Crack initiation stress and strain of jointed rock containing multi-cracks under uniaxial compressive loading: A particle flow code approach

The ratio of crack initiation stress to the uniaxial compressive strength(SCI,B/SUC,B) and the ratio of axial strain at the crack initiation stress to the axial strain at the uniaxial compressive strength(B,UCB,CI,A,A/SSSS) were studied by performing numerical stress analysis on blocks having multi flaws at close spacing's under uniaxial loading using PFC3 D. The following findings are obtained: SCI,B/SUC,B has an average value of about 0.5 with a variability of ± 0.1. This range agrees quite well with the values obtained by former research. For joint inclination angle, β=90°,B,UCB,CI,A,A/SSSS is found to be around 0.48 irrespective of the value of joint continuity factor, k. No particular relation is found betweenB,UCB,CI,A,A/SSSS and β; however, the average B,UCB,CI,A,A/SSSS seems to slightly decrease with increasing k. The variability ofB,UCB,CI,A,A/SSSS is found to increase with k.Based on the cases studied in this work,B,UCB,CI,A,A/SSSS ranges between 0.3 and 0.5. This range is quite close to the range of 0.4to 0.6 obtained for SCI,B/SUC,B. The highest variability of ± 0.12 forB,UCB,CI,A,A/SSSS is obtained for k=0.8. For the remaining k values the variability ofB,UCB,CI,A,A/SSSS can be expressed within ± 0.05. This finding is very similar to the finding obtained for the variability of SCI,B/SUC,B.     

A Numerical Stress-strain Response Model of All Grades of Concretes under Uniaxial Compression

An important problem facing stress-strain response modeling of concrete is the complexity of the compressive strength grades. 21 groups of speeimens with different cubic compressive strength （56.3- 164.9 MPa ） hate beets numerically analyzed. Using only the compressive strength, a stress-strain response model of different concrete grade was established. The numerical simulation model not only qualitatively reproduces the relationship of uniaxial compressive strength, peak value stress and cubic compressive strength, but realizes the consistence of the ascending branch of stress-strain cunts with different strength grades by introducing the correction coefficient k. The results indicate k increases gradually from 0 to approximate 1 with the increase of the compressive strength, corresponding to the transition from the paracurve to straight line branch in stress-strain curves. When k is 0, the madel is identical to the Hognestad equation. A good agreement with the experiment data was obtained.     

Flow stress behavior and processing map of Al-Cu-Mg-Ag alloy during hot compression

The hot deformation behavior of Al-Cu-Mg-Ag was studied by isothermal hot compression tests in the temperature range of 573-773 K and strain rate range of 0.001-1 s^-1 on a Gleeble 1500 D thermal mechanical simulator. The results show the flow stress of Al-Cu-Mg-Ag alloy increases with strain rate and decreases after a peak value, indicating dynamic recovery and recrystallization. A hyperbolic sine relationship is found to correlate well the flow stress with the strain rate and temperature, the flow stress equation is estimated to illustrate the relation of strain rate and stress and temperature during high temperature deformation process. The processing maps exhibit two domains as optimum fields for hot deformation at different strains, including the high strain rate domain in 623-773 K and the low strain rate domain in 573-673 K.     

Calculation and analysis of stress in strata under gob pillars

Aiming at the difficulty in stress analysis for strata under pillars with actual bearing conditions, an approach was proposed to apply multi-sectional linear approximation to the characteristic curves of pillar loads, and stress of strata was calculated under pillars with linear load by calculation method for uniform load. This approach leads to a rapid analyzing method for strata stress under pillars with any form of loads. Through theoretical analysis, strata stress expressions for pillars under linear bearing conditions are obtained. In addition, two concepts, stress increase factor and stress factor, are proposed for the approximate analysis of strata stress by uniform load approximation method. It is also found that the stress increase factor of strata is related to the strata stress factor and the ratio of the minimum load on the pillar’ two ends to the maximum one; and the distribution features of stress factors and the sizes of their influencing areas in strata influenced by overlying pillars are obtained. Combining with the gob pillar conditions of Jurassic coal seam in Tongxin Coal Mine, it is demonstrated that the results obtained by stress distribution analysis of the strata stress in non-influencing areas of pillars with linear bearing through uniform load approximation are in basic accordance with the results obtained for pillars under linear bearing condition. Therefore, it is feasible and accurate to calculate stress in non-influencing area in strata under pillars with linear bearing condition by uniform load calculation method.     

