Aline Le

Floch Floch

Dominique Gien

Christophe Tournamille

Btissam Chami

Anoosha Habibi

Frédéric Galactéros

Philippe Bierling

Rachid Djoudi

Corinne Pondarré

Thierry Peyrard

Aline Floch

France Pirenne
email: france.pirenne@efs.sante.fr

High immunogenicity of red blood cell antigens restricted to the population of African descent in a cohort of sickle cell disease patients

Keywords: Transfusion, low-prevalence antigens, sickle cell disease, immunogenicity, alloimmunization

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Sickle cell disease (SCD) is the most frequent genetic disease in France. Many affected patients require regular transfusions of packed red blood cells (pRBCs) to limit complications and extend patient life-span. [START_REF] Chaturvedi | Evolution of sickle cell disease from a life-threatening disease of children to a chronic disease of adults: The last 40 years[END_REF] Alloimmunization is one of the main complications of transfusion. It can lead to poor transfusion efficacy, a lack of compatible donors, or even life-threatening conditions, such as delayed hemolytic transfusion reaction (DHTR). [START_REF] Pirenne | Management of delayed hemolytic transfusion reaction in sickle cell disease: Prevention, diagnosis, treatment[END_REF] To reduce alloimmunization, RH-(D, C, E, c, e) and KEL1-matched pRBCs are selected for all SCD patients in France, and systematic pre-transfusion cross-match tests are performed.

There is marked red blood cell (RBC) antigen polymorphism between blood donors in France (mostly of Caucasian descent) and SCD patients (mostly of African descent). Some RBC antigens are more prevalent in donors than in patients: C, Fy a , Jk b , S. The corresponding antibodies are readily detectable in pre-transfusion screening tests with standard test RBCs.

Other RBC antigens are almost exclusive to Afro-Caribbean populations, due to specific polymorphisms found in several blood group systems: RH (RH10 or V, RH20 or VS, RH23 or D W , RH30 or Go a …), MNS (MNS6 or He), KEL (KEL6 or Js a ). [START_REF] Reid | The Blood Group Antigen FactsBook[END_REF] Despite a prevalence of over 1% in individuals of African descent, these antigens are said to be of low-prevalence (LP), based on their rarity in the general donor population (mostly of Caucasian descent). These LP antigens can induce alloimmunization and the production of specific Abs. The risk of alloimmunization is higher in SCD patients than in other transfusion recipients, due to their specific inflammatory status, [START_REF] Fasano | Red blood cell alloimmunization is influenced by recipient inflammatory state at time of transfusion in patients with sickle cell disease[END_REF] the frequency of transfusion, and the need to match donor and recipient phenotypes, resulting in a higher probability of SCD patients being exposed to pRBCs from donors of African descent. [START_REF] Noizat-Pirenne | Relevance of blood groups in transfusion of sickle cell disease patients[END_REF][START_REF] Olujohungbe | Red cell antibodies in patients with homozygous sickle cell disease: a comparison of patients in Jamaica and the United Kingdom[END_REF] Alloimmunization to LP antigens can be detected only in extensive studies at specialized reference centers, because these rare antigens are not included in the standard RBC panels used for pre-transfusion screening tests. In practice, these antibodies are sought only in specific situations: DHTR, polyimmunization or positive cross-match test. The occurrence and characteristics of anti-LP antibodies in the general population of SCD patients receiving transfusions therefore remain unknown. In France, cross-match tests are performed before each blood transfusion in SCD patients, to facilitate the detection of Abs against LP antigens.

It is currently impossible to predict individual alloimmunization risk. Antigen immunogenicity [START_REF] Tormey | The persistence and evanescence of blood group alloantibodies in men[END_REF][START_REF] Tormey | Immunogenicity of blood group antigens: a mathematical model corrected for antibody evanescence with exclusion of naturally occurring and pregnancyrelated antibodies[END_REF] is, therefore, an important factor guiding decisions in transfusion medicine, together with the possible clinical consequences of alloimmunization. Antigen immunogenicity indicates the likelihood of an antigen inducing alloantibody formation. In previous studies, the immunogenicity of the KEL1 antigen was used to standardize immunogenicity calculations 9- 11 in situations in which KEL1-matching was not systematic.

The principal aim of this study was to determine the prevalence of antibodies directed against LP antigens specific to the Afro-Caribbean population, in SCD patients receiving blood transfusions. Our secondary aim was to estimate the immunogenicity of these antigens, by calculating antigen exposure rates.

Materials and Methods

Study design

SCD patients with a history of one or more RBC transfusions were included. Each patient underwent molecular testing to predict their RH10, RH20 and KEL6 phenotypes. Each sample from each patient was tested for Abs against the LP antigens RH23, RH30 and MNS6, as well as for Abs against RH10, RH20 and KEL6 for patients with a respective negative phenotype (Fig. 1).

Patients and samples

All SCD patients with a history of transfusions referred to the Etablissement Français du Sang This study was approved by CPP IDF IX/IV (the competent medical ethics committee) under agreement number 10-040.

The sex and age of the patients, together with their transfusion history and previous antibody screening test results, were recorded from the EFS Ile-de-France information system, and all data were anonymized to protect the patients' privacy and confidentiality. The patients had SS, SC, or S-b-thalassemia forms of the disease.

The remainder of the EDTA-anticoagulated blood samples from these patients left over after routine testing was collected. Routine antibody screening and identification was performed in accordance with French recommendations, [START_REF]Arrêté du 26 novembre 1999 relatif à la bonne exécution des analyses de biologie médicale modifié par l'Arrêté du 26 avril 2002[END_REF] on each sample, on the day of inclusion into the study.

Choice of Afro-Caribbean-specific antigens

Six Afro-Caribbean-specific RBC antigens were selected for this study on the basis of their high prevalence in Afro-Caribbean populations or the availability of test RBCs carrying these antigens at the time of the study (Table 1): RH10 (V), RH20 (VS), KEL6 (Js a ), RH23 (D W ), RH30 (Go a ), and MNS6 (He). Table 1 summarizes the main characteristics of the antigens selected, and the molecular backgrounds in which they are expressed.

Molecular analysis

The expression of the three most frequent Afro-Caribbean LP antigens (KEL6, RH10 and RH20) was predicted by molecular analysis for each patient included in the study. We extracted gDNA from leukocytes (Magnapure, Roche, France). Real-time polymerase chain reaction (PCR) assays (5' nuclease assay, Thermo Fisher, USA) were then performed, as previously described. [START_REF] Tournamille | Partial C antigen in sickle cell disease patients: clinical relevance and prevention of alloimmunization[END_REF] The c.712A>G, c.733C>G and c.1006G>T polymorphisms of the RHCE gene (in exons 5 and 7), and c.1790T>C of the KEL gene (exon 17) were detected. We deduced the expression of the RH10 and RH20 antigens from these results (see supplemental data).

