) 0.5Mg-FSP (最大偏移量) 80 圖5-9 經腐蝕後之裂縫傳播路徑光學顯微組織(初始偏移量為6.5mm之stageⅠ階段)：(a) 4.3Mg；(b) 4.3Mg-FSP 81 圖6-1 不同主軸轉速試片延攪拌方面橫截面之光學顯微組織(距表面1.6mm)：(a) F5(500rpm)；(b) F8(800rpm)；(c) F10(1000rpm)；(d) F15(1500rpm) 平均晶粒徑如各圖左下角數據 93 圖6-2 不同主軸轉速攪拌試片攪拌區橫截面中心之微硬度分佈(距上表面1.6mm) 94 圖6-3 不同主軸轉速試片拉伸特徵曲線：(a)應力-伸長率曲線；(b)鋸齒狀應力振幅(Δσ) 與伸長率曲線( εc為臨界應變量) 95 圖6-4 不同主軸轉速攪拌試片應變硬化指數n值與真塑性應變之關係 96 圖6-5 不同主軸轉速試片偏移量與振動週期數關係之D-N曲線(初始偏移量為6.5mm)；(a) D-N曲線；(b)共振壽命 97 圖6-6 不同主軸轉速攪拌試片之投影裂縫長度與振動次數的關係(初始偏移量為6.5mm) 98 圖6-7 裂縫傳播行為之光學OM照片(圖a與b)與裂縫傳播特徵之SEM照片(圖c與d)：(a)、(c) F5；(b)、(d) F15 (D-N曲線在stageⅠ階段) 99 圖6-8 SEM破斷面圖(圖a與b)與OM裂縫傳播路徑(圖c與d)：(a) F5；(b)F15；(c) F8；(d) F15 100 圖6-9 不同主軸轉速攪拌試片Hall-Petch 關係式曲線 101 圖7-1 試料OM顯微組織(距表面1.6mm)：(a) H34-FSP；(b) O-FSP；(c) H34；(d) O (攪拌試片取自攪拌方向橫截面，未攪拌試片取自壓延方向橫截面) 118 圖7-2 試料TEM明視野照片：(a) H34-FSP；(b) O-FSP；(c) H34；(d) O 119 圖7-3 前(退火)處理拉伸試料之拉伸應力-伸長率曲線 120 圖7-4 前(退火)處理振動試料偏移量與振動週期數曲線：(a)加速度1.1G；(b)初始偏移量6.5mm 121 圖7-5 振動試片裂縫傳播行為之光學顯微組織(初始偏移量為6.5mm之stageⅠ階段)：(a) H34-FSP；(b) O-FSP；(c) H34；(d) O 122 圖7-6 振動試片SEM裂縫傳播特徵(初始偏移量為6.5mm之stageⅠ階段)：(a) H34-FSP；(b) O-FSP；(c) H34；(d) O 123 圖7-7 經腐蝕後之裂縫傳播路徑光學顯微組織(初始偏移量為6.5mm之stageⅠ階段)： (a) H34-FSP；(b)O-FSP；(c) H34；(d)O 124 圖7-8 加工前處理試料之光學顯微組織(距表面1.6mm)：(a) H112-FSP；(b) H112-25-FSP；(c) H112；(d) H112-25(攪拌試片取自攪拌方向橫截面，未攪拌母材取自壓延方向橫截面) 125 圖7-9 不同加工前處理攪拌材及母材之TEM明視野照片：(a) H112-FSP；(b) H112-25-FSP；(c) H112-50-FSP；(d) H112 126 圖7-10 不同條件加工前處理母材及攪拌材之應力-伸長率曲線 127 圖7-11不同條件加工前處理母材及攪拌材振動偏移量與振動週期數關係之D-N曲線：(a)、(c)加速度為1.1G；(b)、(d)初始偏移量為6.5 mm 128 圖7-12投影裂縫長度與振動次數的關係(初始偏移量為6.5mm)：(a)不同條件加工前處理攪拌材；(b)不同條件加工前處理母材 129 圖7-13 振動試片裂縫傳播行為之OM照片(初始偏移量為6.5mm之stageⅠ階段)：(a) H112-FSP：(b) H112-50-FSP；(c) H112；(d) H112-50 130 圖7-14 試片經過腐蝕後之裂縫傳播路徑OM組織(初始偏移量為6.5mm之stageⅠ階段)：(a) H112-FSP；(b) H112 131 圖7-15 未攪拌母材及攪拌材之鋸齒狀應力振幅(Δσ) 與伸長率曲線(第一個抖動之應力振幅的伸長率即為εc)：(a)不同條件前(退火)處理；(b)不同條件加工前處理 132 圖7-16 織構從優取向之逆極圖：(a) H34-FSP；(b) O-FSP 133 圖7-17 不同條件前(退火)處理之攪拌試料攪拌方向橫截面之微硬度分佈曲線(距上表面1.6mm) 134 圖7-18 5052鋁-鎂合金不同條件加工前處理攪拌材振動偏移量與振動週期數關係之D-N曲線 135 圖7-19 前(退火)處理母材之應變硬化指數n值與真塑性應變關係 136 圖8-1 鋁-鎂合金拉伸均勻伸長率之摩擦攪拌效應：(a)不同主軸轉速效應；(b)前退火處理效應；(c)冷軋壓延效應 143 圖8-2 5052鋁-鎂合金試料均勻塑性變形範圍之加工硬化率：(a)主軸轉速效應；(b)前退火處理效應；(c)冷軋壓延效應；(d)攪拌試片均勻變形延性與真塑性應變量為0.10之n值關係 144 圖8-3 鋁-鎂合金攪拌試片拉伸n值(真塑性應變量為0.10)與振動D-N曲線stageⅠ斜率關係：(a)不同鎂含量攪拌材；(b)5052鋁-鎂合金攪拌材 145 圖8-4 Al-0.5Mg合金攪拌試片之光學裂縫傳播行為 146

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