Yun-Mei Mei Luo

Luc Chevalier

Éric Monteiro

Shiyong Yan

Gary Menary

Eric Monteiro

Simulation of the Injection Stretch Blow Molding Process: An Anisotropic Visco-Hyperelastic Model for Polyethylene Terephthalate Behavior

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Introduction

The sustainable use of plastics has become a global issue with all major brand owners committed to reducing the use of plastic in packaging through optimized design or recycling initiatives. An area receiving major attention is the use of PET bottles which are currently manufactured at a rate of one million per minute by a process known as Injection Stretch Blow Moulding (ISBM). ISBM begins with injection molding of a test tube like specimen known as a preform that is subsequently re-heated above its glass transition temperature and formed into a mold by a combination of axial stretching by a stretch rod and radial stretching by internal air pressure. The main challenge for manufacturers is to produce containers with as little material as possible but still meet in-service performance requirements such as top load and burst resistance. However the industry still relies a lot on empirical knowledge and trial and error and it recognizes the need to move away from this approach though the use of manufacturing process simulation. The key component of a the process simulation is the constitutive material model to accurately capture the nonlinear viscoelastic behavior of PET over the wide temperature, strain rates and modes of deformation experienced in stretch blow molding.

An accurate model of PET for stretch blow molding must be characterized at temperatures and strain rates typically seen in the process. Nixon et al [1] demonstrated through free blowing preforms whilst monitored via high speed video that the strain rate has an average of 40s -1 [1] whilst it is well recognized in the industry the temperature range of interest is between 90°C and 120°C i.e. just above the glass transition temperature but just below the cold crystallization temperature.

Over the past 30 years there have been numerous attempts to develop models of the non linear viscoelastic behavior of PET for ISBM. Initially researchers ignored the viscous effects and used hyperelastic models (Marckmann et al. [2]). Billon et al [3,[START_REF] Gorlier | The 14th International ESAFORM Conference on Material Forming[END_REF] recognizing the need to include viscous effects and altered the hyperelastic model by making some of the parameters dependent on strain rate however the model proved to be unstable when implemented in forming simulations. Previous work from Chevalier et al [START_REF] Chevalier | [END_REF] based on biaxial experimental data in the strain rate range 0.02 to 2 s -1 clearly demonstrated the need to capture the viscous effects and based on this data a new model known as the G'Sell-Jonas was developed which took into account the effect of strain rate and the typical strain hardening behavior observed in PET. This viscoplastic model was subsequently used by Schmidt et al [6] to demonstrate the potential of combining simulations of stretch blow molding and IR heating to determine the optimum process settings to manufacture a container with a desired thickness profile. The model was further developed by Cosson [7] through the implementation of anisotropy. Whilst this improved model was also able to relate the constitutive behavior with microstructure due to its viscoplastic nature it was still unable to match data produced in experiments performed by Chevalier and Marco [8].

Other approaches to modelling PET in ISBM is the use of viscoelastic models [9,10]. One example includes the work by Schmidt [9] who used a Maxwell like model, however accurate results for predicting the preform shape evolution and strain hardening behaviour were not achievable. It was clear that a combination of viscoelastic and hyperplastic effects were required to capture the behavior of PET. This was recognized by both Boyce et al [11] and Buckley et al [12] who both developed models of PET through the parallel combination of hyperleastic models and viscous models. The model developed by Buckley et al known as the Glass Rubber model was initially developed for the study of hot drawing of PET in industrial film drawing. Menary et al [13] evaluated the model for its ability to capture the behavior of PET in stretch blow molding and benchmarked it against the performance of a hyperleastic model and a creep law in an ISBM simulation. It was demonstrated that the Glass Rubber model was able to accurately predict the final wall thickness of a PET bottle.

Inspired from Figiel and Buckley's work [14], Chevalier et al. [START_REF] Luo | The 14th International ESAFORM Conference on Material Forming[END_REF][START_REF] Chevalier | [END_REF][17] have recently proposed a nonlinear incompressible visco-hyperelastic model to represent the complex constitutive behaviour of PET. Experimental uniaxial and biaxial tests performed on PET were carried out by Menary et al. [18] in Queen's University of Belfast. These tension tests were managed with various tension speeds (strain rate from 1s -1 to 32s - 1 ),.The nonlinear forms of elastic and viscous characteristics were proposed. However, the isotropic version of the model that we proposed [START_REF] Luo | The 14th International ESAFORM Conference on Material Forming[END_REF][START_REF] Chevalier | [END_REF][17] did not reproduce the shape evolution of the perform during blowing: and thus some improvements are needed to fit biaxial tests and free blowing experiments.

In the first section, based on a previous isotropic version of a visco-hyperelastic model build to represent the behavior of PET near the glass transition temperature, we propose an anisotropic version. The theoretical basements of this upgraded anisotropic version are presented. First, an energy function W models the elastic part with the isotropic contribution Wiso and anisotropic one Wani. The isotropic part Wiso depends on the classical invariants and the anisotropic part Wani depends on the new invariants that are associated to the anisotropic material behavior. The stress tensor is obtained from derivation of this energy function W and depends on structural tensor Ai built from the direction of anisotropy. The viscous part is built using a 4 th order tensor to represent the classical orthotropic formulation.

The second section is devoted to the identification procedure to make the model fit with experimental data. This anisotropic version of the visco-hyperelastic model needs both equi-biaxial and constant width to provide an accurate identification. These tests were managed at Queen's University Belfast. A singularity problem appears for the numerical simulation due to asymptotic values for the h function that represents the strain hardening effect in the viscous part. The h function is modified in order to solve this singularity.

Finally, in the third section, thanks to this identification, we can simulate free blowing of PET preform that is close to the industrial stretch blow molding process. We use the software ABAQUS/Explicit for the simulations and our model is implemented via a user-interface VUMAT. Free blowing simulations taking into account the anisotropy, are performed and are successfully compared to the experimental results.

I. An anisotropic visco-hyperelastic model for PET under ISBM condition

An isotropic version of the nonlinear incompressible visco-hyperelastic model has been presented and identified in the author's previous papers [START_REF] Luo | The 14th International ESAFORM Conference on Material Forming[END_REF][START_REF] Chevalier | [END_REF][17]. This model reproduces nicely the equi-biaxial elongation results obtained from experimental tests performed at QUB [18] using strain, strain rate and temperature conditions near ISBM conditions, but this isotropic version did not reproduce accurately the shape evolution of the preform during blowing. Using this version of the model, when the strain reaches the "strain hardening" region in the hoop direction, the material cannot be stretched anymore and this limits the evolution in longitudinal direction. In order to correct this drawback during the free blowing simulation, one needs to introduce anisotropy in both the viscous and elastic parts of the model. This will allow to reproduce accurately the constant width test and will provide accurate simulation of the free blowing of preform.

The Cauchy stress tensor  is developed as a Maxwell like equation with two expressions whether one considers the elastic or the viscous part:

2 2 e e v v p I G p I D     = - +    = - +   (1)
where e

 is an Eulerian strain tensor:

( )

I B e e - = 2 1  , v D
is the viscous strain rate tensor, pe and pv are hydrostatic pressures associated with incompressibility conditions.

e B is the elastic part of the left Cauchy deformation tensor. In a previous isotropic version, G and  were scalar shear modulus and viscosity. Both characteristics were a function of elastic strain components for G and of viscous strain and strain rate for . In the following, we present the anisotropic form of these two parts. First, let's focus on the elastic part.

I.1 Elastic part visco-hyperelastic model

The free energy function W is defined as a function of two series of invariants: the principal invariants of the elastic left Cauchy Green tensor and also more invariants defined in Spencer [START_REF] Spencer | Continuum Theory of the Mechanics of Fibre-Reinforced Composites[END_REF][START_REF]Applications of Tensor Functions in Solid Mechanics[END_REF]. The first series is associated to the isotropic material behavior and can be written as:

( ) ( ) ( )   ( ) e e e e B I B tr B tr I B tr I det , 2 1 , 3 2 2 2 1 = - = = (2)
The second series are the invariants associated to the anisotropic behavior:

=   =   =   =   =   =   (3)
1 n , 2 n et 3 n are the privileged directions of the orthotropic behavior of the PET material. We introduce three second order structural tensors i A . They are obtained from the preferred directions [START_REF] Liefeith | 6th German LS-Dyna Forum[END_REF]:

1 1 1 2 2 2 3 3 3 , , A n n A n n A n n =  =  =  (4)
These structural tensors have to be invariant under the rotation tensor Q out of the symmetry group  , so they have to satisfy the condition [START_REF] Liefeith | 6th German LS-Dyna Forum[END_REF]:

T i i A Q A Q Q  =   (5)
Due to the representation theorem, the strain energy W can be rewritten as both an isotropic part and an anisotropic part:

( ) ( ) ( ) 9 8 7 6 5 4 2 1 3 2 1 , , , , , , , , , I I I I I I W I I W A A A B W ani iso e + = (6)
where Wiso and Wani are isotropic convex functions of their arguments.

We make the assumption that displacements are big enough to neglect the volume variation so : I3=1. The important strain hardening effect that appears during uniaxial or biaxial tension tests needs to be represented by both the hyperelastic part and the viscous part using exponential functions. For the elastic part, Hart-Smith appears to be a good candidate to characterize the free energy function. Consequently, Wiso is only a function of I1 and the total energy function can be written as the following form:

( ) ( ) 2 2 2 1 4 6 1 2 2 3 1 1 1 2 3 1 2 0 0 0 , , , I I I X X X W B A A A G e dX G e dX e dX - - -    = + +    (7)
Cauchy stress tensor is obtained from the strain energy by derivation [START_REF] Weiss | [END_REF]:

( ) ( ) ( ) ( ) 2 , 1 1 ,2 ,2 4

W p I W I W B W B B I W A I W n B n n B n I W A I W n B n n B n

I W A I W n B n n B n   = = - + + -  + +  +  + +  +  + +  +  (8)
where ,i W stands for the partial derivative i WI  . Considering the chosen energy function W (Eq.7), the elastic stress yields to:

( ) ( ) ( ) 2 2 2 26 1 1 2 4 1 3 1 1 4 2 1 6 2 2 2 2 2
I I I pI G e B I G e A I G e A  -  -  - = -+ + + (9)
where G1, G2,  and  are parameters in the elastic part of the Visco-hyperelastic model.

I.2 Viscous part visco-hyperelastic model

In the plane stress case, the deviatoric part of the stress tensor   can be written: We choose specific hi functions [START_REF] Luo | The 14th International ESAFORM Conference on Material Forming[END_REF] for each orthotropic direction (i=1 the hoop direction and i=2 longitudinal direction) (11) with: are parameters in the h function that can be identified from biaxial elongation tests using the previous procedure presented in [START_REF] Luo | The 14th International ESAFORM Conference on Material Forming[END_REF][START_REF] Chevalier | [END_REF][17]. Under the assumption of additivity of the elastic and viscous strain rates, assumption of the pure elastic spin rate and the choice of the Oldroyd equation for tensor e B , the constitutive equation can be obtained.

