guideline for seismic vulnerability reduction in the urban environment

8/13/2019 Guideline for Seismic Vulnerability Reduction in the Urban Environment

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Guidelines for Seismic Vulnerability Reduction in the Urban Environment 43

3.1.6 Quality control

Last point on this section deals with the quality control, which not only becomes animportant issue, but it can be essential to assure the structural integrity of the designedcomponent or reinforcement.

During the fabrication of the different FRP applications on the projects, a number ofcontrol points, to ensure the quality of the methods used, shall have to be considered. These control points are divided into three categories.

Fabrication procedures of the different structural components. Workmanship of the unions to the structure. Testing of the materials used on site to ensure compliance with the design

hypothesis.

3.1.6.1 Check-points during installation

Materials.- Compliance with the characteristics required by the project

- Quality certificates- Ensure that the handling and delivery of the materials comply with therecommendations made by both the designer and manufacturer.

Surface treatment- Ensure that the concrete surface has been prepared in accordance with

the project specifications.- Check for a regular surface- Always try to obtain rounded corners (with a minimum radius of 3cm

where practicable)

- Check that the FRP surface has been properly treated. Adhesive

- Determine the right amount of adhesive- Have the different adhesive components been properly mixed- Make sure that the application operations are completed while the

adhesive is workable. The temperature at which the procedure is carriedout will have a strong influence.


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LESSLOSS Risk Mitigation for Earthquakes and Landslides44

- See that the adhesive layer thickness is the correct one.- Verify the level of vibration of the structure while the adhesive is curing.

Plates- Separation between plate and surface- Plate installation. Check fibre orientation.- Try not to move the plates once they have been bonded to the concrete.- Check for the existence of metallic areas in contact with the carbon fibre

plates.

Fabrication- Amount of resin used. Try to comply with the design amounts.- Check that the mixing proportions are the correct ones.- Following compaction, avoid rough or irregular surfaces during site

installation.- Try not to move the materials after the application- Verify the quality of each plate installed before placing the next one.

Curing- Verify whether the FRP curing has been properly done

Tests- Preparation of specimens in accordance with the specifications

Inspection- Assess the best installation method, vacuum, countermold, air drying or

other methods.

Filing of documents- All the operations shall be documented, or digitally recorded, if deemed

necessary for a better understanding of the works performed.


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3.1.6.2 Site tests

The following table (Table 3-5) describes the possible site tests to be conducted on thematerials used on the project in order to check the manufacturers specifications, whichallow us to assess the feasibility on the on-site element installation.

Table 3-5. Site test specification

Property to be checked Standard Requirements Youngs modulus in deflection EN ISO 178 > 2000 N/mm2

Youngs modulus in compression EN 13412 > 2000 N/mm2Shear strength EN 12188 > 12 N/mm2

Maximum overall expansion for any point EN 12617-1En 12617-3

< 0.1%

Glass transition temperature EN 12614 > 45C, or 20C aboveambient temperature

3.1.6.3 Inspection recommendations

Even though workmanship standards can be very high, there are always factors that arenot taken into account, from the workmanship point of view, and that, after some time,they come to the surface.

For this reason, it shall be necessary to set up a number of inspections on the completed work, in order to ascertain that the reinforcements are fulfilling their function and to beable to correct, in time, any eventual problem that might arise.

The ideal inspection frequency could be set up as follows:

Table 3-6. Inspection recommendations

Structure Inspection Detailed InspectionBridge Every year Every 6 years, or less

Buildings Every year Every 10 years, due to different usage orstructural change

Other structures Depending on use Every 10 years or Depending on use


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Composite materials, by their very nature, hardly need any maintenance while inoperation. Even so, it shall be necessary to conduct a visual inspection to check forcracks, breakages or delaminations that could indicate the level of damage. It shall also benecessary to evaluate eventual damages to the material caused by accidents.

Should the strengthening material have been covered with a protection, this should neverbe removed. The control, therefore, shall focus on an assessment of the tests conductedon those materials.

In order to prevent future mistakes, checks shall be made on the identification of thematerials.

In the event of the covering being of the ultraviolet protection type, said protection shallbe monitored in order to control its condition and proceed to their replacement whereappropriate. It shall be up to the manufacturer of the materials to determine the bestreplacement method and its timing.

Detailed inspection

The peeling of the polymer composites fibre from the concrete can be determined eitherthrough pressure tests or thermography tests. Nowadays, there are no simple tests thatallow us to determine the condition of a joint and its adhesive. The best way to determinethis condition is through the pull-off test, when controlling the specimens at regularintervals. However, this requires a number of very frequent tests and a testing period afterthe execution of the joint.

Another task that has to be performed is the placing of instruments on the bridge to beable to compare the data expected at the beginning to those finally and actually obtained.Should the difference between these data be very great, it shall be necessary to find out why and, on the basis of the results obtained, assess the resisting diagram. Above all, theidea is to try to find out the reason why the model and reality are so different, so that, inthis way, eventual similar situations can be assessed in the future.

If during some of the inspections we find out that the condition of the strengthening isnot up to expectations, we shall proceed to inject resin or to place reinforcement on top.Should the affected area be a large one, we shall have to remove the FRP and proceed toits reinstatement, always in accordance with all the procedures described so far. In thiscase, it shall be necessary to install a sufficiently big strengthening to ensure that loads aretransferred from the old laminate to the new one we have just laid. The newly installedmaterial should have similar characteristics to those of the old one, particularly withregard to the direction of the fibres, strength, strain and thickness.


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3.2 INTEGRATION OF KNOWLEDGE ON FRP RETROFITTED STRUCTURES

3.2.1 Introduction

The use of carbon fibre reinforced polymers (CFRP) for retrofitting a damaged structureis first reported for the strengthening of the Ibach bridge in 1991, Lucern, Switzerland[Meier, 1995]. Since this first application, the use of this technology has increasedexponentially, becoming one of the main applications of composite materials in buildingand civil engineering. In the case of seismic loads, the improvement provided by CFRPreinforcements in the structural capacity makes them a good solution to increase theductility of the structure, preventing structural damage in an earthquake situation.

Most of the existing knowledge about structural reinforcement and/or retrofitting ofreinforced concrete (RC) structures with fibre reinforced polymers (FRP) is based onexperimental simulations, supported and complemented by analytical calculations; and, when the problem is treated using a numerical approach, material nonlinearities areusually linearized and the FRP composite is considered as a single material (i.e.[Rabinovitch and Frostig, 2001]).

On the other hand, the study of composite materials has been one of the major objectivesof computational mechanics in the last decade. The numerical simulation of composite

materials has been done, traditionally, using orthotropic materials with average propertiesof their constituents. With this approximation, no model has been found able to workbeyond the constituents elastic limit state. Thus, these procedures limit the numericalcomputation to elastic cases. Different theories have been proposed to solve thisproblem, taking into account the internal configuration of the composite to predict itsbehaviour. The two most commonly used are herein remarked.

i) Homogenization theory: This method deals with the global problem of compositematerial in a two-scale context. The macroscopic scale uses the composite materials toobtain the global response of the structure; composites are treated as homogeneousmaterials in this scale. The microscopic scale corresponds to an elemental characteristic volume in which the microscopic fields inside the composite are obtained; this scale deals with the component materials. Homogenization theory assumes a periodicalconfiguration of the composite material to relate these two scales [Sanchez-Palencia,1987; Olleret al., 2005].ii) Mixing theory: The first formulation of the mixing theory corresponds to Trusdelland Toupn [Trusdell and Toupn, 1960] and it is based in two main hypothesis:1. Allcomposite constituents have the same strains.2. Each constituent collaborates to thecomposite behaviour according to its volumetric participation. The main problem of themixing theory is the iso-strain condition, which forces a parallel distribution of the


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constituents in the composite. Some improvements to the original formulation can befound in [Caret al., 2000].

