PhD. Julien Giry
email: giry@mmsh.univ-aix.fr

A SPECIFIC SOCIAL FUNCTION OF RUMORS AND CONSPIRACY THEORIES: STRENGHTENING COMMUNITY'S TIES IN TROUBLE TIMES. A MULTILEVEL ANALYSIS

Keywords:

This paper hypothesizes that conspiracy theories and rumors are an act of social conformism. The evaluation of their plausibility, and their success, is collectively determinate regarding the established values of an in-group and the social context. In periods of troubles they flourish to reaffirm them and strengthen community's ties, structures and leaderships. After a theoretical introduction, I will demonstrate this assumption through a multilevel analysis (macro, meso, micro) which considers a wide range of social situations from the French Revolution to neighborhood conflicts and from open riots to latent crises.

At the end of the 1940's, the American Administration was very preoccupied by rumors that circulated throughout the World War II. To understand this phenomenon, several social psychologists were committed to conduct studies [START_REF] Knapp | A Psychology of Rumor[END_REF]Allport, Postman 1947). They assumed that rumors were harmful (Rosnow, Fine, 1976: 26-17) because they deliver false information; that is why they must be fought to preserve the social order (Neubauer, 1999: 6-7). Knapp is particularly representative of this tendency 1 . To enhance peoples' confidence in mainstream media and the Administration, he recommended: 1°) issue /broadcast/spread news as quick as possible through modern media like TV networks and radios; 2°) issue/broadcast/spread news as wide and accessible as possible; 3°) prevent idleness, monotony and personal disorganization. Nonetheless, history and empirical studies have shown that those prescriptions do not work 2 . Quite the opposite, the more information circulates in the public sphere 3 ; the more rumors arise to bypass official statements particularly when governments and mainstream media suffer from a huge lack of confidence.

Rumors reveal trust in the people meanwhile they express, as counter power, defiance against official institutions (Fine, 2007: 7). They suggest that narratives circulating in the social body must be taken for real or acceptable when official statements are to be necessary incomplete, false or manipulated. It brings me to formulate a handful definitions, hypothesis and goals I can summarize in three points.

RESEARCH HYPOTHESIS AND DEFINITIONS

First, rumors considered as "unverified and instrumentally relevant information statements in circulation that arise in contexts of ambiguity, danger or potential threat, and that function to help people make sense and manage risk" (DiFonzo, Bordia, 2007: 19-20) and conspiracy theories (CTs) 4 simply defined as "the conviction that a secret, omnipotent individual or group covertly controls the political and social order or some part thereof, circulates solely on the margins of society" (Fenster, 2008: 1) 5 , develop in already cohesive communities because being involved in the spreading is an act of social conformism (Kapferer, 1990: 64). They flourish to reaffirm dominant and established values of an ingroup at the same time they exclude the outsiders usually negatively portrayed. Rumors and 1 See also : Allport, Lepkin, 1945. 2 For a general the state-of-the-art review on the study of rumors in social sciences, see: Donovan 2007. 3 For discussion: Al-Kandari, 2010: 61-62 4 Or, rumor is "an unverified account or explanation of events, circulating from person to person an pertaining to an object, event, or issue of public concern" (Peterson, Gist, 1951: 159). 5 See also [START_REF] Hall | Aligning Darkness with Conspiracy Theory: The Discursive Effect of African American Interest in Gary Webb's "Dark Alliance[END_REF] argues that CTs are the belief that a group of people ("them") secretly plot to harm another social group ("us") in order to pursuit, archive or maintain their own interest.

[3] CTs circulate in a group which has already clear idea of the dichotomies "the Self/the Others" or "Us/Them" (Aldrin, 2005: 225-248). And, this stereotypic and prejudicial evaluation of the others intensifies when the members of the group feel a threat to their positions or self-esteem [START_REF] Brown | Coming to Terms with Failure: Self-Enhancement and Public Self-Effacement[END_REF]. For peoples who disseminate them, it enhancessymbolically at leastthe feeling to belonging to a superior group. In thy way, rumors and CTs fulfill an "ego-defensive function" [START_REF] Katz | The Functional Approach to the Study of Attitudes[END_REF] which serves to defend and promote what is accepted against different social behaviors. Peoples using this function are more likely to share strong biases and negative stereotypes against others. It conversely offers comfort to individual who want to retreat from world complexity and diversity. This ego-defensive function develops a positive self-image in social gathering. So that, rumors and CTs must be seen as a social process, an acceptable collective deliberation or narrative for the group in which they circulate because they can develop only if they seem plausible regarding the deep-rooted values of a group and the social context. It is to say that the evaluation of the plausibility of the very same narrative differs from one group to another because they do not share the same collective imaginary, collective memory, biases and symbolical stereotypes. Rouquette called this phenomenon implication (1990: 119-120).

For instance, among African Americans, AIDS is mostly view as a human-made or government-made disease not only because they represent half of the infected peoples, but also for AIDS is seen as an instrument of a "Black genocide". As shown in a 1999 survey, "compared with Whites, roughly three times as many Blacks and Hispanics reported that it was 'very or somewhat likely' that AIDS is 'the result of a government plan to intentionally kill a certain group of people by genocide' (27.8% of Blacks, 23.6% Hispanics, 8% of Whites). In the 2003 survey, roughly four times as many Blacks and almost 3 times as many Hispanics compared with Whites (34.1% of Blacks, 21.9% of Hispanics, 8.4% Whites) reported that it was 'very or somewhat likely' that AIDS is 'the result of a government plan to intentionally kill a certain group of people by genocide'" (Russel, Katz, alia., 2011: 40-41).

Put another way, evaluating plausibility of hearsays is not only assessed by individuals, but is linked to interaction contexts and social systems. Plausibility, and its evaluation, is already tied to communities and collective judgments (Fine, 2007: 9). In other words, I challenge the idea that rumors and CTs create ties amongst the peoples who share and repeat them; those ties do preexist and this is the reason why they can circulate within a group (hypothesis 1)6 .

Secondly, even though it is well-known that rumors and CTs flourish in periods of war and political destabilization to mobilize a community in danger, whatever this danger is real or not, I will stress that they also appear in more latent struggles. Rumors and CTs do not need wars, riots or revolutions to emerge; a mere situation a social change or insecurity, a challenge to the in-group's status security [START_REF] Pettigrew | Reactions towards the New Minorities of Western Europe[END_REF] is enough to start them: the rise of new leaders in a stable community [START_REF] Festinger | A Study of Rumor: Its Origin and Spread[END_REF], the arrival of outsiders in a neighborhood (Elias, Scotson, 1965) or the development of trendy clothes stores [START_REF] Morin | La rumeur d'Orléans[END_REF]. This is why I have chosen for the title of this article "trouble times" instead of crisis, struggle, conflict or war. It looks more appropriated to cover all the situations I examine. From riots to latent oppositions in suburbs, I am willing to prove that rumors and conspiracy theories fulfil the social function of strengthening community's ties at all levels (hypothesis 2). To demonstrate this assumption, I will consider three classical levels of social interactions. First, at the macro level, I will remind how rumors and CTs play a significant part in periods of open and violent conflicts regarding the entire society like the French Revolution or ethno-confessional riots in the post-colonial India (1). Secondly, at the meso or intermediary level, I will dwell on limited but dramatic cases of violent confrontation with the authorities of dissident groups such as the events in Jonestown, Guyana, in 1978 andWaco, Texas, in 1993 (2). In this section I will particularly emphasis the Jonestown case because there is a lot a very relevant first hand material about how the dynamics of rumors and conspiracy theories play a significant part in the mass-murder/suicide that happened on November 18 th 1978. Thirdly, at the micro level of a neighborhood, I will argue that even though there is no violent conflict, rumors arise to reaffirmsymbolically at leastthe dominant values and habits of established groups. Then, they contribute to strengthen social conformism and secured old-line leaderships as well. Two cases will be taken into account: an established and cohesive group challenged by outsiders; an established social leadership challenged by an insider trying to improve his own social position (3).

