Strain Rate Effect Of Materials Research Articles

Hysteresis behaviour modelling of woven composite using a collaborative elastoplastic damage model with fractional derivatives

The collaborative model is a new tool to represent visco-elastoplastic damaged material behaviour including hysteresis loops for woven composites under cyclic loading. The model consists of two sub-models. The first one describes a material behaviour during loading path. The elastic and the in-elastic strains as well as the in-ply damage are computed. The second part deals with hysteresis modelling during unloading path using a fractional derivative approach. Just a few parameters are required to represent the hysteresis loops. The material strain-rate effect is also taken into account by two sub-models. The parameters identification methodology is presented and the fractional derivative approximations are detailed. The collaborative model is validated for the woven composite with thermoset and thermoplastic matrixes. The precise estimation of the dissipated energy is possible.

The elastic-plastic dynamic response of stiffened plates under confined blast load

The large-deflection behavior of the clamped stiffened plates subjected to confined blast load is investigated through experimental tests, theoretical calculation and numerical simulation in this paper. The blast load in confined space lasts longer and has more complex form compared to the shock waves from an open space explosion. The influence of elastic-plastic effect on the dynamic response of blast loaded plate should be taken into account in theoretical prediction of permanent displacement. Besides, evident yield lines, which could change the deformed shape of the plates, can be always found around the clamped edges and the diagonals of plates. The global deformation of a plate cannot be represented by a simple shape function of a smooth surface. In this paper, a series of experimental tests of square stiffened plates under confined blast load was conducted. Based on experimental observation and assumed-modes, an elastic-plastic analytical model for blast loaded stiffened plates is presented, in which the effects of yield line pattern and elastic-plastic deformation are considered. The Lagrange motion equation that contains the total strain energy, potential energy and kinetic energy of stiffened plates and blast load system is established and solved. Numerical simulations are performed to investigate the influence of strain rate effect of material and boundary conditions on the dynamic responses of stiffened plates. By comparing the numerical results, the rationality of hypothetic conditions employed in analytical model is verified. The classical rigid-plastic and elastic-plastic methods were also used to calculate the dynamic response and permanent displacements of test specimens. The comparison results showed that the theoretical calculation model presented in this paper is feasible and of high precision and practicability.

Experimental study on granite and the determination of its true strain-rate effect

To accurately determine the true strain-rate effect of granite in split Hopkinson pressure bar (SHPB) tests, systematic experimental studies from quasi-static to dynamic loading on the same batch of granite samples is required. Therefore, firstly, splitting, uniaxial and triaxial compression tests were used to study the mechanical response of granite under different static stress conditions with the MTS rock mechanics test system, and the impact compression tests were performed at different strain-rates by the split Hopkinson pressure bar (SHPB). The test results show that the compressive strength increases with the increase of confinement, but the increase rate decreases as the confinement gets larger. The axial failure strain also increases with the increase of confinement. Failure is related to the composition and structure of granite, as well as the stress state. With increasing confinement, the sample is more constrained, the elastic limit strain becomes smaller, and the elastic modulus becomes larger accordingly. In addition, shear slip failure takes place under triaxial compression. In the dynamic compression tests, the strain-rate affects not only the strength of granite, but also the degree of fragmentation and the breaking pattern. Also, it has been found that the dynamic compressive strength enhancement of rocks under impact loading is due to the combined effects of the material strain-rate, lateral inertia and end friction; however, in SHPB tests they are coupled together and could not be separated from each other. To determine the material strain-rate effect of rocks in the SHPB tests, the dynamic compressive strength enhancement caused by the lateral inertial effect and end friction effect needs to be removed. Assuming that the effect of the material strain-rate, lateral inertia and end friction is uncoupled, the numerical simulation method has been employed to simulate the SHPB tests on granite. The true strain-rate effect of granite in SHPB tests is thus determined.

