Dynamic Stress-strain Relationship Research Articles

The Dynamic Mechanical Constitutive Equation of Concrete under High Temperture

Based on the test by the split Hopkinson Pressure Bar (SHPB), in this papaer the research on the dynamic mechanical properties of concrete under high temperture has been conducted, the influence law of temperature and strain rate on the mechanical peoperties has been analyzed, and the dynamic stress-strain curves of concrete under high temperature have been obtained. Analysis indicate that the concrete strain rate hardening effect is coupled with the high temperature weakening effect. Therefore, on the basis of classical damage theoretical model, in accordance with the concrete high-temperature dynamic mechanical characteristics, a unified equation is established to describe the whole process of concrete dynamic stress-strain relationship under high temperature, which is well coincided with the test results.

Experimental study of dynamic compressive properties of fibre reinforced concrete material with different fibres

This research conducts drop weight impact tests to study the dynamic compressive properties of fibre reinforced concrete (FRC) material with different types of fibres. The impact tests are conducted with an instrumented drop-weight impact system consisting of a hard steel drop weight, two 180 t fast response loadcells, a high-speed video camera, and a fast response data acquisition system. Seven fibre types with different shapes and material properties are considered in the study. They are synthetic fibres, undulated, cold rolled, flattened, hooked end, and two new spiral shape steel fibres developed in this study. A volume fraction of 1% fibre is used in all specimens. The concrete matrix for all FRC specimens is mixed to obtain a compressive strength of 35 MPa. The drop-weight impact experiments are conducted with two different drop heights in order to study the dynamic material properties at different strain rates. The impact forces on top and bottom of specimens are measured to investigate the axial inertia effects and the stress wave propagation effect. The high-speed video camera is used to capture the failure process, displacement and velocity responses of specimens, which are used to estimate the strain and strain rates of the specimen under impact loading. Strain gages are also used for direct strain measurements. The dynamic stress–strain relations and impact resistance of the tested specimens are compared. The influence of fibre shapes on the failure modes, strength and energy absorbing capability of FRC is discussed. The rate sensitivities of the compressive strength, Young’s modulus and toughness of FRC are also examined. The testing results demonstrate that the new spiral steel fibre proposed in this study provides better confinement to concrete matrix and thus better bonding to concrete material, therefore increases the dynamic resistance and energy absorption capacity (toughness) of FRC.

Influence of Fibre Shapes on Dynamic Compressive Behaviour of Fibre Reinforced Concrete

In this paper results are reported of impact tests performed to study the influence of different fibre types on dynamic compressive properties of fibre reinforced concrete (FRC). FRC specimens are prepared with the same concrete and 1% of fibres of different types. The compressive impact tests are conducted with an instrumented drop weight impact system consisting of a hard steel drop weight, two 180t fast response loadcells, a high speed video camera, and a fast response data acquisition system. In this study, six fibre types with different shapes and material properties are considered. They are synthetic fibres, undulated, cold rolled, flattened, hooked end and a new spiral shape steel fibres. The dynamic stress-strain relationship is obtained by fitting the load history from the bottom loadcell to the average strain history captured by the strain gages. The energy absorption capabilities are defined as the area under the stress-strain curve of FRC specimens. The performance of the new spiral shape steel fibre is discussed by comparing the test results with those obtained from specimens reinforced with other types of fibres. The influence of the fibre shapes on the failure modes, ductility and energy absorbing capacity of FRC is discussed.

Dynamic Stress-Strain Relationship of Saturated Clay by Dynamic Triaxial Test

Subgrade diseases are exposed more and more serious with raising speed of existing railway in wide range. Fro the complexity of dynamic stress-strain relationship of soil, dynamic triaxial test was used to analyze .the dynamic mechanics behavior under cyclic train load for saturated soft clay in Yangtze Delta region. Compaction coefficient, confining pressure, dynamic shear strsss ratio, inputing stimulus and loading frequence were taken into account in test. The results show that the dynamic stress-strain curves of soil specimen are provided with prominent hysteretic characteristics and area surrounded by hysteretic curves gradually augment and slope of hysteretic curve decreases with the increase of dynamic shear train amplitude. The strong correlation exists between dynamical stress and strain.