developed by social actors who support CTs. Robert K. Merton called them manifest functions (1968: 73-138). Quite the opposite, latent functions, 3 out of 7, are unconscious, unintended but beneficial. Put another way, manifest functions are the consequences that people observe or expect. They are explicitly stated and understood by the participants in the relevant action whereas latent functions are unexpected in their developments, goals and results. Manifest functions are: 1°) a function of explanation and simplification of the historical process; 2°) a function of reification of the social process; 3°) a function of mobilization; 4°) a function of politicization and legitimization. Latent functions are: 1°) a function of paradoxical rationalization; 2°) a tribunitienne function (Lavau 1981: 342); 3°) a symbolic function.

Finally, this article will highlight the articulation between conspiracy theories and rumors as previously defined. It is to show how rumors as infra-political narratives7 and conspiracy theories as theories of power (Viltard, 2003:92), global and political narratives echo into one another. How the big picture of a largescale conspiracy led by government officials, communist agents or nobles to take over the power interacts with a small picture of local rumors of betrayal, subversion or communism. It will be interesting to illustrate how they fuel and supply each other (hypothesis 3).

To sum up, from the most obvious situations of violent conflicts to the less evident circumstances of latent oppositions, I will show through many examples from different geographical areas that rumors and CTs circulate in already cohesive groups to strengthen their social structures. They also help to reaffirm dominant values and secure established leaderships.

RUMORS AND CTs IN VIOLENT CONFLICTS INVOLVING THE ENTIRE SOCIETY: THE FRENCH REVOLUTION AND THE ETHNO-CONFESSIONAL RIOTS IN THE POST-COLONIAL INDIA

In periods of wars, riots, revolutions or violent conflicts, rumors and CTs often flourish to explain the origin of deep social change as an intentional and secret agency. When established stratus and society collapse, it is easy to believe in evil plots [START_REF] Gorth | The Temptation of Conspiracy Theory, or Why do Bad Things Happen to Good People[END_REF]Campion-Vincent, 2005: 105).

THE FRENCH REVOLUTION AND THE GREAT FEAR OF 1989

It is no question here to deal with theories that emerge after the French Revolution to explain its evens in terms of conspiracy [START_REF] Barruel | Mémoires pour servir à l'histoire du jacobinisme[END_REF]. On the opposite, I will study the dynamics of rumors and CTs during the very revolutionary process to show how they fuel each other and how they reaffirm the established values and status, notably the leadership of the king in the beginning of the Revolution.

Since the 18 th century, rumors of famine plots were part of the French collective imaginary. As well-described by [START_REF] Kaplan | The Famine Plot Persuasion in Eighteenth-century France[END_REF], bread scarcities and its consequent starvations were usually explained in terms of a conspiracy led by cupid ministers, obnoxious -Protestantbankers, stingy storekeepers and shady bakers. Only the king was said not to be part of the plot. Hearsays of speculation on wheat or flour, of overwhelming secret barns, of crops thrown out in the Seine regularly circulated among the French peoples in the cities to explain scandalous prices on bread and basic foods.

At the eve of the Revolution and during its beginning in early summer of 1789, right before the harvest, this vision of a famine plot was anchored in the French collective imaginary and "many peoples came to suspect the existence of a series of threats to themselves and their communities" (Tackett, 2003: 151). Combined with this famine plot theory, numerous rumors came from neighboring villages to announce that, one the one hand, foreign soldiers were invading the country and, on the other hand, thousands gangs of beggars, wanders and villains called brigands were looting the country. The strength and persistence of those rumors mixed with the collapse of the established feudal order started the Great Fear of 1789. The panic was particularly intensive in areas dominated by an oral culture or affected by the highest rises in wheat prices during the preceding months. The Great Fear initiates thus a new wave of rumors about a foreign invasion and CTs dealing with an imminent political subversion. Even the Deputies in Paris were affected by the panic. In their letters dated of July 1789, the idea of local conspiracies or plot famines is largely exhibited whereas it was totally absent a month before and almost forgotten in August (Tackett, 2000: 703).

Analyzing the Great Fear, Lefebvre formulated the thesis that panics and violence were due to the belief in an "aristocratic plot", a conspiracy led by the nobles against the People and the king (1932: 49). The brigands were also believed to be part of this aristocratic plot.

Their mission was to steal and destroy crops to starve the People. If this thesis has been dominant in the 20 th century, recent researches have shown that the link he established between the brigands and the nobles as the origin of the Great Fear is highly questionable. On the contrary, it appears that in the beginning of the Great Fear, rumors of gangs of brigands genuinely strengthened ties and vertical solidarity among communities (Sutherland, 2008: 68). In the zones touched by the panic, there are many examples of nobles and clergymen recruited to lead militias to defend their communities (Tackett, 2003: 158). This situation was observed in Montoire, Brive, Cahors or Limoges. Face with those brigands' rumors, peasants and townsmen reaffirm their confidence in the established seigneurial system and feudal rules.

Unions sacrées between nobles and commoners were declared to face the forthcoming danger and national guards were formed in many villages of Artois, Soissonnais, Maine, Gévaudan or Aquitaine. Furthermore, it is important to notice that during the Great Fear very few acts of physical violence or material destruction were directed toward the nobles. By this time, the nobles and the king of France appeared to be on the People's side whereas the brigands were portrayed as agents of foreign countries or unknown enemies.

But afterward, when the panic was over and the peoples realized that there was actually no gangs of brigands, the idea emerged that those rumors were forged by the nobles including the prince de Condé or the Comte d'Arthois to secure their positions and leaderships (Jolivet, 1930: 134;Tackett, 2004). And, when in some places brigands had really existed, rumors came out to explain they were noble-manipulated or noble-operated. CTs about an "aristocratic plot" are rather a consequence of the Great Fear than its cause. Indeed, when two years later a new cycle of rumors of famine plot appeared, it accused the nobles to lead a vast conspiracy against the people. Whereas in 1789 the nobles where seen as protectors of their communities, in 1791 it was generally admitted they were the enemies of the nation. By this time, many letters addressed to Constituent's Committee enhanced the thesis of a large scale conspiracy ruled by refectory nobles and clergymen against the Constitution, the citizens and the king. It was only after his flight in June 1791 and the discovery of his personal letters that it became clear that monarch had been part of the conspiracy for months.

