Electronic agents on the Internet: A New Way to Satisfy the Consumer

Keywords: Electronic agents, consumer behavior, satisfaction, e-commerce. I.1

Our purpose in this article is to present the concept of electronic agent used in e-commerce and its impact on consumer satisfaction. Electronic agents represent the future of electronic business. They help the consumers in an environment where all the information is available but hard to deal with. We try to study the electronic agent in a consumer decision process perspective and to examine the different sort of agents depending on their relationships with vendors and consumers. Our final aim is to understand the role of electronic agent on consumer satisfaction. For that purpose, we conducted a little empirical study which consist in presenting two types of agents to consumers: a good one and a bad one and to evaluate the level of consumer satisfaction.

Introduction

« The role of the intelligent agent is to assist you. At the edge of information, it signifies that the agent should help you to find information», Bill Gates (2000).

Internet is the 4 th commercial revolution after the stores, the megastores and the self-services [START_REF] Volle | Du marketing des points de vente à celui des sites marchands : spécificités, opportunités et questions de recherche[END_REF]. Whereas, the online sells are lower than expected. The principal reasons advanced by practitioners and numbers of researchers are linked with problems of trust and confidential datas. We argue, with [START_REF] Bakos | Reducing buyer search costs: Implications for electronic marketplaces[END_REF] and [START_REF] Ariely | Controlling the information flow: Effects on consumers' decision making and preferences[END_REF], that the problem is somewhere else, more linked with the consumer information management. On the Internet, all the information is available as in a pure and perfect market [START_REF] Desmet | Politique de prix sur Internet[END_REF]. And this profusion of information is the center of the problem. Consumers are unable to deal with all the available information because their cognitive capacities are limited [START_REF] Simon | Rationality as a process and product of thought[END_REF]. A solution to this problem is the utilization of electronic agents that deal with the information instead of the consumers within their decision process [START_REF] Paraschiv | Gestion des agents intelligents sur l'Internet : l'apport conjoint du marketing et de l'économie[END_REF]. Our purpose is to present the electronic agent and its different applications (I), then to study the possible impact of electronic agent on consumer satisfaction on the Internet in order to justify the presence of those types of agent on web sites (II).

I. What can do an electronic agent?

We decided to present the electronic agent withan example of its capabilities for the consumer. [START_REF] Alba | Interactive home shopping: Consumer, retailer, and manufacturer incentives to participate in electronic marketplaces[END_REF] inspire this example. It will lead us to present the different functions of electronic agents for the consumer. We have studied this example under the prism of the [START_REF] Fishbein | A consideration of beliefs and their role in attitude measurement[END_REF] compensatory model of attitude formation, which mainly consists in the following form:

A i = ∑ j w j . X ij with A i: consumer attitude toward product i w j: importance of attribute j j: an attribute of product j X ij: information's available on attribute j of product i.

In the example, the agent has an influence on every stage of the consumer attitude formation toward the product: -When Jenn tells her agent what she needs in a very imprecise way (some clothes for an evening wedding), she doesn't know which are the alternatives corresponding to her problem definition. Her agent allows her to build her preferences by proposing her different alternatives (dress or trousers). Even then, the agent always takes into account external factors: a wedding means no white dress for the female guests, an evening wedding means a quite fancy dressing. Without the electronic agent, the former equation wouldn't exist. At a former level, the agent has an influence on the attitude formation toward the product by presenting the product, as shown in the following figure (figure 1).

Insert figure 1 here

-Once the problem identified the agent searches for available informations on the different possible products corresponding to the consumer needs. It performs a quite laborious task instead of the consumer himself. It helps determining the X ij as shown in figure 2.

Insert figure 2 here

-By analyzing the problem and defining the type of products corresponding to Jenn's needs, MINIM-ME has also determined which were the different attributes of the seeking product (trousers, dark colors…). Thus, it has a determining influence on j (figure 3). The agent is an expert whereas the consumer is not, principally because the individual isn't always interested in the product choice.

Insert figure 3 here

-By choosing the most important attributes for the consumer depending on his precedent buying and on his declared preferences, the agent determines the w j (figure 4). Instead of the cons umer, it evaluates the different alternatives by rating them.

Insert figure 4 here

-Finally, the agent buys the product and negotiates the price with the distributor. It has an important influence on a variable not taken into account in the former equation but which can be added: informations on exogenous product attributes X k ij, where k represents the agent role. Information is not absolute, it depends on an external intervention: k (figure 5).

Insert figure 5 here

-At the end of the interaction between Jenn and her agent, it proposes her products that she's never asked for at the moment. These proposing are resulting from a dialogue with the distributor (the shirt) or are spontaneously coming from the agent (the moisturizing cream). In both cases, the agent plays the advisor and the preceptor of the buying. It creates the need.

It is possible to appreciate the huge commercial potential of such an electronic agent: by facilitating the process, it leads the consumer to buy online but it also creates the need by its constant interaction with the consumer. The agent realizes a vendor work and becomes a key element of relationship marketing.

I.3. Different types of agents

Whereas this example may seem a little futuristic, the reality isn't so far from it. The example implies that the consumer owns a smart electronic agent, which could be a software linked to his hard drive and programmed by him to correspond to his needs. Others types of agents exists, which are not owned by the consumer or linked to his hard drive: agents owned by the distributors or independent agents owned by independent companies ("Fido the Shopping Doggie, http: //www.Shopfido.com or "Bargain-Finder" d'Andersen Consulting, http: //bf.csstar.ac.com/bf). Now our days, a great number of electronic agents exist for the consumers or for the vendors. A lot of web sites are proposing independent information search agents which are choosing the information on sites opened to them. Let's take some French examples.

The "Galeries Lafayette" are proposing a virtual clothing advisor in which you can enter a picture of you, your size, your hair and skin color…The advisor is creating you a new dressing style, it also gives you make-up and hair style advises.

More complete, Personnalogic is an independent agent that you can find on the web and that gives advises on all sort of products: animals, travels, cars…It gives products a rate depending on your answers to some questions it has formerly asked in order to reveal your consumer profile. If you already know the product that fits with your needs, Personnalogic can establish attributes comparison matrix between different brands. This research manly deals with commercial electronic agent but all the existing electronic agents (medical agent…) are based on the same theoretic and technical foundations: they represent a palliatives to human limited cognitive capabilities. They are also, comparing to usual software, personalized, proactive and adaptive [START_REF] Maes | Agent-mediated electronic commerce: An MIT media laboratory perspective[END_REF]. [START_REF] Maes | Intelligent software[END_REF] defines the electronic agent as a computer program who knows consumer's preferences and can act autonomously for them. Those systems imply the consumer engagement in an interactive process: information sharing, agreement for the agent to accomplish task instead o f the consumer, respecting his preferences and constant improvement of the system. According to [START_REF] Maes | Intelligent software[END_REF], different types of electronic agents exist not necessarily used for business: agents that organize the e-mails, the news, the movies… The common point between all these applications is the utilization more or less complex of the artificial intelligence. Agents can be pre-programmed by the user or by their designer. They also can use collaborative filtering which recommend action by examining passed actions of others users. This system implies a strong collaboration between different sort of agents [START_REF] Maes | Intelligent software[END_REF]. There is a difference between simple agents who are searching and presenting information to the consumer and smart agents that make recommendations depending on the consumers preferences and needs. It is possible to represent the relations between the electronic agent, the vendor and the consumer (figure 6).

Insert figure 6 here

We focus here on supply agent whereas demand agents also exist. Demand agents are agents used by companies to identify consumers and their profile. [START_REF] Richard | Le Rôle des Agents Electroniques dans le commerce électronique[END_REF] defines demand agents as agents that analyze the global demand in order to adapt their offer to market needs. Those agents are a foundation to electronic relationship marketing. They are created to rebuild the relation between the vendor and the consumer but in that case a virtual one replaces the vendor. [START_REF] Richard | Le Rôle des Agents Electroniques dans le commerce électronique[END_REF]. Those agents allow: -The recording of consumer's profiles and preferences in order to personalize the web sites.

-The recording of consumer's successive demands.

-Some recommendations upon commercial supply evolution.

The benefit of using agent is double: the consumer can reach an offer more adapted to his needs, the vendor can better know his client and be more reactive to his changing needs. Now that we have described the different sort of agent and their function for the consumer, we're going to present an empirical study where we try to evaluate the impact of electronic agent on consumer satisfaction.

II. Electronic agent and its impact on consumer satisfaction: an empirical study.

Our purpose is to understand the impact of electronic agent on consumer satisfaction. If agents are supposed to represent the future of electronic commerce, it's because they might have a positive impact on consumer satisfaction. [START_REF] Maes | Agent-mediated electronic commerce: An MIT media laboratory perspective[END_REF] argue that electronic agents may be used at all stages of consumer buying behavior: information search, alternative evaluation, negotiation, buying decision and post-buying evaluation. [START_REF] West | Agents to rescue?[END_REF] add that electronic agent can be useful in all the consumer decision process and not just only his buying process. They identify different types of agent considering the stage of the decision process they act on (table 1). The empirical study we've conducted deals with information search and alternative evaluation agents such as Personnalogic.

