Mixed mode Ⅰ/Ⅱ fracture erperiments of LC4-CS aluminum alloy were conductedby using tension--shear specimens with thicknesses of 2, 4, 8 and 14mm. Fracturemechanisms of thickness effect on mixed mode Ⅰ/Ⅱ fracture ...Mixed mode Ⅰ/Ⅱ fracture erperiments of LC4-CS aluminum alloy were conductedby using tension--shear specimens with thicknesses of 2, 4, 8 and 14mm. Fracturemechanisms of thickness effect on mixed mode Ⅰ/Ⅱ fracture were first examined fromfracture surface morphology to correlate with the macroscopic fracture behavior andstress state. It is found that specimen thickness has a strong influence on mixed modefracture. As thickness varies from thin to thick the macroscopic fracture surfacesappear the characteristics of plane stress state (2mm, 4mm--thick specimen), three--dimensional stress state (8mm--thick specimens), and plane strain state (14mm--thickspecimens), respectively. The specimens of all kinds of thicknesses are typical of ten-sile type failure under mode Ⅰ loading condition and shear type failure under mode Ⅱloading condition. Two distinct features coexist on the fracture surfaces under mixedmode loading conditions, and the corresponding proportion varies with loading mix-ity. Void--growth processes are the failure mechanism in both predominately tensile-and shears--type fractures. The size and depth of dimples on the fracture surface varygreatly with thickness. Therefore, it is extraordinary necessary to take into accountthe thickness effect when a mixed mode fracture criterion is being established.展开更多
A closed-form solution for predicting the tangential stress of an inclusion located in mixed mode Ⅰ and Ⅱ crack tip field was developed based on the Eshelby equivalent inclusion theory. Then a mixed mode fracture cr...A closed-form solution for predicting the tangential stress of an inclusion located in mixed mode Ⅰ and Ⅱ crack tip field was developed based on the Eshelby equivalent inclusion theory. Then a mixed mode fracture criterion, including the fracture direction and the critical load, was established based on the maximum tangential stress in the inclusion for brittle inclusioninduced fracture materials. The proposed fracture criterion is a function of the inclusion fracture stress, its size and volume fraction, as well as the elastic constants of the inclusion and the matrix material. The present criterion will reduce to the conventional one as the inclusion having the same elastic behavior as the matrix material. The proposed solutions are in good agreement with detailed finite element analysis and measurement.展开更多
In this context,four specimens,i.e.(i)circumferentially notched cylindrical torsion(CNCT),(ii)circum-ferentially notched cylindrical direct tension(CNCDT),(iii)edge notch disc bend(ENDB)and(iv)three-point bend beam(3P...In this context,four specimens,i.e.(i)circumferentially notched cylindrical torsion(CNCT),(ii)circum-ferentially notched cylindrical direct tension(CNCDT),(iii)edge notch disc bend(ENDB)and(iv)three-point bend beam(3PBB),were utilized to measure the modesⅠandⅢfracture toughness values of gypsum.While the CNCT specimen provides pure modeⅢloading in a direct manner,this pure mode condition is indirectly produced by the ENDB specimen.The ENDB specimen provided lower KⅢc and a non-coplanar(i.e.twisted)fracture surface compared with the CNCT specimen,which showed a planar modeⅢfracture surface.The ENDB specimen is also employed for conducting pure modeⅠ(with different crack depths)and mixed modeⅠ/Ⅲtests.KIc value was independent of the notch depth,and it was consistent with the RILEM and ASTM standard methods.But the modeⅢfracture results were highly sensitive to the notch depth.While the fracture resistance against modeⅢwas significantly lower than that of modeⅠ,the greater work of fracture under modeⅢwas noticeable.展开更多
Anti-plane punch-through shear test and anti-planefour-point bending test are used to study the crack initiation and propagation under anti-plane shear (Mode Ⅲ) loading. The tensile and shear stresses at the crack ti...Anti-plane punch-through shear test and anti-planefour-point bending test are used to study the crack initiation and propagation under anti-plane shear (Mode Ⅲ) loading. The tensile and shear stresses at the crack tip are calculated by finite element method. The results show that under Mode Ⅲ loading the maximum principal stress σ1 at crack tip is smaller or a little larger than the maximum shear stress τmax. Since the tensile strength of brittle rock is much lower than its shear strength, σ1 is easy to reach its critical value before τmax reaches its critical value and thus results in Mode I fracture. The fracture trajectory is helicoid and the normal direction of tangential plane with the fractured helicoid is along the predicted direction of the maximum principal stress at the notch tip. It is further proved that Mode Ⅰ instead of Mode Ⅲ fracture occurs in brittle rock under Mode Ⅲ loading. The fracture mode depending on the fracture mechanism must be distinguished from the loading form.展开更多
文摘Mixed mode Ⅰ/Ⅱ fracture erperiments of LC4-CS aluminum alloy were conductedby using tension--shear specimens with thicknesses of 2, 4, 8 and 14mm. Fracturemechanisms of thickness effect on mixed mode Ⅰ/Ⅱ fracture were first examined fromfracture surface morphology to correlate with the macroscopic fracture behavior andstress state. It is found that specimen thickness has a strong influence on mixed modefracture. As thickness varies from thin to thick the macroscopic fracture surfacesappear the characteristics of plane stress state (2mm, 4mm--thick specimen), three--dimensional stress state (8mm--thick specimens), and plane strain state (14mm--thickspecimens), respectively. The specimens of all kinds of thicknesses are typical of ten-sile type failure under mode Ⅰ loading condition and shear type failure under mode Ⅱloading condition. Two distinct features coexist on the fracture surfaces under mixedmode loading conditions, and the corresponding proportion varies with loading mix-ity. Void--growth processes are the failure mechanism in both predominately tensile-and shears--type fractures. The size and depth of dimples on the fracture surface varygreatly with thickness. Therefore, it is extraordinary necessary to take into accountthe thickness effect when a mixed mode fracture criterion is being established.