A New Method Combining Lagrangian Analysis with Hopkinson Pressure Bar Technique

Abstract: The Lagrangian analysis method is re‐analysed. It is shown that when a series of particle velocity profiles (or strain profiles) are measured to determine the dynamic stress–strain relation by the Lagrangian analysis, the crux is attributed to how to simultaneously measure both the stress and particle velocity wave profiles at a Lagrangian position by a combining stress–velocity gauge. The related experimental technique has not been satisfactorily solved yet. Thus, a new method combining the Lagrangian analysis with the Hopkinson pressure bar (HPB) technique is proposed. It is shown that the interface between the HPB and the specimen in fact provides such a combining gauge (called 1sv). Based on this technique, the so‐called ‘1sv + nv’ inverse analysis method is developed when particle velocity profiles are measured at n Lagrangian positions, and similarly the so‐called ‘1sv + nε’ inverse analysis method are developed when strain profiles are measured at n Lagrangian positions. The feasibility of the new method is evaluated by numerical simulations for a typical rate‐dependent viscoelastic material polymethyl methacrylate. The good agreement between the known ‘characteristics solutions’ and the present solutions confirms the validity of the proposed new method.

Effect of Specimen Size in the Kolsky Bar

In the current investigation, the effect of specimen size in a Kolsky Bar experiment has been analyzed. By a series of experiments, it has been shown that while determining the dynamic stress-strain relationship of a material using a non-cylindrical specimen, a judicious choice of specimen dimensions helps overcome size effects and estimates the flow stress of the material with reasonable accuracy. Similarly a dependence of the strength of the joint on the overlap area has been observed while finding the dynamic strength of an adhesive-bonded single-lap joint.

Experimental study of dynamic mechanical properties of reactive powder concrete under high-strain-rate impacts

The dynamic mechanical properties of reactive powder concrete subjected to compressive impacts with high strain rates ranging from 10 to 1.1×102 s−1 were investigated by means of SHPB (split-Hopkinson-pressure-bar) tests of the cylindrical specimens with five different steel fiber volumetric fractions. The properties of wave stress transmission, failure, strength, and energy consumption of RPC with varied fiber volumes and impact strain rates were analyzed. The influences of impact strain rates and fiber volumes on those properties were characterized as well. The general forms of the dynamic stress-strain relationships of RPC were modeled based on the experimental data. The investigations indicate that for the plain RPC the stress response is greater than the strain response, showing strong brittle performance. The RPC with a certain volume of fibers sustains higher strain rate impact and exhibits better deformability as compared with the plain RPC. With a constant fiber fraction, the peak compressive strength, corresponding peak strain and the residual strain of the fiber-reinforced RPC rise by varying amounts when the impact strain rate increases, with the residual strain demonstrating the greatest increment. Elevating the fiber content makes trivial contribution to improving the residual deformability of RPC when the impact strain rate is constant. The tests also show that the fiber content affects the peak compressive strength and the peak deformability of RPC in a different manner. With a constant impact strain rate and the fiber fraction less than 1.75%, the peak compressive strength rises with an increasing fiber volume. The peak compressive strength tends to decrease as the fiber volume exceeds 1.75%. The corresponding peak strain, however, incessantly rises with the increasing fiber volume. The total energy Edisp that RPC consumed during the period from the beginning of impacts to the time of residual strains elevates with the fiber volume increment as long as the fiber fraction is not larger than 2%. It turns to decrease if the fiber volume exceeds 2%. The added fibers make various contributions to enhancing the capability of RPC to consume energy at different loading stages. If the fiber fraction is not larger than 2%, the added fibers make more contribution to enhancing the energy consumption ability of RPC in the period before the peak strain than in the period after the peak strain. The impact strain rate, however, distinctively affects the total energy that RPC consumed and the energy consumed in the different loading periods. The higher the impact strain rate, the more the energy consumed in the stages and therefore the higher the dynamic impact toughness. The empirical relationships of the peak compressive strength, corresponding peak strain, residual strain, total consumed energy and the energy consumed in the varied periods with the impact strain rate and the fiber fraction are derived. Four generalized forms of the dynamic impact stress-strain responses of RPC are formulated by normalizing stresses and strains as the generalized coordinates and by taking account of the influences of impact strain rates and fiber volumetric fractions.