Insert table 1 here

II.1. The theoretical impact of electronic agent on consumer satisfaction

In order to apprehend the impact of electronic agents on consumer satisfaction, we are studying the different variables that may have an impact on the perception of the quality of an agent by consumer. [START_REF] Aksoy | The impact of ordered alternative lists on decision quality in online shopping environments: The role of perceived similarity[END_REF] and [START_REF] Urban | Design and evaluation of a trust based advisor on the Internet[END_REF] argue that the consumer satisfaction raise with the perceived quality of an electronic agent. The perceived quality of an agent is a key mediator to consumer satisfaction. We propose the first hypothesis: H1: The perceived quality of an electronic agent has a positive impact on consumer satisfaction toward this agent. Some studies deal with the impact of electronic agent on consumer satisfaction [START_REF] Aksoy | The impact of ordered alternative lists on decision quality in online shopping environments: The role of perceived similarity[END_REF][START_REF] Moon | Int imate exchanges: Using computers to elicit self-disclosure from consumers[END_REF]. They have showed that the use of electronic agents raises the consumer satisfaction. [START_REF] Aksoy | The impact of ordered alternative lists on decision quality in online shopping environments: The role of perceived similarity[END_REF] argues that the consumer perceive the agent as a good one and so is satisfied if the agent acts in the same way that he would have act. She introduces the concept of perceived congruency between the agent decision process and the consumer one. We had previously conducted a qualitative study on consumer perception of electronic agents and had showed that the concept of congruency wasn't used by respondent [START_REF] Wallet-Wodka | Using determinants of buying intermediaries, 30 th Emac International Conference[END_REF]. In this study, we formulate the hypothesis that the perceived congruency of the electronic agent hasn't any significant impact on perceived agent quality. H2: The perceived congruency of the electronic agent hasn't any significant impact on perceived agent quality. [START_REF] Hoque | An information search cost perspective for designing interfaces for electronic commerce[END_REF] and Häubl and Trift (2000) argue that the impact of electronic agent on consumer satisfaction depend on its configuration. An agent is perceived as good or bad depending on his characteristics. For the authors, an electronic agent can articulate the information it provides to the consumer in a complex way or not. The determinant of complexity are the presentation of the information (listed or not), the presence of pop-ups, the degree of details provided on each alternatives and the number of pages before the command. We argue that the complexity of the agent had a negative impact on perceived agent quality. H3: Perceived complexity of an electronic agent has a negative impact on perceived agent quality.

Urban, Sultan and Qualls (1999) and [START_REF] Brynjolfsson | The Great Equalizer? Consumer behavior at Internet shopbots[END_REF] identify the impact of trust on electronic agent utilization by consumers. [START_REF] Cases | La réduction du risque dans le contexte de l'achat électronique sur Internet[END_REF] identify different element that permit reducing the perceived risk on web site. The risk has three main dimensions [START_REF] Mitchell | Re-conceptualizing consumer store image processing using perceived risk[END_REF]: financial, technical and physical. Within these dimensions, different elements can determine the perceived trust of buying electronic agents: -Presence of insurance's and payment security -Data's confidentiality -Free phone number In the following study, we argue that risky electronic agents lead to less perceived quality. H4: Perceived risk of an electronic agent has a negative impact on perceived agent quality.

At least, we introduce the concept of adequacy to demand as an essential antecedent of perceived agent quality. If the agent gives a good answer to the consumer demand, the agent will be perceived as good and the consumer will be more satisfied [START_REF] Wallet-Wodka | Using determinants of buying intermediaries, 30 th Emac International Conference[END_REF]. The quality depends on the adequacy between the answer and the demand. H5: Adequate answers to consumer demands have a positive impact on perceived agent quality.

It is possible to represent those hypotheses within a figure (figure 7).

Insert figure 7 here

II.2. Research methodology

In order to test the four hypotheses presented above, we've decided to conduct an experimentation. We choose to build two electronic agents corresponding to the three last variables: -A good agent: not complex, not risky and giving adequate respond to consumer needs. -A poor agent: complex, risky and giving inadequate respond to consumer needs. The congruency can not be manipulated "a priori". We've measured it "a posteriori" without manipulating it. The purpose of the manipulation is to create variance in the different antecedents of the perceived quality. We've conducted t-test between the two agents in order to test the first hypothesis. The others hypotheses are tested by simple regressions.

We've created two electronic agents specialized on travels. For that purpose, we used Dreamweaver 4. The two agents are totally similar except for the complexity, the risk and the quality has showed in table 2.

Insert table 2 here

We've decided to choose travels because it's a quite funny product for the respondent but it is also difficult to command a travel alone without passing by an intermediary such as a travel agency or a travel web-site. Furthermore, a lot of existing electronic agents are recommending travels on the Internet. Referring to the figure 5, we created a simple independent agent.

We measured the perceived risk, the perceived complexity, the perceived congruency and the perceived quality as well as consumer satisfaction with measurement scales presented in annex 1.

The experimentation has been done on French University students. 61 students have been placed in front of one of the agent. We gave them a scenario to guide their search. The search consisted in finding a trip to Cuba, for two, in December, in order to get some rest, not visiting. The budget was near 1300 Euros per persona. The respondents were given a few moment to search the adequate product. Then they had to answer a questionnaire.

II.3. Main results and implications

30 students were showed the good site and 30 students were showed the poor one.

Before testing our main hypothesis, we have tested the quality of the manipulation with t-test. We've compared the mean of perceived complexity, perceived risk and perceived adequacy within the two agents. The aim was that the good agent receives higher mean of adequacy, lower mean of risk and lower mean of complexity. All the means were going in that sense and all the results were significant which means that the manipulation is correct (annex 2). Further more, for the multi-items scales (more than 2: satisfaction, complexity, risk), we conducted factorial analysis and validity analysis. All the measurement scales appears to be satisfying (annex 1).

We began with the first hypothesis, H1: The perceived quality of an electronic agent has a positive impact on consumer satisfaction toward this agent.

To test that hypothesis, we made a t-test between the good agent and the poor agent one the consumer satisfaction score (the consumer satisfaction is measured by a three-item scale). It appears that for the good agent, the satisfaction score is higher (15,85) than for the poor agent (12,82) and the result is significant (table 3).

Insert table 3 here

The first hypothesis is validated. We can argue that the quality of an electronic agent as a major impact on the consumer satisfaction.

The second hypothesis deals with the link between perceived congruency and perceived quality (H2: The perceived congruency of the electronic agent hasn't any significant impact on perceived agent quality). The aim was to reject the link because the exploratory study didn't show the presence of perceived congruency in the respondent speech. We conducted a simple regression between perceived congruency (in two items) and perceived quality of the agent (in one item) (table 4). The results aren't significant which leads us to accept the second hypothesis.

Insert table 4 here

As we have previously argued, the congruency doesn't have any significant impact on the perceived quality of the agent whereas the impact is positive as argued by researchers.

The third hypothesis deals with the complexity, H3 : Perceived complexity of an electronic agent has a negative impact on perceived agent quality. We tested the hypothesis with a simple regression between perceived complexity and perceived quality. The results aren't significant which means that the impact of complexity on perceived quality isn't clear (table 5). This result is quite interesting. In fact, it is possible to say that for some people, the complexity can have a positive impact on perceived quality (the sign of the adjusted R-square goes in that sense). A complex agent can be seen as a serious one. The third hypothesis is not validated.

Insert table 5 here

The fourth hypothesis was about the impact of risk on perceived quality (H4: Perceived risk of an electronic agent has a negative impact on perceived agent). The risk associated with electronic agent is important in literature. The result of a simple regression between risk and quality shows that the impact is actually positive (table 6). It is significant at a level of 10%. We can not validate the fourth hypothesis because of the poor leve l of signification but it is possible to argue that, we've a bigger sample, the relation would be significant.

Insert table 6 here

At least, the fifth hypothesis (H5: Adequate answers to consumer demands have a positive impact on perceived agent quality) is validated (table 7). It is not a surprise. It's logical that the quality of the agent answer has a positive impact on perceived quality.

Insert table 7 here

Our aim was to study the impact of electronic agent on consumer satisfaction in order to understand their role in electronic commerce. [START_REF] Aksoy | The impact of ordered alternative lists on decision quality in online shopping environments: The role of perceived similarity[END_REF], [START_REF] Urban | Design and evaluation of a trust based advisor on the Internet[END_REF] and Haubl and Trift (2001) argue that the perceived quality of the electronic agent was the main determinant of consumer satisfaction as in the basic models of consumer behavior (such as in [START_REF] Howard | Buying behavior in marketing strategy[END_REF]. The first hypothesis of our empirical study validates this affirmation. We pointed out in the literature that the perceived quality of an electronic agent has some antecedents such as complexity, risk, adequacy and perceived congruency, whereas the impact of the last one wasn't significant for us, regarding a previous exploratory study. The experimentation shows that adequacy (positive impact) and risk (negative impact) had an impact on perceived quality whereas congruency hadn't. The impact of complexity is more complicated to evaluate because it could be different that what we first believed (finally positive but not significant).

