Experimental and numerical study on dynamic mechanical behaviors of shale under true triaxial compression at high strain rate

High-energy gas fracturing of shale is a novel,high efficacy and eco-friendly mining technique,which is a typical dynamic perturbing behavior.To effectively extract shale gas,it is important to understand the dynamic mechanical properties of shale.Dynamic experiments on shale subjected to true triaxial compression at different strain rates are first conducted in this research.The dynamic stress-strain curves,peak strain,peak stress and failure modes of shale are investigated.The results of the study indicate that the intermediate principal stress and the minor principal stress have the significant influence on the dynamic mechanical behaviors,although this effect decreases as the strain rate increases.The characteristics of compression-shear failure primarily occur in shale subjected to triaxial compression at high strain rates,which distinguishes it from the fragmentation characteristics observed in shale under dynamic uniaxial compression.Additionally,a numerical three-dimensional Split Hopkinson Pressure Bar(3D-SHPB),which is established by coupling PFC3D and FLAC3D methods,is validated to replicate the laboratory characteristics of shale.The dynamic mechanical characteristics of shale subjected to different confining stresses are systematically investigated by the coupling PFC3D and FLAC3D method.The numerical results are in good agreement with the experimental data.

Extension of Flow Behaviour and Damage Models for Cast Iron Alloys with Strain Rate Effect

Cast iron alloys with low production cost and quite good mechanical properties are widely used in the automotive industry.To study the mechanical behavior of a typical ductile cast iron(GJS-450)with nodular graphite,uni-axial quasi-static and dynamic tensile tests at strain rates of 10^(-4),1,10,100,and 250 s^(-1)were carried out.In order to investigate the influence of stress state on the deformation and fracture parameters,specimens with various geometries were used in the experiments.Stress strain curves and fracture strains of the GJS-450 alloy in the strain rate range of 10^(-4)to 250 s^(-1)were obtained.A strain rate-dependent plastic flow model was proposed to describe the mechanical behavior in the corresponding strain-rate range.The available damage model was extended to take the strain rate into account and calibrated based on the analysis of local fracture strains.Simulations with the proposed plastic flow model and the damage model were conducted to observe the deformation and fracture process.The results show that the strain rate has obviously nonlinear effects on the yield stress and fracture strain of GJS-450 alloys.The predictions with the proposed plastic flow and damage models at various strain rates agree well with the experimental results,which illustrates that the rate-dependent plastic flow and damage models can be used to describe the mechanical behavior of cast iron alloys at elevated strain rates.The proposed plastic flow and damage models can be used to describe the deformation and fracture analysis of materials with similar properties.

THE OPTIMAL LARGE TIME BEHAVIOR OF3D QUASILINEAR HYPERBOLIC EQUATIONS WITH NONLINEAR DAMPING

We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.

Flow behavior and microstructure of ZK60 magnesium alloy compressed at high strain rate

Flow behavior and microstructure of a homogenized ZK60 magnesium alloy were investigated during compression in the temperature range of 250-400 ℃ and the strain rate range of 0.1-50 s^-1. The results showed that dynamic recrystallization （DRX） developed mainly at grain boundaries at lower strain rate （0.1-1 s^-1）, while in the case of higher strain rate （10-50 s^-1）, DRX occurred extensively both at twins and grain boundaries at all temperature range, especially at temperature lower than 350 ℃, which resulted in a more homogeneous microstructure than that under other deformation conditions. The DRX extent determines the hot workability of the workpiece, therefore, hot deformation at the strain rate of 10-50 s^-1 and in the temperature range of 250-350 ℃ was desirable for ZK60 alloy. Twin induced DRX during high strain rate compression included three steps. Firstly, twins with high dislocation subdivided the initial grain, then dislocation arrays subdivided the twins into subgrains, and after that DRX took place with a further increase of strain.

