Samia Badji
email: samia.badji@cnrs.fr

Education In Extreme Environments, Does Mother's Education Still Matter?

Keywords: child labor, market imperfections, wealth paradox, sub-Saharan Africa JEL codes: 012, D13, J13, J82 child malnutrition, wasting, stunting, underweight, maternal education, mid-upper arm circumference, Somalia JEL classication: I1, I2, I3

This paper looks at child stunting, wasting, underweight and mid-upper arm circumference in the particular context of Internally Displaced Person Camps in Somalia, the country with one of the highest number of IDPs in the world. The focus is on maternal education and two questions are addressed. First, whether the effect of mother education differs inside and outside camps. Second, if the relative advantage of educated mothers over their uneducated counterpart dissipates with time in the camp. Results show a slightly stronger effect of maternal education in the camp for short-to-middle-term health outcomes.The relative advantage of educated mothers increases with time in the camp. In a context of destitution and dependence, the analysis highlights the role played by maternal education not only as a way to improve child health but also as a factor of resilience.

Introduction

Malnutrition and child health in general have been the subject of numerous studies and it has generally been argued that mother's education, was an essential determinant of child health. The relevance of mother's education might however be questioned in environments where her ability to provide care is challenged. Extreme situations often involve addressing the most pressing issues and the provision of education is often left for later.

However if educated mothers could buer extreme events for their children, then providing education may still be deemed relevant as a factor of resilience. To investigate whether education could still matter, we examine Internally Displaced Person (IDP) Camps in Somalia after the famine was declared. The camps oer another perspective to understand how education inuences ospring' health.

IDP camps are comparable to refugee camps except that IDP have not crossed any internationally recognized borders. Families coming into such camps usually had to ee their home because of conict and/or famine and nd themselves in a new environment with almost always no asset and dependent on what the camp may provide. Internally displaced children of conict-aected regions have one of the highest rates of acute malnutrition in the world. However there is no or little research on malnutrition in these camps.

The present study focuses on Somalia which has one of the highest number of IDPs in the world. According to UNHCR, more than 1.3 million people are classied as IDPs in Somalia. More than 60% of them are in an acute food security crisis. Children in IDP camps face the highest food security crisis of the whole country (FSNAU Gu 2012 report). Studying malnutrition in Somali camps is therefore a key element to ght malnutrition overall.

Most research on Somalia focused on its lack of government, (Leeson 2007, Powell, Ford and[START_REF] Powell | Somalia after state collapse: Chaos or improvement[END_REF]. However the North of the country has had institutions working as a government for more than 20 years. It is even more important now as a new government is in place since August 2012 for the whole country, oering new hope to tackle the nationwide issues linked with IDPs. Some studies look at IDPs but focus on host communities (Alix-Garcia and Saah, 2010 for Sudan; and Alix-Garcia, [START_REF] Alix-Garcia | Displaced populations, humanitarian assistance and hosts: A framework for analyzing impacts on semi-urban households[END_REF] for refugees in Tanzania). A study by [START_REF] Engel | Displacement due to violence in Colombia: A level analysis[END_REF] in Colombia investigated internal displacement by examining the household decision of leaving the home. Given the temporary nature of camps, it is quite understandable that no study focused on them. However, in Somalia, the proportion and duration of the situation should trigger more interest.

As mother education is one of the strongest determinant of child health and because IDP camps provide dierent mechanisms for mothers, looking at how educated mothers tackle child malnutrition is crucial. [START_REF] Caldwell | Education as a factor in mortality decline an examination of Nigerian data[END_REF] emphasized the role of maternal education in child mortality in Nigeria. He advances several pathways to explain their relative advantage: they could disrupt with traditional belief typically involving a fatalistic acceptance about illness; they could interact better with medical sta and infrastructure or they could simply have more power inside the (extended) household and have a higher control over health-related decisions.

Number of studies have since addressed mother education and its eect on ospring's survival and health and it is generally agreed that mother's schooling improves child health (using school supply increase, see Günes, 2015;Maiga, 2012 . For a review and a focus on sub-Saharan Africa, see [START_REF] Hobcraft | Women's education, child welfare and child survival: a review of the evidence[END_REF]. Boyle and alii (2006) even argue that education matters more than wealth.

In the context of IDP camps, some of the pathways might be shut down.

First, the typical shift in power structures inside the household will likely be experienced by most women. When a household sets in an IDP camp, it is usually solely the wife and children who settle in while the father remains with the (potential) cattle. Furthermore, women may have ration cards giving them more economic independence and therefore more power for family decisions. As a result many families will experience changes in familial power structures regardless of the mother's education. Second, assistance being provided to all, the usual higher association of educated mothers with health infrastructure (due to a higher association to the modern world or higher self-condence) is no longer limited to the educated mothers.

The aim of this study is two-fold. First, we want to see whether mother education inuences child health in the camps and if so, whether it diers from what can be observed outside camps in Somalia. Second, we want to know how this eect varies with time spent in the camp. Though being displaced should be a temporary situation it can be seen in many parts of the world that this situation may last. If educated mothers simply learn faster, their relative advantage should not last. We nd that the eect of maternal education slightly diers for short to middle term health measures. Educated women are even more eective at tackling malnutrition when they are in the camp than when they are outside. Relying on the pseudo-panel dimension of the data, we nd that the relative advantage of educated mothers widens as time spent in the camp increases. The rest of the paper is structured as follows. The next section describes the data. The third section presents the empirical strategy. Section four shows the results. Section ve discusses the mechanisms and limitations. The last section concludes. the general situation in the nutrition surveys. IDPs are surveyed in camps around 8 cities: Berbera, Borao, Bossaso, Dhuusamareb, Galkayo, Garowe, Hargeysa and Qardho. The data are collected according to a two stage cluster sampling except for camps around Dhuusamareb and Qardho where only a rapid assessment was made. In the Deyr 2011 assessment, data were collected in November for IDP camps and December outside camps. In the Gu 2012 survey, data were collected in May for IDP camps and July for non camps. Dierent individuals were surveyed across the two waves so that the data are not panel data. For security reasons, the south of Somalia was surveyed using focus groups (not household surveys) and cannot be included in our analysis.

Data description

The post Deyr assessment took place after the 2011 famine (ocially declared in July) where four million people, that is more than half of Somalia's population, faced an acute food security crisis. In the Gu 2012 survey, the gure dropped to 2.12 million people (28% of the population). Despite this improvement, the number of people in need remained among the highest in the world. 70% of people in food security crisis live in the South. 236,000 under-ve-year-old children (16% of the child population) are acutely malnourished, 54,000 are severely malnourished, that is, in need of immediate intervention. Focusing on IDPs, 800,000 of the total 1.36 million in the country were in acute food security crisis at the time of the Gu 2012 assessment (gures are taken from the FSNAU Nutrition Gu 2012 Report).

The survey supplies information on age, gender, weight, height and midupper-arm circumference for children aged 6 to 59 months allowing for the computation of four anthropometric outcomes. Information on immuniza-tion, vitamin A supplementation, self-reported illnesses (for the caretaker) and child illnesses (reported by the caretaker) is also available. Information on the caretaker's age and education is collected, that is, information on maternal education is not actually given. However, in our context, clearly, the caregiver is the mother unless she is not present. As we select on 15-49 year old females reporting their mid-upper arm circumference and because the rst reporting should be the mother's, the issue should be very limited. Furthermore, the eect of the person caring for the child also matters. [START_REF] Lindelow | Health as a family matter: Do intra-household education externalities matter for maternal and child health?[END_REF] shows that not only maternal education matters but also education of other (non spouse) household members. Handa (1999)'s work on Jamaica suggests that household education, not necessarily maternal education, strongly correlates with child health. [START_REF] Chen | Mother's education and child health: Is there a nurturing eect[END_REF] found on a survey of adoptees in China that the eect of maternal education on adoptees was similar to the eect on own birth children. In the end, we will interpret the eect of the caretaker's education as the mother's eect even though we cannot guarantee that it is so.

