混合型破裂韌度的預測

The Prediction of Mixed-mode Fracture Toughness

林宗億(Tsung-Yi Lin)

指導教授 ： 蔣長榮

國立清華大學/工學院/動力機械工程學系/碩士(2007年)

摘要

本文針對在實際工程中最常見的混合型Ⅰ/Ⅱ（mixed-mode
Ⅰ/Ⅱ）受力情況的裂縫，從微觀力學的角度，藉由裂縫前端的應力及應變分布，輔以適當破壞準則來預測裂縫受到純粹modeⅠ、mode
Ⅱ及混合型Ⅰ/Ⅱ外力負載下的破裂韌度值（fracture toughness）。本文利用最大正向應力破壞準則與Von Mises等效應變破壞準則所預測出的混合型破裂韌度值和裂縫成長方向與既有文獻在實際實驗所求出的數據做比較，發現Von Mises等效應變破壞準則較符合實際實驗所求的裂縫成長方向。在改變裂縫前端曲率半徑值的情形下，利用前述兩種不同的破壞準則去預測純粹modeI的破裂韌度值中可以發現其破裂韌度值會隨著半徑的縮小而減少。最後將本文所預測出的裂縫破壞角度與實際實驗相比較之下，可以發現實際實驗的結果在KⅠ與KⅡ比值小於1時，其裂縫破壞角度發生在水平方向，而本文所模擬的材料（不鏽鋼）其預測出的裂縫破壞角度則是發生在59.35∘到65.68∘。產生此差異的可能原因包括：（1）實驗設備及試片夾具設計並無法實現純modeⅡ的負載；（2）本文所用的破壞準則是以某一點的應力或應變做為參考；而材料的破壞，特別是裂縫成長方向可能需要考慮該點及其鄰近的應力或應變狀態，甚至要考慮雖不是應力或應變的最大處但卻有較大影響範圍的臨界點。

關鍵字

破裂韌度 ； 最大畸變能準則 ； 最大正向應力準則 ； 混合型裂縫 ； 牛頓-拉夫遜法

並列摘要

Abstract The thesis focus on the mixed-mode Ⅰ/Ⅱ crack which is very common in fracture problem. Study the stress and strain around crack tip by micro mechanics method and exploit the fracture criterion to predict the fracture toughness of pure modeⅠ, pure modeⅡ and mixed-mode Ⅰ/Ⅱ.Two fracture criterion, maximum principle stress theory（MPST） and maximum distortion energy theory（MDET）, are used in this thesis. The fracture toughness of mixed-mode Ⅰ/Ⅱ by MDET is similar to the result of experiment.When using both fracture criterions to predict the fracture toughness of pure modeⅠ,the smaller radius the crack is,the the smaller fracture toughness of pure modeⅠ is. It isn＇t related to the fracture criterions we use.We compare the crack growth angle of pure modeⅡ we predict to the experiment result, and discover that the result don＇t match. The possible reasons are：（1）The experiment equip couldn＇t perfectly simulate the condition of pure modeⅡ.（2）The fracture criterions we use are merely focus on certain point＇s stress or strain, but the crack growth angle of material isn＇tII only related to the certain point but also related to the proximity of the certain point.So it＇s possible that crack growth don＇t occur on the point of maximum stress or strain.

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