Investigation Of Mode Ii Crack Growth Following A Very High Speed Impact

A recoverable plate impact testing technology has been developed for studying fracture mechanisms of mode II crack. With this technology, a single duration stress pulse with submicrosecond duration and high loading rates, up to 10(8) MPam(1/2)s(-1), can be produced. Dynamic failure tests of Hard-C 60# steel were carried out under asymmetrical impacting conditions with short stress-pulse loading. Experimental results show that the nucleation and growth of several microcracks ahead of the crack tip, and the interactions between them, induce unsteady crack growth. Failure mode transitions during crack growth, both from mode I crack to mode II and from brittle to ductile fracture, were observed. Based on experimental observations, a discontinuous crack growth model was established. Analysis of the crack growth mechanisms using our model shows that the shear crack extension is unsteady when the extending speed is between the Rayleigh wave speed c(R) and the shear wave speed c(S). However, when the crack advancing speed is beyond c(S), the crack grows at a steady intersonic speed approaching root 2c(S). It also shows that the transient mechanisms, such as nucleation, growth, interaction and coalescence among microcracks, make the main crack speed jump from subsonic to intersonic and the steady growth of all the subcracks causes the main crack to grow at a stable intersonic speed.

Dynamic Fracture Instability Of Tough Bulk Metallic Glass

We report the observations of a clear fractographic evolution from vein pattern, dimple structure, and then to periodic corrugation structure, followed by microbranching pattern, along the crack propagation direction in the dynamic fracture of a tough Zr41.2Ti13.8Cu12.5Ni10Be22.5 (Vit.1) bulk metallic glass (BMGs) under high-velocity plate impact. A model based on fracture surface energy dissipation and void growth is proposed to characterize this fracture pattern transition. We find that once the dynamic crack propagation velocity reaches a critical fraction of Rayleigh wave speed, the crack instability occurs; hence, crack microbranching goes ahead. Furthermore, the correlation between the critical velocity of amorphous materials and their intrinsic strength such as Young's modulus is uncovered. The results may shed new insight into dynamic fracture instability for BMGs. (C) 2008 American Institute of Physics.

Lattice instability at a fast moving crack tip

A molecular dynamics method is used to analyze the dynamic propagation of an atomistic crack tip. The simulation shows that the crack propagates at a relatively constant global velocity which is well below the Rayleigh wave velocity. However the local propagation velocity oscillates violently, and it is limited by the longitudinal wave velocity. The crack velocity oscillation is caused by a repeated process of crack tip blunting and sharpening. When the crack tip opening displacement exceeds a certain critical value, a lattice instability takes place and results in dislocation emissions from the crack tip. Based on this concept, a criterion for dislocation emission from a moving crack tip is proposed. The simulation also identifies the emitted dislocation as a source for microcrack nucleation. A simple method is used to examine this nucleation process. (C) 1996 American Institute of Physics.

Discontinuous growth mechanisms of mode II crack under high-speed impact conditions

A recoverable plate impact testing technology has been used for studying the growth mechanisms of mode II crack. The results show that interactions of microcracks ahead of a crack tip cause the crack growth unsteadily. Failure mode transitions of materials were observed. Based on the observations, a discontinuous crack growth model was established. Analysis shows that the shear crack grows unsteady as the growth speed is between the Rayleigh wave speed c(R) and the shear wave speed c(s); however, when the growth speed approaches root 2c(s), the crack grows steadily. The transient microcrack growth makes the main crack speed to jump from subsonic to intersonic and the steady growth of all the sub-cracks leads the main crack to grow stably at an intersonic speed.

Dynamic behaviors of mode III interfacial crack under a constant loading rate

In an earlier study on intersonic crack propagation, Gao et al. (J. Mech. Phys. Solids 49: 2113-2132, 2001) described molecular dynamics simulations and continuum analysis of the dynamic behaviors of a mode II dominated crack moving along a weak plane under a constant loading rate. The crack was observed to initiate its motion at a critical time after the onset of loading, at which it is rapidly accelerated to the Rayleigh wave speed and propagates at this speed for a finite time interval until an intersonic daughter crack is nucleated at a peak stress at a finite distance ahead of the original crack tip. The present article aims to analyze this behavior for a mode III crack moving along a bi-material interface subject to a constant loading rate. We begin with a crack in an initially stress-free bi-material subject to a steadily increasing stress. The crack initiates its motion at a critical time governed by the Griffith criterion. After crack initiation, two scenarios of crack propagation are investigated: the first one is that the crack moves at a constant subsonic velocity; the second one is that the crack moves at the lower shear wave speed of the two materials. In the first scenario, the shear stress ahead of the crack tip is singular with exponent -1/2, as expected; in the second scenario, the stress singularity vanishes but a peak stress is found to emerge at a distance ahead of the moving crack tip. In the latter case, a daughter crack supersonic with respect to the softer medium can be expected to emerge ahead of the initial crack once the peak stress reaches the cohesive strength of the interface.