Those results lead to some useful implications for electronic agent designers. Designers should be aware of the level of security they put on an electronic agent. The question of adequacy is very important also but it's the heart of an agent, so it is common sense to say that designer should be aware of creating agents that respond correctly to consumer's needs. The question of complexity leads us to broad the debate and to introduce individual variables such as surfer expertise that could moderate the impact of complexity on perceived quality. Nonetheless, the study has succeeded in proving the link between the quality of an agent and the consumer satisfaction.

Conclusion

To conclude, it will be interesting to conduct that study on different respondents and to take into account some moderators such as surfer expertise or self-confidence. Furthermore, an experimentation with two agents and a situation without agent but just a usual shopbot should be edifying to understand more deeply the impact of agent on consumer satisfaction.

What can be pointed out from the literature on electronic buying agent, such as defined in this paper, is the huge potential of that new distributive formula. The agent acts as if it was the consumer and improves the efficiency of his decision process; furthermore it also raises his satisfaction level. This improvement could lead to more buying intentions and could be the solution to the deceiving results of e-commerce.

Whereas, those encouraging results doesn't really fit with the reality. As a matter of fact, most of the existing agents are disappearing from the web for economic reasons. People doesn't enough agree to pay to use them. Maybe agents doesn't have such an impact on consumer satisfaction if the consumers refuse to pay to use them even after having tried them or maybe, the financial aspect is not congruent with the image of electronic agents as free advisors, helping the community of Internet users? • Simple independent agent: the interactivity exists only between the vendor and the agent in order to provide information to the consumer.

List of figures

Figure 1. The role of agent on product attributes formation

A i = ∑ j w j . X ij
A i = ∑ j w j . X ij
A i = ∑ j w j . X ij
• Simple dependent agent :

• Smart independent agent: interactivity vendor-agent an agent-consumer

• Smart web site dependent agent:

• Smart consumer and web site dependent agent: interactivity agents-agents. We're presenting here the analysis of the more than two-item scales.

Perceived congruency:

This agent acts as I do when I want to buy a trip We didn't run any factorial analysis here because each item represents a well-defined dimension and our aim isn't to regroup the information on fewer dimensions.

Perceived adequacy:

This agent successfully answers to my request considering the trip I was looking for Perceived quality:

I

Figure 2 .

 2 Figure 2. The role of agent on information search

Figure 4 .

 4 Figure 4. The role of agent on alternatives evaluation

Figure 5 .

 5 Figure 5. The negotiating role of the agent

Figure 6 .

 6 Figure 6. Relationships between agents, vendors and consumers.

Figure

  Figure 7. Conceptual framework and research hypothesis

Table 1 . Different types of electronic agent and their function within the cyber-consumer decision process (inspired by West et al., 1998).

 1

	Cyber-consumer decision process		Electronic agent
	Problem definition and preferences	« Tutor »: educates the consumer et allows him to
	construction	discover his preferences ex: Moviecritics
	Information search	« Clerk »:	accomplishes	fastidious	search,
		classification and sorting information tasks ex:
		Personnalogic, Bargainfinder
	Alternatives evaluation	« Advisor »: gives an experts opinion and advise the
		consumer considering his predefined tastes ex:
		Personnalogic
	Decision	No existing agent
	Buying	« Banker »: negotiates and facilitates the buying ex:
		T@T from MIT

Table 2 . Design of the two electronic agents

 2

		Good agent		Poor agent
		-Listed presentation of the		-Non listed presentation of the
		information		information
		-No pop-ups		-Many pop-ups
	Not complex	-Lot of details on each	Complex	-Few details on each alternatives
		alternatives		-Many pages before the
		-Few pages before the		command
		command
		-Presence of insurance's and		-No insurance's nor payment
	Not risky	payment security -Data's confidentiality	Risky	security -No data's confidentiality
		-Free phone number		-No free phone number
	Adequacy	-Adequate answer with the demand -Rated alternatives	Poor adequacy	-Inadequate answer with the demand -Non rated alternatives

Table 3 . T-test for the first hypothesis

 3

		QUALITY N	Mean	Standard deviation	Mean standard error
	SCORE	Good	31	15,8571	2,99028	,56511
	satisfaction Poor	30	12,8276	2,98890	,55502

Measurement scales (those scales were actually in French, we're presenting here a transla tion)

  Each scale is measured in seven points on a Likert scale such as the following one:

	ç Totally disagree					Totally agree è
	1	2	3	4	5	6	7

Perceived complexity (by Cheung, Chang and Lai, 2001): Working

  This agent takes the same decision as I would have taken by myself considering the trip I want to buy

			Cronbach Alpha	% of
	Scale	Items	Without the item	explained	Extraction	Component 1
			Global a: 0,83	variance
	Perceived	C1	0,8105		0,664	0,815
	complexity	C2	0,7523	69,67%	0,800	0,895
		C3	0,7898		0,750	0,866
	Perceived risk (6

with this agent is complicated, it is difficult to understand what's going on Using this agent involves too much time doing mechanical operations (i.e.: data input) It takes too long to learn how to use this agent to make it worth the effort

dimensions by Cases, 2001): Risk dimensions Items Mean Scores

	Private risk	The personal data I'm giving to the agent could be used by others web sites	4,49
	Performance risk	The quality of the found trip by the agent could be lower than my former expectancies	4,22
	Financial Risk	The entire price spent for the trip found by the agent could be higher than anticipated	4,65
	Temporal risk	Buying a trip found by the agent could be a lost of time	4,78
		Using an electronic agent to buy a trip could
	Social risk	put me in disagreement with my friends and	2,19
		relatives
	Payment risk	Paying a trip by the intermediary of the agent could have negative consequences	4,22

  find that the quality of this agent is good considering what I was looking for Each t-test presents significant results at the level of 1%.

	Annex 2. Quality of the manipulation
	Manipulation of the complexity
	Complexity	Sample	Perceived complexity mean	Standard deviation	Mean standard error
	High (poor site)	30	2,4483	0,80117	0,14877
	Low (good site)	31	2,0571	0,51021	0,09642
	Manipulation of the risk
	Satisfaction: Risk Globally, this agent satisfies me Sample High (poor site) 30	Perceived risk mean 4,39	Standard deviation 0,7416	Mean standard error 0,1236
	It leaves me a good impression Low (good site) 31	3,63	°,5563	0,1112
	I would recommend this agent to a friend Manipulation of the adequacy
	Scale Satisfaction Adequacy High (good site) Items S1 S2 S3 Sample Cronbach Alpha Without the item Global a: 0,83 0,89 Perceived adequacy mean 31 4,8355 Low (good site) 30 3,9811	% of explained variance 83,4% Standard deviation 0,6739 0,836	Extraction 0,881 0,850 0,771 Mean standard error Component 1 0,939 0,1273 0,922 0,878 0,1529


V Chabannes
email: chabannes@math.unistra.fr

C Prud'homme
email: prudhomme@math.unistra.fr

M Szopos
email: szopos@math.unistra.fr

R Tarabay
email: tarabay@math.unistra.fr

HIGH ORDER FINITE ELEMENT SIMULATIONS FOR FLUID DYNAMICS VALIDATED BY EXPERIMENTAL DATA FROM THE FDA BENCHMARK NOZZLE MODEL

Keywords: CFD, validation, medical device, open source finite element software

The objective of the present work is to construct a sound mathematical, numerical and computational framework relevant to blood flow simulations and to assess it through a careful validation against experimental data. We perform simulations of a benchmark proposed by the FDA for fluid flow in an idealized medical device, under different flow regimes. The results are evaluated using metrics proposed in the literature and the findings are in very good agreement with the validation experiment.

INTRODUCTION

A challenging benchmark was proposed by the US Food and Drug Administration (FDA) in [START_REF] Hariharan | Multilaboratory particle image velocimetry analysis of the FDA benchmark nozzle model to support validation of computational fluid dynamics simulations[END_REF] in order to assess the stability, accuracy and robustness of computational methods in different physiological regimes. The findings of 28 blinded investigations were reported in [START_REF] Stewart | Results of FDAs first interlaboratory computational study of a nozzle with a sudden contraction and conical diffuser[END_REF] and as critically analyzed in [START_REF] Sotiropoulos | Computational fluid dynamics for medical device design and evaluation: are we there yet?[END_REF], practically all CFD solvers failed to predict results that agreed in a satisfactory manner with the experimental data. Several subsequent papers tackled this question, by employing different numerical approaches: for instance a finite-element based direct numerical simulation method in [START_REF] Passerini | Validation of an open source framework for the simulation of blood flow in rigid and deformable vessels[END_REF] or a large-eddy simulation method in [START_REF] Zmijanovic | About the numerical robustness of biomedical benchmark cases: Interlaboratory FDA's idealized medical device[END_REF].