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 11 0 1 12 0 1 2 22 0 2 44 0 max v v v vv η η T h f d η η T h ,h f d η η T h f d η η T h ε f d  =   =   =    =  ( ) ( ) ( ) ( ) ( ) ( ) ( )                      + +          - - =         + +          - - =         + +          - - =
                  v vref v v v v vref v v v vref v v ε ε ε K ε h K h K h
( ) ( ) ( ) 1
Therefore, equation 9 in plane stress case for the deviatoric part of the stress can be written as:

( ) ( ) ( ) 2 2 2 26 1 1 2 4 1 3 1 1 4 2 1 6 2 2 2 2 2 2 I I I v e D G e B I G e A I G e A     -  -  - = + + (13)
That implies:

v v v d D D d D d                    -   - -         -   =      - -                (14)

II. Identification procedure of the model from equal-biaxial and constant width tensile tests

The authors have previously used a specific h function to model the strain hardening effect during the viscous part of the model (see [START_REF] Luo | The 14th International ESAFORM Conference on Material Forming[END_REF] for details). From an arbitrary choice for the hyperelastic part and for the contribution of the strain rate in the viscous part, one can extract from experimental data, the contribution of the elongational strain in the viscous part. The shape of the obtained curves highlights an ultimate viscous strain but during the numerical simulations using this model, the limit value can be reached and passed: numerical problems arise. More precisely, the singularity problem appears during the ISBM process simulation when the viscous strain is higher than the parameter vlim (Figure 1). Therefore, a purely exponential function is chosen instead of the original h function presented in previous publications.

( ) ( ) ( ) ( )                  + +          - - =         + +          - - = 3 2 2 2 2 1 2 2 3 1 2 2 1 1 1 1 exp exp 1 exp exp 1               v vref v v v vref v v K h K h (15)
The identification process is based on minimizing the square difference between the model and the experimental values of both equi-biaxial and constant width tests. These two problems can be solved quasi-analytically: totally for the equi biaxial test and with a numerical resolution for the constant width. This identification leads to the identified values shown in Table 1. The mean difference between model and experiment highlighted on curves shown Figure 2 is 12.8% for constant width in the elongation direction and 6.2% in the constrained direction. For the equi-biaxial test, the mean difference is 6.3%.

Considering the complexity of the PET behavior and the small number (12) of numerical parameters to be identified in our model, this agreement is good and leads to accurate results.

An analysis of the sensitivity of the model to the parameters value is managed using a partial differentiation technique. In this case, the mean absolute error  depends on each parameter i and can be calculated from equation 16. Each parameter is increased independently by a value of 10%, the sensitivity coefficient di, can be calculated which is the difference between the new mean error new and the error with standard parameters ref.

III. Stretching and blowing simulation of a PET preform

The software ABAQUS / Explicit is used so that geometry definition and meshing operations remains easy. We implement our VHE model via a user interface VUMAT a classical Newton Raphson iterative procedure is used to solve this strongly non linear problem. Figure 3 illustrates the structure of the implementation into the ABAQUS software. One can compute the elastic Cauchy Green tensor Be from equation 14.

III.1 Benefit of the anisotropic model for the free blowing simulation of a PET preform

In order to evaluate the predicting performance of the model, we focus on the simulation of a preform stretched by an internal rod and blown with air at a specific flow rate that generates internal pressure. Using the finite element approach, we will be able to compare the shape and the internal pressure evolution obtained by simulation with experimental data. The preform geometry and the longitudinal stretch rod are meshed by shell elements in ABAQUS. In order to reduce the computing time, we took into account the axi-symmetry of the process and that choice reduces the number of degrees of freedom. The air mass flow injected into the preform / bottle is modelled by an exchange of fluid between components (fluid structure interaction implanted in ABAQUS). This air mass flow modelling has already been described in detail in [1,[START_REF] Salomeia | 24thPPS Conference[END_REF][START_REF] Salomeia | [END_REF]. Nevertheless, CPU time for one complete free blow simulation using a 2.66GHz Pentium4 processor is about six hours.

The previous free blow [START_REF] Mei Luo | 19th ESAFORM Conference[END_REF] and stretch blow simulation results obtained with the isotropic version of the visco-hyper-elastic model failed to represent the real ratio between the length and radius of final bottles. One explanation is that the isotropic model leads to very high viscosity value once the elements are stretched along one direction (here, the hoop direction). Consequently, the elongation in the longitudinal direction is more difficult.

Figure 4 shows the evolution of the bottle shape. One can see that anisotropic version of the model gives a shape evolution that is in good agreement in comparison with the real blown bottle. A free blowing machine developed at Queen's University [1] made possible the experimental measurements. During the test, the stretch rod velocity, the air flow rate, the maximum blowing pressure within the preform cavity are imposed and the preform stretching force and the pressure evolution vs time are measured. The details of experimental set up and the data acquisition system were previously described in [START_REF] Tan | ESAFORM Conference[END_REF][START_REF] Salomeia | Improved understanding of injection stretch blow moulding trough instrumentation process monitoring and modeling[END_REF][START_REF] Nagarajappa | Identification and validation of process parameters for stretch blow moulding simulation[END_REF]. During a SBM process, the hot preform is transformed into a bottle mainly due to the pressure exerted on the inside walls of the preform by the compressed air. The work of Menary et al. [START_REF] Tan | ESAFORM Conference[END_REF] demonstrated that the pressure that builds inside the preform is not a cause but an effect that depends on the amount of air filling the preform and the rate of expansion of the preform. By using the mass flow approach in the simulation, they showed that the preform shape evolution prediction was better than the direct experimental pressure application. Salomeia [START_REF] Salomeia | Improved understanding of injection stretch blow moulding trough instrumentation process monitoring and modeling[END_REF] used an air mass flow model which was described as a function of pressure difference. The mass flow rate is controlled by both the preblow pressure adjuster and the flow limiter. The preblow pressure is 8bar and the mass flow rate has two levels controlled by the flow index (two for low or six for high). The average value of mass flow rate at the higher level is 33.96 ±0.863 g/s, almost four times larger than that of the lower level (8.88±0.195 g/s).

Figure 5 shows the evolution of pressure coming from simulation (discontinuous line) and from experimental results (dots that makes a quasi-continuous line). Considering the complexity of the PET behavior and the small number ( 12) of numerical parameters of our model, and considering that parameter identification is obtained from an idealized biaxially stretched plane specimen, one can conclude that there is a good agreement between this axi-symmetric simulation and free blowing experiment. Consequently, one can have faith in the model and consider other cases for predicting effects on thickness distribution for example.

III.2 Model validation from numerical/experimental comparison of a stretching and blowing simulation of a PET preform

Moreover, two stretch blow simulations have been performed. Figure 6a shows a 'free blowing' like simulation: because of the high air flow rate, the material elongation in the longitudinal direction of the preform goes faster than the stretch rod. No contact occurs between the preform and the stretch rod during this specific blowing. The experimental measurements for this 'free blowing like' simulation is shown in Fig. 4a. Figure 6b shows another simulation with a lower air flow rate, in this case the material longitudinal elongation is slow. The preform is stretched by the rod at first and then in the hoop direction during blowing. This simulation is also compared with the experimental measurements. The stretch rod velocity for each case is given in Figure 7a. Figure 7b shows for each case the air mass flow rate as a function of pressure difference (dP).

Figure 8 shows the distribution of the thickness of the two stretch blowing cases. In the free blowing like simulation Fig. 8a, the mean value of the thickness is about 0.45mm. The aspect ratio (ie. length over radius) is lower than for the second case. Consequently, for the same global length, the thickness will be higher in the second case.

In the stretch blowing simulation case (right side of the figure), the mean thickness is about 0.5mm and the distribution is more homogenous. In both cases, one can see that the thickness is higher in the zone near the neck of the bottle than elsewhere.

Conclusions

We developed an orthotropic visco-hyperelastic model adapted to the severe strainrates and temperatures conditions of the stretch-blow molding process. An orthotropic formalism is used for both elastic and viscous parts and the complex form of the model is presented.

The identification procedure has been achieved using data provided by equi-biaxial and constant width elongation tests managed at QUB at different speeds and temperatures. The best parameters values identified for the model enables to reproduce the experimental results with about 10% difference.

We implemented the orthotropic visco-hyper-elastic model in ABAQUS software and we simulate free blowing of PET perform. The comparison with a real free blowing test validates the anisotropic version of the visco-hyperelastic model for PET near Tg. As a complement, the influence of the air flow rate on the shape evolution and thickness distribution has been managed and high air flow rate leads to larger radius and lower thickness.

LIST OF TABLES

Table (1). Model coefficient values Table (2). Sensitivity of coefficients

  m, a are the classical parameters of Carreau's law ( ) rates that can be taken equal to 1s -1 for sake of simplicity. v d is the equivalent viscous strain rate and v  is the equivalent viscous strain. The chosen expressions for hi functions assure to give the same model as the isotropic one when the strain is purely equi-biaxial. 0  , K, N and vref 

  right side of equation 13. In the following sections, equation 13 can be used to simulate the tension test and the ISBM process.

Figure 2 .Figure 3 .Figure 4 .Figure 5 .Figure 8 .Figure 1 .Figure 2 .Figure 3 .Figure 5 .Figure 6 .Figure 7 .Figure 8 .

 234581235678 Figure 2. (a) Experimental set-up for biaxial test and comparison between experimental results and model simulations for the case 2s -1 and 90°C: (b) Constant Width; (c) Equibiaxial

  Table 2 lists the sensitivity coefficient di of each parameter in our model. The parameter m is clearly the most sensitive parameter. The 4 parameters used in the elastic part of the model have less influence.

	( ) i 	exp CW  exp exp num CW EB   --exp  EB CW =+ 	num EB

TABLE 1 .

 1 Model coefficient values

	G( e  )	G1 (MPa)	Λ1	G2 (MPa)	Λ2
		3	1	2	1
	( ) v fd	λ	a	m	η (MPa.s)
	η( v  , v d , T)	10.51	2	0.23	1.8
	( ) v h 	vref	1	2	3
		1	8.9	-2.6	1

TABLE 2 .

 2 Sensitivity of coefficientsLIST OF FIGURES AND CAPTION Figure 1. Singularity problem using the equation 11 for the h function

	G1 (MPa)	Λ1	G2 (MPa)	Λ2	λ	a
	0.5	4.10 -2	0.8	0.2	8.5	2.10 -5
	m	η (MPa.s)	vref	1	2	3
	112.8	2.5	2	11.1	12.9	14.6


Emmanuel Richaud

PIMM Jacques Verdu

AGING BEHAVIOR AND MODELING STUDIES OF UNSATURATED POLYESTER RESIN AND UNSATURATED POLYESTER RESIN-BASED BLENDS

INTRODUCTION

Unsaturated polyester resins (UPRs) are usually obtained from a prepolymer being a condensation product of unsaturated anhydride (or diacid) and a diol. This highly viscous liquid is dissolved in a reactive low viscosity solvent, commonly styrene (or sometimes methyl methacrylate). The curing is initiated by peroxide and metallic salt catalyst of the peroxide decomposition often called "accelerator". It induces the copolymerization of double bonds hold by both the prepolymer and the solvent to give a network.

