Crack-like Cavity Research Articles

Comparison of high- and low-frequency signal sources for very-long-period seismic events at Asama volcano, Japan

Very-long-period (VLP) seismic events at Asama volcano in central Japan are characterized by a transient signal of 10–20 s duration. Associated with the transient motion, a high-frequency (HF) oscillation within the 5–10 Hz band is observed. We investigated the location and size of the oscillation source in the HF band (HF source) using an amplitude source location method and compared our results with those for the VLP band (VLP source) deduced in our previous waveform inversion study. We analysed 1437 VLP events recorded during an intense observation campaign during 2008–2009, and additional 571 events surrounding an eruptive activity in 2015 (including a VLP event that immediately preceded an eruption). The HF source locations of most events were deeper than the VLP source locations by ∼150 m, although there was almost no time lag between the signals. This suggests a strong connection between the two sources, with one source immediately responding to the other. The eruptive VLP event had an HF source location close to normal VLP events but had a greater event size. We surmise that the HF signal is caused by an inflow of volcanic gas from depth into a semi-vertical crack-like cavity (as imaged in our previous waveform inversion study), and the VLP signal is caused by resultant inflation of the same cavity. The centroid of inflation (VLP source) is near the roof of the cavity, where gas accumulates, whereas the HF oscillation is emitted more intensely from lower and narrower portions of the cavity. This results in source depth differences between the two signal bands. In this model, the inflation rate of the cavity is controlled by the volume flux of the gas inflow, producing similar temporal variations between the VLP and HF signals. According to this model, the eruptive VLP is associated with a greater amount of gas inflow and accumulation, which likely played a key role in the eruption.

Rapid Transient Motion of a Thin Rigid Body in an Elastic Medium

A two-dimensional transient problem on motion of a thin finite rigid body at sub-Rayleigh speed in an elastic medium is analyzed. When the body moves it leaves a semi-infinite crack-like cavity beh...

Simulation of partial closure of a crack-like cavity with cohesion between the faces in an isotropic medium

A mathematical model for the closure of a crack-like cavity with cohesive end zones in an isotropic medium is constructed using methods of elastic theory. It is assumed that the interaction between the surfaces of the crack-like cavity under the action of body and surface forces can lead to the formation of contact zones on their surfaces. Determination of the unknown parameters characterizing the closure of the crack-like cavity reduces to a system of singular integrodifferential equations. The integral equations are converted to a system of nonlinear algebraic equations which is solved by the method of successive approximations. The contact stresses, the interaction forces between the faces of the crack-like cavity, and the size of the contact zone in which the faces of the crack-like cavities are closed are determined.

Partial closure of a crack-like cavity in an isotropic medium

On the basis of elasticity theory, a mathematical model is formulated for the closure of a crack-like cavity in an isotropic medium; the ends of the cavity are subject to the adhesive forces of the material. It is assumed that the interaction of the cavity surfaces under the action of bulk and surface loads may lead to zones of surface overlap. The unknowns that characterize cavity closure may be determined by the solution of a system of singular integrodifferential equations. The integral equations may be reduced to a system of nonlinear algebraic equations and solved by successive approximation. The contact stress, the forces between the edges of the cavity, and the dimensions of the end contact zones are determined.

Cavity Growth Simulation in 2.25Cr–1Mo Steel Under Creep-Fatigue Loading

High temperature components in thermal power plants are subjected to creep-fatigue loading where creep cavities initiate and grow on grain boundaries. Development of a quantitative evaluation method of cavity growth is important for reliable maintenance of these components. In this study, a creep-fatigue test was carried out at 600°C on 2.25Cr–1Mo steel in a scanning electron microscope, and continuous observation of cavity growth behavior during the test was made. Based on the cavity growth observation, existing cavity growth models were modified and the simulated results using the modified model were compared to the observed cavity growth behavior. From the observation, spherical shape cavities initiate and grow up to their length of 2μm on the grain boundaries at the initial stage of damage, and then these cavities change their shape to cracklike and grow until their length reaches around 10μm. Finally, cracklike cavities coalesce with each other to form one microcrack along a grain boundary. It can be concluded that cavity growth rates are controlled by diffusion and power law creep under constrained conditions, based on the theoretical consideration of cavity growth mechanism. Through these discussions, a new cavity growth model was proposed by modifying conventional models. Both spherical and cracklike cavity growth rate equations were derived from the modified cavity growth model. It was indicated that the measured cavity growth rate was well predicted by the growth rate equations, derived from the modified model, and a cavity growth simulation result corresponds to the change in the maximum cavity size with number of cycles under the creep-fatigue loading.

Clarification of Damage Extension Mechanism on 2.25 Cr-1Mo Steel under Creep-Fatigue Loading Condition.

