Kaiwen Xia

Semicircular bend testing with split Hopkinson pressure bar for measuring dynamic tensile strength of brittle solids

We propose and validate an indirect tensile testing method to measure the dynamic tensile strength of rocks and other brittle solids: semicircular bend (SCB) testing with a modified split Hopkinson pressure bar (SHPB) system. A strain gauge is mounted near the failure spot on the specimen to determine the rupture time. The momentum trap technique is utilized to ensure single pulse loading for postmortem examination. Tests without and with pulse shaping are conducted on rock specimens. The evolution of tensile stress at the failure spot is determined via dynamic and quasistatic finite element analyses with the dynamic loads measured from SHPB as inputs. Given properly shaped incident pulse, far-field dynamic force balance is achieved and the peak of the loading matches in time with the rupture onset of the specimen. In addition, the dynamic tensile stress history at the failure spot obtained from the full dynamic finite element analysis agrees with the quasistatic analysis. The opposite occurs for the test without pulse shaping. These results demonstrate that when the far-field dynamic force balance is satisfied, the inertial effects associated with stress wave loading are minimized and thus one can apply the simple quasistatic analysis to obtain the tensile strength in the SCB-SHPB testing. This method provides a useful and cost effective way to measure indirectly the dynamic tensile strength of rocks and other brittle materials.

Static and Dynamic Flexural Strength Anisotropy of Barre Granite

Granite exhibits anisotropy due to pre-existing microcracks under tectonic loadings; and the mechanical property anisotropy such as flexural/tensile strength is vital to many rock engineering applications. In this paper, Barre Granite is studied to understand the flexural strength anisotropy under a wide range of loading rates using newly proposed semi-circular bend tests. Static tests are conducted with a MTS hydraulic servo-control testing machine and dynamic tests with a split Hopkinson pressure bar (SHPB) system. Six samples groups are fabricated with respect to the three principle directions of Barre granite. Pulse shaping technique is used in all dynamic SHPB tests to facilitate dynamic stress equilibrium. Finite element method is utilized to build up equations calculating the flexural tensile strength. For samples in the same orientation group, a loading rate dependence of the flexural tensile strength is observed. The measured flexural tensile strength is higher than the tensile strength measured using Brazilian disc method at given loading rate and this scenario has been rationalized using a non-local failure theory. The flexural tensile strength anisotropy features obvious dependence on the loading rates, the higher the loading rate, the less the anisotropy and this phenomenon may be explained considering the interaction of the preferentially oriented microcracks.

Quantification of dynamic tensile parameters of rocks using a modified Kolsky tension bar apparatus

Abstract For brittle materials, the tensile strength plays an important role in mechanical analyses and engineering applications. Although quasi-static direct and dynamic indirect tensile strength testing methods have already been developed for rocks, the dynamic direct pull test is still necessary to accurately determine the tensile strength of rocks. In this paper, a Kolsky tension bar system is developed for measuring the dynamic direct tensile strength of rocks. A dumbbell-shaped sample is adopted and attached to the bars using epoxy glue. The pulse shaping technique is utilized to eliminate the inertial effect of samples during test. The single pulse loading technique is developed for the effective microstructure analyses of tested samples. Two absorption devices are successfully utilized to reduce the reflection of waves in the incident bar and transmitted bar, respectively. Laurentian granite (LG) is tested to demonstrate the feasibility of the proposed method. The tensile strength of LG increases with the loading rate. Furthermore, the nominal surface energy of LG is measured, which also increases with the loading rate.

Dynamic Shear Rupture in Frictional Interfaces: Speeds, Directionality, and Modes

The goal in designing dynamic frictional experiments simulating earthquake rupture has been to create a testing environment or platform which could reproduce some of the basic physics governing the rupture dynamics of crustal earthquakes while preserving enough simplicity so that clear conclusions can be obtained by pure observation. In this chapter, we first review past and recent experimental work on dynamic shear rupture propagation along frictional interfaces. The early experimental techniques are discussed in relation to recent experimental simulations of earthquakes which feature advanced diagnostics of high temporal and spatial resolution. The high-resolution instrumentation enables direct comparison between the experiments and data recorded during natural earthquakes. The experimental results presented in this chapter are examined in light of seismological observations related to various natural large rupture events and of recent theoretical and numerical development in the understanding of frictional rupture. In particular, the physics and conditions leading to phenomena such as supershear rupture growth, sub-Rayleigh to supershear rupture transition, and rupture directionality in inhomogeneous systems are discussed in detail. Finally, experiments demonstrating the attainability of various rupture modes (crack-like, pulse-like, and mixed) are presented and discussed in relation to theoretical and numerical predictions.