We now present the anthropometric measures. The MUAC or mid-upperarm circumference, gives an indication for both fat reserve and muscle mass and is easy to collect. As argued by Alderman, it is a good estimate for child health [START_REF] O'donnell | health equity using household survey data: a guide to techniques and their implementation[END_REF]Roy, 2011) and can be used to assess the local average health of children. Stunting, wasting and underweight are standard measures. A child is stunted if s/he has a low height-for-age (HAZ). It is a sign of sustained and accumulated episodes of undernutrition and/or repeated infections. Wasting, dened by a low weight-for-height (WHZ), is a sign of acute (moderate or severe) malnutrition and is a result of a weight loss associated with recent periods of starvation or disease. Wasting is by denition less sensitive to age measurement errors typically associated with age heaping in developing countries (as age is only needed at the stage of standardization, not before). Underweighted children are too light for their age (WAZ). It is an intermediate measure between stunting and wasting.

Note that too low for anthropometric measures means more than two standard deviations away from the distribution of healthy children of same age and sex as given by WHO in 2006 [START_REF] Espejo | WHO child growth standards: Methods and development[END_REF]. The score computed from this comparison and measured in standard deviations is called a Z-score. The healthy population for standardization is international which is arguably unsatisfactory. Nonetheless, studies have shown that distributions from upper or middle-class families in developing countries do not dier from international references and heights or weights for refugee children from Asia in the US, converge rapidly to those of American born children (WHO, 1995;Habicht and others, 1974;[START_REF] Yip | Improving growth status of Asian refugee children in the United States[END_REF]. The distinction between moderate (below two standard deviations) and severe (below three) outcomes is not undertaken in the data description so that moderate outcomes comprise severe outcomes. For the regressions, we will specically investigate the Z-score associated with each health outcomes and whether they fall below two standard deviations.

Table 2 presents descriptive statistics and reveals that for any indicator chosen, malnutrition is extremely alarming, especially in the camps. A striking 37% of surveyed children suered from measles, diarrhea, pneumonia or fever in the last month (simply referred to as sick in the table). One in ve child suers from acute malnutrition, 21 % are stunted, 27% are suffering from underweight, 19% of children are wasted and 14 % have a low MUAC. Comparing households inside and outside camps, one nds that the caretaker and the children are both slightly younger inside camps though the dierence is small. Outside camps, the typical household is slightly smaller with 5.3 members including two children. Households in IDP camps seem to be, in general, better taken care of: the source of drinking water seems safer, they are more likely to be vaccinated against measles or to have received the three injections against polio. Mothers are also receiving more injections against tetanus. Children outside camps are on average healthier.

The dierence for wasting is lower than the dierence for stunting probably due to the fact that stunting reects repeated shocks or chronic malnutrition when wasting only shows recent periods of nutritional shock. MUAC usually gives results similar to wasting which is roughly what is found here. Even if children outside camps are doing better than children living in camps, at least 10% are suering from stunting, wasting, underweight or having a low MUAC. Note that children in camps are twice as likely to be registered in a feeding center (consistent with their twice as bad health outcomes).

Regarding the caretaker's education, table 2 shows very low levels of education inside and outside camps. Only one woman out of three completed primary school outside camps and 15% in camps. As assistance (when available) aims at being provided equally, it is possible that schooling no longer matters inside camps. To assess the share of variance accruing to dier-ences between households in camps and household outside camps, a variance analysis is run and both health outcomes and education vary enough within group so that being in a camp does not explain it all. Cities around which the camps are gathered are far from one another and reect dierent intensity at which households may be hit by undernutrition. Climate and in particular rainfall may dier and lead to dierences in agricultural output that may translate into more stressed situations regarding food security. Camps further away from the south have on average better health outcomes. Another variance analysis is run and shows that most of the variation comes from within the camps (as opposed to across camps). All descriptions are based on the Gu 2012 assessment. Results are qualitatively similar for the previous assessment.

Empirical Strategy

Simple comparison strategy

To best investigate health, accurate variables are essential and anthropometric outcomes will be used. They are measured by trained enumerators and do not suer from the reporting bias. The reporting bias is the inability of poorly health aware individuals to notice that their child is sick. Because health aware individuals might not be randomly distributed among educated and uneducated caregivers, the results might be biased. Using anthropometric measures avoid such bias.

To compare the eect of education inside and outside camps, we will simply pool in the same regression households in camps and outside camps and see whether the term education*camp is signicant. With region xedeects, the empirical model assessing the health H ijl of child i, from household j in community l is simply:

P (Y ijl = 1) = β 0 +X i Γ+β 1 edu j +X j ∆+αC j ×edu j +δC j + L l=1 α l r l + ijl (1)
with Y ijl = 1 (H ijl <-2) equals one for a lower than normal Z-score; zero otherwise. X i corresponds to child sex and age, edu j indicating whether caretaker j for child i has at least a primary school level, X j includes caretaker's age and its square, C j indicates if the household lives in a camp, r l = 1 if the area considered is l. Errors are assumed to follow a standard Gaussian distribution.

There is no control related to the father (in particular education) simply because information on the father is lacking. [START_REF] Aslam | Parental education and child health: Understanding the pathways of impact in Pakistan[END_REF] nd that maternal education mattered more for actual health and paternal for vaccination. There is very often, if not always, a strong and positive correlation between spouses' education. To that extent by measuring the caretaker's education, we are capturing the global eect of education in the household.

Wealth is not reported whereas it is an important determinant of child health. It is not clear however that people in camps have any wealth and if so whether some households would actually be wealthier than others. In many countries in sub-Saharan Africa, wealth is often measured by the land quantity or owned cattle which is typically left behind. Wealth is sometimes measured by an asset index and asset possession used to be part of the questionnaires for IDPs. However less than 5% of the population hold each of the assets (and we expect a much lower percentage for the crisis period under study) and for this reason it is no longer collected and therefore building an asset index is not possible. In the end, the regression does not include controls for wealth.

It should be emphasized that it is not possible to capture the causal effect of education. This is not an issue in the sense that our interest lies in assessing the dierential eect between the two groups. If educated mothers are also healthier then they are more likely to be educated and transmit good genes to their child. Innate ability might translate into higher schooling and better care of the children. Finally time preferences translate into more patient individuals being more likely to go to school and also take better care of the children (through more long term investment such as vaccination for example). To summarize, whether in the camps or outside the camps, the eect of education could be overestimated (the level of education is so low that, as argued later, the bias is likely small). Since all biases go in the same direction, the sign of the dierence between the educated and uneducated mothers will be correctly captured. Coming back to the selection into camp bias, we expect this bias to be orthogonal to the bias existing between educated and uneducated women (especially since the unpredictability of the famine can be seen as an exogenous shock for entering camps).

As the conditions outside camps are not representative of what all Somalis experience, another way to look at the eect of the camp is to investigate whether time spent in the camp has any eect which is undertaken hereafter.

Double dierence strategy

We want to see whether the relative advantage of educated mothers vanishes away with time spent in the camp. As the camp provides a homogeneous provision of care, the dierences previously shown might simply translate the ability of educated mothers to take advantage of the newly available opportunities as they arrive. If the relative advantage of educated mothers widens then educated mothers might also be better at utilizing the infrastructure available. We are therefore interested in the interaction term between education and time spent in the camp, duration.

However, duration is not readily available. Fortunately in Deyr 2011 and Gu 2012 assessments, a question regarding the residency status indicates whether households have spent more or less than six months in the camp (they could also report to be residents, i.e. households from the region who came into the camp). Based on this, a double dierence strategy is used.