The wide use of such materials in applications ranging from tanks, tubes, and vessels to shipbuilding or outdoor swimming pools makes it necessary to well understand their long-term stability in the presence of external factors that cause degradation (temperature, oxygen, water, chemicals, radiations, etc.). The present chapter is, hence, aimed at:

• presenting the main mechanisms involved in network degradation; • proposing kinetic schemes and providing the corresponding equations, thereby allowing for the prediction of changes in network structure (at a molecular scale) and the influence of the cited causes of degradation; • using the available structureÀproperty relationships or establishing empirically new ones to determine the effect of the observed changes at microscopic scale on network properties, especially thermomechanical properties.

There are basically two kinds of aging mechanisms.

1. Physical aging basically corresponds to changes in composition (water absorption, plasticizer loss) and in chain conformation, especially when interchain distances are modified, but without modification of the polymer chemical structure. The main kinds of physical aging are structural relaxation (with a decrease of free volume) and physical aging by solvent ingress or plasticizer loss. In this chapter, focus will be placed on humid aging, which induces plasticization and differential swelling, thereby generating strains and thus being a possible cause of matrix or fiberÀmatrix interfacial damage. The latter will favor water penetration into the material and thus the eventual propagation of chemical aging deep sample layers. 2. Chemical aging is due to reactions with external agents such as water, oxygen, solar UV, or ionizing radiations. Since polyesters are often used in contact with water, emphasis will be put on polyester composite interactions with water. In this chapter, particular attention will be paid to the phenomenon of osmotic cracking, in which degradation at the microscopic scale leads to the formation of macroscopic cracks.

CHANGES IN MECHANICAL PROPERTIES OF NETWORKS 9.2.1 NETWORK PLASTICIZATION BY SOLVENTS

The penetration of water or other small molecules into the polymer provokes a strong glass transition temperature (T g ) decrease illustrated, for example, in the case of UPR and its composites [START_REF] Jefferson | Influence of hygrothermal aging on carbon nanofiber enhanced polyester material systems[END_REF].

From a theoretical point of view, let us recall that the free volume theory allows for the change of T g to be predicted in the case of polymer blends and polymerÀsolvent mixtures by the simplified relationship seen in Eq. (9.1). In common "dry" polyester networks, the T g is in the order of 380 K and the T gW is in the order of 120 K. The above relationship can be rearranged as:

1 T g B 1 T gðdryÞ 1 0:0057φ (9.2)
Thus T g is expected to decrease of about 8 K per per percent of absorbed water. In common polyesters, water absorption does not exceed 1À2%. The effects of plasticization are thus limited, but can be critical when the material is submitted to high static loads.

Glassy modulus (E glassy ) depends on the density of cohesive energy: KB11. CED where K is the bulk modulus and CED the Cohesive Energy Density [START_REF] Pascault | Thermosetting polymers, Effect of Crosslink Density on Elastic and Viscoelastic Properties[END_REF]. In the case of plasticized networks, the interchain distance increases, so it is expected that the elastic glassy modulus decreases.

The glassy modulus (E rub ) depends on the elastically active chain concentration. It decreases with plasticizer content [START_REF] Mark | The rubber elastic state[END_REF]:

E rub 5 3 3 φ 1=3 P 3 EAC ½ 3 RT (9.3)
Plastification by water, therefore, results in a decrease in mechanical properties such as glassy and rubbery elastic modulus [START_REF] Jefferson | Influence of hygrothermal aging on carbon nanofiber enhanced polyester material systems[END_REF][START_REF] Morales Arias | Aging in water and in an alkaline medium of unsaturated polyester and epoxy resins: experimental study and modeling[END_REF]. Identically to T g changes, depletions of the glassy and rubbery moduli are expected to be weak since water absorption is low. Moreover, in the absence of any other chemical damages, these changes would be characterized by:

• an equilibrium state, • a reversible aspect.

According to Apolinario et al. [START_REF] Apolinario | Effects of water ageing on the mechanical properties of flax and glass fibre composites: degradation and reversibility[END_REF], the elastic modulus actually plateaus in the case of an immersion at 30 C. The drop of elastic modulus is about 5% (for a 1% water uptake) and samples recover their initial properties after drying. However, this seems to not always be the case [START_REF] Jefferson | Influence of hygrothermal aging on carbon nanofiber enhanced polyester material systems[END_REF], meaning that chemical damage can overlap either in the matrix or at the matrixÀfiber interface.

OSMOTIC CRACKING

Osmotic cracking has, in particular, been observed for water diffusion. Its mechanism can be summarized as follows:

• water diffuses into the polymer and fills a "void" (preexisting cavity) or forms a cluster (see Section 9.3.2); • short soluble molecules (e.g., curing initiator byproducts, unreacted styrene, or short fragments generated from hydrolytic degradation) dissolve in this water phase and lower its chemical potential; • this latter step provokes further diffusion of water through the polymer (which behaves as a permeable membrane) so as to equilibrate its chemical potential. The difference in chemical potential between dissolved and external water results in an osmotic pressure given by van't Hoff's law: A rise in temperature induces an increase in water solubility in polymers and the redissolution of the water phase in polyesters and, thus, possible self-healing. Conversely, a decrease in temperature induces a supersaturation of water in polymers and the initiation of new disk cracks [START_REF] Baek Lee | Water-induced nucleation of disc cracks in selected thermosets[END_REF]. Last, the initiation time for disk cracks would obey the Arrhenius law [START_REF] Gautier | Osmotic cracking nucleation in hydrothermal-aged polyester matrix[END_REF].

CHANGES INDUCED BY CHEMICAL AGING

Jefferson et al. [START_REF] Jefferson | Influence of hygrothermal aging on carbon nanofiber enhanced polyester material systems[END_REF], compared the changes in T g and elastic modulus (at glassy state) in virgin polyester materials (matrices with carbon nanofibers and/or glass fibers), those polyester materials after water immersion (weight gain about 0.1%À1%), and unsaturated polyester (UP) materials immerged in water and then dried.

Their results, illustrated in Fig. 9.2, show that water penetration is not totally reversible. Comparable results were obtained for UP immersion in ethanol (Table 9.1) [START_REF] Barlette Da Cunha | Assessment of chemical and mechanical properties of polymers aiming to replace the stainless steel in distillation column[END_REF]; where mass uptake curves displayed a maximum followed by a decrease ascribed to the leaching of small molecules, and the ultimate stress decreased with ethanol aging. However, one sees that a σ R decrease cannot be explained only by ethanol ingress. Actually, the decrease for σ R is observed to be lower for instances of higher ethanol uptake.

These (irreversible) changes are associated to the chemical degradation described in Section 9.3. The elastic modulus at glassy state actually depends on cohesive energy more than on cross-link density. In the case of hydrolysis, moderately polar ester groups are converted into highly polar ones (carboxylic acids and alcohols). However, there are no studies evidencing an increase in glassy moduli with hydrolysis (see, e.g., Fig. 9.2 where a decrease is observed).

At temperatures above the T g , thermoset networks are in the rubbery state. Elastic behavior is given by the Flory approach, according to which the Young's modulus is proportional to the concentration of elastically active chains, n 0 [START_REF] Mark | The rubber elastic state[END_REF]:

E 5 3ρRT M C 5 3n 0 RT (9.5)
where ρ is the density, M C the average molar mass between cross-links, R the gas constant, and T the absolute temperature. Eq. (9.5) is a theoretical equation valid for ideal networks. The analysis of a wide series of UPR networks has shown that the modulusÀcross-link density is rather:

E 5 3ρRT 3 1 M C 2 1:5 (9.6)
illustrating the effect of dangling chains [START_REF] Bellenger | StructureÀproperty relationships for styrene crosslinked polyesters. I. Network structure and rubbery elastic modulus[END_REF]. It is clear that chemical changes leading to either chain scission or cross-linking will modify the concentration of elastically active chains and later the rubbery modulus. For degraded networks having undergone chain scission (s) and/or cross-linking (x), it can be proposed that:

n 5 n 0 2 ψ 3 s 1 φ 3 x (9.7)
with ψ 5 1 for tetrafunctional networks and ψ 5 3 for trifunctional networks.UPR are possibly tetrafunctional networks but there are degradation studies based on these relationships.

The glass transition of a fully cured network (T gN ) is given by the DiMarzio's equation [START_REF] Dimarzio | On the second-order transition of a rubber[END_REF]:

T gN 5 T gl 1 2 K DM Fn 0 (9.8)
where K DM is the DiMarzio's constant; n 0 is the cross-link density (mol/kg); T gl is the glass transition of a "virtual" linear polymer (n 0 5 0); F is the flex parameter (kg/mol) related to the molar mass per rotatable bond. The calculation of the parameters of DiMarzio's law is illustrated in the case of epoxies [START_REF] Bellenger | Effect of structure on glass transition temperature of amine crosslinked epoxies[END_REF]. In the case of UPR, an attempt to describe glass transition of networks was done [START_REF] Bellenger | StructureÀproperty relationships for styrene crosslinked polyesters. II. Glass transition temperature[END_REF], but it seems that it is only possible to predict T g values with F, T gl , and n 0 coming from structural considerations if K DM is an adjustable parameter. The most obvious reason is the nonideality of polyesters and, in particular, the possible presence of cross-link nodes where:

• the cross-link bridge is made of several homopolymerized styrene (S) units, which can be considered as trifunctional:

E E E E HC CH Sj HC CH
• the cross-link bridge is made of homopolymerized fumarates or maleates, which can be considered as hexafunctional:

E E HC CH S E E HC CH S
One can see here that UPRs are further from ideal networks than epoxies, for example. However, the determination of K DM for virgin networks can allow for the estimation of the residual cross-link density after a chemical aging and later, the concentration in chain scissions and crosslinks.

T g changes induced either by chain scission or cross-linking can be related to changes in yielding properties since it was proposed in thermosetting networks that [START_REF] Pascault | Thermosetting polymers, Yielding and Fracture of Polymer Networks[END_REF]:

σ Y 5 C T g À T À Á (9.9)
and

ε Y 5 T g À T À Á 500 (9.10)
Considering ultimate properties, it seems that both ultimate stress and strain decrease following the initial tensile curve of networks as a "rupture envelope" at least in the case of hydrolyzed networks (Fig. 9.3). Decrease of ultimate stress and strain for various polyester networks having undergone various levels of hydrolysis [START_REF] Bellenger | Lifetime prediction in the hydrolytic ageing of polyesters[END_REF].

Reprinted with the permission of Elsevier.