Influence of cooling rate on solidification behavior of sand-cast Mg-10Gd-3Y-0.4Zr alloy

The effect of the cooling rate ranging from 1.4 °C/s to 3.5 °C/s on the solidification behavior of the sand-cast Mg?10Gd?3Y?0.4Zr alloy was studied by computer aided cooling curve analysis (CA-CCA). With the increase in cooling rate, the nucleation temperature (Tα,N) increases from 634.8 °C to 636.3 °C, the minimum temperature (Tα,Min) decreases from 631.9 °C to 630.7 °C, the nucleation undercooling (ΔTN) increases from 2.9 °C to 5.6 °C, the beginning temperature of the eutectic reaction (Teut,N) increases, the time of the eutectic reaction shortens, solidus temperature decreases from 546.0 °C to 541.4 °C, and solidification temperature range (ΔTS) increases by 6.1 °C. The increased nucleation rate (N&) is supposed to be the main reason for the increased?TN. Increased value (Teut,N?Teut,G) and shortened time of the eutectic reaction cause the change in the volume fraction and morphology of the second phase.

Uniaxial compressive behavior of equal channel angular pressing Al at wide temperature and strain rate range

Uniaxial compressive experiments of ultrafine-grained Al fabricated by equal channel angular pressing(ECAP) method were performed at wide temperature and strain rate range. The influence of temperature on flow stress, strain hardening rate and strain rate sensitivity was investigated experimentally. The results show that both the effect of temperature on flow stress and its strain rate sensitivity of ECAPed Al is much larger than those of the coarse-grained Al. The temperature sensitivity of ultrafine-grained Al is comparatively weaker than that of the coarse-grained Al. Based on the experimental results, the apparent activation volume was estimated at different temperatures and strain rates. The forest dislocation interactions is the dominant thermally activated mechanism for ECAPed Al compressed at quasi-static strain rates, while the viscous drag plays an important role at high strain rates.

High strain rate compressive strength behavior of cemented paste backfill using split Hopkinson pressure bar

The stability of cemented paste backfill(CPB)is threatened by dynamic disturbance,but the conventional low strain rate laboratory pressure test has difficulty achieving this research purpose.Therefore,a split Hopkinson pressure bar(SHPB)was utilized to investigate the high strain rate compressive behavior of CPB with dynamic loads of 0.4,0.8,and 1.2 MPa.And the failure modes were determined by macro and micro analysis.CPB with different cement-to-tailings ratios,solid mass concentrations,and curing ages was prepared to conduct the SHPB test.The results showed that increasing the cement content,tailings content,and curing age can improve the dynamic compressive strength and elastic modulus.Under an impact load,a higher strain rate can lead to larger increasing times of the dynamic compressive strength when compared with static loading.And the dynamic compressive strength of CPB has an exponential correlation with the strain rate.The macroscopic failure modes indicated that CPB is more seriously damaged under dynamic loading.The local damage was enhanced,and fine cracks were formed in the interior of the CPB.This is because the CPB cannot dissipate the energy of the high strain rate stress wave in a short loading period.

Dynamic compressive property and failure behavior of extruded Mg-Gd-Y alloy under high temperatures and high strain rates

For the purpose of investigating the dynamic deformational behavior and failure mechanisms of magnesium under high strain rates,the Split Hopkinson Pressure Bar(SHPB)was used for investigating dynamic mechanical properties of extruded Mg-Gd-Y Magnesium alloy at ambient temperature(300 K),200℃(473 K)and 300℃(573 K)temperature.The samples after compression were analyzed by scanning electron microscope(SEM)and metallographic microscope.Dynamic mechanical properties,crack performance and plastic deformation mechanism of extruded Mg-Gd-Y Magnesium alloy along the extrusion direction(ED)were discussed.The results show that,extruded Mg-Gd-Y Magnesium alloy has the largest dynamic compressive strength which is 535 MPa at ambient temperature(300 K)and strain rate of 2826 s^(−1).When temperature increases,dynamic compressive strength decreases,while ductility increases.The dynamic compression fracture mechanism of extruded Mg-Gd-Y Magnesium alloy is multi-crack propagation and intergranular quasi-cleavage fracture at both ambient temperature and high temperature.The dynamic compressive deformation mechanism of extruded Mg-Gd-Y Magnesium alloy is a combination of twinning,slipping and dynamic recrystallization at both ambient temperature and high temperature.

