Showing papers by "Zdenek P. Bazant published in 2016"

Experimental and Numerical Investigation of Intra-Laminar Energy Dissipation and Size Effect in Two-Dimensional Textile Composites

Abstract: Design of large composite structures requires understanding the scaling of their mechanical properties, an aspect often overlooked in the literature on composites. This contribution analyzes, experimentally and numerically, the intra-laminar size effect of textile composite structures. Test results of geometrically similar Single Edge Notched specimens made of 8 layers of 0 degree epoxy/carbon twill 2 by 2 laminates are reported. Results show that the nominal strength decreases with increasing specimen size and that the experimental data can be fitted well by Bazant's size effect law, allowing an accurate identification of the intra-laminar fracture energy of the material. The importance of an accurate estimation of Gf in situations where intra-laminar fracturing is the main energy dissipation mechanism is clarified by studying numerically its effect on crashworthiness of composite tubes. Simulations demonstrate that, for the analyzed geometry, a decrease of the fracture energy to 50% of the measured value corresponds to an almost 42% decrease in plateau crushing load. Further, assuming a vertical stress drop after the peak, a typical assumption of strength-based constitutive laws implemented in most commercial Finite Element codes, results in an strength underestimation of the order of 70%. The main conclusion of this study is that measuring accurately fracture energy and modeling correctly the fracturing behavior of textile composites, including their quasi-brittleness, is key. This can be accomplished neither by strength- or strain-based approaches, which neglect size effect, nor by LEFM which does not account for the finiteness of the Fracture Process Zone.

Direct Testing of Gradual PostPeak Softening of Notched Specimens of Fiber Composites Stabilized by Enhanced Stiffness and Mass

Abstract: Static and dynamic analysis of the fracture tests of fiber composites in hydraulically servo-controlled testing machines currently in use shows that their grips are much too soft and light for observing the postpeak softening. Based on static and dynamic analysis of the test setup, far stiffer and heavier grips are proposed. Tests of compact-tension fracture specimens of woven carbon-epoxy laminates prove this theoretical conclusion. Sufficiently stiff grips allow observation of a stable postpeak, even under load-point displacement control. Dynamic stability analysis further indicates that stable postpeak can be observed under CMOD control provided that a large mass is rigidly attached to the current soft grips. The fracture energy deduced from the area under the measured complete load-deflection curve with stable postpeak agrees closely with the fracture energy deduced from the size effect tests of the same composite. Previous suspicions of dynamic snapback in the testing of composites are dispelled. So is the previous view that fracture mechanics was inapplicable to the fiber-polymer composites.

Strain Rate Dependent Microplane Constitutive Model for Comminution of Concrete under Projectile Impact

Abstract: The pulverization, fracturing and crushing of materials, briefly called comminution, creates numerous cracks which dissipate a large amount of kinetic energy during projectile impact. At high shear strain rates (10/s − 10/s), this causes an apparent large increase of strength, called ‘dynamic overstress’. This long debated phenomenon has recently been explained by the theory of release of local kinetic energy of shear strain rate in finite size particles that are about to form. The theory yields the particle size and the additional kinetic energy density that must be dissipated in finite element codes. In previous research, it was dissipated by additional viscosity, in a model partly analogous to turbulence theory. Here it is dissipated by scaling up the material strength. Microplane model M7 is used and its stress-strain boundaries are scaled up by theoretically derived factors proportional to the −4/3 power of the effective deviatoric strain rate and to its time derivative. The crack band model with a random tetrahedral mesh is used and all the artificial damping is eliminated from the finite element program. The scaled model M7 is seen to predict the crater shapes and exit velocities of projectiles penetrating concrete walls as closely as the previous models. The choice of the finite strain threshold for element deletion, which can have a big effect, is also studied. It is proposed to use the highest threshold above which a further increase has a negligible effect.