文摘工程结构在制造工艺过程中或使用期间会产生裂纹,对结构断裂路径的预测和研究是防治工程安全问题发生的重要手段。在考虑裂纹尖端应力场常数项T应力的基础上对传统的最大周向应力准则(Maximum tangential stress criterion,MTS)和最小应变能密度因子准则(Minimum strain energy density criterion,SED)进行修正,采用Python语言对ABAQUS的前、后处理和有限元计算模块进行二次开发,通过计算最优解的粒子群算法(Particle swarm optimization,PSO)将修正后的准则编入裂纹自动扩展程序脚本中。利用上述二次开发程序对初始纯Ⅰ型裂纹的扩展路径进行模拟,结果表明:采用ABAQUS脚本程序模拟结果与相关文献实验结果吻合,表明了程序的有效性,进而实现考虑T应力的多种断裂准则对裂纹扩展路径的预测;当T应力值处于一定范围内时,修正的MTS准则无法预测裂纹发生的偏转现象,扩展路径呈直线,此时可采用修正的SED准则进行预测。
基金Project supported by the National Basic Research Program of China (No. 2004CB619303).
文摘A closed-form solution for predicting the tangential stress of an inclusion located in mixed mode Ⅰ and Ⅱ crack tip field was developed based on the Eshelby equivalent inclusion theory. Then a mixed mode fracture criterion, including the fracture direction and the critical load, was established based on the maximum tangential stress in the inclusion for brittle inclusioninduced fracture materials. The proposed fracture criterion is a function of the inclusion fracture stress, its size and volume fraction, as well as the elastic constants of the inclusion and the matrix material. The present criterion will reduce to the conventional one as the inclusion having the same elastic behavior as the matrix material. The proposed solutions are in good agreement with detailed finite element analysis and measurement.
文摘In this context,four specimens,i.e.(i)circumferentially notched cylindrical torsion(CNCT),(ii)circum-ferentially notched cylindrical direct tension(CNCDT),(iii)edge notch disc bend(ENDB)and(iv)three-point bend beam(3PBB),were utilized to measure the modesⅠandⅢfracture toughness values of gypsum.While the CNCT specimen provides pure modeⅢloading in a direct manner,this pure mode condition is indirectly produced by the ENDB specimen.The ENDB specimen provided lower KⅢc and a non-coplanar(i.e.twisted)fracture surface compared with the CNCT specimen,which showed a planar modeⅢfracture surface.The ENDB specimen is also employed for conducting pure modeⅠ(with different crack depths)and mixed modeⅠ/Ⅲtests.KIc value was independent of the notch depth,and it was consistent with the RILEM and ASTM standard methods.But the modeⅢfracture results were highly sensitive to the notch depth.While the fracture resistance against modeⅢwas significantly lower than that of modeⅠ,the greater work of fracture under modeⅢwas noticeable.
基金Project (50374073)supported by the National Natural Science Foundation of China project (2002032256)supported bythe Postdoctor Science Foundation of China
文摘Anti-plane punch-through shear test and anti-planefour-point bending test are used to study the crack initiation and propagation under anti-plane shear (Mode Ⅲ) loading. The tensile and shear stresses at the crack tip are calculated by finite element method. The results show that under Mode Ⅲ loading the maximum principal stress σ1 at crack tip is smaller or a little larger than the maximum shear stress τmax. Since the tensile strength of brittle rock is much lower than its shear strength, σ1 is easy to reach its critical value before τmax reaches its critical value and thus results in Mode I fracture. The fracture trajectory is helicoid and the normal direction of tangential plane with the fractured helicoid is along the predicted direction of the maximum principal stress at the notch tip. It is further proved that Mode Ⅰ instead of Mode Ⅲ fracture occurs in brittle rock under Mode Ⅲ loading. The fracture mode depending on the fracture mechanism must be distinguished from the loading form.
