Granular Materials

Constitutive and Failure Behavior of Concrete and Mortar under Impact Loading

Summary

The need to understand the dynamic behavior of concrete and mortar at high strain rates is of critical importance in a range of applications including airport runways and structures subject to blast or penetration. Under such 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. This part of the research focuses on two aspects of the behavior of concrete and mortar: (1) the dynamic stress-carrying capacity at strain rates above 104 s-1 and pressure above 1 GPa and (2) the dynamic failure behavior under conditions of uniaxial strain generated by planar impact. The materials used are a G-mix concrete and a mortar having the same composition and processing condition as the concrete. The experimental analyses use plate impact and split Hopkinson bar. Normal impact experiments involving impact velocities up to 482 ms-1 are conducted.

Experiments show that the stress-carrying capacity of the materials depends strongly on loading rate and hydrostatic pressure. Under conditions of quasistatic uniaxial stress, the strength for the concrete is approximately 30 MPa. Under the conditions of impact experiments involving elastic steel target plates and impact velocities between 290 and 330 ms-1, the average compressive stresses carried by the concrete are found to be on the order of 1700 MPa, as indicated in the first figure below. The marked increase in stress is attributed to the effect of higher strain rates which are on the order of 104 s-1 and to the effect of lateral confining stresses, which are on the order of 1 GPa. Due to the composite microstructure of the concrete, the deformation and stresses are nonuniform in the experiments. The effect of material inhomogeneity on the measurements is analyzed experimentally. The experimental data obtained provide a characterization of the behavior of concrete under strain rates between 10-3 s-1 ad 105 s-1 and for pressures up to 2 GPa.The analysis of failure behavior focuses on the possible existence of failure waves in mortar similar to those in brittle materials which involve the complete loss of tensile strength under conditions of uniaxial compressive strains during planar plate impact. Such failure waves have a clearly defined front separating intact and failed materials and propagating from the impact face toward the interior of the specimen. VISAR laser interferometry is employed to probe the tensile strength of impacted materials at different locations within the specimen. The results of these experiments are illustrated in the second figure below. Experiments conducted do not provide evidence to support the theory of failure wave occurrence in mortar. While a threshold impact velocity is required to initiate the failure, a clearly defined failure front traveling behind the loading wave at a speed lower than the longitudinal wave speed is not observed. Instead, stress profiles measured by internal PVDF stress gauges show an attenuation of the stress pulse as it travels through the specimens, indicating the processes of microcrack growth and collapse of micro porosities commence with the arrival of the loading wave. This trend is illustrated in the third figure below through the use of three PVDF stress gauges imbedded in a mortar sample. This gradual failure process is in contrast to the sharply defined failure wave front in other brittle materials such as glasses.

Constitutive Behavior of Concrete at High Strain Rates and High Pressures: Experimental Characteriz

Introduction:

Understanding the behavior of concrete under high-strain-rate impact loading is of critical importance in a range of civilian and military applications. The protective concrete shells of nuclear power plants are expected to survive the impact loading from an incoming missile or other sources. Dynamic loading on concrete structures arising from natural hazards such as earthquakes, tornadoes and ocean waves is of great practical concern. Successful destruction of military targets and effective protection of defense structures also require such understanding. Despite some published data, there is still a serious lack of experimental data and understanding concerning the behavior of concrete under conditions involving very high strain rates and high pressures. This need has motivated the current research. The research involves both experimental characterization and numerical simulations.

Experimental Characterization:

The experimental investigation uses split Hopkinson pressure bar (SHPB) and plate impact to achieve a range of loading rate and hydrostatic pressure. The SHPB experiments on mortar involve strain rates on the order of 102-103 s-1 without lateral confinement . The plate impact experiments  subject the materials to deformation at strain rates on 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 MPa 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.

Numerical Simulation:

The response of concrete and mortar under high-strain-rate impact loading are analyzed using fully dynamic finite element simulations. The simulations concern 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 . Analyses focus on the evolution of stress-carrying and energy absorption capacities of concrete under impact loading. 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.