Dynamic Constitutive Relation Research Articles

Dynamic compressive constitutive relation and shearing instability of metallic neodymium

► Dynamic constitutive relation of Nd was determined in first compression of SHPB. ► Deformation of Nd in multi-compression of SHPB were recorded by high-speed camera. ► Constitutive relation of Nd was adjusted in modeling large deformation of Nd. ► Results of SDDM investigation of recovered Nd specimens showed shearing fracture. ► Shearing instability of Nd was estimated with constitutive relation. Based on static tests on MTS and dynamic tests on split Hopkinson pressure bar (SHPB) during the first loading, this study determined the dynamic compressive constitutive relation of metallic Nd. Based on large deformations of metallic Nd specimens generated by the multi-compressive loadings during SHPB tests, and recorded by a high-speed camera, the results of numerical simulations for SHPB test processes were used to extend the determined constitutive relation from small strain to large strain. The shearing instability strain in dynamic compressive deformations of metallic Nd was estimated with the extended constitutive relation according to the criterion given by Batra and Wei, and was compared with the average strain of recovered specimens.

Study on the Simulation of Damage Constitutive Relationship for High Strength and High Performance Concrete

The damage evolution laws of high strength and high performance concrete (HSHPC) are obtained by a large number of experiments on mechanical properties. Based on stochastic damage model, a new damage variable with two parameters is proposed to describe the damage constitutive relationship of HSHPC and the damage constitutive equation is established by boundary conditions. Compared mechanical test result of HSHPC with theoretical calculation, it is shown that the damage constitutive equation can reflect the damage characteristics of HSHPC reasonably. The research identifies a certain theoretical basis for further studying on dynamic and stochastic damage constitutive relationship of HSHPC.

Research on Dynamic Constitutive Relation of Materials Taking Account of Damage Evolution and Fracture Law for High Speed Cutting

The adiabatic shear, which may produce serrated chip, usually occurs for a large number of materials in high speed machining. Adiabatic shear band is an important damage model for metals under high-velocity deformation process. The damage evolution of micro-voids in adiabatic shear bands resulted in material fracture finally. Now the thermal softening effect, the strain rate harding effect and the strain harding effect have been discussed extensively in literature, but there is very little research on its damage effect. Based on the experiments of predecessors, this paper presents a new damage evolution equation that is dependent on strain, strain rate and is suitable for the description of voids damage evolution in adiabatic shear band. The corresponding rate-dependent constitutive relation taking account of damage evolution and temperature are proposed. The predicted results are in good agreement with the experiment datum.

Dynamic Mechanical Property of a Steel

In order to realize the dynamic mechanical property of a steel, the quasic-static and dynamic compressive and tensile mechanical tests of a steel are carried out. Based on the stress-strain curves of the steel, the constitutive relation is presented and it can be used to describe compressive and tensile mechanical property correspondently. The stress-strain curves at different strain rate and the obtained dynamic constitutive relationship show that the flow stress of the steel is increased with strain rate increased. The dynamic tension experimental results show that failure strain and stress of the steel are increased small with strain rate increased, and the fracture of tension sample is ductile fracture.

Deduction and experimental investigation of constitutive relation of liquefaction of saturated sand

According to the existing problems of liquefaction models of saturated sand that were put forward under dynamic action, on the basis of Handin-Drnevich model, a new calculating model of the dynamic constitutive relation of saturated sand was put forward. The model was based on the basic hypothesis of instantaneous limit balance according to the basic principle that the stress estate is the destroyed condition was not overstepped. The calculated method of increment nonlinear was referenced and combined with the excellence of the model of distributed particles. The process of vibrating liquefaction of saturated sand was divided into some areas. And the phenomena of shearing dilatation and unloading shrink of saturated sand were considered. On above basic a new calculating constitutive relation model was proposed. There are a few parameters in the model. The physical means of the parameters are very evident and quantized. They could be obtained from the dynamic triaxial test in door. The model was contrasted and validated with the results of the dynamic triaxial test in door. The comparison of the results of the dynamic triaxial test in door and the calculating results of the model indicates that all sorts of phenomenon appearing in the process of liquefaction of saturated sand could be more perfectly reflected by the model. Especially at the initial stage of development of pore water pressure and strain of saturated sand, the results of the dynamic triaxial test in door are consistent with the calculated results of the model very much. But there is some difference between the results at the anaphase of development of pore water pressure and strain. On the path of stress, the calculating and experimenting ultimate state surfaces are almost identical.

