A repairability index for reinforced concrete members based on fracture mechanics

This paper proposes a repairability index for damage assessment in reinforced concrete structural members. The procedure discussed in this paper differs from the standard methods in two aspects: the structural and damage analyses are coupled and it is based on the concepts of fracture and continuum damage mechanics. The relationship between the repairability index and the well-known Park and Ang index is shown in some particular cases.

Flow and fracture behaviour of FV535 steel at different triaxialities, strain rates and temperatures

The new generation jet engines operate at highly demanding working conditions. Such conditions need very precise design which implies an exhaustive study of the engine materials and behaviour in their extreme working conditions. With this purpose, this work intends to describe a numerically-based calibration of the widely-used Johnson–Cook fracture model, as well as its validation through high temperature ballistic impact tests. To do so, a widely-used turbine casing material is studied. This material is the Firth Vickers 535 martensitic stainless steel. Quasi-static tensile tests at various temperatures in a universal testing machine, as well as dynamic tests in a Split Hopkinson Pressure Bar, are carried out at different triaxialities. Using ABAQUS/Standard and LS-DYNA numerical codes, experimental data are matched. This method allows the researcher to obtain critical data of equivalent plastic strain and triaxility, which allows for more precise calibration of the Johnson–Cook fracture model. Such enhancement allows study of the fracture behaviour of the material across its usage temperature range.

Fracture behaviour of notched round bars made of PMMA subjected to torsion at -60 °C

This paper presents seventy new experimental results from PMMA notched specimens tested under torsion at 60 C. The notch root radius ranges from 0.025 to 7.0 mm. At this temperature the non-linear effects previously observed on specimens of the same material tested at room temperature strongly reduce. The averaged value of the strain energy density over a control volume is used to assess the critical loads to failure. The radius of the control volume and the critical strain energy density are evaluated a priori by using in combination the mode III critical stress intensity factor from cracked-like specimens and the critical stress to failure detected from semicircular notches with a large notch root radius

Finite element simulation of sandwich panels of plasterboard and rock wool under mixed mode fracture

This paper presents the results of research on mixed mode fracture of sandwich panels of plasterboard and rock wool. The experimental data of the performed tests are supplied. The specimens were made from commercial panels. Asymmetrical three-point bending tests were performed on notched specimens. Three sizes of geometrically similar specimens were tested for studying the size effect. The paper also includes the numerical simulation of the experimental results by using an embedded cohesive crack model.The involved parameters for modelling are previously measured by standardised tests.

Fracture of concrete structural members subjected to blast

If reinforced concrete structures are to be safe under extreme impulsive loadings such as explosions, a broad understanding of the fracture mechanics of concrete under such events is needed. Most buildings and infrastructures which are likely to be subjected to terrorist attacks are borne by a reinforced concrete (RC) structure. Up to some years ago, the traditional method used to study the ability of RC structures to withstand explosions consisted on a choice between handmade calculations, affordable but inaccurate and unreliable, and full scale experimental tests involving explosions, expensive and not available for many civil institutions. In this context, during the last years numerical simulations have arisen as the most effective method to analyze structures under such events. However, for accurate numerical simulations, reliable constitutive models are needed. Assuming that failure of concrete elements subjected to blast is primarily governed by the tensile behavior, a constitutive model has been built that accounts only for failure under tension while it behaves as elastic without failure under compression. Failure under tension is based on the Cohesive Crack Model. Moreover, the constitutive model has been used to simulate the experimental structural response of reinforced concrete slabs subjected to blast. The results of the numerical simulations with the aforementioned constitutive model show its ability of representing accurately the structural response of the RC elements under study. The simplicity of the model, which does not account for failure under compression, as already mentioned, confirms that the ability of reinforced concrete structures to withstand blast loads is primarily governed by tensile strength.