Despite of all existing studies on both subjects, experimental tests of FRP reinforcementsand numerical characterization of composite materials, few researches are found in whichthe structural reinforcement of RC structures using FRP is approached using a numericalpoint of view. Thus, the main goal of this work is to join both fields, developing anumerical procedure able to compute RC structures reinforced with FRP. The developedformulation based on the finite element method that allows obtaining the structural

performance of existing structures when they are reinforced and/or retrofitted with FRP. This structural behaviour is obtained taking into account the material non-linearities. Thecode also provides the performance of each constituent material in the structure (forexample, it is possible to know the stress state of the composite reinforcement when thestructure collapses). The code can be used to study the same structure using differentFRP configurations, in order to obtain the most suitable for the case considered. It alsoallows to apply the reinforcement to already damaged structures, reproducing with moreaccuracy the conditions found in real applications.

In next section, the numerical procedures used to simulate RC structures with carbonfibre reinforced polymers (CFRP) reinforcements are described briefly. Afterwards somesimulation examples are exposed, these examples show the validity of the formulationproposed as well as the improvement obtained in the structural capacity when it isreinforced with CFRP. Finally, some conclusions are exposed.

3.2.2 Formulation used to simulate RC structures reinforced and/or retrofitted with CFRP

3.2.2.1 Simulation of Composite Materials

The structural problem of RC structures reinforced with carbon fibre reinforcedpolymers is solved with PLCd [PLCd, 1991]. This is a finite element code, developed atCIMNE (International Center for Numerical Methods in Engineering) and UPC

(Politechnical Univeristy of Catalonia), that works with two and three dimensional solidgeometries. It can deal with kinematics and material nonlinearities. It contains variousconstitutive laws to predict the material behaviour: Von-Mises, Mohr-Coulomb,improved Mohr-Coulomb, Drucker-Prager, etc. [Malvern, 1968; Lublineret al., 1989]. Ituses different integration algorithms to simulate the material: Elastic, visco-elastic,damage, damage-plasticity, etc. [Olleret al., 1990]. Dynamic analysis are developed usingthe Newmark method, [Barbatet al., 1997].


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To deal with composite materials, of the two main existing theories that take into accountcomposites internal configuration: homogenization and the mixing theory, the one usedand presented in this project is based in the last one. The election of the mixing theoryinstead of a homogenization theory is based in the final aim of the code developed,compute real structures reinforced and or retrofitted with CFRP. A homogenizationtheory requires a micro-model for each point of the structure that becomes non-linear. The resolution of a real structure with this procedure generates such a big amount ofdegrees of freedom that the calculation is beyond the computation capabilities ofnowadays personal computers or small servers. On the other hand, the mixing theory

does not increase the degrees of freedom of the problem, as it is only present in theconstitutive section of the finite element code.

a. Classical mixing theory

The classical rule of mixtures was originally developed by Trusdell and Toupin [1960]. Itconsiders that the interaction between the components in a material point of thecomposite is done according to the following hypothesis: (i) each infinitesimal volume ofthe composite contains a finite number of material components; (ii) each componentcontribution to the global behaviour of the composite is proportional to its volumetricparticipation; (iii) all components suffer the same strains (closing equation); (iv) the volume of each component is significantly smaller than the composite volume.

The third hypothesis, in the case of small strains, can be written as:

1 2c nij ij ij ij = = = = (3.2.1)

Where,c ij is the strain tensor for the composite andk

ij is the strain tensor forcomponent k of the composite. According to second hypothesis, the stresses of thecomposite can be computed as the proportional (according to the volumetricparticipation) addition of each component stresses, thus:

1, 1, 1,

k k k k S k k k S cij ij ijkl ij ijkl ij

k n k n k n

k k C k C = = =

= = = (3.2.2) where parameterk k is the volumetric participation of componentk in the composite,defined as:

0

k k dV k dV

= (3.2.3)


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A more detailed explanation of this theory, as well as the extension to the largedeformations case and its numerical implementation can be found in [Car, 2000]

b. Serial/Parallel mixing theory

The main problem of the classical mixing theory is the iso-strain condition, which forcesa parallel distribution of the constituents in the composite (Figure 3-1, iso-strain case). The serial/parallel rule of mixtures (SP RoM) improves the classical mixing theoryreplacing the iso-strain hypothesis for an iso-strain condition in the fibre direction and an

iso-stress condition in the transversal directions, allowing to simulate all componentsdistribution in the composite shown in Figure 3-1. This theory has been developed byRastellini and an extensive description of it can be found in [Rastellini, 2006] and in theDeliverable 49 of the LESSLOSS project ( www.lessloss.org ).

Iso- strain Iso- stress M ixed caseIso- strain Iso- stress M ixed case Figure 3-1. Different distribution of components in a composite material

The main hypothesis in which is based the numerical model of the Serial/Parallel mixingtheory are:

i) Composite is composed by two component materials: fibre and matrixii) Component materials have the same strain in parallel (fibre) directioniii) Component materials have the same stress in serial directioniv) Composite material response is in direct relation with the volume fractions ofcompounding materials

v) Homogeneous distribution of phases is considered in the composite vi) Perfect bounding between components is also considered

The equations that define the stress equilibrium and establish the strain compatibilitybetween components arise form the analysis of the model hypothesis. Thus,

Parallel behaviour: c m f P P P

c m m f f P P P k k

= == +

(3.2.4)


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Serial behaviour: c m m f f S S S

c m f S S S

k k

= += =

(3.2.5)

where, P and S are the parallel and serial components of the stress tensor respectively, P and S are the parallel and serial components of the strain, the superscriptsc , m

and f represent the composite, matrix and fibre materials andmk and f k is the volumetric participation of fibre and matrix in the composite.

In order to verify the compatibility equations, the Serial/Parallel mixing theory proceedsin the following way.

1. First thing to be done is to split the component strain tensor into its serial andparallel parts.

2. Afterwards, a first prediction of the matrix serial strains is computed. With thisinitial prediction and the strain relation of equation(3.2.3), the fibre serial strains can be also obtained.

3. Using each constituent constitutive law, the stresses for matrix and fibre can becalculated, as well as the actualization of each material internal variable.

4. The stress tensors computed in step 3 are split into their serial and parallel partsand the iso-stress condition defined in equation

(3.2.3) is checked. If it is verified, the matrix strain prediction was correct and thecomposite stress can be obtained using equations (3.2.2) and(3.2.3). If the iso-stress condition is not verified, the initial strain prediction

must be corrected and the process must continue in step 3.

The main problem of the Serial/Parallel mixing theory is that the composite material canbe composed, only, by two material components. However, this inconvenient is solved with the laminate procedure exposed in the following section.

c. Laminate Composites

Usually fibre reinforced polymers are composed by different layers with different fibreorientations. The orientation of the fibre can be defined by the engineer in order toobtain the better performance of the composite according to its application. In example,if the CFRP application is a flexural reinforcement, fibres will be disposed in the beamaxis direction while, if the CFRP is applied as a column wrapping, fibres will be orientedin the cross section plane, following the column perimeter.