Samples from 1000 FY:-1,-2 mainland French blood donors were screened by molecular analysis to deduce their RH20 and KEL6 antigen expression. For RH20, only the c.733C>G RHCE polymorphism was explored on such a large scale. In this way, we were able to estimate the prevalence of the RH20 and KEL6 antigens in mainland French donors of African origin.

Serological analysis

We selected a panel of test RBCs expressing the Afro-Caribbean-specific antigens from the collection of the National Immunohematology Reference Laboratory (Centre National de Référence pour les Groupes Sanguins). The test RBCs expressed the following antigens: RH10 and RH20 for test-RBC no. 1, KEL6 and RH23 for no. 2, RH30 for no. 3, MNS6 and RH23 for no. 4.

All samples were screened with this in-house panel using an IgG indirect antiglobulin test (IAT) with untreated and papain-treated RBCs on a gel matrix (Bio-Rad, USA). If molecular analysis predicted the expression of RH10 and RH20 for a patient, the samples from this patient were not screened with test RBC no. 1. Antibody specificities were confirmed with at least two more informative test RBCs expressing the target antigen, and with several test RBCs negative for the antigen.

Antibody adsorption test was performed in accordance with the standard procedures when autoantibodies made it difficult to interpret the antibody screening results.

Immunogenicity and antigen exposure

In this study, we calculated an antigen exposure risk for each pRBC unit received, with a method derived from the equation established by Giblett in 1961. 9 This antigen exposure risk was calculated with no reference to anti-KEL1 alloimmunization, because SCD patients are not exposed to KEL1 antigen in France (systematic KEL1 match) and receive variable numbers of pRBCs, resulting in considerable variation in the frequency of exposure to LP antigens.

Antigen immunogenicity was then compared by matching the calculated antigen exposure rate and alloimmunization rate for each antigen within our cohort. A lower rate of antigen exposure associated with the same number of alloimmunized patents indicated higher antigen immunogenicity.

Antigen prevalence differs between ethnic backgrounds, and exposure rates are therefore influenced by the frequency with which SCD patients receive pRBCs from donors of different ethnic backgrounds. The risk of exposure to Afro-Caribbean LP antigens is considered to be zero for pRBCs from Caucasian donors, and the frequency with which SCD patients receive Afro-Caribbean pRBCs ("intra-ethnic transfusions") is currently estimated at 11.5% in mainland France. [START_REF] Noizat-Pirenne | Transfusion and sickle cell disease: axes of transfusion safety optimization[END_REF] The exposure risk (R) for an antigen per pRBC unit received was calculated as follows:

R=P donor *F*(1-P patient ), where P donor and P patient are the prevalences of the antigen in the donor and patient populations, respectively (P donor = P patient if the donor and patient have the same ethnic background) and F is the frequency with which SCD patients receive pRBCs from Afro-Caribbean donors.

Results

Patients and samples

We included 211 SCD patients in this study. During the collection period, two patients were excluded because they had previously received an allograft of hematopoietic stem cells (HSCs), and two patients were excluded because their DNA (extracted from a single sample with no follow-up sample) was of too low quality for molecular analysis.

Patients had received between 2 and 872 pRBCs (mean: 144) before their enrolment in the study.

For each patient, 1 to 12 successive samples (mean: 1.84 samples per patient) were included in the serological analysis during the collection period. Overall, 389 samples were screened during this study.

Antibody history and antibody screening at inclusion

The patients' antibody history and antibody screening at inclusion are detailed in Table 2. The antibodies against the main RH antigens (D, C, E, c, e) in our cohort result from: (i) transfusion with pRBCs in other countries in which antigen-matching protocols are not performed for these antigens, (ii) previously undetected partial RH antigens, (iii) pregnancy, or (iv) possible autoantibodies that mimic alloantibodies (so-called "mimicking alloantibodies").

Before enrolment in the study, four patients had already tested positive for antibodies against Afro-Caribbean-specific LP antigens: two patients had presented anti-RH20 Abs, one had presented anti-KEL6 + anti-RH20 Abs, and one had presented anti-RH10 + anti-RH20 + anti-RH23 Abs.

At the time of enrolment in the study, 35 patients (16.6%) had positive antibody screening tests (Table 2). Successive plasma samples were tested for some patients, and additional antibodies became detectable after enrolment in three patients. Two of these patients had positive screening tests at inclusion, with anti-RH2 in one patient and autoantibodies in the other subsequently becoming detectable. For the third patient, anti-KEL3 antibodies were detected after enrolment. In all three cases, the antibodies detected had already been detected in the past. Adsorption techniques were required for 17 samples (7 patients) presenting autoantibodies.

Molecular testing

The KEL:-6 phenotype was deduced by molecular analysis for 167 SCD patients (79.1 %). The RH:-20 phenotype was deduced for 118 patients (55.9 %), and the RH:-10 phenotype was deduced for 133 patients (63.0%). Among the 1000 FY:-1,-2 donors screened, the KEL:6 phenotype was deduced for 172 donors (17.2%), and the RH:20 phenotype was deduced for Antibodies against LP antigens specific to the Afro-Caribbean population KEL:6 patients were not tested for anti-KEL6 Abs, and RH:20 and RH:10 patients were not tested for anti-RH20 and anti-RH10 Abs, respectively. All patients were tested for anti-MNS6, anti-RH30 and anti-RH23 Abs.

Antibodies against Afro-Caribbean LP antigens were detected in eight patients (3.8%): anti-MNS6 + anti-RH23 Abs in one patient, anti-MNS6 Abs alone in one patient, anti-RH30 Abs in two patients, and anti-RH23 Abs alone in four patients. Anti-RH23 Abs in three patients and anti-RH30 Abs in one patient were detectable only with papain-treated test-RBCs. No anti-KEL6, anti-RH10 or anti-RH20 Abs were detected. One of the patients with anti-RH23 Abs had previously tested positive for antibodies against RH20 and KEL6, but these antibodies were no longer detectable at the time of the study.

The characteristics of the patients with antibodies against Afro-Caribbean LP antigens detected in this study (P1 to P8), or documented in the patient's medical history (P7 and P9 to P11) are reported in Table 3. No DHTR occurred during the study or during follow-up for patients undergoing further transfusions. Patients P4 and P9 had a history of DHTR.