青藏高原及邻区面波频散反演--岩石圈-软流层体系结构研究

The Qinghai-Tibet Plateau lies in the place of the continent-continent collision between Indian and Eurasian plates. Because of their interaction the shallow and deep structures are very complicated. The force system forming the tectonic patterns and driving tectonic movements is effected together by the deep part of the lithosphere and the asthenosphere. It is important to study the 3-D velocity structures, the spheres and layers structures, material properties and states of the lithosphere and the asthenosphere for getting knowledge of their formation and evolution, dynamic process, layers coupling and exchange of material and energy. Based on the Rayleigh wave dispersion theory, we study the 3-D velocity structures, the depths of interfaces and thicknesses of different layers, including the crust, the lithosphere and the asthenosphere, the lithosphere-asthenosphere system in the Qinghai-Tibet Plateau and its adjacent areas. The following tasks include: (1)The digital seismic records of 221 seismic events have been collected, whose magnitudes are larger than 5.0 over the Qinghai-Tibet Plateau and its adjacent areas. These records come from 31 digital seismic stations of GSN , CDSN、NCDSN and part of Indian stations. After making instrument response calibration and filtering, group velocities of fundamental mode of Rayleigh waves are measured using the frequency-time analysis (FTAN) to get the observed dispersions. Furthermore, we strike cluster average for those similar ray paths. Finally, 819 dispersion curves (8-150s) are ready for dispersion inversion. (2)From these dispersion curves, pure dispersion data in 2°×2° cells of the areas (18°N-42°N, 70°E-106°E) are calculated by using function expansion method, proposed by Yanovskaya. The average initial model has been constructed by taking account of global AK135 model along with geodetic, geological, geophysical, receiving function and wide-angle reflection data. Then, initial S-wave velocity structures of the crust and upper mantle in the research areas have been obtained by using linear inversion (SVD) method. (3)Taking the results of the linear inversion as the initial model, we simultaneously invert the S wave velocities and thicknesses by using non-linear inversion (improved Simulated Annealing algorithm). Moreover, during the temperature dropping the variable-scale models are used. Comparing with the linear results, the spheres and layers by the non-linear inversion can be recognized better from the velocity value and offset. (4)The Moho discontinuity and top interface of the asthenosphere are recognized from the velocity value and offset of the layers. The thicknesses of the crust, lithosphere and asthenosphere are gained. These thicknesses are helpful to studying the structural differentia between the Qinghai-Tibet Plateau and its adjacent areas and among geologic units of the plateau. The results of the inversion will provide deep geophysical evidences for studying deep dynamical mechanism and exploring metal mineral resource and oil and gas resources. The following conclusions are reached by the distributions of the S wave velocities and thicknesses of the crust, lithosphere and asthenosphere, combining with previous researches. (1)The crust is very thick in the Qinghai-Tibet Plateau, varying from 60 km to 80 km. The lithospheric thickness in the Qinghai-Tibet Plateau is thinner (130-160 km) than its adjacent areas. Its asthenosphere is relatively thicker, varies from 150 km to 230 km, and the thickest area lies in the western Qiangtang. India located in south of Main Boundary thrust has a thinner crust (32-38 km), a thicker lithosphere of about 190 km and a rather thin asthenosphere of only 60 km. Sichuan and Tarim basins have the crust thickness less than 50km. Their lithospheres are thicker than the Qinghai-Tibet Plateau, and their asthenospheres are thinner. (2)The S-wave velocity variation pattern in the lithosphere-asthenosphere system has band-belted distribution along east-westward. These variations correlate with geology structures sketched by sutures and major faults. These sutures include Main Boundary thrust (MBT), Yarlung-Zangbo River suture (YZS), Bangong Lake-Nujiang suture (BNS), Jinshajiang suture (JSJS), Kunlun edge suture (KL). In the velocity maps of the upper and middle crust, these sutures can be sketched. In velocity maps of 250-300 km depth, MBT, BNS and JSJS can be sketched. In maps of the crustal thickness, the lithospheric thickness and the asthenospheric thickness, these sutures can be still sketched. In particular, MBT can be obviously resolved in these velocity maps and thickness maps. (3)Since the collision between India and Eurasian plate, the “loss” of surface material arising from crustal shortening is caused not only by crustal thickening but also by lateral extrusion material. The source of lateral extrusion lies in the Qiangtang block. These materials extrude along the JSJS and BNS with both rotation and dispersion in Daguaiwan. Finally, it extends toward southeast direction. (4)There is the crust-mantle transition zone of no distinct velocity jump in the lithosphere beneath the Qiangtang Terrane. It has thinner lithosphere and developed thicker asthenosphere. It implies that the crust-mantle transition zone of partial melting is connected with the developed asthenosphere. The underplating of asthenosphere may thin the lithosphere. This buoyancy might be the main mechanism and deep dynamics of the uplift of the Qinghai-Tibet hinterland. At the same time, the transport of hot material with low velocity intrudes into the upper mantle and the lower crust along cracks and faults forming the crust-mantle transition zone.

