A new specimen geometry-the double edge-cracked Brazilian disk and a relevant fracture analysis byweight function method are proposed for the investigation of rock fracture caused by compression-shear loading. Notonly...A new specimen geometry-the double edge-cracked Brazilian disk and a relevant fracture analysis byweight function method are proposed for the investigation of rock fracture caused by compression-shear loading. Notonly can the mixed mode fracture with any ratio of KⅠ/KⅡ be achieved, but also the pure mode Ⅱ crack extensioncan be obtained. The combined mode fracture analysis for this geometry shows that diametral compression in the far-field can induce a compression-shear stress state in the singular stress field ahead of crack tips. Experimental investi-gations conducted on marble specimens show that the pure mode Ⅱ crack extension can be obtained when the dimen-sionless crack length a＞0.7 and the inclined crack angle 5°≤ψ≤40°. Normalized mode Ⅰ and mode Ⅱ stress inten-sity factors decrease from -0.45 and 2.47 at ψ=5° to -1.65 and 1.52 at ψ=40°, respectively. The strains at threepoints of specimen are also measured in order to investigate the influence of stress singularity on initial crack exten-sion. The results show that the principal orientations of strain at three points are very stable in the loading process.The derived formulae are quite explicit, and the specimen geometry is easy to fabricate and convenient to achieve thepure mode Ⅱ crack extension. Therefore, it can hopefully be used to obtain mode Ⅱ fracture toughness of rock.展开更多
The center cracked Brazilian disk subjected to diametral compressive stress uniformly distributed along parts of its cylindrical surface is used to investigate combined mode fracture of brittle material. A fracture a...The center cracked Brazilian disk subjected to diametral compressive stress uniformly distributed along parts of its cylindrical surface is used to investigate combined mode fracture of brittle material. A fracture analysis is made of this specimen configuration. Explicit formulae for mode Ⅰ and mode Ⅱ stress intensity factor calculation are derived based on boundary integral equation method and related numerical solution given by Atkinson. The proposed formulae are valid in wide range of crack length a/R . This configuration can avoid splitting along load line usually occuring in Brazilian test and permit one to achieve easily pure mode Ⅱ crack growth (crack coplanar extension) and any combination of K Ⅰ and K Ⅱ by a simple alignment of crack orientation with respect to load line. SIF values from the present calculation and finite element solution are also given for comparison.展开更多
A detailed analysis of mode II stress intensity factors(SIFs) for the double edge cracked Brazilian disk subjected to different diametral compression is presented using a weight function method. The mode II SIFs at cr...A detailed analysis of mode II stress intensity factors(SIFs) for the double edge cracked Brazilian disk subjected to different diametral compression is presented using a weight function method. The mode II SIFs at crack tips can be obtained by simply calculating an integral of the product of mode II weight function and the shear stress on the prospective crack faces of uncracked disk loaded by a diametral compression. A semi-analytical formula for the calculation of normalized mode II SIF, f _Ⅱ, is derived for different crack lengths (from 0.1 to 0.7) and inclination angles (from 10° to 75°) with respect to loading direction. Comparison between the obtained results and finite element method solutions shows that the weight function method is of high precision. Combined with the authors previous work on mode I fracture analysis, the new specimen geometry can be used to study fracture through any combination of mode I and mode II loading by a simple alignment of the crack relative to the diameter of compression loading, and to obtain pure mode II crack extension. Another advantage of this specimen geometry is that it is available directly from rock core and is also easy to fabricate.展开更多
基金Project (50274074) supported by the National Natural Science Foundation of China
文摘A new specimen geometry-the double edge-cracked Brazilian disk and a relevant fracture analysis byweight function method are proposed for the investigation of rock fracture caused by compression-shear loading. Notonly can the mixed mode fracture with any ratio of KⅠ/KⅡ be achieved, but also the pure mode Ⅱ crack extensioncan be obtained. The combined mode fracture analysis for this geometry shows that diametral compression in the far-field can induce a compression-shear stress state in the singular stress field ahead of crack tips. Experimental investi-gations conducted on marble specimens show that the pure mode Ⅱ crack extension can be obtained when the dimen-sionless crack length a＞0.7 and the inclined crack angle 5°≤ψ≤40°. Normalized mode Ⅰ and mode Ⅱ stress inten-sity factors decrease from -0.45 and 2.47 at ψ=5° to -1.65 and 1.52 at ψ=40°, respectively. The strains at threepoints of specimen are also measured in order to investigate the influence of stress singularity on initial crack exten-sion. The results show that the principal orientations of strain at three points are very stable in the loading process.The derived formulae are quite explicit, and the specimen geometry is easy to fabricate and convenient to achieve thepure mode Ⅱ crack extension. Therefore, it can hopefully be used to obtain mode Ⅱ fracture toughness of rock.
文摘The center cracked Brazilian disk subjected to diametral compressive stress uniformly distributed along parts of its cylindrical surface is used to investigate combined mode fracture of brittle material. A fracture analysis is made of this specimen configuration. Explicit formulae for mode Ⅰ and mode Ⅱ stress intensity factor calculation are derived based on boundary integral equation method and related numerical solution given by Atkinson. The proposed formulae are valid in wide range of crack length a/R . This configuration can avoid splitting along load line usually occuring in Brazilian test and permit one to achieve easily pure mode Ⅱ crack growth (crack coplanar extension) and any combination of K Ⅰ and K Ⅱ by a simple alignment of crack orientation with respect to load line. SIF values from the present calculation and finite element solution are also given for comparison.
文摘A detailed analysis of mode II stress intensity factors(SIFs) for the double edge cracked Brazilian disk subjected to different diametral compression is presented using a weight function method. The mode II SIFs at crack tips can be obtained by simply calculating an integral of the product of mode II weight function and the shear stress on the prospective crack faces of uncracked disk loaded by a diametral compression. A semi-analytical formula for the calculation of normalized mode II SIF, f _Ⅱ, is derived for different crack lengths (from 0.1 to 0.7) and inclination angles (from 10° to 75°) with respect to loading direction. Comparison between the obtained results and finite element method solutions shows that the weight function method is of high precision. Combined with the authors previous work on mode I fracture analysis, the new specimen geometry can be used to study fracture through any combination of mode I and mode II loading by a simple alignment of the crack relative to the diameter of compression loading, and to obtain pure mode II crack extension. Another advantage of this specimen geometry is that it is available directly from rock core and is also easy to fabricate.
