Spalling characteristics of high-temperature treated granitic rock at different strain rates

The dynamic spalling characteristics of rock are important for stability analysis in rock engineering.This paper presented an experimental investigation on the dynamic spalling characteristics of granite with different temperatures and strain rates.A series of dynamic spalling tests with different impact velocities were conducted on thermally treated granite at different temperatures.The dynamic spalling strengths of granite with different temperatures and strain rates were determined.A model was proposed to correlate the dynamic spalling strength of granite,high temperature and strain rate.The results show that the spalling strength of granite decreases with increasing temperature.Moreover,the spalling strength of granite with a higher strain rate is larger than that with a lower strain rate.The proposed model can describe the relationship among dynamic spalling strength of granite,high temperature and strain rate.

Analytical Solutions to Strain Rates of Reinforced Concrete Simply Supported Slabs under Blast Loads

Based on the Duhamel integral, a couple of analytical solutions are derived to predict the strain rates of concrete and steel reinforcement in reinforced concrete slabs under blast loads and to estimate their variation over depth of a cross-section along the entire length of the member. The analytical approach utilizes the single-degree-of-freedom mode for the analysis of reinforced concrete simply supported one-way panels subjected to blast loads. These analytical solutions can give the strain rate profile for any cross-section at any time and permit variations of strain rate in each time step of numerical iteration method, thus making it possible to directly incorporate strain rate effects into non-linear dynamic response analysis of structural members subjected to blast loads.

Strain Rate Effect on the Response of Blast Loaded Reinforced Concrete Slabs

Dynamic Increase Factor (DIF) due to strain rate effect was examined with documented experimental work done by Razaqpur, et al. In the experiment work, two 1000 × 1000 × 70 mm reinforced concrete slabs were constructed. The slabs were subjected to blast loads generated by the detonation of either 22.4 kg or 33.4 kg of ANFO located at a 3.0 m standoff. Blast wave characteristics, including incident and reflected pressures and reflected impulses were measured. The slabs were modeled by explicit analysis with or without strain rate effect to study their behavior under blast load to compare their predicted and observed behavior. The predicted post-blast damage and mode of failure for each model is compared with the observed damage of experimental work. It was concluded that when the dynamic increase factor added to concrete and reinforcement materials due to strain rate effect, the behavior of model under blast load become closer to experimental work.

Dynamic Response of Pultruded Glass-Graphite/Epoxy Hybrid Composites Subjected to Transverse High Strain-Rate Compression Loading

In a previous study, the energy absorption and dynamic response of different combinations of cylindrical fiber-reinforced pultruded hybrid composite samples made of unidirectional glass and graphite fiber/epoxy, were investigated under longitudinal compression loading. It was found that placing glass fibers in the inner core of composites resulted in a higher ultimate compressive strength and specific energy absorption. In this study, the dynamic responses of pultruded glass-graphite/epoxy hybrid specimens with rectangular cross-section subjected to transverse compression loading are reported. Crack initiation and propagation was monitored using a high-speed video camera, and the effects of hybridization were analyzed. It was found that the location of glass or graphite fibers inside the pultruded composites has no significant effect on the ultimate compressive strength under such transverse compression loading. The energy absorption in all the hybrid specimens was almost identical. Graphite/epoxy composite showed higher specific energy absorption due to its lower density, and glass/epoxy composite had the lowest specific energy absorption.

Relationship between diameter of split Hopkinson pressure bar and minimum loading rate under rock failure

In order to investigate the relationship between bar diameter and loading rate of the split Hopkinson pressure bar(SHPB) setup under the failure of rock specimen and realize the medium strain rate loading of specimen,new SHPB setups with different elastic bar's diameters of 22,36,50 and 75 mm were constructed.The tests were carried out on these setups at different loading rates,and the specimens had the same diameter of elastic bars and same ratio of length to diameter.The test results show that the larger the elastic bar's diameter is,the less the loading rate is needed to cause specimen failure,they show good power relationship,and that under the same strain rate loading,specimens are broken more seriously with larger diameter SHPB setup than with smaller one.