INTERFACIAL DAMAGES IN COMPOSITES

In UPRÀglass fiber composites, it is known that the interface is a domain where water is expected to be more soluble than in the matrix [START_REF] Chateauminois | Study of the interfacial degradation of a glass-epoxy composite during hygrothermal ageing using water diffusion measurements and dynamic mechanical thermal analysis[END_REF] as well as being subject to a faster diffusion. The consequences of aging are then worst in the case of composites in which water promotes:

• matrixÀfiber decohesion [START_REF] Faguaga | Effect of water absorption on the dynamic mechanical properties of composites used for windmill blades[END_REF] evidenced by a decrease in the interfacial shear strength [START_REF] Gautier | Interface damage study of hydrothermally aged glass-fibrereinforced polyester composites[END_REF] • composite delamination [START_REF] Gautier | Interface damage study of hydrothermally aged glass-fibrereinforced polyester composites[END_REF] • the hydrolysis of coupling agents [START_REF] Ishida | A fourier-transform infrared spectroscopic study of the hydrolytic stability of silane coupling agents on E-glass fibers[END_REF]

CONCLUSION

The failure of UPR and UPR composites originate from physical aging (i.e., diffusion of small molecules in the network without changes in its architecture) and/or chemical aging (i.e., irreversible mechanisms inducing chain scissions and/or cross-linking). The main mechanisms associated with these degradation modes will be presented in Section 9.4, Mechanisms of Chemical Degradation.

Some of these changes can be described using polymer physics laws from values of water uptake or concentration in cross-link. If these latter can be described by kinetic law, it may permit the changes in engineering properties (and later the lifetime) to be predicted.

MECHANISMS OF PHYSICAL AGING BY SOLVENT INGRESS

COMPATIBILITY WITH ORGANIC SOLVENTS

Sorption isotherm for organic solvents into polymers is described by the FloryÀHuggins equation:

ln P P 0 5 lnð1 2 φ p Þ 1 φ p 1 χφ 2 p (9.11)
in which P/P 0 is the water activity in the external medium around the polymer; φ p is the polymer volume fraction in the polymerÀwater mixture; and χ is the polymerÀsolvent interaction expressing the affinity of polymers for certain chemicals ("like seeks like"). It can be calculated by:

χ 5 V m RT Á δ polymer 2δ solvent À Á 2 (9.12)
δ being the solubility parameter with δ UP B 22 MPa 1/2 [START_REF] Deslandes | Solubility parameter of a polyester composite material[END_REF]. Low χ values correspond to high polymerÀpenetrant compatibility. It is, hence, not surprising that aromatic halogenated solvents such as chlorobenzene display a high affinity with UPR [START_REF] Ajithkumar | Sorption and diffusion of organic solvents through interpenetrating polymer networks (IPNs) based on polyurethane and unsaturated polyester[END_REF][START_REF] Ajithkumar | Sorption behaviour of interpenetrating polymer networks based on polyurethane and unsaturated polyester[END_REF], whereas apolar solvents (cyclohexane) or highly polar solvents (water) are poorly soluble in polyesters. Extensive tables reporting the compatibility of different kinds of UPR with several sorts of fluids and chemicals can be found in Ref. [START_REF] Baur | Unsaturated Polyester Resins, Chemical Resistance of Thermosets[END_REF].

The diffusion of solvents into UPR has been scarcely investigated in existing literature. The transport phenomena of penetrants in polymers can be described by [START_REF] Masaro | Physical models of diffusion for polymer solutions, gels and solids[END_REF]:

M t ð Þ M N 5 k 3 t n (9.13)
M(t) and M N being the mass uptake at any time and at the theoretical equilibrium, respectively, and n describing the mechanism of diffusion. Schematically:

• n 5 0.5 means that the diffusion obeys Fick's law as often observed in polymer networks when the polymer chains have a high mobility allowing an easy penetration of the solvent (with the diffusion rate, R diff , being slower than the polymer relaxation rate, R relax ). • n 5 1 means that the diffusion is either anomalous, that is, the diffusion and relaxation rates are almost of the same order or otherwise it means that the diffusion rate is much higher than the relaxation rate of a given polymer so that a sharp diffusion profile is observed.

The "diffusion" aspects will be recalled in more detail in the case of water (see Section 9.3.2). According to Deslandes, the diffusivity of chemicals in UPR is first driven by their viscosity since diffusivity increases with reciprocal viscosity [START_REF] Deslandes | Relationship between morphology and solvent interactions of a polyester composite material[END_REF].

The resistance to several chemicals seems to be improved by the addition of large quantities (about 40%) of microscopic fillers such as ATH, mica, or calcium carbonate [START_REF] Khalafallah | Chemical and other properties of unsaturated polyester under various environmental conditions[END_REF] or small quantities (typically 1%À5%) of nanoclays [START_REF] Jaya Vinse Ruban | Chemical resistance/thermal and mechanical properties of unsaturated polyester-based nanocomposites[END_REF]. On the contrary, the presence of microvoids increases both the equilibrium concentration and the sorption rate [START_REF] Deslandes | Relationship between morphology and solvent interactions of a polyester composite material[END_REF].

SORPTION AND DIFFUSION OF WATER

Water is a highly polar solvent, therefore, its solubility in polyester is expected to be very low along with the subsequent damage. However, water is able to react with the ester groups of UPR so that the physical aging of water (reversible) is often accompanied by irreversible damages [START_REF] Jefferson | Influence of hygrothermal aging on carbon nanofiber enhanced polyester material systems[END_REF] occurring either in the matrix or at the fiberÀmatrix interface. Humid aging is, hence, by far one of the most important mechanisms for UPR degradation. Beside the chemical interaction (described in Section 9.4.1), two key parameters describe the polymerÀwater interaction:

• the polymer affinity with water (the hydrophilicity or solubility), and • the rate of water penetration into the polymer matrix (the diffusivity).

Solubility

In composite matrices such as UPs, Henry's law is often used to describe the sorption of water in a matrix. It can be written as:

C S 5 σ 3 a (9.14)
where C s is the equilibrium concentration of water in the polymer, σ is the solubility coefficient, and a is the activity of water (i.e., the ratio of its external pressure over the saturation pressure at the considered temperature). σ is in the order of 0.36À0.42 cm 3 /mmol [START_REF] Marais | Water diffusion and permeability in unsaturated polyester resin films characterized by measurements performed with a water-specific permeameter: analysis of the transient permeation[END_REF] corresponding to about 1% of water uptake after an immersion aging. The general shape of curves for water ingress is depicted in Fig. 9.4 [START_REF] Lee | Interactions of water with unsaturated polyester, vinyl ester and acrylic resins[END_REF] (In some cases, the difference between type ➃ and ➂ curves is unclear, particularly since relatively high quantities of polymerization initiator and catalyst are used and can be extracted by surrounding water). According to Fig. 9.4, determining the true equilibrium mass uptake is not always easy since other mechanisms can overlap, in particular the effects of hydrolysis (particularly very strong mass loss at long immersion durations) on mass uptake curves is observed only at elevated temperatures [START_REF] Capiel | Diffusion and hydrolysis effects during water aging on an epoxy-anhydride system[END_REF]. Despite this issue, the orders of magnitude of equilibrium water uptake are reported in Tables 9.2 and 9.3 together with available experimental details [27,30À32].

It is often proposed to describe water absorption in polymer by [START_REF] Morel | Structure-water absorption relationships for amine-cured epoxy resins[END_REF]:

H 5 w m 3 M 1800 5 X n i H i (9.15)
where M is the molar mass of the repetitive unit; n i is the number of groups able to bind with H i molecules of water, and w m is the equilibrium water absorption (expressed in wt.%).

In the case of polyesters, the hydrophilicity in networks is expressed as [START_REF] Bellenger | Water sorption in styrene crosslinked polyesters[END_REF]:

k 5 k 1 3 ester ½ 1 k 2 3 ether ½ 1 k 3 3 chain ends ½ (9.16)
Here, the term [chain ends] accounts for acid or alcohol groups loacted at the extremity of prepolymers. More precisely, it seems that the contribution to hydrophily of those acids and alcohols is higher than ethers and esters. The effect of diacid or diol on the hydrophilicity of prepolymers has been illustrated for example in [START_REF] Bélan | Relationship between the structure and hydrolysis rate of unsaturated polyester prepolymers[END_REF]. Maleates have been shown to increase the hydrophilicity either in prepolymers [START_REF] Bélan | Relationship between the structure and hydrolysis rate of unsaturated polyester prepolymers[END_REF] (Fig. 9.5) or in cross-linked networks [START_REF] Bélan | Water swelling of polyester networks[END_REF].

Relative mass uptake

Time

Level of solubility

FIGURE 9.4
Theoretical shape of kinetic curves for water uptake and possible subcases. ➀ Water uptake without chemical aging or leaching. ➁ Water uptake followed by hydrolysis. ➂ Water uptake accompanied by leaching of unreacted chemicals. ➃ Water uptake followed by hydrolysis and extraction of hydrolysis byproducts. According to Table 9.2, increasing the styrene (S) content induces a decrease in maximal water uptake consistently with the fact that S units are almost apolar and unable to interact with water molecules. It was even proposed that:

w max 5 w max prepol 1 2 s ð Þ (9.17)
Where s is the styrene weight fraction. It is, however, difficult to correlate the polyester hydrophilicity with prepolymer one: it was for example observed that prepolymers are almost 3-times more hydrophilic than corresponding polymerized network [START_REF] Bélan | Relationship between the structure and hydrolysis rate of unsaturated polyester prepolymers[END_REF]. Two reasons are proposed: first, copolymerization with styrene induces a certain hindrance of the ester groups decreasing their affinity to water, and secondly, there is no obvious link between water affinity of prepolymer being at rubbery state and networks being usually in glassy state.

According to Table 9.3, there is a small but positive effect of postcuring on the affinity of polyesters to water (i.e., water uptake increases with post curing). Two reasons might be envisaged:

• post curing generates groups with a higher affinity to water (e.g., it can be imagined that the ester groups held by maleate are less hydrophilic than the succinate groups obtained after polymerization of the double bonds). • the disappearance of unreacted groups (e.g., styrene) is higher in incompletely cured UPRs, which lowers the maximal level of mass uptake and permits a shift from strong type ➃ behavior (Fig. 9.4) to more moderate behavior, that is, type ➃ curves with a lower rate of mass depletion or even type ➂ curves.

From Eq. (9.13), the effect of temperature is expected to obey Arrhenius law [START_REF] Merdas | Factors governing water absorption by composite matrices[END_REF]:

C S 5 C 0 3 exp 2 E RT (9.18)
where E 5 E S 1 E P , E S and E P being the activation energies, respectively, for solubility coefficient and for water vapor pressure. The fact that the equilibrium concentration increases with temperature for any given kind of UP network [START_REF] Bellenger | Water sorption in styrene crosslinked polyesters[END_REF][START_REF] Bélan | Water swelling of polyester networks[END_REF] means that E S 1 E P . 0, that is, E S . 243 kJ/mol [START_REF] Merdas | Factors governing water absorption by composite matrices[END_REF]. Henry's law means that the sorption isotherm displays a linear shape. However, experimental data sometimes display a positive curvature (Fig. 9.6). If the latter cannot be fitted by Eq. (9.10) with a fixed χ value (or rather that χ decreases with water affinity), it means that water first dissolves randomly in the polymer matrix (at low water activity) and then forms clusters, that is, aggregates of dimers or trimers or more water molecules (at higher water activity).