ETHNO-CONFESSIONAL RIOTS IN THE POST-COLONIAL INDIA: RUMORS AND CTs AS SELF-FULFILLING PROPHECIES

Since its independence, India regularly faces ethnic violence and confessional riots that alternatively opposed Hindus and Muslims, and Hindus and Sikhs. Through those periods rumors arise in each ethnic group to reaffirm its cohesiveness, itsrighteousvalues and remind how evil and rotten the other one is. As noted by Allport and Postman (1947: 182), rumors "firm pre-exiting attitudes rather than forming new ones." Reinforcing and justifying (pre)existing biases and stereotypes seem to be very powerful in rumors and CTs that lead to ethno-confessional violence [START_REF] Kakar | The Color of Violence. Cultural Identities, Religion and Conflict[END_REF](Kakar, , 2005;;[START_REF] Horowitz | The Deadly Ethnic Riots[END_REF]. All the more so, rumors of violence are enforcing the dynamics of violence. Everything happens as if "rumors-generated violence has the perfect effect of confirming" (Bhavnani, Findley, Kuklinski, 2009: 877-878) the rumors' veracity or at least plausibility. Rumors of violence and subsequent violence are then engaged in vicious circle which must be seen as a self-fulfilling prophecy as defined by

[8] Merton (1948: 195) 8 . And, this process and dynamics of circulation of social and ethnic hate leading to extreme violence are particularly clear in the Indian post-colonial era.

Since 1947 at least, animosity and violence tend to be part of the relationships between Hindus and Indian Muslim minorities accused to be agents of Pakistan. In both communities, The same process of circulation of social hate through rumors and CTs leading to violence characterize the relationships between Hindus and Sikhs. In the everyday life, Sikhs' narratives usually represent Hindus as liars, snakes, weak and effeminate whereas Hindus' hearsay portray Sikhs as heavily armed violent and fanatic snakes too. Crystallized in rumors,

8 "The self-fulfilling prophecy is, in the beginning, a false definition of the situation evoking a new behavior which makes the original false conception come true. This specious validity of the self-fulfilling prophecy perpetuates a reign of error. For the prophet will cite the actual course of events as proof that he was right from the very beginning."

those stereotypes and biases fueled hostility and violence between the communities as selffulfilling prophecies. In 1984, the tensions were brought at a climax after the assassination of Prime Minister Indira Gandhi [START_REF] Das | Specificities: Official Narratives, Rumor, and the Social Production of Hate. Social Identities: Journal for the Study of Race[END_REF] when hostility and animosity spread by rumors turned into violence against the Sikhs. They were accused of separatism, disloyalty to India and made responsible of original violence against Hindus in Punjab. Rumors also circulated that Sikhs were celebrating Mrs. Gandhi's death, had poisoned water and bread or killed hundreds of Hindus in a Delhi Station (Tambiah, 1996: 237). Sometimes Mrs. Gandhi's assassination was even claimed as the first step of a grand conspiracy mastered by the Sikhs.

On the Sikhs' side, rumors echoed that there was a conspiracy going on to transform their community into a "weak race" [START_REF] Das | Specificities: Official Narratives, Rumor, and the Social Production of Hate. Social Identities: Journal for the Study of Race[END_REF].

Such narratives were indeed endorsed by Sikhs and Hindus leaders in a systematic dualism separating the self from the other. Not only the peasants or working men did so. "Contrary to the notion that certain classes of people are protected from the mesmerising effect of rumours (e.g., the educated), I found that many professionalsbureaucrats, teachers, and medical doctorsinhabited for a time that twilight zone in which it was difficult to know whether it was wiser to believe in rumours or in the official versions of events." [START_REF] Das | Specificities: Official Narratives, Rumor, and the Social Production of Hate. Social Identities: Journal for the Study of Race[END_REF] Hence, those educated peoples and communities' leaderslike Bhindranwale for the Sikhs or Akali Dal for the Hinduswho had espoused some extreme beliefs deep-rooted in the collective imaginary of their communities played a decisive role in the dissemination of violencepromoting rumors, the mobilization of crowds and the reaffirmation of ethnic solidarity that led to violence, riots and murders. And the more communities' leaders and educated peoples interacted with the rest of their community, the more this process was powerful (Bhavnani, Findley, Kuklinski, 2009: 890). Dealing with negative stereotypes on Sikhs and rumors of mass murder committed or about to be committed, Hindus leaders organized their communities. They formed militias to led punitive expeditions that turned into massacre and reciprocal violence from the Sikhs that justified further acts of cruelty. The self-fulfilling prophecy was tragically realized.

To summarize, rumors and CTs based on ethno-cultural or ethno-confessional prejudices and stereotypes powerfully contribute to the production and circulation of social hate and the exaltation of in-group values, status and "identities". Particularly fluid in periods of riots, violence or political destabilization, their movements create the conditions under which ingroups "become pitted against each other in fear and mutual hatred, constructing images of

[10]
self and other" (Das, 1998: 109). Rumors of violence fueled the fire of violence which justify, legitimate and reinforce preexisting stereotypes or prejudices as a self-fulfilling prophecy.

RUMORS AND CTs CIRCULATING IN DISSIDENT GROUPS IN VIOLENT CONFRONTATION WITH THE AUTHORITIES: THE DISASTERS OF JONESTOWN AND WACO

If the first situation I have just examined involved the entire society in a violent conflict, the second section considers how the dynamics of rumors and CTs that lead dissident groups to mass-suicide/murder. Through many letters or testimonies, I mainly focus on the events of Jonestown to show how rumors were decisive to strengthen Jim Jones leadership on his followers. As a new religious movement, not to say a cult organization, the Peoples Temple saw itself and its leader as the targets of a big government conspiracy. Starting from that, rumors and CTs played a preponderant part in the life of the community. It was also a way to reinforce solidarity and ties among Jones' followers.

The second case is investigated in shorter terms and from a different point of view for two main reasons. First, despite of less first-hand material, it seems clear that the dynamics that led to the disaster of Waco in 1993 was very similar to what happened in Jonestown.

Consequently, I will study how the reminding of Jonestown and its aftermath was omnipresent during the siege of Waco. On the one hand, the Branch Davidians and their leader David Koresh declared that the government wanted to destroy them because of its antireligiousness just like it did in Jonestown. Then several rumors or imminent attacks flourished in the compound before and during the siege. On the other hand, the authorities were influence by the portrait of Koresh they had themselves drawn: a heavily armed Jim Joneslike failed personality and guru leading his community to mass-suicide. 1962 because he feared a nuclear apocalypse, Jones came back in the United-States in 1964 to establish his Peoples Temple in California. Self-proclaimed reincarnation of Jesus, Jones was at the head of more than 20 000 followers, mostly African Americans from lower social classes. They had to leave all their goods to the Temple and live in community. Accused of sexual abuses on children, frauds, physical punishments on adults or phony miracles by former-members [START_REF] Kilduff | Inside Peoples Temple[END_REF], Jones spread among his followers the idea that those accusations were part of a government conspiracy to destroy the Temple. According to Jones, racist and conservative politicians wanted to nip his plan of a socialist mixed-race society in the bud. In 1977, Jones and some 800 of his most devoted followers left to Guyana to create their heaven on earth: Jonestown.

THE MASS-SUICIDE

If the settlement in Jonestown was highly enthusiastic (Traver, 1977a(Traver, , 1977b;;[START_REF] Chaikin-Alexander | Letter to His Grandparents[END_REF] 9 , the atmosphere quickly turned into fear and state of siege mentality. Jones was more and more violent and paranoid. He multiplied physical punishment and transformed his follower into slaves. Jones, as ex-members testified, created "a conspiratorial atmosphere and the impression among the people that (they) were under attack almost continually in order to (…) maintain some organizational cohesiveness" [START_REF] Chaikin-Alexander | Letter to His Grandparents[END_REF]. For instance, Jones spread that the United States government had marshaled Black peoples in concentration camps (Barkun, 2013: 72-76), was conducting a "Black genocide" (Goldberg, 2001: 159-188), was responsible of Dr. King and President Kennedy' assassinations, the KKK was patrolling at the borders and a nuclear war was about to start [START_REF] Berthillier | Jim Jones, la folie meurtrière d'un gourou[END_REF].