Risk of antigen exposure

The calculated rate of antigen exposure is shown in Table 4. The prevalences of the RH10, RH20 and KEL6 antigens deduced by molecular analysis in our SCD or donor populations were used to calculate the risk of antigen exposure. For antigens RH23, RH30 and MNS6 we used antigen prevalence data from other studies (see Table 1).

For the purposes of comparison, we also estimated the risk of exposure to the FY1 (Fy a ) antigen for our cohort. This calculated risk takes into account exposure to pRBCs from both donors of Caucasian descent and donors of African descent. These donor populations have different FY1 antigen prevalence, this antigen having a much higher prevalence in individuals of Caucasian descent. We considered donors of African descent to have levels of FY1 expression similar to that in our SCD patients, most of whom originated from West and Central Africa (5.2%). The vast majority of donors in mainland France are of Caucasian descent, and the collection of ethnicity-related data is prohibited in France. It was, therefore considered reasonable to assume that the pRBCs received by SCD patients during transfusion were from a donor of African descent in 11.5% of cases [START_REF] Noizat-Pirenne | Transfusion and sickle cell disease: axes of transfusion safety optimization[END_REF] and from a Caucasian donor in 88.5% of cases. The calculated risk of exposure to the FY1 antigen in the SCD patients of our cohort is therefore 53.6% per pRBC unit received, consistent with previous observations. [START_REF] Noizat-Pirenne | Transfusion and sickle cell disease: axes of transfusion safety optimization[END_REF] Similarly, the risk of exposure to the MNS3 (S) antigen and JK2 (Jk b ) antigens was 38.6% and 40.1% per pRBC unit received, respectively.

A comparison between the rate of exposure to antigens and the number of alloimmunizations in our cohort showed the Afro-Caribbean LP antigens to be highly immunogenic (Table 5). Indeed, the rates of exposure to FY1, JK2 and MNS3 were at least 10 times those for any of the Afro-Caribbean-specific LP antigens, for similar numbers of patients displaying alloimmunization.

Discussion

Many SCD patients require regular transfusions of pRBCs to limit complications.

Improvements in the management of blood transfusions in these patients through the prevention of alloimmunization (selection of RH-(D, C, E, c, e) and KEL1-matched pRBCs for all SCD patients and systematic pre-transfusion cross-match tests) have helped to increase the life expectancy of SCD patients. However these developments raise new issues. Intra-ethnic transfusion rates are increased by antigen-matching protocols for FY, JK, MNS antigens, particularly for immunized patients, and SCD patients are increasingly being exposed to Afro-Caribbean-specific antigens, which are absent in donors of Caucasian descent and not detected during routine antibody screening, unlike LP antigens which are common in French persons of Caucasian descent and can be detected in pre-transfusion screening tests with standard test-RBCs. [START_REF]Arrêté du 26 novembre 1999 relatif à la bonne exécution des analyses de biologie médicale modifié par l'Arrêté du 26 avril 2002[END_REF] We show here that 3.8% of SCD patients have detectable antibodies against Afro-Caribbeanspecific LP antigens. These findings highlight the need to maintain cross-matching protocols for SCD patients, as long as test RBCs do not express these antigens, although this precaution is unlikely to be sufficient on its own. Surprisingly, none of the antibodies found in this study were directed against KEL6, RH10 or RH20 antigens, despite the high prevalence of these antigens in individuals of African descent, resulting in high rates of exposure. The exposure rates calculated for RH10 and RH20 antigens were 2.68% and 2.94%, respectively, and that for KEL6 was 1.56% per pRBC unit received.

Moreover, no anti-RH10, anti-RH20 or anti-KEL6 antibodies were detected during the study in the four patients with a history of anti-KEL6, -RH10 and/or -RH20 alloimmunization. These findings suggest that antibodies against KEL6, RH10 and RH20 antigens are highly evanescent.

They can be detected only over short periods, and cross-match tests may yield negative results shortly after alloimmunization. Most of the plasma samples studied here were collected from patients enrolled in chronic transfusion programs, at least one month after the previous transfusion episode, so evanescent antibodies may not have been detected.

Anti-RH23, anti-RH30 and anti-MNS6 antibodies were detected in this study. Even though all patients included underwent multiple transfusions, we cannot rule out the natural occurrence of these Ab. In any case, Ab detected in SCD patients should always be taken into account for future pRBC transfusions. The rate of anti-RH23 alloimmunization was particularly high (2.4%), given the rarity of the RH23 antigen within Afro-Caribbean populations. [START_REF] Chown | A New Rh Antigen and Antibody[END_REF][START_REF] Chown | The RH antigen D W (Wiel)[END_REF] Anti-RH30 antibodies were detected consistently over the course of three months (six successive samples), with no decrease in reactivity, in one of our patients. The calculated exposure rates for the RH23, RH30 and MNS6 antigens were all below 1% per pRBC unit received. This rate of exposure is much lower than that for the FY1 antigen (53.6% per pRBC unit received) calculated for our cohort. Despite this high rate of exposure to FY1 antigens, only five of the patients had currently detectable antibodies against FYI or a history of such antibodies. Conversely, the number of alloimmunizations directed against RH23, RH30 or MNS6 antigens detected was unexpectedly high. This shows that RH23, RH30 and MNS6 antigens are highly immunogenic.

The high immunogenicity of the RH23 and RH30 antigens, and the slower evanescence of antibodies directed against these antigens may account for the higher rate of detection of these antibodies in our study. Additional evidence for the high immunogenicity of the RH23, RH30 and MNS6 antigens is provided by the occurrence of alloimmunization in patients who had undergone only a few transfusions (< 10 pRBC units for P2 and P7, and < 30 pRBC units for P4, P9 and P10).

