Nikos Bozionelos
email: nbozionelos@audencia.com

Giorgos Bozionelos
email: gbozionelos@gmail.com

Panagiotis Polychroniou

Konstantinos

Beatrice Van Der Heijden

Konstantinos Kostopoulos
email: kkostopoulos@eada.edu

Mentoring Receipt and Personality: Evidence for Non-Linear Relationships

Keywords: Mentoring receipt, protégés, personality, Big-Five, quadratic, inverted Ushaped, multi-source, context, common method

published or not. The documents may come

mentors towards protégés (e.g., an industrious employee may attract a mentor or a mentor may prefer to provide more advice to a receptive than to a non-receptive protégé).

The idea that personality plays substantial part in interpersonal processes and outcomes, such as mentoring receipt, adheres to the dispositional perspective to organizational behavior (e.g., see Staw, Bell, & Clausen, 1986;Staw & Cohen-Charash, 2005). The dispositional view asserts that enduring dispositional traits, such as personality, determine individual outcomes across situations and settings, and through time. With respect to the present theme, this means that individuals with similar personality profiles must show consistency across settings and over time in the extent to which they receive mentoring. Hence, information on one's personality can enable the informed prediction of whether this individual will develop mentoring relationships.

However, despite the importance of the issue, empirical research on the link between mentoring receipt and personality is limited, as authors stress [START_REF] Dougherty | The role of personality in employee developmental networks[END_REF]Turban & Lee, 2007). Most important, extant research, albeit certainly contributory, has two drawbacks. First, that research is inconsistent in utilization of personality framework.

Existing studies utilize a variety of frameworks, including the instrumentality-expressiveness [START_REF] Fagenson | The mentor advantage: Perceived career/job experiences of protégés versus non-protégés[END_REF][START_REF] Kirchmeyer | Change and stability in managers' gender roles[END_REF][START_REF] Scandura | The effects of sex and gender role orientation on mentorship in male-dominated occupations[END_REF]) and the needs model [START_REF] Fagenson | Mentoring: who needs it? A comparison of protégés' and nonprotégés' needs for power, achievement, affiliation and autonomy[END_REF][START_REF] Fagenson-Eland | Personality predictors of protégé mentoring history[END_REF], isolated traits [START_REF] Allen | Mentoring and protégé narcissistic entitlement[END_REF][START_REF] Wang | The role of mentor trust and protégé internal locus of control in formal mentoring relationships[END_REF] or collections of isolated traits [START_REF] Aryee | Antecedents of early career stage mentoring among Chinese employees[END_REF]Turban & Dougherty, 1994). This hinders the extraction of parsimonious conclusions because of different degrees of compatibility between personality frameworks and overlap between their traits. For example, extant studies employ the traits of instrumentality, locus of control, Type A personality, need for power, and self-monitoring.

These traits overlap in various degrees (e.g., [START_REF] Lippa | Gender diagnosticity: A new Bayesian approach to genderrelated individual differences[END_REF][START_REF] Morrison | Personality correlates of the five-factor model for a sample of business owners/managers: Associations with scores on self-monitoring, type A behavior, locus of control and subjective well-being[END_REF].

However, neither do these traits refer to the same construct, nor do they share the same characteristics, nor do they overlap to the same degree. Therefore, utilization of a single personality framework that contains mutually orthogonal traits and provides a comprehensive description of human personality will improve clarity and enhance understanding.

Second, research so far investigates only relationships of linear nature between personality and mentoring receipt. However, the presence of curvilinear relationships is within reason. Ignoring the presence of curvilinearity can lead to erroneous conclusions over the nature and magnitude of associations (e.g., Trevor, Gerhart, & Boudreau, 1997;[START_REF] Iversen | Returns to schooling in selfemployment[END_REF], and that includes associations between personality and its outcomes [START_REF] Vasilopoulos | Personality and training proficiency: Issues of bandwidth-fidelity and curvilinearity[END_REF]. These limitations suggest that additional investigations on the subject may be beneficial.

The Present Research

The research here investigates the relationship between personality and mentoring receipt from both a linear and a quadratic (in particular, inverted U-shaped) perspective with the utilization of the Big-Five personality framework. The Fig-Five, which contains the five mutually orthogonal traits of emotional stability, extraversion, openness to experience (hereinafter "openness"), agreeableness and conscientiousness, has accumulated extensive empirical support on its validity (e.g., [START_REF] Digman | Personality structure: Emergence of the five factor model[END_REF][START_REF] Goldberg | The structure of phenotypic personality traits[END_REF][START_REF] Mccrae | Toward a new generation of personality theories: Theoretical contexts for the five-factor model[END_REF][START_REF] Wiggins | Personality structure: The return of the Big Five[END_REF]. Furthermore, the Big-Five possesses the critical properties of parsimony and comprehensiveness, because the model describes human personality in terms of a manageable number of traits that encompass virtually every aspect of the personality sphere (see, for example, [START_REF] Ashton | A hierarchical analysis of 1,710 English personality-descriptive adjectives[END_REF][START_REF] O'connor | A quantitative review of the comprehensiveness of the five-factor model in relation to popular personality inventories[END_REF]. In addition, the structure of the Big-Five is robust across cultures [START_REF] Mccrae | Personality trait structure as a human universal[END_REF][START_REF] Schmitt | The geographic distribution of big five of personality traits: Patterns and profiles of human self-description across 56 nations[END_REF]. This signifies that conclusions on the relationship between personality and mentoring within a particular culture can serve as reference point in the consideration of that relationship within other national cultural contexts. This is of importance in light of the state of globalization today (e.g., Al Ariss, 2010).

Because of the above critical properties, the Big-Five holds the status of the most acceptable trait personality theory [START_REF] Barrick | Personality and performance at the beginning of the new millennium: What do we know and where do we go next[END_REF][START_REF] John | Paradigm shift to the integrative Big-Five trait taxonomy: History, measurement, and conceptual issues[END_REF]). An illustration of its widespread acceptance as parsimonious descriptor of human personality is that serious criticisms of its validity and comprehensiveness virtually ceased after the mid 1990s (see review by [START_REF] John | Paradigm shift to the integrative Big-Five trait taxonomy: History, measurement, and conceptual issues[END_REF]. This recognition accompanies the model in organizational research too, where authors use the Big-Five as the personality framework of reference (see, for example, [START_REF] Ones | In support of personality assessment in organizational settings[END_REF]. To illustrate, meta-analytic research employs the Big-Five to conclude on the link of personality with a host of processes and outcomes in the work environment, ranging from key constructs such job performance [START_REF] Barrick | Personality and performance at the beginning of the new millennium: What do we know and where do we go next[END_REF]Chiaburu, Oh, Berry, Li, & Gardner, 2011), work motivation (Judge & Ilies, 2002), work attitudes [START_REF] Judge | Five-factor model of personality and job satisfaction: A meta-analysis[END_REF], and leadership (Judge, Bono, Illies, & Gerhardt, 2002) to less prominent constructs, such as entrepreneurial intentions [START_REF] Zhao | The relationship of personality to entrepreneurial intentions and performance: A meta-analytic review[END_REF]. Therefore, utilization of the Big-Five taxonomy when investigating the relationship of mentoring receipt with protégés' personality will maximize the contribution of the research (see also Turban & Lee, 2007).

Conceptualization and measurement of mentoring receipt

For validity purposes researchers must clearly define the type of mentoring relationship the research focuses on [START_REF] Allen | The state of mentoring research: A qualitative review of current research methods and future research implications[END_REF][START_REF] Haggard | Who is a mentor? A review of evolving definitions and implications for research[END_REF]. This step is necessary because forms of mentoring relationships (e.g., formal, informal, vertical, horizontal) vary in terms of dynamics [START_REF] Allen | The state of mentoring research: A qualitative review of current research methods and future research implications[END_REF]; which means that simultaneous consideration of various types of mentoring increases the likelihood of confounding. In the present research the focus is exclusively on informal traditional mentoring, which refers to a naturally evolving developmental relationship between two members of the same organization who are of unequal status. The reasons are the following: First, informal traditional mentoring represents the prototype mentoring relationship (e.g., [START_REF] Eby | Alternative forms of mentoring in changing organizational environments: A conceptual extension of the mentoring literature[END_REF][START_REF] Higgins | Reconceptualizing mentoring at work: A developmental network perspective[END_REF]; second, as they evolve naturally such relationships are more likely to reveal the role of personality. This is because effects of personality are most discernible in situations of low external constraints (Whithey, Gellatly, & Annet, 2005).

Formal mentoring arrangements, for example, conform to certain rules and regulations, hence, they certainly impose more interactional constraints than informal mentoring relationships; and third, informal mentoring accrues more benefits than formal mentoring [START_REF] Underhill | The effectiveness of mentoring programs in corporate settings: A meta-analytical review of the literature[END_REF]. Therefore, informal traditional mentoring must have priority in novel investigations.

The present research conceptualizes and measures mentoring received as the totality of the mentoring experience of the individual. This conceptualization encompasses both whether the individual has ever had relationships with mentors and the amount of mentoring the individual has received in those mentoring relationships.

Hypotheses

The development of hypotheses makes use of only those extant studies that employ Big-Five traits (i.e., the studies by [START_REF] Aryee | Antecedents of early career stage mentoring among Chinese employees[END_REF][START_REF] Haggard | Who is a mentor? A review of evolving definitions and implications for research[END_REF]Dougherty, 1994). The reason is the imperfect fit of non-Big-Five traits into to the Big-Five model, which seriously compromises the validity of pertinent conjectures [START_REF] Hurtz | Personality and job performance: The big five revisited[END_REF][START_REF] Salgado | The five factor model of personality and job performance in the European Community[END_REF].

Hence, in the research at hand development of hypotheses primarily draws upon logical reasoning, and secondarily upon findings of the very limited existing empirical research on personality and mentoring that employs traits of the Big-Five.

