Tensile behavior of carbon fiber bundles at different strain rates

Quasi-static and high strain rate tensile tests have been performed on T700 carbon fiber bundles and complete stress-strain curves at the strain rate range of 0.001 s^− 1 to 1300 s^− 1 were obtained. Results show that strain rate has negligible effect on both ultimate strength and failure strain, and T700 carbon fiber can be regarded as strain rate insensitive materials. On the basis of the fiber bundles model and the statistic theory of fiber strength, a damage constitutive model based on Weibull distribution function has been developed to describe tensile behavior of T700 fiber bundles. And the method to determine the statistic parameters of fibers by tensile tests of fiber bundles is established, too.     

Tension behavior of unidirectional glass/epoxy composites under different strain rates

By considering wide applications of composite materials, having a proper knowledge of them under dynamic loading is necessary. In order to study the effects of strain rates on the behavior of the materials, special testing machines are needed. Most of the research in this field is focused on applying real loading and gripping boundary conditions on the testing specimens. In this study, behavior of unidirectional glass fiber reinforced polymeric composites under uni-axial loading is determined at quasi-static and intermediate strain rates of 0.001–100 s⁻¹. The tests were performed using a servo-hydraulic testing apparatus equipped with a strain rate increase mechanism. For performing the tests, a jig and a fixture are designed and manufactured. The performance of the test jig was evaluated and found to be adequate for testing of composites. Dynamic tests results are compared with the results of static tensile tests carried out on specimens with identical geometry. Experimental results show a significant increase of the tensile strength by increasing the strain rate. The tensile modulus and strain to failure are also observed to increase slightly by increasing the strain rate.     

Experimental study on dynamic damage evolution of concrete under multi-axial stresses

The effect of stress state on the dynamic compressive strength and the dynamic damage evolution process of concretes are investigated by use of a Spilt Hopkinson Pressure Bar (SHPB) and the ultrasonic technique. The columned concrete specimen is encircled by a steel sleeve. The multi-axial loading includes the axial and the radial loadings. The axial loading is supplied by the incidence bar, and the radial ones are produced by the steel sleeve. Analysis of the dynamic damage evolution of the samples is based on the measurement of the changes of ultrasonic wave velocities before and after the impact tests. The waveforms in the test bars, the stress strain curves, the confining pressure of the specimen, the dynamic compressive strength and other information about the samples are obtained during the SHPB experiments. The results of the tests show that the loading rate and stress states of the specimen apparently influence the damage evolution process in concretes. The dynamic damage evolutions are accelerated with the increase of the strain rate and are delayed significantly under the confined pressure.     

Modeling of cyclic stress–strain behavior and damage mechanisms under thermomechanical fatigue conditions

A multi-component model was applied to predict the cyclic stress–strain response of different alloys under thermomechanical fatigue conditions based upon isothermal hysteresis loops. A ductile AISI 304 L-type stainless steel and two high strength alloys, the near-α titanium alloy IMI 834 and the nickel-base superalloy IN 100, were chosen as test materials. These represent alloys with rather different dislocation slip modes, stress–strain characteristics and damage mechanisms. Model predictions are compared with experiments and the differences in cyclic stress–strain response and damage mechanisms under isothermal and thermomechanical fatigue conditions, respectively, are discussed based upon microstructural observations.     

The mechanical properties of ionoplast interlayer material at high strain rates

Ionoplast material has been recently introduced and extensively used as interlayer material for laminated glass to improve its post-glass breakage behavior. Due to its sound mechanical performance, the applications of laminated glass with ionoplast interlayer have been widely extended to the protection of glass structures against extreme loads such as shock and impact. The properties of this material at high strain rates are therefore needed for properly analysis and design of such structures. In this study, the mechanical properties of ionoplast material are studied experimentally through direct tensile tests over a wide strain rate range. The low-speed tests are performed using a conventional hydraulic machine at strain rates from 0.0056 s⁻¹ to 0.556 s⁻¹. The high strain-rate tests are carried out with a high-speed servo-hydraulic testing machine at strain rates from approximately 10 s⁻¹ to 2000 s⁻¹. It is found that the ionoplast material virtually exhibits elasto-plastic material properties in the strain rate range tested in this study. The testing results show that the material behavior is very strain-rate dependent. The yield strength increases with strain rate, but the material becomes more brittle with the increase in strain rate, with the ultimate strains over 400% under quasi-static loading, and decreasing to less than 200% at strain rate around 2000 s⁻¹. The testing results indicate that simply applying the static material properties in predicting the structure responses of laminated glass with ionoplast interlayer subjected to blast and impact loads will substantially overestimate the ductility of the material and lead to inaccurate predictions of structure response. The testing results obtained in the current study together with available testing data in the literature are summarized and used to formulate the dynamic stress–strain curves of ionoplast material at various strain rates, which can be used in analysis and design of structures with ionoplast material subjected to blast and impact loads.     