The rst dierence lies in the comparison of households who spent less than six months in the camp, later referred as new; with households who spent more (old). Note that it will cancel out any year specic eect. The second dierence compares regressions for Deyr 2011 and six months later (i.e. Gu 2012). The assessments not constituting panel data, the analysis therefore consists in exploiting the pseudo-panel dimension of the data and the following assumptions are made: The eect of education on health for the new people is captured by:

β 0 edu + β 1 edu × duration = β 0 edu + β 1 edu × d
The Deyr 2011 survey has two groups of people: the new and the old. Old

β 0 edu + β 1 edu × D β 0 edu + β 1 edu × (D + 6) New β 0 edu + β 1 edu × d β 0 edu + β 1 edu × d Dierence (Old -New) β 1 edu × (D -d) β 1 edu × (D + 6 -d)
Dierentiating out the eect in the Gu 2012 survey from the eect in the Deyr 2011 survey, one obtains the dierential eect of mother education according to whether she has spent six more months in the camp:

[β 1 edu × (D + 6 -d)] -[β 1 edu × (D -d)] = 6β
β 0 edu + β 1 edu × D β 0 edu + β 1 edu × (D + 6)
New in 2011, old in 2012

β 0 edu + β 1 edu × d β 0 edu + β 1 edu × (d + 6)
New in 2012

β 0 edu + β 1 edu × d Dierence (Old -New) β 1 edu × (D -d) β 1 edu (α(D + 6) + (1 -α)(d + 6) -d) = β 1 edu × (α(D -d) + 6)
d stands for the duration of households who spent less than six months; D > d stands for those who spent more than six months. α is the share of people old in Deyr 2011.

Finally dierentiating out between the two dates, one obtains:

β 1 edu × ((1 -α)(d -D) + 6) (2)
Of course, assuming α close to one, leads to the previous case and it is as if we had the four previous groups. α can a priori be assessed from the proportion of newcomers in Deyr 2011 and to the extent that the population and proportion are roughly the same six months later the values of α, d and D can be recovered. Assuming that people who spent less than six months in the camp have spent on average 3 months and that people who spent more than six months spent on average two years (based on qualitative interviews with the enumerators) leads to d = 3 and D = 24. From the data, (1 -α) could be assessed to equal 0.12. However the number of people who spent less than six months seems too small for dierentiating out any eect in Berbera, Bossaso, Burao and Hargeysa. Withdrawing these camps leads to

(1 -α) = 0.18. With the preceding values, one obtains:

β 1 edu ((1 -α)(d -D) + 6) = β edu (0.18(3 -24) + 6) = β 1 edu 2.22
So that the double dierence strategy would capture the average additional eect of education when spending an extra 2.22 months in the camp.

Our evaluation of α might be an upper bound (newcomers are more likely to leave and therefore their proportion six months later is supposed to be smaller) and the extra number of months is a priori between 2.22 and 6.

In the rest of the paper this value is only referred to as spending an extra semester in the camp.

P (Z < -2) =α 0 edu + α 1 edu × duration + α 2 duration + α 3 × 1 (t=2012) + α 4 × 1 (t=2012) × duration + α 5 edu × 1 (t=2012) + α 6 edu × 1 (t=2012) × duration + ΓX c + L l=1 α l r l + X c
1 (t=2012) × more6m × edu , that is, coecient α 6 .
As a robustness check, the result section considers a similar model with the Z-score as the dependent variable and adds mother's health as a control.

Results

Among the city camp surveyed, three are in the North West where information outside the camp is lacking. A test of mean comparison between camps in the North West and the other camps showed no statistically signicant dierence for wasting and for education but did for the incidence of stunting and low mid-upper arm circumference. As the eect of education between camps in the North West and North East was found statistically dierent in the regressions (not shown) and no information outside camps in the North West is available, camps in that region are dropped. Camps next to Dhuusamareeb are removed since information on maternal education is missing for the Deyr 2011 assessment. For the Gu 2012 assessment, there were no signiciant dierence whether the camp was included in the sample or not.

Table 3 presents the coecient for the probit model in equation 1 2 . Table 2 The coecients of the probit models are reported as opposed to the marginal eect as the interest lies in knowing whether there is a dierential eect between the groups of educated and uneducated mothers [START_REF] Puhani | The treatment eect, the cross dierence, and the interaction term in nonlinear dierence-in-dierence models[END_REF]. Unsurprisingly the magnitude of the interaction term (with a computation that accounts for the fact that this magnitude is not reected by the marginal eect of the interaction term as highlighted by [START_REF] Ai | Interaction terms in logit and probit models[END_REF]) leads to similar conclusions. show a statistical dierence inside and outside camps. The total eect of education is also signicant for underweight. In the end, table 3 shows that the eect of education varies for short-to-middle term health outcomes. Table 4 mirrors this result with the total eect of education being signicant and positive for the four health outcomes. However, none of the health outcomes seem to be impacted dierently according to whether the caregiver lives in the camp or not 3 . This indicates that the eect of education in the camp is particularly salient to combat malnutrition more to simply improve the nutritional status which seems consistent with the opportunity that a camp may oer.

We now turn to the second estimation strategy. that the eect of maternal education on child health can dier for stunting and underweight. However, computing the total eect of education, it is only signicant and negative for the underweight outcome. This indicates that as time spent in the camp increases, educated mothers interact more or better in their new environment. Table 6 indicates the same patterns for the Z-scores.

The regression in column 3, with the weight for age Z-score (associated with underweight) indicates a dierential impact for educated mothers who spent a semester more in the camp. The total eect of education is positive and signicant at the 5% level, thereby conrming the results associated with underweight.

The previous estimations were based on having a cut-o value discriminate children in poor health from children in better health. Studies using Z-score are usually able to partial out the eect of parental health. For example, studies examining height-for-age (associated with stunting) usually control for the mother's height. In the dataset, there is no clear measure when investigating whether the z-score falls below two standard deviations.

to account for the caregiver's health. A measure of self-reported health is available such measures might be biased if some mothers fail to realize that they are sick. Another objective measure is available, the mid-upper arm circumference of the mother. There is no standardization available for this measure as the debate regarding the relevant cut-o point for adult MUAC has not been settled yet. If we nevertheless include a measure of the mid-upper arm circumference of the caretaker, we nd similar results as shown in the appendix tables 8 and 7. Controls regarding pregnancy or lactating status (which may be of particular interest when using the caretaker's arm circumference as a control) of the caretaker do not change the results.

These results are robust to the inclusion of camps in the North West 4 . To summarize the results, the comparison showed that educated mothers were more eective at tackling wasting inside the camps and that their relative advantage in tackling underweight increases with time spent in the camp.

Discussion

The previous section reveals that the situation inside and outside camps diers slightly for short-to-middle-term outcomes. The eect of mother's education was signicantly dierent only for wasting. Examining the dierential eect of education after spending an extra semester in the camp, we nd that children of educated women are doing even better as measured by a higher weight for age (and a lower probability for underweight). As wasting is an indicator of short term health and underweight more of a short to mid-4 Namely camps close to Hargeysa, as the two other city camps had less than 5% of newcomers and were therefore excluded.

dle term outcome, it is possible that certain amount of time in the camp is needed in order to see how the last episodes (which must have happened in the camp to see the actual eect of the camp) were handled by educated and uneducated caregivers. This would explain why the dierential eect for underweight is only captured when specically looking at the evolution of the eect of education in the camp and not when comparing with educated mothers outside the camps 5 . Indeed when we compare households inside and outside the camps, the households inside the camps might have been there

for a short time, yet all households are pooled together regardless of the time spent in the camp.