High temperature components are subjected to creep-fatigue loading where creep cavities initiate and grow on grain boundaries. Development of a quantitative evaluation method of cavity growth is important for reliable meintenance. In this study, a creep-fatigue test was carried out at 600°C on 2.25 Cr-1Mo steel in a scanning electron microscope and continuous observation of cavity growth behavior was made. Based on the cavity growth observation, previously proposed cavity growth models were modified and a simulation result by the modified model was discussed by comparing with observed cavity. From the observation, spherical shape cavities initiate and grow up to their length of 2 μm on the grain boundary at initial stage of damage and these cavites change their shape to crack-like to grow until their length reaches around 10 μm. Both spherical and crack-like cavity growth equations, which consider diffusion and power low creep as driving force under constrained condition, were derived. Measured cavity growth rate is well expressed by the derived equations and a cavity growth simulation result corresponds to the change in the maximum cavity size with cycles.

A comparative examination of superplastic flow and fracture in metals and ceramics

Although metals and ceramics can exhibit superplastic elongations to failure of >500%, there are significant differences in their mechanical behavior and fracture characteristics. The transition from superplastic to non-superplastic behavior at low stresses is sensitive to impurity content. However, with an increase in purity, while the transition is retarded to lower stresses in metals, the transition occurs at higher stress in ceramics. The cavitation behavior also appears to be different. While metallic alloys typically exhibit rounded small cavities suggesting quasi-equilibrium diffusion growth, ceramics display crack-like cavity profiles indicating surface diffusion controlled cavity growth.

Cavity Growth in Polycrystalline Materials under Grain Boundary Diffusion Creep and Transition from Cavity to Crack

The stress distribution along grain boundaries in polycrystalline materials under the grain boundary diffusion creep (Coble creep) condition is numerically analyzed in order to elucidate the effect of the grain boundary network on cavity growth. The stress gradient at the cavity tip, which is proportional to the changing rate of the cavity volume, points out that the triple junction of grain boundaries interferes with cavity growth, though the cavity grows faster after the tip goes beyond it. The deceleration effect due to the triple junction diminishes as the cavity becomes larger. The transition from "crack-like cavity" to "crack" is also discussed on the basis of the stress field near the tip. The "crack" and the "cavity" are distinguished by the fact that the former possesses the stress singularity in the vicinity of the tip while the latter does not. The calculation reveals that the transition under the Coble creep condition does not take place before the cavity length exceeds 15 grain boundaries. On the other hand, the transgranular deformation due to dislocation creep drastically accelerates the transition.

Cavity Growth in Coble Creep of Polycrystalline Materials and Transition from Cavity to Crack.

The stress distribution along grain boundaries of polycrystalline materials ahead of a under Coble creep (grain boundary creep) condition is numerically analyzed in order to elucidate the effect of the grain boundary network on growth. The stress gradient at the tip, which is proportional to the changing rate in the volume, points out that the grain boundary triple points interfere with the growth, though the grows faster beyond them. The deceleration effect due to the triple points diminishes as the becomes larger. The transition from crack-like cavity to crack is also discussed on the basis of the stress distribution. Crack-like cavity and crack are distinguished by the fact that the latter possesses stress singularity in the vicinity of the tip while the former does not. The calculation reveals that the transition under the Coble creep condition does not take place before the length exceeds 15 grain boundaries. The transgranular deformation due to dislocation creep drastically accelerates the transition.

Mechanisms of intergranular cavity growth in Ni 3Al (Zr, B)

A technique based on hydrogen embrittlement has been used to study the morphology and growth characteristics of grain boundary cavities in a Ni 3Al alloy. The technique facilitates brittle intergranular fracture of specimens previously tested at elevated temperatures. This capability makes it possible to distinguish cavities that have formed by cavity coalescence and also determine cavity shape in three dimensions. Contrary to earlier reports of crack-like cavity growth, the results indicate that the shapes of individually growing cavities in Ni 3Al are consistent with quasi-equilibrium cavity growth theory. Cavity size measurements have also been compared with predictions of both quasi-equilibrium and crack-like cavity growth models. These results also support the finding that cavity growth in Ni 3Al occurs in a quasi-equilibrium manner. The observations further suggest that the formation of crack-like cavities is primarily due to coalescence and, therefore, not representative of the growth mechanism of individual cavities.