Stresses induced by post-tensioned anchor in jointed rock mass

A new analytical study on stresses around a post-tensioned anchor in rocks with two perpendicular joint sets is presented. The assumptions of orthotropic elastic rock with plane strain conditions are made in derivation of the formulations. A tri-linear bond-slip constitutive law is used for modeling the tendon-grout interface behavior and debonding of this interface. The bearing plate width is also considered in the analysis. The obtained solutions are in the integral forms and numerical techniques that have been used for evaluation. In the illustrative example given, the major principal stress is compressive in the anchor free zone and compressive stress concentrations of 815 k Pa and 727 k Pa(for the anchor load of 300 k N) are observed under the bearing plate and the bond length proximal end, respectively. However, large values of tensile stresses with the maximum of-434 k Pa are formed at the bond length distal end. The results obtained using the proposed solution are compared very those of numerical method(FEM).     

Mechanical behaviors of polycrystalline NiTi SMAs of various grain sizes under impact loading

This work presents mechanical properties of the NiTi polycrystalline superelastic shape memory alloys(SMA) of 5 different grain sizes under high-speed impacts. The amorphous, nanocrystalline(40, 80, 120 nm) and coarse grain(20 μm) sheets are manufactured with cold rolling and suitable heat treatments. A Hopkinson tensile bar is used to perform tests up to 45 m/s. Highspeed camera system and digital image correlation method are used to get the strain field and particle velocity field at a sampling frequency of 2×10~6 frames/s with a resolution of 924×768 pixels. Nominal stress-strain curves are obtained for all the sheets with a strain rate of about 1000 s~(-1) and they have a similar evolution to the quasi-static case but with much higher stress levels. The rate sensitivity is increased with the grain size and the stress level can reach up to a 70% growth for a coarse grain sheet but be totally insensitive for the amorphous sheet in the strain rate from 10~(-4) to 10~3 s~(-1). A single transformation front can be found under high-speed impact(45 m/s) at the early loading stage. The speed of the transformation front is calculated from strain time histories and the highest front speed of 811 m/s is observed which is never observed before. It also reveals that the front speed depends also on the grain size. With the same loading speed, the bigger the grain size is, the slower the transformation front speed is.     

Experimental research on coal seam similar material proportion and its application

In this paper, the optimization design of the low strength mechanical test and orthogonal test have been analyzed in order to simulate the mechanical properties of thick and extra-thick coal seam accurately in a similar material simulation test. The results show that the specimen can reach a wider range of strength when cement has been used compared to that of gypsum, suggesting that cement is more suitable for making coal seam in similar material simulation tests. The uniaxial compressive strength is more sensitive to cement than coal or sand. The proportion of coal and sand do not play a decisive role in uniaxial compressive strength. The uniaxial compressive strength and specimen density decrease as the mass percent of coal and aggregate–binder ratio rise. There is a positive correlation between uniaxial compressive strength and density. The No. 5 proportion(cement: sand: water: activated carbon: coal = 6:6:7:1.1:79.9)was chosen to be used in the similar material simulation test of steeply dipping and extra-thick coal seam with a density of 0.913 g/cm~3 and an uniaxial compressive strength of 0.076 MPa which are in accordance with the similarity theory. The phenomenon of overburden stratum movement, fracture development and floor pressure relief were obtained during the similar material simulation test by using the proportion.     