Effects of different pull-out loading rates on mechanical behaviors and acoustic emission responses of fully grouted bolts

Due to the influence of mining disturbance stress,it is of great significance to better understand the bearing characteristics of fully grouted bolts under different pull-out loading rates.For this purpose,a series of laboratory pull-out tests were conducted to comprehensively investigate the effects of different pull-out loading rates on the mechanical performance and failure characteristics of fully grouted bolts.The results show that the mechanical performance of the anchored specimen presents obvious loading rate dependence and shear enhancement characteristics.With the increase of the pull-out loading rates,the maximum pull-out load increases,the displacement and time corresponding to the maximum pull-out load decrease.The accumulated acoustic emission(AE)counts,AE energy and AE events all decrease with the increase of the pull-out loading rates.The AE peak frequency has obvious divisional distribution characteristics and the amplitude is mainly distributed between 50-80 dB.With the increase of the pull-out loading rates,the local strain of the anchoring interface increases and the failure of the anchoring interface transfers to the interior of the resin grout.The accumulated AE counts are used to evaluate the damage parameter of the anchoring interface during the whole pull-out process.The analytical results are in good agreement with the experimental results.The research results may provide guidance for the support design and performance monitoring of fully grouted bolts.

Molecular dynamics analysis on bending mechanical behavior of alumina nanowires at different loading rates

The molecular dynamics(MD)model ofα-Al_(2)O_(3) nanowires in bending is established by using LAMMPS to calculate the atomic stress and strain at different loading rates in order to study the effect of loading rate on the bending mechanical behaviors of theα-Al_(2)O_(3) nanowires.Research results show that the maximum surface stress−rotation angle curves ofα-Al_(2)O_(3) nanowires at different loading rates are all divided into three stages of elastic deformation,plastic deformation and failure,where the elastic limit point can be determined by the curve symmetry during loading and unloading cycle.The loading rate has great influence on the plastic deformation but little on the elastic modulus ofα-Al_(2)O_(3) nanowires.When the loading rate is increased,the plastic deformation stage is shortened and the material is easier to fail in brittle fracture.Therefore,the elastic limit and the strength limit(determined by the direct and indirect MD simulation methods)are closer to each other.The MD simulation result ofα-Al_(2)O_(3) nanowires is verified to be valid by the good agreement with the improved loop test results.The direct MD method becomes an effective way to determine the elastic limit and the strength limit of nanoscale whiskers failed in brittle or ductile fracture at arbitrary loading rate.

Comprehensive study on quasi-static and dynamic mechanical properties and wear behavior of Mg–B4C composite compacted at several loading rates through powder metallurgy

The present study aims to fabricate and evaluate the mechanical properties and wear behavior of Mg metal matrix composite,reinforced by 0,1.5,3,5 and 10 vol.%B4C microparticles.Mg−B4C samples were fabricated at 450℃ and under different loading rates by using split Hopkinson bar(SHB),drop hammer(DH)and Instron(QS)at strain rates of 1600,800 and 0.008 s–1,respectively.The mechanical properties including microhardness,quasi-static and dynamic compressive strengths and wear behavior of samples were experimentally investigated.The results show that,the hardness of SHB and DH samples is obtained to be 20.2%and 5.7%higher than that of the QS sample,respectively.The wear rate and wear mass loss of Mg–10.0%B4C samples fabricated by SHB were determined lower than those of the QS sample by nearly 33%and 39%,respectively.The quasi-static compressive strengths of Mg−5.0%B4C are improved by 39%,30%and 29%for the SHB,DH and QS samples,respectively,in comparison with the case of pure Mg.Furthermore,it is discovered that the dynamic compressive strength of samples is 51%−110%higher than their quasi-static value with respect to the B4C content.