We aim at contributing to the effort of improving the reliability and reproducibility of computational studies by performing a thorough validation of the fluid solver developed in the open source finite element library Feel++ [START_REF] Prud'homme | Feel++: A Computational Framework for Galerkin Methods and Advanced Numerical Methods[END_REF]. In the current investigation, we present results corresponding to three Reynolds numbers 500, 2000 and 3500 obtained by using a direct numerical simulation method of the Navier-Stokes equations. In particular we implement and compare low order as well as high order approximations including for the geometry and we discuss some issues not previously reported in the literature.

METHODOLOGY

Benchmark description. The FDA benchmark nozzle model provides a comprehensive dataset of experimental measures using a well-defined geometry corresponding to an idealized medical device (see Figure 1 for a schematic sketch of the domain and [1, Sec. 2.1] for the precise dimensions of each part). Five sets of data spanning laminar, transitional and turbulent regimes are made available; we focus in the current work on the flow regime specifications described in Figure 1.

The comparison with experimental data is made in terms of (i) wall pressure difference (normalized to the mean throat velocity) versus axial distance; and (ii) axial component of the velocity (normalized to the mean inlet velocity) along the centerline:

∆p norm = p z -p z=0 1 2 ρ f u 2 t and u norm z = u z u i , where u 2 t = 4Q πD 2 t , u i = 4Q πD 2 i , (1)
and Q is the volumetric flow rate retrieved from Re t (see Figure 1, right panel). Furthermore, we present results on two validation metrics reported in [START_REF] Stewart | Results of FDAs first interlaboratory computational study of a nozzle with a sudden contraction and conical diffuser[END_REF], also assessed in [START_REF] Passerini | Validation of an open source framework for the simulation of blood flow in rigid and deformable vessels[END_REF]: a conservation of mass error metric E Q (on a percentage basis) and a general validation metric E z comparing average experimental velocity data with computed axial velocities.

Fluid equations and numerical approach. We now turn to the mathematical and the numerical setting. We consider the homogeneous, incompressible, unsteady Navier-Stokes equations, which read in conservative form: find (u, p) such that

ρ ∂u ∂t + (u • ∇)u -µ∆u + ∇p = 0, div(u) = 0, in Ω × I.
The set Ω ⊂ R 3 represents the spatial domain described in Figure 1. I = (0, T ) is the time interval, u and p are the velocity and pressure of the fluid and ρ and µ are the density and the dynamic viscosity of the fluid, respectively. We supplement the equations with initial and boundary conditions. At t = 0s, the fluid is considered to be at rest, u(x, t) = 0. A Poiseuille velocity profile is imposed on Γ inlet , homogeneous Dirichlet condition on Γ wall and a free outflow on Γ outlet .

We refer to [8, Sec. 2] regarding the variational formulation, the finite element discretization including low to high order geometry as well as the time discretization. We choose the generalized Taylor-Hood finite element for the velocity-pressure discretization; the notation P N +1 P N G kgeo is used to specify exactly the discretization spaces for the velocity, pressure and geometry, respectively.

The benchmark hereafter is developed in the framework of the Finite Element Embedded Library in C++, Feel++ [START_REF] Prud'homme | Feel++: A Computational Framework for Galerkin Methods and Advanced Numerical Methods[END_REF], that allows to use a very wide range of Galerkin methods and advanced numerical techniques such as domain decomposition. The ingredients include a very expressive embedded language, seamless interpolation, mesh adaption and seamless parallelization. Regarding the computational domain, we used GMSH. The construction used the following steps: (i) start with a 2D geometry embedding the benchmark metric locations and customizing characteristic mesh size depending on the region and (ii) extrude by rotation to obtain the device geometry. Finally we use the PETSC interface developed in Feel++ and in particular the FieldSplit preconditioning framework to implement block preconditioning strategies such as PCD [START_REF] Elman | Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics[END_REF]. Note that PCD requires specific tuning with respect to boundary conditions.

RESULTS AND CONCLUSIONS

h min h max h average N elt M0 1.9 • 10 -4 2.9 • 10 -3 1.3 • 10 -3 412 575 M1 1.6 • 10 -4
1.8 • 10 -3 7.6 • 10 -4 830 000 M2 1.4 • 10 -4 1.96 • 10 -3 6 • 10 -4 3 400 000 M3 8.5 • 10 -5

1.7 • 10 -3 3.5 • 10 -4 7 000 000 M4 6. We perform simulations for three Reynolds numbers evaluated in the throat Re t = 500, 2000, 3500, with several mesh refinements and polynomial order approximations. The fluid's prescribed density is ρ = 1056 kg m 3 and viscosity µ = 0.0035P a.s. The mesh characteristics are described in Table 1. At Re t = 500, the simulation is carried out until t = 3s, time reasonably close to the steady state, and we choose the time step equal to ∆t = 10 -3 . At Re t = 2000 (resp Re t = 3500), the numerical experiments were carried out until t = 0.45s (resp t = 0.4s), time when the turbulent regime was fully developed and we set ∆t = 10 -4 .

Figure 2 shows the results in the three flow regimes for the normalized axial velocity and the normalized pressure difference along the z axis, respectively. In each case, we can see satisfactory agreement with the experimental data. However, for Re t = 2000, we observe that the numerical jet breakdown point is captured further downstream than the experimentally observed breakdown point. As recently highlighted in [START_REF] Zmijanovic | About the numerical robustness of biomedical benchmark cases: Interlaboratory FDA's idealized medical device[END_REF], the prediction of the axial location of the jet breakdown is extremely sensitive to numerical parameters, therefore a possible explanation of this mismatch may be the accuracy of the numerical integration. Finally, we illustrate in Figure 3 the computation of metrics E z and E Q for several mesh refinements at Re t = 500. The metric E z takes small values in each numerical experiment, identifying a good agreement betweeen computed and experimental data, and displays only small variations with respect to mesh refinement. On the other hand, the metric E Q is more sensitive to this factor: error doesn't exceed the ∼ 2% except for the coarse mesh M 0 where, in two locations, the error increases up to ∼ 10%. Furthermore, we note that the P 3 P 2 G 1 approximation doesn't improve the results for the coarse mesh, but that a satisfactory error below 2% is retrieved when using a P 2 P 1 G 2 approximation. Additional tests to complement the study of the impact of high order approximation are ongoing.

Conclusions and perspectives

We validated our computation fluid dynamic framework against this FDA benchmark for three different regimes and different discretization and solution strategies. Perspectives include a full report on our findings including in terms of iteration and timing performances as well extending our results to the turbulent range.

Figure 1 :

 1 Figure 1: Computational domain (top) and flow regime specifications (bottom); Re i and Re t : Reynolds number in the inlet section and throat section, respectively.

Figure 2 :

 2 Figure 2: Comparison between experimental data and numerical results for the normalized axial velocity along z (left) and the normalized pressure difference along z (right), for Re t = 500 (top) Re t = 2000 (middle) and Re t = 3500 (bottom).

Figure 3 :

 3 Figure 3: Validation metrics E z (left) and E Q (right) for Re t = 500.

Table 1 :

 1

	3 • 10 -5	2.0 • 10 -3 5.8 • 10 -4 2 879 365
	M5 1.4 • 10 -4	2.6 • 10 -3 4.1 • 10 -4 3 200 000

Characteristic lengths of the different meshes: h min , h max , h average are respectively the minimum, maximum and average edge length in the meshes and N elt is the number of tetrahedra.

Acknowledgments

The authors wish to thank Mourad Ismail for the fruitful discussions we had. Moreover we would like to acknowledge the support of (i) Center of Modeling and Simulation of Strasbourg (Cemosis), (ii) the ANR MONU-Vivabrain (iii) the LabEx IRMIA and (iv) PRACE for awarding us access to resource Curie based in France at CCRT as well as GENCI for awarding us access to resource Occigen based in France at Cines


Xiao Ma

Allan Matthews

Evaluation of abradable seal coating mechanical properties

Keywords: Abradable seal coatings, Scratch testing, Progressive Abradability, Hardness Abradability

Three proprietary plasma-sprayed coatings, based on Ni-graphite, Al-Si-graphite and Al-Si-polyester, were chosen for evaluation by the use of a (low speed) scratch tester, as a means of assessing the per-formance of abradable coatings. The scratch test behaviour was also correlated with the mechanical properties of the coatings (elastic modulus, microhardness and ultimate tensile strength). The results obtained were compared with those from industrial trials, to ascertain if the scratch test could be used as a relatively cheap and effective alternative to expensive engine trials. We have shown that the Pro-gressive Abradability Hardness, abbreviated below as PAH, can be utilised as a measure of abradability in the scratch test, and can be related to the mechanical properties, in a manner consistent with engine test-bed findings. We have also found that the abradability and the PAH can change with scratch length due, we believe, to coating compression and densification ahead of the slider. In this work, the PAH has been related to coating hardness, ultimate tensile strength and elastic modulus.