As has been argued in the introduction, the typical power structure change inside the household is unlikely driving the eect of education. Also the ability to manipulate the modern world, as care is provided equally, is unlikely to occur. However if the eect of education is not strictly in the higher probability to interact with medical infrastructure but in their better utilization, then the eect of education will still occur and should be higher for short term outcomes inside camps than outside camps where medical care might be less available (medical aid provided in IDP camps usually aims at addressing immediate needs though vaccination, which is not only for short-term outcomes and is always provided when possible). This explanation seems to t in with the results obtained. Indeed, the eect on underweight is stronger inside camps (actually there seems to be no eect of 5 In the simple comparison, the total eect for underweight was signicant, it was simply not signicantly dierent from the eect that educated mothers had on their ospring outside camps.

education outside camps). The total eect of education for wasting was not signicant the interaction on its own was still suggesting a potentially dierent eect of education inside camps.

If the eect of maternal education transits through this better utilization of health infrastructure, then as long as aid and health care are provided, this eect should hold. Provided that it is only about utilizing health infrastructure better, then uneducated mothers should be able to learn and catch up their educated counterparts so that the relative dierence of educated mothers should vanish away 6 . The results focusing on the comparison of educated and uneducated mothers in the camp according to time spent in the camp showed that on the contrary the relative advantage of mother education increased as time spent in the camp increased. A possible explanation is that educated mothers are more likely to notice when their child is sick. If it is so, then in addition to the care provided quasi uniformly in the camp, educated mothers might interact faster whenever their child needs assistance.

We come back to the potential non causal eect of education. As education is not instrumented, one could think that the caretaker's schooling encompasses dierent preferences for the present, better health or higher ability that would overestimate the eect of education. As argued, the previous strategy assessed the dierential eect of education when in the camp 6 [START_REF] Thomas | How does mother's education aect child height? Journal of human resources[END_REF] nd on Brazilian data that almost all of the impact of mother's education could be explained by indicators of her access to information so that both the availability and procession of information are determinant in the impovement of a child's health.

so that the implications of not assessing the eect were very limited.

We would like to add here that the endogeneity of education when schooling levels are low is likely small as well. Indeed taking the endogeneity linked with health, it can be argued that missing days of schooling or paying less attention to school because one is sick, might have stronger implications for higher level of education. The primary schools are relatively more widespread than other types of school and to that extent any distance that could discourage less healthy children to be sent to school is likely to be more important for higher level of schools. Time preferences are often linked to the relative cost of schooling compared with the future potential foregone revenues.

Clearly the cost of schooling as a real cost (in terms of transportation for example) or as an opportunity cost (if the child could be working/helping) is higher as the level of education increases and therefore the time preferences are less obvious for such low level of schooling. Second, we are interested in the dierential eect of being in a camp. The fact that preferences for the present could be dierent inside and outside camps is arguable. What is even more arguable, would be to believe that these preferences could induce a dierent eect of the education on the health outcomes measured between households inside the camps and households outside the camps, knowing that we are controlling for the eect of the camp. A priori, endogeneity issue should be removed by (at least) the double dierence strategy.

The fact that time spent in the camp tend to increase the dierences between educated and uneducated mothers might not necessarily be true for all amount of time spent in the camp. It is possible that for households who have already spent a year and a half in the camp, the is no longer true. Because time spent in the camp cannot be assessed and because only two assessments were available, assessing a non linear eect of time spent in the camp is dicult. Adding more waves would certainly not allow for a non linear assessment either as the assumption that households remain in the camp is dicult to defend for a longer period of time, in particular its exogeneity. As each person in the camp has been there for a dierent amount of time, it is at least possible to say that on average spending an extra semester gives a stronger advantage to educated mothers.

Conclusion

This paper has examined how maternal education aects her ospring's health in the context of internally displaced person camps. Comparing households inside camps with households outside camps, we nd that the eect of mother's education diers for wasting. We also compare households inside camps depending on their length of stay and we nd that education is still an important factor for tackling malnutrition. The eect of mother's education seems to be increasing with time spent in the camp for underweight and the associated weight for age so that the advantage of mothers with at least primary schooling does not vanish away. In a context of destitution, the results highlight the role played by maternal education on child health not only as a way to improve child health but also as a factor of resilience.

  Somalia has been under civil war since Siad Barre's regime collapse in 1991. The North with Puntland in the East and Somaliland in the West, rapidly separated from the South and gained security while South-Central Somalia is still unstable. In addition to the conict, the famine hit the country in 2011 and left many pastoralists destitute which exogenously increased the number of IDPs in the whole country. The Food Security and Nutrition Analysis Unit for Somalia (FSNAU) was created to provide data and analysis on food security, nutrition and livelihoods. It has been conducting surveys since 1994 and since 2011 it provides, coordinating with other UN agencies, representative surveys for the Northern and Central regions of Somalia twice a year. The present study relies on two nutrition assessments called the (post) Deyr 2011 and the (post) Gu 2012 1 . As children represent the most sensitive segment of the population, their assessment is used as an indicator for 1 Gu and Deyr are Somalia's rainy seasons.

•

  Assumption A: The population of old and new people in Deyr 2011 are similar to the old people in Gu 2012, except for the fact that they have spent six more months in the camp. • Assumption B: New individuals have spent an amount of time d (in months) in the camp. In other words, new people in Deyr 2011 had on average spent d ∈ (0, 6) months in the camp at the time of the Deyr 2011 survey. People considered as new in Gu 2012 had also spent an average of d months in the camp at the time of the Gu 2012 survey.

  In the Gu 2012 survey, taking place six months after the Deyr 2011, we have three groups of people: the new in 2012, and, among the old in 2012, those who were old in 2011 and those who were new in 2011 (that is the new in 2011 become old in 2012). The double dierence strategy would consist in comparing the four groups made up of: people new in 2011 (who spent d months in the camp), people new in 2012 (who also spent d months in the camp), old people in 2011 (who spent D > d months in the camp), and nally old people in 2011 six months later (who spent D + 6 months in the camp). Again, as we do not have panel data, new people six months later should be read as a group representative of the people new in 2011, interviewed in Gu 2012 and old people six months later should be read as a group representative of the people old in 2011 interviewed in Gu 2012.The eect of education on each group is best described by the

  1 edu However this is not exactly what we have. New households in 2011 became old households in 2012. And old households in 2011 are still old households in 2012. To that extent, among the old households in 2012, it is not possible to distinguish who was also old in 2011 from who was new in 2011. In other words, the old group in 2012 (the group in bold in the previous table) is not solely composed of the old households from 2011. The groups at hand are the four groups illustrated in the following table: proportion of old households in Deyr 2011 (and (1 -α) the proportion of new households in Deyr 2011).