Radial explosion strain and its fracture effect from confined explosion with charge of cyclonite

Instrumented experiments were conducted in concrete models to study the explosion-induced radial strain and fracture effect of rock-like media under confined explosion with a charge of cyclonite. As a charge was exploded, two different radial strain waves were sequentially recorded by a strain gage at a distance of 80 mm from the center of charge. Through the attenuation formula of the maximum compressive strain(εrmax), the distribution of εrmax and its strain rate（ ） between the charge and gage were obtained. The effect of the two waves propagating outwards on the radial fracture of surrounding media was discussed. The results show that the two waves are pertinent to the loading of shock energy （Es） and bubble energy （Eb） against concrete surrounding charge, respectively. The former wave lasts for much shorter time than the latter. The peak values of εrmax and of the former are higher than those of the latter, respectively.

Rate-Sensitive Numerical Analysis of Dynamic Responses of Arched Blast Doors Subjected to Blast Loading

Current practice in analysis and design of blast doors subjected to blast loading considers only simple boundary conditions and material properties. The boundary conditions and material properties, in fact, have considerable influence on the response of blast doors subjected to blast loading. In this paper, the dynamic responses of a reinforced concrete arched blast door under blast loading were analyzed by the finite element program ABAQUS, combined with a previously developed elasto-viscoplastic rate-sensitive material model. And the effect of the surrounding rock mass and contact effect of the doorframe were also taken into account in the simulation. It is demonstrated that the strain-rate effect has considerable influence on the response of reinforced concrete blast door subjected to blast loading and must be taken into account in the analysis.

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.

Numerical study of RC beams under various loading rates with LS-DYNA

Having an accurate understanding of concrete behavior under effects of high strain rate loading with the aim of reducing incurred damages is of great importance. Due to complexities and high costs of experimental research, numerical studies can be an appropriate alternative for experimental methods. Therefore, in this research capability of the finite element method for predicting concrete behavior at various loading conditions is evaluated by LS-DYNA software. First, the proposed method is presented and then is validated in three stages under different conditions. Results of load-lnidspan displacement showed good agreement between experimental and finite element results. Capability of finite element method in analyses of beams under various rates of loading was also validated by low error of the results. In addition, the proposed method has reasonable ability to evaluate reinforced concrete beams under various loading rates and different conditions.

Calculation of the Distribution Rule of Equivalent Strain Rate near Explosive Welding Interface

The objectives of this study were to analyze the distribution of equivalent strain rate near the stagnation point and probe into the effects of colliding angle on strain rate. An ideal fluid model of symmetrically colliding was used to research them. Calculations showed the equivalent strain rate and the colliding half angle are closely related to each other with the material geometrical size and explosive velocity selected, the equivalent strain has large gradient within several jet thicknesses near the stagnation point, the maximal strain points are lined up along a beeline, but a curve near the stagnation point. With different colliding angles, they can be fitted by using exponential curve. That is, the exponential curve can be regarded as the token curve in explosive welding..

Dynamic behavior of frozen soil under uniaxial strain and stress conditions

The split Hopkinson pressure bar （SHPB） method is used to investigate the dynamic behavior of the artificial frozen soil under the nearly uniaxial strain and uniaxial stress conditions. The tests are conducted at the temperatures of -3 ℃, -8 ℃, -13℃, -17℃, -23℃, and -28℃ and with the strain rates from 900 s^-1 to 1500 s^-1. The nearly uniaxial stress-strain curves exhibit an elastic-plastic behavior, whereas the uniaxial stress-strain curves show a brittle behavior. The compressive strength of the frozen soil exhibits the positive strain rate and negative temperature sensitivity, and the final strain of the frozen soil shows the positive strain under the nearly uniaxial strain is greater rate sensitivity. The strength of the frozen soil than that under the uniaxial stress. After the negative confinement tests, the specimens are compressed, and the visible cracks are not observed. However, the specimens are catastrophically damaged after the uniaxial SHPB tests. A phenomenological model with the thermal sensitivity is established to describe the dynamic behavior of the confined frozen soil.

