Novel damage constitutive models and new quantitative identification method for stress thresholds of rocks under uniaxial compression

Four key stress thresholds exist in the compression process of rocks,i.e.,crack closure stress(σ_(cc)),crack initiation stress(σ_(ci)),crack damage stress(σ_(cd))and compressive strength(σ_(c)).The quantitative identifications of the first three stress thresholds are of great significance for characterizing the microcrack growth and damage evolution of rocks under compression.In this paper,a new method based on damage constitutive model is proposed to quantitatively measure the stress thresholds of rocks.Firstly,two different damage constitutive models were constructed based on acoustic emission(AE)counts and Weibull distribution function considering the compaction stages of the rock and the bearing capacity of the damage element.Then,the accumulative AE counts method(ACLM),AE count rate method(CRM)and constitutive model method(CMM)were introduced to determine the stress thresholds of rocks.Finally,the stress thresholds of 9 different rocks were identified by ACLM,CRM,and CMM.The results show that the theoretical stress−strain curves obtained from the two damage constitutive models are in good agreement with that of the experimental data,and the differences between the two damage constitutive models mainly come from the evolutionary differences of the damage variables.The results of the stress thresholds identified by the CMM are in good agreement with those identified by the AE methods,i.e.,ACLM and CRM.Therefore,the proposed CMM can be used to determine the stress thresholds of rocks.

Thermal damage constitutive model for rock considering damage threshold and residual strength

With the gradual depletion of mineral resources in the shallow part of the earth,resource exploitation continues to move deeper into the earth,it becomes a hot topic to simulate the whole process of rock strain softening,deformation and failure in deep environment,especially under high temperature and high pressure.On the basis of Lemaitre’s strain-equivalent principle,combined with statistics and damage theory,a statistical constitutive model of rock thermal damage under triaxial compression condition is established.At the same time,taking into account the existing damage model is difficult to reflect residual strength after rock failure,the residual strength is considered in this paper by introducing correction factor of damage variable,the model rationality is also verified by experiments.Analysis of results indicates that the damage evolution curve reflects the whole process of rock micro-cracks enclosure,initiation,expansion,penetration,and the formation of macro-cracks under coupled effect of temperature and confining pressure.Rock thermal damage shows logistic growth function with the increase of temperature.Under the same strain condition,rock total damage decreases with the rise of confining pressure.By studying the electron microscope images(SEM)of rock fracture,it is inferred that 35.40 MPa is the critical confining pressure of brittle to plastic transition for this granite.The model parameter F reflects the average strength of rock,and M reflects the morphological characteristics of rock stress–strain curves.The physical meanings of model parameters are clear and the model is suitable for complex stress states,which provides valuable references for the study of rock deformation and stability in deep engineering.

Analysis of the damage threshold of the GaAs pseudomorphic high electron mobility transistor induced by the electromagnetic pulse

An electromagnetic pulse（EMP）-induced damage model based on the internal damage mechanism of the Ga As pseudomorphic high electron mobility transistor（PHEMT） is established in this paper. With this model, the relationships among the damage power, damage energy, pulse width and signal amplitude are investigated. Simulation results show that the pulse width index from the damage power formula obtained here is higher than that from the empirical formula due to the hotspot transferring in the damage process of the device. It is observed that the damage energy is not a constant, which decreases with the signal amplitude increasing, and then changes little when the signal amplitude reaches up to a certain level.

Study on the critical stress threshold of weakly cemented sandstone damage based on the renormalization group method

During the microstructural analysis of weakly cemented sandstone,the granule components and ductile structural parts of the sandstone are typically generalized.Considering the contact between granules in the microstructure of weakly cemented sandstone,three basic units can be determined:regular tetrahedra,regular hexahedra,and regular octahedra.Renormalization group models with granule-and pore-centered weakly cemented sandstone were established,and,according to the renormalization group transformation rule,the critical stress threshold of damage was calculated.The results show that the renormalization model using regular octahedra as the basic units has the highest critical stress threshold.The threshold obtained by iterative calculations of the granule-centered model is smaller than that obtained by the pore-centered model.The granule-centered calculation provides the lower limit(18.12%),and the pore-centered model provides the upper limit(36.36%).Within this range,the weakly cemented sandstone is in a phase-like critical state.That is,the state of granule aggregation transforms from continuous to discrete.In the relative stress range of 18.12%-36.36%,the weakly cemented sandstone exhibits an increased proportion of high-frequency signals(by 83.3%)and a decreased proportion of low-frequency signals(by 23.6%).The renormalization calculation results for weakly cemented sandstone explain the high-low frequency conversion of acoustic emission signals during loading.The research reported in this paper has important significance for elucidating the damage mechanism of weakly cemented sandstone.