4

  presents the estimates the underlying height for age, weight for height, weight for age and the mid-upper arm circumference (muac). The rst column of table 3 in panel A shows the results with local xed eects of the logit regression of the four health outcomes for people living outside camps. The second column for households living in the camps and the third column for both samples. Panel B shows the same regressions without regional xed eects. To partially account for local characteristics, the specications without xed eects controls for the prevalence of malnutrition at the local level. Results are similar whether these controls are included or not.More generally the results are similar with or without xed eects (which may be due to the large areas taken into account for the xed eects) and we focus on panel A. The results of the third column panel A indicates that the eect of the caregiver's education is signicantly dierent inside and outside camps for wasting. The total eect of education (by itself and through its interaction) is also signicant and negative. None of the other outcomes

Figure 1 :

 1 Figure 1: Map of Somalia with main cities, including the cities with the IDP camps in the survey.

Table 1 :

 1 Table1shows the dieren-tiation that is actually taking place when the double dierence strategy is used. Arrivals in the camps, assessment period and eect of education

	Deyr 2011	Gu 2012
	Old in 2011 and 2012

Table 1

 1

simplied the notations by showing only the eect for education, yet the model is (removing individual and mother subscripts) :

  encompasses child gender, age, its square, age of the caretaker and its square. 1 (t=2012) is an indicator equal to one if the assessment corresponds to Gu 2012. duration is time spent in the camp. Note that the value of duration is not known (as d and D are not known and we do not impute

	called more6m equal to one if households been there for more than
	six months (zero otherwise) is introduced. The eect on health of spending
	an extra semester in the camp interacted with education will be captured by
	the values we assessed to them into the regression). Instead, an indicator

  Table 5 displays the coecients for the double dierence regressions with region xed eects. The camps next to Bossaso are dropped because the number of households present for less than six months is too small to capture any eect. As a result, only the camps next to Galkayo, Garowe and Qardho are used. The results show

Table 3 :

 3 Probit estimations for the binary health of children 7 -59 months old

		Panel A: Fixed eects	Panel B: No xed eects
	Stunting
	primary school (edu)	-0.121	-0.109	-0.124	-0.150	-0.107	-0.149
		(0.093)	(0.095)	(0.092)	(0.092)	(0.095)	(0.091)
	Camp			0.335**			0.050
				(0.154)			(0.093)
	Camp * edu			0.007			0.029
				(0.132)			(0.131)
	Wasting
	primary school (edu)	0.058	-0.169*	0.058	0.059	-0.165*	0.061
		(0.088)	(0.100)	(0.088)	(0.088)	(0.100)	(0.088)
	Camp			0.085			-0.015
				(0.371)			(0.182)
	Camp * edu			-0.238*			-0.240*
	Underweight			(0.133)			(0.133)
	primary school (edu)	-0.202**	-0.179*	-0.201**	-0.217**	-0.180*	-0.214**
		(0.092)	(0.093)	(0.092)	(0.091)	(0.093)	(0.091)
	Camp			0.686*			0.185
				(0.386)			(0.195)
	Camp * edu			0.007			0.018
	mid-upper arm circumference < -2		(0.130)			(0.130)
	primary school (edu)	0.000	-0.099	0.002	0.004	-0.112	0.002
		(0.095)	(0.104)	(0.093)	(0.094)	(0.104)	(0.093)
	Camp			0.021			0.072
				(0.098)			(0.074)
	Camp * edu			-0.122			-0.125
				(0.139)			(0.139)
	N	1602	1720	3322	1602	1720	3322
	Population	Not Camp	Camp	all	Not Camp	Camp	all
	FE	Yes	Yes	Yes	No	No	No
	*p<.10, ** p<.05, *** p<.01; standard errors clustered at the household level in paren-
	theses. Controls include child gender, gender interacted with age, an order three poly-
	nomial for the child's age and an order three polynomial for caretaker's age. Region
	xed eects included when indicated.

Table 5 :

 5 Double dierence strategy p<.10, ** p<.05, *** p<.01; standard errors clustered at the household level in parentheses. Controls include child gender, gender interacted with age, an order three polynomial for the child's age and an order three polynomial for caretaker's age. Region xed eects included. p<.10, ** p<.05, *** p<.01; standard errors clustered at the household level in parentheses. Controls include child gender, gender interacted with age, an order three polynomial for the child's age and an order three polynomial for caretaker's age. Region xed eects included.

		Stunting	Wasting	Underweight
	more6m	-0.040	-0.137	-0.014	-0.193
		(0.128)	(0.137)	(0.126)	(0.136)
	1 (t=2012)	-0.038	-0.159	-0.033	-0.315
		(0.179)	(0.197)	(0.177)	(0.208)
	more6m # t	-0.164	0.212	-0.112	0.200
		(0.196)	(0.214)	(0.193)	(0.225)
	edu	-0.413	-0.291	-0.486	0.113
		(0.310)	(0.359)	(0.320)	(0.306)
	more6m # edu	0.410	0.124	0.359	-0.311
		(0.338)	(0.388)	(0.346)	(0.344)
	1 (t=2012) # edu	0.635	0.448	0.814*	0.023
		(0.452)	(0.515)	(0.462)	(0.487)
	more6m # 1 (t=2012) # edu -0.863*	-0.483	-0.973*	0.085
		(0.501)	(0.559)	(0.506)	(0.540)
	N	1720	1720	1720	1720
	Total eect edu (p-value)	0.157	0.194	0.069	0.589
	FE	Yes	Yes	Yes	Yes

**

Table 7 :

 7 Double dierence strategy controlling for the health p<.10, ** p<.05, *** p<.01; standard errors clustered at the household level in parentheses. Controls include child gender, gender interacted with age, an order three polynomial for the child's age and an order three polynomial for caretaker's age. Region xed eects included. A polynomial of order three is introduced to account for the caretaker's mid-upper arm circumference.

		(1)	(2)	(3)	(4)
		Stunting	Wasting	Underweight	Muac<-2
	more6m	-0.046	-0.145	-0.026	-0.206
		(0.128)	(0.137)	(0.126)	(0.136)
	1 (t=2012)	-0.040	-0.144	-0.028	-0.297
		(0.179)	(0.197)	(0.177)	(0.208)
	more6m# 1 (t=2012)	-0.160	0.202	-0.109	0.189
		(0.196)	(0.214)	(0.193)	(0.226)
	primary school (edu)	-0.425	-0.317	-0.504	0.075
		(0.309)	(0.361)	(0.322)	(0.306)
	more6m # edu	0.424	0.151	0.383	-0.275
		(0.338)	(0.389)	(0.348)	(0.345)
	1 (t=2012) # edu	0.652	0.482	0.834*	0.071
		(0.452)	(0.517)	(0.463)	(0.489)
	more6m# 1 (t=2012) # edu -0.880*	-0.511	-0.996**	0.047
		(0.501)	(0.560)	(0.507)	(0.542)
	N	1720	1720	1720	1720
	Total eect edu (p-value)	0.161	0.213	0.070	0.625
	FE	Yes	Yes	Yes	Yes

*

Table 8 :

 8 Double dierence strategy controlling for the caregiver's health p<.10, ** p<.05, *** p<.01; standard errors clustered at the household level in parentheses. Controls include child gender, gender interacted with age, an order three polynomial for the child's age and an order three polynomial for caretaker's age. Region xed effects included. A polynomial of order three is introduced to account for the caretaker's mid-upper arm circumference.

		(1)		(3)	(4)
		height for age	weight for height	weight for age	muac
	more6m	0.047	0.088	0.093	0.048
		(0.122)	(0.110)	(0.096)	(0.092)
	1 (t=2012)	-0.147	0.121	0.011	0.094
		(0.165)	(0.169)	(0.137)	(0.130)
	more6m # 1 (t=2012)	0.255	-0.195	-0.007	-0.028
		(0.178)	(0.181)	(0.148)	(0.140)
	edu	0.238	0.147	0.252	0.338
		(0.283)	(0.266)	(0.240)	(0.275)
	more6m # edu	-0.201	0.017	-0.116	-0.247
		(0.305)	(0.287)	(0.258)	(0.289)
	1 (t=2012) # edu	-0.326	-0.648*	-0.668**	-0.522
		(0.407)	(0.377)	(0.330)	(0.353)
	more6m # 1 (t=2012) # edu	0.490	0.637	0.766**	0.456
		(0.436)	(0.408)	(0.357)	(0.375)
	N	1720	1720	1720	1720
	Total eect edu (p-value)	0.049	0.185	0.016	0.788
	FE	Yes	Yes	Yes	Yes