Although linear relationships have priority in terms of testing in social sciences, relationships of curvilinear nature also demand consideration, especially when adequate logical underpinning exists (e.g., [START_REF] Jackofsky | Turnover and job performance: An integrated process model[END_REF][START_REF] Williams | Another look at the relationship between performance and voluntary turnover[END_REF]. The form of non-linear relationship that appears likely in the association between mentoring receipt and personality is the quadratic. Quadratic relationships exist in two forms, U-shaped and inverted U-shaped. U-shaped relationships signify associations that are negative and positive for low and high values of predictor variables, respectively. Relationships of inverted U-shape display the reverse pattern. The authors have reason to expect that quadratic, and in particular inverted U-shaped, equations describe best the link of mentoring receipt with most of the Big-Five traits.

Emotional stability involves composure, confidence, and low tendencies towards development of anxiety. Low emotional stability (or neuroticism) encompasses suspiciousness, irritability and hostility. Therefore, individuals who score low on emotional stability should hesitate to involve themselves in relationships with mentors because of their general suspiciousness and lack of poise. In line with this reasoning, Turban and Dougherty (1994) find a positive relationship between emotional stability and attempts to initiate relationships with mentors. In addition, mentors should hesitate to approach individuals who score low on emotional stability because mentors allegedly prefer as protégés those who display confidence [START_REF] Kram | Mentoring at work: Developmental relationships in organizational life[END_REF][START_REF] Melanson | Qualities of the ideal protégé[END_REF]. Furthermore, low emotional stability relates to distancing behavior [START_REF] Brookings | An interpersonal circumplex/five-factor analysis of the rejection sensitivity questionnaire[END_REF]. This type of behavior from the part of the protégé should reduce the amount of mentoring the protégé receives. H1: Emotional stability has a positive linear relationship with mentoring received.

Characteristics of extraversion include sociability, gregariousness, optimism, tendencies towards action, assertiveness and ambition. Extraverts proactively seek social encounters in the work place (e.g., [START_REF] Gruman | Socialization preferences and intentions: Does one size fit all?[END_REF], thus, they must have greater propensity to approach mentors. Indeed, [START_REF] Aryee | Antecedents of early career stage mentoring among Chinese employees[END_REF] report a positive association between extraversion and attempts to initiate relationships with mentors. In addition, [START_REF] Kram | Mentoring at work: Developmental relationships in organizational life[END_REF] suggests that mentors prefer assertive and outgoing protégés. Hence, they should approach extraverts as protégés because extraverts tend to display these behavioral patterns [START_REF] John | Paradigm shift to the integrative Big-Five trait taxonomy: History, measurement, and conceptual issues[END_REF]. Furthermore, within mentoring relationships extravert protégés, because of their sociability, would interact more with their mentors and, hence, they would receive more mentoring.

However, although extraversion must generally offer advantage in mentoring receipt, presence of the trait above a certain level may not be of benefit or may even hurt the relationship. For example, high extraversion may bring inability to inhibit socially inappropriate behaviors or to suppress the expression of excessive ambition; which may repulse a potential mentor or render an existing mentor reluctant to fully devote oneself in the relationship. Indeed, extraverts demonstrate lower levels of self-control, that is lower capability to regulate the expression of emotions and impulses that are socially inappropriate [START_REF] Zabelina | The psychological tradeoffs of self-control: A multi-method investigation[END_REF]; and mentors view negatively protégé behaviors that indicate excessive ambition [START_REF] Eby | The protégé's role in negative mentoring experiences[END_REF]. Furthermore, mentors may consider that those who display strong extraversion do not need their help. For instance, extraverts are apt at developing networks [START_REF] Wolff | The relationship between networking behaviors and the big five personality dimensions[END_REF]. This may make the mentor consider that helping the protégé with functions such as sponsorship, exposure, acceptance and friendship (that network ties also provide) is redundant. This reasoning directs towards the possibility of inverted U-shaped relationship. H2: An equation of inverted U-shaped curve describes the relationship between extraversion and mentoring received more accurately than a positive linear equation.

Openness encompasses multiplicity of interests, inquisitiveness, information seeking, imagination and creativity. Individuals with higher scores on openness must have greater interest in relationships with mentors because such relationships can expose them to novel perspectives, and can provide them information on their job and the organization. In line with this view, empirical research finds that openness relates to seeking performance feedback from others [START_REF] Wanberg | Predictors and outcomes of proactivity in the socialization process[END_REF]. Furthermore, mentors report more attraction towards protégés who show interest in learning and in exposure to different viewpoints because mentoring such individuals is more likely to satisfy the mentors' need to pass their wisdom [START_REF] Allen | The mentor's perspective: A qualitative inquiry and future research agenda[END_REF]. Finally, within the relationship those with greater inquisitiveness and orientation towards learning should receive more mentoring.

However, strong openness may act as inhibitor for mentoring receipt. Vivid imagination and a wide range of interests, for example, may render the protégé unable to focus on his or her tasks. Evidence shows that high openness is a disadvantage in tasks that require intense concentration [START_REF] Rose | Psychological predictors of astronaut effectiveness[END_REF]. This may discourage a potential mentor, or dishearten an existing mentor and make him/her hesitant to commit to the relationship. In line with this conjecture, empirical research shows that mentors evaluate their relationships with protégés negatively when protégés lack focus in their work [START_REF] Eby | The protégé's role in negative mentoring experiences[END_REF]. Furthermore, within mentoring relationships, protégés with excessive inquisitiveness and multiple interests may experience difficulty to maintain their attention to their mentors, and this should limit the amount of mentoring they receive. In concurrence with this argument, [START_REF] Dougherty | The role of personality in employee developmental networks[END_REF] suggest that individuals with high scores on openness have difficulties to dedicate themselves to single intensive developmental relationships, like a relationship with a mentor, and have the tendency to form multiple relationship ties instead. The above points suggest that association of inverted-U-shape is likely. H3: An equation of inverted U-shaped curve describes the relationship between openness and mentoring received more accurately than a positive linear equation.

Agreeableness encompasses altruism, tender-mindedness, sensitivity to the needs of others, trust and modesty. Due to their trusting and altruistic nature agreeable individuals must be more prone to approach mentors, but also mentors themselves must develop attraction to such individuals. In line with this argument, people are more likely to select as friends those who score high on agreeableness [START_REF] Selfhout | Emerging late adolescent friendship networks and big five personality traits: A social network approach[END_REF]. In addition, within the mentoring relationship, those who score high on agreeableness, due to their sensitive, altruistic and modest disposition, would reciprocate the positive gestures of their mentors.

Indeed, agreeable individuals have the tendency to demonstrate commitment [START_REF] Spagnoli | Personality and organisational commitment: The mediating role of job satisfaction during socialisation[END_REF], and are more likely to act in a trustworthy way and reciprocate positive acts of others [START_REF] Ben-Ner | Trusting and trustworthiness: What are they, how to measure them, and what affects them[END_REF]. This must strengthen the involvement of both parties, and increase the amount of mentoring receipt. Finally, protégé trust towards the mentor leads to more mentoring (Chun, [START_REF] Litzky | Emotional intelligence and trust in formal mentoring programs[END_REF]; hence, due to their trusting disposition those who score high on agreeableness should receive more mentoring once in the relationship.

However, the benefits of agreeableness for mentoring receipt may decrease when levels of the trait become excessive. For example, individuals with high levels of altruism and very strong tendencies for self-sacrifice may assign low priority to their own personal development and careers [START_REF] Judge | The big five personality traits, general mental ability, and career success across the life span[END_REF]; hence, they may overlook opportunities to establish relationships with mentors, or may pay inadequate attention to functions that pertain to career development within the mentoring relationship. In addition, mentors may at points lose their enthusiasm with protégés who display strong agreeableness. This is because, as seen, mentors show more interest in protégés who demonstrate strong career prospects, and agreeable individuals are less likely to achieve hierarchical advancement [START_REF] Bozionelos | The relationship between disposition and career success: A British study[END_REF]. H4: An equation of inverted U-shaped curve describes the relationship between agreeableness and mentoring received more accurately than a positive linear equation.

Conscientiousness encompasses industriousness, reliability, achievement-striving, selfdiscipline, perseverance and sense of duty. Because of these features conscientiousness is the strongest personality correlate of job performance [START_REF] Barrick | Personality and performance at the beginning of the new millennium: What do we know and where do we go next[END_REF][START_REF] Ng | Human capital and objective indicators of career success: The mediating effects of cognitive ability and conscientiousness[END_REF]. Mentors express preference for protégés who display aspects of conscientiousness (e.g., dependability), and for protégés who display actual contextual (e.g., enthusiasm at work) or task performance [START_REF] Allen | The mentor's perspective: A qualitative inquiry and future research agenda[END_REF][START_REF] Allen | Protégé selection by mentors: What makes the difference?[END_REF]. These preferences mean that mentors must approach those who score higher on conscientiousness and, hence, such individuals must have greater likelihood of receiving mentoring.

Indeed, in a longitudinal study, [START_REF] Singh | Who gets a mentor? A longitudinal assessment of the rising star hypothesis[END_REF] find that those who are in the fast-track for promotion, and who others presumably view as better performers, are more likely to obtain a mentor. Furthermore, conscientious individuals have a strong orientation towards achievement and self-improvement (e.g., [START_REF] Schuler | Development and construct validation of a job-related achievement motivation test[END_REF].

This orientation should dispose them to seek and pay more attention at their mentors' advice and role behaviors, which means that within mentoring relationships conscientious individuals must receive more mentoring.