Effect of structurally-induced lateral confinement on split Hopkinson pressure bar test specimens of concrete-like materials

In dynamic testing of concrete-like materials, there is a need in distinguishing structural effects from genuine strain-rate effects. In this paper, this generic problem is studied by numerical simulations based on a phenomenological material model available in the commercial finite element (FE) code Abaqus. The numerical results show that the increase of the dynamic increase factor (DIF) with the increase of strain-rate in concrete-like materials in a Split Hopkinson Pressure Bar (SHPB) test is a phenomenon related not only to material strain-rate effects but also to structural effects. It was found that dilation, surface friction and lateral inertia cause lateral confinement, which enhances DIF when the strain-rate is greater than a transition strain-rate in the order of 102 s−1 . Although, genuine strain-rate effect may exist as suggested by meso-scale simulations in previous investigations, the findings in this study show that structural effects have a significant contribution to the increase of DIF, and therefore, it is necessary to correctly calibrate existing phenomenological models and interpret the results obtained from split Hopkinson pressure bar (SHPB) tests.

The Research of Strain Rate of Common Bolt Materials

In this article, quasi-static tensile and dynamic tensile tests of three common bolt materials (three kinds of steels) were conducted, and their stress-strain curves at various strain rates were obtained. By this means, the mechanical properties of three common bolt materials were analyzed. Based on the John-Cook model, author established the constitutive relation models of three materials which could describe their strain rate dependence, and used these models in the numerical simulation. The research show us that bolt material strain rate effect not only could affect the bolt impact strength, but also could not be ignored in the study of impact strength of equipments connected by bolts. The research has great significance to the study of impact resistance strength of equipments and bolts.

Numerical Investigation of the Dynamic Compressive Behaviour of Rock Materials at High Strain Rate

The dynamic compressive strength of rock materials increases with the strain rate. They are usually obtained by conducting laboratory tests such as split Hopkinson pressure bar (SHPB) test or drop-weight test. It is commonly agreed now that the dynamic increase factor (DIF) obtained from impact test is affected by lateral inertia confinement, friction confinement between the specimen and impact materials and the specimen sizes and geometries. Therefore, those derived directly from testing data do not necessarily reflect the true dynamic material properties. The influences of these parameters, however, are not straightforward to be quantified in laboratory tests. Therefore, the empirical DIF relations of rock materials obtained directly from impact tests consist of contributions from lateral inertia and end friction confinements, which need be eliminated to reflect the true dynamic material properties. Moreover, different rocks, such as granite, limestone and tuff have different material parameters, e.g., equation of state (EOS) and strength, which may also affect the DIF of materials but are not explicitly studied in the open literature. In the present study, numerical models of granite, limestone and tuff materials with different EOS and strength under impact loads are developed to simulate SHPB tests and to study the influences of EOS and strength, lateral inertia confinement and end friction confinement effects on their respective DIFs in the strain rate range between 1 and 1,000 s−1. The commercial software AUTODYN with user-provided subroutines is used to perform the numerical simulations of SHPB tests. Numerical simulation results indicate that the lateral inertia confinement, friction confinement and specimen aspect (L/D) ratio significantly influence DIF obtained from impact tests and the inertia confinement effect is different for different rocks. Based on the numerical results, quantifications on the relative contributions from the lateral inertia confinement and the material strain rate effect on DIF of granite, limestone and tuff material compressive strength are made. The effects of friction coefficient, L/D ratio and rock type on DIF are discussed. Empirical relations of DIF with strain rate for the three rock materials representing the true material strain rate effect are also proposed.