Influence of confi ning pressure and impact loading on mechanical properties of amphibolite and sericite-quartz schist

In order to investigate the dynamic mechanical properties of amphibolite and sericite-quartz schist under confi ning pressure, two rocks are subjected to impact loadings with different strain rates and confi ning pressures by using split Hopkinson pressure bar equipment with a confi ning pressure device. Based on the experimental results, the stress-strain curves are analyzed and the effects of confi ning pressure and strain rates on the dynamic compressive strength, peak strain and failure mode are summarized. The results show that:(1) The characteristics of two rocks in the ascent stage of the stressstrain curve are basically the same, but in the descent stage, the rocks gradually show plastic deformation characteristics as the confi ning pressure increases.(2) The dynamic compressive strength and peak strain of two rocks increase as the strain rate increases and the confi ning pressure effects are obvious.(3) Due to the effect of confi ning pressure, the normal stress on the damage surface of the rock increases correspondingly, the bearing capacity of the crack friction exceeds the material cohesion and the slippage of the fractured rock is controlled, which all lead to the compression and shear failure mode of rock. The theoretical analysis and experimental methods to study the dynamic failure mode and other related characteristics of rock are useful in developing standards for engineering practice.

Dynamic response and failure behavior of rock under static-dynamic loading

Dynamic response and failure behavior of rock under static-dynamic loading were studied. The effects of initial static load on the total energy dissipated during the failure process of specimen were analyzed. To simulate the engineering situation that in-situ rock experienced and obtain the dynamic loading with an intermediate strain rate, a low cycle fatigue load with the frequency from 0.5 to 5 Hz was adopted by servo-controlled Instron material testing system. The results show that the obtained strain rate increase with the increase of load frequency. The initial static load has great influence on both the energy and dynamic response of rock. Both the energy and the maximum failure load P_f decreases with the increase of initial static load. P_f under the static-dynamic loading is larger than that under only the static loading but less than that under only the dynamic loading. The load-displacement curves become nonlinear as the pre-added static load reaches the transition point which is about one third of static strength. With the increase of initial static load, Young’s modulus decreases and poisson ratio increases. It shows that rock has a lower strength and a tendency to soften under a higher initial static load. Rock may be broken more easily static-dynamic loading than under only the dynamic loading. The proposed method is useful in the investigation of constitutive relationship and failure behavior of rock under quasi-dynamic loading.

Experimental investigation of rigid confinement effects of radial strain on dynamic mechanical properties and failure modes of concrete

In this study,to confirm the effect of confining pressure on dynamic mechanical behavior and failure modes of concrete,a split Hopkinson pressure bar dynamic loading device was utilized to perform dynamic compressive experiments under confined and unconfined conditions.The confining pressure was achieved by applying a lateral metal sleeve on the testing specimen which was loaded in the axial direction.The experimental results prove that dynamic peak axial stress,dynamic peak lateral stress,and peak axial strain of concrete are strongly sensitive to the strain rate under confined conditions.Moreover,the failure patterns are significantly affected by the stress-loading rate and confining pressure.Concrete shows stronger strain rate effects under an unconfined condition than that under a confined condition.More cracks are created in concrete subjected to uniaxial dynamic compression at a higher strain rate,which can be explained by a thermal-activated mechanism.By contrast,crack generation is prevented by confinement.Fitting formulas of the dynamic peak stress and dynamic peak axial strain are established by considering strain rate effects(50–250 s-1)as well as the dynamic confining increase factor(DIFc).

Rate-dependent mechanical behavior of jointed rock with an impersistent joint under different infill conditions

Transition in the rate-dependent mechanical response of rock was investigated due to the presence of impersistent joint with different infill conditions.Four types of samples,i.e.intact,jointed with no grouting,jointed and grouted with cement,and jointed and grouted with epoxy,were fabricated using model material.A series of dynamic split Hopkinson pressure bar(SHPB) tests was conducted on prepared samples with strain rates varying between 53-130 salong with static uniaxial compression tests(10s).Progression of fracture/failure along samples was monitored using high-speed imaging and digital image correlation(DIC).Strength was observed to be significantly lower for jointed samples as compared to intact samples.However,the increasing trend of strength with strain rates remained similar for all types of samples.Epoxy was observed to be a better grout due to greater improvement in the strength of epoxy grouted jointed samples than cement grouted samples under both static and dynamic conditions.Significant changes were observed in fracture behavior(initiation,pattern and mechanism)with strain rate for intact and jointed unfilled/grouted samples.Fracturing was dominated by shear and tensile cracks at high strain rates compared to tensile cracks at low strain rates in all samples.Unlike static loading conditions,the location of cracks initiation shifts away from joint tips with increasing strain rate and depending upon existing infill conditions(unfilled/grouted).