High strain rate compression behavior for Sn–37Pb eutectic alloy, lead-free Sn–1Ag–0.5Cu and Sn–3Ag–0.5Cu alloys

This paper emphasized on studying the high strain-rate compression behavior of the unleaded Sn–3Ag–0.5Cu (SAC305), Sn–1Ag–0.5Cu (SAC105) solders and the traditional Sn–37Pb eutectic solder. The split Hopkinson pressure bar (SHPB) apparatus was used to conduct high strain rate tests in order to characterize the associated high rate mechanical response of these alloys. Specimens were tested at strain rates ranging from 380 to 3030 s −1 to obtain the dynamic stress–strain relationship for the Sn–37Pb, SAC305 and SAC105 alloys. The tested soft and ductile samples experienced a large amount of elastoplastic deformation due to impact test. In the high strain rate range studied, limited strain rate hardening effect was observed for SAC305, SAC105 and Sn–37Pb alloys studied. The strain rate sensitivity parameter ( m) related to the power law creep equation was also calculated for the present solder materials at specific strain values. In addition, the saturation stresses for the leaded and lead-free solders at the strain rate range studied are also reported.

Experimental study of stress wave propagation across a filled rock joint

Dynamic properties of rock joints are of great interest to mining engineers, seismologists and geoscientists in characterizing the dynamic mechanical behavior of discontinuous rock mass. An experimental study of stress wave propagation across filled rock joints has been carried out using a modified Split Hopkinson Pressure Bar (SHPB) apparatus. Two granitic bars cored from a rock site were used as the incident and transmitter pressure bars in the SHPB tests, while a sand layer of different widths and water contents sandwiched between the two bars was adopted to simulate the filled joint. Each pressure bar was mounted with two strain gauges with a specific spacing. A wave separation method was used to process the test data. The dynamic stress–strain relation of the filled rock joints was derived from the separated strain waves. Finally, the dynamic stress–strain relations from the tests were curve-fitted by using the least square regression method and compared with a traditional joint model. It was found that the wave separation method is very effective for the SHPB tests using short granitic pressure bars. It was also concluded that the joint width and water content had significant effects on the dynamic stress–strain relation of the filled rock joints. Existing joint models were not able to sufficiently describe such dynamic properties of the filled rock joints.

Undrained dynamical behavior of Nanjing flake-shaped fine sand under cyclic loading

A series of dynamic behavior tests on Nanjing flake-shaped fine sand were performed by using the WFI cyclic triaxial apparatus made in England. The dynamic behaviors of Nanjing flake-shaped fine sand under different static deviator stress levels and cyclic stress ratios were studied. Through comparing the effective stress path under cyclic loading with static loading, the processes of liquefaction of saturated Nanjing flake-shaped fine sand with development of dynamic pore-water pressure, including the initial compact state, compression state and dilative state, were investigated. The variation of the shear stiffness with the number of cycles and cyclic strain was investigated by analyzing the secant shear modulus in each unload-reload loop of dynamic stress-strain relationship. And by means of the exponential function, the empirical equations of the relationship between secant shear modulus Gsec, shear modulus ratio Gsec/Gmax and cyclic strain e were established based on series of test results. The results show that according to different combinations of static deviator stress and cyclic stress, two kinds of failure patterns with deviator stress reversal or no deviator stress reversal are observed in the samples tested in this series, including cyclic mobility and the failure of accumulation residual strain. In addition, the degradation of dynamic shear modulus is due to the development of vibration pore-water pressure and it is observed that the shear modulus reduces with the progressive number of cycles.