Antibodies against Afro-Caribbean LP antigens have been detected in previous studies, but this is the first study to have determined the prevalence of anti-RH10, anti-RH20, anti-RH23, anti-RH30, anti-KEL6 and anti-MNS6 antibodies at a given time within a cohort of polytransfused SCD patients. Some previous studies did not specify whether there had been any systematic screening for these antibodies. [START_REF] Rosse | Transfusion and alloimmunization in sickle cell disease. The Cooperative Study of Sickle Cell Disease[END_REF][START_REF] Castro | Predicting the effect of transfusing only phenotype-matched RBCs to patients with sickle cell disease: theoretical and practical implications[END_REF][START_REF] Nickel | Immunophenotypic parameters and RBC alloimmunization in children with sickle cell disease on chronic transfusion[END_REF] The transfusion protocols in some studies were different from that used here (no matching for RH2, RH3, RH4, RH5 and KEL1 antigens, [START_REF] Rosse | Transfusion and alloimmunization in sickle cell disease. The Cooperative Study of Sickle Cell Disease[END_REF] or intraethnic transfusions 23 only), whereas other studies were limited to specific populations (pediatric [START_REF] Nickel | Immunophenotypic parameters and RBC alloimmunization in children with sickle cell disease on chronic transfusion[END_REF] or non-SCD 10 patients). The findings of these studies cannot, therefore, be directly transposed onto current transfusion practices for SCD patients in our country at our hospital. In these studies, antibody prevalences in SCD patients ranged from 0.3% to 5.6% for anti-KEL6 Abs, and from 1.7% to 4.4% for anti-RH30 Abs. Not all studies distinguished between anti-RH10 and anti-RH20 Abs, and the reported prevalence of these antibodies ranged from 0.4% to 1.1%. The results of these previous studies are consistent with our findings of low immunization rates or evanescence for anti-RH10 and anti-RH20 Abs and of high immunogenicity for RH30. The difference in anti-KEL6 immunization rates may be due to antibody screening being performed sooner after transfusion in previous studies, and due to the transfusion of ethnically matched RBCs, resulting in higher rates of exposure, in the study by Chou and colleagues. [START_REF] Chou | High prevalence of red blood cell alloimmunization in sickle cell disease despite transfusion from Rh-matched minority donors[END_REF] The evanescence of antibodies [START_REF] Tormey | The persistence and evanescence of blood group alloantibodies in men[END_REF][START_REF] Harm | A centralized recipient database enhances the serologic safety of RBC transfusions for patients with sickle cell disease[END_REF] and immunogenicity of antigens [START_REF] Winters | RBC alloantibody specificity and antigen potency in Olmsted County, Minnesota[END_REF] have already been studied for some Afro-Caribbean-specific antigen-antibody combinations. Antibody evanescence appears to be variable, but only a few patients with Afro-Caribbean-specific antibodies were available in the studies. In a non-SCD population, [START_REF] Winters | RBC alloantibody specificity and antigen potency in Olmsted County, Minnesota[END_REF] the immunogenicity of the KEL6, RH10 and RH30 antigens was found to be relatively high, similar to that of RH3, and almost three times higher than that of FY1. This immunogenicity was also higher than that of the minor antigens JK2 and MNS3.

In addition to antigen immunogenicity, it is also important to consider the potential consequences of alloantibody formation. SCD patients constitute a very specific population, due to their inflammatory status and their need for multiple transfusions. They are prone to alloimmunization, and the clinical consequences can be disastrous, leading to life-threatening delayed haemolytic transfusion reactions (DHTRs). Most cases of DHTR occur in alloimmunized patients, [START_REF] Noizat-Pirenne | Relevance of alloimmunization in haemolytic transfusion reaction in sickle cell disease[END_REF] but it is often difficult to implicate one specific antibody. Several cases of DHTR have been imputed to anti-RH30 [START_REF] Larson | Delayed hemolytic transfusion reaction due to anti-Go(a), an antibody against the low-prevalence Gonzales antigen[END_REF] or anti-KEL6 [START_REF] Anderson | Delayed hemolytic transfusion reaction due to anti-Js(a) in an alloimmunized patient with a sickle cell syndrome[END_REF][START_REF] Taddie | A delayed transfusion reaction caused by anti-K6[END_REF] antibodies, and others have been observed following polyimmunization to several LP antigens, including RH10 and KEL6, [START_REF] Aygun | Clinical significance of RBC alloantibodies and autoantibodies in sickle cell patients who received transfusions[END_REF][START_REF] Nickel | Impact of red blood cell alloimmunization on sickle cell disease mortality: a case series[END_REF] RH23 and RH30. [START_REF] Noizat-Pirenne | Rituximab for prevention of delayed hemolytic transfusion reaction in sickle cell disease[END_REF][START_REF] Noizat-Pirenne | The use of rituximab to prevent severe delayed haemolytic transfusion reaction in immunized patients with sickle cell disease[END_REF] A case of hemolytic disease of the newborn has also been attributed to anti-KEL6 alloimmunization. [START_REF] Donovan | Hemolytic disease of the newborn due to anti-Js a[END_REF] The greatest caution is therefore required when antibodies against LP antigens are detected in an SCD patient. Systematic testing for the presence of these antibodies in cases of DHTR should help to determine their clinical significance.

We did not include the LP antigen RH32 in this study because of the high prevalence of partial RH2 antigens in SCD patients, [START_REF] Tournamille | Partial C antigen in sickle cell disease patients: clinical relevance and prevention of alloimmunization[END_REF] resulting in little or no RH:2 pRBCs being used for transfusions in French SCD patients in recent years. Furthermore, it was not possible to trace RH:2 pRBCs back to Caucasian or Afro-Caribbean donors, due to the frequency of the RH:2 phenotype in all ethnicities. Other Afro-Caribbean LP antigens could have been considered (e.g. RH42, RH43, RH48, RH49, RH54) but were not included in this study because of the limited availability of test RBCs carrying these antigens. Furthermore, alloimmunization to these antigens is probably extremely rare, and no severe clinical consequences have been described for most of them.

In our country, SCD patients receive pRBCs strictly matched for the main antigens of the RH system (D, C, E, c, e) and the KEL1 antigen, and antigen-negative protocols are used for patients with partial D or C antigens. Extended antigen matching for FY, JK, MNS blood groups [START_REF] Castro | Predicting the effect of transfusing only phenotype-matched RBCs to patients with sickle cell disease: theoretical and practical implications[END_REF][START_REF] Wilkinson | Molecular blood typing augments serologic testing and allows for enhanced matching of red blood cells for transfusion in patients with sickle cell disease[END_REF][START_REF] Lasalle-Williams | Extended red blood cell antigen matching for transfusions in sickle cell disease: a review of a 14-year experience from a single center (CME)[END_REF] and intra-ethnic transfusions [START_REF] Olujohungbe | Red cell antibodies in patients with homozygous sickle cell disease: a comparison of patients in Jamaica and the United Kingdom[END_REF][START_REF] Chou | High prevalence of red blood cell alloimmunization in sickle cell disease despite transfusion from Rh-matched minority donors[END_REF][START_REF] Natukunda | Red blood cell alloimmunization in sickle cell disease patients in Uganda[END_REF] have been shown to reduce overall alloimmunization in SCD patients, but blood donor varies varies, depending on the country and such "high-level" strategies are difficult to implement in most settings. [START_REF] Klapper | Transfusion Practice: Toward extended phenotype matching: a new operational paradigm for the transfusion service[END_REF][START_REF] Karafin | Barriers to using molecularly typed minority red blood cell donors in support of chronically transfused adult patients with sickle cell disease[END_REF][START_REF] Kacker | Economic evaluation of a hypothetical screening assay for alloimmunization risk among transfused patients with sickle cell disease[END_REF] The risk of alloimmunization for the antigens of the FY, JK and MNS blood groups is, therefore, the main concern when managing blood transfusions in SCD patients in mainland France.