The presence of clusters can be evidenced either:

• experimentally using dielectric spectroscopy [START_REF] Garden | A dielectric study of water uptake in epoxy resin systems[END_REF] or FTIR [START_REF] De Nicola | Local structure and dynamics of water absorbed in poly(ether imide): a hydrogen bonding anatomy[END_REF], or • theoretically from ZimmÀLundberg analysis allowing for the assessment of the MCS (mean cluster size) [START_REF] Zimm | Sorption of vapors by high polymers[END_REF][START_REF] Lundberg | Clustering theory and vapor sorption by high polymers[END_REF] from the clustering function:

f ZL 5 G 11 ν 1 5 2 1 2 φ 1 À Á 3 @a 1 =φ 1 @a 1 ! T;P 2 1 (9.19)
where G 11 is a cluster integral for water and ν 1 and ϕ 1 are the partial molecular volume and volume fraction of water, respectively. When f ZL is below 21 value, no clustering occurs. MCS is thus given by:

MCS 5 1 1 φ 1 3 G 11 ν 1 (9.20)
MCS can also be estimated from χ values used for simulating the sorption isotherm:

MCS 5 1 1 2 2χφ 1 1 1 2 φ 1 À Á : @χ @lnφ 1 T;P (9.21)
Fillers usually reduce the permeation of water (and many other chemicals) [START_REF] Chirayil | Nanofibril reinforced unsaturated polyester nanocomposites: morphology, mechanical and barrier properties, viscoelastic behavior and polymer chain confinement[END_REF]. It seems, however, that there is an optimum effect. In the case of highly filled UP composites, the water uptake is even shown to clearly increase with filler content [START_REF] Das | Mechanical and water swelling properties of waste paper reinforced unsaturated polyester composites[END_REF]. This can be explained by the Sorption isotherm of water in Unsaturated Polyester Resin (UPR) together with the estimation of mean cluster size [START_REF] Marais | Permeametric and microgravimetric studies of sorption and diffusion of water vapor in an unsaturated polyester[END_REF]. competition of two phenomena. First, fillers increase tortuosity [START_REF] Wolf | How the shape of fillers affects the barrier properties of polymer/non-porous particles nanocomposites: a review[END_REF] and maybe decrease the hydrophilicity of matrices, second, however, their presence favors the existence of an interface where water is preferentially absorbed and diffuses faster [START_REF] Chateauminois | Study of the interfacial degradation of a glass-epoxy composite during hygrothermal ageing using water diffusion measurements and dynamic mechanical thermal analysis[END_REF]. Natural fibers promote strong water absorption [START_REF] Cruz | An experimental study of water absorption in polyester composites reinforced with macambira natural fiber[END_REF].

The case of interpenetrating polymer networks (IPNs) was illustrated in studies dealing with vinyl ester networks (BisGMA cured with styrene) mixed with epoxy systems. Interestingly, it seems that the water uptake for 50:50 networks made of epoxy/diamine and polyester is closer to values observed for epoxy/diamine. It is hence suggested that blending only affects the preexponential factor (see Eq. 9.18) rather than the activation energy [START_REF] Merdas | Water absorption by uncrosslinked polymers, networks and IPNs having medium to high polarity[END_REF].

Diffusivity

Several models describe the rate of water diffusion in polymers:

1. Case I diffusion is observed when the characteristic time for diffusion is shorter than the typical time of polymer motions. In this case, the rate of water uptake, M(t)/M N, increases linearly with time. 2. Fick's law is observed when the characteristic time for diffusion is higher than the typical time of polymer motions. In this case, the rate of water uptake, M(t)/M N, increases linearly with the square root of the time. Another key characteristic of Fickian diffusion is the existence of a plateau at a long exposure time (contrarily to Langmuir diffusion).

Relative mass uptake can be simulated from the analytical resolution of Fick's law [START_REF] Crank | The Mathematics of Diffusion[END_REF]:

M t ð Þ M N 5 1 2 8 π 2 3 X N n50 1 2n11 ð Þ 2 3 exp 2 D 3 2n11 ð Þ 2 3 π 2 3 t 4e 2 (9.22)
If the relative mass uptake linearly increases with the square root of time, the diffusion obeys Fick's law and D can be calculated from the slope. This equation actually admits an approximate solution for low levels of water sorption (M/M N ,0.6):

MðtÞ M N 5 4 e 3 ffiffiffiffiffiffiffiffiffiffi ffi D 3 t π r (9.23)

3.

The "Langmuir" law is observed when the water diffusing in a given polymer is either "free" or "bound," that is, if it displays some "strong" interactions with some sites of the polymer structure (e.g., water-unreacted oxiranes in the case of epoxy/diamine matrices) [START_REF] Popineau | Free/bound water absorption in an epoxy adhesive[END_REF]. One of its main experimental features is the existence of a double sorption plateau. There is, however, no evidence of "Langmuir" diffusion in polyesters.

Experimentally, the linearity of mass uptake versus square root of the time is sometimes an approximation. However, most authors have assumed the diffusion obeys Fick's law so as to assess the diffusivity values given in Table 9.4.

Despite the experimental scattering [START_REF] Bellenger | Water sorption in styrene crosslinked polyesters[END_REF], it seems that D obeys Arrhenius law:

D 5 D 0 3 exp 2 E D RT (9.24)
For the materials given in Table 9.3, E D takes a value close to 25À30 kJ/mol.

Fick's law is based on the assumption that diffusivity does not change with the penetrant concentration. However, a concentration-dependent diffusivity was observed [START_REF] Marais | Permeametric and microgravimetric studies of sorption and diffusion of water vapor in an unsaturated polyester[END_REF] as depicted in Fig. 9.7 showing unambiguously the existence of a non-Fickian process; since the plot of relative mass uptake does not intersect a 0 for t 5 0, and the water diffusivity depends on its concentration which was mathematically modeled as:

D 5 D 0 3 expðγ 3 cÞ (9.25)
where γ is a plastification coefficient describing the fact that the sorption of the penetrant increases free volume in the matrix which facilitates its diffusion. A complete investigation by Marais et al. [START_REF] Marais | Permeametric and microgravimetric studies of sorption and diffusion of water vapor in an unsaturated polyester[END_REF] shows that D is multiplied by about 3 when water activity increases from 0.2 to 1 (Fig. 9.7).

In conclusion, water diffusion in UPR seems to be Fickian at first, but the finest investigations (featuring tests under several water activities) suggest a more complex mechanism for water diffusion. This remains to be linked with the structure of UPR. As previously discussed, it was observed that:

• the interaction of UPRs with water leads first to a weight increase corresponding to water absorption, but later a mass decrease is observed corresponding to the leaching of small molecules even in fully cured matrices [START_REF] Gautier | Interface damage study of hydrothermally aged glass-fibrereinforced polyester composites[END_REF]. • UPRs display a strong drop in their mechanical properties in the presence of gaseous ethanol at 90 C or 115 C [START_REF] Barlette Da Cunha | Assessment of chemical and mechanical properties of polymers aiming to replace the stainless steel in distillation column[END_REF], whereas ethanol is only poorly soluble in UP.

The main reason is the existence of chemical damage (chain scission reactions-Table 9.5) overlapping with the physical damage (plastification of the network by the absorbed fluid). The rate of chain scissions formation is, in principle, given by:

ds dt 5 k 3 E 0 2 s ð Þ3 w (9.26)
where k is the rate constant of hydrolysis, E 0 the initial concentration of hydrolysable groups (esters), w the water concentration, and s the concentration of chain scissions. Eq. ( 9.25) can be integrated as:

s 5 E 0 3 1 2 exp 2 k 3 w 3 t ð Þ ½ (9.27)
And simplified as:

sBk 0 3 E 0 3 w 3 t (9.28)
Hence, it seems possible, in principle, to predict the rate of degradation from relatively simple data: water affinity, concentration of esters (depending on the structure of prepolymer and styrene content), and rate constant of prepolymer hydrolysis. This simplified approach only gives a rough estimation of degradation since there are many complications including either chemical: (1) copolymer effect, (2) autocatalytic effects, (3) chain end effects, or physical factors: (4) changes in hydrophilicity with aging conversion degree, (5) effects linked to water diffusion.

1. The copolymer effect: the hydrolysis rate constant in UP made of phtalate and maleate/fumarate is observed to differ from values observed in corresponding pure phthalate or maleate/fumarate UPs due to esterÀester interactions or hindrance by styrene [START_REF] Bélan | Relationship between the structure and hydrolysis rate of unsaturated polyester prepolymers[END_REF]. 2. Autocatalytic effects: Hydrolysis generates a carboxylic acid which can act as a catalyst of further hydrolysis events. The differential system becomes [START_REF] Richaud | Crosslink density changes during the hydrolysis of tridimensional polyesters[END_REF]:

ds dt 5 k 0 3 E 0 2 s ð Þ3 w 1 k cat 3 E 0 2 s ð Þ3 s 3 w (9.29)
Some examples of the autocatalytic hydrolysis of polyester-based polymers can be found in Refs. [START_REF] Popineau | Free/bound water absorption in an epoxy adhesive[END_REF][START_REF] Antheunis | Autocatalytic equation describing the change in molecular weight during hydrolytic degradation of aliphatic polyesters[END_REF], but the case of UPR has not been investigated. 3. The chain ends are possibly more reactive than constitutive units located in the middle of chains [START_REF] Bellenger | Lifetime prediction in the hydrolytic ageing of polyesters[END_REF] (Scheme 9.1).

4.

Changes in water affinity induced by hydrolysis: esters (being moderately polar) are converted into much more hydrophilic species (carboxylic acid, alcohol). It is, hence, possible that water equilibrium uptake is expressed as [START_REF] Bellenger | Lifetime prediction in the hydrolytic ageing of polyesters[END_REF]:

w 5 w 0 1 a 3 s (9.30)
where s expresses the number of hydrolysis events. The systematic study of hydrolysis (or even aging) induced changes in water affinity remains, however, scarcely studied. 5. Water diffusion effects: water is submitted to competition between the reactions of hydrolysis and diffusion from the surface layers to deeper layers. This results in the existence of a degraded layer, the thickness of which can be approximated by [START_REF] Bellenger | Lifetime prediction in the hydrolytic ageing of polyesters[END_REF]:

z 2 5 D w k w ½ (9.31) CH O C O C O H O CH 3 CH 2 CH OH CH 3 CH 2 C C O H O O O H + H 2 O SCHEME 9.1
Self-decomposition of chain ends in UPR.

Since water solubility hardly depends on temperature, the thickness of this degraded layer depends on temperature:

E z 5 1 /2 E D À E k ð Þ (9.32)
It is well documented that E D , E k so the thickness of the degraded layer measured at elevated temperature (during an accelerated aging test) is quite different from the value observed in "service" conditions. Such diffusion-reaction coupling can be predicted using numerical models [START_REF] Yagoubi | A fully coupled diffusion-reaction scheme for moisture sorptionÀdesorption in an anhydride-cured epoxy resin[END_REF][START_REF] Yagoubi | Monitoring and simulations of hydrolysis in epoxy matrix composites during hygrothermal aging[END_REF]. Some experimental values (for hydrolytic aging together with other aging modes) are given in Table 9.6.