Effect of Fracture Criteria on Taylor Impact Fracture

Taylor impact test on aluminum alloy 7A04-T6 presented in a previous study has been numerically evaluated using the finite element code ABAQUS/Explicit in this paper. The influence of fracture criterion in numerical simulations of the deformation and fracture behavior of Taylor rod has been studied. The following fracture criterions, included a modified version of Johnson-Cook, the Cockcroft-Latham(C-L), the constant fracture strain, the maximum shear stress and the maximum principle stress fracture models, have been used in this paper. Model constants for each criterion are calibrated from material tests. The modified version of Johnson-Cook fracture criterion with the stress triaxiality cut-off idea used can give good prediction to the Taylor impact fracture behavior. However, the C-L fracture criterion with only a constant required for calibrating by a simple test is found to give reasonable predictions. Unfortunately, the other three criteria are not able to repeat the experimentally obtained fracture behavior. The result indicates that the stress triaxiality cut-off idea is necessary to predict the Taylor impact fracture.     

Hot compressive deformation behavior and constitutive relationship of Al-Zn-Mg-Zr alloy with trace amounts of Sc

Abstract： The hot deformation behaviors of AI-Zn-Mg-Sc-Zr alloy were investigated in a temperature range of 340-500℃ and a strain rate range of 0.001-10 s 1 using uniaxial compression test on Gleeble-1500 thermal simulation machine. The results show that the flow stress increases with increasing strain and tends to be constant after a peak value. The flow stress increases with increasing strain rate and decreases with increasing deformation temperature. The phenomenon of dynamic recovery and dynamic recrystallization can be observed by microstructural evolutions. Based on the hyperbolic Arrhenius-type equation, the true stress-true strain data from the tests were employed to establish the constitutive equation considering the effect of the true strain on material constants （α, β, Q, n and A）, which reveals the dependence of the flow stress on strain, strain rate and deformation temperature. The predicted stress-strain curves are in good agreement with experimental results, which confirms that the developed constitutive equations are suitable to research the hot deformation behaviors of Al-Zn-Mg-Sc-Zr alloy.     

Flow stress behavior of Al-Cu-Li-Zr alloy containing Sc during hot compression deformation

The flow stress behavior of Al-3.5Cu-1.5Li-0.25（Sc＋Zr） alloy during hot compression deformation was studied by isothermal compression test using Gleeble-1500 thermal-mechanical simulator. Compression tests were preformed in the temperature range of 653-773 K and in the strain rate range of 0.001-10 s^-1 up to a true plastic strain of 0.7. The results indicate that the flow stress of the alloy increases with increasing strain rate at a given temperature,and decreases with increasing temperature at a given imposed strain rate. The relationship between the flow stress and the strain rate and the temperature was derived by analyzing the experimental data. The flow stress is in a hyperbolic sine relationship with the strain rate,and in an Arrhenius relationship with the temperature,which imply that the process of plastic deformation at an elevated temperature for this material is thermally activated. The flow stress of the alloy during the elevated temperature deformation can be represented by a Zener-Hollomon parameter with the inclusion of the Arrhenius term. The values of n,α and A in the analytical expressions of flow stress σ are fitted to be 5.62,0.019 MPa^-1 and 1.51×10^16 s^-1,respectively. The hot deformation activation energy is 240.85 kJ/mol.     

Influence of static pre-loading on the dynamic bending strength of concrete with particle element modeling

Experimental tests show that static pre-loading has a significant effect on the dynamic strength of concrete.Based on meso-scale particle element model,numerical simulations of dynamic bending tests with pre-loading are performed.Complete stress–strain relationships are then obtained.Significant increase in dynamic strength is found when the pre-loadings are imposed within the elastic limit of concrete.However,when the imposition of pre-loadings reaches the plastic or softening range,dynamic strengths may gradually decrease along with the increase in pre-loadings.The distribution of energy components and the failure modes are discussed to explain the mechanisms of the phenomena.     

