Models are presented and discussed which predict the influence of stress rate or strain rate on the tensile strength of concrete. Three of them are based on linear fracture mechanics and two on thermodynamics. It is shown that four models are appropriate and useful in the low to medium stress rate whereas two can predict realistic values at high stress rates. Finally a proposal is made how to apply the knowledge to engineering practice.

This paper deals with the rate effects on concrete and reinforcements, especially unfavorable effects for the dynamic design of concrete or reinforced concrete structures. The rate effects on concrete are divided into two effects, the rate effect on stress-strain relations and that on fracture criteria of concrete which bringsabout occasionally the unfavorable and brittle fractures of concrete and reinforced concrete structures.

It is also described that the brittle fractures are usually caused by the rapid propagation of cracks generated in concrete under the high rate loadings, which can be said to be one of the rate effects on concrete.

For rational and accurate analysis of concrete structures subjected to impact or impulsive loads the knowledge of crack propagation under such dynamic loads is essential. Cracks frequently propagate under mixed-mode (opening and sliding: mode I and mode II) conditions. The rate of loading effects on the mechanical properties have been attributed to the rate sensitivity of crack propagation. The strain-rate effects may be different in mode I and mode II fracture of concrete. Single edge notched beams were subjected to varying rates of loading, to establish the mode I Stress Intensity Factor, KI vs. Crack Velocity, V, relationship for mortar and concrete. Impact tests were conducted using a Modified Instrumented Charpy Impact Test System. The rate of crack growth was obtained using brittle ‘Krak Gages'.

Mode I test results lead to the following conclusions. (1) Slow (prepeak) crack growth for concrete is larger than that of mortar, at a given strain rate. (2) Pre-peak crack growth decreases with increase in strain-rate. This could be the reason for decrease in pre-peak non-linearity at higher strain rates. Hence LEFM approach may be valid at high rates of loading. (3) log KI - log V relationship is non-linear especially at the higher rates of loading.

Three D.C.B. tests (Double Cantilever Beam) under different loading histories have shown that the applied crack opening rates can have an effect on the KIC fracture toughness values computed on the basis of linear elastic behavior of concrete. This assumption can be well justified for a certain range of crack opening rates, outside of which viscous phenomena must be taken in account. The concepts of ductile and brittle fracture appear then as related to the crack opening rate.

The subcritical crack growth parameter (n) has been determined both from the variation in the crack velocity (V) with stress intensity (K) in double torsion specimens, and from the variation in critical stress intensity (Klc) with loading rate (x) in single edge-notch bend specimens. As in previous cases for hardened cement paste (HCP), and other inhomogeneous materials, the value of n determined using double torsion specimens (˜70) was higher than that determined using SENB (˜30).

Backscattered electron image examination of cracks in polished sections of HCP has shown that all of the components, both hydration products and anhydrous phases, are involved in determining crack paths although, as expected; calcium silicate hydrate and calcium hydroxide form the majority of the crack path; unnhydrated cement cores are resistant to crack growth and cause the crack to deviate around them. There is some evidence that crack growth occurs by the formation and coalescence of microcracks ahead of the crack tip, with only a limited formation of an actual process zone.

The dynamic fracture of concrete in tension is studied by applying a continuum damage model developed by the author and his coworkers [1–3]. In this model, the degree of damage in concrete corresponds to the fraction of concrete volume that has been tension relieved, and tensile microcracking has been taken as the damage mechanism. In compression, the concrete is assumed to respond in an elastic/perfectly plastic manner. Strain-rate effects have been explicitly included in the model. Accumulation of damage in the material is reflected by the progressive weakening of the material stiffness. Examples involving center- and edge-cracked plate specimens subjected to the action of step and ramp loads are used to demonstrate the material responses predicted by the model. The bulk pressure versus strain relationships at locations close to the crack tip clearly show strainsoftening behavior. The damage tends to localize around the crack and its extent in the specimen is dependent upon both the crack geometry and the loading type. These results are presented and their implications are discussed.

This paper focuses on the establishment of a simple damage surface that allows the use of a vector representation of damage to be applied in a two or three dimensional framework. Specifically for contrast to some types of tensor representations [1], the surface is developed in such a manner to allow maximum damage to occur in planes adjacent to the plane of maximum tensile strain. The limitations of this surface then are pointed out. Comparison of this postulate with recent data from Jan van Mier [2] is also presented.

Results of dynamic tensile strength tests of concrete, produced by the authors and other investigators, were used to study the effects of strain rate on the tensile strength of concrete. The influence of moisture content and compressive strength of concrete, and type of test (splitting tension, flexure, or direct tension) on the strain rate-sensitivity of the tensile strength were evaluated. An empirically developed expression is presented for the dynamic-to-static ratio of concrete tensile strength in terms of the rate of straining.