A thermo-mechanical damage constitutive model for deep rock considering brittleness-ductility transition characteristics

This paper developed a statistical damage constitutive model for deep rock by considering the effects of external load and thermal treatment temperature based on the distortion energy.The model parameters were determined through the extremum features of stress−strain curve.Subsequently,the model predictions were compared with experimental results of marble samples.It is found that when the treatment temperature rises,the coupling damage evolution curve shows an S-shape and the slope of ascending branch gradually decreases during the coupling damage evolution process.At a constant temperature,confining pressure can suppress the expansion of micro-fractures.As the confining pressure increases the rock exhibits ductility characteristics,and the shape of coupling damage curve changes from an S-shape into a quasi-parabolic shape.This model can well characterize the influence of high temperature on the mechanical properties of deep rock and its brittleness-ductility transition characteristics under confining pressure.Also,it is suitable for sandstone and granite,especially in predicting the pre-peak stage and peak stress of stress−strain curve under the coupling action of confining pressure and high temperature.The relevant results can provide a reference for further research on the constitutive relationship of rock-like materials and their engineering applications.

Laser-induced damage threshold in HfO_2/SiO_2 multilayer films irradiated by β-ray

Post-processing can effectively improve the resistance to laser damage in multilayer films used in a high power laser system. In this work, HfO_2/SiO_2 multilayer films are prepared by e-beam evaporation and then β-ray irradiation is employed as the post-processing method. The particle irradiation affects the laser induced damage threshold(LIDT),which includes defects, surface roughness, packing density and residual stress. The residual stress that is relaxed during irradiation changes from compressive stress into tensile stress. Our results indicate that appropriate tensile stress can improve LIDT remarkably. In view of the fact that LIDT rises from 8 J/cm^2 to 12 J/cm^2, i.e., 50% increase, after the film has been irradiated by 2.2×10^(13)/cm^2 β-ray, the particle irradiation can be used as a controllable and desirable postprocessing method to improve the resistance to laser induced damage.

High laser damage threshold coatings and damage testing technology

The laser-induced damage threshold(LIDT) of optical coating is a limited factor for development of a high peak power laser. The automatic damage testing facility was built to determine the LIDT of optics at 1 064 nm and 355 nm.. The cleanning and processing procedure of the substrate and coating technique were improved, and the damage resistance of high-reflective coating at 1 064 nm was increased.

Improvement of laser damage thresholds of fused silica by ultrasonic-assisted hydrofluoric acid etching

Polished fused silica samples were etched for different durations by using hydrofluoric（HF） acid solution with HF concentrations in an ultrasonic field. Surface and subsurface polishing residues and molecular structure parameters before and after the etching process were characterized by using a fluorescence microscope and infrared（IR） spectrometer, respectively. The laser induced damage thresholds（LIDTs） of the samples were measured by using pulsed nanosecond laser with wavelength of 355 nm. The results showed that surface and subsurface polishing residues can be effectively reduced by the acid etching process, and the LIDTs of fused silica are significantly improved. The etching effects increased with the increase of the HF concentration from 5 wt.% to 40 wt.%. The amount of polishing residues decreased with the increase of the etching duration and then kept stable. Simultaneously, with the increase of the etching time, the mechanical strength and molecular structure were improved.