Compressive behavior of closed-cell aluminum alloy foams at medium strain rates

Compressive behavior of closed-cell aluminum alloy foams at strain rates of 10⁻³-450 s⁻¹ has been studied experimentally. The fully stress-strain curves of specimens at medium strain rates were obtained using the High Rate Instron Test System, which can maintain a constant loading rate. The experimental results show that plateau stress and energy absorption capacity are remarkable dependent on strain rate, while the densification strain has a negligible dependence.     

Plastic behavior and constitutive relations of DH-36 steel over a wide spectrum of strain rates and temperatures under tension

To understand the plastic characteristics of DH-36 steel, uniaxial tensile tests have been performed on dog bone samples. The strain rate range is from 0.001 to 3000/s, and the initial specimen temperatures are 293–800 K. To obtain the isothermal flow stress at high strain rates, dynamic recovery technique in Hopkinson Tension Bar has been used, and the interrupt and reloading tests have been performed. The value of strain rate sensitivity has been calculated based on the isothermal stresses at different strain rates. Similar to results from compressive tests, the dynamic strain aging has been observed under tension. Microstructure analysis of the samples after interrupt tests has been carried out by scanning electron microscopy (SEM). The results show that: (1) the strain rate sensitivity value is ∼0.0115 in terms of the isothermal flow stress (uncoupled with temperature) at a given strain, corresponding to 0.0045 coupled with temperature; (2) the 3rd dynamic strain aging (DSA) occurs at some relatively constant strain rates within certain temperature region under tension; DSA shifts to higher temperature or even disappears with increasing strain rates. Finally, in depth analysis of the data based on dislocation mechanisms, it leads to a physically based model which has taken into account the 3rd DSA effects. Good agreement between the theoretical prediction and experimental results has been obtained.     

A testing technique for concrete under confinement at high rates of strain

A testing device is presented for the experimental study of dynamic compaction of concrete under high strain rates. The specimen is confined in a metallic ring and loaded by means of a hard-steel Hopkinson pressure bar (80 mm diameter, 6 m long) allowing for the testing of specimens large enough regarding the aggregate size. The constitutive law for the metal of the ring being known, transverse gauges glued on its lateral surface allow for the measurement of the confining pressure. The hydrostatic and deviatoric responses of the specimen can then be computed. The proposed method is validated by several numerical simulations of tests involving a set of four different concrete-like behaviours and different friction coefficients between the cell and the specimen. Finally, three tests performed with the MB50 concrete at three different strain rates are processed with the method and are compared with literature results for the same material under quasi-static loadings.     

Simulation of strain localization with gradient enhanced damage models

The incorporation of higher order strain gradients into the constitutive equations of continuum damage mechanics is presented. Thereby, not only scalar-valued isotropic damage models but also anisotropic damage models allowing for directional dependent stiffness degradation are elaborated. An elegant possibility of describing anisotropic material behavior based on the microplane theory is demonstrated. Its conceptual simplicity originates from the idea of modeling the material behavior through uniaxial stress–strain laws on several individual material planes. For each plane individual damage loading functions are introduced allowing for different failure modes. In order to account for long ranging microstructural mechanisms, second-order gradients of the strains are incorporated in each of these damage loading functions. The overall response can be determined by an integration of the resulting microplane laws over the solid angle. The features of gradient enhanced continuum damage are demonstrated by means of several selected examples.     