However, the beneficial effect of conscientiousness for mentoring receipt may discontinue or reverse for strong levels of the trait. Individuals with extreme conscientiousness may focus excessively on task accomplishment and this may lead them to disregard social interaction. Indeed, conscientiousness relates to perfectionism [START_REF] Egberink | Conscientiousness in the workplace: Applying mixture IRT to investigate scalability and predictive validity[END_REF], which in turn relates to deficits in social interaction [START_REF] Flett | Dimensions of perfectionism, psychological adjustment, and social skills[END_REF]. This may reduce probabilities of obtaining a mentor and may also reduce the amount of mentoring receipt within a relationship. Furthermore, highly industrious and dutiful individuals may over-concern themselves with their duties and tasks, and neglect their social image. In line with this conjecture, those who score high on conscientiousness are more likely to be workaholic [START_REF] Aziz | Exploring the relationship between workaholism facets and personality traits: A replication in American workers[END_REF]. Workaholics, in turn, are more likely to behave in interpersonally destructive ways, such as acting rudely or publicly embarrassing others [START_REF] Galperin | Uncovering the relationship between workaholism and workplace destructive and constructive deviance: An Exploratory study[END_REF], or experience burnout [START_REF] Guglielmi | Self-efficacy and workaholism as initiators of the job demands-resources model[END_REF], which must deduct from their social image. This may act as deterrent for potential mentors. This may also cause resentment of an existing mentor and spoil the relationship, hence, reduce quantity and quality of mentoring receipt. The above reasoning also directs towards a relationship of inverted-U-shape. H5: An equation of inverted U-shaped curve describes the relationship between conscientiousness and mentoring received more accurately than a positive linear equation.

Overview of Studies

Two independent studies investigate the hypotheses. The studies differ only with respect to the nature of the sample and the measurement of the Big-Five. In both studies, criteria for participant inclusion are identical: (1) Participants are not self-employed; (2) participants are in full-time employment; (3) employing organizations do not have formal mentoring schemes in place; and (4) participants have at least two years of tenure, an adequate interval for the development of a mentoring relationship (e.g., [START_REF] Chao | Mentoring phases and outcomes[END_REF] and for personality traits to exert detectable effects on social outcomes [START_REF] Helmreich | The honeymoon effect in job performance: Temporal increases in the predictive power of achievement motivation[END_REF].

All measures are identical between the studies apart from the Big-Five measure. The first study assesses the Big-Five with self-reports and the second study with peer reports. This is in line with calls for utilization of multi-source data in mentoring research [START_REF] Allen | The state of mentoring research: A qualitative review of current research methods and future research implications[END_REF]. And will also provide information on consistency of relationships with assessment of the Big-Five from different raters.

Study 1

Method

Setting and Participants

Participants were 212 individuals (134 women and 78 men) attending advanced courses in management related subjects in a Business School in the north of the United Kingdom. Of 343 respondents, those 212 fulfilled the inclusion criteria. Distribution and completion of the personality measure took place on a different occasion from the rest of the measures.

Descriptive statistics are presented in Table 1. Participants were employed in a variety of occupations and organizational roles (ranging from specialist technical jobs to purely managerial roles), organizational types and industry types. Of the participants, 77.4% were employed in the service industry, a proportion that is very close to the proportion of employees working in the service industry in the UK (Department of Trade and Industry, 2007). The majority of participants were married or co-habiting (57.5%); held at least undergraduate degrees (61.3%); and occupied non-supervisory (32.9%), junior management (20.3%) or middle management (30.7%) positions.

Measures

Mentoring received. The measurement of mentoring received adheres to accumulated knowledge that mentoring relationships vary widely with respect to the scope and intensity of mentoring functions they provide. In essence, they form a continuum with no mentoring occupying the one end and the full breadth of mentoring functions occupying the other end.

Early seminal work (e.g., [START_REF] Kram | Mentoring at work: Developmental relationships in organizational life[END_REF][START_REF] Zey | The mentor connection[END_REF] implies this variance, which more recent empirical research corroborates. In particular, [START_REF] Ragins | Marginal mentoring: The effects of type of mentor, quality of relationship, and program design on work and career attitudes[END_REF] and [START_REF] Ensher | Comparison of traditional, step-ahead, and peer mentoring on protégés support, satisfaction, and perceptions of career success: A social exchange perspective[END_REF] conclude that the breadth and intensity of functions mentoring relationships provide vary widely, and stress that mentoring relationships are unequal with respect to amount of mentoring protégés receive [START_REF] Ragins | Marginal mentoring: The effects of type of mentor, quality of relationship, and program design on work and career attitudes[END_REF](Ragins et al., , p. 1177)).

The operationalization of mentoring received in the study at hand incorporates the above knowledge and involves two steps. In the first step, participants are asked to indicate (in a binary "yes" or "no" item) whether they have had at least one mentor during their employment with their current employer, after considering the following definition: "A mentor is generally defined as a higher-ranking and more experienced individual in the work environment who is committed to providing personal or career support to another individual, the protégé. A person's mentor does not have to be one's immediate superior and the relationship needs not to be formally arranged by the organization. Some people have had no mentors while other people have had many different mentors in their careers."

In the second step, those who respond positively in the first step complete a scale that contains nine items from Dreher and Ash (1990) on a 5-point response format (1: not at all, 5: to a great extent). The scale asks respondents to consider their employment with their current employer and indicate the extent to which "a higher-ranking individual (this need not be limited to one person) who had advanced experience and knowledge" has provided a variety of functions for them. Items cover all nine mentoring functions the literature identifies (e.g., [START_REF] Kram | Mentoring at work: Developmental relationships in organizational life[END_REF]Tepper, Shaffer, & Tepper, 1996), including the five career-instrumental functions (e.g., the item "given or recommended you for challenging assignments that presented opportunities to learn new skills?" corresponds to the challenging assignments function), and the four socioemotional functions (e.g., "served as a role model" corresponds to the role modeling function). Cronbach  for this study was .88. A test with a sample of 91 executive MBA students (whose responses were not included in the research reported here) revealed no relationship (r = .07, ns) between scores on the scale and scores on the Crowne-Marlowe social desirability scale [START_REF] Crowne | The approval motive: Studies in evaluative dependence[END_REF]. This indicates that social desirability does not affect responses to the instrument.

All participants, those who reported that they had had at least one mentor and those who reported that they had had no mentors, were included in the analysis. Scores for the former were set equal to their scores on the scale; and the latter were assigned the minimum possible score on the scale (i.e., nine). That process ensures that measurement of mentoring received is in line with accumulated knowledge, because this method is able to tap variations between individuals in the amount of mentoring they have received, from one or more mentors. This process also accounts for cases of individuals who have had no experience in mentoring receipt, who are assigned the lowest score on the scale. Both studies in the research at hand utilize this method of measuring mentoring received. Some authors have employed analogous, though simpler, operationalizations [START_REF] Aryee | Antecedents of early career stage mentoring among Chinese employees[END_REF]Bozionelos, 2004a;[START_REF] Bozionelos | How providing mentoring relates to career success and organizational commitment: A study in the general managerial population[END_REF].

Big-Five traits. These were assessed with the NEO Five-Factor Inventory [START_REF] Costa | Revised NEO Personality Inventory (NEO PI-R) and NEO Five-Factor Inventory (NEO-FFI) professional manual[END_REF]) that includes 60 personal statements, 12 for each Big-Five trait, in a 5-point response format (1: strongly disagree, 5: strongly agree). [START_REF] Costa | Revised NEO Personality Inventory (NEO PI-R) and NEO Five-Factor Inventory (NEO-FFI) professional manual[END_REF] report Cronbach alphas in a range of .68 for agreeableness to .86 for conscientiousness. Alphas for the present sample are .87, .62, .72, .60 and .82 for emotional stability, extraversion, openness, agreeableness and conscientiousness, respectively.

Controls. Single items assessed gender (male: 1, female: 2); age (in years); educational attainment: CSE or below (coded 1) to Graduate degree (coded 6); marital status (single: 1, co-habiting: 2, married: 3); tenure (in years); starting and current organizational grade:

"subordinate" (coded 1) to "CEO" (coded 7); and staff (coded 1) or line (coded 2) position.

An item that asked the socio-economic level of respondents' family when they were at the age of 15 (upper class: 5 to working class: 1), assessed socio-economic origin. Both studies utilize these controls.

In this study only, single items also assessed organizational size, "below 20" (coded 1) to "more than 1000" (coded 6); sector type (public: 1, private: 2); and industry type (service:

1, manufacturing: 2).

Results

Table 1 presents Pearson correlation coefficients. Hierarchical regression tests the hypotheses. The first step includes the controls. In line with recommendations for detecting quadratic relationships [START_REF] Cohen | Applied multiple regression/correlation analysis for the behavioral sciences[END_REF], the second step contains the first-order terms of scores on the Big-Five traits. The third, and final, step contains the second-order (i.e., squared) terms of scores on the Big-Five traits. In all steps variables enter the equation by forcible entry. The regression makes use of centered scores on Big-Five traits because this assists in the interpretation of results in quadratic equations (Cohen et al., 2003, p. 204). Significance testing uses values from one-tailed distribution due to existence of specific hypotheses. Both studies use the same data-analytic methodology.

Tables 1 and2 here.

Table 2 presents the final regression model. The first-order term ( = .19, t = -2.29, p < .05) of emotional stability makes a significant contribution to mentoring received over and above the controls, while the second-order term does not ( = .05, t = .53, ns). The sign of the first-order term indicates a linear positive association that supports Hypothesis 1.

The second-order terms of extraversion ( = .17, t = 2.61, p < .01), openness ( = -.26, t = -3.61, p < .001) and agreeableness ( = -.22, t = -3.14, p < .01) make significant contributions to mentoring received over and above the contributions of controls and firstorder terms. This suggests presence of quadratic relationships. The signs of the coefficients of second-order terms provide information on the direction of curvature [START_REF] Cohen | Applied multiple regression/correlation analysis for the behavioral sciences[END_REF].

The negative signs of second-order terms for openness and agreeableness indicate relationships of inverted U-form, which are in line with H3 and H4, respectively. On the other hand, the positive sign of the second-order term for extraversion suggests a relationship of Uform, which has the reverse curvature from the hypothesized. This indicates no support for Hypothesis 2.