However, as antigen-matching protocols for FY, JK, MNS are always recommended for immunized patients, the proportion of donors of African descent recruited in mainland France is increasing. Immunized patients are considered "high responders", [START_REF] Silvy | Red blood cell immunization in sickle cell disease: evidence of a large responder group and a low rate of anti-Rh linked to partial Rh phenotype[END_REF] and immunization against Afro-Caribbean LP antigens is likely to become an increasingly important issue as the proportion of intra-ethnic transfusions increases. [START_REF] Yee | Red blood cell minor antigen mismatches during chronic transfusion therapy for sickle cell anemia[END_REF] In the most extreme case, if all SCD patients received pRBCs from donors of African descent, the rate of exposure to LP antigens would increase to as much as 24.6% per pRBC unit received for the most prevalent Ag (RH20), whereas FY1 exposure rates would be only 5% per pRBC unit received. Routine antibody screening would be inefficient, and the frequency of undetectable antibodies against LP antigens would increase. The high immunogenicity of some of these antigens and the evanescence of Abs, as shown here, might also create new difficulties in the management of blood transfusions for patients, which we need to anticipate. 1: Main characteristics of the selected antigens specific to the Afro-Caribbean population, according to Reid and colleagues, 3 except for the polymorphisms necessary for RH23 Ag expression and its prevalence in Afro-Carribbeans. [START_REF] Omi | Detection of Rh23 in the partial D phenotype associated with the D(Va) category[END_REF][START_REF] Flegel | DCS-1, DCS-2, and DFV share amino acid substitutions at the extracellular RhD protein vestibule[END_REF][START_REF] Lopez | A D+ blood donor with a novel RHD*D-CE(5-6)-D gene variant exhibits the low-frequency antigen RH23 (D(W) ) characteristic of the partial DVa phenotype[END_REF][START_REF] Chown | A New Rh Antigen and Antibody[END_REF][START_REF] Chown | The RH antigen D W (Wiel)[END_REF] (Ag : antigen)

TABLES

(

  EFS) Ile-de-France (Créteil) for routine antibody screening by the Henri Mondor University Hospital SCD Center (Créteil, France) and the pediatric center of the Créteil Intercommunal Hospital (CHIC, Créteil, France) between November 2013 and March 2014 were eligible for inclusion in the study.

-Table 2 :

 2 MNS3 + anti-JK2 -anti-FY3 + anti-JK2 -anti-FY3 + anti-MNS3 + anti-JK2 + anti-DO1 History of antibody detection and antibodies detected on screening at inclusion (* the Abs of low clinical significance are: autoantibodies and/or natural Abs and/or antibodies against LP antigens not related to Afro-Caribbean populations (RH8 (C w ), KEL3 (Kp a ), LU1 (Lu a ) and YT2 (Yt b )) and/or Abs of unspecified specificity; †one or more associated Abs of low clinical significance may also be detected).

P9 39 F

 39 anti-RH2, -RH3, -RH8, -RH10, -RH20, -RH23, -RH32, -FY3, -LE1, -KN, auto-Ab antibefore the detection of anti-

Table 1 : Ag prevalences: Ag Common name Gene(s) Polymorphism(s) necessary for the Ag's expression, or allele in Afro- Caribbeans in Caucasians or other populations

 1

	RH10	V	RHCE	c.733G and c.1006G	30%	Caucasians: 1%
	RH20	VS	RHCE	c.733G	26 to 40%	Other populations: <0.01%
	RH23	D W (Weil)	RHD	RHD alleles with all or part of RHCE exon 5	1 -3,6%	All populations: <0.01%
	RH30	Go a	RHD	allele RHD*04.01 (or DIVa)	2%	Caucasians: <0.01%
	KEL6	Js a	KEL	c.1790C	20%	Caucasians: <0.01%
		He	GYPB or hybrid alleles	alleles GYPB*06.01, GYPB*06.02, GYPB*03N.02, GYPB*03N.04
	MNS6				3 to 7%	Caucasians: 0%
		(Henshaw)	within the GYP gene family	or hybrid alleles GYP*101.04 or GYP*505
	Table

Table 2 :

 2

	Ab specificity

Table 3 :Table 3 :

 33 Characteristics of patients presenting Afro-Caribbean-specific antibodies, detected during this study (P1 to P8), or recorded in the patient's medical history (P7 and P9 to P11). (* all pRBCs were received before the detection of Abs against Afro-Caribbean LP antigens, except in P11, † only detectable with papain-treated test RBCs; US: unspecified specificity, LP: low prevalence)

		Age				Anti-LP Ab detected
			Sex	History of Ab detection	Ab screening at inclusion		Number of pRBC units received*
		(y)				during this study
	P1	21	M	auto-Ab	negative	anti-MNS6 + anti-RH23 †	318
	P2	44	M	anti-MNS3, -FY5, -YT2, anti-LE1, auto-Ab	anti-RH3 + anti-MNS1+ US Ab	anti-MNS6	5
	P3	33	F	anti-RH3 + US Ab	anti-RH2 + auto-Ab	anti-RH30	78
	P4	34	F	anti-RH2, -JK2, auto-Ab	negative	anti-RH23 †	30
	P5	34	M	none	negative	anti-RH23	165
	P6	54	M	auto-Ab	negative	anti-RH30 †	181
	P7	31	F	anti-RH20, -KEL6	negative	anti-RH23	4
	P8	13	F	none	negative	anti-RH23 †	120

Acknowledgments

The study was supported by a Grant of the Agence Nationale de la Recherche (ANR) and by the Etablissement Français du Sang (APR 2011-2014)

The authors would like to thank Vintuya Muralitharan and Diannyl Adenet for technical assistance, and Sadaf Pakdaman for her help with sample collection.

Authorship contributions

FP, TP and AF designed the study. AF and DG performed the molecular and serologic analyses.

CT supervised the technical analyses and made substantial contributions to conception and design. AH and BC co-ordinated the collection of samples and data. AF, FP, CT, TP analyzed and interpreted the results. AF and FP wrote the manuscript, which all authors critically reviewed.