Experimental study on mechanical behaviors of pseudo-ductile cementitious composites under biaxial compression

Experimental investigation was conducted to characterize the responses of pseudo-ductile cementitious composites (PDCCs) when subjected to uniaxial and biaxial compression.The PDCCs is a class of fiber reinforced cementitious composites with ultra-high ductility by using a low volume fraction (2%) of polyvinyl alcohol (PVA) fiber.Two different strength grades of PDCC were examined with cubic specimen size of 100 mm in the tests.The specimens were loaded with a servo-hydraulic jack at different stress ratios.The principle stresses and strains of the specimens were recorded,and the failure modes with various stress states were examined.The test results indicated that the ultimate strength of PDCCs increased due to the lateral confinement in the other principal stress direction,and the maximum ultimate strength occurred at the biaxial stress ratio of 0.25,which was very different from common concrete material.For the PDCC specimens,the biaxial strength may be lower than the uniaxial strength when subjected to biaxial compression with the stress ratio of 1.0,and the failure mode showed a shear-type failure because of the bridging effect of fibers.Finally,a failure criterion was proposed for PDCCs under biaxial compression.     

Sheet metal hardening curve determined by laminated sample and its adaptability to sheet forming processes

The hardening curve for sheet metal can be determined from the load-displacement curve of tensile specimen with rectangular cross-section. Therefore,uniaxial compression test on cylinder specimen made from laminated sample is put forward. Considering the influence of anisotropy on hardening properties and the stress state in popular forming process,plane strain compression test on cubic specimen made from laminated sample was advanced. Results show that the deformation range of hardening curves obtained from the presented methods is wide,which meets the need for the application in sheet metal forming processes. In view of the characteristics of methods presented in the paper and the stress strain state of various forming processes,the adaptability of the two methods presented in this paper is given.     

Elastodynamic stress intensity factor due to three-dimensional concentrated transient loading on the faces of a crack

The dynamic stress intensity factor for a semi-infinite crack in an otherwise unbounded elastic body is analyzed The crack is subjected to a pair of suddenly applied point loads on its faces at a distance l away from the crack tip The solution of the problem is obtained by superposition of the solutions of two simpler problems. The first of these problems is Lamb' s problem, while the second problem considers a half space with its surface subjected to the negative of the normal displacement induced by Lamb's problem in the range x>0. The latter is solved by means of integral transforms together with the application of Weiner-Hopf technique and Cagniard-de Hoop method. An exact expression is derived for the mode I stress intensity factor as a function of time for any point along the crack edge. Some features of the solution are discussed.     

Stress analytical solution for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform distributed pressure

The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common cases.Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given.The power series method of complex function is used.The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted.The distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0,45 and 90,are obtained.An example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials.In that way,stress concentration at the inner surface can be alleviated and the stress distribution is more uniform.This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.     

Mathematical Insight into Moderate Inversion Gate Delay Variability for Ultradeep Submicron Digital Circuit Design

Voltage scaling has been extensively used in industry for decades to reduce power consumption. In recent years, exploring digital circuit operation in moderate inversion has created an interest among researchers due to its immense capability to provide a perfect tradeoff between high performance and low energy operation. But circuits operating in moderate inversion are susceptible to process variations and variability. To compute variability, statistical parameters such as the probability density function (PDF) and cumulative distribution function (CDF) are required. This paper presents an analytical model framework for delay calculations utilizing log skew normal distribution for ultradeep submicron technology nodes up to 22 nm. The CDF of the proposed model is utilized to calculate minimum and maximum delays with 3σ-accuracy providing better accuracy than the conventional methods. The obtained results are also compared with Monte Carlo simulations with errors lying within the acceptable range of 2%-4%.     