The knowledge of the loading rate influence on the tensile strength of concrete is of considerable importance in engineering practice. The safety of several concrete structures subjected to impact and impulsive loads is often controlled by the tensile strength and stress-strain behaviour because these properties greatly influence the cracking of concrete, bond properties of reinforcing steel and behaviour under shear forces.

High strain rates lead to substantial modifications in the stress-strain (or stress-displacement) response of fiber reinforced concrete in tension. These modifications include higher strength and corresponding strain, as well as smaller displacement at failure.

The purpose of this paper is to investigate the behavior of fiber reinforced concrete under impact tensile loading, and to study the effect of strain rate on the post-cracking strength of the composite. The variation of the tensile strength of the matrix with the reinforcement parameters such as volume fraction Vf and aspect ratio |/φ of the fibers is also studied ip this paper. A special emphasis is placed on the stress-displacement relationship of steel fiber reinforced concrete in its post-cracking range. An empirical model of the stress- displacement relationship as a function of the strain rate is developed from experimental data from tensile tests on dogbone shape notched tensile prisms. The model highlights the effects of strain rate and fiber properties on the post-cracking strength of the composite, as well as the displacement at failure. The effect of strain rate on the post-cracking toughness of fiber reinforced concrete is also addressed. The literature on impact effects on concrete in tension (plain and fiber reinforced) is briefly reviewed in this paper, and so is the state of the art of testing techniques for strain rate effects.

Finite-element codes for structural response of reinforced concrete use as a parameter the unconfined compressive strength of the concrete, fc', which is sometimes increased by an arbitrary factor for dynamic loading. The objective of this research is to determine the rate dependence of fc' and eventually to model the rate-dependent constitutive behavior. Results of tests with a small Kolsky bar system and of a newly built larger system on concrete with a maximum aggregate size 1/2 inch are reported with strain rates at the maximum stress from 50 to 800/sec for mortar and from 5 to 120/sec for concrete. An apparent rate dependence up to almost twice the static strength is observed for both. The mortar shows an apparent linear dependence, while the high-strength concrete shows an approximately logarithmic dependence on the strain rate at the maximum stress, over the dynamic range observed. Some questions about specimen size effects and about how much of the apparent strain-rate effect is really a lateral inertia confinement effect are as yet unresolved. Continuing research is focused on observation of the lateral motion to assess lateral inertia effects in unconfined specimens and on passive confinement by steel jackets. Future efforts will be directed toward constitutive modeling.

Much is known about the tensile fracture, both brittle and ductile: theories are well developed. There is no equivalent theory for compressive failure. A generalized theorem has been developed based on the concept of cohesive strength and the fact that tensile stresses frequently develop around the surface of voids in a material subject to compression. The theory does not produce criteria on critical flaw size. The latter should result from an energy criterion. It is shown, however, that modelling compression cracks as zero width flaws results in no energy change as the crack extends: an anomalous result compared with experimental findings. Allowing compression cracks to have finite width results in strain energy reduction as the ‘crack’ gets larger. A three-dimensional ellipsoid has been used as a model of a compression ‘crack’. Strain energy reduction in the medium, due to the presence of the void, is shown to depend on both its shape and its size. Initial estimates of a compressive G - a compressive energy release rate as the ‘crack’ extends - also suggest a dependence on both size and shape of the cavity. The results indicate further investigation is warranted.

Since good constitutive laws are required to model correctly the behaviour of concrete under impact loading, it is necessary to determine the complete stress-strain response of concrete at varying strain rates. Conflicting evidence emerges about whether the critical compressive strain (defined as the strain observed at maximum stress) increases or decreases with an increasing strain rate. In this paper, a comprehensive description is given of the brittle fracture process for plain concrete under static and impact loading. The strain rate dependance of tensile microcrack growth is used to explain both the increase in strength and the increase in critical compressive strain that can occur at high strain rates. More extensive experimental results are required to determine the fundamental changes in behaviour that occur as the loading rate is increased and, thus, facilitate the development of a more precise failure model for concrete.

Submicroscopic cracking within cement paste is studied for monotonic and short-term sustained loading. Loading times range from 1.25 minutes to 4 hours. Water cement ratios of 0.3 and 0.5 are used. Specimens are loaded to preselected strains and immediately unloaded. The specimens are then sliced with a diamond saw and viewed in a scanning electron microscope. Crack traces are cataloged based on length, width and orientation. The crack traces are converted to three dimensional crack distributions, which are in turn used to determine the degree of softening due to cracking. The results indicate that for loading to a fixed strain, slow loading results in less cracking than rapid loading. However, at the same stress-strength ratio, rapid loading results in fewer cracks. The results indicate that the role of submicroscopic cracking in the nonlinear behavior of cement paste increases with strain rate.