A Yousfi

S Fréour

F Jacquemin

M Rahmani

H Osmani

R Guillen

A study of the mechanical behavior of thermo-oxidized composite lamina

Keywords:

, qui répond aux mathématiques qu'au modèle auto-cohérent de Eshelby-Kröner modèle auto-cohérent. Les stress locaux ont également été comparés avec les résultats obtenus en utilisant la méthode des éléments finis: les deux approches prédisent des résultats proches.

INTRODUCTION

Due to their very interesting specific mechanical properties, carbon-reinforced epoxy laminates are considered as serious candidates for the replacement of metals, metallic alloys and cermets for industrial applications such as structural parts for the next generation supersonic aircrafts [START_REF] Ye | Functionalized Composite Structures for New Generation Airframes: a Review[END_REF].

The lifetime scheduled for the structural elements of supersonic aircraft approximately corresponds to 20,000 cycles in a range of temperatures varying between -55 °C and 120 °C, with a total length of the plateau at 120 °C of 80,000 h (10 years) [START_REF] Bellenger | Ageing of a Carbon Epoxy Composite for Aeronautic Applications[END_REF].

Such high temperatures over long periods cause a thermal ageing of the resin of elements composite of structure leading to thermal oxidation of external ply of material. Before 1990, few studies have been conducted on thermal aging of organic matrix composites reinforced with carbon fiber.

Indeed, before this date, the use of these materials has been limited to a field of rather low temperatures between -50 °C and +70 °C, which correspond to the thermal load experienced in service by structural parts of, for example, subsonic aircraft and helicopters. Recently, the problem arose when such organic matrix composites have been considered for applications under severe environmental conditions from a thermal point of view (temperatures of about 250 °C, air pressure higher than 1 atmosphere) [START_REF] Hergenrother | Development of Composites, Adhesives and Sealants for High-Speed Commercial Airplanes[END_REF][START_REF] Brunner | Proceedings of the 39 th International SAMPE Symposium and Exhibition[END_REF].

The laminated composites exposed to high temperatures are subject to degradation caused mainly by thermal oxidation of their organic matrix. It induces the growth of oxidized layer of reduced thickness in the subsurface of the composite parts. This superficial phenomenon leads to weight loss and alters the mechanical behavior [START_REF] Bowles | Specimen Geometry Effects on Graphite / PMR-15 Composites during Thermal Oxidative Aging[END_REF][START_REF] Madhukar | Thermo-Oxidative Stability and Fiber Surface Modification Effects on the Inplane Shear properties of Graphite / PMR-15 Composites[END_REF].

The diffusion-reaction model coupled to a mechanistic scheme has been proposed in [START_REF] Ho | 12 th European Conference on Composite Materials[END_REF], in order to predict the behaviour of epoxy matrices experiencing thermal ageing. It can predict the oxidation products concentration profiles, from which the oxidized layer thickness and weight losses are determined. The thermal oxidation of matrix induces a fragility of the near surface area from which the mechanical properties are different to those of the bulk, unaffected by oxidation material.

The purpose of this work is the multi-scale analysis of the consequences of the thermal-oxidation of epoxy matrices on the intrinsic mechanical properties of the external composite ply, on the one hand, and on the internal mechanical states of composite structure according to the considered mechanical loading, on the other hand.

This work includes five sections. The first section is dedicated to the influence of thermal oxidation on the mechanical properties of composite ply.

The second section presents the Eshelby-Kröner self-consistent model: its constitutive laws are given for the estimation of effective thermal elastic properties of composite ply (stiffness tensor and coefficient of thermal expansion).

The third section is devoted to the coupling of the classical lamination theory and analytical scale-transition relations for local stress determination in both constituents of composite plies subjected to a thermo-elastic loading.

The fourth section describes the conclusions of the present study, while the fifth offers a number of perspectives for future developments in this field of research.

EFFECTIVE PROPERTIES OF A THERMOOXIDIZED COMPOSITE PLY

Oxydation model and results

Various model enabling to achieve the numerical computation of oxidation process in pure epoxies or epoxy matrix composites have been proposed in the literature [START_REF] Colin | A New Method for Predicting the thermal Oxidation of Thermoset Matrices. Application ton an Amine Crosslinked Epoxy[END_REF][START_REF] Tandon | Modeling of Oxidative Development in PMR-15 Resin[END_REF]. Simulations of isothermal aging at 150 °C of an epoxy resin during various ageing lengths demonstrated that the oxidized layer thickness was not growing beyond 200 µm whereas the oxidation products concentration were continuously increasing in the affected layer [START_REF] Ho | 12 th European Conference on Composite Materials[END_REF].

Results obtained through ultra-micro indentation tests on epoxy resin, after 100 h, 600 h and 1000 h of isothermal aging at 150 °C show that a polynomial relation between elastic indentation modulus and oxidation products concentration occurs '(1)' [START_REF] Ho | 12 th European Conference on Composite Materials[END_REF]:

4045 Q 592 Q 4 . 57 Y 2 m + + - = (1)
where m Y is the elastic modulus of the epoxy matrix, expressed in GPa, Q is the oxidation products concentration (mol/l) which is space and time dependent. The evolution of the Young's modulus of the matrix during the thermal oxidation process is displayed on figure 1. The matrix is considered as an isotropic material, which Poisson's ratio 35 . 0 m = ν is assumed due to the lack of available information on its evolution, as independent of state of thermal oxidation process, while its shear modulus is deducted from the classical relation:

) Y 1 ( 2 Y G m m m + = (2)
Fig. 1: Evolution of the elastic modulus as a function of the oxidation products concentration

Comparison with the behavior of unaffected matrix

The thermal oxidized matrix is stiffer than the unaffected matrix in a ratio varying between 1 and 1.38. The matrix properties of a thermally oxidized ply can be very different from those of the corresponding unaffected ply, so that three main consequences due to the thermal oxidation of composite structure can be expected: a variation of i-the effective macroscopic properties of composite plies, ii-the profiles of macroscopic stress in the structure and iii-the localization of the macroscopic mechanical states (stress and strain) in both constituents of each ply (fiber and matrix).

The three above listed expected consequences of thermo-oxidation are multi scale phenomena, either explicitly, in the case of items i-and iii-, (i-being an homogenization problem, whereas iii-is related to localization problem), or implicitly, in the case of item ii-, which implies the knowledge of the macroscopic effective properties of the composite ply (resulting from the estimates achieved in i-).

In order to be able to treat each of these aspects, a scale-transition model is required. This model is described below in section 3.