In terms of structureÀproperties relationships, existing data show that maleates and fumarates are more unstable than isophthalates and orthophthalates because of higher hydrolysis rate constants and higher hydrophilicity. Generally, isophthalates induce a higher stability than orthophthalates [START_REF] Ashbee | Water damage in polyester resins[END_REF][START_REF] Bélan | Hydrolytic stability of unsaturated polyester prepolymers[END_REF]. Neopentyl glycol induces a higher stability than propylene glycol [START_REF] Bélan | Hydrolytic stability of unsaturated polyester prepolymers[END_REF][START_REF] Scott | Weathering resistance of plastics composites. Article 6 in the series -Composite materials and the designer[END_REF] and ethylene glycolÀbased polyesters are also quite unstable [START_REF] Bélan | Relationship between the structure and hydrolysis rate of unsaturated polyester prepolymers[END_REF].

As hydrolysis at moderate temperatures (typically below UPRÀglass transition) is an aging mode leading to polymer failure, there is an increasing interest in using hydrolysis as a recycling mode for UPR networks by regenerating feedstock (in particular the diol). Subcritical water (with the use of strong alkali: NaOH or KOH) can potentially allow for the recovery of a great part of glycol after a treatment at 230 C for 1 hour [START_REF] Nakagawa | Recycling thermosetting polyester resin into functional polymer using subcritical water[END_REF]. There are, however, some complexities linked to high temperature hydrolysis in the presence of additives (KOH, phenol) in UPR where secondary reactions (typically above 200 C) can generate a wide variety of chemicals [START_REF] Sokoli | Towards understanding the breakdown and mechanisms of glass fiber reinforced polyester composites in sub-critical water using some of the most employed and efficient additives from literature[END_REF].

THERMAL AGING

Thermal degradation is a radical in chain mechanism. At relatively high temperatures ( . 200 C), the thermolysis of the polymer backbone is by far the main source of radicals, whereas at "moderate" temperatures (,150 C, i.e., in UPR service conditions), the thermal decomposition of hydroperoxides becomes kinetically prominent.

In the case of thermal degradation at high temperatures, a kinetic analysis of nonisothermal degradation curves suggested that degradation first occurs on styrene groups [START_REF] Baudry | Thermal degradation and fire behaviour of unsaturated polyester with chain ends modified by dicyclopentadiene[END_REF] in good agreement with the analysis of volatiles [START_REF] Shih | Thermal degradation behaviour and kinetic analysis of unsaturated polyesterbased composites and IPNs by conventional and modulated thermogravimetric analysis[END_REF].

The case of thermal aging of UPRs at moderate temperatures (at which the main source of radical generation is hydroperoxides) is in part different. In the case of thermal aging of polyester monitored by FTIR, Arrieta et al. [START_REF] Arrieta | Thermal oxidation of vinyl ester and unsaturated polyester resins[END_REF] observed that the main chemical change was the formation of an anhydride (Fig. 9.8). Their interpretation was that anhydrides are formed by the oxidation of methylene in the α-position of the ester group. They confirmed their reasoning from analysis of a thermally oxidized prepolymer (where anhydrides were also observed) and from the absence of acetophenone groups characteristic of polystyrene oxidation [START_REF] Gardette | Photooxidation mechanisms of styrenic polymers[END_REF].

The most plausible mechanism is based on the radical attack of CÀH in the α-position of the ester groups. The main consequences of this mechanism are the formation of anhydride and some chain scissions (Scheme 9.2). Another consequence of thermal aging at high temperatures is the high yield of volatiles resulting from advanced chain scission processes (Table 9.4). According to Arrieta et al. [START_REF] Arrieta | Thermal oxidation of vinyl ester and unsaturated polyester resins[END_REF], they can occur even under an inert atmosphere (i.e., from the direct thermolysis of the polymer), but are strongly accelerated by oxygen (Fig. 9.9). Shih et al. [START_REF] Shih | Thermal degradation behaviour and kinetic analysis of unsaturated polyesterbased composites and IPNs by conventional and modulated thermogravimetric analysis[END_REF] studied the high temperature thermal degradation of epoxyÀpolyester IPNs. According to their results:

• Modulated thermogravimetric analysis (TGA) curves can permit the extraction of kinetic parameters of apparent kinetic models for nonisothermal degradation. It seems that epoxy allows for the thermal stability of UPR and IPNs to be improved, which later display kinetic parameters in between those of UPR and epoxies. The authors, however, stated that the degradation of UPR and epoxy in IPNs do not interfere. • Pyrolysis tests followed by GC/MS for thermal degradation at relatively high temperature analysis reveal that almost the same degradation products are evolved from IPNs and epoxies (mainly bisphenol-A, isopropenyl phenol, and phenol), whereas the products characterizing the thermal degradation of polyesters (in particular styrene monomers, dimers, and even trimers) are absent. Those two results can be considered as somewhat difficult to reconcile. The durability of IPNs thus appears to be an open issue.

Identically to hydrolytic aging, a degraded layer is generated [START_REF] Papet | Diffusion controlled radiochemical oxidation of low density polyethylene-I: depth dependence of morphological changes[END_REF] due to a diffusion-reaction coupling as schematized in Fig. 9.10.

FIGURE 9.9

Kinetic curves for mass loss for a UP network thermally aged at 160 C [START_REF] Arrieta | Thermal oxidation of vinyl ester and unsaturated polyester resins[END_REF].

Reprinted with the permission of Elsevier.

Its thickness can be approximated by [START_REF] Audouin | Role of oxygen diffusion in polymer ageing: kinetic and mechanical aspects[END_REF][START_REF] Langlois | Physical aspects of the thermal oxidation of crosslinked polyethylene[END_REF]:

TOL 2 5 D O2 3 O 2 ½ r OX (9.33)
where r OX is the oxidation rate on the surface of polymer, D O 2 and [O 2 ] are the oxygen diffusivity and concentration in a given polymer matrix, respectively. It is hence crucial to determine the oxygen transport properties in UP matrices. Some values as reported by Pauly [START_REF] Pauly | The radiation resistance of thermoset plastics-III. Oxygen permeation experiments[END_REF] are presented in Table 9.7.

RADIOLYTIC AGING

The effect of irradiation on UPs was described by Wilski [START_REF] Gilfrich | The radiation resistance of thermoset plastics-VI. Unsaturated polyester plastics[END_REF] in the case of high-dose irradiation under an inert atmosphere, and lower dose irradiation under air.

The results unambiguously show competition between two phenomena. The first one occurs in the absence of oxygen and results in an increase (at least in the earliest exposure doses, i.e., lower than 1 MGy) of thermomechanical properties (deflection temperature being linked to T g , flexural and impact strengths). The second one is favored by the presence of oxygen and induces the depletion of the mentioned properties (Fig. 9.11).

The most reasonable explanation is common with other polymers and is based on the existence of a degraded layer as developed in Section 9.4.2.

➀ Under nitrogen (or in the bulk of thick materials where aging mechanisms are anaerobic), irradiation generates radicals reacting by coupling (cross-linking): This supplementary radiation induced cross-linking improves the mechanical properties as observed by Charlesby et al. [START_REF] Charlesby | The irradiation of unsaturated polyester resins[END_REF] in the case of the radio-curing of UPR. Polyester resins were made from terephthalic acid, fumaric acid, and butanediol 1,4. D is expressed in cm 2 /s, S in cm 23 /Pa, P 5 D 3 SNB: For data from Ref. [START_REF] Arrieta | Thermal oxidation of vinyl ester and unsaturated polyester resins[END_REF], it was assumed that E P 5 E D and E S 5 0.

➁ In the presence of oxygen (or in the oxidized layer of bulk materials), alkyl radicals react with oxygen and lead to peroxyl radicals and later hydroperoxides; the decomposition of which generating several products among which are chain scissions:

P 1 O 2 -POO POO 1 PH-POOH 1 P POOH-PO 1 HO PO -P 5 O 1 chain scissions
In the case of the irradiation of thick UPR materials, both phenomena can simultaneously occur; their relative proportion depending on the depth in the irradiated polymer.

Another reason for the heterogeneity in irradiated polymers is the attenuation of irradiation in the thickness:

I I 0 5 expð2 μ 3 zÞ (9.34)
where I 0 is the initial intensity of γ-ray, I is the intensity of the ray transmitted from a shielding material of thickness x, and μ is the linear attenuation coefficient.

It was observed that the use of lead monoxide particles (with a weight fraction of about 5%) made possible the attenuation of a coefficient comparable to concrete for Cs-137 or Ir-192 sources, but that even highly filled (more than 30%) UPRs could not efficiently shield Co-60 radiations [START_REF] Bagheri | Thermal resistance, tensile properties, and gamma radiation shielding performance of unsaturated polyester/nanoclay/PbO composites[END_REF].

PHOTOAGING

Polyesters are reported to undergo photolytic processes such as the conversion of fumarates into maleates, the dimerization and decomposition of maleates (Scheme 9.3) [START_REF] Michaille | Photolyse et photo-oxydation de polyesters insatures-1. Comportement du polymaleate de propylene glycol reticule ou non[END_REF], and the photocleavage of esters (Scheme 9.4) [START_REF] Michaille | Photolyse et photo-oxydation de polyesters insatures-2. Comportement du polymaleate-isophtalate de propylene glycol reticule ou non[END_REF]:

Photoaging also induces an in-chain radical oxidation mechanism, but in which radicals mainly come from some side reactions of radicals (such as those created in Scheme 9.4) and the decomposition of peroxides and hydroperoxides.

The relative rate of photolytic and photooxidation processes depends on the temperature, nature, and intensity of the spectral source, on the molar absorptivity of compounds (and subsequently the Properties of unsaturated polyester during irradiation [START_REF] Gilfrich | The radiation resistance of thermoset plastics-VI. Unsaturated polyester plastics[END_REF]. thickness of material) [START_REF] Franc ¸ois-Heude | A general kinetic model for the photothermal oxidation of polypropylene[END_REF], and on the presence of oxygen. For example, according to [START_REF] Michaille | Photolysis and photo-oxidation of unsaturated polyesters[END_REF], phthalates and fumarate/maleate groups are responsible for absorption at long wavelength ( . 300 nm), whereas the photooxidation at short wavelength might involve S units as well [START_REF] Geuskens | Photo-oxidation of polymers-I: a quantitative study of the chemical reactions resulting from irradiation of polystyrene at 253.7 nm in the presence of oxygen[END_REF]. In summary:

• radicals are created either from the photolysis of an impurity or of hydroperoxides and ketones: • several termination mechanisms can coexist depending on the concentration of oxygen [START_REF] Richaud | Effect of oxygen pressure on the oxidation kinetics of unstabilised polypropylene[END_REF]:

P 1 P -inactive products P 1 POO -inactive products POO 1 POO -inactive products
In UPRs, several reactive sites are suspected to be involved. The appearance of yellowing products absorbing at 295À400 nm (similarly to polystyrene) led Michaille et al. [START_REF] Michaille | Photolyse et photo-oxydation de polyesters insatures-1. Comportement du polymaleate de propylene glycol reticule ou non[END_REF] to propose a photooxidation mechanism in which styrene units are the main oxidation site (Scheme 9.5).