The signs of the regression coefficients of first-order terms inform on the direction of relationships at the mean scores of the predictor variables [START_REF] Cohen | Applied multiple regression/correlation analysis for the behavioral sciences[END_REF]. The value of the predictor (i.e., personality trait) that verifies the first derivate of the corresponding univariate quadratic equation for zero (meaning that the tangent line at that point is parallel to the x-axis) represents the point of bending. The negative coefficient ( = -.13) of the firstorder openness term suggests that the direction of the relationship is negative at the mean value of openness scores. In particular, the relationship turns negative at -.55 SDs from the mean of the trait. The positive coefficient ( = .16) of the first-order agreeableness term suggests that the direction of the relationship is still positive at the mean score of agreeableness: the slope turns negative at 1.20 SDs above the mean of the trait. Finally, the positive first-order coefficient ( = .12) of extraversion suggests that the direction of the relationship has already become positive at the mean score of the trait. In fact, the slope turns upwards at -.75 SDs from the mean score of extraversion.

Finally, the significance of the first-order term ( = .21, t = 2.83, p < .01) of conscientiousness in conjunction with the non-significance of the second-order term ( = -.02, t = -.26, ns) means that a linear equation describes the relationship best. This indicates no support for Hypothesis 5.

Discussion

The positive linear association of emotional stability with mentoring received suggests that, in line with expectations, increases in emotional stability associate with increases in amount of mentoring receipt for the whole spectrum of values of the trait. The pattern is exactly the same for conscientiousness. This means that increases in features such as industriousness, diligence, assiduity, perseverance and dutifulness constantly accompany increases in probability to receive mentoring. The difference from emotional stability is that the finding for conscientiousness is not in line with the expectation for a concave curve.

Apparently, therefore, negative states that strong conscientiousness may associate with, such as workaholism, do not harm mentoring receipt, at least in the context this particular sample reflects.

The results for openness and agreeableness are in line with expectations. The specifics of the inverted U-shaped curve for openness suggest that mentoring receipt increases along with openness until a point near the mean score of the trait and at that point the upwards trend reverses. Regarding agreeableness, the particulars of the curve suggest that the switch in the direction of the relationship from positive to negative occurs well after the mean agreeableness score (in fact, the change in the slope occurs near the top scores on the trait in the sample). This indicates that unless possessing extreme levels of the trait, agreeable individuals have an advantage in terms of mentoring receipt over their less agreeable counterparts. This highlights the difference with the pattern for openness, whose benefits for mentoring receipt cease at earlier point.

The result for extraversion suggests that as scores on the trait increase from low to moderate mentoring receipt decreases. This is at odds with the expectation. On the other hand, the direction of the relationship reverses well before (nearly one standard deviation below) the mean score of the trait. This means that the negative trend limits itself to a restricted range of scores at the lower part of the extraversion continuum. Therefore, the specifics of the curve imply a positive overall trend in the relationship (Cohen et al., 2003, p. 204). This is visually illustrated in Figure 1. Dougherty et al.'s (2007) suggestion helps to develop an account, albeit post-hoc, for this observed pattern. Dougherty et al. suggest that those who score low on extraversion (i.e., introverts) still need social interaction, but they need more focused interaction; and for this reason they seek exclusive developmental relationships, such as relationships with mentors. This is in line with the finding that decreases in extraversion at the low range of scores of the trait associate with increases in amount of mentoring received. However, as extraversion moves away from its low scores, that is from introversion, the features of the trait take over and, hence, shifts from mediocre scores upwards increase the likelihood to receive mentoring. In addition, extraverts must also benefit from that potential mentors are more likely to notice them. Therefore, the slope becomes steeper as one moves towards the positive pole of the trait. In essence, therefore, they are only those with average extraversion who are disadvantaged in terms of probabilities to receive mentoring.

Figure 1 here.

Study 2

Method

The main purpose of the second study is to test the hypotheses in a sample of different nature. The sample of the first study was highly heterogeneous both occupationally and structurally. The setting of the second study is chosen to represent a particular function within a single organization; hence, providing a sample with much greater occupational and structural homogeneity. A sample of this nature should inform on the extent to which the findings of the first study are applicable within particular settings. An additional purpose of the second study was to conduct the investigation by obtaining measures of the Big-Five and mentoring received from different sources.

Setting and Participants

Participants were 131 individuals (48 women and 83 men) from the Information Systems function of a large British company that operates in the financial services sector.

These were those of 145 individually approached respondents who fulfilled the criteria for inclusion. Table 3 presents descriptive statistics. Most participants had university education (69.5%), and were professionals performing specialist technical jobs (51.9%), while the rest held supervisory (32.8%) and management positions within technical disciplines.

Measures

Measurement of mentoring received and of the controls (that did not include organizational size, sector type, and industry type) was identical to the first study. Cronbach for the mentoring received scale in Study 2 was .80.

Big-Five traits. These were assessed by peers using Saucier's (1994) mini-markers.

Eight unipolar adjectives on a nine-point scale (1: extremely inaccurate, 9: extremely accurate) assess each Big-Five trait. Examples for emotional stability include "moody" (reverse scoring) and "relaxed"; for extraversion: "talkative" and "shy" (reverse scoring); for openness: "creative" and "unintellectual" (reverse scoring); for agreeableness: "sympathetic" and "harsh" (reverse scoring); and for conscientiousness: "systematic" and "sloppy" (reverse scoring). Each participant handed the personality questionnaire along with a return envelope to a peer of the same gender to complete (see [START_REF] Goldberg | The development of markers for the big-five factor structure[END_REF][START_REF] Saucier | Mini-markers: A brief version of Goldberg's unipolar big-five markers[END_REF]. Instructions to peers asked that they return completed questionnaires sealed to participants, who returned these, along with their own completed questionnaires, personally to the researcher. Cronbach alphas were .84, .84, .64, .84 and .82 for emotional stability, extraversion, openness, agreeableness and conscientiousness, respectively.

Results

Table 3 presents the inter-correlations. Table 2 presents the results of hypotheses testing.

Table 3 here.

The first-order term of emotional stability ( = .19, t = 2.26, p < .05) makes a significant contribution to mentoring received over and above the controls, while the second-order term does not ( = .06, t = .75, ns). The positive coefficient of the first-order term indicates support for Hypothesis 1. The second-order terms of openness ( = -.19, t = -4.19, p < .001) and agreeableness ( = -.25, t = 2.96, p < .01) make significant contributions to mentoring received over and above the controls and the first-order terms. The negative sings of the coefficients indicate curvatures of inverted-U-shape, hence, support for Hypotheses 3 and 4.

The signs of the first-order coefficients suggest that the directions of the relationships are still positive at mean scores of the traits. In particular, the points where the slopes turn negative are .96 SDs and .19 SDs above the mean scores of openness and agreeableness, respectively. Neither the second-order term of extraversion ( = .04, t = .55, ns) nor the second-order term of conscientiousness ( = -.06, t = -1.03, ns) make significant contributions to the equation. This suggests no support for Hypotheses 2 and 5. The first-order term of conscientiousness is not significant ( = .06, t = .81, ns), suggesting no presence of linear relationship either, but the first-order term of extraversion is marginally significant ( = .11, t = 1.62, p < .06) with the relationship in the positive direction.

Figure 2 here.

Discussion

The result for emotional stability is in line with expectations and in line with the result of the first study (in fact, effect coefficients for this trait are identical in the two studies).

Increases in emotional stability appear to provide an advantage for mentoring receipt along the whole spectrum of the trait. The findings for openness and agreeableness concur with the expectation for inverted U-form relationships, and the particulars of the curves indicate that for the greater part of their continua increases in scores on these traits associate with increases in amount of reported mentoring receipt. With regards to openness, increases in its amount bring no more benefit and may become a disadvantage for receiving mentoring only when the trait becomes very strong (i.e., beyond one standard deviation above the mean). A discrepancy with the pattern of the first study is that in the second study openness continues to pay dividends for mentoring receipt well beyond its mean score, while in Study 1 the trait ceases to do so before its mean. Nevertheless, the forms of the relationships for emotional stability, openness and agreeableness do show consistency between the two studies.

The result for extraversion indicates association of positive linear trend. Though this does not lend support to the corresponding hypothesis, it concurs with the idea that the features of extraversion must bring mostly benefits with respect to mentoring receipt (i.e., first part of the reasoning behind Hypothesis 2). The positive linear relationship of extraversion in the second study is also compatible with the overall positive trend of its association in the first study.

Increases in conscientiousness are not associated with increases in likelihood to report mentoring receipt; hence, the features of conscientiousness do not appear to convey an advantage within the context of Study 2. This is discrepant with the corresponding finding of the first study (that, however, does not support the respective hypothesis for quadratic relationship either). The general discussion tackles these findings.

Overall, the results of the two studies show substantial, if not remarkable, consistency (in essence, the results concur with respect to the relationships of four out of the five traits).

Discrepancies of substance are limited. The Big-Five markers of Study 2 demonstrate convergent validity with the NEO of Study 1 [START_REF] Goldberg | The development of markers for the big-five factor structure[END_REF][START_REF] John | Paradigm shift to the integrative Big-Five trait taxonomy: History, measurement, and conceptual issues[END_REF], and selfand peer-report assessments of personality generally show good agreement [START_REF] Ready | Self-and peer-reported personality: Agreement, trait ratability, and the "self-based heuristic[END_REF]. Hence, the setting rather than the measurement is the most likely cause of these discrepancies. Furthermore, if the causes of the discrepancies lie in the measurement of the Big-Five then these must have been more widespread. The general discussion touches the issue of context. Finally, though not directly relevant to hypotheses, the Big-Five traits account for greater proportions of variance in mentoring received in the second study (31.9%), which uses peer assessments of personality, than in the first study (11.2%) that uses self-reports. This pattern makes implications regarding alleged validity improvements with multi-source measurement methodologies over self-report methodologies.

