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.

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.

Laser-induced damage on large-aperture fused silica gratings

Two sets of laser-damage experiments on large-aperture fused silica optics have been carried out in a high-power laser facility. Severe damage has been found on the grating which presented dense craters on the front surface. This phenomenon is quite different from other fused silica optics, which are damaged on the rear surface. The damage possibility due to the redeposition layer was ruled out by acid-etching the grating＇s front surface. The remarkable stimulated Brillouin scattering （SBS） effect was observed in grating and the reason for the front surface damage is thought to be the backward SBS.

Characteristics of Laser-Induced Surface and Bulk Damage of Large-Aperture Deuterated Potassium Dihydrogen Phosphate at 351 nm

Deuterated potassium dihydrogen phosphate damage performance at 351 nm is studied on a large-aperture laser system. Bulk and rear-surface damage are initiated under the 3ω fluences of 6.T J/cm2 and 33/cm2, and show different growth characteristics under multiple laser irradiations with the fluence of 6 J/cm2. The size and number of bulk damage keep unchanged once initiated. However, surface damage size also does not grow, while surface damage number increases linearly with laser shots. Different damage thresholds and growth behaviors suggest different formations of bulk and surface damage precursors. The cause of surface damage is supposed to be near-surface absorbing particles buried under the sol-gel coating.

Subsurface defect characterization and laser-induced damage performance of fused silica optics polished with colloidal silica and ceria

This paper mainly focuses on the influence of colloidal silica polishing on the damage performance of fused silica optics. In this paper, nanometer sized colloidal silica and micron sized ceria are used to polish fused silica optics. The colloidal silica polished samples and ceria polished samples exhibit that the root-mean-squared （RMS） average surface roughness values are 0.7 nm and 1.0 rim, respectively. The subsurface defects and damage performance of the polished optics are analyzed and discussed. It is revealed that colloidal silica polishing will introduce much fewer absorptive con- taminant elements and subsurface damages especially no trailing indentation fracture. The 355-nm laser damage test reveals that each of the fused silica samples polished with colloidal silica has a much higher damage threshold and lower damage density than ceria polished samples. Colloidal silica polishing is potential in manufacturing high power laser optics.

The compatibly large nonlinear optical effect and high laser-induced damage threshold in a thiophosphate CsInP_(2)S_(7)constructed with[P_(2)S_(7)]^(4-)and[InS_(6)]^(9-)

It is challenging to cooperatively improve the nonlinear optical(NLO)efficiency and the laser-induced damage threshold(LIDT).This work reports a novel IR NLO materials CsInP_(2)S_(7)(CIPS)designed by combination the strategies of alkali metals substitution and microscopic NLO units PS4 introduction based on AgGaS_(2).CIPS was composed of strongly distorted[InS_(6)]^(9-)octahedra and[P_(2)S_(7)]4-dimers constructed by corner-sharing[PS_(4)]^(3-),which increase the NLO efficiency and decrease thermal expansion anisotropy simultaneously.Compared with AgGaS_(2),CIPS exhibited strong phase matchable NLO response ca.1.1×AGS@2.1μm,high LIDT ca.20.8×AgGaS_(2),and IR transparency up to 15.3μm.Structural analysis and theoretical investigation confirmed that large SHG effect and ultrahigh LIDT of CIPS originated from the synergistic contribution of[InS_(6)]^(9-)octahedra and[P_(2)S_(7)]4-dimers.These results indicate that CIPS is a promising NLO candidate in the mid-IR region,and this study provides a new approach for developing potential NLO-LIDT compatible materials.

Microstructure and 355 nm Laser-Induced Damage Characteristics of Al₂O₃Films Irradiated with Oxygen Plasma under Different Energy

Al2O3 films were prepared using electron beam evaporation at room temperature. The samples were irradiated with oxygen plasma under different energy. The variations in average surface defect density and root mean square (RMS) surface roughness were characterized using an optical microscope and an atomic force microscope. Surface average defect density increased after plasma treatment. The RMS surface roughness of the samples decreased from 1.92 nm to 1.26 nm because of surface atom restructuring after oxygen plasma conditioning. A 355 nm laser-induced damage experiment indicated that the as-grown sample with the lowest defect density exhibited a higher laser-induced damage threshold (1.12 J/cm2) than the other treated samples. Laser-induced damage images revealed that defect is one of the key factors that affect laser-induced damage on Al2O3 films.

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.

Correlation of polishing-induced shallow subsurface damages with laser-induced gray haze damages in fused silica optics

Laser-induced damage in fused silica optics greatly restricts the performances of laser facilities. Gray haze damage,which is always initiated on ceria polished optics, is one of the most important damage morphologies in fused silica optics.In this paper, the laser-induced gray haze damages of four fused silica samples polished with CeO2, Al2O3, ZrO2, and colloidal silica slurries are investigated. Four samples all present gray haze damages with much different damage densities.Then, the polishing-induced contaminant and subsurface damages in four samples are analyzed. The results reveal that the gray haze damages could be initiated on the samples without Ce contaminant and are inclined to show a tight correlation with the shallow subsurface damages.