KEL-TI介质的地震波场响应与成像方法研究

To deal with the problems in multi-component converted seismic wave exploration in coal fields, the wave propagating features and imaging methods of multi-component converted waves in coal measure strata are researched in this thesis firstly. The relations between viscoelasticity and anisotropy in coal measure strata are analyzed to build KEL-TI model, and which seismic wave propagating and attenuating features are researched. The disadvantages of converted wave imaging methods based on common converted point gather are analyzed and constant velocity no NMO converted wave imaging method based on common scattering point gather is put forward, according to Huygens-Fresnel principle, which applicabilities in the elastic isotropic, elastic TI and KEL-TI situations are discussed. To different model simulation data, the common scattering point gathers’ and stacked profiles’ features are analyzed. The results show that the method can image compressional waves and converted waves with high precision. Secondly, the resolution enhancing theories and methods of converted wave are researched by Rayleigh wave suppressing, converted wave static correction and poststack inverse-Q filtering. 1) The polarization filter is designed by the instantaneous polarization information of seismic waves, and the Rayleigh wave suppressing method is researched. From the spectrum analysis before and after filtering, it can be derived that the amplitudes are kept relatively. 2) To constant velocity no NMO converted wave imaging method, the static correction method based on common equivalent offset point gather is put forward and tested to the actual converted waves. 3) The relation between equivalent quality factor of converted wave, compressional wave quality factor and the ratio of compressional to shear wave velocity is derived. The compressional wave quality inversion method by first arrivals of none-offset VSP is researched, and which is then transformed to the equivalent quality factor to perform inverse-Q filtering of actual converted waves. The result has shown that the method can recover the high frequency energy of converted waves. At last, the theories and methods researched in this thesis are practiced to the 3D3C seismic exploration in Guqiao coal mine in Huainan and achieve good results.

印度与欧亚板块强烈相互作用区深部结构特征研究

The central-south Tibet is a part of the products of the continental plate collision between Eurasia and India. To study the deep structure of the study area is significant for understanding the dynamics of the continental-continental collision. A 3-D density model matched well with the observations in the central-south Tibet was proposed in this study. In addition, this study has also used numerical simulation method to prove that Quasi-Love (QL) wave is deduced by anisotropy variation but not by lateral heterogeneity. Meanwhile, anisotropy variation in the upper mantle of the Qiangtang terrane and Lhasa terrane is detected by the QL waves observed in recorded seismograms. Based on the gravity modeling, some results are summarized as follows: 1) Under the constrain of geometrical structure detected by seismic data, a 3-D density model and Moho interface are proposed by gravity inversion of the central-south Tibet. 2) The fact that the lower crustal densities are smaller than 3.2 g/cm3, suggests absence of eclogite or partial eclogitization due to delamination under the central-south Tibet. 3) Seismicity will be strong or weak in the most negative Bouguer gravity anomaly. So there is no a certain relationship between seismicity and Bouguer gravity anomaly. 4) Crustal composition are determined after temperature-pressure calibration of seismic P wave velocity. The composition of lower crust might be one or a mixture of: 1. amphibolite and greenschist facies basalt beneath the Qiangtang terrane; 2. gabbro-norite-troctolite and mafic granulite beneath the Lhasa terrane. Because the composition of the middle crust cannot be well constrained by the above data set, the data set published by Rudnick & Fountain (1995) is used for comparison. It indicated the composition of the middle crust is granulite facies and might be pelitic gneisses.Granulite facies used to be interpreted as residues of partial melting, which coincidences with the previous study on partial melting middle crust. Amphibolite facies are thought to be produced after delamination, when underplating works in the rebound of the lower crust and lithospheric mantle. From the seismology study, I have made several followed conclusions: 1) Through the numerical simulation experiment of surface wave propagating in heterogeneity media, we can find that amplitude and polarization of surface wave only change a little when considering heterogeneity. Furthermore, it is proved that QL waves, generated by surface wave scattering, are caused by lateral variation of anisotropy but not by heterogeneity. 2) QL waves are utilized to determine the variation of uppermost mantle anisotropy of the Tibetan plateau. QL waves are identified from the seismograms of the selected paths recorded by the CAD station. The location of azimuth anisotropy gradient is estimated from the group velocities of Rayleigh wave, Love wave and QL wave. It suggests that south-north lateral variation of azimuthal anisotropy locates in Tanggula mountain, and east-west lateral variation in the north of Gandese mountain with 85°E longitude and near the Jinsha river fault with 85°E longitude.