MULTI-SCALE ANALYSIS

Introduction

Scale transition models are based on a multiscale representation of materials. In the case of composite materials, for instance, a two-scale model is sufficient:

-The properties and mechanical states of either the resin or its reinforcements are respectively indicated by the superscripts m and f . These constituents define the so-called 'pseudo macroscopic' scale of the material [START_REF] Sprauel | First European Powder Diffraction International Conference on X-Ray Stress Analysis[END_REF].

-Homogenization operations performed over its aforementioned constituents are assumed to provide the effective behavior of the composite ply, which defines the macroscopic scale of the model. It is denoted by the superscript I . This definition also enables to consider an uni-directional reinforcement at macroscopic scale, which is a satisfactorily realistic statement, compared to the present design of composite structures.

As for the composite structure, it is actually constituted by an assembly of the above described composite plies, each of them possibly having the principal axis of their reinforcements differently oriented from one to another. This approach enables to treat the case of multi-directional laminates, as shown, for example, in [START_REF] Fréour | On an Analytical Self-Consistent Model for Internal Stress Prediction in Fiber-Reinforced Composites Submitted to Hygroelastic Load[END_REF].

Within scale transition modeling, the local properties of the i-superscripted constituents are usually considered to be known (i.e. the pseudo macroscopic stiffness, i L and coefficients of thermal expansion i M ), whereas the corresponding effective macroscopic properties of the composite structure (respectively, I L and I M ) are a priori unknown and results from (often numerical) computations.

Among the numerous, available in the literature scale transition models, able to handle such a problem, most involve rough-and-ready theoretical frameworks: Voigt [START_REF] Voigt | Lehrbuch der Kristallphysik[END_REF], Reuss [START_REF] Reuss | [END_REF], Neerfeld-Hill [14,[START_REF] Hill | Proc. Phys. Soc[END_REF], Tsai-Hahn [START_REF] Tsai | Introduction to Composite Material's[END_REF] and Mori-Tanaka [START_REF] Tanaka | [END_REF]18] approximates fall in this category. This is not satisfying, since such a model does not properly depict the real physical conditions experienced in practice by the material. In spite of this lack of physical realism, some of the aforementioned models do nevertheless provide a numerically satisfying estimation of the effective properties of a composite ply, by comparison with the experimental values or others, more rigorous models.

Both Tsai-Hahn and Mori-Tanaka models fulfil this interesting condition [START_REF] Jacquemin | A Hygroelastic Self-Consistent Model for Fiber-Reinforced Composites[END_REF]20]. Nevertheless, in the field of scale transition modelling, the best candidate remains Kröner-Eshelby self-consistent model [START_REF] Eshelby | Proc. Roy. Soc[END_REF][START_REF] Kröner | [END_REF], because only this model takes into account a rigorous treatment of the thermohygro-elastic interactions between the homogeneous macroscopic medium and its heterogeneous constituents, as well as this model enables handling the microstructure (i.e. the particular morphology of the constituents, especially that of the reinforcements).

Determination of the effective macroscopic thermo-elastic properties of composite plies

According to Eshelby-Kröner self consistent model, the homogenization relation enabling to determine the macroscopic elastic stiffness of a composite ply from the properties of the constituents is:

[ ] m , f i 1 I i I i I I ) L L ( : E : L L = - + - = (3)
In equation ( 3), I stands for the fourth-order identity tensor, whereas the name given to the tensor I E often changes from one article to another (it is called, for example, Hill tensor, or Morris tensor, depending on which work from [28,29] is considered). Morris's tensor expresses the dependence of the localization tensor on the morphology assumed for the matrix and its reinforcements [28] L (some examples are given in [START_REF] Kocks | Texture and Anisotropy[END_REF][START_REF] Mura | Micromechanics of Defects in Solids[END_REF]). The homogenization relation satisfied by the macroscopic coefficients of thermal expansion of a composite ply writes as follows:

[ ] m , f i i i 1 I i I 1 I I M : L : I ) L L ( : E : L M = - - + - = (4)
Only a few study studies were dedicated to the oxidation effects on the mechanical behavior of organic matrix composites. It was nevertheless shown in [START_REF] Bowles | [END_REF] that the properties of carbon fibers are stable below 300 °C.

As a consequence, the variation of mechanical properties of thermo-oxided laminates only depend on the evolution of the matrix properties. Evolutions of the effective longitudinal and transverse macroscopic elastic moduli, as a function of the oxidation products concentration are shows on figures 2 and 3, for a composite containing a carbon fiber volume fraction equal to 60 %. The effective mechanical properties of the oxidized composite ply were determined, during the oxidation process, through Eshelby-Kröner self-consistent homogenization procedure '(3)' (curve 'KESC'). The results were compared to the corresponding properties estimated according to the finite element method (FEM "curve"). According to figure 2 and4, the longitudinal effective properties (i.e. in the direction parallel to axis of the reinforcing fibers), are, in first approximation, independent from the state of thermal oxidation process of the polymer matrix constituting the considered composite ply.

Actually, a relative deviation weaker than 1 % is observed at the end of the oxidation process for the Young's modulus, while the longitudinal macroscopic coefficient of thermal expansion remains almost constant (and tends towards zero). This result is explained by the fact that in the fiber direction, a unidirectional ply presents thermo-mechanical properties which are controlled by the properties of a single constituent: the fiber.

Experimental results on composite plies in similar circumstances, i.e. in cases when the carbon fibers exhibit constant properties, while those of the matrix significantly vary, corroborates the results of our simulations: longitudinal effective macroscopic properties of composite plies do not vary as a function of the properties polymer matrix (at least in the case that the composite ply contains a high volume fraction of fibers) [27]. On the contrary, the effective macroscopic properties of a composite ply, in the direction transverse to the reinforcements axis, do significantly depend on the state of thermal oxidation process experienced by the polymer matrix constituting the ply.

In fact, the relative variation of transverse Young modulus of oxidized ply compared to the reference value (unaffected ply) can reach 12 % at the term of oxidation process (and spreads so that the variation for transversal coefficient of thermal expansion is 3.5%). The reader will notice that this relative variation depends him even on the volume fraction of reinforcements in the composite ply and may reach 38 % in the pure matrix at the end of the oxidation process.

STUDY OF THE MULTI-SCALE MECHANICAL STATES EXPERIENCED BY THE COMPOSITE STRUCTURE

Determination of mechanical states within the constituents of a composite ply subjected to thermo-elastic loading

Analytical relations satisfying the fundamental assumptions of Eshelby-Kröner selfconsistent model, enabling to proceed to the localization of the macroscopic strains within the matrix were established in [START_REF] Fréour | On an Analytical Self-Consistent Model for Internal Stress Prediction in Fiber-Reinforced Composites Submitted to Hygroelastic Load[END_REF].