Under this scope, the limitation of the Serial/Parallel mixing theory (SP RoM) to onlytwo materials is not such, as the composites used are usually defined by multiple layerscomposed by only two components: fibre and matrix. Thus, the SP RoM formulation can


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be applied to each layer of the composite and, afterwards, compute the compositebehaviour composing the performance of each constituent layer. To obtain the laminatebehaviour, the classical mixing theory is applied to each lamina.

Applying the classical mixing theory to the different layers of the composite implies theassumption that all laminas of the laminate are under the same strain conditions. Thisassumption can be considered correct, as the different laminas usually have fibreorientation distributions disposed in such a way that provide the laminate with an in-plane homogeneous stiffness.

At this point, it must be said that not all the layers have to behave according to the S/PRoM hypothesis. Sometimes, between fibre oriented layers, a randomly oriented one isdisposed. Having random oriented fibres, the layer behaves as an isotropic material andthe best theory to be applied to predict its behaviour is the Classical mixing theory. Thus,the composite performance is obtained according to the following procedure:

1. For a given strain of the composite, the strain of each composite layer is obtainedapplying the Classical mixing theory.

1 2c L L Ln = = = = (3.2.6)2. Each layer stress is obtained using the Serial/Parallel mixing theory in case of fibre

oriented layers or the Classical Mixing theory in case of randomly oriented layers (orin other cases of iso-strain behaviour such as single materials layers).

Lk Lk ; using Classic mixing theory or SP RoM (3.2.7)3. The stresses of the composite are obtained composing the stresses obtained in each

composite layer.

1

nc Lj Lj

j

k =

= (3.2.8)

3.2.2.2 Other Formulations Developed to Simulate CFRP Reinforcements

Having defined the main formulation frame, in which the code works and deals withcomposite materials, there are other formulations in it that are used to obtain a betterperformance of the finite element code and that are required to obtain a betterapproximation of the mechanical behaviour of the RC structures reinforced with CFRP.In this chapter, all of them are briefly described.


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a. Two dimensional and three dimensional elements

The original version of PLCd only dealt with two dimensional problems. Due to thecomplexity of some geometries required to study CFRP reinforcements, one of therequired implementations was to extend all formulations included in PLCd to the threedimensional case. The way in which a finite element code deals with two dimensional andthree dimensional cases can be studied in detail in [Oate, 1995; Zienkiewicz and Taylor,1991]

b. Anisotropy using a mapping space theory This theory is based on the transport of all the constitutive parameters and the stress andstrain states of the structure, from a real anisotropic space, to a fictitious isotropic space.Once all variables are in the fictitious isotropic space, an isotropic constitutive model canbe used to obtain the new structure configuration. This theory allows consideringmaterials with high anisotropy, such as composite materials, using all the techniques andprocedures already developed for isotropic materials.

All the anisotropy information is contained in two fourth order tensors. One ofthem, ijkl A

, relates the stresses in the fictitious isotropic space ( ij ) with the stresses in

the real anisotropic space ( ij

) and the other one,ijkl

A , does the same with the strains. The relation of both spaces for the strains and the stresses is exposed in equations (3.2.9).

:

:

ij ijkl ij

ij ijkl ij

A

A

==

(3.2.9)

A more detailed description of this methodology, the extension to large strains and itsnumerical implementation can be obtained in [Car et al., 2001 and Car, 2000]

c. Fibre-matrix debonding

The apparition of matrix cracks in a composite material is usually followed by a relativemovement between the fibres and the matrix. This lost of adherence implies a stiffnessreduction in the composite material. This phenomenon is introduced in the elastic limitof the material as a modification of its yield surface criterion. The new fibre elastic limitbecomes:

[ ]{ } fibmat fib N mat N fib N fib R r f f f f /)(2;)(;)(min)( = (3.2.10)


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Where fib R f )( is the new fibre strength, fib

N f )( is the nominal fibre strength,mat

N f )( is the matrix nominal strength and mat fib N f )( is the fibre-matrix interface

nominal strength. Equation (3.2.10) shows that the debonding happens when one of thecomposite constituents reaches its nominal strength (considering the fibre-matrixinterface as a constituent). The nominal resistance values are obtained from the materialproperties. The numerical implementation of this phenomenon is described in [Car, 2000and Oller, 2002]

d. Construction stages algorithm

Retrofit a structure implies the addition of the structural reinforcement once the originalstructure is already damaged. TheConstruction Stages Algorithm implemented in PLCDpermits running the numerical simulation during the desired load cases, with only somestructural elements active on the structure. At a certain load case, new elements can beadded without stopping the calculation process. These new elements are free of strainsand stresses when they are activated.

The algorithm requires having all elements defined in the structure. The elastic strains aredivided in two components, and active and a non-active, equation (3.2.11). If the elementis not present in the structure, all strains correspond to the non-active part, equation(3.2.12), while, if the element is active, all strains corresponding to the non-activesituation will be removed, equation (3.2.13), from the total strain. Stresses are computedconsidering only the active elements, equation (3.2.14).

e NA

e A

e += (3.2.11)

0; == e Aee NA (3.2.12)

e NA

ee A = (3.2.13)

e A

ee C = (3.2.14)

This procedure is explained with more detail in [Martinezet al., 2006; CIMNE, 2006]

e. Compression strength of composites

Although CFRP reinforcements are not recommended to be used to resist compressiveforces [Rabinovich, 2002], there are many situations in which this load state can be found. This aspect is of special relevance in the case of structures subjected to seismic loads, where the sign of the load is reversed as the earthquake evolves. Thus, a procedure toobtain the compression strength of CFRP composites is required in order to take into


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account this sort of situations. The main failure cause of compressed CFRP is the fibrebuckling phenomenon. Fibres are very slender elements and their second order effectsare avoided by the matrix elastic restrain. However, as damage in matrix evolves, fibrerestrain becomes weaker and fibre buckling occurs.

In all existing bibliography, the fibre buckling problem is solved by using differentmethodologies to obtain a general expression for the composite limit compression stress. This expression is only valid for the composite material and is obtained taking intoaccount different characteristics of the composite components. Alternatively, in the

present work, the composite material is modelled using the S/P rule of mixtures. Thus,the fibre buckling problem must be solved in terms of the composite components,considering their interaction, and not in terms of the composite by itself.

The interaction between fibres and matrix appears when the composite is compressed:matrix restrain fibres avoiding their transversal movement. Under this approach, matrixcan be considered as an elastic restriction of fibres, and the fibre-matrix system can berepresented as it is shown in Figure 3-2. In this figure the movement of the fibres in caseof compression has been represented in dashed lines. Fibre behaviour is analogous to theresponse that is obtained in a curved bar under unilateral restrain. This analogy is used toformulate the fibre buckling problem. A detailed explanation of the formulation relatedto this problem can be found in [Martinezet al., 2007]

Figure 3-2. Fibre-matrix system. Fibre behaviour when the composite is compressed

3.2.2.3 Efficiency Improvement of the Developed Code

Beside the different formulations included in PLCd code to deal with the CFRP

reinforcement of RC structures, it is necessary to pay special attention to the codeperformance in order to improve its computation efficiency. The finite elementsimulation of a complete structure requires a large number of elements, which requires alot of memory and computing time. Hence, all effort put in obtain a more efficient code will be recovered when the simulations are performed. Two different code improvementshave been developed in this field


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a. Tangent constitutive stiffness tensor

Depending on the constitutive equation used in a composite constituent material, thetangent constitutive tensor cannot be obtained analytically. One solution is to use, in thismaterial, the initial stiffness matrix, which will lead to the equilibrium state but willrequire a large amount of structural iterations. Thus, in order to obtain a fast and reliablealgorithm, the expression of the tangent constitutive tensor is required. To obtain it, when no analytical expression exists, a numerical derivation using a perturbation methodis performed. According to Crisfield [Crisfield, 91], the definition of the tangentconstitutive tensor is:

:t = C (3.2.15) where,

[ ] [ ]1 2 1 211 1

1

; andn nt t

nt

t t n nn

c c

c c

= = =

C (3.2.16)

The definition of the tangent constitutive tensor, equation (3.2.15), shows that the variation of stresses due to an increment in the value of the j element of depends onthe values of the j column of t C . Thus, writing the j column of t C as,

1 2

T t t t t j j j njc c c = c (3.2.17)

the stress variation is:

j t j j = c (3.2.18)

being t jc the unknown

The perturbation method consists of applying a small perturbation to the strain vectorand, using the constitutive equation of the material, determines the variation that will beobtained in the stress tensor due to this perturbation. At this point, the j column of thetangent constitutive tensor can be computed as:

jt j

j

=c (3.2.19)


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The smaller the value applied to the perturbation, the better the approximation obtainedfor the tangent constitutive tensor. Having defined a perturbation value, j , theperturbed stress is computed using the constitutive equation of the material applying thefollowing input strain:

1 T

j j n = + (3.2.20)

And the stress variation due to the perturbation is obtained subtracting the originalconverged stress from the computed one:

j = (3.2.21)

This procedure must be repeated for all strain components in order to obtain thecomplete expression of the tangent constitutive tensor. Hence, the numerical cost ofusing a perturbation method is rather high. However, this procedure allows obtaining anaccurate approximation to this tensor for any constitutive equation used, ensuring theconvergence of the numerical process in few steps.

b. Improvement of the database system

One of the main advantages of the mixing theory compared to a homogenization theoryis that the computational cost is much lower, as the number of degrees of freedom of theproblem is not modified by taking into account the composite components. However,taking into account all composite components increase significantly the amount ofinformation that has to be stored for each gauss point.

The information stored, in a finite element code, for each gauss point are the strains, thestresses and the internal variables. If the strain and stress tensors have dimensionn andthe number of state variables ism , the amount of memory required for each gauss pointif only one material is considered in it is:2n+m real values.

If now, instead of having one single material, the material defined in the gauss point is acomposite made by three different layers, and each layer containing two differentcomponents, it will be required to save for each layer the strains and stresses and for eachcomponent of each layer the strains, stresses and internal variables. This leads to:

3 layers require 3 x (2n) real values =6n real values

Each layer has two components, each one requiring 2n+m real values

= 3 x (2 x (2n+m)) =12n + 6m real values

Thus, in total, the amount of real values required for the gauss point is: 18n + 6m


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This example shows how, with only a three layer composite, the amount of variables thatmust be stored increase nearly by nine, which increases nearly by nine the amount ofmemory required to solve the problem.

Being aware of this problem, an optimization of the variables stored by PLDCd code hasbeen performed. PLCd was first developed as a finite element code to compute smallstructures made of just one material. Thus, the code was not optimized and a lot ofuseless variables were stored for each gauss point. All these variables have been removed.It have also been removed all variables that, being previously stored, can be computed

again when necessary. With these two main measures, the code requirement of memoryhas been reduced nearly a 70 % in the case of the concrete frame that will be shown insection 3.2.3.3 of present document.

3.2.2.4 Making the Code More User Friendly

a. Pre and post processing using GiD

When solving the structural problem of a RC structure reinforced with CFRP, theamount of information required by the finite element code PLCd is large and complex todefine. In the case of the three dimensional framed structure that is exposed in section3.2.3.3, the input data file has more than 6500 lines. In these cases, is necessary to have afriendly environment to define the input data file.

GiD [GiD, 2007] is a pre and post processor, developed at CIMNE, which can becustomized to interact with any existing finite element code. This customization includestwo main features, one corresponds to the data that can be defined over the structure andthe second one is the writing of the input data file in a format able to be recognized bythe finite element code. Both features have been included in the PLCd problem typedefinition, which allows defining completely the input data file to be used by PLCd codeusing GiD.

Following figures show some screen captures obtained during the definition of the

concrete frame used to obtain the CFRP reinforcement behaviour in a push-over analysis(section 3.2.3.3 of the present document).

Another improvement related to the interaction of PLCd with GiD corresponds to theouput result file. Initially, PLCd exported each composite material in a layer and eachcomponent material was exported in a different layer inside the first layer. This is, if twoelements had different composite materials ( comp1 and comp2 , in example), and bothcomposites have, as a constituent material, polymeric matrix, matrix results of compositecomp1 will be stored in the layermat-comp1 and matrix results ofcomp2 will be stored in


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mat-comp2 . Hence, to see the stresses in matrix materials, different layers must be activatedand the results cannot be seen at once.

This way of storing the results has been changed and now all simple materials are storedin the same layer. Doing so it is possible to see the stresses of all matrix material at once,being easier to have a global comprehension of the material behaviour of the structureusing the graphical interface provided by GiD. Also, this way of storing results reducessignificantly the dimension of the output file.

Figure 3-3. Assignation, to the different volumes composing the concrete frame to be modelled, ofthe different composite materials and construction stages


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Figure 3-4. Definition of the different composite materials existing on the structure by the numbermaterial constituents and their volumetric participation. Beneath can be seen somematerial data defined for the simple materials.

b. Creation of an ANSYS usermat with the mixing theory

The commercial finite element code ANSYS [ANSYS, Inc, 2007] allows the user

definition of material constitutive equations or, as are called by the code,usermat s. Withthis option, ANSYS code becomes more versatile, as it can be customized for someparticular applications. With the aim of increase the applicability of the formulationdeveloped to deal with RC structures reinforced with CFRP, ausermat containing thelamination formulation using the rule of mixtures (both, the Classical and theSerial/Parallel) has been programmed.

ANSYSusermat is called when the code is at the gauss point level. The subroutine receivesthe strains of the gauss point and has to return to the main code the stresses of the gausspoint, the tangent constitutive tensor and the internal variables actualized to the newconfiguration [ANSYS, Inc, 2005].

This application has been already developed and, at this stage of the project, is beingtested in order to assure the correct behaviour of the material definition in all possiblesituations related with composite materials and, more precisely, with the reinforcement ofstructures using carbon fibre reinforced polymers (CFRP).


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3.2.3 Numerical examples of the formulation proposed. CFRP reinforcements ofRC structures

3.2.3.1 Code Validation: Bending Reinforcement of a RC Beam

In this section, a numerical simulation of a bending reinforced beam is presented andused to validate all the formulations proposed and exposed in previous section. This caseshows the efficiency of the serial/parallel rule of mixtures to deal with this sort ofstructural problems, as it is able to reproduce the complex mechanical behaviour found inthe beam with an acceptable computational cost. The numerical results are validated with

experimental values. The studied beam is defined in the paper by Spadea [Spadeaet al. 1998]. Its geometry and the reinforcements applied to it are shown in Figure 3-5.

Figure 3-5. Geometry and reinforcement of the beam studied

The red (thick) line displayed in the bottom of the beam corresponds to the FRPreinforcement. This is made of carbon fibres embedded in a polymeric matrix. Thecontent of fibres is 60 % and the composite thickness is 1.2 mm. The finite elementmodel developed to simulate the beam reinforcement is shown in Figure 3-6. This is a 3Dfinite element made with linear hexahedrons.