Correlation between Coating Adhesion and Damage Threshold: Simple Method of Reliability Assessment for Optoelectronic Applications

It is demonstrated that inherent coating adhesion and damage threshold are correlated for Ta2O5 and HfO2 coatings widely used in optoelectronic devices. By utilizing a newly proposed 1-h boiling water test combined with the optical aging under high-power laser irradiation, we show that an optical coating that survives the 1-h boiling water test withstands the damage threshold, ensuring the field service life even in harsh environments. Besides the standard evaluation methods, which may have limitations for applications required in harsh environments, the 1-h boiling water test can serve as an alternative method of reliability assessment for optical coatings. A heuristics herein can be used as a gating item for qualification of optical coatings for various applications.

Damage and economical threshold of yellow stem borer (Tryporyza incertulas) on rice

Systematic measurements to damage and yieldloss due to yellow stem borer (YSB) weremade in the single crop and double crop areasof Hangzhou, Jiaxing, and Huzhou cities,northern Zhejiang Province in 1987-1994. YSBeggmasses were released on rice plants at 0,1, 3, 6, 9, 12 eggmasses per plot (equal to0, 495, 1 500, 3 000, 4 500, and 6 000eggmasses per hectare) from tillering to head-ing. The plot size was 20 m~2. There were 3replications randomly lined. The results in 6locations during 4-6 years of 1987-1994showed that the grain losses caused by eacheggmass at tillering stage was 59.11±2.99 g,elongating 63.18±1.51 g, and heading 74.58

Experimental verification of bridge seismic damage states quantified by calibrating analytical models with empirical field data

Bridges are one of the most vulnerable components of a highway transportation network system subjected to earthquake ground motions. Prediction of resilience and sustainability of bridge performance in a probabilistic manner provides valuable information for pre-event system upgrading and post-event functional recovery of the network. The current study integrates bridge seismic damageability information obtained through empirical, analytical and experimental procedures and quantifies threshold limits of bridge damage states consistent with the physical damage description given in HAZUS. Experimental data from a large-scale shaking table test are utilized for this purpose. This experiment was conducted at the University of Nevada, Reno, where a research team from the University of California, Irvine, participated. Observed experimental damage data are processed to identify and quantify bridge damage states in terms of rotational ductility at bridge column ends. In parallel, a mechanistic model for fragility curves is developed in such a way that the model can be calibrated against empirical fragility curves that have been constructed from damage data obtained during the 1994 Northridge earthquake. This calibration quantifies threshold values of bridge damage states and makes the analytical study consistent with damage data observed in past earthquakes. The mechanistic model is transportable and applicable to most types and sizes of bridges. Finally, calibrated damage state definitions are compared with that obtained using experimental findings. Comparison shows excellent consistency among results from analytical, empirical and experimental observations.

3D random Voronoi grain-based models for simulation of brittle rock damage and fabric-guided micro-fracturing

A grain-based distinct element model featuring three-dimensional （3D） Voronoi tessellations （randompoly-crystals） is proposed for simulation of crack damage development in brittle rocks. The grainboundaries in poly-crystal structure produced by Voronoi tessellations can represent flaws in intact rockand allow for numerical replication of crack damage progression through initiation and propagation ofmicro-fractures along grain boundaries. The Voronoi modelling scheme has been used widely in the pastfor brittle fracture simulation of rock materials. However the difficulty of generating 3D Voronoi modelshas limited its application to two-dimensional （2D） codes. The proposed approach is implemented inNeper, an open-source engine for generation of 3D Voronoi grains, to generate block geometry files thatcan be read directly into 3DEC. A series of Unconfined Compressive Strength （UCS） tests are simulated in3DEC to verify the proposed methodology for 3D simulation of brittle fractures and to investigate therelationship between each micro-parameter and the model＇s macro-response. The possibility of numericalreplication of the classical U-shape strength curve for anisotropic rocks is also investigated innumerical UCS tests by using complex-shaped （elongated） grains that are cemented to one another alongtheir adjoining sides. A micro-parameter calibration procedure is established for 3D Voronoi models foraccurate replication of the mechanical behaviour of isotropic and anisotropic （containing a fabric） rocks. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Two localized CO_2 laser treatment methods for mitigation of UV damage growth in fused silica