Modeling of dynamic expansion of thick‐walled cylinder under high strain rate loading with strain rate sensitivity analysis

This paper presents an analysis of the dynamic behavior of thick‐walled cylinder using Levy‐Mises flow rule in the assumption of a non‐linear strain rate hardening behavior under high strain rate loading. The theoretical model to be developed in this work applies indirect use of dynamic strength of material characterized by a non‐linear relation and instant boundary condition based on Jones‐Wilkins‐Lee equation of state to establish differential equation for radial expansion velocity. Detailed discussion will be given with emphasis on the main aspects of the cylinder behaviour, i.e. radial displacement, internal pressure, strain rate, flow stress, radial and tangential stress and the influence of different material rate sensitive exponent. Results show a good agreement with the analytical solutions proposed here.     

Properties of strain hardening ultra high performance fiber reinforced concrete (UHP-FRC) under direct tensile loading

Enhanced matrix packing density and tailored fiber-to-matrix interface bond properties have led to the recent development of ultra-high performance fiber reinforced concrete (UHP-FRC) with improved material tensile performance in terms of strength, ductility and energy absorption capacity. The objective of this research is to experimentally investigate and analyze the uniaxial tensile behavior of the new material. The paper reviews and categorizes a variety of tensile test setups used by other researchers and presents a revised tensile set up tailored to obtain reliable results with minimal preparation effort. The experimental investigation considers three types of steel fibers, each in three different volume fractions. Elastic, strain hardening and softening tensile parameters, such as first cracking stress and strain, elastic and strain hardening modulus, composite strength and energy dissipation capacity, of the UHP-FRCs are characterized, analyzed and linked to the crack pattern observed by microscopic analysis. Models are proposed for representing the tensile stress–strain response of the material.     

Stress-strain behavior of reinforcing steel and concrete under seismic strain rates and low temperatures

This study investigates experimentally the uniaxial stress-strain behavior of reinforcing steel bars and concrete cylinders under various combinations of earth-quake-type strain rate (quasi-static to 0.1 /s) and temperature typical of summer and winter conditions in cold urban regions (+20°C to −40°C). The main objective of these tests was to give an indication of the combined effects of these two parameters on the uniaxial, monotonic, stress-strain curves of these materials. The results of the tensile tests indicate that the yield strength and the tensile strength of reinforcing steel increase moderately as both the strain rate increases and the temperature drops. The results of the compressive tests indicate that the compressive strength and Young’s modulus of concrete increase significantly as the strain rate increases and the temperature decreases.

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Résumé Cette étude a pour but d’évaluer expérimentalement le comportement uniaxial d’éprouvettes d’acier d’armature et de cylindres de béton. Des essais furent réalisés pour différentes combinaisons de températures (+20°C à −40°C) et de taux de déformation typiques d’événements sismiques (quasi-statique à 0.1 /s). L’objectif principal de ces essais était de donner une indication sur les effects combinés de ces deux paramètres sur les courbes contrainte-déformation, uniaxiales et monotones de ces matériaux. Les résultats de ces essais en traction indiquent que la limite élastique et la résistance à la traction de l’acier d’armatures s’accroissent légèrement lorsque que l’on observe à la fois une hausse du taux de déformation et une baisse de la température. Les résultats des essais de compression indiquent que la résistance à la compression et le module d’Young du béton augmentent de manière significantive quand le taux de déformation augmente et que la température baisse.

     

Constitutive modeling of nitrogen-alloyed austenitic stainless steel at low and high strain rates and temperatures

In this paper, microstructures-based constitutive relations are introduced to simulate the thermo-mechanical response of two nitrogen-alloyed austenitic stainless steels; Nitronic-50 and Uranus-B66, under static and dynamic loadings. The simulation of the flow stress is developed based on a combined approach of two different principal mechanisms; the cutting of dislocation forests and the overcoming of Peierls–Nabarro barriers. The experimental observations for Nitronic-50 and Uranus-B66 conducted by Guo and Nemat-Nasser (2006) and Fréchard et al. (2008), respectively, over a wide range of temperatures and strain rates are also utilized in understanding the underlying deformation mechanisms. Results for the two stainless steels reveal that both the initial yielding and strain hardening are strongly dependent on the coupling effect of temperatures and strain rates. The methodology of obtaining the material parameters and their physical interpretation are presented thoroughly. The present model predicts results that compare very well with the experimental data for both stainless steels at initial temperature range of 77–1000 K and strain rates between 0.001 and 8000 s⁻¹. The effect of the physical quantities at the microstructures on the overall flow stress is also investigated. The evolution of dislocation density along with the initial dislocation density contribution plays a crucial role in determining the thermal stresses. It was observed that the thermal yield stress component is more affected by the presence of initial dislocations and decreases with the increase of the originated (initial) dislocation density.     