Introduction

Turbo-engine efficiency is governed by the maximum pressure and the operating temperature [START_REF] Plc | The Jet Engine[END_REF]. Particularly in the last two decades the turbomachinery industry has been making every effort to optimise these two crucial factors, for example by enhancing the operating temperature using temperature-tolerant superalloys and thermal barrier coating systems, and incorporating appropriate aerodynamic features. A primary design requirement is to minimise the clearance between the rotating blades and the casing, so that the air can be transferred to the compressor as efficiently as possible to provide thrust and reduce fuel consumption [START_REF] Ghasripoor | Abradable coatings increase gas turbine engine efficiency[END_REF]. Abradable seal coatings have achieved great success on this regard and are now been used extensively in both aero-engines and land-based turbo generators [START_REF] Dowson | Development of abradable and rubtolerant seal materials for application in centrifugal compressors and steam engines[END_REF].

Abradable seal coatings have been engineered to minimise the clearance between blade-tips and casing to enhance gas-turbine performances [START_REF] Plc | The Jet Engine[END_REF][START_REF] Ghasripoor | Abradable coatings increase gas turbine engine efficiency[END_REF]. During operation, gas-turbine blades rotate at a very high speed (typically 3000-10,000 rpm or higher for aeroengines) and may therefore rub the casing due to either thermal expansion, misalignment or rotation-induced strains [START_REF] Ghasripoor | Abradable coatings increase gas turbine engine efficiency[END_REF][START_REF] Ma | Investigation of abradable seal coatings[END_REF]. Abradable seal coatings are applied in between the blade-tips and the casing to prevent such catastrophic contact while maintaining minimum clearance between them. An earlier paper was written by the authors [START_REF] Ma | Investigation of abradable seal coatings[END_REF] that mainly focused on an investigation of using scratch testing to determine abradability. It will be referred to as "the investigation paper" in the rest of this paper.

In order to achieve the required performance, the optimal microstructure developed typically consists of a metal matrix supplying desirable erosion and oxidation resistance and a solid lubricant phase such as graphite to provide abradability [START_REF] Clegg | NiCrAlbentonite thermal spray powder for high temperature abradable seals[END_REF][START_REF] Faraoun | Improvement of thermally sprayed abradable coating by microstructure control[END_REF]. While abradable seal coating materials are usually evaluated using high speed rubbing rigs by replicating the aerodynamics and contact environments inside gas-turbine engines [START_REF] Chupp | Applying abradable seals to industrial gas turbines[END_REF] or other forms of alternative laboratory high speed tests [START_REF] Yi | Friction and wear behaviour and abradability of abradable seal coating[END_REF][START_REF] Bryggman | Force and energy measurements during controlled grooving-a basic study of abrasive wear[END_REF][START_REF] Kennedy | Single-pass rub testing of abradable seal materials[END_REF][START_REF] Kennedy | Single pass rub phenomena-analysis and experiment[END_REF][START_REF] Liang | Evaluation of abradability of porous seal materials using a single pendulum scratch test[END_REF], this paper introduces investigation of several abradable materials using laboratory facilities, including the method of scratch testing to determine their abradability. The Progressive Abradability Hardness (PAH) has been proposed as a measure of abradability and shown to be well-related to other mechanical properties. In the investigation paper [START_REF] Ma | Investigation of abradable seal coatings[END_REF] this concept was introduced, and the present paper provides more information on the work, and associated modelling.

Experimental details and theories

Elastic modulus, microhardness and ultimate tensile strength were measured for the abradable seal coatings. The detailed specimen shapes and dimensions are listed in Table 1.

Elastic modulus evaluation

An elastic modulus evaluation was performed using a cantilever beam bending test configuration, shown in Fig. 1. The experimental setup and derivation of the elastic modulus of coatings have been detailed in the investigation paper [START_REF] Ma | Investigation of abradable seal coatings[END_REF].

Microhardness evaluation and finite element simulation

The theories surrounding hardness testing are well known [START_REF] Hetzner | Microindentation hardness testing of materials using ASTM E384[END_REF][START_REF] Bell | Recent developments in hardness testing and their implications for standardisation[END_REF]; however the plastic deformation which takes place under and around an indenter can be complex and can adversely affect the final hardness value if, for example, the plastic deformation volume incorporates the substrate [START_REF] Buckle | Science of Hardness Testing and its Research Applications[END_REF][START_REF] Jonsson | Hardness measurements of thin films[END_REF][17][START_REF] Burnett | Assessment of coating hardness[END_REF]. In film hardness testing, a theoretical treatment aiming at eliminating substrate influence is a necessity. In order to calculate the plastic deformation volume, a rule of thumb [START_REF] Buckle | Science of Hardness Testing and its Research Applications[END_REF] and an experimentally validated expression found by Lawn et al. [19] were compared. The rule of thumb states that the radius of the plastic volume around an indenter is roughly ten times the radius of the indentation; Lawn's theory relates the radius with the diagonal length of the indentation, the semi-angle of the indenter and the material's elastic modulus and hardness by: In which b is the radius of the plastic volume, a is the half diagonal length of the indentation. E and H are the elastic modulus and hardness of the tested film. ϕ is the indenter semi-angle. Although the hardness of abradable seal coating materials is primarily evaluated by the R15Y test [START_REF] Ma | Investigation of abradable seal coatings[END_REF]20], in our work microhardness evaluation was conducted using a Mitutoyo model HM-101 microhardness tester, which has been detailed in the investigation paper [START_REF] Ma | Investigation of abradable seal coatings[END_REF]. To calculate the plastic region both approaches were followed and results were compared.

b a = E H 1/2 ctg 1/3 ϕ (1)

Ultimate tensile strength evaluation

Abradable coating materials are mechanically weak in tension and it is not possible to debond them as intact coatings from the substrates for UTS evaluation. A method was therefore found to assess the coating UTS with the coatings remaining on the substrates.

When the load is applied to the specimen, it is supported by both the coating and the substrate. However, when the coating is relatively weak, as is the case here, the influence of the substrate in supporting the load is obviously greater. Failure of a coatingsubstrate composite system can occur due to either tensile cracking or delamination, depending on adhesion [START_REF] Bull | Evaluation of coatings[END_REF].

One of the two failure modes occurs eventually in the tensile test; whichever occurs first depends on the relative strengths and the adhesion between the coating and substrate [START_REF] Bull | Evaluation of coatings[END_REF]. Abradable coatings have porous structures and low UTS values [START_REF] Clegg | NiCrAlbentonite thermal spray powder for high temperature abradable seals[END_REF], and are thus more likely to fracture prior to major coating delamination. The coating fractures abruptly whereas the detachment of coating takes place progressively. Therefore the load-extension curve was expected to represent a sudden drop as the coating breaks, followed by a period of instability corresponding to gradual coating detachment.

The experiment setup and calculation procedures are detailed in the investigation paper [START_REF] Ma | Investigation of abradable seal coatings[END_REF]. All the samples were pulled until failure and load-extension curves were recorded by the tester at each 0.02 mm of extension.

Progressive Abradability Hardness (PAH)

The PAH may also be termed 'specific energy' [START_REF] Liang | Evaluation of abradability of porous seal materials using a single pendulum scratch test[END_REF] or alternatively, 'specific grooving energy' [START_REF] Kennedy | Single-pass rub testing of abradable seal materials[END_REF] (since it is defined as the work done per volume of abraded material), and can be measured by scratching a stylus across a surface. Its value is given by

H a = W V (2)
where H a is the PAH, W is the energy consumed during the scratching process (i.e., the work done by the scratching stylus) and V is the groove volume. The term measures how difficult it is to abrade a material in terms of the energy needed to produce scratch grooves. Materials that have high abradability have low PAH values and vice versa [START_REF] Bryggman | Force and energy measurements during controlled grooving-a basic study of abrasive wear[END_REF][START_REF] Kennedy | Single-pass rub testing of abradable seal materials[END_REF][START_REF] Liang | Evaluation of abradability of porous seal materials using a single pendulum scratch test[END_REF]. This concept was put forward in a slightly different form by Vingsbo and Hogmark [START_REF] Vingsbo | Single-pass pendulum grooving-a technique for abrasive testing[END_REF], who described the specific energy as a quantitative indication of the abrasion resistance of steels. Vingsbo suggested the specific energy be more accurately obtained by dividing the energy by the mass loss. Later, in the 1980's the energy-dissipation concept was used for measuring the abradability of gas path sealing by Kennedy and Hine [START_REF] Kennedy | Single-pass rub testing of abradable seal materials[END_REF] and a single-pass pendulum apparatus was implemented as it provided a relatively fast, impact-like rubbing process where the energy consumed in the process could readily be assessed from the swing angles before and after the scratching. They evaluated the groove volume rather than mass loss as the latter was difficult to measure and groove volume was related more directly to the deformation created. During our scratch tests, forces in both normal and transverse directions, displacement of the indenter and acoustic emission were recorded by the controlling unit at a sampling interval of 0.1 mm, enabling the calculation of energy consumed and groove volume produced by the stylus. Fig. 2 shows the rationale of the method.