Effect of strain rate and water-to-cement ratio on compressive mechanical behavior of cement mortar

Effects of strain rate and water-to-cement ratio on the dynamic compressive mechanical behavior of cement mortar are investigated by split Hopkinson pressure bar(SHPB) tests. 124 specimens are subjected to dynamic uniaxial compressive loadings.Strain rate sensitivity of the materials is measured in terms of failure modes, stress-strain curves, compressive strength, dynamic increase factor(DIF) and critical strain at peak stress. A significant change in the stress-strain response of the materials with each order of magnitude increase in strain rate is clearly seen from test results. The slope of the stress-strain curve after peak value for low water-to-cement ratio is steeper than that of high water-to-cement ratio mortar. The compressive strength increases with increasing strain rate. With increase in strain rate, the dynamic increase factor(DIF) increases. However, this increase in DIF with increase in strain rate does not appear to be a function of the water-to-cement ratio. The critical compressive strain increases with the strain rate.

In-plane Tensile Behaviors of Bi-axial Warp-Knitted Composites under Quasi-static and High Strain Rate Loading

The in-plane tensile behaviors of bi-axial warp-knitted(BWK) composites under quasi-static and high strain rates loading were experimentally analyzed in this article. The tensile tests were conducted along warp direction( 0°) and weft direction( 90°) at quasi-static rate of 0. 001 s^(-1) and high strain rates ranging from 1 450 to 2 540 s^(-1),respectively. It is found that the significant strain rate sensitivity can be observed in the stress-strain curves of BWK composites. The fracture morphologies of BWK composites demonstrate that the tensile failure modes are shear failure and fiber breakage under the quasi-static testing condition while interface failure and fibers pullout are at high strain rates.

Dynamic Behavior of Interest Rates in China

This paper intuitively examines the dynamic behavior of two highly relevant interest rates in China. The first one is the government rate, which is decided and published by the central bank and can be simulated by pure jump process. Estimation of the jump intension is given out. And by different robustness test, it keeps stable. The jump size has met the condition to make interest rate within reasonable bounds and shown some meaning of economic cycle behavior. The second one is the market rate, which is estimated by spline approximation based on the transaction data of government bonds. Several models, including Vasicek model, Vasicek-GARCH （1,1） model, CIR model, and CIR-GARCH（1,1）, are empirically tested and the best performance is done by the Vasicek-GARCH（1,1） model. Furthermore, the estimate bias problem due to the near unit root process is tested and evidenced by both traditional methods and GPH test. Impact of government rate on market rate is finally checked and analyzed.

Effect of Cooling Rate on the Solidification Behavior and Microstructure of SiC_w/Al-18Si Composites

Al-18Si alloy reinforced with 15%,20% and 25%(volume fraction) SiC whiskers were prepared by squeeze casting technique and the solidification behavior and microstructure of as-prepared composites at different cooling rates were studied by DSC,optical microscope,SEM and TEM.The results show that silicon phase is nucleated on SiC whiskers.With the increase of cooling rate,the degree of undercooling increases in the composites as well as in the alloys.The increase of cooling rate leads to a reduction in the size of eutectic Al-Si and also changes its morphology from short stick to equiaxed.However,the change of primary Si is complex.The primary Si size is refined,and then coarsened with increasing cooling rate.The primary Si morphology of composites changes from agglomerate to stick.

Study on the Dynamic Behavior of Tungsten Alloy at Strain Rates up to 5 000 s^(-1)

The dynamic stress-strain curves of 93% tungsten (W) alloy in the forged state at strain rates up to (5 000 s^(-1)) and in the temperature range from 223 K to 473 K were measured with the split Hopkinson pressure bar (SHPB) technique. Based on the above experimental data a dynamic constitutive equation considering the effects of strain rate, temperature and the special microstructure of such a kind of W-alloy was proposed. The numerical simulation for the experimental process with this constitutive equation was also carried out, the results show that the constitutive relationship constructed in this paper is very satisfactory for representing the dynamic responsive behavior of material..