Polyester prepolymer can also undergo radical attack depending on the concentration of styrene as a cross-linking agent [START_REF] Michaille | Photolyse et photo-oxydation de polyesters insatures-1. Comportement du polymaleate de propylene glycol reticule ou non[END_REF]. In other words, the tertiary CÀH group of S units would be more oxidizable than poly(propylene glycol maleate) or poly(propylene glycol isophthalate), but at a low styrene concentration, these later become the predominant sites of propagation. A part of this "duality" can be explained from the relative kinetics of propagation: Here 1 would correspond to styrene units and 2 to prepolymer units. The relative rates of propagation would be:

P 1 OO 1 P 1 H-P 1 OOH 1 P 1
r 11 r 12 5 k 11 P 1 H ½ k 12 P 2 H ½ (9.35) O C O C H CH C O O C O O C O C H CH C O O C HOO CH 2 O C O C H CH C O O C HO°°O CH 2 O C O C H CH C O O C H CH 2 CH 2 °O C O C H CH C O O C O H CH 2
FTIR: 1690 cm -1 UV: 300-450 nm SCHEME 9.5

Mechanism of radical oxidation of styrene in unsaturated polyester resin (UPR).

There are some relationships linking structure and sensitivity to oxidation according to which [START_REF] Korcek | Absolute rate constants for hydrocarbon autoxidation. XXI. Activation energies for propagation and the correlation of propagation rate constants with carbonÀhydrogen bond strengths[END_REF] In other words, it can be concluded that the oxidative degradation of UPR must be described by a cooxidation model [START_REF] Richaud | Co-oxidation kinetic model for the thermal oxidation of polyethylene-unsaturated substrate systems[END_REF], which requires a complex stage of kinetic parameters estimation.

Those equations linking reactivity (the rate constant) with structure (the bond dissociation energy) also permit for the confirmation of why neopentyl glycol permits a decrease in the oxidation effects compared to propylene glycol [START_REF] Michaille | Photolysis and photo-oxidation of unsaturated polyesters[END_REF] because of the absence of tertiary (weak) CÀH bonds.

One of the most undesired consequences of photoaging and photooxidation is the yellowing of the material. Several processes might be responsible including:

1. Photolytic processes (i.e., occurring without oxygen) can induce a strong change in the aspect of UP materials, featuring gloss, and color changes. Michaille et al. [START_REF] Michaille | Photolysis and photo-oxidation of unsaturated polyesters[END_REF] pointed out that the photolysis of phthalate is identical to that observed in the photolysis of polybutylene terephthalate (PBT) [START_REF] Tabankia | Photo-chemical degradation of polybutyleneterephthalate: Part 1-Photooxidation and photolysis at long wavelengths[END_REF] (Scheme 9.6). Then radicals recombine to give several kinds of benzophenones responsible for yellowing:

C O O C O
The work of Geuskens also revealed the role of polyenes formed during the photolysis of polystyrene absorbing at 280À450 nm [START_REF] Geuskens | Photo-oxidation of polymers-I: a quantitative study of the chemical reactions resulting from irradiation of polystyrene at 253.7 nm in the presence of oxygen[END_REF]:

CH 2 C CH CH n < 4
2. Under oxygen, radicals formed in S units can react with oxygen and generate benzalacetophenone (Scheme 9.7) or α-β-unsaturated ketone (Scheme 9.8).

According to Sampers [START_REF] Sampers | Accelerated weathering of unsaturated polyester resins. Aspects of appearance change[END_REF], it seems that:

• yellowing is, in particular, caused by interactions between UV radiations below 360 nm displaying a strong absorption with the prepolymer itself (meanwhile polystyrene sequences and some cobalt accelerator seem to display a very limited absorption). • color changes seem to be driven rather by the photolysis of the polyester sequences compared to styrene unit sequences where the effect of oxygen is relatively limited. The oxidation of structures formed by photolysis results in less absorbent groups.

Identically to thermal and radiolytic aging, the photochemical degradation of UPR is accompanied by the formation of an oxidized layer. Interestingly, the thermal degradation of UP is characterized by a lower oxidation rate than photochemical one so that the thickness of the oxidized layer was observed to be about 600 μm for thermal oxidation at 160 C versus only 140 μm in the case of photooxidized UP (despite the fact that photochemical aging is performed at lower temperatures than thermal aging).

It has been observed that photodegraded UPR can undergo cross-linking [START_REF] Michaille | Photolysis and photo-oxidation of unsaturated polyesters[END_REF]. Several mechanisms are responsible including the dimerization of phthalate units (similarly to PBT photolysis under vacuum [START_REF] Tabankia | Photo-chemical degradation of polybutyleneterephthalate: Part 1-Photooxidation and photolysis at long wavelengths[END_REF]) and the double bond opening of unsaturated structures formed by the photolysis of S units (Scheme 9.9):

CONCLUSION

This chapter described the aging mechanisms of UP-based materials. Degradation mechanisms were first addressed from the structureÀproperties involved to describe the consequences of aging on mechanical properties.

Physical aging mechanisms were presented. UPs are sensitive to some chemicals, but engineers have at their disposal rules for predicting compatibility and avoiding undesirable permeation effects. Water is, in essence, poorly soluble in UPs but its diffusion is accompanied by the hydrolysis of ester groups which is an an aggravating factor. Chemical mechanisms (hydrolytic, radiochemical, photochemical, and thermal) were thus presented together with some models predicting the rate of hydrolysis or the thickness of degraded layers, etc.). The main complexity for implementing them is the nonideal structure of UP where several reactive sites exist and whose reactivity depends on their chemical environment.

P 5

 5 RTΣc i(9.4) c i being the concentration in soluble molecules in the "cavity."At a certain stage, the osmotic pressure exceeds the polymer stress at break, which induces an osmotic cracking. It results in a well recognizable disk crack with radial lines[START_REF] Gautier | Osmotic cracking nucleation in hydrothermal-aged polyester matrix[END_REF] (Fig.9.1).

FIGURE 9 . 1

 91 FIGURE 9.1 Microscopic observations of disk cracks for osmotic cracking.

FIGURE 9 . 3

 93 FIGURE 9.3

FIGURE 9 . 5

 95 FIGURE 9.5 Hydrophilicity of prepolymer as a function of diacid or diol.

FIGURE 9 . 6

 96 FIGURE 9.6

t 1/ 2 M 1 a = 0. 2 DFIGURE 9 . 7

 21297 FIGURE 9.7 Plot of relative mass versus square root of the time for UP at 25 C.

FIGURE 9 . 8 FTIR 1 FTIR: 3465 cm - 1 SCHEME 9 . 2

 981192 FIGURE 9.8 FTIR spectra of a UPR (A) and its prepolymer (B) thermally oxidized at 160 C [58].Reprinted with the permission of Elsevier.

FIGURE 9 . 10

 910 FIGURE 9.10 Degradation profile of oxidized materials (NB: x 5 0 and x 5 L correspond to edges in contact with atmospheric air).

  FIGURE 9.11

1 FTIR 1 SCHEME 9 . 3 1 SCHEME 9 . 4

 1193194 SCHEME 9.3Mechanisms of photoisomerization and photodimerization of fumarate units.

6

 6 Mechanism of photodissociation.

9 A

 9 SCHEME 9.9A possible mechanism of cross-linking.

Table 9 .

 9

		1 Changes for Unsaturated Polyesters Resin (UPR)
	Composites in Presence of Ethanol
		Mass Uptake (%)	Ultimate Stress (MPa)
	T ( C)	7 Days	30 Days	0 Days	30 Days
	90	3.2	1	393	166
	115	2.5	0.3		142

Table 9 .

 9 2 Effect of Diol, Styrene Content, Prepolymer, and Temperature on the Water Solubility of Unsaturated Polyester Resin (UPR) (NB: All isotherms display the shape ➀, Fig. 9.4)

	Prepolymer	Diol	Styrene (%)	Catalyst	T ( C)	HR (%)	W H2O (%)
	M (50%) 1 I (50%)	PG	38	MEKP (1.5%) 1 Co Oct (0.2%)	25		0.65	[27]
	M (50%) 1 I (50%)	PG	38	MEKP (1.5%) 1 Co Oct (0.2%)	25		0.56	[27]
	M (50%) 1 I (50%)	PG	38	MEKP (1.5%) 1 Co Oct (0.2%)	25		0.85	[30]
	M (46%) 1 I (54%)	PG	44	MEKP (1.5%) 1 Co Oct (0.5%)	30		0.72	[31]
	M (46%) 1 I (54%)	PG	44	MEKP (1.5%) 1 Co Oct (0.5%)	40		0.89	[31]
	M (46%) 1 I (54%)	PG	44	MEKP (1.5%) 1 Co Oct (0.5%)	50		0.91	[31]
	M (46%) 1 I (54%)	PG	42	MEKP (1.5%) 1 Co Oct (0.5%)	30		0.84	[31]
	M (46%) 1 I (54%)	PG	42	MEKP (1.5%) 1 Co Oct (0.5%)	40		1.02	[31]
	M (46%) 1 I (54%)	PG	42	MEKP (1.5%) 1 Co Oct (0.5%)	50		1	[31]
	M (46%) 1 I (54%)	PG	40	MEKP (1.5%) 1 Co Oct (0.5%)	30		1.12	[31]
	M (46%) 1 I (54%)	PG	40	MEKP (1.5%) 1 Co Oct (0.5%)	40		1.36	[31]
	M (46%) 1 I (54%)	PG	40	MEKP (1.5%) 1 Co Oct (0.5%)	50		1.44	[31]
	M (70%) 1 I (30%)	PG	45	MEKP (1.5%) 1 Co Oct (0.5%)	30		1.12	[31]
	M (70%) 1 I (30%)	PG	45	MEKP (1.5%) 1 Co Oct (0.5%)	40		1.36	[31]
	M (70%) 1 I (30%)	PG	45	MEKP (1.5%) 1 Co Oct (0.5%)	50		1.44	[31]
	M (46%) 1 I (54%)	NPG	45	MEKP (1.5%) 1 Co Oct (0.5%)	30		0.47	[31]
	M (46%) 1 I (54%)	NPG	45	MEKP (1.5%) 1 Co Oct (0.5%)	40		0.56	[31]
	M (46%) 1 I (54%)	NPG	45	MEKP (1.5%) 1 Co Oct (0.5%)	50		0.75	[31]
	M (46%) 1 I (54%)	DEG	38	MEKP (1.5%) 1 Co Oct (0.5%)	30		1.06	[31]
	M (46%) 1 I (54%)	DEG	38	MEKP (1.5%) 1 Co Oct (0.5%)	40		1.29	[31]
	M (46%) 1 I (54%)	DEG	38	MEKP (1.5%) 1 Co Oct (0.5%)	50		1.58	[31]
	M (46%) 1 I (54%)	DPG	42	MEKP (1.5%) 1 Co Oct (0.5%)	30		0.74	[31]
	M (46%) 1 I (54%)	DPG	42	MEKP (1.5%) 1 Co Oct (0.5%)	40		0.92	[31]
	M (46%) 1 I (54%)	DPG	42	MEKP (1.5%) 1 Co Oct (0.5%)	50		1.14	[31]
	M (46%) 1 I (54%)	PG	43	MEKP (1.5%) 1 Co Oct (0.5%)	30		0.97	[31]
	M (46%) 1 I (54%)	PG	43	MEKP (1.5%) 1 Co Oct (0.5%)	40		0.92	[31]
	M (46%) 1 I (54%)	PG	43	MEKP (1.5%) 1 Co Oct (0.5%)	50		1.16	[31]
	M 1 I	PG	45	MEKP (1.5%) 1 Co Oct (0.5%)	30		0.85	[32]
	M 1 I	PG	45	MEKP (1.5%) 1 Co Oct (0.5%)	50		0.83	[32]
	M 1 I	PG	45	MEKP (1.5%) 1 Co Oct (0.5%)	70		1.08	[32]

M, maleate; I, isophthalate; PG, propylene glycol; NPG, neopentyl glycol; DPG, dipropylene glycol; DEG, diethylene glycol.