*

For the sake of comparison and clarity, the results displayed restrict the population in camps to be the same as the population in camps used for the double dierence strategy afterwards. The double dierence strategy requires dropping the camps around Bossaso.If they were included, we would nd similar results: the relationship with education is signicantly dierent only for short to middle term health outcomes and appears only

Appendix


M Zerrad
email: mehdi.zerrad@insa-lyon.fr

N Totaro

R G Rinaldi

B Eller

Experimental characterization and numerical modeling of short-glass-fiber composite for vibroacoustic applications

In order to design vehicles with diminished CO2/km emissions level, car manufacturers -among alternativesaim at reducing the weight of their vehicles. One of the solutions pursued consists in the replacement of metallic structural parts by light weight polymer based composites ones. Naturally, with these new parts, NHV (Noise, Vibration and Harshness) engineers now face the challenge to predict their vibrational responses. In the present study, focusing on PA6 reinforced glass fiber oil pan, mechanical and microstructural characterizations, dynamic mechanical analysis (DMA) and X-ray tomography measurements respectively were performed and evidenced that the complex modulus of the parent material not only depends on temperature and frequency but also on humidity content and loading direction. The effect of temperature and humidity content was also evidenced on the vibratory response of the oil pan. Further experimental (modal analysis) and numerical (finite element modeling) comparisons up to 2000 Hz were conducted, showing that simplistic material's descriptions are not satisfactory.

Introduction

To diminish the ecological impact of their vehicles accordingly to new legislation, car manufacturersamong alternatives-aim at reducing their weight. One of the solutions advocated by the NVH (Noise, Vibration and Harshness) engineers is the replacement of metallic materials in structural parts by light weight polymer based composites. However, the use of these materials confronts engineers to the challenge of mastering their vibration and acoustic modeling taking into account the complex features of these new constitutive materials. Indeed, the mechanical performance of these composites depends on the intrinsic properties of the constituents (matrix and fillers), their respective volume fractions and various microstructural parameters such as the shape factor, dispersion and arrangement of the reinforcing fillers [START_REF] Bernasconi | Analysis of the effect of mechanical recycling upon tensile strength of a short glass fibre reinforced polyamide 6,6[END_REF]. Here, the Young's modulus and the loss factor (damping) of Polyamide 6 filled with 35% by mass short glass fibers (denoted PA6-GF35 hereafter) depend on temperature [START_REF] Crupi | Application of Digital Image Correlation for the effect of glass fibres on the strength and strain to failure of polyamide plastics[END_REF], frequency [START_REF] Steffens | Method for Simulating the NVH Behavior of Plastic Materials[END_REF], moisture [START_REF] Bernasconi | Analysis of the dependence of the tensile behaviour of a short fibre reinforced polyamide upon fibre volume fraction, length and orientation[END_REF], and the distribution of lengths and fiber diameters [START_REF] Bernasconi | Analysis of the dependence of the tensile behaviour of a short fibre reinforced polyamide upon fibre volume fraction, length and orientation[END_REF][START_REF] Bernasconi | Local anisotropy analysis of injection moulded fibre reinforced polymer composites[END_REF], their volume fractions [START_REF] Crupi | Application of Digital Image Correlation for the effect of glass fibres on the strength and strain to failure of polyamide plastics[END_REF] and their orientations [START_REF] Horst | Influence of fibre orientation on fatigue of short glassfibre reinforced Polyamide[END_REF].

Thus, our study focuses on the characterization of the various microstructural parameters of PA6-GF35 and on the understanding of their impact on the macroscopic vibration behavior of an automobile oil pan. More precisely, the effects of frequency, temperature, moisture and imposed loading in relation to the fibers' orientation on the complex modulus of the material is investigated. Consequently, the influence of temperature and moisture level on the vibratory response of the structure is also pursued. Finally, experimental and numerical modal analyses of the oil pan over a frequency range from 0 Hz to 2000 Hz are performed and compared, showing that a simple model with a constant complex Young modulus can be considered valid only at low frequencies (below 600 Hz). Longer term, the aim of this study is to assess the degree of accuracy required for the constitutive law to propose a persuasive test/calculation confrontation and use analytic predictive model such as the Cox-Krenchel model which allows to predict the Young's modulus with account for the microstructural parameters previously mentioned.

System under study: PA6-GF35 oil pan

The oil pan illustrated in figure 1 is a PA6-GF35 injection-molded part. The structure is constituted by a "main structure" assimilated to the general shape of the part, and numerous ribs that are stiffening the structure. Figure 1a also shows that the oil pan contains a metal tube and metal rings inserted in ten holes which are used to assembly the oil pan with the block cylinder. Dried, the part weighs 995.4 g including the aforementioned metal parts (m filter fixation = 110 g and m rings = 38 g). 2 Effect of temperature on the PA6-GF35

Effect of temperature on the vibration behavior of the structure

To assess the impact of temperature on the PA6-GF35 oil pan, transfer function measurements were carried out for four different temperatures: 20°C, 50°C, 80°C and 110°C (the latter being the operating temperature of the oil pan in the vehicle). The oil pan has been previously dried at 80°C under vacuum and measurements were performed for a constant humidity content of about 0.3%. The oil pan was suspended by an elastic link in an INSTRON® thermo-regulated chamber and the vibration measurements were performed using an impact hammer (average on five impacts) over a frequency range 0 Hz to 2000 Hz on a single measurement point randomly yet conveniently chosen. Figure 2 shows that the higher the temperature, the lower the natural frequencies. The observed offsets are limited to few Hz at low frequency but can exceed 100 Hz above 500 Hz. This means that the increase of the temperature decreases the Young's modulus of the constitutive material. In addition, the damping is highly increased as can be seen at resonance peaks in Figure 2. The variabilities of these measurements are only due to variations of the material properties. Indeed, a reproducibility study involving 4 operators was conducted to evaluate the influence of both the mounting and the operator on the measured transfer functions. The results are presented in Figure 3 showing that the four transfer functions of the four operators overlap over the entire frequency range investigated. To highlight the effect of temperature on the PA6-GF35 part, transfer functions measurements were also carried out on an aluminum oil pan (m Aluminum oil pan = 2.68 kg) for the same temperature range. The results are reported in figure 4 showing that the temperature has a slight impact on the aluminum oil pan More precisely, slight shifts of the resonance peaks to lower frequencies can be observed when increasing the temperature, with the offset increasing as the resonance frequency increases; for instance, above 1000 Hz, the offset is about 10 Hz. The curves also allow to observe that, close to 2000 Hz, peaks are more damped for higher temperatures. However, when comparing Figure 4 and Figure 3, it is clear that even if the trends are the same for both parts, meaning the decrease of the Young modulus and increase of the damping of the parent materials, the effect of temperature is more pronounced for the PA6-GF35.

Effect of temperature on the viscoelastic properties of the PA6-GF35

Dynamic Mechanical Analysis (DMA) were used to measure the complex modulus E* for prescribed frequencies and temperatures. Practically, a small amplitude sinusoidal loading displacement is imposed to the sample and the force signal, also sinusoidal but shifted, is measured. From both signals, the storage modulus E' (assimilated to the Young's modulus and denoted E hereafter), the loss modulus E'' and the loss factor tanδ can be computed. They relate to the complex modulus E* as follow:

E * = E ′ + i E ′′ = E ′ (1 + i tan δ) (1)
DMA analysis in three-point bending was performed on a cuboidal sample of dimensions 2.3 x 4.7 x 20 mm 3 and humidity content of 1.4%. The specimen was cut in the "main structure" of the oil pan and tested without prior treatment. Three frequencies (0.2 Hz, 1 Hz and 5 Hz) were tested for temperatures ranging from 0°C to 150°C (the engine operation temperature being 110°C). The results are reported in Figure 5 where the changes of the Young's modulus (see a) and loss factor (see b) as a function of temperature are shown for the three frequencies listed above. The higher the temperature the lower the Young's modulus, decreasing from a maximum value of 9000 MPa at 0°C to about 3000 MPa to 150°C. The maximum damping, often identified as the glass transition temperature Tg of the PA6 matrix (at 1Hz), is located at about 25°C, shifting towards higher temperature when the loading frequency increases. The temperature measured here is characteristic of PA6 materials plasticized by water [START_REF] Ed | Nylon plastics handbook[END_REF].