Overall Discussion

The research at hand focuses on the relationship of the Big-Five of personality with mentoring receipt. The results indicate that the Big-Five accounts for substantial variance in mentoring receipt over and above demographic, human capital and structural factors, with all Big-Five traits demonstrating links. In addition, the move from linear to quadratic equations brings considerable increase in the capacity of personality to explain variance. This means that the role of personality in mentoring is stronger and more complicated than what simple linear associations advise.

The forms of the associations show substantial agreement between the two studies. This implies considerable generalizability across occupational and organizational contexts.

Hence, the findings support the dispositional approach to organizational behavior because: (1) the Big-Five explains sizable variance in mentoring receipt over and above a host of personal, occupational and organizational demographics, and (2) the patterns of association show substantial congruence between the two studies, which represent different settings.

Emotional stability demonstrates a remarkably consistent link with mentoring receipt across the two studies. The nature of the relationship indicates that in the whole of its spectrum higher levels of that trait constantly correspond to greater amounts of mentoring receipt. This means that qualities such as calmness, patience, confidence and a positive outlook of situations offer a continuous advantage in terms of receiving mentoring. Emotional stability is the only Big-Five trait within the construct of core self-evaluations, whose advocates view as a dispositional kernel that heavily influences the way individuals perceive themselves and their environment [START_REF] Bono | Core self-evaluations: A review of the trait and its role in job satisfaction and job performance[END_REF]. The present findings, therefore, concur with the placement of emotional stability into a central spot in human disposition.

Conscientiousness also has a linear relationship with mentoring receipt. However, this relationship appears only in one of the studies, albeit the one that utilizes the most structurally and occupationally heterogeneous sample and, hence, arguably bears most resemblance to the general working population. This means that in the general case increases in the strength of the trait convey an advantage in the mentoring receipt arena. On the other hand, the lack of relationship in the technically-oriented occupational context of the second study implies exceptions to the general case.

Presumably tasks, procedures and quality specifications are more standardized within technically-oriented environments. Such standardization may suppress the effects of conscientiousness on job performance, thus rendering variance in conscientiousness among employees more difficult to discern. Indeed, some research suggests that conscientiousness does not relate to performance when tasks are technical and heavily prescribed [START_REF] Mohammed | Technical-administrative task performance, leadership task performance, and contextual performance: Considering the influence of team-and task-related composition variables[END_REF]. This means that conscientious employees may be less distinguishable in such environments. That would reduce the likelihood for mentors to notice them and approach them as protégés. The fact that conscientiousness has the lowest variance among the Big-Five traits in the second study (where, to remind, peers assess the Big-Five) corroborates this tentative account.

Openness and agreeableness demonstrate inverted U-shaped associations with mentoring receipt in both studies. For the greater part of their ranges increases in the strength of these traits augments the likelihood of receiving mentoring, but strong presence of the traits does not offer a mentoring advantage anymore and may in fact bring a handicap. This means that creativity, interest in learning and inquisitiveness on the one hand, and cooperativeness, trust, altruism and sensitivity on the other hand are for the most part helpful in obtaining a mentor and receiving mentoring functions.

Extraversion also displays a relationship of overall positive trend with mentoring receipt. Apart from a limited range of scores near its negative pole (i.e., introversion) in one of the studies, increases in the strength of the trait accompany increases in amount of mentoring receipt. Hence, characteristics such as sociability, energy and action tendencies appear to provide a constant advantage in terms of mentor attraction and receiving mentoring functions.

The slight discrepancy between the two studies with respect to extraversion may reflect the effects of context. The context of the second study is a technologically oriented occupational setting, where typical jobs involve the development and maintenance of various types of information systems. Jobs of that nature primarily demand ability to concentrate and maintain attention to the task, which fits introverts more than extraverts (e.g., see [START_REF] Beauducel | Energetical bases of extraversion: Effort, arouse, EEG, and performance[END_REF][START_REF] Blumenthal | Extraversion, attention, and startle response reactivity[END_REF]. This may lead to filtering that renders most individuals in that occupational context low on extraversion. Indeed, in the second study extraversion has by far the lowest mean score of the Big-Five traits. Presuming that the characteristics of extraversion yield an advantage for an employee in terms of a mentor noticing him/her, this signifies that the effects of such characteristics become stronger in a low extraversion environment because in such an environment they are scarce. This explains the positive relationship of extraversion with mentoring receipt even near the low pole of the trait in the second study. On the other hand, in the setting of Study 1, which is presumably more representative of the general work environment, the relationship is negative in the vicinity of low extraversion. As seen, this is may be the outcome of introvert's very strong preference for developing intense exclusive relationships. Of course, this is a tentative account that needs testing.

Limitations

The Big-Five is remarkably stable during adulthood [START_REF] Judge | The big five personality traits, general mental ability, and career success across the life span[END_REF], which justifies the assignment of cause to personality traits and of effect to mentoring receipt when applying the criterion of temporal stability. According to this criterion, more temporally stable variables are normally causes while less temporally stable factors are normally effects [START_REF] Davis | The logic of causal order[END_REF]. This offers some confidence about causality despite the cross-sectional design.

The research has taken precautions against common method bias: ensuring anonymity, using temporal separation in the completion of questionnaires of personality and mentoring, and offering the option of feedback on personality (e.g., see [START_REF] Podsakoff | Common method biases in behavioral research: A critical review of the literature and recommended remedies[END_REF]. Furthermore, the second study utilizes multi-source measurement. In addition, the mentoring scale is immune to social desirability, a potential source of common method effects [START_REF] Podsakoff | Common method biases in behavioral research: A critical review of the literature and recommended remedies[END_REF]. Therefore, the possibility for presence of common method variance in the findings is rather low.

The issue of common method bias deserves some more consideration because of substantial attention in recent years; which has led to automatic attribution of inferior quality status to research that employs exclusively self-report measures. This is despite that empirical and quantitative review research [START_REF] Crampton | Percept-percept inflation in microorganizational research: An investigation of prevalence and effect[END_REF][START_REF] Malhotra | Common method variance in IS research: A comparison of alternative approaches and a reanalysis of past research[END_REF] concludes that common method bias is an overstated threat to validity. In the second study, which utilizes peer assessments of personality, the Big-Five accounts for much greater amounts of variance than in the first study, which utilizes self-reports. Considering that the measurement of mentoring is common in the two studies two explanations ensue: (1) indeed common method bias is not as serious an issue as assumed to be; (2) adoption of simple measures, such as careful choice or development of instruments, separate measurement of core variables, and offering feedback, are very effective means against common method bias.

In either case, the present research contributes towards the counter-argument (e.g., see Spector, 2006) that the attention paid to common method bias is disproportional to the real threat.

Responses to the mentoring measure represent participants' own perceptions, which may not be accurate [START_REF] Welsh | Are you my mentor? Informal mentoring mutual identification[END_REF]. Nevertheless, empirical research suggests substantial agreement between protégés and mentors in the amount of mentoring that flows within the relationship [START_REF] Waters | The role of formal mentoring on business success and self-esteem in participants of a new business start-up program[END_REF]. In addition, for certain mentoring functions, such as socioemotional functions, perceptions of protégés are probably more accurate than perceptions of mentors (see [START_REF] Waters | The role of formal mentoring on business success and self-esteem in participants of a new business start-up program[END_REF]. Hence, selfreport measures may represent the most valid method for assessing receipt of mentoring.

Directions

The substantial consistency of the findings of the two studies, in line with the dispositional approach, suggests that the way Big-Five traits relate to mentoring receipt largely generalize across contexts. Nevertheless, inter-study consistency is not perfect, and as seen in detail above, the occupational setting may moderate some relationships. Therefore, future research must investigate for occupational and organizational moderators. In addition, individual characteristics may also affect the pattern of certain relationships. Self-monitoring (Snyder, 1974) is such a characteristic. Self-monitoring reflects the extent to which individuals carefully monitor and modify their behavior according to social cues in order to project favorable public image. High self-monitors may sense in the behavior of their mentors or potential mentors the negative impressions excessive display of acts associated with openness and agreeableness create, and may suppress or manage pertinent behaviors accordingly. This means that for high self-monitors the relationship of these traits with mentoring receipt may not include a bending point (i.e., the relationship is linear and positive) while for low self-monitors the inverted-U-shape curvature is more pronounced.

The universality of the Big-Five does not mean that its traits relate in the same way with work and other outcomes across cultures [START_REF] Mccrae | Personality trait structure as a human universal[END_REF][START_REF] Van Emmerik | Associations of culture and personality with McClelland's motives: A cross cultural study of managers in 24 countries[END_REF]. Therefore, research in other cultural clusters, or even in other countries of the Anglo-Saxon cluster, is advisable. For example, the British society, like those of other individualistic English-speaking and West-European countries, values and encourages autonomous and independent thinking over conformism and obedience [START_REF] Schwartz | A theory of cultural value orientations: Explication and applications[END_REF]. On the other hand, Confucian and South Asian societies endorse conformism and compliance over intellectual and emotional autonomy (e.g., Bond & Smith, 1996;[START_REF] Schwartz | A theory of cultural value orientations: Explication and applications[END_REF]. This may mean that openness does not relate in the same way to mentoring receipt in those societies because superiors may not appreciate openness-related behaviors from their subordinates. As another example, high neutrality is a characteristic of British culture. A neutral culture, as opposed to an affective culture, signifies nonappreciation and discouragement of overt expression of felt emotions (Trompenaars, 1993). This invites the possibility that those Big-Five traits that pertain to experience and expression of emotions, like emotional stability and extraversion (e.g., [START_REF] Watson | On traits and temperament: General and specific factors of emotional experience and their relation to the Five-Factor model[END_REF], relate more strongly with mentoring receipt in affective cultures.

The present era of globalization has brought an unprecedented movement of individuals across national borders. The extent to which personality traits have consistency in their relationships with mentoring receipt across cultures has essence for those who move across national boundaries (see also [START_REF] Baruch | Career issues[END_REF]. Research in various national settings will contribute towards the development of pertinent advice for individuals and organizational agents alike.