DYNAMIC TENSILE AND COMPRESSIVE STRESS-STRAIN CHARACTERISTICS OF MAGNESIUM ALLOYS AT ELEVATED TEMPERATURES

The dynamic stress-strain characteristics of magnesium alloys have not been clarified sufficiently. Thus, the study investigated both the compressive and tensile dynamic stress-strain characteristics of representative magnesium alloys: AZ61A-F, ZK60A-T5 and AZ31B-F at wide strain rate and temperature ranges. About the strain rate dependency, the dynamic stresses are higher than the static ones under both compressive and tensile loads at elevated temperatures; however the dynamic stress-strain relations change slightly in the dynamic strain rate range. Thus, the magnesium alloys has little strain rate dependence. However, the elongation of the dynamic stress-strain relations under tensile load tends to be larger than that of static one. About the temperature dependency, the yield and flow stresses of the investigated magnesium alloys under compressive load decrease abruptly at temperatures higher than about 600 K in the wide strain rate range. Meanwhile, the ones under tensile load decrease with the temperature more gently. Totally, the magnesium alloys exhibit low temperature dependence. Furthermore, as well known, the yield stresses caused under the tensile load exhibit about twice as high as those under compressive load. This study verified that such a characteristic can be observed over a wide strain rate and temperature ranges.

Tensile Mechanical Properties of AM50A Alloy by Hopkinson Bar

An ultralight magnesium alloy AM50A has been investigated for its potential to be used in aerospace and automotive industry. The dynamic stress strain relation of aluminum 6061 T6 and the magnesium alloy AM50A have been obtained by using the Hopkinson bar apparatus. The strain rates range between 600 s-1 and 1300 s-1. The Al 6061 T6 results tally well with those in literature. The magnesium alloy AM50A displays about 50% higher tensile stress at the strain rate of about 1300 s-1 than at static.

Elasto/Visco-Plastic Impact of Two Equivalent Spheres Made of SUJ2

Impacts spheres are one of the basic problem in engineering field. The severity of impact is generally characterized by Coefficient of Restitution. This paper intends to investigate the effects of inelastic deformation on the Coefficient of Restitution in direct central impact of two equivalent spheres. The experiments of diret central impact of two spheres were conducted for bearing steel balls (JIS SUJ2). The steel balls were impacted by pendulum motions. Static tensile tests and split Hopkinson bar tests were conducted to obtain the static and dynamic stress-strain relations of SUJ2. The test pieces and the spheres were annealed under same condition before the experiments. The rise of yield stress with the strain rate was confirmed. The author han already dealt with the elastoplastic impact of SUJ2 balls. The elasto-plastic analysis underestimated the Coefficient of Restitution. Present paper deals with the elasto/visco-plastic impact of SUJ2 balls. Coefficients of Restitution and contact duration obtained from the experiments and those obtained from Finite Element Analysis were compared. It was shown that the experimental results were simulated well by elasto/visco-plastic analysis considering the dynamic stress-strain relation for SUJ2. It was recognized that the effect of dynamic stress-strain relation could not ignore in the low speed impacts.

413 等価二球の反発特性に及ぼす材料特性のひずみ速度依存性の影響

In this paper, Static tensile test and split hopkinson pressure bar test was carried out in order to obtain the static and dynamic stress-strain relations of SUJ2. The experiments of direct central impact of two spheres were conducted for bearing steelballs(JIS SUJ2). In the experiment the steel balls were impacted by pendulum motion and air gun. The relation between coefficient of restitution and impact velocity was obtained from the experiments. Elasto-plastic andElasto/Visco-plastic analyses were carried out by using the finite element method(F.E.M). Then the experimental and analyticalresults were compared and they agreed well.

Dynamic fracture behavior of layered alumina ceramics characterized by a split Hopkinson bar

The dynamic stress–strain relationships of the alumina with alternately dense and porous layers were characterized by a split Hopkinson bar. The yield stress increased with increasing the impact velocity at a fixed porosity, and at a given strain rate, the plateau region prolonged and the yield stress decreased with increasing the porosity. The layered alumina exhibited similar dynamic fracture behavior with the aluminum alloy foam.

