D.A. Cendón

Generalizations and specializations of cohesive crack models

Abstract This paper presents an overview of the cohesive crack model, one of the basic models used so far to describe the fracture of concrete and other quasibrittle materials. Recent developments and needs for further research are discussed. The displayed evidence and the discussion are based on considering the cohesive crack model as a constitutive assumption rather than an ad hoc model for the behaviour ahead of a preexisting crack. Topics addressed are fracture of unnotched specimens, mixed mode fracture, diffuse cracking, anomalous stress–strain curves, size effect and asymptotic analysis, and strength of structural elements with notches.

Modelling the fracture of concrete under mixed loading

A simple and efficient numerical procedure for mixed mode fracture of quasibrittle materials is shown: This technique predicts crack trajectories as well as load-displacement or load-CMOD responses. The model is based on the cohesive crack concept and uses the local mode I approach. Numerical results agree quite well with three experimental sets of mixed mode fracture of concrete beams; one from Arrea and Ingraffea, another from García, Gettu and Carol and from a nonproportional loading by the authors. In constrast to more sophisticated models, this method offers two major advantages: it requires only material properties measured by standardized methods and it can easily be implemented with general multipurpose finite element codes.

A discrete crack approach to normal/shear cracking of concrete

This paper presents a numerical procedure for mixed mode fracture of quasi-brittle materials. The numerical procedure is based on the cohesive crack approach and extends it to mixed mode fracture. The crack path is obtained, and the mixed mode fracture model is incorporated into the crack path. The crack model is based on the formulation of the classical plasticity. The model is incorporated into a commercial finite element code by an user subroutine and is contrasted with experimental results. The numerical results agree quite well with two experimental sets of mixed mode fracture of concrete beams; one from Arrea and Ingraffea, the other from a nonproportional loading by the authors. Two other sets of experimental fracture results were modeled based on double-edge notched testing. The numerical procedure, mainly based on standard properties of the material measured by standard methods, predicts the experimental records of the load versus displacement at several control points of the specimens for three homothetic sizes of specimen.

Influence of shear parameters on mixed-mode fracture of concrete

The influence of the mode II fracture parameters on the mixed mode fracture experimental tests of quasibrittle materials is studied. The study is based on experimental results and numerical analyses. For the numerical study, a procedure for mixed mode fracture of quasibrittle materials is presented. The numerical procedure is based on the cohesive crack approach, and extends it to mixed mode fracture. Four experimental sets of mixed mode fracture were modelled, one from Arrea and Ingraffea and another from a nonproportional loading by the authors, both with bending concrete beams. Two other sets of experimental fracture were modelled, based on double-edge notched testing; in these tests an important mode II is beforehand expected. The numerical results agree quite well with experimental records. The influence of the main parameters for mode II fracture on the mixed mode fracture is studied for the four experimental set of tests and compared with these results. In all them, large changes in the mode II fracture energy hardly modify the numerical results. The tangential and normal stresses along the crack path during the loading proccess are obtained, also with different values of the mode II fracture energy. For the studied experimental tests it is concluded that the crack is initiated under mixed mode but propagated under predominant mode I. This allows a development of mixed mode fracture models, mainly based on standard properties of the material measured by standard methods, avoiding the problems associated with the measurement of mode II fracture parameters, such as mode II fracture energy and cohesion.

Blast Response Analysis of Reinforced Concrete Slabs: Experimental Procedure and Numerical Simulation

A series of blast loading experiments are performed with the aim of providing experimental data for the development and adjustment of numerical tools needed in the modeling of concrete elements subjected to blast. To this end, an experimental setup that allows testing up to four concrete elements simultaneously under the same blast load is developed. Altogether four detonation tests are conducted, in which 12 slabs of two different concrete types are subjected to the same blast load. Results of the experimental program are validated by numerical simulation using two different material models for the prediction of concrete behavior. Major assets of the experimental setup presented are the reduction of scattering on detonation tests and its cost effectiveness. Results from tests and numerical simulations suggest that the ability of reinforced concrete structures of withstanding blast loads is primarily governed by their tensile strength.