The exclusive focus on traditional informal mentoring represents a conscious, validity enhancing, choice. Nevertheless, the relationship of the Big-Five with mentoring receipt demands investigation within formal and non-traditional (e.g., lateral mentoring, which takes place between peers) mentoring relationships as well. Non-traditional developmental relationships, like peer-mentoring (e.g., [START_REF] Mcmanus | Peer mentoring relationships[END_REF], acquire special importance these days due to flattening of organizations, stretching of the workforce, and employment uncertainty. These phenomena reduce the amount of time managers can dedicate to subordinates and suppress their motivation to provide mentoring [START_REF] Allen | The mentor's perspective: A qualitative inquiry and future research agenda[END_REF]. The dynamics of lateral and traditional mentoring are dissimilar (e.g., less power differential), hence, the effects of personality may also differ.

Finally, the implications of the present research extend beyond the domain of mentoring. Although many critical workplace outcomes clearly relate to personality, authors pose questions on its substantive contribution, invoking rather weak relationships with key outcomes (e.g., [START_REF] Hurtz | Personality and job performance: The big five revisited[END_REF]. However, extant research on correlates of personality mostly assumes and tests linear associations. The present findings imply that the contribution of personality is substantially stronger and more complicated than currently believed because non-linear relationships appear at play. This adds to calls and emerging literature (e.g., [START_REF] Vasilopoulos | Personality and training proficiency: Issues of bandwidth-fidelity and curvilinearity[END_REF] on the curvilinear perspective to the association of personality with work processes and outcomes, which opens a new horizon that future research ought to explore.

Figure 2

 2 Figure 2 presents the curves.

Figure 1 .

 1 Figure 1. The curves that depict the quadratic relationships in Study 1.

Figure 2 .

 2 Figure 2. The curves that depict the quadratic relationships in Study 2.

Table 1

 1 Study 1: Descriptive Statistics and Inter-correlations (N = 212) Correlations  |.11|, |.12|, |.16|, |.21| are significant at p < .1, p < .05, p < .01, p < .001, respectively.

	________________________________________________________________________________________________________________________________
		M	SD	1	2	3	4	5	6	7	8	9	10	11	12
	________________________________________________________________________________________________________________________________
	1. Age	33	7.44	__
	2. Socioeconomic origin	2.4	.99	-.30	__
	3. Educational attainment	4.4	1.14	-.11	.15	__
	4. Starting grade	2.2	1.42	.21	-.07	.18	__
	5. Tenure	6.4	6.32	.50	-.26	-.33	-.24	__
	6. Organizational grade	3.2	1.56	.28	-.12	.10	.63	.14	__
	7. Mentoring received	3.7	.82	-.18	-.16	-.10	-.12	.17	.13	__
	8. Emotional stability	3.5	.62	-.02	.01	-.04	.03	-.08	.13	.04	__
	9. Extraversion	3.7	.45	-.25	.20	.07	-.08	-.19	0	.14	-.31	__
	10. Openness	3.5	.48	.13	.04	.25	.06	-.09	.14	-.10	.07	.02	__
	11. Agreeableness	4.2	.43	-.24	.27	.18	-.32	-.01	.35	.20	-.23	.32	-.02	__
	12. Conscientiousness	3.8	.52	-.09	-.24	-.13	.04	-.04	.13	.18	-.24	.29	-.16	.20	__
	________________________________________________________________________________________________________________________________
	Note.

Table 2

 2 Results of Hierarchical RegressionsTesting the Hypotheses ___________________________________________________________________________________________________________________________ Beta coefficients in the final models are presented. Adjusted R 2 values are presented. † p < .1 * p < .05. ** p < .01. *** p < .001.

				Study 1 (N = 212)					Study 2 (N = 131)
				t value 						t value
	___________________________________________________________________________________________________________________________
	Step 1: forcible entry
		Gender	-.04	-.39					.20	3.53**
		Marital status	-.24	-2.76**					.22	3.74***
		Age	-.16	-1.98*					-.49	-7.74***
		Socioeconomic origin	-.24	-3.39***					.47	9.52***
		Educational attainment	-.07	-.96					-.55	-11.16***
		Starting grade	-.22	-2.27*					.31	4.26*
		Tenure	.10	1.09					.06	.67
		Current grade	.43	4.16 ***					-.51	-5.97***
		Staff vs. line	.05	.51					.35	6.07***
	 	 Public vs. private	.02	.23
		Services vs. manufacturing	-.02	-.33
	Org. size R 2 / F  	-.07	-1.18 .221 / 5.99***					.504 / 15.7***
	_____________________________________________________________________________________________________________________________

Table 3

 3 Study 2: Descriptive Statistics and Inter-correlations (N = 131) Correlations  |.11|, |.12|, |.16|, |.21| are significant at p < .1, p < .05, p < .01, p < .001, respectively.

	______________________________________________________________________________________________________________________________
		M	SD	1	2	3	4	5	6	7	8	9	10	11	12
	______________________________________________________________________________________________________________________________
	1. Age	37	7.53	__
	2. Socioeconomic origin	2.3	.83	-.30	__
	3. Educational attainment	4.6	.82	-.03	.31	__
	4. Starting grade	1.4	.89	.28	.02	-.08	__
	5. Tenure	7	6.85	.41	-.12	-.23	-.28	__
	6. Organizational grade	2.3	1.27	.34	.14	-.05	.49	.34	__
	7. Mentoring received	3.6	.58	-.33	.35	-.36	.13 .	-.15	.04	__
	8. Emotional stability	7.3	1.06	.26	-.01	.13	-.05	.37	.23	-.01	__
	9. Extraversion	4.4	1.26	-.09	-.03	.07	-.08	.11	.15	-.04	-.03	__
	10. Openness	5.4	.83	.22	-.02	-.09	-.26	.57	.31	-.01	-.41	.22	__
	11. Agreeableness	5.5	.91	.36	-.22	-.21	.12	.46	.23	.08	-.52	.15	.44	__
	12. Conscientiousness	5.6	.79	.14	.03	-.10	-.24	.44	.13	.03	-.53	.01	.56	.45	__
	______________________________________________________________________________________________________________________________
	Note.

 International, 17, 255-275. Spector, P. E. (2006). Method variance in organizational research: Truth or urban legend?

Organizational Research Methods, 9, 221-232. Staw, B. M., Bell, N. E., & Clausen, J. A. (1986). The disposition approach to job attitudes: A lifetime longitudinal test. Administrative Science Quarterly, 31, 56-77. Staw, B. M., & Cohen-Charash, Y. (2005). The dispositional approach to job satisfaction: More than a mirage, but not yet an oasis. Journal of Organizational Behavior, 26, 59-78. Snyder, M. (1974). Self-monitoring of expressive behavior. Journal of Personality and Social Psychology, 30, 526-37.


M Montoya

M Calamaz

D Gehin

F Girot

Evaluation of the performance of coated and uncoated carbide tools in drilling thick CFRP/aluminium alloy stacks

Keywords: Drilling, Composite/aluminium stacks, Tools wear, Holes quality, Thrust force

This paper aims to establish the wear mechanisms of coated and uncoated tungsten carbide drills when drilling carbon fibre reinforced plastics (CFRP)/aluminium alloy (Al) stacks. During the drilling experiments, thrust forces were measured. A scanning electron microscope (SEM) and a numerical microscope, provided with a scanning device, were periodically used to analyse tool wear mechanisms and to measure wear progression of the tool cutting edges. For both coated and uncoated drills, abrasion was the dominant tool wear mechanism, affecting the entire cutting edges. Higher wear was observed on uncoated tools which caused a significant increase in thrust force during drilling both Al and CFRP materials. The influence of these phenomena on the quality of the holes and on the generated roughness was also discussed.

Introduction

Nowadays, due to technological advances in the field of materials, the use of high-performance composites has become very current in fields, such as aeronautics or aerospace. To get a better strength to weight ratio, these materials combined with aluminium (Al) or titanium alloys (Ti), are stuck together to create a hybrid material. This assembly technique minimises positioning faults during drilling operations but greatly increases machining difficulties.

The drilling process parameters could be very different between drilling carbon fibre reinforced plastics (CFRP) and Al material due to their different material properties. Therefore, drilling multi-materials, such as CFRP/Al have become a real challenge for manufacturing engineers.

Drilling is a machining operation which has already been widely investigated. These studies can be split in two research axes. The first one works on the drilling of Al and provides many results on chip formation [START_REF] Batzer | Chip morphology and hole surface texture in the drilling of cast aluminum alloys[END_REF], tool wear or temperature reached during machining [START_REF] Nouari | Effect of machining parameters and coating on wear mechanisms in dry drilling of aluminium alloys[END_REF]. The second one is represented by research carried out on composite materials, with studies on the prediction of forces [START_REF] Lachaud | Drilling of composite structures[END_REF] and delamination [START_REF] Hocheng | Comprehensive analysis of delamination in drilling of composite materials with various drill bits[END_REF] during drilling process or on tool wear [START_REF] Iliescu | Modeling and tool wear in drilling of CFRP[END_REF].

However, few publications have been focused on the optimisation of multi-materials machining process.

In 2001, Ramulu et al. [START_REF] Ramulu | A study on the drilling of composite and titanium stacks[END_REF] published one of the first studies on drilling of multi-material stacks (graphite/bismaleimide-Ti). Their work has shown that, to minimise delamination during drilling, the best stack sequence is CFRP on the top and metal on the bottom. They also studied the influence of tool material (HSS, HSS-Co and carbide) and cutting conditions on thrust forces, tool wear and holes quality. Park et al. [START_REF] Park | Tool wear in drilling of composite/titanium stacks using carbide and polycrystalline diamond tools[END_REF] investigated drilling of CFRP/Ti stacks in terms of tool wear mechanism when using carbide and polycrystalline diamond tools. They highlighted cutting edge abrasion due to the CFRP and adhesion of the Ti on tool cutting edges and flank faces.