Estudio de la tolerancia al daño de los materiales y sistemas de pretensado

La mayoría de las estructuras de hormigón pretensadas construidas en los últimos 50 años han demostrado una excelente durabilidad cuando su construcción se realiza atendiendo las recomendaciones de un buen diseño así como una buena ejecución y puesta en obra de la estructura. Este hecho se debe en gran parte al temor que despierta el fenómeno de la corrosión bajo tensión típico de las armaduras de acero de alta resistencia. Menos atención se ha prestado a la susceptibilidad a la corrosión bajo tensión de los anclajes de postensado, posiblemente debido a que se han reportado pocos casos de fallos catastróficos. El concepto de Tolerancia al Daño y la Mecánica de la Fractura en estructuras de Ingeniería Civil ha empezado a incorporarse recientemente en algunas normas de diseño y cálculo de estructuras metálicas, sin embargo, aún está lejos de ser asimilado y empleado habitualmente por los ingenieros en sus cálculos cuando la ocasión lo requiere. Este desconocimiento de los aspectos relacionados con la Tolerancia al Daño genera importantes gastos de mantenimiento y reparación. En este trabajo se ha estudiado la aplicabilidad de los conceptos de la Mecánica de la Fractura a los componentes de los sistemas de postensado empleados en ingeniería civil, empleándolo para analizar la susceptibilidad de las armaduras activas frente a la corrosión bajo tensiones y a la pérdida de capacidad portante de las cabezas de anclajes de postensado debido a la presencia de defectos. Con este objeto se han combinado tanto técnicas experimentales como numéricas. Los defectos superficiales en los alambres de pretensado no se presentan de manera aislada si no que existe una cierta continuidad en la dirección axial así como un elevado número de defectos. Por este motivo se ha optado por un enfoque estadístico, que es más apropiado que el determinístico. El empleo de modelos estadísticos basados en la teoría de valores extremos ha permitido caracterizar el estado superficial en alambres de 5,2 mm de diámetro. Por otro lado la susceptibilidad del alambre frente a la corrosión bajo tensión ha sido evaluada mediante la realización de una campaña de ensayos de acuerdo con la actual normativa que ha permitido caracterizar estadísticamente su comportamiento. A la vista de los resultados ha sido posible evaluar como los parámetros que definen el estado superficial del alambre pueden determinar la durabilidad de la armadura atendiendo a su resistencia frente a la corrosión bajo tensión, evaluada mediante los ensayos que especifica la normativa. En el caso de las cabezas de anclaje de tendones de pretensado, los defectos se presentan de manera aislada y tienen su origen en marcas, arañazos o picaduras de corrosión que pueden producirse durante el proceso de fabricación, transporte, manipulación o puesta en obra. Dada la naturaleza de los defectos, el enfoque determinístico es más apropiado que el estadístico. La evaluación de la importancia de un defecto en un elemento estructural requiere la estimación de la solicitación local que genera el defecto, que permite conocer si el defecto es crítico o si puede llegar a serlo, si es que progresa con el tiempo (por fatiga, corrosión, una combinación de ambas, etc.). En este trabajo los defectos han sido idealizados como grietas, de manera que el análisis quedara del lado de la seguridad. La evaluación de la solicitación local del defecto ha sido calculada mediante el empleo de modelos de elementos finitos de la cabeza de anclaje que simulan las condiciones de trabajo reales de la cabeza de anclaje durante su vida útil. A partir de estos modelos numéricos se ha analizado la influencia en la carga de rotura del anclaje de diversos factores como la geometría del anclaje, las condiciones del apoyo, el material del anclaje, el tamaño del defecto su forma y su posición. Los resultados del análisis numérico han sido contrastados satisfactoriamente mediante la realización de una campaña experimental de modelos a escala de cabezas de anclaje de Polimetil-metacrilato en los que artificialmente se han introducido defectos de diversos tamaños y en distintas posiciones. ABSTRACT Most of the prestressed concrete structures built in the last 50 years have demonstrated an excellent durability when they are constructed in accordance with the rules of good design, detailing and execution. This is particularly true with respect to the feared stress corrosion cracking, which is typical of high strength prestressing steel wires. Less attention, however, has been paid to the stress corrosion cracking susceptibility of anchorages for steel tendons for prestressing concrete, probably due to the low number of reported failure cases. Damage tolerance and fracture mechanics concepts in civil engineering structures have recently started to be incorporated in some design and calculation rules for metallic structures, however it is still far from being assimilated and used by civil engineers in their calculations on a regular basis. This limited knowledge of the damage tolerance basis could lead to significant repair and maintenance costs. This work deals with the applicability of fracture mechanics and damage tolerance concepts to the components of prestressed systems, which are used in civil engineering. Such concepts have been applied to assess the susceptibility of the prestressing steel wires to stress corrosion cracking and the reduction of load bearing capability of anchorage devices due to the presence of defects. For this purpose a combination of experimental work and numerical techniques have been performed. Surface defects in prestressing steel wires are not shown alone, though a certain degree of continuity in the axial direction exist. A significant number of such defects is also observed. Hence a statistical approach was used, which is assumed to be more appropriate than the deterministic approach. The use of statistical methods based in extreme value theories has allowed the characterising of the surface condition of 5.2 mm-diameter wires. On the other hand the stress corrosion cracking susceptibility of the wire has been assessed by means of an experimental testing program in line with the current regulations, which has allowed statistical characterisasion of their performances against stress corrosion cracking. In the light of the test results, it has been possible to evaluate how the surface condition parameters could determine the durability of the active metal armour regarding to its resistance against stress corrosion cracking assessed by means of the current testing regulations. In the case of anchorage devices for steel tendons for prestressing concrete, the damage is presented as point defects originating from dents, scratches or corrosion pits that could be produced during the manufacturing proccess, transport, handling, assembly or use. Due to the nature of these defects, in this case the deterministic approach is more appropriate than the statistical approach. The assessment of the relevancy of defect in a structural component requires the computation of the stress intensity factors, which in turn allow the evaluation of whether the size defect is critical or could become critical with the progress of time (due to fatigue, corrosion or a combination of both effects). In this work the damage is idealised as tiny cracks, a conservative hypothesis. The stress intensity factors have been calculated by means of finite element models of the anchorage representing the real working conditions during its service life. These numeric models were used to assess the impact of some factors on the rupture load of the anchorage, such the anchorage geometry, material, support conditions, defect size, shape and its location. The results from the numerical analysis have been succesfully correlated against the results of the experimental testing program of scaled models of the anchorages in poly-methil methacrylate in which artificial damage in several sizes and locations were introduced.