Numerical analysis of concrete material properties at high strain rate under direct tension

The tensile strength of concrete material increases with the strain rate. The dynamic tensile strength of concrete material is usually obtained by conducting laboratory tests such as direct tensile test, spall test or splitting test (Brazilian test). It is commonly agreed now that the DIF obtained from dynamic impact test is affected by lateral inertia confinement. Therefore, those derived directly from testing data do not necessarily reflect the true dynamic material properties. The influence of the lateral inertia confinement, however, is not straightforward to be quantified in laboratory tests. Moreover, concrete is a heterogeneous material with different components, but is conventionally assumed to be homogeneous, i.e. cement mortar only, in most previous experimental or numerical studies. The aggregates in concrete material are usually neglected owing to testing limitation and numerical simplification. In the present study, a mesoscale concrete material model consisting of cement mortar, aggregates and interfacial transition zone (ITZ) is developed to simulate direct tensile tests and to study the influences of the lateral inertia confinement and heterogeneity on tensile strength of concrete material with respect to strain rates between 1/s and 150/s. The commercial software AUTODYN with user provided subroutines is used to perform the numerical simulations of SHPB tests. The model is verified by testing data obtained by others. Numerical simulation results indicate that the lateral inertia confinement contributes to the dynamic increase factor (DIF) of concrete material tensile strength. The lateral inertia confinement effect is specimen size and strain rate dependent. Based on the numerical results, discussions on the relative contributions from the lateral inertia confinement and the material strain rate effect on DIF of concrete material tensile strength are made. Empirical relations are proposed to remove the influence of the lateral inertia confinement in dynamic impact tests on dynamic concrete material strength. The effect of aggregates inside the concrete specimen on its dynamic strength is also investigated. The results demonstrate that it is very important to include aggregates in experimental and numerical studies of concrete material dynamic strength, otherwise significant inaccuracy might be induced.

Investigation of the influence of design and material parameters in the progressive collapse analysis of RC structures

This contribution deals with the modelling of reinforced concrete (RC) structures in the context of progressive collapse simulations. One-dimensional nonlinear constitutive laws are used to model the material response of concrete and steel. These constitutive equations are introduced in a layered beam approach, in order to derive physically motivated relationships between generalised stresses and strains at the sectional level. This formulation is used in dynamic progressive collapse simulations to study the structural response of a multi-storey planar frame subjected to a sudden column loss (in the impulsive loading range). Thanks to the versatility of the proposed methodology, various analyses are conducted for varying structural design options and material parameters, as well as progressive collapse modelling options. In particular, the effect of the reinforcement ratio on the structural behaviour is investigated. Regarding the material modelling aspects, the influence of distinct behavioural parameters can be evaluated, such as the ultimate strain in steel and concrete or the potential material strain rate effects on the structural response. Finally, the influence of the column removal time in the sudden column loss approach can also be assessed. Significant differences are observed in terms of progressive failure patterns for the considered parametric variations.

Determination of strain rate dependent through-thickness tensile properties of textile reinforced thermoplastic composites using L-shaped beam specimens

The presented work focuses on a methodology to characterise strain rate dependent strength and elastic properties of textile reinforced composites in laminate through-thickness direction. Here, for the characterisation L-shaped beam specimens are used. The investigated composite is a fabric reinforced thermoplast made of hybrid E-glass/polypropylene yarns. The analytical solution for the determination of the through-thickness tensile strength as proposed by Lekhnitskii and Shivakumar is verified by means of an optical deformation analysis and is extended for thew determination of the through-thickness elastic modulus. Finally, the possibility of the strain rate dependent characterisation is investigated and a Johnson–Cook based modelling approach is used to represent the apparent strain rate dependency of the through-thickness failure onset. The methodology is successfully used to capture the material strain rate effects with the according strength values and model parameters over a strain rate range of 10 −4 s −1 to 10 s −1 as well as the elastic modulus.

Delay-active damage versus non-local enhancement for anisotropic damage dynamics computations with alternated loading

Abstract Anisotropic damage thermodynamics framework allows to model the concrete-like materials behavior and in particular their dissymmetric tension/compression response. To deal with dynamics applications such as impact, it is furthermore necessary to take into account the strain rate effect observed experimentally. This is done in the present work by means of anisotropic visco-damage, by introducing a material strain rate effect in the cases of positive hydrostatic stresses only. The proposed delay-damage law assumes no viscous effect in compression as the consideration of inertia effects proves sufficient to model the apparent material strength increase. High-rate dynamics applications imply to deal with wave propagation and reflection which can generate alternated loading in the impacted structure. In order to do so, the key concept of active damage is defined and introduced within both the damage criterion and the delay-damage evolution law. At the structural level, strain localization often leads to spurious mesh dependency. Three-dimensional Finite Element computations of dynamic tensile tests by spalling are presented, with visco-damage and either without or with non-local enhancement. Delay-damage, as introduced, regularizes the solution in fast dynamics. The location of the macro-crack initiated is found influenced by non-local regularization. The strain rate range in which each enhancement, delay-damage or non-local enhancement, has a regularizing effect is studied.

