Numerical Investigation of Dynamic Rock Fracture Toughness Determination Using a Semi-Circular Bend Specimen in Split Hopkinson Pressure Bar Testing

Abstract

The International Society for Rock Mechanics (ISRM) has suggested a notched semi-circular bend technique in split Hopkinson pressure bar (SHPB) testing to determine the dynamic mode I fracture toughness of rock. Due to the transient nature of dynamic loading and limited experimental techniques, the dynamic fracture process associated with energy partitions remains far from being fully understood. In this study, the dynamic fracturing of the notched semi-circular bend rock specimen in SHPB testing is numerically simulated for the first time by the discrete element method (DEM) and evaluated in both microlevel and energy points of view. The results confirm the validity of this DEM model to reproduce the dynamic fracturing and the feasibility to simultaneously measure key dynamic rock fracture parameters, including initiation fracture toughness, fracture energy, and propagation fracture toughness. In particular, the force equilibrium of the specimen can be effectively achieved by virtue of a ramped incident pulse, and the fracture onset in the vicinity of the crack tip is found to synchronize with the peak force, both of which guarantee the quasistatic data reduction method employed to determine the dynamic fracture toughness. Moreover, the energy partition analysis indicates that simplifications, including friction energy neglect, can cause an overestimation of the propagation fracture toughness, especially under a higher loading rate. Keywords Dynamic fracture toughness Á Discrete element method Á SHPB Á Rate dependent Á Energy partition Abbreviations DEM Discrete element method ISRM International Society for Rock Mechanics NSCB Notched semi-circular bend SHPB Split Hopkinson pressure bar SIF Stress intensity factor a Crack length of the NSCB sample (m) a a Dimensionless crack length of the NSCB sample A b Cross-section area of the pressure bars (m 2 ) A s Area of the fracture surface (m 2 ) B Thickness of the NSCB sample (m) dF s Increment of the shear force (N) ds Increment of the relative displacement (m) E bYoung's modulus of the elastic bars (MPa) E bond Potential energy stored in bonds (J) E contact Potential energy stored in contacts (J) E friction Friction energy (J) E kinetic Kinetic energy (J) f Im Values of the contact force m on the barspecimen incident interface (N) f Tm

An experimental and theoretical comparison of CCNBD and CCNSCB specimens for determining mode I fracture toughness of rocks

“…Chevron bending (CB) method 16,17 Three-point bending Chevron-notched short rod (SR) method 16,17 Direct tension Cracked chevron notched Brazilian disc (CCNBD) method [18][19][20][21][22][23][24][25] Brazilian-type compression Cracked straight-through Brazilian disc method [26][27][28][29][30][31] Brazilian-type compression Modified ring method 32 Brazilian-type compression Hollow centre cracked disc method 33 Brazilian-type compression Cracked chevron notched semicircular bending (CCNSCB) method [34][35][36] Three-point bending Straight-crack semicircular bending (SCB) method [37][38][39][40] Three-point bending Flattened Brazilian disc method 41 Brazilian-type compression Edge-cracked triangular method 42 Three-point bending Four point bend rectangular beam method 5…”

Investigation of rock fragmentation during rockfalls and rock avalanches via 3‐D discrete element analyses

“…The configuration of the numerical SHPB test is taken from Xu et al . []. The input parameter values of the simulations were selected by trial and error (see Table ), to ensure the overall shear strength and deformation of the coal rock specimen can match experimental results.…”

Experimental and Numerical Evaluation of Rock Dynamic Test with Split-Hopkinson Pressure Bar

“…By comparing the accurate numerical result with the experimental waveform, the coefficient can be obtained to reduce the number of errors. Xu et al confirmed the validity of this DEM model to reproduce the dynamic fracturing and the feasibility to simultaneously measure key dynamic rock fracture parameters, including initiation fracture toughness, fracture energy, and propagation fracture toughness [11]. The damage and rupture process of coal-rock is accompanied by acoustic emission (AE) by Wen et al [12]; the results show that coal-rock's size influences the uniaxial compressive strength, peak strain, and elastic modulus of itself.…”