A study on the drilling of multi-layer materials consisting of CFRP, titanium and Al has been carried out by Brinksmeier et al. [START_REF] Brinksmeier | Drilling of Multi-layer composite materials consisting of carbon fiber reinforced plastics (CFRP), titanium and aluminum alloys[END_REF]. In their study, the influence of coatings and tool geometry on tool wear, forces, holes quality and chip formation has been analysed. The main problems occurred in multi-material drilling were highlighted: CFRP delamination and tearing, metal burr formation, intensive tool wear and a difference between diameters measured in each material.

Zitoune et al. [START_REF] Zitoune | Study of drilling of composite material and aluminium stack[END_REF] studied the influence of cutting conditions, tool diameter and wear on thrust forces, holes quality and chip formation, when drilling a CFRP and an Al (2024) hybrid material. These tests were carried out on thin plates having a thickness of about 7.2 mm (4.2 mm of CFRP and 3 mm of Al). Some trends found in their work are similar to those found by Rawat et al. [START_REF] Rawat | Characterization of the dry high speed drilling process of woven composites using Machinability Maps approach[END_REF] and Batzer et al. [START_REF] Batzer | Chip morphology and hole surface texture in the drilling of cast aluminum alloys[END_REF] when drilling these two materials separately.

This paper aims to establish the wear mechanisms of coated and uncoated tungsten carbide (WC) drills when drilling CFRP/Al (7010) stacks. The wear (quantity and tool edge profile) evolution with the number of holes was also investigated. The influence of these phenomena on the thrust force and on the quality of the holes (the diameter, the difference between the diameter measured in the CFRP and the one measured in the Al part, the generated hole wall roughness) was discussed. The impact of the aluminium chips evacuation on the hole quality in the CFRP was also investigated.

Experimental setup

Workpiece materials

The composite part of the hybrid material was a preimpregnated woven sample made of T800 carbon fibres and an epoxy matrix. This multidirectional composite had a thickness of about 7 mm and an average ply thickness of about 0.19 mm. The layer stacking sequence was non symmetric. The metal part was a 7010 Al in metallurgical state T7451 and it was 14 mm thick. The composite and aluminium parts were assembled using an epoxy adhesive filled with aluminium powder, named FILLERALU.

Drilling experiment

Coated and uncoated twist drills were used for drilling tests. All drills had the same geometry in terms of flute length (25 mm), point angle (124°) and helix angle (30°). The drill designated as tool A was uncoated and diamond, TiAlCrN and AlTiSiN-G coatings were used on tools B-D, respectively. Table 1 summarises drill geometry and coatings.

The stack sequence, CFRP on the top and metal on the bottom, was established with the industrial partner. This sequence generates less composite delamination as shown by Ramulu et al. [START_REF] Ramulu | A study on the drilling of composite and titanium stacks[END_REF]. Drilling experiments were performed on a 5-axis CNC horizontal machining center (Hera, FATRONIK). The dynamometer (9257B, Kistler) was clamped on the machining table, and the workpiece was attached to an aluminium plate and bolted on the dynamometer. The thrust forces were transmitted from the dynamometer to a signal amplifier (5019A, Kistler), then to a DAQ card (6062 E, NI) and recorded on a computer using Lab-View data acquisition software. Cutting conditions are summarised in Table 2. Due to their dissimilar properties, CFRP and Al are two materials that have very different optimal machining settings. Despite this, the use of the Al optimal machining settings was recommended by the tool supplier. The drilling operations were carried out using a chip removing cycle. A micro-quantity lubrication system was used to provide a mist coolant throughout the operation with a constant flow rate of 16 mL/min. In the literature, the number of holes drilled to perform a study on tool wear during drilling CFRP/Al stacks rarely exceeds more than 100 holes. Tools tested in this study were used to drill 250 holes.

Analysis devices

After drilling tests, hole quality was investigated by measuring the diameter, the hole wall roughness and damages at the hole entrance. Diameters were measured in two levels in CFRP, at 1.5 mm from the hole entrance (H1) and at 1.5 mm from the exit (H2) but also at the mid-thickness of the aluminium (H3) plate. An inside micrometre was used for these measures (T&O, accuracy= 4 μm). The hole wall roughness was measured using a contact rugosimeter (MITUTOYO SURFTEST SV600). The hole entry damages were investigated with a numerical microscope (VHX-1000, KEYENCE). The analysis software of this microscope has an algorithm (Depth from Defocus) that uses fine changes in texture to estimate height data. With the microscope software 3D tool edge geometry can be obtained. The 2D profile can then be extracted from the 3D model and used to measure cutting edge sharpness and the local wear quantity (LWQ). The latter is obtained by comparing the current profile of the cutting edge to the first one (of the unworn tool). An example can be seen in Fig. 1a where T0 designates the cutting edge profile of the unworn drill and T250 the profile after drilling 250 holes. This wear quantity is expressed by an area unit (in square micrometres). The analysis of 2D profiles also allows us to estimate flank wear and the cutting edge radius. These measures were performed on three locations on the tool cutting edges: at 200 μm from the drill corner, at the centre and at 200 μm from the junction between the first and the second cutting edges, as seen in Fig. 1b. In addition, tool wear mechanisms were identified using a scanning electron microscope (SEM).

3 Results and discussion

Wear measurement and analysis of its evolution

Flank wear V B is defined in the norm ISO 8688:1 as follows:

"The flank wear is measured in a parallel direction to the wear facet and in a perpendicular direction to the initial cutting edge, for example from the initial cutting edge to the wear facet limit which cuts the initial flank face". Generally, using an electronic and/or an optical microscope, it is possible to measure the length between the current cutting Fig. 3 LWQ measured on three locations on the cutting edge edge and the last point worn on the flank face (V BSEM in Fig. 2).

This type of measurement, done by Rawat et al. [START_REF] Rawat | Wear mechanisms and tool life management of WC-Co drills during dry high speed drilling of woven carbon fibre composites[END_REF] to evaluate tool wear in drilling woven carbon fibre composites, has shown a high sensibility of the wear on the rake face. As shown in Fig. 2, the wear on the rake face has a direct impact on the value of V BSEM. If the wear on the rake face increases more rapidly than the wear on the flank face, a higher LWQ should be obtained but a smaller value of V BSEM . Consequently, this parameter (V BSEM ) is not really suitable to describe the wear progression.

From the 2D cutting edge profiles, the actual flank wear value (V B in Fig. 2) can be obtained. It is also possible to estimate, from the tool edge profiles superposition, the amount of the material locally lost by the tool (grey surface in Fig. 2)

The measurement of the LWQ, on three locations on the cutting edge, has shown the non-proportionality of the LWQ with the radial position of the measurement location (Fig. 3). The higher LWQ is found at the drill corner and it decreases up to the drill point.

All the drills have the same unworn profile, except the cutting edge radius. Therefore, in Figs. 4a and5a, only the unworn profile of the drill A is shown. TiAlCrN (tool C) and AlTiSiN-G (tool D) coatings were not efficient. Their flank wear was very close to the one measured on the uncoated tool A (Fig. 4b). As shown in Fig. 4a, the cutting edge profiles of these tools are also similar.

Diamond coated tool B is the only really effective one. For this tool, the coating breakage occurred after drilling 150 holes. The flank wear measured on this coated drill is 50 % lower than that measured on the uncoated drill (tool A), as shown in Fig. 5b. As for the LWQ, the use of a diamond coating allows a drill wear decrease of about 80 %.

Wear mechanisms

Figure 6 shows the SEM images of the rake and the flank drill faces, beginning with the unworn stage (hole 0) up to hole 250. These images show that the drill cutting edge was mainly affected by abrasion wear, but some adhesion of Al can also be identified on the cutting edges. The abrasion was the main wear mechanism identified on the uncoated tool. Some adhesion can also be seen on the tool rake face but far from the cutting edge (tool A in Fig. 8). The coated drills underwent abrasion, followed by coating failure on the As it can be seen on Fig. 6, the SEM images show the coating failure after the 5th hole, for tools C and D. The coating was removed all along the cutting edge. After drilling 75 holes, these tools can be considered as uncoated because extended areas on the flank and rake faces lost their coating. Therefore, the drilling tests were stopped after 75 holes. For uncoated tools, abrasion was observed on the chisel edge, on the corner, on the primary and on the second cutting edges. Before the coating failure, coated drill B underwent the same type of wear as the uncoated drill. It was subjected to abrasion, followed by coating failure on the cutting edge. After the coating failure, an aluminium layer replaced it on the cutting edge and created a build-up edge (BUE). This adhesive wear is then the site of WC attrition. The BUE, stuck on the cutting edge, tears CW particles when it is removed, as observed on Fig. 7a,b.

CW Aluminium adhesion

Adhesion was also observed on the tool rake face. Grinding processes, carried out to prepare drill flutes, generate a relatively rough surface. Therefore, Al adheres on the rake face. The amount of Al deposited on the tool depends on the surface roughness. With a thin layer coating, like for tools C and D, the coating thickness was unable to totally erase the grinding marks (Fig. 8). It can be observed that the coating takes the surface profile and the same amount of material adheres on the tool, as for the uncoated drill. The diamond coating thickness was able to "erase" the previous grinding marks (see tool B on Fig. 8). Therefore, for this coating, less Al alloy has stuck on the rake face, as seen in Fig. 8.

Thrust forces

For the first hole, when the drills are unworn, the average thrust force of the uncoated drill A is from 30 to 50 % lower than the thrust forces of the coated drills B-D (Fig. 9), mainly due to the cutting edge sharpness. Cutting edge radius was 9 μm for tool A, 11 μm for tools C and D, and 15 μm for tool B. This difference concerning the cutting edge sharpness is the consequence of the coating thickness.