704 低降伏点鋼の動的応力 : ひずみ関係のひずみ履歴依存性に関する検討(GS-3 強度・破壊(1))

704 低降伏点鋼の動的応力 : ひずみ関係のひずみ履歴依存性に関する検討(GS-3 強度・破壊(1))

Modelling of dynamic behaviour of concrete materials under blast loading

In order to model the behaviour of concrete structures under blast loading, it is essential to be able to model the dynamic strength and other strain rate dependent properties of the concrete material. In this paper, a constitutive model for predicting the dynamic strength and damage of concrete subjected to blast loading is developed. The model stems from the continuum fracture mechanics of microcrack nucleation, growth and coalescence to formulate the evolution of damage. The concrete is assumed as homogeneous continuum with pre-existing microcracks. Damage to concrete is defined as the probability of fracture at a given crack density, obtained by integrating a crack density function over time. Based on the damage function, the stress response at a particular time, and hence the dynamic stress–strain relationship, can be established for a given strain-rate. The required material constants representing initial crack properties are derived from material dynamic strength tests. Comparison with available test results shows that the proposed model can give consistent prediction of the dynamic behaviour of concrete materials. Nominal fragment sizes of concrete and fracture strain energy are also derived which can be useful in an energy-based concrete break-up and debris throw prediction procedure.

A complete three-dimensional finite element analysis of the bar-bar tensile impact apparatus

A complete three-dimensional FEM model of the Bar-Bar Tensile Impact Apparatus (BTIA) is constructed, in which the slots in the bars and the glue layers between the bars and the flat-shaped specimen are included. For elastic-plastic specimen material, Ly12cz aluminum alloy, the process of tensile impact experiments is simulated and the matching relation between the specimen geometry and the bars is investigated. Based on the FEM analysis, an iterative method is proposed to design a reasonable specimen geometry for obtaining the true dynamic stress-strain relation for a certain specimen material.

Evaluation of Dynamic Stress-Strain Relations of Ti-Alloys and Al-Alloys Based on the Thermally Activated Process Concept

Since titanium and aluminum alloys are the most promising structural materials for the high velocity vehicles, the impact tensile strength of the materials is presently investigated. Three kinds of aging treatments on the beta-titanium alloy and two on the 6061 aluminum alloy were performed, and the tensile deformation behaviors were identified in the wide range of the temperature and the strain rate. The stress- strain relations of the titanium alloy significantly depend on the temperature and the strain rate investigated. Thermally activated process concept was applied to explain the experimental results, and the stress-strain relations at high strain rates were well understood with taking account of adiabatic heating effect. In the case of the aluminum alloy, the temperature and the strain rate effects are significant only in the low temperature range. Both for the alloys investigated, the stress-strain curves depend on the microstructures, while the temperature and the strain rate effects are almost independent of the different aging treatments.

Dynamic shear stress of tough-pitch copper at high strain and high strain-rate

Dynamic shear tests for the tough-pitch copper at high strain and high strain rate was performed. The Split Hopkinson Pressure Bar (SHPB) compression test system was modified to yield a shear deformation in the specimen. Hat-shaped specimens for the tough-pitch copper were adopted to generate high strain of γ=3–4 and high strain-rate of γ=104/s. The dynamic analysis by ABAQUS 5.5/EXPLICIT code verified that shear zone can be localized in hat-shaped specimens. A proper impact velocity and the axial length of the shear localization region were determined through the elastic wave analysis. The displacement in a hat-shaped specimen is limited by a spacer ring which was installed between the specimen and the incident bar. The shear bands were obtained by measuring the direction of shear deformation and the width of deformed grain in the shear zone. The decrease of specimen length has been measured on the optical displacement transducer. Dynamic shear stress-strain relations in the tough-pitch copper were obtained at two strain-rates.