Roozbeh Babaeizadeh Malmiry

Nicolas Perry
email: nicolas.perry@ensam.eu

Complexity Management in Product/Process Simultaneous Design for Implementing a Fresnel Thermodynamic Solar Plant

Keywords: product-process interaction, design methodology, mobile factory design, complexity management, solar power plant, Fresnel

Fresnel mirror in thermodynamic solar power plant technology is an efficient power resource in many potential countries. The key challenge is cost effectiveness of the product and its settling. The importance of using this technology redounded in writing this paper to propose a methodology in order to design this system considering its complexities. Because of the dependency of the product with process of production and installation of this solar plant, a simultaneous design methodology is required. Moreover, a concept of movable factory, from one solar farm site to another one, is also discussed which is identified as a proper solution for such project with reusability.

Introduction

As Tsao stated, "In any given hour, more energy from the sun reaches earth than is used by the entire human population in a given year" [START_REF] Tsao | Solar FAQs[END_REF]. In addition to this fact, solar power, with free and available source of energy in many countries, has the minimum environmental damages among different types of renewable energies [START_REF] Jayakumar | Resource Assessment Handbook[END_REF]. Considering these advantages, although, recently there was a fast growth in solar generation but still according to US Energy information administration; only 13% of energy is supplied from renewable energies which less than 1% of that is from solar energy [START_REF]A Grand Challenge for the Twenty-first Century: Commercializing Solar Energy[END_REF], [START_REF] Quoilin | Concentrating Solar Power Plants[END_REF]. Therefore, solar energy and specifically the technology of Fresnel mirror has chosen as target market for this paper.

Fresnel Thermodynamic Solar (FTS) technology is a new generation of concentrated solar plants to use the thermal energy of the sun. A FTS system uses the heat of sunray as solar energy and reflects and concentrates this energy by a Fresnel mirrors over a flow of fluid to create steam. This paper focuses on this technology of concentrated solar power plant but the method and discussions can be applied to any other type of project with similar nature.

The target project is to produce and install a 500,000 m² solar farm (i.e. 50,000 reflectors of 10m² and 136 receptors of 240m long each) in 6 months. This plant is sup-posed to supply energy for at least 40 years [START_REF] Babaeizadeh Malmiry | Product-Process Interaction Analysis: Design of Mobile Factory for Fresnel Thermodynamic Solar Plant[END_REF]. Logistics aspects suggest a movable factory as a relevant solution instead of manufacturing in one place and shipping all the material. In addition, the temporary factory needs to be movable to produce for at least in five different locations.

One of the main issues is the interaction of product with production. Therefore, in the product development aspects, the ease of production and installation method in the process of product design needs to be considered. So, it would be a concurrent designing. To sum up, lack of a systematic methodology for this concurrent designing, together with time limit and the concept of movable factory, makes the design process relatively complex.

Thus, the hypothesis of this paper is to introduce a methodology to design a product and process for planting a FTS system taking into account the complexity of the design process.

Complexity and Variability Management in Design

According to Seth Lloyd, there are several ways to use the word "complexity" [START_REF] Lloyd | Complexity as Thermodynamic Depth[END_REF]. It can be the amount of computation, scale of measure, or amount of effort which is needed to manufacture a product [START_REF] Suh | Axiomatic Design: advances and applications[END_REF]. The design method of this solar plant is considered as a complex system because;

1. The scale of project considering the required effort is relatively large, 2. The target time limit compared with the size of the project is short, 3. The concept of movable factory is needed to be applied, 4. The product and process is closely dependent on each other. So, with a methodological design, by means of movable factory, a large part of this complexity would be solved. In addition, different levels of variability as presented by ElMaraghy, have to be faced in this project which leads to a high level of complexity that should be managed [START_REF] Elmaraghy | [END_REF]. Al-Hakima promotes graph representation to map this complexity [START_REF] Al-Hakima | A Graph-theoretic Approach to Conceptual Design with Functional Perspectives[END_REF]. At the information level, the interactions and the exchanged knowledge also have to be mapped [START_REF] Bernard | LC Universal Model for the Enterprise Information System Structure: Innovation in Life Cycle Engineering and Sustainable Development[END_REF].