The PAH can be expressed as

H a = i=1 F Ti • D Pi + i=1 F Ni • (D i+1 -D i ) i=1 A i (D) • D Pi (3)
where F T and F N are the tangential force and normal force recorded by the scratch tester. D P and D i are the ploughing and indentation displacement of the indenter. D is the indentation depth and A is the groove cross section area that is a function of the indentation depth, and is used to calculate the groove volume. The subscript "i" indicates parameters for the ith discretised segment.

A detailed description of this model has been given in the investigation paper [START_REF] Ma | Investigation of abradable seal coatings[END_REF]. In an attempt to determine the coating material abradability, a CSM Instruments Revetest Scratch Tester was used to scratch the samples in a controlled, relatively slow manner that applied a progressively increasing normal load to the samples. A Rockwell C 120 • diamond cone with a 200 m tip radius was used as the slider that was drawn across the samples at a constant speed of 10 mm/min. An acoustic sensor attached to the load arm was used to detect the acoustic emission during scratching. An initial screening trial stage was performed in the first place to define a maximum usable load so that no gross coating spallation would occur. Considering the geometry and a moderate loading rate, two end loads (50 N and 100 N) were evaluated in the screening trial stage to make sure the adhesion critical load would not be reached during the actual scratch testing.

No observable sudden changes of frictional force were detected by the transducer at either load, and this showed all the samples were not prone to adhesive failure during the tests. Therefore, the following loading procedure was carried out on all the samples, producing five scratch grooves with lengths of 0.9 mm, 2.9 mm, 4.9 mm, 6.9 mm and 9.9 mm on each sample. The five grooves were kept 1.5 mm apart and parallel to each other. A 1 N initial load was applied to enable the starting point to be clearly distinguished. The loading was increased progressively at a rate of 100 N/min, making the end loads 10 N, 30 N, 50 N, 70 N and 100 N. All six scratched samples were then examined by SEM.

Coatings

The three abradable coating materials were plasma sprayed using standard equipment to Sulzer Metco proprietary spraying parameters. Their compositions (from datasheets [20,23,24]) are specified in the investigation paper [START_REF] Ma | Investigation of abradable seal coatings[END_REF].

Metco 308NS is based on nickel-graphite cermet powder with a microstructure of a continuous nickel matrix embedded with a graphite solid lubricant and a controlled amount of pores [20]. Metco 313NS uses an aluminium silicon alloy-graphite composite powder with microstructure of a continuous aluminium silicon alloy matrix with graphite and porosity uniformly distributed throughout [23]. Metco 601NS is a blend of aluminium, silicon and polyester powder. The microstructure is a continuous aluminium silicon alloy matrix with dispersion of polyester particles, which provide abradability and a low friction coefficient [24]. The Metco 450NS bondcoat consists of a nickel-aluminium alloy matrix (80Ni-20Al wt.%) and was deposited by thermal spraying beneath the abradable coatings to enhance bonding. Coating materials were sprayed on low alloy steel strips of different sizes. The elastic modulus (E) of the steel strips was 172.4 GPa, and the Vickers hardness was 171 H v (kgf/mm 2 ).

Results and discussion

Elastic modulus evaluation

The results for elastic modulus evaluations are shown in Table 2. The results show a decrease in the elastic modulus from Metco 308NS to Metco 313NS to Metco 601NS, all of which have extremely low elastic moduli compared to the substrate and the Metco 450 NS bondcoat. It is also shown that measured elastic moduli become lower at higher loads (Table 2). This could be attributed partly to plastic deformation of the samples, suggested by the fact that at higher loads the index of the dial gauge did not always rotate back to the starting point. Although pre-test calculation had been performed to ensure that no major plastic deformation would take place, considering the multi-phase structure of abradable coatings, certain phases, i.e. graphite or polyester, might still have plastically deformed, leading to this low measured elastic modulus phenomenon at high loads. No dependency between elastic modulus values and abradable coating thickness was evident. A clear increase of measured elastic modulus was found when bondcoats were present.

Microhardness evaluation

Metco 308NS has the highest microhardness readings, followed by Metco 313NS and then Metco 601NS. All three candidate materials show different hardness readings with different applied loads as shown in Fig. 3. This is likely to be due to the fact that the proportion of phases contained in the sampled area (indentation) might vary and thus the contribution of a given phase to each reading can differ. This is supported by the fact that towards higher loads the scatter of microhardness readings decreases as the indenter samples more material. However, Metco 308NS was observed to show decreased hardness at the higher load, attributable to the indentation size effect [START_REF] Bull | Evaluation of coatings[END_REF] due to a greater proportion of elastic recovery of the indentation at lower loads. Note that before the finalisation of the hardness values each indentation had to be evaluated to determine whether there was likely to be a substrate influence on the reading, resulting in a 'composite hardness' effect. The results of the predicted plastic regions beneath the indenter are shown in Table 3.

Since the thinnest coating thickness was 2.1 mm, no indentation led to any "composite hardness effect", according to both the rule of thumb and Lawn's expression. Note the "one tenth" rule of thumb predicts much smaller plastically deformed volumes than the theory of Lawn.

A possible explanation of the difference between three approaches is that the theory by Lawn [19] is more suitable for materials with a low Y/E ratio, e.g. stainless steel and other non work-hardening materials and the rule of thumb is usually used for hard, brittle coatings (most likely ceramic coatings) that have high Y/E ratios. Abradable materials exhibit extremely low elastic moduli, making them materials with high Y/E ratios along with work-hardenable metals, ceramics and glasses, but their response to mechanical loading is obviously different to these materials due to soft and loose structure. A comparison of their relevant properties is given in Table 4 [START_REF] Booser | Tribolgy Data Handbook[END_REF] (elastic moduli of abradable seal coatings are taken from measurements; compressive yield strength is taken as one third of the Vickers hardness from microhardness measurements).

The actual deformation mechanisms of abradable coatings can be illustrated by comparing how materials with high and low Y/E ratios behave under mechanical loading. Johnson [START_REF] Johnson | The correlation of indentation experiments[END_REF] and Tabor [START_REF] Tabor | The Hardness of Metals[END_REF] described different deformation responses to Vickers hardness measurement, shown Fig. 4. Tabor's theory pointed out that the material surface would pile-up at either side of the indenter, and the geometry of the pile-up was determined by the normal and friction stress between the indenter and the sampled material, which can be analysed by the slip line field within the plastic zone. This theory was suggested to be applicable for materials with low Y/E ratios. Johnson's expanding spherical cavity model described a different situation that is applicable to materials with high Y/E ratios. It was believed that only when a hydrostatic core existed beneath the indenter could plastic deformation take place prior to cracking, outside which was an elastic region that surrounded that hydrostatic core. However, we believe that neither of the two scenarios can well describe the behaviours of abradable seal coatings. No hydrostatic core is needed for accommodating plastic deformation, and the stress-concentrated edges of the indentation simply densify rather than pile-up; on the other hand, an elastic hinterland should exist due to high Y/E ratios. Therefore, the true plastically deformed regions of abradables were believed to lie in between that predicted using rule of thumb and the theory of Lawn.

Ultimate tensile strength evaluation

The load-extension curves were recorded by the tester every 0.02 mm, as shown in Fig. 5. Points A, E, G are where fracture was observed to occur for Metco 308NS, Metco 313NS and Metco 601NS, respectively, after which the coatings were gradually detached until fully debonded from the substrate at points B, F, H. Metco 313NS debonded earlier than Metco 308NS with a smaller extension at point F. The rest of curves behave similarly, indicating substrate extension, except for Metco 601NS that shows an abrupt drop of load, corresponding to an observed coating break within the grips.

It is worth noticing that in the vicinity of an extension of 1.5 mm, all the coatings failed. The extension at these coating fracture points largely exceeded the maximum elastic extension of the mild steel substrate, indicating the substrate must have plastically deformed by the time that these fractures occurred, therefore the load the substrate supported was considered as the product of its flow stress and the instantaneous cross-sectional area. The ultimate tensile strength evaluation shows a decreasing tendency from Metco 308NS to Metco 313NS and finally to Metco 601NS, as for the elastic modulus and the microhardness.

The ultimate tensile strength of each material was thus determined, as shown in Table 5.

Scratch testing 3.4.1. PAH measurement

Since the PAH is defined as the work done per unit volume of material abraded, any increase in PAH reflects a real increase in scratching resistance [START_REF] Ma | Investigation of abradable seal coatings[END_REF][START_REF] Liang | Evaluation of abradability of porous seal materials using a single pendulum scratch test[END_REF]. It can be seen from Fig. 6 that Metco 308NS shows a clearly increasing PAH when the scratch length was increased. Metco 601 however, shows a rather stable PAH whereas Metco 313 is in between. The increase of the PAH at long scratches is attributed to coating densification and, possibly, a work hardening effect, which is a result of their different microstructures and compositions. The stable PAH of Metco 601 suggests that no densification From the microstructure point of view, Metco 308NS has the highest amount of porosity (15 vol%) that can accommodate material densification during scratching whereas Metco 601NS has the least (5 vol%); In terms of composition, a large amount of metallic phase (85 vol%) in Metco 308NS can be a source of work hardening.