各向异性介质中的地震面波和S波分裂

Surface wave propagation in the anisotropic media and S-wave splitting in China mainland are focused in this M.S. dissertation. We firstly introduced Anderson parameters in the research of surface wave propagation in the anisotropic media were deduced, respectively. By applying the given initial model to the forward calculation of Love wave, we compared dispersion curves of Love wave in the anisotropic media with the one in the isotropic media. the results show that, although the two kind of results are similar with each other, the effect of anisotropy can not be neglected. Furthermore, the variation of anisotropy factors will result in the variation of dispersion curves, especially for high-mode one. The method of grid dispersion inversion was then described for further tectonic inversion. We also deduced inversion equation on the condition that the layered media is anisotropic, and calculated the phase-velocity partial derivatives with respect to the model parameters, P- and S-wave velocities, density, anisotropic parameters for Rayleigh wave and Love wave. Having analyzed the results of phase-velocity partial derivatives, we concluded that the derivatives within each period decreased with the depth increasing, the phase-velocity of surface wave is sensitive to the S-wave velocities and anisotropic factors and is not sensitive to the densities of layers. Dispersion data of Love wave from the events occurred during the period from 1991 to 1998 around the Qinghai and Tibet Plateau, which magnitudes are more than 5.5, have been used in the grid dispersion inversion. Those data have been preprocessed and analyzed in the F-T domain. Then the results of 1°*1° grid dispersion inversion, the pure path dispersion data, in the area of Qianghai and Tibet Plateau were obtained. As an example, dispersion data have been input for the tectonic inversion in the anisotropic media, and the results of anisotropic factors under the region of Qianghai and Tibet Plateau were initially discussed. As for the other part of this dissertation. We first introduced the phenomena of S-wave splitting and the methods for calculation the splitting parameters. Then, We applied Butterworth band-pass filter to S-wave data recorded at 8 stations in China mainland, and analyzed S-wave splitting at different frequency bands. The results show the delay time and the fast polarization directions of S-wave splitting depend upon the frequency bands. There is an absence of S-wave splitting at the station of Wulumuqi (WMQ) for the band of 0.1-0.2Hz. With the frequency band broaden, the delay time of S-wave splitting decreases at the stations of Beijing (BJI), Enshi (ENH), Kunming (KMI) and Mudanjiang (MDJ); the fast polarization direction at Enshi (ENH) changes from westward to eastward, and eastward to westward at Hailaer (HIA). The variations of delay time with bands at Lanzhou (LZH) and qiongzhong (QIZ) are similar, and there is a coherent trend of fast polarization directions at BJI, KMI and MDJ respectively. Initial interpretations to the results of frequency band-dependence of S-wave splitting were also presented.

Oscillatory Instability of Rayleigh-Marangoni-Benard Convection in Two-Layer System