Coupled model of initiation and propagation of corrosion in reinforced concrete

Corrosion of reinforcing steel in concrete due to chloride ingress is one of the main causes of the deterioration of reinforced concrete structures. Structures most affected by such a corrosion are marine zone buildings and structures exposed to de-icing salts like highways and bridges. Such process is accompanied by an increase in volume of the corrosión products on the rebarsconcrete interface. Depending on the level of oxidation, iron can expand as much as six times its original volume. This increase in volume exerts tensile stresses in the surrounding concrete which result in cracking and spalling of the concrete cover if the concrete tensile strength is exceeded. The mechanism by which steel embedded in concrete corrodes in presence of chloride is the local breakdown of the passive layer formed in the highly alkaline condition of the concrete. It is assumed that corrosion initiates when a critical chloride content reaches the rebar surface. The mathematical formulation idealized the corrosion sequence as a two-stage process: an initiation stage, during which chloride ions penetrate to the reinforcing steel surface and depassivate it, and a propagation stage, in which active corrosion takes place until cracking of the concrete cover has occurred. The aim of this research is to develop computer tools to evaluate the duration of the service life of reinforced concrete structures, considering both the initiation and propagation periods. Such tools must offer a friendly interface to facilitate its use by the researchers even though their background is not in numerical simulation. For the evaluation of the initiation period different tools have been developed: Program TavProbabilidade: provides means to carry out a probability analysis of a chloride ingress model. Such a tool is necessary due to the lack of data and general uncertainties associated with the phenomenon of the chloride diffusion. It differs from the deterministic approach because it computes not just a chloride profile at a certain age, but a range of chloride profiles for each probability or occurrence. Program TavProbabilidade_Fiabilidade: carries out reliability analyses of the initiation period. It takes into account the critical value of the chloride concentration on the steel that causes breakdown of the passive layer and the beginning of the propagation stage. It differs from the deterministic analysis in that it does not predict if the corrosion is going to begin or not, but to quantifies the probability of corrosion initiation. Program TavDif_1D: was created to do a one dimension deterministic analysis of the chloride diffusion process by the finite element method (FEM) which numerically solves Fick’second Law. Despite of the different FEM solver already developed in one dimension, the decision to create a new code (TavDif_1D) was taken because of the need to have a solver with friendly interface for pre- and post-process according to the need of IETCC. An innovative tool was also developed with a systematic method devised to compare the ability of the different 1D models to predict the actual evolution of chloride ingress based on experimental measurements, and also to quantify the degree of agreement of the models with each others. For the evaluation of the entire service life of the structure: a computer program has been developed using finite elements method to do the coupling of both service life periods: initiation and propagation. The program for 2D (TavDif_2D) allows the complementary use of two external programs in a unique friendly interface: • GMSH - an finite element mesh generator and post-processing viewer • OOFEM – a finite element solver. This program (TavDif_2D) is responsible to decide in each time step when and where to start applying the boundary conditions of fracture mechanics module in function of the amount of chloride concentration and corrosion parameters (Icorr, etc). This program is also responsible to verify the presence and the degree of fracture in each element to send the Information of diffusion coefficient variation with the crack width. • GMSH - an finite element mesh generator and post-processing viewer • OOFEM – a finite element solver. The advantages of the FEM with the interface provided by the tool are: • the flexibility to input the data such as material property and boundary conditions as time dependent function. • the flexibility to predict the chloride concentration profile for different geometries. • the possibility to couple chloride diffusion (initiation stage) with chemical and mechanical behavior (propagation stage). The OOFEM code had to be modified to accept temperature, humidity and the time dependent values for the material properties, which is necessary to adequately describe the environmental variations. A 3-D simulation has been performed to simulate the behavior of the beam on both, action of the external load and the internal load caused by the corrosion products, using elements of imbedded fracture in order to plot the curve of the deflection of the central region of the beam versus the external load to compare with the experimental data.