Dynamic damage constitutive relation of mesoscopic heterogenous brittle rock under rotation of principal stress axes

A micro-mechanics-based model is developed to investigate microcrack damage mechanism of four stages of brittle rock under rotation of the principal stress axes. They consist of linear elastic, non-linear hardening, rapid stress drop and strain softening. The frictional sliding crack model is applied to analyze microcracks nucleation, propagation and coalescence. The strain energy density factor approach is applied to determine the critical condition of microcrack nucleation, propagation and coalescence. The inelastic strain increments are formulated within the framework of thermodynamics with internal variables. Rotation of principal stress axes affect the dynamic damage constitutive relationship and the failure strength of brittle rock.

Dynamic Constitutive Relation of EMC

In this paper, dynamic properties of EMC were studied at different temperatures and different strain rates. Firstly EMC was investigated by quasi-static tests. Secondly a series of dynamic compressive experiments of EMC were conducted using the Split Hopkinson Pressure Bar (SHPB) at sectional height of strain rates. Thirdly EMC constants in ZWT model were determined from experiments. Corresponding measurements were conducted at temperatures ranging from 20°C to 160°C. The results indicate that the yield strength and flow stress of EMC increase remarkably with the increase of strain rate and it is shows that the assembled curve is fit good accordance with actual the experimental curve. However, the yield strength of EMC is a little change with the increase of temperature which is ranging from 20°C to 160°C.

Experimental Research on the Dynamic Constitutive Relation of Pure Iron at Elevated Temperatures and High Strain Rates

The experiment of dynamic mechanical behaviors test of pure iron is carried out at wide temperatures range(293～1 073 K) and high strain rates(2 000～8 500 s-1) with split Hopkinson pressure bar,which is installed with heating device and synchro assembly system.The stress-strain curves of material under temperature-strain rate coupling actions are obtained.The mechanism of effect of temperature and strain rate on the plastic flow stress of pure iron is discussed.The studies show that the pure iron has evident heat softening effect,strain rate strengthening effect and strain hardening effect,and flow stress increases with temperature decreasing and strain rate increasing.The Johnson-Cook constitutive model that is fitted by stress-strain curves obtained from experiments can provide satisfactory prediction of the plastic flow stress of pure iron.

A Dynamic Hysteresis Constitutive Relation for Giant Magnetostrictive Materials

Giant Magnetostrictive Materials (GMM), such as Terfenol-D materials, have complex nonlinear and hysteresis properties especially when the materials under pre-stresses are in a bias magnetic field and a time-varying excitation field. In order to totally describe the constitutive behavior of GMM, a static and nonlinear anhysteretic constitutive relation is analytically established by the thermodynamic theory and the theory of the Weiss molecular field. Having considered the energy loss of GMM arising from a time-varying field, such as AC magnetic field, a dynamic hysteresis constitutive relation for Terfenol-D materials is obtained in this paper. This constitutive relation can totally display the magnetic-elastic-thermal coupling properties and the effect of varied operating conditions on the minor magnetostriction loop of GMM, and are in good agreement with existing experimental data.

Calculating of the Temperature Distribution of Primary Shear Zone in Orthogonal High Speed Cutting Based on the Non-Uniform Volume Moving Heat Source

A method was presented for calculating the temperature distribution of primary shear zone in orthogonal high speed cutting based on the non-uniform volume moving heat source. The temperature distribution of primary shear zone in orthogonal high speed cutting was calculated by the dynamic plastic constitutive relationship and the distribution of strain and strain rate of primary shear zone. The results show that the temperature distribution of primary shear zone is uneven, from the original plane to the cutoff plane, the cutting temperature increases continuously. In the middle of primary shear zone, the change of cutting temperature is larger, at the position near to original plant and cutoff plane, the change of cutting temperature is smaller. The cutting temperature increases with the increase of cutting speed and cutting depth, but decreases with the increase of rake angle. The comparison with existing method shows that the method presented in this paper is not only available, but also simple, convenient and more accord with the fact of orthogonal high speed cutting.

