以四點彎曲試驗決定I+II型斷裂韌度之有限元素數值模擬

A Finite Element Numerical Simulation of Mode I+II Fracture Toughness Determination Using A Four-Point Bending Test

10.30069/MM.201912_63(4).02

李權仁(Chuan-Jen Lee)

斷裂力學 ； 斷裂韌度 ； 彎曲試驗 ； 有限元素分析 ； ABAQUS ； Fracture toughness ； Bending test ； Finite element analysis (FEA) ； ABAQUS

鑛冶：中國鑛冶工程學會會刊

63卷4期（2019 / 12 / 01）

20 - 37

繁體中文

在工程環境中，結構物的破壞多源自材料內部微小裂隙發展。在線彈性條件下，當應力場強度增大到某一臨界值，裂紋便失穩擴展而導致材料斷裂，這個臨界或失穩擴展的應力強度因子即斷裂韌度。前人針對不同材料與形狀之試體進行不同形式之斷裂力學試驗決定斷裂韌度，研究含裂縫之材料在受力變形作用下抵抗斷裂之能力。本研究根據賴俊仁（2001）以花崗岩與張育源（2017）以砂岩所製作之單裂縫矩型與圓柱試體進行四點彎曲試驗所得之材料參數（楊氏模數、泊松比、破壞負載與邊界條件），建立一套ABAQUS有限元素模型，計算裂縫尖端鄰近處應力及其距離，再換算試體之I與II型斷裂韌度。本研究分別對純I型、純II型與I+II複合型斷裂韌度之試驗模型選取之不同跨距，進行ABAQUS有限元素分析。針對不同元素選用、網格劃分（全域和局部撒點方式）、節點密度大小、實縫及虛縫缺口之繪製方式，進行數值模擬並比較相關結果。將本研究所得結果與Wang et al.（1977）比較，當裂隙比例介於0.25與0.45之間，I與II型無因次校正因子絕對偏差率均小於5 %。

In the engineering environment, the destruction of structures is mostly due to the growth of tiny cracks inside the material. The fracture criteria can be established by several methods of mechanical tests, and the fracture toughness can be measured. In this study, the models were established by ABAQUS. The simulation was based on the single edge-cracked four-point bending tests of granite specimens from the study of Lai (2001) and sandstone specimens from the study of Zhang (2017). The material parameters including Young's modulus and Poisson's ratio in ABAQUS models of this study were adopted from their studies. The stress at the fracture and the distance from the crack tip were evaluated. Then, the mode I and the mode II fracture toughness can be obtained. Comparing the experimental results with simulation results of ABAQUS, the applications of the finite element analysis under different scenarios of element selection, meshing, nodal density and notch drawing method were discussed. The simulated values of the mode I and the mode II fracture toughness were compared with the experimental data, and the values of correlation factors were assessed. The deviation rates of correlation factors of mode I and mode II fracture toughness are less than 5% when crack ratio are between 0.25 and 0.45.

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