Rheological behavior of continuous roll casting process of aluminum alloy

The rheological behavior of aluminum alloy and its influencing factors in physical simulation of continuous roll casting process were studied by using a Gleeble-1500 thermal-mechanical simulation tester with a set of special clamp system. The relationships between the flow stress and the strain rate in the deformation process of simulating roll casting experiment were obtained. The results show that four different characteristic stages exist in the temperature range of the whole rheological process. The first occurs when the temperature is higher than 600℃, which belongs to the creep deformation stage; the second occurs when the temperature lies in the range of 500 - 600℃, and it can be regarded as the high temperature and low stress level deformation stage; the third occurs when the temperature decreases to the range of 300 - 500℃, it is considered to be the middle stress level deformation stage; the last occurs when the temperature is less than 300℃ and the strain rate is less than 1.00 s^-1 , it belongs to middle stress level deformation stage. But when the strain rate is larger than 1.00 s^-1, it belongs to the high stress level deformation stage. And the relative constitutive models suitable for the four different stages of continuous roll casting process were established through multivariate linear regression analysis of the experimental data.     

Correlation between the cyclic stress behavior and microstructure in 316LN based on the analysis of hysteresis loops

Total strain controlled cyclic test was performed on 316 LN under uniaxial loadings. Through the partitioning of hysteresis loops, the evolution of two components of cyclic flow stress, the internal and effective stresses, was reported. The former one determines the cyclic stress response. Based on the transmission electron microscopic（TEM） observation on specimens loaded with scheduled cycles, it is found that planar dislocation structures prevail during the entire cyclic process at low strain amplitude, while a remarkable dislocation rearrangement from planar structures to heterogeneous spatial distributions is companied by a cyclic softening behavior at high strain amplitude. The competition between the evolution of the intergranular and the intragranular components of the internal stress caused by the transition of slip mode induces the cyclic hardening and softening at high strain levels. The intergranular internal stress represents the most part of the internal stress at low strain level.     

Correlation of the positive stress ratio effects on fatigue crack propagation rate of aluminium alloys based on a new parameter da/dS

In-situ SEM （Scanning Electron Microscope） observation of fatigue crack propagation in aluminium alloys reveals that crack growth occurs in a continuous way over the time period during the load cycle. Based on this observation, a new parameter da/dS is introduced to describe the fatigue crack propagation rate, which defines the fatigue crack propagation rate with the change of the applied stress at any moment of a stress cycle. The relationship is given between this new parameter and the conventional used parameter da/dN which describes the fatigue crack propagation rate per stress cycle. Using this new parameter, an analysis has been performed and a model has been set up to consider the effect of the applied stress ratio on the fatigue crack propagation rate. The obtained results have been used to correlate the published test data and a good correlation has been achieved. This method is very easy to use and no fatigue crack closure measurement is needed, therefore this model is significant in engineering application.     

Strength and elastic properties of sandstone under different testing conditions

A laboratory experimental program performed on Wuhan sandstones was presented under monotonic loading, partial cyclic loading during loading path and sine wave cyclic loading with different strain rates to compare uniaxial compression strength and elastic properties （elastic modulus and Poisson ratio） under different conditions and influence of pore fluid on them. When the loading strain rates are 10^-5, 10^-4 and 10^-3/s, uniaxial compression strengths of dry sandstones are 82.3, 126.6 and 141.6 MPa, respectively, and that of water saturated sandstones are 70.5, 108.3 and 124.1 MPa, respectively. The above results show that the uniaxial compression strength increases with the increase of strain rate, however, variation of softening coefficient is insignificant. Under monotonic loading condition, tangent modulus increases with an increment of stress （strain） to a maximum value at a certain stress level, beyond which it starts to decline. Under the partial cyclic loading during loading path condition, unloading or reloading modulus is larger than loading modulus, and unloading and reloading moduli are almost constants with respect to stress level, especially unloading modulus. Under the sine wave cyclic loading condition, tangent modulus and Poisson ratio display asymmetric ‘X＇ shape with various strain, and the average unloading modulus is larger than the average loading modulus.