A first climax was reached when Jones convinced himself that the American army was about to invade Jonestown to kill him. A six day siege started. Peoples were confined in a hysterical atmosphere of apocalypse and forced to go through "Withe Nights", kinds of mass-suicide training sessions [START_REF] Chaikin-Alexander | Letter to His Grandparents[END_REF]. Resulting from this paranoid and fear atmosphere, Jones managed to strengthen the community around him. He convinced his followers that to face this obsequious conspiracy it was necessary to commit suicide and it was better to die than living in the forthcoming American dictatorship. In 1978, rumors of fascist invasions or imminent murders were the daily narratives that circulated in Jonestown. In the middle of the jungle, rumors were the main source of information for isolated residents who had almost no contact with peoples from outside and very little access to media. In their last letters, peoples of Jonestown described a situation of extreme tension and the omnipresence of a conspiratorial atmosphere (Grunnet, 1978a(Grunnet, , 1978b;;[START_REF] Johnston | Letter to President Carter from Jonestown[END_REF] that led them to accept a mass-suicide as a revolutionary act of resistance 10 (Alexander, 1978; Moore, 1978).

Finally, the tragic end happened on 18 th November 1978, Jim Jones persuaded his followers to give a cyanide-laced Kool-Aid drink to their children and inject themselves cyanide (Bratich, 2003: 377-378). During this final "White Night", "residents proclaimed their willingness to take the lives of their own children rather than leave them for the fascists find" [START_REF] Moore | A Dream Deferred: The Promise and Pathos of Peoples Temple[END_REF]. The visit of Congressman Ryan who investigated allegation of abuses in Jonestown and the defection of a few members led to the disaster. After Ryan and defectors' assassinations, Jones told his followers that there was no way to get back in the life they used to live: thousands of fascist soldiers were about to invade Jonestown to jail, torture or kill them. They had to commit mass-suicide/murder to save them, especially the children.

Afterward, the Jonestown episode and its mass-suicide/murder started many CTs which play a very decisive part in the dynamics of the Waco disaster in 1993.

2.2. THE TRAGIC ENDING OF THE SIEGE OF WACO, TEXAS: 2 8th FEBRUARY -19 th APRIL 1993 19 th April 1993, after a 51 days siege, the FBI launched an attack against the Branch Davidians' complex in Waco in order to "flush them out" according to President Clinton's words. Live broadcasted on TV networks, flames quickly appeared over the compound and at least seventy-four men, women and children died. Immediately, who started the fire became the main question. Did the Davidians start themselves the blaze as part of a suicide pact? Or, was it arson stared by the FBI? According to a Time Magazine poll on August 1999, 61% of the Americans agreed the second option (Mulloy, 2003: 718). Even if the official report stated that it was the Davidians who actually started the fire (1993)it was confirmed in the final report in November 2000 [START_REF] Danforth | Final report to the Deputy Attorney General concerning the 1993 confrontation at the Mt. Carmel Complex[END_REF], many CTs flourished to explain what really happened in Waco 11 .

10 Jones and his followers re-appropriated the concept of "revolutionary suicide" from the Black Panthers Party for Self-Defense. In the 1960's radical groups from the left developed the idea that the American government had planned a grand conspiracy to destroy progressive movements. They considered that die-fighting was a political act of resistance and it was better to die that living in a "fascist" or racist country.

11 Two years later to the day, far right activist Timothy McVeigh bombed a federal building in Oklahoma City to protest against the government cover-up for the "massacre". He was convinced that the government ruled a conspiracy against the American people.

arise as an act of social conformism that remind and strengthen in-groups structures as well as they exclude outsiders or challengers. The criterion which fuels this socio-dynamics was the long-time residency in the neighborhood. We are assisting at the "resourcization" of duration as a strong agent of discrimination particularly powerful when there is no objective criterion of differentiation. "In Winston Prava, newcomers are victims of segregation, stigmatization and rejection although there is no difference of "race", language, national culture or class. Among the ones who are rejected, most of them are most of the time blue collars or from working class origin" (Wieviorka, 1997: 13), just like peoples from the zone 2. Put another way, even though there is no sociological differences between peoples living in zones 2 and 3, there is racism without race and class struggle without class antagonism in Winston Prava. Generations after generations, Old families had monopolized the sources of power and prestige and developed a collective charisma which gave them a unique social position and superiority. This "capital of duration" (Heinich 1997: 80), or I better say capital of establishment, is visible through three patterns used to strengthen the socially established structures: 1°) endogamy and social reproduction among the "old mother centered family"; 2°) pubs, local clubs and family networks as institutions of socialization and segregation; 3°) dissemination of rumors, gossips and negative cliché-based stereotypes. In hearsays circulating in the zones 1 and 2, peoples from the third one were portrayed as a dirty, drunkard and violent colony of cockneys living in wetland or haunts of rats. The zone 3 was in addition known as an area full of criminals and prostitutes.

OLD RESIDENTS AND NEWCOMERS: ESTABLISHED

Hence, gossips and rumors are not a peripheral or independent phenomenon. They are constitutive of the social life of the community living in the second zone for they constantly testify of its superiority and the positive image of itself (Elias, Scotson, 1994: 89). The egodefensive function of those tales is at once to integrate and exclude peoples (Elias, Scotson, 1994: 100-101) of the righteous community entwined in a cohesive network of families who share common interests, biases and sense of their own superiority (Elias, Scotson, 1994: 5).

Despite this, it is important to state that those rumors and gossips are never directed toward a single person but against peoples of the third zone as a global entity (Heinich, 1997: 81-85).

Most of the time, peoples from the zones 2 and 3 know each other, they work in the same factories and are personally in good terms (Elias, Scotson, 1994: xvi-xvii). But, peoples from the second zone collectively testified how they felt disappointed and upset when some outsiders settled in their neighborhood and how they perceived the newcomers as a threat to their way of life. Here was the origin of supporting rumors and gossips about the superiority of the "Village" and its residents and negative ones on the collective indignity of the newcomers/outsiders (Elias, Scotson, 1994: xvi-xvii).

Vilifications setting in motion the socially inferior group's own sense of shame or guilt feelings with regard to some inferiority symbols, some signs of the worthlessness attributed to them and the paralysis of their power to strike back which goes hand in hand with it, from thus part of the social apparatus with which socially dominant and superior groups maintain their domination and superiority over socially inferior groups. Individual members of the inferior group are always supposed to be tarred by the same brush. They cannot escape from the group stigmatization individually, just as they cannot escape individually from the lower status of their group (Elias, Scotson, 1994: 102-103).

In this way, rumors and gossips which circulate in the second zone enhance the cohesiveness of the "Village" and underline their self-constructed image of superiority and righteousness. They in addition play a significate part in the perpetuation of social control and conformism and they contribute to strengthen family's ties and collective charisma as well. At the same time, they disseminate negative cliché-based prejudices and stereotypes in the collective imaginary of peoples who live in the second zone. Rumors and gossips turn finally the newcomers into definitive outsiders that must be feared and drifted apart.

Consequently, the premise that Mrs. C. was a communist agent was quickly accepted by the residents.