The evolution of the Young's modulus with temperature obtained by DMA confirms the observations made previously about the impact of temperature on the vibrational response of the PA6-GF35 oil pan, justifying why the measured natural frequencies are shifted to lower frequencies and why the damping is increased when the tested temperature is increased. 3 Effect of humidity content on the PA6-GF35

Effect of humidity content on the vibration behavior of the structure

In order to understand the effect of humidity content on the vibration behavior of the oil pan of PA6-GF35, transfer function measurements were performed at ambient temperature for three humidity contents. To do so, the oil pan was dried in air at 70 ° C for 10 days to reach a humidity level close to 0 %, and subsequently immersed in a water bath for two weeks to get a significant humidity content. The evolution of the humidity content has been followed by weighing the oil pan. Finally, measurements were carried out for humidity contents of 0.4%, 3.1%, and 5.2%. The results presented in Figure 6 show that humidity content has a significant influence on the vibration behavior of the PA6-GF35.

Figure 6: Transfer functions (acceleration over force) of the PA6-GF35 oil pan for three different levels of moisture: 0.4%, 3.1% and 0.4%.

It can be noticed that the higher the humidity content in the material the more the natural frequencies are shifted to lower frequencies with an offset greater than 100 Hz above 200 Hz. In other words, the lower the humidity content, the greater the stiffness of the part, i.e. the greater the Young's modulus of the parent material)

We can also notice that damping is greater at high humidity. Indeed, figure 6 shows that for the transfer function measured at 5.2% of humidity the resonance peaks disappear completely above 1000 Hz. It is worth noting that moisturized PA6-based materials exhibit their glass transition temperature Tg around room temperature (as already discussed with the DMA results in Figure 5b, here coinciding with the testing temperature [START_REF]Mechanical performance of polyamides with influence of moisture and temperature -Accurate evaluation and better understanding[END_REF]).

Effect of humidity content on the parent material

To further evidence the importance of the humidity content on the mechanical performance of PA6-GF35 around ambient temperature, the humidity content was changed on one sample and the complex modulus measured by DMA. The various states are obtained by drying (vacuum oven) and immersion in water bath, and the content was monitored by weighing the specimen. Furthermore, the weighing was performed before and after each test to confirm that the humidity content remained constant throughout the test.

Figure 7 shows the evolution of the Young's modulus as a function of the humidity content between 30 ° C and 70 ° C. The study shows that the Young's modulus decreases when the humidity content increases; at 30°C, the modulus drops from 8000 MPa for the driest case (0.3% moisture) to 4200 MPa for the most waterlogged case (2.6% moisture). The DMA results are consistent with the vibration behavior of the PA6-GF35 part when the PA6 matrix is dried, its glass transition temperature Tg is around 50°C [START_REF] Reimschuessel | Water on Glass Transition Temperature and Young's Modulus of Nylon 6[END_REF], so the more the material is wet the more its glass transition temperature is shifted to the low temperature. In the case of this study, the curves in figure 6 has been measured at ambient temperature, so the loss factor (damping) increases when moisture level increases (Figure 5).

Effect of the glass fiber on the viscoelastic properties of the PA6-GF35

PA6-GF35 microstructural characterization

X-rays tomography is a non-destructive 3D imaging technique which allows to observe a material microstructure at the micron scale. The sample is positioned between the source and the detector so that the gray level of a reconstructed 2D image reflect differences in absorption of X-rays. In the case of PA6-GF35, this technique is particularly suited for dissociating the fibers from the matrix and thus study the geometrical properties of these last.

Here, a 2.5x2.5x2.5xmm 3 volume of material located in the main structure has been imaged at 2 microns resolution.

Figure 8 shows a series of images illustrating the sizes, orientations and dispersion of fibers (white elements) in this limited volume of material. It should be noted that the planes 3 and 4 display sections of the all thickness of the oil pan. Images 1 and 2 correspond to planes parallel to the mold surface, and reveal that approaching the free surface (the surfaces contacting the mold during the injection step), the fibers are relatively randomly oriented in the plane parallel to the mold surface. The fibers' orientations are typical of injection molded parts, where the mold promotes cooling and solidification of the fibers in a disordered state [START_REF] Bernasconi | Analysis of the effect of mechanical recycling upon tensile strength of a short glass fibre reinforced polyamide 6,6[END_REF]. The Comparison of images 3 and 4 highlight a higher fiber density near the center of the thickness, also a consequence of the injection process [START_REF] Horst | Influence of fibre orientation on fatigue of short glassfibre reinforced Polyamide[END_REF]. The evolution of the through-thickness fiber concentration is also qualitatively observed in images 1 and 2, the density of fibers being substantially greater in the central region (e/2). To quantify the fiber content and its variations, the images are "thresholded" to separate the matrix (dark voxels) from the fibers (light voxels) and FIJI © algorithm [10] has been used to calculate the corresponding volume fraction of fibers with respect to the 3 main directions of the cubic scanned region. Finally the fiber volume fraction with respect to the relative position along the 3 axis are calculated and displayed in figure 8b. The profiles are homogeneous and uniform for the two directions collinear to the surface of the mold. Conversely, the fiber density varies depending on the position along the thickness, in accordance with the qualitative observations made in figure 2a. In the scanned volume, the average volume fraction of fibers is approximately 0.2, which is in agreement with the mean mass fraction (35%). The X-rays tomography also allows to reconstruct a 3D image of the material (see inset in figure 8a). Such reconstruction, performed close to the free surface, confirms that the fibers are oriented in a preferred direction: the direction of the material's flow during the injection, suggesting an anisotropic behavior, studied in the following.

Mechanical anisotropy of a PA6-GF35 sample

Tests were conducted to test the hypothesis of mechanical anisotropy suggested by the X-ray study of the microstructure. More specifically, DMA measurements in bending mode were performed on the same sample along two preferred directions which are detailed in Figure 9a. The comparison between the Young's modulus measured in the vicinity of ambient temperature is given in figure 9b. A difference of about 2000 MPa is observed, corresponding to a relative change of about 30%, confirming the anisotropy of PA6-GF35. It is worth noting that testing two samples aligned or perpendicular to the major fibers orientation axis should lead to greater discrepancies.

5 Modal analysis test/calculation correlation of the PA6-GF35 oil pan and moisture influence

Experimental modal analysis

An experimental modal analysis was performed on a PA6-GF35 oil pan. The measurements of the acceleration/force transfer functions were made on a frequency range of 0 Hz to 2000 Hz with the oil pan suspended by an elastic link. A fixed accelerometer was mounted on a measuring point and impacts have been applied on the 182 points of the oil pan. The measurements were conducted at an average temperature of 27 °C .The mass of the oil pan was 1005 g comprising the mass of the tube (110 g) and the metal inserts (38.6 g). Measurements were post-processed using the PULSE B & K software to extract the natural frequencies and modes shapes using a modal analysis algorithm.