Modelling Explosions Using ALE Meshes: TheInfluence Of Mesh Refinement In Pressures AndIn Efforts Induced By Blast/structure Interaction

Hydrocodes are becoming a very important tool for simulation of explosive loads and the interaction between the shock wave and possible structures stroked. Landmine explosions and the damage induced when they explode under an armoured vehicle are good examples of this. However this type of simulation usually requires very complex meshes, which must also be able to reproduce a large number of elements involved in the simulation, such as the explosive, the air, the wheels, the transmission...etc. Furthermore, the problem worsens if we take into account that very small size element meshes are required if we are looking for a good accuracy of the calculations, especially when we want a good approximation for the sharp pressure peaks that appear during an explosion. In this work, numerical results are presented from a research focused on the study of the mesh refinement influence in this type of problem. The study has been focused specially in two fundamental variables: time-pressure history and the time-integral of pressure with respect to time history.

Measurement of fracture properties of concrete at high strain rates

An analysis of the spalling technique of concrete bars using the modified Hopkinson bar was carried out. A new experimental configuration is proposed adding some variations to previous works. An increased length for concrete specimens was chosen and finite-element analysis was used for designing a conic projectile to obtain a suitable triangular impulse wave. The aim of this initial work is to establish an experimental framework which allows a simple and direct analysis of concrete subjected to high strain rates. The efforts and configuration of these primary tests, as well as the selected geometry and dimensions for the different elements, have been focused to achieve a simple way of identifying the fracture position and so the tensile strength of tested specimens. This dynamic tensile strength can be easily compared with previous values published in literature giving an idea of the accuracy of the method and technique proposed and the possibility to extend it in a near future to obtain other mechanical properties such as the fracture energy. The tests were instrumented with strain gauges, accelerometers and high-speed camera in order to validate the results by different ways. Results of the dynamic tensile strength of the tested concrete are presented. This article is part of the themed issue ‘Experimental testing and modelling of brittle materials at high strain rates’.

Fracture Behavior of Notched Round Bars Made of Gray Cast Iron Subjected to Torsion

This paper presents 25 new experimental results from gray cast iron notched specimens tested under torsion loading. V-notch (with an opening angle of 120°) is considered with a root radius ranging from 0.1 to 2.0 mm. Plots of torque loads versus twist angles are recorded varying the notch root radius. Such results can help in evaluating numerical and theoretical models of the fracture of notched components under mode III loading. The second part of the paper deals with a discussion on the experimental results. A non-conventional application of the strain energy density is carried out showing a good agreement between experimental results and theoretical fracture assessments and it is used to justify the link between nominal and local fracture approaches.

The Cohesive Crack Model Applied to Notched PMMA Specimens Obeying a Non Linear Behaviour under Torsion Loading

This article presents a new material model developed with the aim of analyzing failure of blunt notched components made of nonlinear brittle materials. The model, which combines the cohesive crack model with Henckys theory of total deformations, is used to simulate an experimental benchmark carried out previously by the authors. Such combination is achieved through the embedded crack approach concept. In spite of the unavailability of precise material data, the numerical predictions obtained show good agreement with the experimental results.

An Experimental and Numerical Study of Ballistic Impacts on a Turbine Casing Material at Varying Temperatures

An experimental and numerical study of ballistic impacts on steel plates at various temperatures (700°C, 400°C and room temperature) has been carried out. The motivation for this work is the blade-off event that may occur inside a jet engine turbine. However, as a first attempt to understand this complex loading process, a somewhat simpler approach is carried out in the present work. The material used in this study is the FV535 martensitic stainless steel, which is one of the most commonly used materials for turbine casings. Based on material test data, a Modified Johnson-Cook (MJC) model was calibrated for numerical simulations using the LS-DYNA explicit finite element code. To check the mesh size sensitivity, 2D axisymmetric finite element models with three different mesh sizes and configurations were used for the various temperatures. Two fixed meshes with 64 and 128 elements over the 2 mm thick plate and one mesh with 32 elements over the thickness with adaptive remeshing were used in the simulations. Both the formation of adiabatic shear bands in the perforation process and the modeling of the thermal softening effects at high temperatures have been found crucial in order to achieve good results.