But, "rumor rarely appears as itself: it goes with its share of proofs which confirm its undeniable credibility. In some way, its strength resides in its structuring effect on our perception: it gives sense to numerous facts that either we have never paid attention or the sense never looked clear. It gives us a coherent system to explain a large number of scattered facts: in this, it satisfies our need for order in the understanding of surrounding phenomena" (Kapferer, 1990: 93). So that, a cognitive process of reorganization took place and several evens of the past involving Mr. C. were double-checked in the light of the rumor. Regarding the premise of "avowed communism", it was clear that Mrs. C., a long-time communist agent, settled in the neighborhood to spy or subvert it and the movie shown in a meeting was communist propaganda and its music composed by Aaron Copland 14 "sounded Russian".

Everything was added up to support the premise of communism and discredit Mrs. C. and the new leaders.

Rumors conversely became supporting narratives for the old leaders. Not only did they put an end to the social activities of the ascending leaders but also preserved and reaffirm the old leadership structures. The tenant's committee concurrently strengthen is prestige in the community because it seemed not soft on communism. When rumors aroused, the committee contacted the regional management office which sent the community organizer in the neighborhood. It was answered to be careful because communist agents may have infiltrated some social program. Resultantly, Mrs. C. and a few other new leaders were totally ostracized by the rest of the community. The situation went even worse when the "avowed communist" had to face vicious anti-Semitic slanders from the overwhelming WASP majority.

Finally, with the distance of History it is interesting to obverse that a local rumor of communist-supported activities interacts with the big picture of a so-called communist conspiracy to take over the United States during the "Witches Hunt". Like in the neighborhood studied by Festinger, it appears that "the issue of communism in the United States was of much greater concern to the elite" (Gibson, 1988: 519) to secure its leadership. This dynamics concern both local and national elites 15 throughout the United States (Stouffer, 1955: 40-44). Quite the opposite, if obviously the American citizens were strongly anti-14 During the McCarthyism's era, Copland was accused of being a communist agent and was blacklisted. 15 See how Richard Nixon used in 1948 the Alger Hiss case as a political springboard (Huret 2009: 73-74).

[18] communist, only 1% of them spontaneously pointed out in polls communism as the number one danger that the United States had to face (Toinet, 1984: 76).

CONCLUSION

To sum-up, rumors and CTs develop in already cohesive communities as an act of social conformism (ego-defensive function). Collectively accepted as plausible, they reaffirm and strengthen through a process of fides implicita the dominant values, established structure and secured leadership of an in-group at the same time they exclude the outsiders and challengers usually negatively portrayed. Rumors circulate then in a group which has already clear idea of its own superiority and of the dichotomies "the self/the others" or "us/them". They are particularly pro-active and powerful when the members and all the more so the leaders of the in-group feel a threat to their positions. Sometimes, no matters they are right or wrong, prejudices and stereotypes contented in rumors turn into self-fulfilling prophecy which feed rumors in a vicious circle. Rumors and CTs design scapegoats who are responsible of all the evil things from wars to a mere change in the social structure of a neighborhood. This dynamics of rumors and CTs is particularly obvious in the migrant crisis of the middle of the 2010's. Portrayed in European media and radical political discourses as outsiders or possible terrorists, refugees are accused of being agent of destabilization and subversion. Their religion, their habits or their "culture" are presented like a threat to our Christian civilization. Many more prejudices and negative stereotypes circulates in rumors and CTs. For instance, Renaud [START_REF] Camus | Le Grand Remplacement[END_REF], a French far right activist, prophesizes that in the fifty coming years, Europe will be an Islamic area thanks to the complicity of governments and European institutions. He called this phenomenon "le grand replacement"the great substitution. Muslim peoples from Arabic areas will flood Europethrough hidden agencyto reduce European Christian peoples into dhimmis or barely tolerated minorities (Bat Ye'Or, 2005). Alexander, P. (1978). Letter to Her Father about "Revolutionary Suicide".

REFERENCES:

  rumors and CTs feed animosity, mutual fears and social hate that sometimes end up in violence. In Hindus areas, rumors disseminate negative appraisals on Muslims. They are accused to kill or to burn Hindus alive, rape their women, kidnap their children, poison the food and the milk or castrate non-Muslims. They are also portrayed as coward terrorists heavily armed acting secretly by night against Hindus' interests. Put together, all those rumors reflect the Hindu's deep-rooted bias of Muslims disloyalty. In other words, Muslims are accused to run grand conspiracy against India and Hinduism. Reciprocally, in Muslims areas, hearsays report that Hindus are threating Islam by forcing Muslims to convert to Hinduism, they kill, kidnap or rape children and women, they poison the food and the milk, they destroy mosques and they are heavily armed as well. All combined, those rumors enhance the longstanding fear of Muslims being swamped by Hindus and then wiped out. And, as observed byKakar (2005: 54-55), this set of rumors was particularly strong and highly spread in the ethnoconfessional riots of 1947 during the partition of India and Pakistan. They were used as selfjustification for extreme violence in both communities which felt in mortal danger. In the riots of 1969 inAhmedabad, 1990 in Hyderabad and 2002 in Ahmedabad again, the same rumors circulated again within both ethnic groups. In this mirrors and scales game, perpetrators of the ones are the victims of the others and, mastering anxiety and fears, rumors and CTs play their social function. In strengthening individual identities with his/her group, they contribute to reactive ethno-confessional solidarities. In subsuming individuals to the group, rumors reinforce its cohesiveness and sense of superiority by exalting its collective values, memory, imaginary and "identity".

  VS. OUTSIDERSTo enlighten the functions of rumors in situation of latent opposition between established and outsiders, it is necessary to consider the classical enquiry conducted by Elias and Scotson in Winston Prava, an industrial neighborhood in the outskirts of Leicester in the 1960's.Winston Prava was divided in three sections: the first zone was a middle class area and zones 2 and 3 were blue collars. The zone 2, nicknamed "the Village", was the first area built in 1860 by the founder of Winston Prava, Charles Winston. Residents of zone 2 developed since then a sense of community and collective history. "They went through a collective processfrom the past to the future via the presentwhich gave them a stock of common memories, ties and dislikes" noted Wieviorka in his preface to the French edition(1997: 55). When the estate located in the zone 3 was built in the late 1940's, an "us versus them" (ego-defensive function) relationship was immediately elaborated between established peoples from zones 1 and 2 and the newcomers.

  Aldrin, Ph. (2005). Sociologie politique des rumeurs. Paris: PUF. Al-Kandari, A. A. J. (2010). Arab News Networks and Conspiracy Theories about America: a Political Gratification Study. Journal of Arab and Muslim Media Research, 3 (1-2), 59-76.

Of course this function of rumors and CTs is not the only one. In a yet unpublished research report[START_REF] Giry | A Functionalist Analysis of Conspiracy Theories: Conspiracy Theories and their Social Functions[END_REF] I argue that CTs fulfil at least seven social functions. Most of them (4 out of

7) are intentionally and consciously

This does not deny the insight that rumors can deal with politics or political actors (e.g.: Melania Trump does not share her husband bed, Emmanuel Macron is actually gay, etc.) bur they are not or rarely political themselves.