The cutting edge radii of all the drills have the same value prior to being coated, between 6 and 9 μm. With a thickness of 4-6 μm, the diamond coating is the thicker one and logically the higher cutting edge radius is observed for tool B. The same phenomenon was observed by Cheung [START_REF] Cheung | Cutting edge preparation using magnetic polishing and its influence on the performance of high-speed steel drills[END_REF] and Franke [START_REF] Franke | Drilling of long fiber reinforced thermoplasticsinfluence of the cutting edge on the machining results[END_REF] in drilling steel and long fibre reinforced thermoplastics, respectively. In their study, the cutting edge radius varies from 7 to 42 μm and was obtained with a cutting edge preparation done by magneto-abrasive machining or magnetic polishing.

CFRP and Al have dissimilar mechanical properties. Therefore the thrust force generated by drilling has different magnitudes. As shown in Fig. 9, the force generated by CFRP drilling was lower than that produced in the aluminium, on the first hole. Zitoune et al. [START_REF] Zitoune | Influence of machining parameters and new nanocoated tool on drilling performance of CFRP/Aluminium sandwich[END_REF] obtained a similar trend, using comparable drill diameters. Brinksmeyer et al. Average thrust force on the first hole [START_REF] Brinksmeier | Drilling of composites and resulting surface integrity[END_REF] found opposite trends, higher thrust forces in CFRP than in Al, but the drill diameter was higher (16 mm).

The average thrust forces increase with the number of drilled holes (Fig. 10a). The thrust forces generated by the uncoated drill, gradually rise in both CFRP and Al alloy. This trend was also observed for the coated drill B, but it was lower. This increase is mainly due to the tool wear. The thrust force grow is dissimilar between the two materials. For the aluminium, the increase of thrust force is asymptotic near the 250th hole while for the CFRP, the thrust force continues to increase. This implies that the thrust force measured in the CFRP can become higher than that observed in the aluminium, as for tool A on the 250th hole. influence of the drill micro-geometry and therefore, of the wear on the thrust force.

After the diamond coating breakage (tool B after 150 holes), the average thrust force in the aluminium plate shows almost an asymptotic evolution. This trend could be explained by: (1) a material softening due to high temperatures or (2) an auto-optimisation of the tool geometry. As shown in Fig. 10, the thrust force does not decrease during the Al drilling. Therefore, no metal softening was observed.

The benefit of the diamond coating on thrust force is shown in Fig. 10. For the same cutting conditions, the use of a diamond coating can decrease the force (by limiting wear) by 65 % when drilling CFRP and by 35 % in Al.

Hole quality

Hole quality was investigated by measuring hole diameters, CFRP damage and hole wall surface roughness.

Hole diameter

Figure 11a-d shows that the evolution of the diameter of the holes with the number of drilled holes is relatively stable, especially for tools A and B. This stability was also observed by Benezech et al. [START_REF] Benezech | Study of manufacturing defects and tool geometry optimisation for multi-material stack drilling[END_REF]. It can also be seen that the diameter of the holes drilled in CFRP (H1 and H2 in Fig. 11) is bigger than the one measured in the Al alloy. Some additional experiments have shown that opposite trends can be obtained following the used cutting condition and particularly, the lubrication condition. Without lubrication and for the same tool geometry, the diameter of the holes drilled in CFRP remains the same but bigger diameters are produced in the aluminium. Therefore, diameters of the holes drilled in Al are becoming bigger than those produced in the CFRP. This difference can be due to thermal phenomena that occur during the drilling process. A diameter difference in CFRP and in the metal part was also noted by Shyha et al. [START_REF] Shyha | Hole quality assessment following drilling of metallic-composite stacks[END_REF].

The difference between the average diameter in both altitudes in CFRP, and the diameter in metal, noted ΔØ, is shown in Fig. 12. Best results are observed for drills A and B with a ΔØ of 8 to 9 μm against 16 to 18 μm for drills C and D. As it can be seen in Figs. 11 and12, the presence of a coating has little or no influence on the diameter difference (ΔØ). No diameter deviation was observed with the number of holes, as it can be seen in Fig. 11. With a similar drill diameter, different results were obtained by Benezech et al. [START_REF] Benezech | Study of manufacturing defects and tool geometry optimisation for multi-material stack drilling[END_REF] where the diameter difference was nearly 30 μm.

CFRP damage

The CFRP damage at the hole entrance, shown in Fig. 13b, was observed whatever the drill used, starting with the first hole. Therefore, it can be concluded that this phenomenon is not due to the tool wear. It can be caused by the tool geometry, as described by Hocheng et al. [START_REF] Ho-Cheng | Delamination during drilling in composite laminates[END_REF], where the drill flute pulls out the first layers of the composite material. Or, in the case of a multi-material, this damage can be due to the metallic chip evacuation through the hole, as observed by Brinksmeier et al. [START_REF] Brinksmeier | Drilling of Multi-layer composite materials consisting of carbon fiber reinforced plastics (CFRP), titanium and aluminum alloys[END_REF]. The last hypothesis has been proved in our case by observations made before aluminium part drilling and chip evacuation. Due to the chip removing cycle, the drilling process can be stopped at any time. For ten holes, the drilling process was stopped before creating aluminium chips. A workpiece photo was taken at this moment and no CFRP damage was observed, as it can be seen in Fig. 13a. After completed drilling process, the CFRP damage reaches more than 2 mm (Fig. 13b). The drill flute does not guide the chip enough all along its length and, as seen by a CCD high speed camera, the metal chip is in contact with the hole entrance. As shown in Fig. 13b, this damage is not localised all around the hole entrance. It is situated in places where the direction of the chip movement (due to drill rotation) and the fibre orientation creates a -45°angle. In this configuration, similar damages have been observed by Iliescu [START_REF] Iliescu | Approche expérimentale et numérique de l'usinage des composites carbone/epoxy[END_REF] during CFRP cutting.

Hole wall roughness

As it can be seen in Fig. 14, the hole wall roughness on the first 50 drillings was similar for uncoated (A) and coated (B) tools. The same roughness level was found by Zitoune et al. [START_REF] Zitoune | Influence of machining parameters and new nanocoated tool on drilling performance of CFRP/Aluminium sandwich[END_REF] in their study on the influence of machining parameters on drilling performance of CFRP/aluminium stacks. The roughness of the holes performed by the uncoated tool (A) increases with the number of drilled holes, in both materials (Fig. 14a,b). This phenomenon is greatly problematic, because the roughness can become higher than the one required in the aeronautics industry. Currently, the maximum acceptable roughness in aeronautics is 1.6 μm in Al and 3.2 μm in CFRP. In the Al, the roughness increase is slight and remains at an acceptable level. In the CFRP part, the uncoated tool produces hole wall roughnesses higher than 3.2 μm, after 75 drilled holes.

The increasing of the roughness is due to the wear undergone by tool A and its rapid growth. Sharp cutting edges generate no defect on the holes wall (Fig. 15a) and low roughness is measured. When the tool cutting edge sharpness becomes too low, the drill is unable to cut the carbon fibres. These fibres are rather pulled out than cut, especially when the cutting direction and the fibres create a -45°angle. As a consequence, little cavities are generated on the holes wall (Fig. 15b) and therefore, the roughness increases. The same phenomenon was observed by Iliescu [START_REF] Iliescu | Approche expérimentale et numérique de l'usinage des composites carbone/epoxy[END_REF] when drilling CFRP plates.

Low hole surface roughness with a good stability in time (Fig. 14) is obtained by diamond coated tool B, due to its slight evolution of the cutting edge profile (Fig. 5a).

Conclusions

Cutting forces, holes quality and tool wear analysis on coated and uncoated carbide drills were analysed for the drilling of CFRP/Al stacks.

Two types of wear were highlighted above: abrasive and adhesive wear. Abrasion was the strongest wear mechanism observed in CFRP/Al drilling, due to the highly abrasive carbon fibres. The results have shown that, as the number of drilled holes increases, the thrust forces generated by both coated and uncoated drills gradually increase in both CFRP and Al parts, mainly due to the tool wear.

The study has also highlighted the influence of the evolution of the drill micro-geometry (and therefore, of the tool wear) on the thrust force.

Lower flank wear and thrust forces and, therefore, good hole quality were obtained when using the diamond coating.

The study has shown that the CFRP damage at the hole entry is due to the aluminium chips evacuation and it is not, in our case, due to the tool geometry.

Fig. 1 a

 1 Fig. 1 a Cutting edge profile for tool A at 200 μm from the drill corner after 5, 50 and 250 holes compared with the unworn profile (T0). b Measurement location on the cutting edge to obtain 2D edge profile

Fig. 4 aFig. 5 a

 45 Fig. 4 a Cutting edge profiles near the drill corner after 75 holes for drills B-D. b Flank wear evolution with the number of holes (located at 200 μm from the drill corner) for drills A-D

  Fig. 6 SEM images of drills flank faces

Fig. 7 a

 7 Fig. 7 a Attrition phenomenon on the cutting edges for tool B. b Zoom of the zone of interest, in chemical contrast (magnitude, 2,500)

Fig. 8 Fig. 9

 89 Fig.8SEM images of rake faces of unworn and worn drills (after 75 holes)

Fig. 10 aFig. 11

 1011 Fig. 10 a Evolution of average thrust force with the number of holes. b Thrust force signal on hole No. 200 (for one of the five cutting passages in Al plate)

Fig. 12 ΔØ

 12 Fig.12ΔØ evolution with the number of drilled holes

Fig. 14

 14 Fig. 14 Roughness Ra for the a CFRP part and b Al part

Fig. 15

 15 Fig. 15 CFRP hole wall on the a 1st and b 250th hole drilled by the uncoated tool A

Table 1

 1 Drill geometries and coatings

	Tool	A	B	C	D
	Margin		Double
	Drill diameter (mm)		6
	Flute length (mm)		25
	Web thickness (mm)		1.36
	Point angle (°)		124
	Helix angle (°)		30
	Coating	-	Diamond	TiAlCrN	AlTiSiN-G