The usage of the S/P rule of mixtures allows considering all the reinforcement detailsfound in the beam using a coarse mesh. In Figure 3-6 it is also included the compositematerials composition. As can be seen, a single finite element contains, in this particularcase, up to three different component materials. The steel reinforcements are consideredas fibres, whose orientation is defined by the bar direction. The FRP reinforcement has

been included adding new finite elements to reproduce with more accuracy its position inthe beam.


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MAT-01: Concrete (100 %) MAT-02: Concrete (57 %)

Longitudinal Steel (42 %) Vertical Steel (1 %)

MAT-03: Concrete (99 %) Vertical Steel (1 %)

MAT-04: Concrete (98 %) Vertical Steel (1 %) Horizontal Steel (1 %)

MAT-05: Concrete (99 %) Horizontal Steel (1 %)

MAT-06: Polymeric Matrix (34 %)

Long.Carbon Fibr. (66%) Figure 3-6. Finite element model developed to realize the numerical simulation

The results obtained with this simulation are compared with the experimental resultsreported by Spadea [Spadeaet al., 1998]. Figure 3-7 shows the capacity curve of the beamfor the numerical and the experimental simulations. This is, vertical displacement of thebeam, in the point where the force is applied, against the load value. This figuredemonstrates the agreement between numerical and experimental results, which provesthe ability of the method to perform this sort of simulations. Figure 3-7 also includes theresults obtained with a numerical simulation of the same beam without FRPreinforcements. The comparison between the results obtained for the reinforced and for

the non-reinforced beam shows the improvement obtained in the beam performance when it is reinforced with FRP.

Figure 3-7. Force-displacement graph comparing the experimental and the numerical results

One of the main advantages of the proposed finite element formulation is that it allowsobtaining the structural behaviour of all its components, their failure causes, their strain-stress state, etc. In Figure 3-8 some results maps, corresponding to the final computedstep, are represented. These show the most relevant information obtained from thenumerical simulation. Figure 3-8a displays the plastic damage in concrete, which shows


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that the failure cause of the beam are the tensile stresses in concrete at midspan. In Figure3-8b and Figure 3-8c it is depicted the plastic damage obtained for the longitudinal steelreinforcement and for the polymeric matrix, respectively. These two figures show thatboth materials have reached their yield stress when the beam failure occurs. Finally,Figure 3-8d shows the stresses in carbon fibres. As it can be seen, they are at less than ahalf of their load capacity (the fibre elastic limit stress defined is: 2300e = MPa)

F IGURE 3-8a. Plastic damage in concrete F IGURE 3-8b. Plastic damage in long. steel reinf.

F IGURE 3-8c. Plastic damage in polymeric matrix F IGURE 3-8d. Long. stress in carbon fibres [kp/cm 2]

Figure 3-8. Results maps obtained with the finite element model of the beam

3.2.3.2 Code Validation: CFRP Retrofitting of a Beam

Two different numerical models have been developed to study the effect of retrofitting astructure, depending on the existing damage in the beam when the CFRP reinforcementis applied to it. These are:

Sp3D-Rt2: The CFRP reinforcement is applied when damage starts in concrete

material. Sp3D-Rt3: CFRP reinforcement is applied when steel starts yielding.

Results obtained with these two models are compared with those obtained when thebeam is not reinforced (Sp3D-R0 model) and when the beam is reinforced from thebeginning of the loading process (Sp3D-R1 model). The capacity curve obtained for eachmodel is shown in Figure 3-9:


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Figure 3-9. Comparison between the CFRP reinforcement and retrofitting by using capacity curves

These results show that the structural stiffness does not depends on when thereinforcement is applied to the structure. The structure stiffness obtained when the CFRPreinforcement is applied after the steel yielding (Sp3D-Rt3 model) does not differsignificantly form the structure stiffness obtained after steel yielding in the reinforcedmodel (Sp3D-R1). However, retrofitting a structure implies that, when the CFRPreinforcement starts collaborating, the deformation and damage of the structure is largerthan if it had been reinforced from the beginning. Damage reduces the load capacity ofthe beam while deformation can make the serviceability state unacceptable (i.e. when a

load of 25 kN is applied to the structure, beam deformations are 45 % larger in theretrofit model, Sp3D-Rt3, than in the reinforced one, Sp3D-R1).

3.2.3.3 Reinforcement of a Framed Structure using CFRP

This structure was already presented in Deliverable 49 ( www.lessloss.org ). However, thesimulation presented in this Technical Report is new, as now the problem is solved withthe Serial/Parallel mixing theory. This theory provides a most stable and robust code which provide more reliable simulations.

The main objective of the present simulation is to use the developed formulation to verify the capability of CFRP reinforcements to increase the strength of concrete frames when seismic loads are applied to them. Concrete framed structures are common inbuilding and civil engineering; one of the most stressed zones of these structures, underseismic loads, are the connecting joints between beams and columns. In many occasions,these joints show a lack of strength that can be improved with CFRP. The developedmodels reinforce the frame joint with two different CFRP configurations, in order tostudy the ability of the reinforcements to increase the frame strength and to find out which configuration offers better results.


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a. Model description

The concrete frame to be studied is defined with the geometry and the steelreinforcement commonly used in buildings. Figure 3-10 shows the geometry consideredand Figure 3-11 shows the steel reinforcement and the description of the CFRPreinforcement that will be applied to the frame joint. The beam cross section, as well asits steel reinforcement, is dimensioned in such a way to assure the structural failure in thebeam, near the joint, in order to increase the effects of CFRP in the frame joint. Thestructure is loaded with a horizontal force P applied in the middle of the frame joint (seeFigure 3-10).

Figure 3-10. Geometric definition of the framed structure considered in the simulation

Figure 3-11. Reinforcements applied to the concrete frame

Two dimensional and three dimensional models have been developed for the concreteframe. 2D models have been used to calibrate the mesh to be used, as they require lesscomputational effort than 3D models. Results obtained with 2D models are compared with the 3D ones to validate the accuracy of each simulation. Three different structuresare considered to study the effect of CFRP reinforcements on the frame joint. These are:


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2D-noR and 3D-noR: Two and three dimension concrete frame without CFRPreinforcements

2D-R and 3D-R: Two and three dimension concrete frame with the upperand lower CFRP reinforcements defined in Figure 3-11

2D-LR and 3D-LR: Two and three dimension concrete frame with the upper,lower and lateral CFRP reinforcements

All composite materials existing in the concrete frame are defined by combination of fourdifferent basic materials, which are defined in Table 3-7. CFRP reinforcement is 1.2 mm

thick and is composed of 66 % of carbon fibres and 34 % of polymeric matrix. In thecase of the upper and lower reinforcements, the fibres are oriented following thestructure longitudinal axis. In lateral reinforcements, two layers of CFRP are applied tothe frame, in which the fibres are oriented at +0 and +90 respect the horizontal.

Table 3-7. Mechanical characteristics of the constituent materials used to define the compositematerials existing in the framed structure.

Yield Stres [MPa] Fracture Energy[kPam]

Material Yieldcriterion

YoungModulus[ MPa ]

PoissonModulus

Compr. Tensile Compr. Tensile

Concrete Mohr-Coulomb

2.5104 0.20 30.0 3.0 50.0 0.5

SteelReinf. Von-Mises 2.110

5 0.00 270.0 270.0 2000.0 2000.0

Polymericmatrix

Mohr-Coulomb 1.210

4 0.20 87.5 29.2 36.0 3.0

CarbonFibres Von-Mises 1.510

5 0.00 2300.0 2300.0 2000.0 2000.0

b. 2D results

The structural behaviour of the frame joint for the different reinforcements applied to thestructure is studied using the capacity curves obtained for each model (Figure 3-12). Thedisplacement considered corresponds to the horizontal displacement suffered by thepoint where the load is applied. This displacement depends on the column, beam andjoint stiffness. As the column and the beam are not modified in the different models, ifthe joint stiffness is increased with the different applied reinforcements, the force--displacement graph will reflect this increment.