Research on the Behavior and Egg Fertilization Rate of Dwarf Layers and White Leghorn Chickens Fed in Floor-Rearing System

Influenced by animal welfare requirements and expensive labor cost, producers tend to feed layers in non-cage system such as floor rearing. With the development of commercial lines of dwarf layers, the property of dwarf layers＇ natural mating is drawing more and more attention. In this study, the authors hybridized Nongda Ill dwarf layers with White Leghorn chickens in floor-rearing system to research whether dwarf layers had defect in natural mating. Two steps of experiments were performed. The authors detected the fertilization rate of collected eggs, observed chickens＇ behavior in step I when a hen from other group was suddenly put into and recorded copulation number of every group in step II from 7：30 to 19：30. The results indicated that drawf cocks were as good as Leghorn cocks in natrual mating under floor-rearing system while drawf hens were better than Leghorn hens. Observation results showed no difference on reaction to intermixed hens between drawf layers and Leghorn layers. The best proportion of male to female for drawf layers was 1：8 in this experiment and dwarf cocks tended to mate dwarf hens rather than Leghorn hens.

Click-Through Rate Prediction Network Based on User Behavior Sequences and Feature Interactions

In recent years,deep learning has been widely applied in the fields of recommendation systems and click-through rate(CTR)prediction,and thus recommendation models incorporating deep learning have emerged.In addition,the design and implementation of recommendation models using information related to user behavior sequences is an important direction of current research in recommendation systems,and models calculate the likelihood of users clicking on target items based on their behavior sequence information.In order to explore the relationship between features,this paper improves and optimizes on the basis of deep interest network(DIN)proposed by Ali’s team.Based on the user behavioral sequences information,the attentional factorization machine(AFM)is integrated to obtain richer and more accurate behavioral sequence information.In addition,this paper designs a new way of calculating attention weights,which uses the relationship between the cosine similarity of any two vectors and the absolute value of their modal length difference to measure their relevance degree.Thus,a novel deep learning CTR prediction mode is proposed,that is,the CTR prediction network based on user behavior sequence and feature interactions deep interest and machines network(DIMN).We conduct extensive comparison experiments on three public datasets and one private music dataset,which are more recognized in the industry,and the results show that the DIMN obtains a better performance compared with the classical CTR prediction model.

Effects of Strain Rate and Texture on the Tensile Behavior of Pre-strained NiCr Microwires

The stress–strain behavior and strain rate sensitivity of pre-strained Ni80Cr20（Ni20Cr） were studied at strain rates from 4.8×10^（–4）s^（–1） to 1.1×10^（–1）s^（–1）. Specimens were prepared through cold drawing with abnormal plastic deformation. The texture of the specimen was characterized using electron backscatter diffraction. Results revealed that the ultimate tensile strength and ductility of the pre-strained Ni20Cr microwires simultaneously increased with increasing strain rate. Twinning-induced negative strain rate sensitivity was discovered. Positive strain rate sensitivity was present in fracture flow stress, whereas negative strain rate sensitivity was detected in flow stress values of σ_（0.5%） and σ_（1%）. Tensile test of the pre-strained Ni20Cr showed that twinning deformation predominated, whereas dislocation slip deformation dominated when twinning deformation reached saturation. The trends observed in the fractions of 2°-5°, 5°-15°, and 15°-180° grain boundaries confirmed that twinning deformation dominated the first stage.

A STUDY ON VOLTAMMETRIC BEHAVIOR OF INDIGO CARMINE AND ITS MIXTURE WITH AMARANTH AT MERCURY FILM ELECTRODE ON SILVER SUBSTRATE

The voltammetric behavior of indigo carmine at mercury film electrode on a silver substrate (MFES) was studied in this paper. It was found that indigo carmine gave a sensitive reduction peak at a potential (Vp) of -0.11 V at pH 4.0 in aqueous solution. The MFES gave good reproducibility and life time. The peak currents (ip) depended lipearly on the concentrations of indigo carmine free 0 to 100 ng/ml. The Vp and Ip of indigo carmine at MFES were independent of the concentrations of amaranth at pH 4.0, the Vp of amaranth was -0.24 V at this pH. The differences of Vp between both colorants enabled to distinguish indigo carmine free amaranth.