Three abradable coating materials with bondcoats represent very similar PAHs which are considerably smaller than for samples coated only with abradable coatings. Furthermore, rather than being densified, their PAHs decrease towards higher loads and longer scratch lengths. Their acoustic emission curves were also found to be very smooth (not shown here), suggesting the primary accommodation mechanism was plastic deformation. This observation was unexpected and is believed to be due to a different stress field around the stylus induced by the bondcoats.

SEM scratch surface topography examination

Scratch surface topography is a good indicator of the underlying deformation mechanisms. All the scratch grooves were examined under SEM; it was noticed that scratch grooves on the same sample had almost identical appearances. There was no gross coating spallation detected, as it had been eliminated by the screening trial stage, and this is inconsistent with the stable frictional force. The acoustic emission, however, shows occasional peaks, indicating that both plastic deformation and coating fracture were present during the scratching.

As discussed before, Metco 308NS was densified considerably during scratching, leading to a great increase in PAH. Its scratch topography is smooth and dense, and there is no evidence of coating fractures, as shown in Fig. 7.

The darker graphite colonies were dislodged and dragged along the scratch, and the removed graphite debris was crushed beneath the stylus into the nickel matrix, again leading to densification. The relatively high strength of Metco 308NS leads to a greater constraining effect of the undeformed material to the pressurised material beneath the stylus, which adds to densification. However, cracking was observed along the nickel-graphite interfaces and within the graphite colonies where the bonds are relatively weak, and those cracks account for minor peaks and valleys in the acoustic emission curve. They appear in the grooves as concentric semicircle, which is typical of tensile cracks. As the slider scratches the surface, the normal and tangential stresses produce excessive tensile stress at the rear part of the contact spot, as well as the edges of the groove, therefore material behind the contact is fractured due to very low ultimate tensile strength [START_REF] Bull | Failure modes in scratch adhesion testing[END_REF]. Conformal cracks that usually occur because of buckling of material in front of the slider were not observed on any of the samples, due to the fact that the loose structure can accommodate large compressive stress prior to failure.

In comparison, more tensile cracks were observed on Metco 313NS surface, as shown in Fig. 8. The appearance of Metco 313NS groove shows a topography that is apparently less dense, in agreement with the PAH. Unlike the Metco 308NS, the cracks are not confined along the aluminium-graphite interfaces but extend within the aluminium matrix. This is attributable to the low strength of the aluminium matrix coupled with a large amount of graphite (up to 22 vol%).

Metco 601NS has a completely different groove topography from the other two, as shown in Fig. 9. In situ coating spallation and chipping were observed both within the groove tracks and along the edges on Metco 601NS. This indicates that when the samples were scratched, the material ahead of the stylus was fractured and spalled due to a low compressive strength, as determined by the experiments. However, the rather large coating thickness ensured that coating detachment from the substrate did not occur. This morphology can be further attributable to the different responses of the aluminium matrix and polyester solid lubricant phase. Polyester has extremely low flexural strength and elastic modulus; as a result the stored energy tends to induce considerable elastic recovery (as opposed to the aluminium matrix). Chipping was found both within the track and at the groove edges, suggesting that chips were removed and crushed back into the track. The rather flat chipping morphology signifies that the collapsed material was pressed by the passing stylus, as shown in Fig. 9. Since most of the material collapsed and spalled ahead of the stylus instead of undergoing plastic deformation, there is no indication of densification, resulting in a rather stable PAH. The amount of acoustic emission can be directly related to cracking during deformation, which is shown in Fig. 10 [4]. It can be found that the acoustic emission of Metco 601NS was remarkable and unstable during the scratching, indicating the onset of crackings. Metco 308NS on the other hand showed a very stable and much smaller acoustic emission.

Another possible explanation of the low PAH detected for Metco 601NS could be related to a finding by Maozhong Yi et al. [START_REF] Yi | Friction and wear behaviour and abradability of abradable seal coating[END_REF], who stated that a complete film layer, containing carbon and oxygen diffused from the polyester, was found adhered to the counterpart ring in a block-ring wear testing. This film decreased the friction coefficient. Since such a friction reduction would decrease the energy consumed in the scratching process, this would also decrease the PAH. In our tests the polyester was smeared onto the tool, leaving a surface topography as shown in Fig. 9.

It is worth noticing that when a Metco 450NS bondcoat was added in between the coatings and the substrates, all the three samples have a rather smooth and dense scratched topography, with less cracking present. The stable and limited acoustic emission proves this, and the reason, as stated before, is due to the compressive stress that the bondcoat imposed on to the abradable materials which retarded crack propagation, especially in regions that were subject to tensile stress and would have otherwise fractured.

SEM scratch cross-sectional topography

The specimens were also sectioned and examined under an SEM, as shown in Fig. 11. Dominant deformation mechanisms were distinguished, e.g., whether the deformation was accommodated by coating fracture or plastic deformation. As a result of the scratching slider, plastic deformation led to densification, characterised by crushed layers of materials, e.g., deformed pores and graphite colonies. The materials were squeezed and aligned in a parallel pattern. Fig. 11(a) and (b) illustrate that in the case of Metco 308NS, a considerable amount of material beneath the drawing stylus underwent plastic deformation resulting in significant densification. Metco 308NS without a bondcoat beneath showed obvious evidence of densification, but the densified region was constrained in a smaller volume, compared to that with a bondcoat. Hardly any porosity can be found in the adjoining densified regions but they gradually become visible further beneath. Conversely, porosity can be seen through the whole picture where there is a bondcoat added underneath. The pores, however, are squeezed and deformed into the shape coinciding with the stylus profile, but are still visible, indicating a reduced degree of densification but a larger region affected.

The expected densification regions are almost invisible in the pictures of Metco 313NS since most of the pores beneath the stylus remain round-shaped and are evenly distributed, even in areas close to the groove edges, as shown in Fig. 11(c) and (d). This is however contradictory to the scratch surface topography and the PAH, both indicating there should have been some regions where densification took place.

Fig. 11(e) shows no indication of plastic deformation and densification of Metco 601NS, but instead there are cracks present both within the aluminium matrix and the aluminium-polyester interfaces. In the pictures of coatings with bondcoats, as shown in the right column, cracks are largely reduced and become virtually unobservable. The polyester becomes aligned conforming to the stylus profile. This shows that Metco 601NS with a bondcoat indeed underwent some level of plastic deformation and the level of coating fracture was reduced by the bondcoat. The reason for the bondcoat effectively decreasing the PAH and densification is not fully understood, but we speculate that the bondcoat enhances the interfacial stiffness and will have altered the stress field beneath the stylus.

Measure of abradability

Previous papers using erosion systems [START_REF] Faraoun | Improvement of thermally sprayed abradable coating by microstructure control[END_REF] and sliding wear test [START_REF] Yi | Friction and wear behaviour and abradability of abradable seal coating[END_REF] suggested a material's abradability could be related to other mechanical properties such as hardness and ultimate tensile strength. Instead, the PAH has been proposed in this paper as an indicator of scratch resistance. The PAH can reflect the material's abradability such that: (1) a high PAH indicates low abradability and vice versa; (2) an increasing PAH indicates densification, and is thus also an indication of abradability. PAH has also been shown to be influenced by other mechanical properties. Metco 308NS has the highest elastic modulus, microhardness and ultimate tensile strength, followed by Metco 313NS and Metco 601NS. This influence is related to the degree of densification. It can be clearly found that when the hardness, elastic modulus and ultimate tensile strength increase, the PAH shows a large increase when tested at longer scratches, suggesting a decreasing abradability, as shown in Fig. 12. Metco 308NS has a large variation of PAH at different scratch lengths, showing a considerable amount of densification, followed by Metco 313NS and Metco 601NS. As stated and interpreted before, it is believed that the degree of densification has a link with these other mechanical properties. A material's intrinsic properties and its response to scratching, e.g., fracture or densification, in conjunction, determine its abradability and abrasion or erosion resistance.

It is also suggested that when rating abradable seal coatings, both points (1) and ( 2) mentioned above have to be considered. Point (2) is more relevant with material's dynamic behaviour and is worth studying. Therefore, an important point is that in order to study how the coatings react dynamically under scratching, their progressive behaviours have to be measured by either: (1) performing multiple scratching processes with different lengths and measuring the average PAH of each scratch lengths; (2) performing single scratching but progressively measuring the PAH.