First, the product is designed in a parameterized way (1st level of complexity). Indeed this design has to be adapted to the process of production and installation. Taking into account this potential product variability, the mobile factory has to be designed and optimized, (2nd level of complexity). Moreover, the manufacturing system has its geographical dependencies in terms of logistic aspects, power and water supply as well as potential local supply (3rd level of complexity). All these design solutions should minimize the cost of solar field considering the concentration factor and on the other side the cost of mobile factory should have return on investment after five times solar plant installation [START_REF] Syndicat | Directory of the French Solar Thermodynamic Industry[END_REF].

Dealing with solar field design requires defining the objective. This objective mainly could be to have maximum energy from a field, to have minimum field area to achieve a desired amount of energy, or to maximize the energy obtained from collector unit area of a field [START_REF] Weinstock | Optimal solar field design of stationary collectors[END_REF].

There are other related comple culty of protect the installation p project area and environment con

Methodology

In the past, many designs hav based on years of experience and Therefore, the methodological de dation for engineers in order to i and-error processes [START_REF] Suh | Axiomatic Design: advances and applications[END_REF].

The design process in this proj starts from early stage of produ process definitions. Thus, a go orientation could be a top-do approach from macro model extracting energy from sun to mi model of components and charact istics. This model is shown i figure 1.

As Nam Suh stated in the bo mapping between "what we wan one interpretation, this definitio uct/implantation itself and the pro definition can be adapted to our g process of achieving the product. on the other side, in the process o tion method also must be consid proaches give possible representa According to axiomatic design then the functional domain whic tional requirements map the phy finally the process domain (see fig

The process needs to be divide the process domain, after literatur based on the stages of the process related methods among the trad methods to create a new method by brainstorming and taking ideas This approach has led to create eye on the limitations of the pr availability, and required specifi term reliability. Then the best me Fig. 1. Top-down approach for design of FTS [START_REF] Babaeizadeh Malmiry | Product-Process Interaction Analysis: Design of Mobile Factory for Fresnel Thermodynamic Solar Plant[END_REF] plexities in the process as well. For instance the diffin process from environmental effects because of large ondition of locations such as deserts.

ave been made empirically, iteratively and intuitively, nd creativity with involvement of much trial and error. design has been created to establish a theoretical founto increase the creativity and reduce the iterative trialroject oduct/ good down el of micro acterin book of "Axiomatic design", design is the process of ant to achieve" and "how we want to achieve" [START_REF] Suh | Axiomatic Design: advances and applications[END_REF]. In ition can be interpreted as mapping between prodprocess of designing the product/implantation. But, this r goal which is the design of product, and design of the ct. Since the process must be based on the product and s of designing the product, the production and installasidered. Product/Process and Behavioral modeling apntation of these interactions [START_REF] Qian | Function-Behavior-Structure Paths and Their Role in Analogy-Based Design[END_REF], [START_REF] Umeda | Functional Reasoning in Design[END_REF]. ign, first the aim of the project should be identified and hich includes the functional requirements. These funchysical domain which includes design parameters and figure 2) [START_REF] Labrousse | Generic FBS concept for Process/Product/Resource integration[END_REF]. ided into sections to be evaluated. For each section, in ture review and examining the basic available methods ess, there are three simple steps; first, choosing the best raditional methods; second, combining the traditional od; and third, the innovative ideas which are obtained eas from similar methods. ate some possible conceptual solutions with keeping an project. These limitations are time, budget, resource ifications for the product with high quality and longethod according to the criteria should be chosen. .

Solar energy

In every stage of design, all the effective factors need to be considered. Figure 3 shows the main factors for a thermodynamic solar plant as IDEF0 (The complete IDEF3 diagram for this project is available in [START_REF] Babaeizadeh Malmiry | Product-Process Interaction Analysis: Design of Mobile Factory for Fresnel Thermodynamic Solar Plant[END_REF]). As it is illustrated in this chart, in the design process, all the material flow, processes, controls and resources should be taken into account. The economical solution will depend on the manufacturing processes and mainly on organizational issues such as material purchase, implementation time, energy and fluid access for the factory.