Two methods：high-power,short-time,single-shot irradiation（Method A） and low-power,long-time,multi-shot irradiation（Method B） are investigated to mitigate the UV damage growth in fused silica by using a 10.6-μm CO2 laser.To verify the mitigation effect of the two methods,the laser induced damage thresholds（LIDTs） of the mitigated sites are tested with a 355-nm,6.4-ns Nd：YAG laser,and the light modulation of the mitigation sites are tested with a 351-nm continuous Nd：YLF laser.The mitigated damaged sites treated with the two methods have almost the same LIDTs,which can recover to the level of pristine material.Compared with Method A,Method B produces mitigated sites with low crater depth and weak light modulation.In addition,there is no raised rim or re-deposited debris formed around the crater edge for Method B.Theoretical calculation is utilized to evaluate the central temperature of the CO2 laser beam irradiated zone and the radius of the crater.It is indicated that the calculated results are consistent with the experimental results.

Corneal damage effects induced by infrared optical parametric oscillator radiation at 3743 nm

The main aim of this paper is to investigate the corneal damage effects induced by mid-infrared optical parametric oscillator(OPO)radiation.Experiments were performed to determine the corneal damage thresholds of New Zealand white rabbit at the wavelength of 3743 nm for ex-posurédurations of 0.1 s,1.0 s and 10.0 s.Through slit-lamp biomicroscope and histopathology,corneal injury characteristics were revealed.The damage thresholds were 3.73 J/cm^(2),7.91 J/cm^(2)and 31.1 J/cm^(2),respectively,for exposure durations of 0.1 s,1.0 s and 10.0 s.The damage data was correlated by an empirical equation:Radiant exposure at the threshold=9.72×exposure duration,^(0.46)where the units of radiant exposure and exposure duration were J/cm^(2)and second.At near-threshold level,corneal injuries at 1 h post-exposure mainly involved the epithelium,and the epithelium damages repaired at 24-h post-exposure.There are sufficient safety margins be-tween the damage thresholds and the maximum permitted exposures from current international laser safety standard IEC 60825-1.

Mechanism of micro-waviness induced KH_2PO_4 crystal laser damage and the corresponding vibration source

The low laser induced damage threshold of the KH2PO4 crystal seriously restricts the output power of inertial confinement fusion.The micro-waviness on the KH2PO4 surface processed by single point diamond turning has a significant influence on the damage threshold.In this paper,the influence of micro-waviness on the damage threshold of the KH2PO4 crystal and the chief sources introducing the micro-waviness are analysed based on the combination of the Fourier modal theory and the power spectrum density method.Research results indicate that among the sub-wavinesses with different characteristic spatial frequencies there exists the most dangerous frequency which greatly reduces the damage threshold,although it may not occupy the largest proportion in the original surface.The experimental damage threshold is basically consistent with the theoretical calculation.For the processing parameters used,the leading frequency of micro-waviness which causes the damage threshold to decrease is between 350-1 μm-1 and 30-1 μm-1,especially between 90-1 μm-1 and 200-1 μm-1.Based on the classification study of the time frequencies of microwaviness,we find that the axial vibration of the spindle is the chief source introducing the micro-waviness,nearly all the leading frequencies are related to the practical spindle frequency（about 6.68 Hz,400 r/min） and a special middle frequency（between 1.029 Hz and 1.143 Hz）.

Damage Mechanics of Ferrite Ductile Iron under Uniaxial Stress

According to the principle of damage mechanics,the damage characteristics of ferrite nodular cast iron under uniaxial stress were studied by measuring electric resistance. The results show that the damage in nodular cast iron occurs when the applied stress is more than a certain extent,and the damage variable increases with stress. The evolutional law of damage variable as a function of stress was obtained.The damage threshold of nodular cast iron increases with nodularity,but it is below the yield strength,which provides reference significance to the design of machinery structure and the choice of materials.The critical damage variable is not related to the nodularity,which is about 0. 060-0. 068.