ANALYSIS OF DYNAMIC STRESS-STRAIN RELATIONSHIP OF LOESS

This paper aims to study dynamic properties of loess. This study is helpful to the subject on how to avoid or decrease the seismic disasters on loess ground. Dynamic triaxial tests are carried out with saturated remoulded soil samples taken form loess sites in Xi'an, China. Dynamic stress and strain relationship as well as the rule of the accumulated residual strain are obtained from the test results. Linear relationship between accumulated residual strain and vibration circle under constant amplitude circular loading is presented. A hypothesis about the accumulated residual strain is proposed. 1D dynamic constitutive relationship model which can well describe the real relationship between dynamic stress and strain under irregular dynamic loading is established. Numerical program with this model is developed and an example is tested. Numerical results of hysteresis loop, accumulated residual strain, amplitude of dynamic stress and damping ratio show good agreement with test results. It is indicated that the hypothesis of accumulated residual strain and the 1D dynamic constitutive relationship model can accurately simulate the dynamic triaxial tests of saturated remoulded loess.

Effects of temperature and strain rate on dynamic properties of concrete

To study the dynamic properties of the concrete subjected to impulsive loading, stress-time curves of concrete in different velocities were measured using split Hopkinson pressure bar (SHPB). Effects of temperature and strain rate on the dynamic yield strength and constitutive relation of the concrete were analyzed. The dynamic mechanical properties of the reinforced concrete are subjected to high strain rates when it is at a relatively low temperature. But with temperature increasing, the temperature softening effect makes the strength of the concrete weaken and the impact toughness of the concrete is saliently relative to strain rate effect. So, strain rate effect, strain hardening and temperature softening work together on the dynamic mechanical capability of concrete and the relation between them is relatively complex.

Approach to minish scattering of results for split Hopkinson pressure bar test

Split Hopkinson pressure bar(SHPB) apparatus, usually used for testing behavior of material in median and high strain-rate, is now widely used in the study of rock dynamic constitutive relation, damage evolvement mechanism and energy consumption. However, the possible reasons of sampling disturbance, machining error and so on often lead to the scattering of test results, and bring ultimate difficulty for forming general test conclusion. Based on the stochastic finite element method, the uncertain parameters of specimen density ρs, specimen radius Rs, specimen elastic modulus Es and specimen length Ls in the data processing of SHPB test were considered, and the correlation between the parameters and the test results was analyzed. The results show that the specimen radius Rs has direct correlation with the test result, improving the accuracy in preparing and measuring of specimen is an effective way to improve the accuracy of test and minish the scattering of results for SHPB test.

Constitutive Relation of Yunjialing Anthracite Under Medium Strain Rate

Abstract By means of the split Hopkinson pressure bar (SHPB) testing system, this paper presents a dynamic constitutive relation of anthracite at a strain rate of e=5–85s−1. Generally, the dynamic stress-strain curve for this kind of anthracite under uni-axial compression has the following four stages: a non-linear loading stage, a plastic yielding stage, a strain-strengthening stage and an unloading breakage stage. Correspondingly, the initial elastic modulus Eb, the yielding strength σs and the ultimate strength σb increase along with an increasing strain rate. The time-dependent elasticity was identified when we analyzed the mechanical properties of anthracite. Based on characteristics of measured dynamic stress–strain curves and an analysis of existing rock dynamic constitutive models, as well as a preparatory simulation, a new visco-elastic damage model has been introduced in this paper. A linear spring is put parallel to two Maxwell units with different relaxation times to express two distinct plastic flows. The damage D is equal to [Eb–E(ɛi)]/Eb, where Eb is the beginning modulus and the E(ɛi) is the slope of a connected line between the origin point and any other point on a tested stress-strain curve. In the new constitutive model, one Maxwell unit with low relaxation time φ1 is used to describe the response of anthracite to a low strain rate, while the other, with a high relaxation time φ2 describes the response of anthracite to a high strain rate. Simulated stress-strain curves from the new model are consistent with the measured curves.