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Figure 3-12. Capacity curves obtained with the 2D models

Figure 3-12 shows that the upper and lower CFRP reinforcements (2DF-R model) do notimprove significantly the frame behaviour. This improvement is only found when lateralreinforcements are applied to the concrete frame. All three curves present a region wherethe load reduces, to start increasing again afterwards. These points correspond to thedevelopment of a plastic hinge in the structure. At this load step the structure adopts anew strength mechanism and can increase its load capacity. Comparing the load appliedto the structure until the development of the plastic hinge, the lateral reinforcements(2DF-LR model) increase in a 25 % the structural load capacity when compared with the

non--reinforced model (2DF-noR). This increment is only a 4 % if the structure isreinforced only with upper and lower CFRP.

A better comprehension of the effects of each reinforcement can be obtained studyingthe points where the plastic hinges are formed. Figure 3-13 shows the longitudinal strainsof each model at their last computed step. The cross sections where the plastic hinges areformed are the ones with larger strains.

Figure 3-13 shows that applying only the upper and lower CFRP reinforcements theplastic hinge moves from the beam to the inner part of the joint, where noreinforcements are applied. Thus, the presence of CFRP does not modify substantiallythe beam behaviour and, once the hinge has been formed, both structures behavesimilarly (as it can be seen in Figure 3-12). On the other hand, when the lateralreinforcement is applied to the structure, it restrains damage in the frame joint and movesthe plastic hinge to the cross section where no CFRP reinforcement is applied, whatallows the structure to increase its load capacity and its stiffness.


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( a ) ( b )

( c )Figure 3-13. Plastic hinges in the concrete frame. 2D models. a) model without CFRP reinforcement,

b) model with upper and lower CFRP, c) model with upper, lower and lateral CFRP

c. 3D results

The study by means of three dimensional models is also performed, as in the case of 2Dmodels, by means of the capacity curves (Figure 3-14). The main difference found whencomparing these results with the 2D ones is that the 3D models are stiffer and can reachlarger loads than the 2D models. This is because the concrete confinement is betterreproduced in this case, as steel stirrups are modelled taking into account their 3Ddistribution and not only in one of their directions. Hence, concrete can reach largerstresses, which increase the stiffness and strength of the structure.

Figure 3-14 shows that plastic hinges in the non-reinforced model (3DF-noR) and in thereinforced model (3DF-R) appear for the same load and displacement as in the reinforcedbeam model (2DF-LR), as a consequence of the increment of concrete strength.However, in the three dimensional simulation, plastic hinges appear before in thereinforced model than in the non-reinforced one. The explanation of this effect is shownin Figure 3-15 (maximum strains in the unreinforced beam model (3DF-noR) before and


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after the formation of the plastic hinge) and in Figure 3-16 (the same results in the case ofthe 3DF-R model).

Figure 3-14. Capacity curves obtained with the 3D models

Figure 3-15. Crack evolution in the 3DF-noR model (model without CFRP reinforcement)

Figure 3-16. Crack evolution in the 3DF-R model (model with upper and lower CFRP)


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According to these figures, the cross section in which the plastic hinge develops is nearlythe same in both models. But, as this cross section is closer to the initial damage in thereinforced model than in the non-reinforced one, it is easier to simulate the plastic hinge when the beam is reinforced. Thus, even if the CFRP reinforcement increases the jointstiffness, in this case the frame plastic hinge appears for lower loads when thisreinforcement is applied than when the joint is not reinforced.

More differences are found when comparing the three dimensional model with the twodimensional one, in the case in which lateral CFRP reinforcements are applied to the

frame joint (3DF-LR model). The first difference is that the formation of a plastic hingeis not visible in the capacity curve. This is because no section is completely damaged when the algorithm loses its convergence.

However, the main difference is found when looking at the most damaged section. Thestrains in the lateral sections of the frame joint (Figure 3-17a) have a similar behaviour tothat of the 2D case: strains are larger in the cross section where the CFRP reinforcementfinishes than in the frame joint. But when the strains in a longitudinal section of thestructure are studied (Figure 3-17b), they show that the plastic hinge is developed in theframe joint, as happens in the 3DF-R model. Two dimensional models consider theCFRP reinforcement applied along the whole cross section while actually it is appliedonly to the lateral surfaces. Thus, the reinforcement can avoid structural cracks on thesurface of the structure but cannot restrain them inside the joint. This effect can beobserved with more accuracy in Figure 3-18, where a zenith view of the strains in thecolumn section just below the frame joint is displayed.

Figure 3-17. Plastic hinge in the 3DF-LR model. Lateral view

These last figures show that the structure presents the same structural failureindependently of the CFRP reinforcement configuration applied to it. Thus, it can beconcluded that the only effect of the lateral CFRP reinforcement over the frame joint isto delay the apparition of cracks in it and the following plastic hinge. However, this delayis enough to allow a load 20 % larger in the frame when the horizontal displacement in it


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is of 3.0 cm, increment more than sufficient to consider this reinforcement typology thebest option to improve concrete framed structures seismic strength.

Figure 3-18. Elements with larger deformations in the 3DF-LR model. Zenith view

The results also show the necessity of using three dimensional elements depending on thesimulation to be performed. When the distribution of CFRP reinforcements is notuniform along the whole cross section, 2D simulations can provide incorrect results.However, even if the effectiveness of lateral reinforcements is reduced in the 3D model,the structural strength improvement is significant enough to consider this reinforcementconfiguration as the best option to reinforce the column-beam joint of RC framestructures.

3.2.4 CONCLUSIONSIn this technical report have been exposed the different numerical procedures developedto solve in a reliable and efficient way the problem of reinforcement and/or retrofittingof reinforced concrete (RC) structures using fibre reinforced polymers (FRP). Due to thecomplexity of the problem to be solved, efforts have been directed not only to thenumerical procedures that allow performing the structural simulation but also to theefficiency of the code and the way the user interacts with it.

Of all the formulations developed to solve the problem of FRP reinforcement of RCstructures, is of special relevance the general formulation of the mixing theory to deal with laminated composites. This is, the division of the composite in its differentcomponents until reaching the constituent material, which will be the one that willprovide the structural behaviour of the composite. This formulation can be understood asa manager of constitutive equations and is the one that allows dealing with thereinforcement problem, taking into account all its particularities, without increasing theproblem numerical size beyond the computational limits. The good performance of thistheory has been proved with the different simulations presented in section 3.2.3 of thepresent document.


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Besides the mixing theory formulation, other numerical procedures have been developedto deal with the particular case of FRP reinforcements. The most relevant of them are theanisotropy using a mapped space theory and the fibre matrix debonding. Special attentionmust be paid in the construction stages algorithm, which allows performing simulationsof retrofitted structures (section 3.2.3.2). These simulations have shown that, even theFRP performance do not vary significantly if it is applied as a reinforcement or as aretrofit, the structural deformations and the stresses are larger if the FRP is applied whenthe structure is already damaged. Finally, it has to be said that the compression strengthformulation has not been tested yet in a FRP reinforcement simulation, however, first

results obtained permit be optimistic about its performance and validity. To improve the code efficiency it has been revised in detail, deleting all data and variablesnot required to solve the problem. It has also been implemented a numerical derivationprocedure, used to obtain the constitutive tangent matrix, in order to reach the structuralequilibrium in the fewer number of iterations possible.