Results compared to test-bed findings

The conditions in which our experiments were performed were very different from actual engine operation, i.e., our results of the abradability were obtained at much lower strain rates. However, by comparing our results with technical datasheets provided by Sulzer Metco Ltd., it is found that similar conclusions have been drawn [20,23,24]. The datasheets provided by them suggest that the Metco 308NS coating has good erosion resistance but moderate abradability [20]. This is mainly due to the greater proportion of nickel matrix and the limited amount of graphite and porosity. The Metco 313NS is claimed to possess a balance of abradability and erosion resistance [23]. The Metco 601NS [24] is claimed to have a high degree of abradability with essentially no blade tip wear, excellent oxidation resistance up to a temperature of 345 • C and good resistance to thermal shock. Therefore, although the scratch testing can by no means replicate the actual operating conditions of a gas-turbine engine, it gives reasonable results, thus it could be used as a cheap and easy laboratorial alternative to high speed test.

Wear resistance and abradability are opposing properties [START_REF] Faraoun | Improvement of thermally sprayed abradable coating by microstructure control[END_REF]. Therefore, conclusions can also be drawn regarding this property. The scratch tests indicate that Metco 308NS experienced considerable densification during the scratching that enhanced its wear resistance, which explains the fact that Metco 308NS is primarily developed for the compressor stages in turbine engines where extremely aggressive particulate matter is present and therefore erosion resistance is crucial [20]. In comparison, the Metco 601NS shows a rather low but stable PAH with virtually no densification taking place, which implies a good abradability but on the other hand poor erosion resistance. The Metco 313NS exhibits moderate PAH and densification halfway between that of Metco 308NS and Metco 601NS, and this could be an indicator of a desirable combination of both good abradability and erosion resistance.

The resemblance between the results of our evaluation on the abradable seal coatings and manufactures' qualitative conclusions suggests scratch testing could be an effective laboratory alternative to high speed engine rigs to determine a seal coating's abradability. The relationships between other mechanical properties and abradability indicate that the approach that was adopted is logical. However, it should be emphasised here that although these relationships between abradability and other mechanical properties such as hardness [START_REF] Faraoun | Improvement of thermally sprayed abradable coating by microstructure control[END_REF][START_REF] Yi | Friction and wear behaviour and abradability of abradable seal coating[END_REF] and UTS [START_REF] Faraoun | Improvement of thermally sprayed abradable coating by microstructure control[END_REF] have been pointed out in previous papers, it was also suggested that none of these mechanical properties on their own can be used to rate and design abradable seal coating materials since abradability is also influenced by other factors such as composition and microstructure. Several exceptions to general mechanical properties relationships regarding hardness and abradability have been documented [START_REF] Faraoun | Improvement of thermally sprayed abradable coating by microstructure control[END_REF], suggesting measurements such as hardness and UTS can only be used as supportive experimental procedures. On the other hand, the success of abradable seal coatings depends on achieving an optimisation of two conversely related properties, the abradability and erosion resis-tance, and this is based on a full insight into the deformation mechanisms. Our approach using the scratch test is more revealing and is certainly superior to only using hardness or UTS as an indicator of abradability. Compared to other techniques involving specific grooving energy, i.e. the pendulum test, the scratch test enables the continuous study of material response to scratching, and the knowledge obtained can be used in optimisation of coating design.

Conclusions

(1) The PAH (Progressive Abradability Hardness) is demonstrated as an appropriate measure of coating abradability, as it is a direct indicator of the ease or difficulty with which the material can be abraded, though in a low speed test. It is influenced by factors such as material's intrinsic properties such as composition and microstructure, as well as deformation conditions. (2) Results from the evaluations using scratch testing are in agreement with test-bed conclusions of abradability, and this proves that scratch testing maybe an effective alternative, while being a relative low cost method. (3) Mechanical properties such as elastic modulus, hardness and UTS have been shown to have a relationship with the PAH measurement, but they should not be used alone for abradability evaluation. (4) Metco 601 has the best abradability, followed by Metco 313NS

and Metco 308NS, according to our results, which agrees with industrial conclusions.

and Sulzer Metco Ltd. for providing useful datasheets concerning the coatings tested.

Fig. 1 .

 1 Fig. 1. The cantilever beam bending arrangement used for elastic modulus determination.

Fig. 2 .

 2 Fig. 2. The moving indenter and its displacements.

Fig. 3 .

 3 Fig. 3. Microhardness results in terms of the coating thickness (sample 1: 2.1 mm thickness of coating; sample 2: 2.4 mm thickness of coating; sample 3: 3 mm thickness of coating) and load. (a) Metco 308NS; (b) Metco 313NS; (c) Metco 601NS.

Fig. 4 .

 4 Fig. 4. The two deformation modes encountered during indentation: (a) Johnson's modification of the expanding spherical cavity model for materials of higher Y/E; (b) Tabor's surface pile-up model.

Fig. 5 .

 5 Fig. 5. Load-extension curves during the UTS evaluation.

Fig. 6 .

 6 Fig. 6. PAH measurements.

Fig. 7 .

 7 Fig. 7. Metco 308NS Scratch groove topography.

Fig. 8 .

 8 Fig. 8. Metco 313NS Scratch groove topography.

Fig. 9 .

 9 Fig. 9. Metco 601NS Scratch groove topography.

Fig. 10 .

 10 Fig. 10. Acoustic emission of abradable coating materials during 4.9 mm scratching.

Fig. 11 .

 11 Fig. 11. Scratched groove cross-sectional appearance: (a) Metco 308NS; (b) Metco 308NS + bondcoat; (c) Metco 313NS; (d) Metco 313NS + bondcoat; (e) Metco 601NS; (f) Metco 601NS + bondcoat.

Fig. 12 .

 12 Fig. 12. Relation of PAH to other mechanical properties.

Table 1

 1 Details of specimens used for evaluations.

	Evaluations Materials	Amounts Dimensions		Deposition
							pattern
				Length	Width	Thickness
				(mm)	(mm)	(mm)
						1.62
		Metco 308NS	3	10	12	Each
	Hardness	Metco 313NS	3	10	12	material
		Metco 601NS	3	10	12	was
						produced with three thicknesses,	On one side
						2.1, 2.4, 3,
						exclusive of
						substrate
	Ultimate	Metco 308NS	1	50	12	3 for all
	tensile	Metco 313NS	1	50	12	exclusive of
	strength	Metco 601NS	1	50	12	substrate
	Scratch test	Metco308NS Metco313NS Metco601NS	1 1 1	15 15 15	12 12 12	2.1 for all exclusive of substrate

Table 2

 2 Results of elastic modulus evaluation (bc = bondcoat).

	Applied dead weight (N)	Substrate	Metco 450NS	Metco 308NS	Metco 313NS	Metco 601NS	Metco 308NS + bc	Metco 313NS + bc	Metco 601NS + bc
		Elastic modulus (GPa)
	1.88	158.3	269.5	4.4	3.8	2.5	4.9	4.7	3.5
	3.76	180.9	260.4	4.5	3.2	2.2	4.1	3.7	2.7
	9.8	178.0	239.6	2.8	2.3	1.6	4.2	3.3	1.9

Table 3

 3 Predicted plastically deformed region sizes.

	Material	Load (kgf)	Plastic region radius (mm)
			Rule of thumb	b a = E H	1/2	ctg 1/3 ϕ (Lawn et al. [19])
	Metco	0.1	0.113		0.316
	308NS	0.2	0.164		0.460
		0.01	0.046		0.119
	Metco 601NS	0.025 0.05 0.1	0.075 0.097 0.132		0.194 0.253 0.344
		0.2	0.194		0.505
		0.01	0.047		0.142
	Metco 313NS	0.025 0.05 0.1	0.071 0.092 0.127		0.217 0.283 0.388
		0.2	0.197		0.603
	Table 4
	Mechanical properties of various materials.
	Material			Elastic	Compressive	Yield strength
				modulus	yield	(MPa) /Elastic
				(GPa)	strength	modulus (GPa)
					(MPa)
	Ceramics	SiN SiC		310 430	570 820	1.8 1.9
	Glass	96% silica glass	72	240	3.3
	Abradable	Metco 308NS	3.95	11.3	2.9
	coating	Metco 313NS	3.11	7.4	2.4
	materials	Metco 601NS	2.08	6.9	3.3
	Metals	bronze Aluminium,		120	33	0.3
		Heat treatable	207	120	0.6
		4340 steel

Table 5

 5 Ultimate tensile strength evaluation results.

	Materials	Coating	Maximum	Maximum	UTS
		cross-section	loading	coating	(MPa)
		area (mm 2 )	registered (N)	load (N)
	Metco 308NS	16.5	4883	1459.2	48.6
	Metco 313NS	16.5	4118	694.3	23.1
	Metco 601NS	16.5	3682	258.3	8.6

Acknowledgements

For assistance in the sample provision the authors would like to express appreciation to Mr. D. Anderson and his staff at Plasma Coatings Ltd. We also thank Dr. J.C. Avelar-Batista Wilson and Dr. J. Housden of Tecvac Ltd. for assisting the authors in carrying out the initial scratch tests. Later scratch tests were carried out with the help and assistance of research staff in Professor J. de Hosson's group at Groningen University in the Netherlands, and we also appreciate that help. Thanks also to staff of Rolls-Royce plc.