Modelling of corrosion-induced cover cracking in reinforced concrete by an embedded cohesive crack finite element

Corrosion of a reinforcement bar leads to expansive pressure on the surrounding concrete that provokes internal cracking and, eventually, spalling and delamination. Here, an embedded cohesive crack 2D finite element is applied for simulating the cracking process. In addition, four simplified analytical models are introduced for comparative purposes. Under some assumptions about rust properties, corrosion rate, and particularly, the accommodation of oxide products within the open cracks generated in the process, the proposed FE model is able to estimate time to surface cracking quite accurately. Moreover, emerging cracking patterns are in reasonably good agreement with expectations. As a practical case, a prototype application of the model to an actual bridge deck is reported.

A computer program for bridge retrofitting

This paper summarizes the work developed in order to establish a framework for seismic retrofitting of bridges. In this context, the first objetive is to find a numerical model to evaluate the damage induced in a structure, under seismic action, as an index of its vulnerability. The model used has the adventage that is based on concepts of fracture mechanics and concentrated plasticity. As a result, the work is based on basic principles. The performance of this model is being evaluated. Some results of the computer program developed for this purpose are shown.

An embedded cohesive crack model for finite element analysis of quasi-brittle materials

This paper presents a numerical implementation of the cohesive crack model for the anal-ysis of quasibrittle materials based on the strong discontinuity approach in the framework of the finite element method. A simple central force model is used for the stress versus crack opening curve. The additional degrees of freedom defining the crack opening are determined at the crack level, thus avoiding the need for performing a static condensation at the element level. The need for a tracking algorithm is avoided by using a consistent pro-cedure for the selection of the separated nodes. Such a model is then implemented into a commercial program by means of a user subroutine, consequently being contrasted with the experimental results. The model takes into account the anisotropy of the material. Numerical simulations of well-known experiments are presented to show the ability of the proposed model to simulate the fracture of quasibrittle materials such as mortar, concrete and masonry.

Modelling of chloride transport in non-saturated concrete : from microscale to macroscale

A model for chloride transport in concrete is proposed. The model accounts for transport several transport mechanisms such as diffusion, advection, migration, etc. This work shows the chloride transport equations at the macroscopic scale in non-saturated concrete. The equations involve diffusion, migration, capillary suction, chloride combination and precipitation mechanisms. The material is assumed to be infinitely rigid, though the porosity can change under influence of chloride binding and precipitation. The involved microscopic and macroscopic properties of the materials are measured by standardized methods. The variables which must be imposed on the boundaries are temperature, relative humidity and chloride concentration. The output data of the model are the free, bound, precipitated and total chloride ion concentrations, as well as the pore solution content and the porosity. The proposed equations are solved by means of the finite element method (FEM) implemented in MATLAB (classical Galerkin formulation and the streamline upwind Petrov-Galerkin (SUPG) method to avoid spatial instabilities for advection dominated flows).