The code is now more user friendly as all the problem can be defined using GiD pre-processor, and all output results can be studied with GiD post-processor. Also, to makethe developed formulation more accessible, the mixing theory developed to deal withlaminate composite will be soon accessible as ausermat for ANSYS users.

The conclusion that all all formulations exposed are valid and useful to solve the FRPreinforcement problem has been obtained form the study of the different simulationsperformed with them. However, the objective of these simulations was not only to verifythe formulations implemented in the finite element code, but also to study in which waythe simulations of structural reinforcements of CFRP must be developed to obtainaccurate results. The simulation that has provided more information in this aspect hasbeen the framed structure one. This simulation has shown the necessity to work withthree dimensional elements to obtain an adequate behaviour of the structure. Twodimensional elements suppose a constant distribution of the materials along the wholecross section. When the structure has not the same composition along its cross section,the supposition that these properties can be extended to the whole section can

overestimate the structural performance, as happens with lateral CFRP reinforcements inthe frame simulation.

Finally, all simulations have proven the improvement obtained in the structuralperformance when it is reinforced or retrofitted with fibre reinforced polymers. Thisimprovement depends on the type of reinforcement applied and on the level of existingdamage in the structure when the reinforcement is applied. Both aspects can becontrolled now, with the formulation described in this work, in order to obtain the bestFRP configuration to reinforce the structure considered.


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3.3 EXPERIMENTAL DATA ON DURABILITY AND FATIGUE RESISTANCE

This section will deal with a summary on the main factors that have an influence on thedurability and the fatigue resistance of composites materials. Thus, the section is dividedinto two clearly distinct parts, one of them dealing with durability and the second onedealing with the fatigue resistance.

3.3.1 Durability

The durability characteristics of FRP (Fibre Reinforced Polymers) materials have been,and are, the subject of intense review, with special emphasis on the three most commontypes of fibres, currently used in polymeric composites: glass, carbon and aramid fibres.However, due to their wide application and utilization in Civil Engineering, most of theavailable information focuses on glass fibre degradation. An up-to-date summary of themain characteristics is given below.

3.3.1.1 Fibres environmental degradation

a. Glass fibre

Glass fibres are the most commonly used in Civil Engineering applications, because theyare the cheapest (Jamond 2000) and, therefore, it is important that we should understandtheir behaviour when exposed to hostile environments. Although it is commonknowledge that glass fibres degrade in the presence of water and of acid, alkaline orsaliferous solutions, the most serious occurs in alkaline solutions (as reported by research work on the subject). A good example is the alkaline water coming from concrete pores, which turns this environment into one of the most critical for glass fibres, due to thehydration of the cement. Therefore, many durability surveys are aimed at determining thealkali resistance of GFRP (Glass Fibre Reinforced Polymers). Additionally, there aredebates still raging about the severity of saliferous environments on this type of fibres, which have proved to be more serious than watery and acid environments, but as seriousas the degradation in alkaline environments (Chin 1997).

The different glass compositions available on the market read as follows: (1) E-Glass(Electric Grade Glass) is the cheapest and more widely used for general purpose jobs;(2) S-Glass (Strength Glass) has greater mechanical properties than E-Glass, but costsmore; (3) AR-Glass (Alkali Resistant Glass) is an improved version of E-Glass, to withstand alkaline attacks through the addition of zirconium.


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b. Aramid fibre

Aramid fibres are particularly susceptible to water, as these are organic polymeric fibresand they are known to absorb water (Bank 1995). As happens with glass fibres, the Absorption of water can cause the total degradation of the aramid fibres, mainly thanksto the greater stresses caused by expansion. In addition, solutions such as sodiumhydroxide and hydrochloridic acid cause accelerated hydrolysis in the most commonaramid fibres (Kevlar 49), especially when temperature and stresses combine (Hunston2000).

c. Carbon fibre

Studies on carbon fibre reinforced composites are numerous due to their extensive use inthe aerospace industry (Bank 1995). Carbon fibres offer higher rigidity and specificstrength than glass fibres. In addition, they are resilient, even in chemical environmentsand do not absorb water. Machida (1995) points out that they are highly resistant to acid,alkaline and organic environments. Due to these characteristics, carbon fibres are beingincreasingly used in applications where light, high strength, structures are called for.However, carbon fibres exhibit two drawbacks: (1) they are galvanically inactive and,therefore, the cathodic reaction can play an important role in the degradation of thecomposite, between the polymer and the graphite, that is to say in the interface (Tucker

1990). This can get worse when the carbon fibres come into contact with any metal, suchas those present in external reinforcements, or with saliferous water; and (2) they are a lotmore expensive than glass fibres.

Many studies have been undertaken to observe the typical degradation, both physical andchemical, of carbon fibres in different environments (acid, alkaline and distil water), butno deterioration mechanism has been found and so none is available (Sen 1998).

3.3.1.2 Accelerated Ageing Models

The accelerated tests main purpose is to predict the system service life; to achieve this,three essential items of information are required: 1) data showing the degradation of theproperties of the material, which are going to be predicted in the service life; 2) ananalytical or statistical model to extrapolate the data for long term purposes; and 3) aproper definition of the failure mechanism of the test samples; in the event of differentfailure modes being obtained in the simulated accelerated models, the predictions shallnot be valid.

Katsuki & Uomoto (1997) apply Ficks Law to simulate the degradation of the GFRProds quantitatively, by predicting the reduction of the tension strength in acceleratedtests, where the results coincided well with the measured results. This Law is deemed


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adequate to predict the loss of strength of the tendons or rods. Arrhenius Law can beused to determine the diffusion rate in non-accelerated temperatures and,consequently, the strength reduction rate under non-accelerated conditions.

Valter Dejke et al (2001) in his thesis, assumes that the service life at differenttemperatures can be derived from Arrhenius Law. Using this approximation, it ispossible to transform the exposure time under accelerated conditions into real applicationtimes, using the time factor (Time Shift Factor, TSF). For example, 1.5 years at 60Capproximately equals 50 years in open air conditions in southern Sweden (which means a

yearly temperature of 7C). In addition, it provides mathematical expressions to calculatethe weight gain and the concentration of the profiles of the materials when they arepenetrated by a liquid, which can be water, an alkaline solution or any fluid medium. Allthe above equations assume that the diffusion of the liquid inside the material isdistributed in accordance with Ficks Law.

Different experts have obtained, from several surveys, numerous data about thedegradation characteristics of the FRP. However, what the industry needs is a forecast ofthe service life. The behaviour of the tested materials, together with the degradationcharacteristics, by themselves, is not sufficient to perform service life predictions. That isthe reason why numerous models have been developed to interpret the results fromaccelerated tests. These models consider the information from the tests as input data andpredict the system service life.

a. Degradation models

As the degradation model becomes more complex, so does the model used to describe it. That is the reason why it is so difficult to develop a model of degradation of FRP with very complex durability mechanisms. The lack of knowledge about the true meaning andabout the use of the accelerated tests may lead to incorrect conclusions about the testedproduct and even result in high costs for the development of the product (Nelson 1990).

Although there exist, in the literature, several proposed models, which are widely used,

each has its own limitations and assumptions. It must be born in mind that there are noanalytical models that take into account the degradation mechanisms and that accuratelyestimate the service life of the materials subjected to accelerated tests. On the other hand,it is very difficult to simulate in the accelerated tests the actual environmental conditionsto which the materials are exposed when they are in operation. Because of this and due toall the aforesaid uncertainties, the service life predicting models must be used withextreme care.