Bird strike simulation on sandwich composite structure of aircraft radome

A methodology for the numerical simulation of bird strike on a nose radome structure of an aircraft is presented. The simulation technique is based on a non-linear dynamic finite element analysis and is performed in two steps. The first step deals with the choice of suitable material models capable of representing the behaviors of the material systems used in the impact process. The second step deals with the numerical simulation of bird strike on aircraft radome structure. The influence on the numerical results of the critical modeling issues such as the mesh density, the substitute bird flexibility and contact interfaces parameters are discussed briefly, and the of strain rate effect of material is presented by comparing the calculations. Then, the analytical method is employed to predict the amount of energy absorbed by the radome structure. As the impact location varys, the tendency of the energy absorbed by the structure is given.

On flexible protection and stiff protection for structure safety under explosive/impact loading

Some examples of both flexible protection and stiff protection were discussed in connection with the authors research results to explore influences of stress wave effects and material strain-rate effects on structure safety protection under intense dynamic loads. Results display that in studies on structure safety protection under intense dynamic loading, either the loading is due to shock waves or projectile impact, wave propagation effects and material strain-rate effects for the structure itself and the around media, as well as the interaction between them, should be taken into account.

ひずみ速度依存性を考慮した薄肉円筒の軸方向衝突における第一ピーク荷重

ひずみ速度依存性を考慮した薄肉円筒の軸方向衝突における第一ピーク荷重

Numerical Modelling of Masonry Wall Response to Blast Loads

Masonry walls are commonly used in both residential and office buildings as either load-carrying structural components or partition walls. Failure of a load-carrying masonry wall to terrorist bombing attack or accidental gas explosion could result in collapse of the structure. The debris generated from the failed masonry wall will also impose great threats to the building occupants. Therefore dynamic response and failure of masonry walls to blast loads must be evaluated for safety assessment of building structures. In this study, a recently developed homogenised orthotropic masonry material model with strain rate effect is used to model masonry material damage. The model consists of a pressure-sensitive strength envelope, an equation of state and a double exponential damage model. In addition, an innovative approach based on the combined facture mechanics and continuum damage mechanics theory is used to estimate the masonry fragment size distributions. The method estimates masonry wall fragmentation process in two steps to avoid eroding away the masonry material. Numerical simulations of a 2.88 x 2.82 m masonry wall to blast loads generated from TNT explosions of different weights and at different standoff distances are carried out. The material strain rate effects on masonry wall dynamic responses are discussed. The numerically predicted masonry fragment size distributions are also presented.

Dynamic crushing of sandwich panels with prismatic lattice cores

The dynamic out-of-plane compressive response of stainless steel corrugated and Y-frame sandwich cores have been investigated for impact velocities ranging from quasi-static to 200 ms −1. Laboratory-scale sandwich cores of relative density 2.5% were manufactured and the stresses on the front and rear faces of the dynamically compressed sandwich cores were measured using a direct impact Kolsky bar. Direct observational evidence is provided for micro-inertial stabilisation of both topologies against elastic buckling at impact velocities below 30 ms −1. At higher impact velocities, plastic waves within the core members result in the front face stresses increasing with increasing velocity while the rear face stresses remain approximately constant. While the finite element calculations predict the rear face stresses and dynamic deformation modes to reasonable accuracy, the relatively slow response time of the measurement apparatus results in poor agreement between the measured and predicted front face stresses. The finite element calculations also demonstrate that material strain-rate effects have a negligible effect upon the dynamic compressive response of laboratory-scale and full-scale sandwich cores.

