Cohesive Crack Modeling of Influence of Sudden Changes in Loading Rate on Concrete Fracture

-The results of an experimental study of a sudden change in loading rate on the fracture behavior of normaland high-strength concrete specimens of three different sizes are reported. Geometrically similar three-point bend specimens were subjected to either a sudden 1000-fold increase or a 10-fold decrease of the loading rate. It was observed that for a large increase of the loading rate, the post-peak softening can be reversed to hardening followed by a second peak of the stress-strain diagram. A sudden decrease of the loading rate initially causes a steeper softening slope of this diagram. The results are similar for normal and high strength concrete specimens. The viscoelastic cohesive crack model with the rate-dependent softening law is used to model the experimental results. INTRODUCTION ALTHOUGH CLASSICAL fracture mechanics is a rate-independent theory, the strength and fracture properties of Portland cement concrete and other cementitious materials, as well as many other brittle materials, depend on the loading rate [1-3]. One source of the rate sensitivity observed in brittle materials, such as concrete, is thermally activated crack growth [4, 5]. The explanation of the rate sensitivity of crack growth is well known--the probability that the thermal vibration energy of an atom or molecule would exceed the activation energy barrier of the bond increases with the superimposed potential due to the applied stress. A second source of rate sensitivity is creep of the material in the bulk of the specimen, which alters the stress field near the crack tip [6-10]. The rate effects in concrete fracture have been thoroughly investigated at fast, dynamic loading rates, in which the time to reach peak load is less than 1 s [11-13]. Creep is negligible at fast loading rates but the inertial effects complicate the observed fracture behavior [14]. Creep effects, which have insufficient time to develop at fast, dynamic loading rates, dominate the fracture behavior at slow, static loading rates [15]. The fracture behavior of concrete structures with rates corresponding to the times to reach the peak load ranging up to many years is of great practical interest. This knowledge is needed to predict the long-term cracking and failure of large fracture-sensitive structures, such as concrete dams. In a detailed study, Ba~ant and Gettu [16] investigated the rate effect in the static range with the time to peak load ranging from 1 s to 2.5 days. They showed the fracture toughness to decrease with a decreasing loading rate, similar to what had already been known for the dynamic range [17]. As a new, surprising result, the effective length of the fracture process zone was also found to decrease with a decreasing rate. From their study, the existence of a strong interaction between the fracture properties and the creep of concrete became clear. The results of Ba~ant and Gettu, which are limited to constant loading rates, have been modeled successfully by B~ant and Li [18] using a viscoelastic cohesive crack model with a rate-dependent softening law. Their model of fracture in a viscoelastic medium consists of a nonlinear version of the cohesive crack model, in which the process zone is considered to be of finite size. This model is applicable to the crack initiation stage; the crack-growth stage can be obtained as the asymptotic limit. The cohesive stress distribution in the process zone ahead of the actual crack tip is considered as 987 e r on l. , .6, , 5 right 5 ier i nce . n ed 944/95 .50 SI E CK ELING ENCE EN GES ING RETE TURE