Experimental and Numerical Study of the Influence of Prefabricated Crack Width on the Fracture Toughness of NSCB Specime
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ORIGINAL PAPER
Experimental and Numerical Study of the Influence of Prefabricated Crack Width on the Fracture Toughness of NSCB Specimens Sheng Zhang1,3 · Longfei Wang1,2 · Mingzhong Gao3 Received: 20 June 2019 / Accepted: 22 July 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract The accuracy measurement of rock fracture toughness is one of the basic tasks of rock fracture mechanics. In order to study the influence of the width of the prefabricated crack on the fracture toughness of rock, the failure process of notched semi-circular bend (NSCB) specimens with four sizes and five different width of the prefabricated crack was studied by experimental and numerical methods. The influence of the width of the prefabricated crack on the peak load, crack initiation position, dimensionless stress intensity factor and fracture toughness is analyzed and discussed. The results show that the peak load and fracture toughness of NSCB increase with the increase of the width of the prefabricated crack, and the smaller the specimen size is, the larger the increase is. When the width of the prefabricated crack is less than 1.3 mm, the crack initiates at the dichotomy of the prefabricated crack tip; when the width of the prefabricated crack is greater than or equal to 1.3 mm, the crack initiates near the corner of the prefabricated crack tip. If NSCB specimen is adopted to determine the fracture toughness of limestone, it is recommended that the width of prefabricated crack should be less than 1.3 mm. The conclusions provide a reference for the fabrication of NSCB specimens and the accurate measurement of limestone fracture toughness. Keywords Prefabricated crack width · Fracture toughness · Notched semi-circular bend · Crack initiation position List of Symbols LEFM Linear elastic fracture mechanics CB Chevron notched three-point bend NSCB Notched semi-circular bend CSTFBD Cracked straight through flattened Brazilian disc E Young’s modulus Cd Longitudinal wave velocity R Radius of the NSCB specimen KIc Fracture toughness d Phase field
* Mingzhong Gao [email protected] 1
School of Energy Science and Engineering, Collaborative Innovation Center of Coal Work Safety, Henan Polytechnic University, Jiaozuo 454001, Henan, China
2
School of Civil Engineering, Chongqing University, Chongqing 400045, China
3
Guangdong Provincial Key Laboratory of Deep Earth Sciences and Geothermal Energy Exploitation and Utilization, Institute of Deep Earth Sciences and Green Energy, College of Civil and Transportation Engineering, Shenzhen University, Shenzhen 518060, China
𝛱 Potential energy 𝜓e (𝜀) Elastic energy density 𝛺 Elastic body 𝜺 Strain tensor 𝜺− Compressive strain tensor 𝜓e− (𝜀) Negative elastic energy densities 𝜕𝛺 External boundary 𝜕𝛺u Displacement boundary ū Preserved displacement H(x, t) Strain-history field 𝛼0 Dimensionless prefabricated crack length SIF Stress intensity factor CCNBD Cracked chevron notched Brazilian disc HCFBD Holed-cracked flattened Brazilian disc FPZ Fracture
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