The relation between shock-state particle velocity and free surface velocity : A molecular dynamics study on single crystal Cu and silica glass

We investigate the ratio Rrp of the free surface velocity to the shock-state particle velocity during shock wave loading with molecular dynamics simulations on two representative solids, single crystal Cu, and silica glass. The free surface velocity is obtained as a function of the particle velocity behind the shock front (or shock stress) for loading on Cu along ⟨100⟩, ⟨110⟩, and ⟨111⟩, and on the isotropic glass. Rrp≥1 for Cu and Rrp<1 for silica glass, and it increases with shock strength; the simulations agree well with the experimental results. For supported shock loading of silica glass at 30–90 GPa, the SiIV–SiVI transition occurs upon shock, inducing substantial densification and thus small Rrp (0.65–0.78). For single crystal Cu, Rrp deviates from 1 near the Hugoniot elastic limit and reaches ∼1.2 at 355 GPa for ⟨100⟩ shock. Rrp is anisotropic, e.g., it is about 1.02, 1.08, and 1.06 for shock loading to about 80 GPa along ⟨100⟩, ⟨110⟩, and ⟨111⟩, respectively. Such an anisotropy is mostly due to t...

Depth of Cracking beneath Impact Craters: New Constraint for Impact Velocity

Both small‐scale impact craters in the laboratory and less than 5 km in diameter bowl‐shaped craters on the Earth are strength (of rock) controlled. In the strength regime, crater volumes are nearly proportional to impactor kinetic energy. The depth of the cracked rock zone beneath such craters depends on both impactor energy and velocity. Thus determination of the maximum zone of cracking constrains impact velocity. We show this dependency for small‐scale laboratory craters where the cracked zone is delineated via ultrasonic methods. The 1 km‐deep cracked zone beneath Meteor Crater is found to be consistent with the crater scaling of Schmidt (1) and previous shock attenuation calculations.

Impact induced damage beneath craters

Ackermann et al. (1975) described the subsurface structure of Meteor Crater and identified a fractured rock zone extending to about 1 km deep. The depth of the fractured/damage zone can be used to extract information about the impact cratering process. We impacted rock samples (San Marcos gabbro) in the laboratory and imaged the damage structure using both dicing and tomography methods. We propose a simple model to describe the damage zone depth based on the laboratory measurements. The model agrees well with other methods for the estimation of the projectile size of Meteor Crater and it may be used for estimates of damage around craters of other planets and moons.

Dynamic Tensile Failure of the Rock Interface Between Tuff and Basalt

The dynamic tensile strength properties of the rock interface and its host rocks sampled from the Baihetan Hydropower Station from Western China were measured using a split Hopkinson pressure bar (SHPB). The results were compared with those for its two host rocks. The dynamic tensile strengths of the two host rocks, tuff and basalt have typical loading rate dependence. However, the dynamic response of the rock interface is much more complicated and at a given loading rate, varies between those of tuff and basalt. To explain the observation, numerical simulation using the discrete element method (DEM) was conducted to determine the detailed tensile failure process of the rock interface. The numerical simulation verifies that the variation of the dynamic tensile strength of the rock interface is a result of the variation of the interface geometry.

Observation of microscopic damage accumulation in brittle solids subjected to dynamic compressive loading

Dynamic failure of brittle materials is a fundamental physical problem that has significantly impacts to many science and engineering disciplines. As the first and the most important step towards the full understanding of this problem, one has to observe dynamic damage accumulation in brittle solids. In this work, we proposed a methodology to do that and demonstrated it by studying the dynamic compressive damage evolution of a granitic rock loaded with a modified split Hopkinson pressure bar system. To ensure consistency of the experimental results, we used cylindrical rock samples fabricated from the same rock core and subjected them to identical incident loading pulse. Using a special soft recovery technique, we stopped the dynamic loading on the samples at different strain levels, ranging from 0.3% to 1.4%. Therefore, we were able to recover intact samples loaded all the way to the post-peak deformation stage. The recovered samples were subsequently examined with X-ray micro-CT scanning machine. Three dimensional microcrack network induced by the dynamic loading was observed and the evolution of microcracks as a function of the dynamic loading strain was obtained.

Smart film for crack monitoring of concrete bridges

In the field of structural health monitoring of concrete bridges, one of the most challenging problems is the crack identification. In our previous study, we proposed a crack-sensitive skin to monitor the crack initiation and development in a structure and to visualize them remotely using computer. However, the material used in the sensitive skin is not suitable for large-scale structural monitoring. In this article, magnetic wire smart film is proposed for crack monitoring of large-scale concrete structures. Fabrication of the smart film, the working principle of the film, and the application of the film on a real bridge will be presented and discussed. The results show that the smart film is a good technique for crack monitoring of large-scale concrete structures.In the field of structural health monitoring of concrete bridges, one of the most challenging problems is the crack identification. In our previous study, we proposed a crack-sensitive skin to monitor the crack initiation and development in a structure and to visualize them remotely using computer. However, the material used in the sensitive skin is not suitable for large-scale structural monitoring. In this article, magnetic wire smart film is proposed for crack monitoring of large-scale concrete structures. Fabrication of the smart film, the working principle of the film, and the application of the film on a real bridge will be presented and discussed. The results show that the smart film is a good technique for crack monitoring of large-scale concrete structures.