Preparation and laser induced damage properties of rare earth doped BAS glass

Rare earth doped B2O3-Al2O3-SiO2 glass （RExBAS, x=5, 10, 20; RE=La, Sm） were prepared by solid state reaction method. Optical transmission spectra of such glass were characterized by ultraviolet spectrometers, and 1064 nm laser induced damage performance was investigated through the method of ＂1-on-1＂. The results indicated that there was a strong absorptive peak near 1064 nm in SmxBAS glass, the peak was enhanced with increasing x. While LaxBAS glass was transparent to 1064 nm laser, at the same time, the results of laser induced damage showed that the anti-laser induced damage performance of such glass was strengthened with the addition of rare earth oxide. Furthermore, the laser induced damage threshold （LIDT） of SmxBAS glass was significantly higher than that of LaxBAS glass. Consequently, Sm^3＋ doping was favor in the improvement of anti-laser induced damage performance for BAS glass.

A Monte Carlo Simulation of Radiation Damage of SiC and Nb Using JA-IPU Code

MC （Monte Carlo） simulation code, JA-IPU is used to study radiation damage of SiC irradiated to spallation neutron and AmBe neutron spectra. The code is based on the major physical processes of radiation damage on incorporation of atomic collision cascade and limited to 10 MeV neutron energy. A phenomenological relation for radiation swelling is also derived. Based on the calculation of swelling, DPA （displacement per atom）, defect production efficiency and effective threshold energy, Efff from the data of MC simulation, SiC is inferred to be a highly radiation resistant material when compared with Nb and Ni metals which are used in composition of several reactor steels. Experimental results of hill-hock density measured using AFM （atomic force microscopy）, also confirm radiation resistant behavior of SiC.

The influence of space environmental factors on the laser-induced damage thresholds in optical components

This paper systematically investigated the impact mechanisms of proton irradiation,atomic oxygen irradiation and space debris collision,both individually and in combination,on the laser damage threshold and damage evolution characteristics of HfO_(2)/SiO_(2) triple-band high-reflection films and fused silica substrates using a simulated near-Earth space radiation experimental system.For the high-reflection film samples,the damage thresholds decreased by 15.38%,13.12% and 46.80% after proton,atomic oxygen and simulated space debris(penetration) irradiation,respectively.The coupling irradiation of the first two factors resulted in a decrease of 26.93%,while the combined effect of all the three factors led to a reduction of 63.19%.Similarly,the fused silica substrates exhibited the same pattern of laser damage performance degradation.Notably,the study employed high-precision fixed-point in situ measurement techniques to track in detail the microstructural changes,surface roughness and optical-thermal absorption intensity before and after proton and atomic oxygen irradiation at the same location,thus providing a more accurate and comprehensive analysis of the damage mechanisms.In addition,simulations were conducted to quantitatively analyze the transmission trajectories and concentration distribution lines of protons and atomic oxygen incident at specific angles into the target material.The research findings contribute to elucidating the laser damage performance degradation mechanism of transmissive elements in near-Earth space environments and provide technical support for the development of high-damage-threshold optical components resistant to space radiation.

Exploring fs-laser irradiation damage subthreshold behavior of dielectric mirrors via electrical measurements

With ultrafast laser systems reaching presently 10 PW peak power or operating at high repetition rates,research towards ensuring the long-term,trouble-free performance of all laser-exposed optical components is critical.Our work is focused on providing insight into the optical material behavior at fluences below the standardized laser-induced damage threshold(LIDT)value by implementing a simultaneous dual analysis of surface emitted particles using a Langmuir probe(LP)and the target current(TC).HfO_(2) and ZrO_(2) thin films deposited on fused silica substrates by pulsed laser deposition at various O_(2) pressures for defect and stoichiometry control were irradiated by Gaussian,ultrashort laser pulses(800 nm,10 Hz,70 fs)in a wide range of fluences.Both TC and LP collected signals were in good agreement with the existing theoretical description of laser–matter interaction at an ultrashort time scale.Our approach for an in situ LIDT monitoring system provides measurable signals for below-threshold irradiation conditions that indicate the endurance limit of the optical surfaces in the single-shot energy scanning mode.The LIDT value extracted from the LP-TC system is in line with the multipulse statistical analysis done with ISO 21254-2:2011(E).The implementation of the LP and TC as on-shot diagnostic tools for optical components will have a significant impact on the reliability of next-generation ultrafast and high-power laser systems.