Modeling of structures subjected to impact: concrete behaviour under high strain rate

This paper deals with a viscoplastic model which is the natural way to take into account the rate effect. Consideration of viscosity averts the habitual mesh sensitivity when strain softening is introduced by preserving the well-posedness of the initial boundary value problem. Modeling can constitute an alternative to experimentation not in order to predict the material response, but to try to understand and to evaluate the rate effect. Numerical simulation of the split test Hopkinson pressure bar gives an idea of dynamic concrete behaviour: forces of inertia, inertial confinement, structural effect and rate effect. Finally, the model is used to simulate a reinforced concrete beam submitted to impact.     

Fracture energy of concrete at high loading rates in tension

The effect of high loading rates in tension on the failure energy and strength of concrete is reported in this paper. High loading rates exceeding 5000 GPa/s corresponding to strain rates higher than ∼120 s⁻¹ can be applied by use of Hopkinson bar set-up designed to produce spall. Tension tests were performed on cylindrical specimens made of micro-concrete. At high loading rates, or strain rates, the failure energy of micro-concrete, as well as the strength, was found to substantially increase.     

Dynamic behavior of concrete at high strain rates and pressures: II. numerical simulation

The response of concrete and mortar under high-strain-rate impact loading are analyzed using fully dynamic finite element simulations. The analyses concern the load-carrying capacity, energy absorbency and the effect of the microstructure. The simulations focus on the plate impact configuration used in the experimental part of this research, allowing for direct comparison of model predictions with experimental measurements. A micromechanical model is formulated and used, accounting for the two-phase composite microstructure of concrete. Arbitrary microstructural phase morphologies of actual concrete used in impact experiments are digitized and explicitly considered in the numerical models. The behavior of the two constituent phases in the concrete are characterized by an extended Drucker–Prager model that accounts for pressure-dependence, rate-sensitivity, and strain hardening/softening. Model parameters are determined by independent impact experiments on mortar and through a parametric study in which the prediction of numerical simulations is matched with measurements from experiments on concrete and mortar. Calculations show that significant inelastic deformations occur in the mortar matrix under the impact conditions analyzed and relatively smaller inelastic strains are seen in the aggregates. The influence of aggregate volume fraction on the dynamic load-carrying capacity of concrete is explored. The strength increases with aggregate volume fraction and an enhancement of approximately 30% over that of mortar is found for an aggregate volume fraction of 42%. Numerical simulations also show increasing energy absorbency with increasing aggregate volume fraction and provide a time-resolved characterization for the history of work dissipation as the deformation progresses.     

Dynamic behavior of concrete at high strain rates and pressures: I. experimental characterization

Understanding the behavior of concrete and mortar at very high strain rates is of critical importance in a range of applications. Under highly dynamic conditions, the strain-rate dependence of material response and high levels of hydrostatic pressure cause the material behavior to be significantly different from what is observed under quasistatic conditions. The behavior of concrete and mortar at strain rates of the order of 10⁴ s⁻¹ and pressures up to 1.5 GPa are studied experimentally. The mortar analyzed has the same composition and processing conditions as the matrix phase in the concrete, allowing the effect of concrete microstructure to be delineated. The focus is on the effects of loading rate, hydrostatic pressure and microstructural heterogeneity on the load-carrying capacities of the materials. This experimental investigation uses split Hopkinson pressure bar (SHPB) and plate impact to achieve a range of loading rate and hydrostatic pressure. The SHPB experiments involve strain rates between 250 and 1700 s⁻¹ without lateral confinement and the plate impact experiments subject the materials to deformation at strain rates of the order of 10⁴ s⁻¹ with confining pressures of 1–1.5 GPa. Experiments indicate that the load-carrying capacities of the concrete and mortar increase significantly with strain rate and hydrostatic pressure. The compressive flow stress of mortar at a strain rate of 1700 s⁻¹ is approximately four times its quasistatic strength. Under the conditions of plate impact involving impact velocities of approximately 330 ms⁻¹, the average flow stress is 1.7 GPa for the concrete and 1.3 GPa for the mortar. In contrast, the corresponding unconfined quasistatic compressive strengths are only 30 and 46 MPa, respectively. Due to the composite microstructure of concrete, deformation and stresses are nonuniform in the specimens. The effects of material inhomogeneity on the measurements during the impact experiments are analyzed using a four-beam VISAR laser interferometer system.     