Despite its extensive use, low tensile strength has been recognized as one of the major drawbacks of concrete. Although one has learned to avoid exposing concrete structures to adverse static tensile load, these cannot be shielded from short duration dynamic tensile stresses. Such loads originate from sources such as impact from missiles and projectiles, wind gusts, earthquakes and machine vibrations. The need to accurately predict the structural response and reserve capacity under such loading has led to an interest in the mechanical properties of the component materials at high rates of straining.

One method to improve the resistance of concrete when subjected to impact and/or impulsive loading is by the incorporation of randomly distributed short fibers. Concrete (or Mortar) so reinforced is termed fiber reinforced concrete (FRC). Moderate increase in tensile strength and significant increases in energy absorption (toughness or impact-resistance) have been reported by several investigators in static tests on concrete reinforced with randomly distributed short steel fibers. A theoretical model to predict fracture toughness of FRC is proposed. This model is based on the concept of nonlinear elastic fracture mechanics.

As yet no standard test methods are available to quantify the impact resistance of such composites, although several investigators have employed a variety of tests including drop weight, swinging pendulums and the detonation of explosives. These tests though useful in ascertaining the relative merits of different composites do not yield basic material characteristics which can be used for design.

The author has recently developed an instrumented Charpy type of impact test to obtain basic information such as load-deflection relationship, fracture toughness, crack velocity and load-strain history during an impact event. From this information, a damage based constitutive model was proposed. Relative improvements in performance due to the addition of fibers as observed in the instrumented tests are also compared with other conventional methods.

Dynamic fracture of two impact loaded, plain concrete, three-point bend specimens was simulated using a dynamic finite element model. A three-segment fracture process zone, which was established in a previous static analysis, together with a tensile overload fracture criterion were used to propagate the crack from the tension side of the unnotched beams. Reasonable agreement between the measured and computed velocities at two points on one beam and estimated and computed average crack velocities was obtained.

Flexural specimens of hardened cement paste, fibre reinforced concrete, and conventionally reinforced concrete were tested in an instrumented dropweight impact machine, employing a 345 kg mass impact hammer dropped from a height of 500 mm. The crack development in the specimens was monitored using high speed motion picture photography, carried out at about 10,000 frames per second. It was found that, for all three specimens, some crack branching occurred. The cracks did not propagate in a continuous fashion; they appeared to arrest occasionally, and then began to grow again. However, it appeared as if the crack velocities reached a maximum value very soon after the impact occurred; they then decreased, and finally increased again just prior to failure. The average crack velocities were in the range of about 75 to 115 m/s.

The behaviour under impact loading of concrete beams, reinforced with both smooth and deformed steel reinforcing bars, was studied. Tests were carried out using an instrumented drop-weight impact apparatus, with a 345 kg mass hammer, and drop heights of up to 2.36 m. It was found that, under certain circumstances, the steel reinforcement itself fractured. This behaviour is discussed with reference to the drop height, the type of reinforcement, and the strength of the concrete matrix.

The characteristic of a new form of high strength polymer grid are outlined and its possible uses as reinforcement in concrete subjected to dynamic loading are discussed. Details are given of a test programme in which concrete slabs reinforced with a range of grid types in various configurations have been subjected to explosive loading from contact charges of plastic explosive. A range of both transient and post-test measurements were taken. Results are presented showing how the various damage parameters measured vary with the position and number of polymer grids used in the slabs. The results of the transient measurements are used to suggest mechanisms for damage formation. It is concluded that these polymer grids are effective in restraining explosively generated damage in concrete slabs and that in many circumstances their light weight and their inherent resistance to normal corrosion processes may give them significant advantages over conventional steel reinforcement.

Tests have been undertaken in the Imperial College concrete laboratories to study the effect of cyclic loading upon the compressive strength, the stress-strain relationship and the energy absorption and dissipation characteristics of concrete prisms at variable strain rates. Comparison is made with prisms loaded monotonically at similar strain rates. Prisms were confined by high-tensile steel bolts inserted horizontally in two orthogonal directions through pre-formed ducts, and the annular space between ducts and bolts was grouted with high strength epoxy resin. Both steel and concrete deformational response was measured. Significant enhancement of the strength and ductility of the concrete was obtained. Specimens displayed large energy absorption and dissipation capacity under cyclic loading. The validity of an envelope curve to describe cyclic behaviour is discussed.