The effect of laser beam size on laser-induced damage performance

The influence of laser beam size on laser-induced damage performance, especially damage probability and the laser-induced damage threshold （LIDT）, is investigated. It is found that damage probability is dependent on beam size when various damage precursors with different potential behaviors are involved. This causes the damage probability and the LIDT to be different between cases under a large-apertnre beam and a small-aperture beam. Moreover, the fluenee fluctuation of the large-aperture laser beam brings out hot spots, which move randomly across the beam from shot to shot. Thus this leads the most probable maximum fluenee after many shots at any location on the optical component to be several times the average beam fluence, These two effects result in the difference in the damage performance of the optical component between the cases under a large-aperture and small-aperture laser.

Laser-induced Damage of 355 nm High-reflective Mirror Caused by Nanoscale Defect

Al2O3/SiO2 multilayer high-reflective（HR） mirrors at 355 nm were prepared by electron beam evaporation, and post-irradiated with Ar/O mixture plasma. The surface defect density, reflective spectra, and laser-induced damage characteristics were measured using optical microscopy, spectrophotometry, a damage testing system, and scanning electron microscopy（SEM）, respectively. The results indicated that moderate-time of irradiation enhanced the laser-induced damage threshold（LIDT） of the mirror, but prolonged irradiation produced surface defects, resulting in LIDT degradation. LIDT of the mirrors initially increased and subsequently decreased with the plasma processing time. SEM damage morphologies of the mirrors revealed that nanoscale absorbing defects in sub-layers was one of the key factors limiting the improvement of LIDT in 355 nm HR mirror.

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.

Continuous gradient fusion class activation mapping: segmentation of laser-induced damage on large-aperture optics in dark-field images

Segmenting dark-field images of laser-induced damage on large-aperture optics in high-power laser facilities is challenged by complicated damage morphology, uneven illumination and stray light interference. Fully supervised semantic segmentation algorithms have achieved state-of-the-art performance but rely on a large number of pixel-level labels, which are time-consuming and labor-consuming to produce. LayerCAM, an advanced weakly supervised semantic segmentation algorithm, can generate pixel-accurate results using only image-level labels, but its scattered and partially underactivated class activation regions degrade segmentation performance. In this paper, we propose a weakly supervised semantic segmentation method, continuous gradient class activation mapping(CAM) and its nonlinear multiscale fusion(continuous gradient fusion CAM). The method redesigns backpropagating gradients and nonlinearly activates multiscale fused heatmaps to generate more fine-grained class activation maps with an appropriate activation degree for different damage site sizes. Experiments on our dataset show that the proposed method can achieve segmentation performance comparable to that of fully supervised algorithms.

Non-blind super-resolution reconstruction for laser-induced damage dark-field imaging of optical elements

The laser-induced damage detection images used in high-power laser facilities have a dark background,few textures with sparse and small-sized damage sites,and slight degradation caused by slight defocus and optical diffraction,which make the image superresolution(SR)reconstruction challenging.We propose a non-blind SR reconstruction method by using an exquisite mixing of high-,intermediate-,and low-frequency information at each stage of pixel reconstruction based on UNet.We simplify the channel attention mechanism and activation function to focus on the useful channels and keep the global information in the features.We pay more attention on the damage area in the loss function of our end-toend deep neural network.For constructing a high-low resolution image pairs data set,we precisely measure the point spread function(PSF)of a low-resolution imaging system by using a Bernoulli calibration pattern;the influence of different distance and lateral position on PSFs is also considered.A high-resolution camera is used to acquire the ground-truth images,which is used to create a low-resolution image pairs data set by convolving with the measured PSFs.Trained on the data set,our network has achieved better results,which proves the effectiveness of our method.

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.

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.

Damage threshold influenced by polishing imperfection distribution under 355-nm laser irradiation

A systematic interpretation of laser-induced damage in the nanosecond regime is realized with a defect distribution buried inside the redeposited layer arising from a polishing process. Under the 355-nm laser irradiation, the size dependence of the defect embedded in the fused silica can be illustrated through the thermal conduction model. Considering CeO2 as the major initiator, the size distribution with the power law model is determined from the damage probability statistics. To verify the accuracy of the size distribution, the ion output scaling with depth for the inclusion element is obtained with the secondary ion mass spectrometer. For CeO2 particulates in size of the depth interval with ion output satisfied in the negative exponential form, the corresponding density is consistent with that of the identical size in the calculated size distribution. This coincidence implies an alternative method for the density analysis of photoactive imperfections within optical components at the semi-quantitative level based on the laser damage tests.