All the letters mentioned are retrieved from: http://jonestown.sdsu.edu/?page_id=18985 Acceded: September October 2016.

committee member for France Program MHALEC (2017-2019): WG 3,

During the siege Koresh and his followers were persuaded that the American government wanted to kill them as part of a conspiracy against religious liberties. For him, it became clear that the government was allied with Babylon (Bitter, 2003: 171) and the siege they underwent was the 5 th seal of Apocalypse. Many rumors of imminent attacks, of tanks and "black helicopters" (Barkun, 2013: 70-72) roaming around their complex reinforce their conviction that the End would come soon at the same time they strengthen the community. Koresh and his followers viewed themselves as martyrs. What more, Koresh had a full conscience that he was portrayed as a Jim jones-kind guru in media and for that reason he would be killed by the government. He also believed that if he surrendered, he would have to face an iniquitous trial.

On the other side, the FBI considered Koresh as a heavily armed half-guru half-crook who sexually abused children and wanted to lead his community in mass-suicide. In their understanding of the standoff, the parallel with Jonestown was omnipresent (Luca, 2006: 115). For the authorities, Koresh's Bible babble was not understandable. It was clear that he was using delaying tactics to destroy the proofs against him and preparing a mass-suicide.

When Koresh broke is words to release the children after he had spoken on TV networks, the FBI mind was definitively made-up. "Tension was at climax […] because of the competition engaged on the perception of the moral order of the world, on the values, on differences of rationality and on concurrent authorities which should prime: state or god" (Luca, 2006: 118).

Finally, interactions between the religious-based conspiratorial vision of Koresh and his followers and the FBI Jonestown-like scenario led to disaster. As rumors of an ineluctable assault spread, Koresh and his groups were more and more bound and ready to die while the authorities were more and more convinced that they collectively planned to commit suicide since the beginning. Like in the ethno-confessional riots, the dynamics of rumors and CTs revealed a self-fulfilling prophecy and the siege of Waco ended up in a pool of blood. problem of social organization and communication when they had the privilege to observe from its origin the spread of a rumor. In a poor shipyard workers neighborhood, the inactive local tenant's committee was challenged in its leadership. With the help of a community organizer, peoples in the neighborhood started several social programs such as the development of a nursery school. Consequently, the local leadership "was now mainly in the hands of peoples who had previously not been active" (Festinger, Cartwright, alia., 1948: 468) while the leadership of the tenant's committee and its secretary's one were waning.

RUMORS AND CTs

Among those new leaders, Mrs. C. was particularly involved and considered in the nursery school activities. A couple of weeks later, all this well-advanced project was definitively stopped. Rumors had arisen: the new leaders were communists; no one could trust them. The program was communist-based and Un-American. Surprisingly, only residents were pointed out by rumors. Mrs. C. was the main target of the rumors whereas the community organizers who started the programs were spared despite outsiders.

Let's study carefully the dynamics of those rumors which must be seen activities in the local church, they started the rumor that Mrs. C. was an "avowed communist" (Festinger, Cartwright, alia., 1948: 471) who read communist newspapers and had radical opinions. Their positions of "experts" (Kapferer, 1990: 80) or better-informed peoples played a strategic part in dissemination of the rumor 12 . Through a process of fides implicita 13implicit trust (Aldrin, 2005: 200), the secretary and Mr. M. appeared as the most qualified peoples to evaluate the rumor's credibility and give it a chance to spread in the neighborhood.

12 See also: Rouquette (1990: 120) argues that personal implication of trustees plays a significant part in the dissemination of rumors. 13 Fides implicita is a social process of symbolic violence in which dominated peoples (young, less-educated, less-informed peoples, etc.) entrustsupposedlymore qualified peoples (the dominants) to judge or evaluate a social situation or phenomenon. See: Bourdieu, 1984: 245.


D Wagner

N Ranc

Experimental study of Portevin-Le Châtelier plastic instabilities by infrared pyrometry -Type A to type B transition

Introduction

In general, at the macroscopic scale the plastic strain in materials is homogeneous. However, under certain conditions of temperature and strain rate, it can become heterogeneous. There is then localization of the plastic strain. The dynamic strain aging (DSA) phenomenon which occurs in some material under certain temperature and strain rate can cause a localization of the plastic strain in the form of bands called bands of Portevin Le Chatelier (PLC). For a tensile test at imposed strain rate, they are associated on the tensile curve with repeated serrations resulting from a succession of stress drops. In the case of test at imposed stress rate, the PLC bands are characterized by discontinuities in the form of levels of strain. This localization of the plastic strain can appear in materials with different crystal lattice (mild steels, austenitic stainless steels, aluminium alloys, zirconium alloys…). At the macroscopic scale, this phenomenon [START_REF] Baird | Dynamic Strain Aging in : The Inhomogeneity of Plastic Deformation[END_REF][START_REF] Cuddy | Some aspects of serrated yielding in substitutional solid solutions of iron[END_REF][START_REF] Mccormick | A model for the Portevin-Le Chatelier effect in substitutional alloys[END_REF][START_REF] Strudel | Interactions des dislocations avec les impuretés mobiles in Dislocations et déformation plastique[END_REF][5][START_REF]Continuum Models for Materials with Microstructure[END_REF][START_REF] Wagner | [END_REF][8][9], induces an increase in flow stress, ultimate tensile strengh and work hardening coefficient, as well as a decrease in ductility (elongation, reduction of area and fracture toughness) which can be detrimental. At the microscopic scale, this phenomenon is explained by the dynamic interaction of mobile dislocations with the solute atoms in insertion or substitution. Mac Cormick [START_REF] Mccormick | A model for the Portevin-Le Chatelier effect in substitutional alloys[END_REF] showed that the slip of dislocations is not continuous, but discontinuous. Dislocations are stopped temporarily on the obstacles (forest, precipitates…) during a waiting time tw. During this waiting time, an additional anchoring of dislocations by the diffusion of the solute atoms occurs. The serrations on the stress strain curve obtained at imposed strain rate can be classified in three types according to the spatiotemporal appearance of these bands ( [START_REF] Cuddy | Some aspects of serrated yielding in substitutional solid solutions of iron[END_REF][START_REF] Strudel | Interactions des dislocations avec les impuretés mobiles in Dislocations et déformation plastique[END_REF][START_REF] Brindley | Yield point phenomena in substitutional alloys[END_REF][START_REF] Lacombe | L'effet Portevin -Le Chatelier, ses caractéristiques et ses conséquences sur les hétérogénéités de déformation plastique[END_REF][START_REF] Rodriguez | Strain Aging, Dynamic[END_REF][START_REF] Mccormick | Propagative instabilities : an experimental view[END_REF][START_REF] Lebyodkin | Spatiotemporal dynamics of Portevin-Le chatelier effect : experiment and modelling[END_REF]). The type C corresponds to the chaotic formation of the bands (discontinuous and not correlated). Each stress drop on the tensile curve corresponds to the formation of one band. The type B corresponds to the discontinuous but regular formation of the bands (each new band is created just above the previous one and so on). Each created band is characterized by a stress drop on the stress strain curve too. Type A bands correspond to a continuous propagation of a band from one edge of the specimen to the other. With each type of band (A, B or C) is associated a type of serration on the stress strain curve, more or less easily identifiable. The occurrence of these different types of bands which correspond to various spatiotemporal types of localization depends on external parameters (level of strain, strain rate, temperature, stiffness of the tensile machine, geometry and surface quality of the samples) and internal parameters (alloy composition, crystal lattice, microstructure and solute atoms type and content, density of mobile dislocations, type of obstacles (forest, precipitates…), grain size of alloy). The influence of the external parameters (strain rate and temperature) was studied the most in literature. When the strain rate increases (the waiting time of dislocations decreases) or the temperature decreases (mobility of the diffusing species decreases) the localization of the bands evolves from the type C to the type B then type A. Today, the transitions between these various types of bands are not still clearly explained, and the phenomenon modelling is difficult and supplementary knowledge is needed in the mechanism of DSA. In order to study the spatiotemporal evolution of PLC bands, various authors used the optical extensometry technique (Ziegenbein et al. in 2000 [15], Casarotto et al. in 2003 [16], Klose et al. in 2003 [17], Casarotto et al. in 2005 [18], the technique of speckle interferometry (Shabadi et al. in 2004 [19]), the technique of digital image correlation from a speckle pattern in order to obtain the strain field (Jiang et al. in 2005 [20]). The acquisition frequency of these different devices is about few tens of Hertz. In 2005, Tong et al. [START_REF] Tong | Time-resolved strain mapping measurements of individual Portevin-LeChatelier deformation[END_REF] and more recently, Ait-Amokhtar et al. [22] used an ultra high speed camera and a technique of digital image correlation to determine the strain field during the formation of a PLC band. This technique allows to visualize very precisely the band formation. Since few years, various authors have developed infra-red thermography technique in order to study PLC bands [23][24][25]. Indeed the plastic strain is accompanied by a dissipation of the mechanical work in heat what causes generally an increase in the temperature. This technique seems very promising because enables to have a high acquisition frequency during the tensile test (until 400Hz in [24]). The objective of this paper is more precisely to study with infrared pyrometry technique the influence of the strain and the strain rate on PLC type bands. Within this framework we were interested in an aluminium-copper alloy which enables us to have the PLC phenomenon at ambient temperature. In a first part the experimental device and the analysis method used in this study will be described. In a second part, the results obtained for the type A, type B and type C bands will be presented. Then the evolution of the bands parameters according to strain and strain rate will be detailed and the type Atype B transition will be more particularly discussed.