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b. Constant Rate Models

These have been established analytical models which link all the variables involved(temperature, saliferous solutions, etc.) under the application of a constant accelerationfactor. The close formulation of these models is very hard to obtain, because thedegradation models are not well known in most cases. In addition, it is possible thatdeviations in the model might occur over prolong periods of time.

c. Power Law Models Equation Chapter 3 Section 3

The Power Law models are the most widely used among the simple speed models ofaccelerated tests. These models have the degradation rate represented by a Powerfunction of a degradation factor as shown by equation (3.3.1). It must be born in mindthat the long-term degradation rate is always the same in these models, as their implies(Nelson 1990).

=' V (3.3.1)

Where:

' : The degradation rate.

: A constant of the material.

V : Degradation factor.

d. Exponential Models

These models are very similar to those used with Powers Law. The degradation rate isrepresented by an exponential function of the stress, as shown in equation (3.3.2) (Nelson1990)

=' exp( )V (3.3.2)

Where:

' : Rate of degradation.

, : Constants of the material.

V : Accelerated stress.


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e. Eyring Model

The general formulation of the Eyring model contains two environmental load variables,one of which is the temperature. The other is the load. This can be the mechanical load,the humidity or the existing density. The general formulation of the Eyring model isshown in equation (3.3.3).

=

' exp V

V T T

(3.3.3)

Where:


, , , : Constants of the material and of the degradation mechanism.

T : Temperature in K.

f. Arrhenius Stabilised-Status Temperature Acceleration Model

This model can be used when the temperature is the only acceleration factor and the

main concern are the chemical reactions (Caruso 1998). Arrhenius degradation rate canbe formulated like equation (3.3.4) (Nelson 1990)

=

' ' exp

E A

kT (3.3.4)

Where:


E : Activation energy of the chemical reaction in electron volts.

k : Boltzmanns constants, 8.617x10 -5 electron volts per C.

T : Absolute temperature in K.

A : A constant of the test conditions and failure of the material.

The acceleration factor for this model can be written like equation (3.3.5) to relate thedegradations in accelerated environments to those under service conditions (Nelson1990):


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= =

1 1exp

' 'n E AF

k T T (3.3.5)

Where:

AF : Acceleration factor.

n E : Activation energy for the degradation mechanism and for the material.

: life-cycle at the reference temperature T(K).

' : life-cycle at elevated temperature T(K).

k : Boltzmanns constant.

Arrhenius Law models are still being debated and have not been internationally acceptedyet. They can only be used to draw comparisons between those materials whosedegradation can be simulated with this Law.

The Time Shift (TS) technique is used to represent the ageing effect, using a long-termhorizontal Time Shift (Gates 1997). Moreover, by representing the temperature effectsalong with this technique in accelerated tests, a description is given of the level ofacceleration of an environmental exposure which is obtained when the temperature isincreased (Valter 2001). However, it does not properly represent ageing, except for shortperiods of time.

3.3.2 Fatigue of composites

Fatigue is the condition for which a material cracks or it fails as a result of repeated effort(cyclic loading). From an engineered point of view, it should be defined like thepermanent, located and progressive structural change that takes place in a material subjectto repeated or fluctuating deformations. In general, these deformations are presented to

smaller efforts that the last tensile strength of the material in a static test, and theyfrequently appear for smaller efforts that the fluency limit of the material. The fatigue canaffect practically all the engineering materials subject to cyclic efforts. Cyclic effortsinclude repetitive external loads and thermal efforts that result from heating andalternated cooling.

The fatigue life of a component or material is defined as the total number of necessaryeffort cycles to cause failure. It is an important concept that one frequently studies in thelaboratory, for what the obtained information can apply to designs and components in


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real service. The most common method of studying the fatigue life is to use cyclic loadsof constant width and to register the number of cycles to failure.

Tests data of the fatigue life are generally presented in the form of the curvesS - N wherethe alternating efforts,S , - the maximum applied tension - are represented in terms of thenumber of cycles, N , to failure. In Figure 3-19 theS - N curve of a quasi-isotropic carbon-epoxy system can be observed. The study of these curves reveals that when the level ofthe applied stress is diminished, the quantity of cycles until failure increases. The fatiguelimit is defined as the effort level beyond which failure does not take place due to fatigue.

However, most materials do not have this limit, so that frequently the fatigue limit ofmany materials is specified as the effort that will not produce failure of the material below106 cycles. Furthermore, composites generally present a higher resistance to the fatiguethat translates itself in a superior fatigue limit and requires special treatment. The first factto highlight is that theS - N curve, which appears in Figure 3-19, seems to follow a directline when it is represented in a logarithmic scale. Then it can be represented usingexperimental data by means of an exponential law in which the parameters are easilyestimated by means of a simple lineal regression. This characteristic, commonly acceptedbelow one million cycles, is not the case above that limit. For applications of high cyclesit is recommended to use a law that includes more adjustment parameters.

Figure 3-19. S-N curve of a Carbon T300/Epoxi 5208 [0/90/45]s laminate

3.3.2.1 Factors affecting the fatigue life. Damage mechanisms

Several factors affect the fatigue life, but they can be classified in three main groups:mechanical, microstructural and environmental factors. The first two are related to theapplied stress and stress concentrations. Hence, important improvements in the fatiguelife can be obtained by means of a proper design and a careful attention of themechanical factors that occur in a particular fatigue situation. Microstructural factors playan important role, considering that the microstructural orientation is very pronounced in


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an anisotropic material. As for the environment, they can be considered as special casesof fatigue and include thermal effects, contact fatigue and the effects of corrosion.

In general, the effect of fatigue is the reduction of the strength or the residual stiffness,and the possible failure, after applying a finite number of load cycles. These load cyclesare smaller in magnitude than the necessary load to produce failure in a single cycle. Therefore, some process of fatigue damage has to occur that reduces the materialstrength under load.

In all ways, this damage is not uniform, that is, not all the volume of the material elementsuffers the same stress reduction. Generally, the damage process consists of a series ofdiscrete events that cause a non-uniform or inhomogeneous response of the material. Infact it is probable that the most universal characteristic in fatigue is the inhomogeneousdeformation. According to above-mentioned consequence, the fatigue effect is composedof a series of micro-geometric contributions, such as microcracking that produces localconcentrations, which in turn generate additional damage.

A basic physical principle behind any cycle-dependent behaviour is the appearance ofnon-conservative deformation that modifies the internal nature or the geometry of thematerial, and its capacity to respond to histories of continuous load. Non-conservativedeformation implies that the part of the energy absorbed by the material through thestress or the applied displacements is not stored as energy of deformation, but isdissipated as the driving force of internal processes, as the formation and growth ofmicrocracks, as thermodynamic events, as atomic or molecular redistribution and aschemical events. Although not all the non-conservative processes produce fatigue in thesense that they do not reduce the residual strength, the stiffness or the service life, it isknown that the damage processes for fatigue are not conservative; this implies adependence of the behaviour of the materials on the load history.

For composites of interest in civil engineering applications, especially those with fibres ofhigh modulus, the different micro-events that contribute to the development of thedamage process are classified in the following categories:

Microcrack formation Chemical damage Plastic deformation Delamination Separation of fibres and matrix Interface failure


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Generally, a reinforcement material is chosen to provide a great strength and stiffness tothe composite, while the matrix material i

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