Experimental and numerical investigation of static and dynamic axial crushing of circular aluminum tubes

A comprehensive experimental and numerical study of the crash behavior of circular aluminum tubes undergoing axial compressive loading is performed. Non-linear finite element analyses are carried out to simulate quasi-static and dynamic test conditions. The numerical predicted crushing force and fold formation are found to be in good agreement with the experimental results. A summary of available analytical solutions is presented in order to estimate the mean crushing load and establish a comparison between these analytical loads and the experimental one. Some observations are made on the influence of geometrical imperfections and material strain rate effect.

Rail Vehicle Design for Crashworthiness. 1st Report. Development of Carbody Structure for High Energy Absorption and Calculation Method for Crashworthiness.

In these days, crashworthiness design has been required more frequently in rail vehicle. The results of static strength test of an end underframe that absorbs most of the crash energy were presented, as well as numerical simulations. By comparing both results, the numerical simulations were found to be adequately accurate. Then, a new and highly crashworthy structure was proposed. Both of the test and the numerical simulation confirmed that the structure worked well to absorb the crash energy. Further, effects of welding strength, geometrical initial imperfection, and strain rate on the crashworthiness were discussed. Especially, strain rate effect of materials is important to evaluate crashworthiness accurately.

Axial impact behavior and energy absorption efficiency of composite wrapped metal tubes

Axial impact crushing behavior and energy absorption efficiency of glass/epoxy composite externally wrapped circular metal tubes have been studied in this paper. Predicted instantaneous velocity and displacement formulae are presented and compared with experimental results. Four typical collapse modes are identified, and effects that contribute to the energy absorption capability, such as strain rate, composite wall thickness, fiber ply orientation, and mechanical properties of metals, are studied. By including the influence of the material strain rate effects on metals, the simplified analytical model proposed by Hanefi and Wierzbicki has been extended to impact loadings.

Design and modeling of precision solid liner experiments on Pegasus

Pulsed power driven solid liners may be used for a variety of physics experiments involving materials at high stresses. These include shock formation and propagation, material strain-rate effects, material melt, instability growth, and ejecta from shocked surfaces. We describe the design and performance of a cylindrical solid liner that can attain velocities in the several mm/μs regime, and that can be used to drive high-stress experiments. An approximate theoretical analysis of solid liner implosions is used to establish the basic parameters (mass, materials, and initial radius) of the driver. We then present one-dimensional and two-dimensional simulations of magnetically driven, liner implosions which include resistive heating and elastic–plastic behavior. The two-dimensional models are used to study the effects of electrode glide planes on the liner’s performance, to examine sources of perturbations of the liner, and to assess possible effects of instability growth during the implosion. Finally, simulations are compared with experimental data to show that the solid liner performed as predicted computationally. Experimental data indicate that the liner imploded from an initial radius of 2.4 cm to a target radius of 1.5 cm, and that it was concentric and cylindrical to better than the experimental resolution (60 μm) at the target. The results demonstrate that a precision solid liner can be produced for high-stress, pulsed power applications experiments.

Strain-Rate Effects in the Dynamic Buckling of a Simple Elastic-Plastic Model

The phenomenon of dynamic buckling is examined when the influence of material strain-rate sensitivity is retained in the basic equations for a simple elastic-plastic model with linear strain hardening when subjected to an impact by a mass. Two approaches are proposed for taking into account the material strain-rate effects and both use the Cowper-Symonds constitutive equation. The critical impact velocities depend on the impact mass and are determined for a wholly elastic material, a strain-rate insensitive elastic-plastic material and an elastic-plastic material with a dynamic yield force together with linear or nonlinear hardening due to the strain-rate effects. The results obtained show that both strain-rate sensitive models predict impact velocities which are higher than those predicted by the strain-rate insensitive idealization and that the influence of any initial imperfections is important for the three material models considered.