High strain rate effects on direct tensile behavior of high performance fiber reinforced cementitious composites

Direct tensile behavior of high performance fiber reinforced cementitious composites (HPFRCCs) at high strain rates between 10 s⁻¹ and 30 s⁻¹ was investigated using strain energy frame impact machine (SEFIM) built by authors. Six series of HPFRCC combining three variables including two types of fiber, hooked (H) and twisted (T) steel fiber, two fiber volume contents, 1% and 1.5%, and two matrix strengths, 56 MPa and 81 MPa, were investigated. The influence of these three variables on the high strain rate effects on the direct tensile behavior of HPFRCCs was analyzed based on the test results. All series of HPFRCCs showed strongly sensitive tensile behavior at high strain rates, i.e., much higher post cracking strength, strain capacity, and energy absorption capacity at high strain rates than at static rate. However, the enhancement was different according to the types of fiber, fiber volume content and matrix strength: HPFRCCs with T-fibers produced higher impact resistance than those with H-fibers; and matrix strength was more influential, than fiber contents, for the high strain rate sensitivity. In addition, an attempt to predict the dynamic increase factor (DIF) of post cracking strength for HPFRCCs considering the influences of fiber type and matrix strength was made.     

A physical phenomenon which can explain the mechanical behaviour of concrete under high strain rates

The free water in concrete underlies the various physical mechanisms that shape the mechanical behaviour of the material. In this article we attempt to show, through an experimental observation and a theoretical assumption, that the mechanical behaviour of concrete under high strain rates could be explained by a coupling between one of these physical effects and the process of cracking in the material. The assumption about the physical mechanism involved is made more to understand what happens inside the material than to lead to quantitative predictions.

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Resume L'eau libre au sein du béton est à l'origine de différents mécanismes physiques qui interviennent dans le comportement mécanique du matériau. Dans le cadre d'une coopération européenne, l'Université de Technologie de Delft et le LCPC avaient étudié le comportement dynamique du béton (c'est à dire, dans le cas présent, sous de grandes vitesses de déformation), en s'intéressant essentiellement à l'influence, sur ce type de comportement, de l'humidité interne du matériau. Les essais étaient réalisés sur la barre de Hopkinson de Delft qui permet de solliciter, en traction directe, des éprouvettes de béton à des vitesses de déformation pouvant aller jusqu' à 10 s⁻¹. Un micro-béton était testé dans deux conditions d'hygrométrie interne: complètement sec, et humide. On a constaté qu'en ce qui concernait le béton humide, la résistance à la traction directe augmentait avec la vitesse de déformation, phénomène connu pour la plupart des matériaux, alors que cette dépendance n'existait pas pour le béton sec. Dans cet article on propose une hypothèse quant au mécanisme physique qui permettrait d'expliquer cette augmentation de la résistance à la traction du béton avec la vitesse de déformation. Il s'agit de l'effet Stefan qui peut être décrit succinctement de la manière suivante: l'existence d'un mince film visqueux (eau ou huile par exemple) entre deux cales parfaitement planes et parallèles, et distantes d'une certaine longueurh, conduit à la création d'une force de rappel lorsque l'on tente d'écarter les deux cales avec une vitesse h. Plus la vitesse est grande, plus cette force de rappel le sera. Dans un béton, les cales séparées par un ménisque d'eau ne sont autres, par analogie, que les parois des micropores et des capillaires.