Materials and experimental device

2.1.Materials

The material used in this study is an aluminium-copper alloy EN AW 2024 (4% copper) heat treated at 500°C during 30 minutes and then water quenched. Immediately after quench, the copper concentration content in substitutional solid solution is high and this alloy is sensitive to DSA in a temperature range around 20°C.

Mechanical tests

Immediately after quench, tensile tests were carried out on a screw driven machine at the ambient temperature. Prismatic specimens of 12mm wide, 3mm thickness and 60mm length were machined. The specimen's surface was in the as-rolled condition. In order to study the influence of the strain rate on PLC phenomenon, five tests were carried out at various imposed strain rate ranging between 2.38 x 10 -4 s -1 and 2.14 x 10 -2 s -1 (table 1). The measurement of the temperature field on the specimen surface is carried out with a pyrometry technique. Thus an infra-red camera ( CEDIP type Jade) whose spectral range is between 3.9µm and 4.5µm is used. The power radiated by the surface of the specimen is collected by an optical system made up of a 50mm focal length objective which is focused on the matrix of the camera. The spatial resolution is of 0.3mm by pixel. An aperture time of the camera of 1500µs allows to detect temperatures ranging between 5°C and 50°C. The noise of the camera is around 20mK. Except in the case of test 1, the refresh frequency of the camera is of 320Hz what corresponds to a period of 3.125 ms. For data storage reasons during the long tests, the refresh frequency during test 1 is reduced to 25Hz or improved to 500Hz in order to have a greater precision in a part of the test. The pyrometer is calibrated on a black body in order to obtain the relation between the signal delivered by the camera and the temperature of the observed surface. In order to neglect the effect of the surface emissivity on the determination of the temperature, all the specimens are covered with a fine coat of black paint.

Results and discussion

3.1. Macroscopic appearence of the bands

Observation of type A bands

For the tests (2), ( 3), ( 4) and for weak nominal strain, a continuous propagation of a plastic strain front (type A band) occurs. The figure 1a shows the temperature evolution versus time in a point B located at the center of the specimen. A sudden increase in the temperature is measured when the plastic strain front crosses on the point B. For the test (2) at a nominal deformation of 3.9% (figure 1a), the temperature increment is estimated at 0.18°C. The figure 1b shows three thermographies when the band crosses on the measurement points A, B and C defined on the figure 1a. The increment of temperature is calculated with the initial temperature field at the time t 0 = 7.409s corresponding to the beginning of the band propagation on the right-hand side of the specimen. These three thermographies allow to determine the slope angle of the propagation front with the axis of the specimen and to measure the propagation velocity of this plastic strain front. In the case of the test ( 2) and for a nominal strain of 3.9% we find an angle of 63±1° and a propagation velocity of 49.5 mms -1 between the points C and B and 48.6 mms -1 between the points B and A.

Observation of type B bands

For the tests (2), (3) and (4) at higher strains, we can notice the presence of a discontinuous propagation of type B bands. They are characterized on the stress strain curve (figure 2) first by regular small serrations (a) of increasing amplitude during the test and second by more significant serrations (b). Each small serrations correspond to the formation of one PLC band and the stronger serrations correspond to the formation of several PLC bands at the extremity of the specimen. This aspect was detailed in [23]. Figure 2 shows the conventional stress-strain curve and the temperature measured on three points of the sample noted A, B and C and spaced of 24.5 mm (figure 1a). The temperature recordings at the A, B, C points (figure 2) show a sudden increase of the temperature when a band goes in front of the measurement point. Figure 3 shows the evolution of the temperature in the center of two consecutive bands according to the time. We can notice an increase in the temperature which corresponds to the plastic strain during each band formation. In the case of the test (3) (figure 3), for a nominal strain of 15.8%, the temperature increment during the formation of the first band (t = 13.291s) is 0.74°C. This curve allows to define the time of band formation and the time between two consecutive bands noted respectively tf and tmb. The time of band formation is defined as the time corresponding to the temperature increase from 5% to 95% of the total temperature increment in the band (see figure 3). In the case of the test (3), for a nominal strain of 15.8%, the time of band formation can be estimated at 7.8ms for the first band and 6.3ms for the second. Figure 3 also allows to define the time between two consecutive band formations. We suppose that the moment of band formation is the time when the increase in temperature in the band reaches 50% of the total temperature increment. In the case of figure 3, time between two band formations is about 51.7ms for a nominal strain of 15.8%. From thermographies of temperature increment, other geometric characteristics can be measured (see details in [25]). The slope angle between the band direction and the specimen traction axis is of 61±1°. In the case of the test (3) and for a nominal plastic deformation of 15.81%, the bandwidth along the traction axis noted d and the distance between two consecutive bands (b) (a) noted  are respectively equal to 2.9±0.15 mm and 1.4±0.15 mm. This bandwith is measured from temperature measurement along the specimen axis.

Observation of type C bands

For lower strain rate (for example 2.38 x 10 -4 s -1 for the test (1)), the stress strain curve does not present any more significant serrations corresponding to the formation of bands on the edges of the specimen as in the case of type B. Regular stress jumps are then observed whose amplitude is more significant than in the case of type B bands and increases during the test [25]. These serrations are always associated with the formation of PLC bands but those are formed in a random way along the specimen (type C bands). For a nominal strain of 13.7%, we can measure a time between two bands of 3.7s and a slope angle of the band with the specimen axis of 58±1°. In order to measure with sufficient precision the duration of band formation, we carried out a thermal recording at a frequency of 500Hz. Then, we find for a nominal strain of 13.7% and a strain rate of 2.38 x 10 -4 s -1 a duration of band formation of 3.7ms. The temperature increment in the band is of 1.04°C and the bandwidth is of 3.7±0.15 mm.