Constitutive model of rock under static-dynamic coupling loading and experimental investigation

The importance of study on constitutive model of statically loaded rock experiencing dynamic load is set forth, and the studying methods on dynamic constitutive model are classified according to the current studying status. By way of combining statistic damage model and viscoelastic model, uni-axial and multi-axial constitutive models of statically loaded rock experiencing dynamic load (static-dynamic coupling constitutive model) under intermediate strain rate are established. The verification experiment on 2D constitutive model under different static stress and dynamic stress with different frequencies is designed and performed. It is found that there is a good agreement between the experimental stress-strain curves and the theoretical stress-strain curves.

ON CRACK-TIP STRAIA ENERGY RELEASE RATE IN NON-PRINCIPAL DIRECTIONS OF ELASTICITY FOR SIMPLE LAYER PLATE OF COMPOSITE MATERIALS

In this paper,the fracture problem in non-principal directions of elasticity for a simple layer plate of linear-elastic orthotropic composite materials is studied.The formulae of transformation between characteristic roots,coefficients of elastic compliances in non-principal directions of elasticity and corresponding parameters in principal directions of elasticity are derived.Then,the computing formulae of strain energy release rate under skew-symmetric loading in terms of engineering parameters for principal directions of elasticity are obtained by substituting crack-tip stresses and displacements into the basic formula of the strain energy release rate.

Design and Performance Evaluation of a Sustained Load Dual Grip Creep Testing Machine

The design and performance evaluation of a sustained load creep testing machine was undertaken in this research. The design was motivated by the need to make locally available, a cost effective, technically efficient, and easily operated creep testing facility;for creep behaviour studies of materials. Design drawings and purchase of materials and components for the design were undertaken after thorough evaluation of the following design and materials selection criteria: design principle and theory, local availability of raw materials and components required for the design, material properties, cost of materials and design, ease of utilization and maintenance, and basis of testing and data capture. The machine casing and frame, heating chamber (consisting of the furnace and a dual specimen mounting stage), load lever and hanger system, and the electro-technical components;were fabricated and coupled following the produced design specifications. The machine was tested and its performance was assessed using its heating efficiency, repeatability and reproducibity of experimental test results, maintainability and cost-effectiveness as criteria. It was observed from repeat tests that the machine has the capacity of generating reliable data for computing creep strain-time results. The efficiency and temperature regulating capacity of the heating unit of the machine were also observed to be very satisfactory. The cost of the design was about 112,000 Naira ($700.00) which is cheaper in comparison to similar commercial creep testing machines from abroad. The machine was also found not to pose maintenance or repairs challenges.

Implicit and Explicit Analysis of the Response of Blast Loaded Reinforced Concrete Slabs

Implicit and explicit analyses were examined with experimental work done by Razaqpur et al. In the experiment work, two 1000 × 1000 × 70 mm reinforced concrete slabs were constructed. The slabs were subjected to blast loads generated by the detonation of either 22.4 kg or 33.4 kg of ANFO located at a 3.0 m standoff. Blast wave characteristics, including incident and reflected pressures and reflected impulses were measured. The slabs were modeled by implicit and explicit analysis to study their behavior under blast load to compare their predicted and observed behavior. The post-blast damage and mode of failure of each slab were observed. It was concluded that explicit analysis provides better modeling than implicit analysis.

Vibration pore water pressure characteristics of saturated fine sand under partially drained condition

Vibration pore water pressure characteristics of saturated fine sand under partially drained condition were investigated through stress-controlled cyclic triaxial tests employed varied fine content of samples and loading frequency. In order to simulate the partially drained condition, one-way drainage for sample was implemented when cyclic loading was applied. The results show that the vibration pore water pressure's response leads the axial stress and axial strain responses, and is lagged behind or simultaneous with axial strain-rate's response for all samples in this research. In addition, the satisfactory linear relationship between vibration pore water pressure amplitude and axial strain-rate amplitude is also obtained. It means that the direct cause of vibration pore water pressure generation under partially drained conditions is not the axial stress or axial strain but the axial strain-rate. The lag-phase between pore water pressure and axial strain-rate increases with the increase of the fine content or the loading frequency.