Due to the length of these equations, they will not be provided in the present work, so that the interested reader should refer to '(18)'-'(19)' of [START_REF] Fréour | On an Analytical Self-Consistent Model for Internal Stress Prediction in Fiber-Reinforced Composites Submitted to Hygroelastic Load[END_REF]. The corresponding stress tensor experienced by the matrix can be deduced from its strain state through: [START_REF] Bowles | Specimen Geometry Effects on Graphite / PMR-15 Composites during Thermal Oxidative Aging[END_REF] The mechanical states experienced by the reinforcements can be deduced from Hill's averages relations over stresses and strains [28]:

            σ ε ε ε σ ε ε ε σ = σ
m 11 m L 2 L 2 L 2 L 2 L 2 L 2 (5) With        ∆ + - ε + ε + ε = σ ∆ + - ε + ε + ε = σ ∆ + - ε + ε + ε = σ T ) L 2 L ( M ) ( L L T ) L 2 L ( M ) ( L L T ) L 2 L ( M ) ( L L
m f m I f f 1 σ ν ν - σ ν = σ ; m f m I f f 1 ε ν ν - ε ν = ε (7)
The variation of the internal macroscopic stresses I 11 σ and I 22 σ have been calculated during the one edge thermal oxidation process of a composite laminate submitted to either a longitudinal or a transverse external load. The results obtained for the macroscopic mechanical states were localized within the constituents using the above described scale transition relations.

The curves for both the macroscopic and local stresses experienced by the external ply have been displayed on figures 5-6 (in the cases that a longitudinal or a transverse external load was considered, respectively). On the same figures, the stress states predicted for the thermo-oxidized laminate were compared to the corresponding stresses calculated for the unaffected material.

The mechanical states predicted from the effective macroscopic properties provided by Eshelby-Kröner Self-Consistent model were compared to the mechanical states calculated from the effective macroscopic properties deduced from finite elements analysis.

Figures 5 and6 underline the consequences of a thermal oxidation on the multi-scale mechanical states. In the case that the composite structure is submitted to a longitudinal external load, the multi-scale internal stresses experienced by the oxidized ply are independent from the oxidation process state.

This result comes from the independence from the oxidation state exhibited by the macroscopic effective properties in the longitudinal direction (see section 4 of the present work).

On the contrary, in the case when the composite plate is submitted to a transverse mechanical loading, the internal stresses experienced by the oxidized ply and its very constituents differ from those that would have been undergone by an unaffected ply: the macroscopic stress increases during the thermal oxidation, as a consequence of the increased effective stiffness of the thermo-oxided ply.

Oxidized ply

Unaffected ply At the scale of the constituents: i) the stress concentration in the reinforcing fiber does not vary at all as a function of the oxidation products concentration, since the properties of the carbon fibers are unchanged during the thermal-oxidation process.

ii) the epoxy matrix experiences an increasing stress state during the thermal oxidation process, which can be attributed to the increased stiffness of this constituent induced by the thermal-oxidation. Actually, composites are generally designed so that the reinforcements concentrate the stresses.

Moreover, in practice, damage and failure initially often takes place in the subsurface of a mechanical part. Thus, an increased stress experienced by the resin of the external ply is, a priori not favourable to the durability of the composite structure. These considerations can help to explain the worst durability of thermooxided composite structures, observed in practice, by comparison with the reference behaviour of the unaffected by oxidation structure.

Oxidized ply

Unaffected ply

CONCLUSIONS

In this work, the consequences due to the thermal oxidation of the epoxy resin constituting a composite structure were investigated, for the first time, through a scale transition approach. The results obtained through the scale transition method were compared to finite elements calculations, with a rather good agreement. The scale transition approach demonstrates that the effective properties and mechanical states of the external ply of a composite structure having experienced a thermal oxidation process do not strongly differ from the corresponding reference values of the ply unaffected by the thermal oxidation.

On the opposite, the local properties and mechanical states of the matrix constituting the ply affected by thermal oxidation do strongly vary as a function of the thermal oxidation process state. It was demonstrated that both the evolutions of the mechanical properties and mechanical states in the epoxy after the thermal oxidation were not compatible with an enhanced durability of the structure, especially in the case that a transverse external load had to be undergone.

PERSPECTIVES

The scope of the present study was limited to the consequences of the thermal oxidation of the polymer matrix on the evolutions of the properties and mechanical states of composite materials during a subsequent loading at ambient temperature.

Nevertheless, the composite experiencing thermal ageing are often subjected to thermal mechanical loads at high temperature. Under these conditions, the polymer matrix exhibits a visco-elastic behavior. This leads to an effective visco-elastic behavior of the composite plies at macroscopic scale. In order to take into account these physical phenomena, a visco-elastic scale transition model will be developed. This model will be used in order to achieve the prediction of the effective thermomechanical behaviour (stiffness tensor and coefficients of thermal expansion) of the composite plies as a function of time and temperature. Thereafter, it will be possible to proceed to the localization of the mechanical states within the constituents of each ply of the studied composite structure.

Moreover, practical studies, published in the literature, report an evolution of the yield strength of epoxies during the thermal oxidation process. Multi-scale failure criteria, enabling to take into account these experimental results will be developed in further works, in order to rigorously investigate the durability of structures having been submitted to thermal oxidation processes.

=

  . It can be expressed as a function of Eshelby tensor I esh It has to be underlined that both Hill's and Eshelby's tensor components are functions of the macroscopic stiffness I

Fig. 2 :Fig. 3 :Fig. 4 :

 234 Fig. 2: Longitudinal macroscopic effective elastic modulus of a composite ply, as a function of the oxidation products concentration

Fig. 5 :

 5 Fig. 5: Longitudinal ( 11 σ ) and transverse ( 22 σ ) stresses concentrations in the constituents of the external ply, the composite structure being subjected to a longitudinal stress 11 σ = 100 MPa

Fig. 5 :

 5 Fig. 5: Longitudinal ( 11 σ ) and transverse ( 22 σ ) stresses concentrations in the constituents of the external ply, the composite structure being subjected to a longitudinal stress 22 σ = 50 MPa ST: Scale-transition; comp: composite; mat: matrix; FEM: finite element method

Table 1

 1 displays the local properties of carbon fiber considered in order to achieve the homogenization calculations.

Table 1 :

 1 Local properties of carbon fiber T300[26]

	1 Y (GPa)	2 Y , 3 Y (GPa)	12 ν , 13 ν	12 G (GPa)	23 G (GPa)
	230	15	0.2	15	7