Evolution of the characteristics of the bands according to the nominal strain and strain rate

Taking into account the precision of our experimental device, we did not measure significant variation of the slope angle of the bands between the 3 types. However, we highlighted a slight increase in the bandwidth from type B to type C ( On the other hand, it is more interesting to measure the time between two band formations tmb (figure 4)(case of type B and type C), the time of band formation tf (figure 5) (case of type B and type C), the apparent propagation velocity (figure 6) (type A, type B) and the increment of plastic deformation in a band (figure 7)(type A, type B and type C) (for details, see [25]). Figure 4 shows the evolution of the time between two band formations according to the nominal strain for four strain rates when this quantity is measurable. It is noted that time between two band formations increases with the nominal strain and decreases when the strain rate increases. The increase of the time between two band formations with the nominal strain was already noted by Jiang et al. [20] in an Al4%Cu alloy. More recently Ait-Amokhtar et al. [22] also showed in experiments that this time between two bands (called reloading time) increases when the nominal strain increases. This effect can be explained by the fact that the waiting time of mobile dislocations and thus the time between two band formations increase with the strain. Indeed, we can express the waiting time tw according to elementary plastic deformation noted  and the strain rate: tw =  /  . It can be consider that the elementary plastic deformation increases linearly with the strain [26]. An increase in the nominal strain thus results in an increase in the waiting time and thus an increase in the time between two band formations. The relation also allows to explain the increase in the waiting time and thus in the time between two band formations with a decrease in the strain rate. For the type C (obtained for low strain rate or high temperature) the diffusion of solute atoms is enhanced, the anchoring of mobile dislocations increases and so the time between two bands (so the waiting time tw) increases and is greater than in type B. The evolution of the band formation time (figure 5) has been measured for test (3) in the case of type B band. For the type C, this time of band formation has been measured from the test performed at low strain rate with a camera frequency of 500Hz. For  =13.7%, we find a duration of band formation of 3.7ms. The values which we find in this study are the same order as those measured by Louche et al [24] (the development time of the band is estimated at 10 ms in an alloy Al-4wt.%Mg) and by Tong et al. [START_REF] Tong | Time-resolved strain mapping measurements of individual Portevin-LeChatelier deformation[END_REF](the development time of the band is estimated between 3ms and 5ms in an alloy Al-2.5wt.%Mg). However no data is available in the literature concerning the evolution of this time of band formation according to the nominal strain. For type C, the time for the band formation is smaller than in type B. The band spacing (measured for type B only and not reported here, for more details see [25]) is constant or decreases weakly with the strain. No effect of the strain rate can be detected. Figure 6 represents the apparent propagation velocity according to the nominal strain. As the distance between two band remains constant or decreases weakly when the strain increases and the time between two band formations increases when the strain increases, a decreasing apparent speed is well noted when the strain increases. An increase in the apparent propagation velocity with the strain rate of the test can also be highlighted. If we put on figure 6, the values of propagation velocities of the plastic strain front in the case of the bands of type A, we can observe a continuity between this front velocity and the apparent propagation velocity of the type B bands.

Figure 7 shows the temperature increment associated with each band according to the nominal strain and the strain rate.

Type A -type B transition

During the test (3), a transition from type A bands towards type B bands appears when the nominal strain increases. The value of the nominal strain when the transition occurs is difficult to evaluate, because in a strain range around this transition we show at the same time bands of type A and bands of type B. Also it is easier to define the strain range of the transition. We can estimate this transition strain range between 5% and 6%.

In order to explain this transition from type A to type B, we are more particularly interested in the comparison between time of band formation and time between two band formations. Fig. 4 shows the evolution of the time between two band formations (tmb) according to the nominal strain when this quantity is measurable. It is noted that time between two band formations increases with the nominal strain. On Fig. 4, we can show that the evolution of the time between two band formations follows a linear law with the nominal strain in a log-log diagram. Thus, we can write a relation between t mb and the nominal strain :

tmb = A B with A = 0.15s et B = 0.6068 (for test (3)) (1)
The standard deviation between the experimental results and the regression is of 0.07s. Fig. 6 shows the evolution of the time of band formation (tf) according to the nominal strain in the case of the bands of type B. The curve on Fig. 6 highlights a reduction in the time of band formation with the strain. In a log-log diagram, this evolution can be considered as linear. A linear regression enables us to obtain a power law evolution of the time of band formation according to the strain:

tf = F G with F = 0.0008s and G = -1.0925 (2)
On the Fig. 8, the time between two bands formations tmb and the time of band formation tf are plotted versus  from equations ( 1) and (2). For one strain, the two straight lines intersect. On the left hand of the intersection, the time of band formation tf is greater than the time between two bands formations tmb .

In this case, it is impossible to distinguish two consecutive band formations and we are in a continuous propagation of the plastic strain front that is to say in type A band. From Fig. 8, the intersection is for the same order of deformation that the experimental value (5-6%) determined for the transition type A-type B for the test performed for this study.

Conclusion

In this paper, we studied the Portevin Chatelier bands of type A, B and C in a Aluminium Copper alloy using the temperature measurement technique of infra-red thermography. We are more particularly interested in the study of the band characteristics such as the distance between two consecutive bands, the time of band formation, the time between two band formations, the bandwidth, the slope angle with the axis of the specimen and the temperature increment in the bands. We also studied the evolution of these various characteristics according to the nominal strain and the strain rate. In particular, we highlighted an increase in the time between two band formations and a reduction in the time of formation with an increase in the nominal strain. We noted that in the case of bands of type B which corresponds to a discontinuous propagation, the time of band formation is lower than the time between two band formations. We also showed that the type A -type B transition from a continuous propagation towards a discontinuous propagation corresponds to the equality between the time of band formation and the time between two band formations.

Fig. 1 .

 1 Fig. 1. Test (2) at a nominal strain  = 3.88% a) temperature evolution in the center of the specimen during the type A band propagation, b) fields of temperature increment.

t = 8 .

 8 650 s; band on A point t = 8.14375 s; band on B point t = 7.64687 s; band on C point Temperature increment in °C

Fig 2 . 3 Fig. 3 .

 233 Fig 2. Stress-strain curve and temperature evolution for test 3

Figure 4 .Figure 6 .

 46 Figure 4. Evolution of tmb Figure 5. Evolution of tf

Figure 8 .

 8 Figure 8. Comparison between tmb and tf

Table 1 :

 1 Tests conditions 2.3 Temperature measurement

	Test reference	Refresh	Type of bands	Strain rate in s -1
		frequency	observed
	(1)	25Hz and	Type C	2.38 x 10 -4
		500Hz
	(2)	320Hz	Type A et Type B	4.76 x 10 -3
	(3)	320Hz	Type A et Type B	1.19 x 10 -2
	(4)	320Hz	Type A et Type B	2.14 x 10 -2

table 2

 2

	).
	Test reference Strain rate in s -	Observed type	Slope	Bandwith
	1	band	band
	(2) at  = 3.88% 4.76 x 10 -3	A	631°	----
	(3) at  = 15.8% 1.19 x 10 -2	B	611°	2.90.15 mm
	(1) at  = 13.7% 2.38 x 10 -4	C	581°	3.70.15 mm

Table 2 .

 2 Slope band and bandwidth measurements from type A to type B