Effects of rigid grains separation on the diffusive growth of crack-like cavities on grain boundaries

Previous analyses of diffusive growth of grain boundary cavities in the limiting case of a crack-like mode under the rigid grain assumption have assumed that the effect of grains separation rate on the cavity growth rate is negligible. This is more valid when the cavity growth rates are very high. Here, we investigate the appropriateness of this assumption at lower cavity growth rates by incorporating the contribution of the rigid grains separation rate in the analysis. The resulting geometry of the crack-like cavity near its tip is given. This information is used to set boundary conditions for the rigid grain model. Numerical results for the applied stress versus the cavity growth rate are presented. They are compared with those given by Chuang, Kagawa, Rice and Sills (1979), whose analysis assumes the rate of separation of the grains to be small compared to the cavity growth rate. Comparison with the results of Chuang et al. (1979) for the rupture time based on cavity growth to coalescence is also made.

Overview no. 2: Non-equilibrium models for diffusive cavitation of grain interfaces

Existing models for the diffusive growth of voids on grain interfaces, at elevated temperature, are for the most part based on quasi-equilibrium assumptions: surface diffusion is assumed to be sufficiently rapid that the cavity has a rounded, equilibrium shape, and hence cavity growth is assumed to be rate-limited only by grain boundary diffusion. However, creep rupture cavities sometimes have narrow, crack-like shapes and it is appropriate to investigate non-equlibrium models for diffusive rupture. We do so here by comparing the quasi-equilibrium model to another limiting case based on a narrow, crack-like cavity shape. Criteria for choosing between the models are given on the basis of representative relaxation times for the surface diffusion process, and also by examining the properties of a ‘self-similar’ solution for cavity shape. By a suitable choice of parameters which measure the growth rate, this solution can be made to give results corresponding to either limiting case, and aids the interpolation between them. The results suggest that if s is the ratio of the applied stress to that which just equilibrates cavities against sintering, then for circular cavities on a grain boundary with diameter equal to a quarter of their average center-to-center spacing, the quasi-equilibrium mode applies when s < 1 + 6 Δ and the crack-like mode when s > 2 + 9 Δ. Here αD is the ratio of surface to grain boundary diffusivity. Also, the stress dependence of the growth rate and rupture lifetime is established in each case, and the results are discussed in relation to the interpretation of experimental data.

The extension of hydrogen blister-crack array in linepipe steels

Hydrogen induced fracture in linepipe steels is characterized by the formation of internal blisters caused by hydrogen precipitation at an inclusion-matrix interface, followed by the formation of blister-crack array by cracking the region connecting the blisters through the action of internal hydrogen pressure and external stress. The manner of extension of the hydrogen induced fracture of this type is considerably influenced by the presence of external stress: in the absence of the external stress fracture develops by linking the blisters which are formed in stacked arrays out of a plane approximately perpendicular to the external stress axis. Shear stress distribution induced around the blister is sensi-tively influenced by the external stress applied parallel to the blister plane; therefore, it is expected that the manner of extension of the blister-crack array should be influenced by the external stress. In the present paper the above mentioned influence of the external stress on the manner of extension of the hydrogen induced fracture is explained based on stress analysis around a hydrogen gas pressurized crack-like cavity under stress.

Trees “Pierced” by other Trees

COLONEL GREENWOOD'S answer (NATURE, vol. ix. p. 463) to Mr. J. J. Murphy encourages me to mention a botanical phenomenon which I witnessed in 1865, but have scarcely ever mentioned before for fear of being disbelieved. I was standing on the bank of the little river Evenlode, in Oxfordshire, looking at an old pollard willow trunk about six feet high, when I observed in the decayed wood of the tree an upright sort of staff resembling a dark-coloured old school ruler, and of about that size. I knocked away some of the touchwood above and below, and found my ruler lengthened each way. At the point where it would naturally issue at the top, I found a small twig of undoubted ash, of which the leaves were fully expanded, sprouting up among the branches of willow. Upon clearing away a little more rotten wood I laid bare another ruler, which, like the first, appeared to lengthen upward to the top of the trunk and downward to the ground, but there was no second twig of ash above. The “rulers” were rough where they were totally enclosed by the willow, and had put forth little threadlike rootlets. But the part which I found exposed to the air was smoother and looked like a true branch, but was darker than the usual colour of ash. I afterwards drew the proprietor's attention to the tree, but he could not suggest any explanation. I daresay it is there and in the same condition to this day; if anyone wished it, I could easily describe where it might be found. One explanation I have had offered is, that an ash-seed had fallen down a deep crack in the willow. But there was no sign of such a crack—no crack-like cavity—one of the “rulers” being totally and closely enveloped with the rotten wood, and the other very nearly so. Whether it would have been possible for an ash-seed to germinate in a crack which must have been at least four feet deep and probably much deeper, and was open at the top only and was certainly no larger than the shoot which it formed, is a question I must leave to botanists. Another explanation was, that as ash-roots travel for a considerable distance underground, it was possible that two such roots, finding suitable pabulum in the rotten trunk of the willow, had turned upwards. But this also I must leave to men of science, and notably to Col. Greenwood.