Table 9 .

 9 [START_REF] Mark | The rubber elastic state[END_REF] Effect of Postcuring on Shape of Sorption Isotherm (Fig.9.4) and Water Solubility in Unsaturated Polyester Resin (UPR)[START_REF] Lee | Interactions of water with unsaturated polyester, vinyl ester and acrylic resins[END_REF]

	Prepolymer	Catalyst	T ( C)	HR (%)	Isotherm	W H2O (% w/w)
	O (60%) 1 M (40%)	MEKP (1%) 1 CN (0.3%) 1 DMA (0.05%) AC	30	75	➀	0.8
	O (60%) 1 M (40%)	MEKP (1%) 1 CN (0.3%) 1 DMA (0.05%) PC	30	75	➀	0.8
	O (60%) 1 M (40%)	BPO (1%) 1 DMA (0.3%) AC	30	75	➂	0.8
	O (60%) 1 M (40%)	BPO (1%) 1 DMA (0.3%) PC	30	75	➃	0.7
	I	BPO (2%) 1 DMA (0.3%) AC	30	75	➀	0.6
	I	BPO (2%) 1 DMA (0.3%) PC	30	75	➀	0.5
	I	MEKP (0.5%) 1 CN (0.3%) 1 DMA (0.05%) AC	30	75	➀	0.4
	I	MEKP (0.5%) 1 CN (0.3%) 1 DMA (0.05%) PC	30	75	➀	0.5
	I	MEKP (4%) 1 CN (0.3%) 1 DMA (0.1%) AC	30	75	➀	0.55
	O (60%) 1 M (40%)	MEKP (1%) 1 CN (0.3%) 1 DMA (0.05%) AC	65	75	➁	1
	O (60%) 1 M (40%)	MEKP (1%) 1 CN (0.3%) 1 DMA (0.05%) PC	65	75	➁	1.3
	O	BPO (1%) 1 DMA (0.3%) AC	65	75	➃	0.6
	O	BPO (1%) 1 DMA (0.3%) PC	65	75	➃	1
	I	MEKP (4%) 1 CN (0.3%) 1 DMA (0.1%) PC	65	75	➀	1
	I	MEKP (0.5) 1 CN (0.3%) 1 DMA (0.05%) PC	65	75	➀	1
	I	MEKP (0.5) 1 CN (0.3%) 1 DMA (0.05%) AC	65	75	➃	0.75
	I	BPO (2%) 1 DMA (0.3%) AC	65	75	➃	0.7
	I	BPO (2%) 1 DMA (0.3%) PC	65	75	➃	0.7

MEKP, methyl ethyl ketone peroxide; CN, cobalt naphthanate; DMA, N,N-dimethylaniline; BPO, benzoyl peroxide; AC, as cast; PC, post cured.

Table 9 .

 9 [START_REF] Morales Arias | Aging in water and in an alkaline medium of unsaturated polyester and epoxy resins: experimental study and modeling[END_REF] Experimental Values of Water Diffusivities in Unsaturated Polyester Resin (UPR)[START_REF] Bellenger | Water sorption in styrene crosslinked polyesters[END_REF]

	Prepolymer	Diol	Styrene (%)	Catalyst	T ( C)	D (mm 2 /s 1 )
	M (46%) 1 I (54%)	PG	44	MEKP (1.5%) 1 Co Oct (0.5%)	30	6.9 3 10 29
	M (46%) 1 I (54%)	PG	44	MEKP (1.5%) 1 Co Oct (0.5%)	40	12 3 10 29
	M (46%) 1 I (54%)	PG	44	MEKP (1.5%) 1 Co Oct (0.5%)	50	(14À19) 3 10 29
	M (46%) 1 I (54%)	PG	42	MEKP (1.5%) 1 Co Oct (0.5%)	30	5.6 3 10 29
	M (46%) 1 I (54%)	PG	42	MEKP (1.5%) 1 Co Oct (0.5%)	40	8.6 3 10 29
	M (46%) 1 I (54%)	PG	42	MEKP (1.5%) 1 Co Oct (0.5%)	50	10 3 10 29
	M (46%) 1 I (54%)	PG	40	MEKP (1.5%) 1 Co Oct (0.5%)	30	2.1 3 10 29
	M (46%) 1 I (54%)	PG	40	MEKP (1.5%) 1 Co Oct (0.5%)	40	2.7 3 10 29
	M (46%) 1 I (54%)	PG	40	MEKP (1.5%) 1 Co Oct (0.5%)	50	3.8 3 10 29
	M (70%) 1 I (30%)	PG	45	MEKP (1.5%) 1 Co Oct (0.5%)	30	10 3 10 29
	M (70%) 1 I (30%)	PG	45	MEKP (1.5%) 1 Co Oct (0.5%)	40	13 3 10 29
	M (70%) 1 I (30%)	PG	45	MEKP (1.5%) 1 Co Oct (0.5%)	50	22 3 10 29
	M (46%) 1 I (54%)	NPG	45	MEKP (1.5%) 1 Co Oct (0.5%)	30	10 3 10 29
	M (46%) 1 I (54%)	NPG	45	MEKP (1.5%) 1 Co Oct (0.5%)	40	13 3 10 29
	M (46%) 1 I (54%)	NPG	45	MEKP (1.5%) 1 Co Oct (0.5%)	50	18 3 10 29
	M (46%) 1 I (54%)	DEG	38	MEKP (1.5%) 1 Co Oct (0.5%)	30	6.8 3 10 29
	M (46%) 1 I (54%)	DEG	38	MEKP (1.5%) 1 Co Oct (0.5%)	40	11 3 10 211
	M (46%) 1 I (54%)	DEG	38	MEKP (1.5%) 1 Co Oct (0.5%)	50	21.5 3 10 29
	M (46%) 1 I (54%)	DPG	42	MEKP (1.5%) 1 Co Oct (0.5%)	30	11.7 3 10 29
	M (46%) 1 I (54%)	DPG	42	MEKP (1.5%) 1 Co Oct (0.5%)	40	16.5 3 10 29
	M (46%) 1 I (54%)	DPG	42	MEKP (1.5%) 1 Co Oct (0.5%)	50	23 3 10 29
	M (46%) 1 I (54%)	PG	43	MEKP (1.5%) 1 Co Oct (0.5%)	30	12.5 3 10 29
	M (46%) 1 I (54%)	PG	43	MEKP (1.5%) 1 Co Oct (0.5%)	40	16 3 10 29
	M (46%) 1 I (54%)	PG	43	MEKP (1.5%) 1 Co Oct (0.5%)	50	24.5 3 10 29

Table 9 .

 9

	5 Several Aging Modes and Their Consequences at
	Macromolecular Level
			Thermal	Radio	Photolysis and
		Hydrolysis	Oxidation	Oxidation	Photooxidation
	Chain scission	1	1	1	1
	Cross-linking	0	Post	Post polymerization, irradiation under
			polymerization	vacuum or of thick materials

Table 9 .

 9 6 Values of Thickness of Degraded Layers for Various Aging Conditions

	Aging	Experimental			z degraded
	Mode	Conditions	Kinetic Parameters	(µm)
	Hydrolysis	100 C 2 100%HR	D w 5 (6 6 1) 3 10 211 m 2 /s	E Dw 5 25À30 kJ/mol	450À1200
				(Table 9.4)
			k 0 5 (4À30) 3 10 27 s 21	E H 5 65 kJ/mol [47]
	Photoaging	60 CÀSEPAP		E DO2 5 20À45 kJ/mol	140
		12À24		(Table 9.7)
	Thermal
	aging

Table 9 .

 9 7 Oxygen Permeation Parameters for Unsaturated Polyester Resin (UPR)

			Sample
	Main Components (%)	Thickness (cm)	T ( C)	10 15 3 P	10 8 3 D	E D (kJ/mol)	10 7 .S	E S (kJ mol 21 )	Refs.
	UP resin	25	0.2	23	1.04	0.57	35	1.82	0	[63]
	Limestone	52.7		40	2.24	1.26		1.78
	Short GF	15		60	5.21	2.77		1.88
	UP resin	26	0.18	23	3.08	1.03	45	3	2 1	[63]
	Limestone	26		40	7	2.8		2.5
	China clay	38.3		60	17	8		2.13
	Up resin	100	0.02	25	0.66	3.6	20.8	0.18	Ã	[58]
				100	2.34	19.5		0.12
	Up resin	32	0.02	25	0.29	2.3	21.6	0.13	Ã	[58]
	ATH 1 Zn Borate	68		100	2.36	13.3		0.18

  :• the competition between each propagation reaction depends on the concentration of the reactive sites (propylene glycol or styrene), and • using reasonable values of BDE (375 for S CÀH, 395 kJ/mol for propylene glycol ones), propagation rate constants can cross, that is, that k 312 . k 321 at moderate temperatures and k 321 . k 312 at higher temperatures.

	logk ij 30 C ð Þ5 16:2 À 0:0477 3 BDE j	(9.36)
	E ij 5 0:55 3 BDE j À 262 À Á	(9.37)
	if i is a secondary peroxyl radical and j the broken CÀH. While,
	logk ij 30 C ð Þ5 15:2 À 0:0477 3 BDE j	(9.38)
	E ij 5 0:55 3 BDE j À 262 À Á	(9.39)
	if i is a tertiary peroxyl radical.
	One can easily verify that:

  Formation of benzalacetophenone.Formation of α-β-unsaturated ketone.

		°O						OH			H 2 O
	C H	CH 2 C O	CH 2			C CH 2 C O °+ CH 2 C CH C O°C H 2	C CH C	O	H 2 C °SCHEME
		9.7
	H	H	H				O	OH	H	H		H O°H H
	C	CH 2 C	CH 2 C	CH 2	X°2	C	CH 2 C	CH 2 C	CH 2	C	CH 2 C	CH 2 C	CH 2
						. O 2
						3. PH
			CH 2 C	O	2 C C H °1.	CH 2 C H	CH 2		C H 2	H C CH 2 C	CH 2	C H 2	C	O C	H C	CH 2
	SCHEME 9.8

E OX 5 50 kJ/mol[START_REF] Arrieta | Thermal oxidation of vinyl ester and unsaturated polyester resins[END_REF]