Numerical modal analysis

Cox-Krenchel model

The Cox-Krenchel model has been suggested to predict the Young's modulus of short fiber composite with account for the reinforcement specificities (orientation, concentration, aspect ratio …). In our case, with the composite, the matrix and the fibers depicted with the subscripts PA6-GF35, PA6 and f respectively, the modulus of the composite is expressed as follow:

E PA6-GF35 = η 0 ν f E f (1 - tanh(ns) ns ) + (1 -ν f ) E PA6 (2)
n = √ 2E PA6 E f (1 -ν PA6 )ln ( 1 ν f ) (3)
s = L w d (4)
where 𝜂 0 is the orientation factor which varies between 0.3 (random fiber orientation) to 1 (fibers oriented in the same direction). 𝜈 𝑓 , 𝐿 𝑤 and 𝑑 correspond to the fiber volume fraction, the average length and the average fiber diameter respectively. These quantities can be measured after pyrolysis of the composite and observation of the remaining fibers with a scanning electron microscope (SEM). Naturally, the frequency, temperature and moisture dependencies of the Young's modulus evidenced experimentally are integrated in the matrix Young's:

E PA6 = f(temperature, frequency, moisture)
Since the purpose of this work is to identify the level of sophistication necessary to model the complex Young modulus of the system to obtain a good calculation/test correlation, the numerical simulations were performed with the most simplistic numerical model with a homogeneous isotropic Young's modulus, as detailed in the paragraph below.

Correlation with homogenous isotropic Young's modulus

The numerical modal analysis of the oil pan was performed on a frequency range of 0 Hz to 2000 Hz. The Poisson's ratio used is  = 0.33 and the density is ρ = 1400 kg/m 3 , consistent with experimental measurements. Three Young's modulus obtained by DMA and corresponding to three different humidity levels (see Figure 7 and Table 1) were used for calculations in order to see the influence of humidity content on the modal analysis correlation.

The modulus E=5550 MPa corresponds to the temperature and humidity conditions under which the vibration test was performed.

Moisture (%) Young's modulus (MPa) 0.3 7545 1.3 5550 2.6 4064

Table 1: DMA Modulus of the PA6-GF35 for different humidity content.

The oil pan was meshed with parabolic tetra elements and 534717 degrees of freedom. The metallic tube and rings were modeled with punctual mass elements CONM2 with mass values of 110 g for the filter attachment tube and of 3.86 g for each ring respectively. The calculation was performed using the finite element code Nastran©.

The MAC (Modal Assurance Criterion) index is used to assess the mode shapes calculation / test correlation. A MAC value of 1 indicates a perfect correlation between experimental and numerical mode shapes. Conversely, a value of 0 indicates a non-existent correlation. It is commonly accepted that the correlation is satisfactory for a MAC index higher than 0.8.

The comparison between the measured modes and computed ones are presented in Figure 10. Modeling the oil pan with a homogeneous isotropic modulus obtained by DMA yields a good test/calculation correlation only at low frequency (below 600 Hz). From 600 Hz to 1500 Hz, the mode shapes are mostly undetected or less correlated, indicating that the numerical model solely consisting of an isotropic fixed Young's modulus is too simplistic compared to the anisotropic and frequency dependent behavior evidenced in the above.

Figure 10: Modal analysis calculation/test correlation of the PA6-GF35 for three different Young's modulus at three different moisture level: triangles: E=4064 MPa; squares: E=5553 MPa; diamonds: E=7545 MPa. Colored circles represent the experimental eigen-frequencies (size of the circle represent the degree of correlation between numerical and experimental mode shapes, biggest is best).

It is also observed that from 600 Hz to 1500 Hz mode shapes are mostly undetected or less correlated, indicating that the experimental modal analysis does not help, as such, to conclude the representativeness of a numerical model with such a Young's modulus, simplistic compared to the reality of the material behavior, evidenced as anisotropic and frequency dependent in the above.

The calculations with Young's modulus corresponding to the moisture contents of 0.3% and 2.6% show the same trend and confirm the impact of the moisture on natural frequencies of the oil pan: the natural frequencies of the wettest cases are lower than those of the dry case, justified by an important decrease of the parent material's modulus.

Finally, it will therefore be necessary to refine the model in order to approach the reality, with taking into account the effect of the frequency and the anisotropy of Young' modulus [START_REF] Risitano | Analisi numerica-sperimentale dell'influenza delle caratteristiche elastiche dei materiali compositi sulle proprietà di vibrare[END_REF]. Obviously, the damping frequency dependency has to be considered as well.

Conclusion

In this study the impact of temperature and humidity on the vibration response of the PA6-GF35 oil pan has been evidenced and discussed/justified by studying the effect of these parameters on the mechanical behavior of the constitutive composite material. Indeed, the PA6-GF35 material was characterized and a "multi-layer" structure leading to heterogeneous Young's modulus depending on the geometry and more specifically the thickness (a consequence of reinforcing fillers) evidenced.

The low frequency room temperature Young's modulus obtained by DMA for a prescribed humidity content was used as an input in a calculation of numerical modal analysis and allowed performing a comparison with the experimental modal analysis. It was found that natural frequencies and mode shapes test/calculation correlation is relevant up to a frequency of 600 Hz. However, at higher frequencies the small number of modes detected by experimental modal analysis does not allow the observation of the oil pan vibrational behavior between and 600 Hz and 2000 Hz. In addition, modal analysis calculations were performed for two Young's moduli corresponding to two different humidity contents to evidence the strong effect of the contained humidity on the vibrational response of the structure.

Frequency response test/calculation correlations have to be made to get a more accurate correlation at mid frequency. Also, taking into account the frequency dependence of the matrix (for both the modulus and the Numerical predictions for different humidity content damping) and the materials anisotropy resulting from the fibers orientation have now to be considered to model in a more relevant manner the real behavior of the short fiber reinforced polymer based composite [START_REF] Calmels | Anisotropic Damping Behavior of Reinforced Plastic Parts for NVH Simulations[END_REF], and ultimately the vibration response of the pan. To do so, the use of the Cox-Krenchel shear lag model is currently pursued.

Figure 1 :

 1 Figure 1: (a) PA6-GF35 oil pan. The bottom right image shows the mounted metal rings. The top right image highlights a section of the "main structure" and ribs from a cutting element of the oil pan. (b) Aluminum oil pan (N.B. both images are not on the same scale).

Figure 2 :

 2 Figure 2: Effect of temperature on the transfer functions (acceleration over force) of the PA6-GF35 oil pan.

Figure 3 :

 3 Figure 3: Transfer functions obtained by four different operators on the PA6-GF35 oil pan at a constant temperature (Tamb) and moisture.

Figure 4 :

 4 Figure 4: Effect of temperature on the transfer functions (acceleration over force) of the aluminum oil pan over a frequency range from 0 Hz to 2000 Hz.

Figure 5 :

 5 Figure 5: Young's modulus and the loss factor as a function of temperature and frequency obtained by DMA on a PA6-GF35 sample cut from the oil pan.

Figure 7 :

 7 Figure 7: Young's modulus measured by DMA as a function of the moisture level (percent values next to the curves) and temperature at 1 Hz.

Figure 8 :

 8 Figure 8 : (a) Tomography X-rays images of a sample cut from the oil pan and a 3D reconstruction of a volume of glass fibers near the surface of the mold with a dimension of 500x500x500 m 3 (Voxel size = 8 µm 3 ). (b) Glass fibers volume fractions in the 3 main directions of the scanned volume. N.B. Grayscale curves coincide with the color code of the axis system schemed in (a).

Figure 9 :

 9 Figure 9: (a) 3-points bending tests, and illustration of the arrangement of fibers relative to the loading. (b) Effect of orientation of the loading on the Young's modulus measured in 3-points flexion by DMA. Several measurement series demonstrate the repeatability of measurements.

Acknowledgements

This work was performed within the framework of the Labex CelyA of université de Lyon, operated by the French National Research Agency (ANR-10-LABX-0060/ ANR-11-IDEX-0007).

The authors would like to thank Misses A. Hautier and C. Rougier for their assistance for conducting this study.