The convective instabilities in two or more superposed layers heated from below were studied extensively by many scientists due to several interfacial phenomena in nature and crystal growth application. Most works of them were performed mainly on the instability behaviors induced only by buoyancy force, especially on the oscillatory behavior at onset of convection (see Gershuni et. Al.(1982), Renardy et. Al. (1985,2000), Rasenat et. Al. (1989), and Colinet et. Al.(1994)) . But the unstable situations of multi-layer liquid convection will become more complicated and interesting while considering at the same time the buoyancy effect combined with thermocapillary effect. This is the case in the gravity reduced field or thin liquid layer where the thermocapillary effect is as important as buoyancy effect. The objective of this study was to investigate theoretically the interaction between Rayleigh-Bénard instability and pure Marangoni instability in a two-layer system, and more attention focus on the oscillatory instability both at the onset of convection and with increasing supercriticality. Oscillatory behavious of Rayleigh-Marangoni-Bénard convective instability (R-M-B instability) and flow patterns are presented in the two-layer system of Silicon Oil (10cSt) over Fluorinert (FC70) for a larger various range of two-layer depth ratios (Hr=Hupper/Hdown) from 0.2 to 5.0. Both linear instability analysis and 2D numerical simulation (A=L/H=10) show that the instability of the system depends strongly on the depth ratio of two-layer liquids. The oscillatory instability regime at the onset of R-M-B convection are found theoretically in different regions of layer thickness ratio for different two-layer depth H=12,6,4,3mm. The neutral stability curve of the system displaces to right while we consider the Marangoni effect at the interface in comparison with the Rayleigh-Bénard instability of the system without the Marangoni effect (Ma=0). The numerical results show different regimes of the developing of convection in the two-layer system for different thickness ratios and some differences at the onset of pure Marangoni convection and the onset of Rayleigh-Bénard convections in two-layer liquids. Both traveling wave and standing wave were detected in the oscillatory instability regime due to the competition between Rayleigh-Bénard instability and Marangoni effect. The mechanism of the standing wave formation in the system is presented numerically in this paper. The oscillating standing wave results in the competition of the intermediate Marangoni cell and the Rayleigh convective rolls. In the two-layer system of 47v2 silicone oil over water, a transition form the steady instability to the oscillatory instability of the Rayleigh-Marangoni-Bénard Convection was found numerically above the onset of convection for ε=0.9 and Hr=0.5. We propose that this oscillatory mechanism is possible to explain the experimental observation of Degen et. Al.(1998). Experimental work in comparison with our theoretical findings on the two-layer Rayleigh-Marangoni-Bénard convection with thinner depth for H<6mm will be carried out in the near future, and more attention will be paid to new oscillatory instability regimes possible in the influence of thermocapillary effects on the competition of two-layer liquids

Diffraction integral formulas of the pulsed wave field in the temporal domain

To resolve the diffraction problems of the pulsed wave field directly in the temporal domain, we extend the Rayleigh diffraction integrals to the temporal domain and then discuss the approximation condition of this diffraction formula. (C) 1997 Optical Society of America.

Distributed Temperature Sensing System Based on Rayleigh Scattering BOTDA

A distributed temperature sensor based on Rayleigh scattering Brillouin optical time domain analysis (Rayleigh-BOTDA) is proposed in this paper. The sensor uses Rayleigh backscattering effect of microwave modulated pulse base sidebands as probe wave and a high sensitive photon counting detector for Brillouin signal intensity detection. Compared with a conventional BOTDA system, the Rayleigh-BOTDA effectively suppresses polarization-induced signal fluctuation resulting in improved signal intensity. The experimental scheme presented is simplified by using a single laser with one-end access. The temperature accuracy of the new sensing system was demonstrated as 1 degrees C on spatial resolution of 3 m.

Statistical distribution of nonlinear random wave height

A statistical model of random wave is developed using Stokes wave theory of water wave dynamics. A new nonlinear probability distribution function of wave height is presented. The results indicate that wave steepness not only could be a parameter of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. Wave height data taken from East China Normal University are used to verify the new distribution. The results indicate that the new distribution fits the measurements much better than the Rayleigh distribution.

Numerical Analysis of a Dual Polarization Mode-Locked Laser with a Quarter Wave Plate

Dynamical behaviors and frequency characteristics of an active mode-locked laser with a quarter wave plate (QWP) are numerically studied by using a set pf vectorial laser equation. Like a polarization self-modulated laser, a frequency shift of half the cavity mode spacing exists between the eigen-modes in the two neutral axes of QWP. Within the active medium, the symmetric gain and cavity structure maintain the pulse's circular polarization with left-hand and right-hand in turn for each round trip. Once the left-hand or right-hand circularly polarized pulse passes through QWP, its polarization is linear and the polarized direction is in one of the directions of i45o with respect to the neutral axes of QWP. The output components in the directions of i45" from the mirror close to QWP are all linearly polarized with a period of twice the round-trip time.

Temperature measurement of reflected shock wave by using chemical indicator

This report describes a new method for measuring the temperature of the gas behind the reflected shock wave in shock tube, corresponding to the reservoir temperature of a shock tunnel, based on the chemical reaction of small amount of CF4 premixed in the test gas. The final product C2F4 is used as the temperature indicator, which is sampled and detected by a gas chromatography in the experiment. The detected concentration of C2F4 is correlated to the temperature of the reflected shock wave with the initial pressure P-1 and test time tau as parameters in the temperature range 3 300 K < T < 5 600 K, pressure range 5 kPa < P1 <12 kPa and tau similar or equal to 0.4 ms.