Study of concrete cracking during accelerated corrosion tests in reinforced concrete

Cracking of reinforced concrete can occur in certain environments due to rebar corrosion. The oxide layer growing around the bars introduces a pressure which may be enough to lead to the fracture of concrete. To study such an effect, the results of accelerated corrosion tests and finite ele- ment simulations are combined in this work. In previous works, a numerical model for the expansive layer, called expansive joint element , was programmed by the authors to reproduce the effect of the oxide over the concrete. In that model, the expansion of the oxide layer in stress free conditions is simulated as an uniform expansion perpendicular to the steel surface. The cracking of concrete is simulated by means of finite elements with an embedded adaptable cohesive crack that follow the standard cohesive model. In the present work, further accelerated tests with imposed constant cur- rent have been carried out on the same type of specimens tested in previous works (with an embedded steel tube), while measuring, among other things, the main-crack mouth opening. Then, the tests have been numerically simulated using the expansive joint element and the tube as the corroding electrode (rather than a bar). As a result of the comparison of numerical and experimental results, both for the crack mouth opening and the crack pattern, new insight is gained into the behavior of the oxide layer. In particular, quantitative assessment of the oxide expansion relation is deduced from the ex- periments, and a narrower interval for the shear stiffness of the oxide layer is obtained, which could not be achieved using bars as the corroding element, because in that case the numerical results were insensitive to the shear stiffness of the oxide layer within many orders of magnitude

An experimental and numerical study of the pattern of cracking of concrete due to steel reinforcement corrosion

In this work, cracking of concrete due to steel reinforcement corrosion is experimentally and numerically studied. The tests combined accelerated corrosion—to generate the cracks—with impregnation under vacuum with resin containing fluorescein—to enhance their visibility under ultraviolet light. In parallel, a model—called expansive joint element—was developed to simulate the expansion of the oxide and finite elements with an embedded adaptable cohesive crack were used to describe concrete cracking. The results show that a good agreement exists between the experimental and numerical crack patterns, which constitutes promising progress towards a comprehensive understanding of corrosion-induced cracking in reinforced concrete.

Cover cracking of the reinforced concrete due to rebar corrosion induced by chloride penetration

Este artículo estudia el proceso de fisuración del hormigón por corrosión de la armadura. Se presenta un modelo de transporte de cloruros en el hormigón, que contempla la no-linealidad de los coeficientes de difusión, las isotermas de absorción y el fenómeno de convección. A partir de los resultados de penetración de cloruros, se establece la corrosión de la armadura con la consiguiente expansión radial. La fisuración del hormigón se estudia con un modelo de fisura embebida. Los dos modelos (iniciación y propagación) se incorporan en un programa de elementos finitos. El modelo se contrasta con resultados experimentales, obteniéndose un buen ajuste. Una de las dificultades es establecer el umbral de concentración de cloruros que da lugar al inicio de la corrosión de la armadura.This paper is focused on the chloride-induced corrosion of the rebar in RC. A comprehensive model for the chloride ingress into concrete is presented, with special attention to non-linear diffusion coefficients, chloride binding isotherms and convection phenomena. Based on the results of chloride diffusion, subsequent active corrosion is assumed and the radial expansion of the corroded reinforcement reproduced. For cracking simulation, the Strong Discontinuity Approach is applied. Both models (initiation and propagation corrosion stages) are incorporated in the same finite element program and chained. Comparisons with experimental results are carried out, with reasonably good agreements being obtained, especially for cracking patterns. Major limitations refer to difficulties to establish precise levels of basic data such as the chloride ion content at concrete surface, the chloride threshold concentration that triggers active corrosion, the rate of oxide production or the rust mechanical properties.

Numerical simulation of the transition from densely distributed to localized cracking.

8th International Conference on Fracture Mechanics of Concrete and Concrete Structures (FraMCoS8).