Mixed Mode Dynamic Fracture in Particulate Reinforced Functionally Graded Materials

A detailed analytical and experimental investigation is presented to understand the dynamic fracture behavior of functionally graded materials (FGMs) under mode I and mixed mode loading conditions. Crack-tip stress, strain and displacement fields for a mixed mode crack propagating at an angle from the direction of property gradation were obtained through an asymptotic analysis coupled with a displacement potential approach. This was followed by a comprehensive series of experiments to gain further insight into the behavior of propagating cracks in FGMs. Dynamic photoelasticity coupled with high-speed photography was used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the FGMs. Dynamic fracture experiments were performed using different specimen geometries to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor (K ID ) and crack-tip velocity ( $${\mathop a\limits^ \cdot }$$ ) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar $${\mathop a\limits^ \cdot }$$ -K ID relation was also obtained for matrix material (polyester) for comparison purposes. The results obtained show that crack propagation velocities in FGMs were about 80% higher than the polyester matrix. Crack arrest toughness was found to be about 10% lower than the value of local fracture toughness in FGMs.

有限要素法 (ADINA) によるRCはり衝撃挙動解析に関する研究

High safety is generally required for a reinforced concrete structure from impact force under various situations. While many research organizations have proposed the analytical technique, it is hard to say that the general-purpose analyzing method for impact behavior is fully established. In this research, various examinations are performed about the analysis model and the dynamic constitutive relation using one of general-purpose finite element method software ADINA (Automatic Dynamic Incremental Nonlinear Analysis). The applicability and its validity to impact analysis have been shown.

Stress Wave Propagation for Nonlinear Viscoelastic Polymeric Materials at High Strain Rates

ABSTRACTWithout knowing the dynamic constitutive relation of materials under high strain rates, no wave propagation can be correctly analyzed. A Series of experimental and theoretical investigation at high strain rates revealed that the nonlinear viscoelastic behavior of polymers and the related composites are well described by the Zhu-Wang-Tang (ZWT) nonlinear viscoelastic constitutive equation. The impulsive reponse of ZWT materials consists of a rate independent nonlinear elastic response and a high frequency linear viscoelastic response. The dispersion and attenuation of nonlinear viscoelastic waves mainly depend on the effective nonlinearity and the high frequency relaxation time θ2. An “effective influence distance” or “effective influence time” is defined to characterize the wave propagation range where θ2 dominates the impact relaxation process.

SW—Soil and Water: Mechanical Properties of Soils under Explosive Loading

A series of stress histories were detected successfully by plate explosive impact, using piezoelectric crystal gauges pre-positioned at different depths of clayey and sandy soils. The soil dynamic constitutive relation was obtained from the measured stress histories, by fitting a stress–depth–time surface. Results showed that the stress–strain curves had obvious stagnant-return phenomena, strain rate effect and waveform dissipation. These properties are important for correct evaluation of the dynamic behaviour of soils. Different deformation characteristics of soils were found at different depths. The surface layer displayed fluid elastoplastic property, while the middle and deeper layer displayed viscoplastic and elastic properties, respectively.

Laminated core modeling under rotational excitations including eddy currents and hysteresis

This article presents a numerical model for the electromagnetic analysis of hysteretic-laminated cores under rotational excitations. The computational approach is based on the finite element solution of a two-dimensional field magnetic problem in a homogeneous structure, where the skin effect due to macroscopic eddy currents in the lamination depth is included through a generalized dynamic constitutive relationship between B and H. The proposed model, after validation, is applied to the analysis of a laminated disk, evaluating the effects of the supply frequency and distorsion on power losses and B–H loops.

Dynamic damage constitutive model of concrete in uniaxial tension

A dynamic damage constitutive relationship for concrete in uniaxial tension is, with certain hypotheses, achieved through the constitutive model together with some performance tests of high rate deformation. The results predicted by the present theory agree pretty well with those obtained from experiments.