Product Design

In brief, the product in this project consists of two main parts, "reflectors" and "receptors". These two parts are supposed to be installed and work together. So, the process of designing depends on each other. According to the proposed process in Figure 2, first, the characteristics of the product need to be examined. Since the product doesn't exist to be examined, the aim of the product is scrutinized. For instance, the reflectors are expected to reflect the sunray in the most efficient way to the receptors. Moreover, it needs to be rotatable to follow the sunray during the day. Based on these primary objectives, one can characterise the product and shall proceed to the next steps for designing the rotators, connectors, mirrors and the main challenge which is the support. After, these characteristics become more in detail such as size and geometry, structure of support and so on to satisfy the required accuracy and rigidity.

For designing the receptor, with the same procedure, the objective is to receive the concentrated sunray. To obtain this goal, the receptor must contain pipes for the flux Fig. 3. Four domains for design of FTS Fig. 4. Key parameters for FTS system analysis [START_REF] Babaeizadeh Malmiry | Product-Process Interaction Analysis: Design of Mobile Factory for Fresnel Thermodynamic Solar Plant[END_REF] and also should have an insulator to prevent heat release. This system must implement in the height. Therefore, the receptor must contain several tubes with special material to resist from heat while it conducts the heat to the flux. These pipes need to be hanged using holders. Moreover, the cover of receptor, needs to have flexibility to keep straighten in case of thermal expansion which might be different in top and the bottom side. Also, this cover must carry the insulator too.

Process Design

Beside the product characteristics, the method of production and installation of the plant also needs to be specified. This method is considered as "process" in this paper.

As process, managing resources such as material, machines, labor as well as facilities and working conditions are also included. Since our product has two parts of reflector and receptor, one production process has to be designed for each product. Because of dependency of production method with product, the number of process to design would be the combination of these two. It means that, if there are x number of solutions for designing of reflectors and y number of solutions for designing of receptors, there needs to be z number of solutions for processes which z ≥ x×y considering x and y are dependent. In spite of manufacturing, we also have to design a method(s) to install these elements. Note that, because of the interaction of these two parts, the installation of them must be adopted to each other and also to the criteria. The main criteria for process are: i) ability to produce the whole solar farm elements within 6 months, ii) reusability for at least 5 times, iii) install and uninstall of the factory in two months, iv) ability to move, v) adoptability with different locations. So, factors such as time, reusability, reliability, adoptability and mobility need to be considered during the process of design (figure 2). In this case also the similar methodology of design should be followed. Different stages of the production and assembly line as well as installation stage need to be examined. In most of the production and installation stages, the process is known and could be applied. By considering the criteria, the most suitable method should be chosen and any method needs to be adjusted along with the goal domain.

The production environment has an important role in this project. For instance access to energy, working temperature, dust and etc. will affect the plant and working facilities design. The installation equipment should be portable to cover large area. Levels of portability which will be discussed in next section also need to be chosen. In several design solutions, dividing the processes of production and installation is not appropriate. Modular design of the factory can be applied using shipping containers as structure module.

Product/Process Evaluation Tool

As it is mentioned earlier, one of the most complex issues in this project is the interaction of design factors in this project. Interaction between the different levels and product-process is mapped using graph representation as illustrated in figure 4. For cost evaluation, reusability of the mobile factory needs to be considered. Assuming five times for reusability, the total cost will be calculated as;

݈ܽݐܶ ݐݏܿ ݂ ݎ݈ܽݏ ݐ݈݊ܽ ൌ ሾ ൈ ݐݏܥ ݂ ݈ܽ݅ݎ݁ݐܽ݉ ൈ ݐݏܥ ݊ǡ݅ݐܽݐݎݏ݊ܽݎ݂ܶሺ ݎܾܽܮ ǥ ሻ ൈ ݐݏܥ ݂ ሿݕݎݐ݂ܿܽ ൗ (1)

Movable Factory Design

As an initial idea for this project, the project supposed to be implemented in North Africa but the special resources are available in source country which is considered as France. By special resource, it is meant materials and machines which are not found in many places (especially North Africa) as well as experts, robots and customized equipment. In addition, the process supposed to be used for more than one project. In this case, the first idea could be to build the product in origin and transport to the destination.

As table 1 illustrates, the cost of transportation for only reflectors panel will be about 775 k€ which makes the project non economical. While, if the material is transported instead of ready panels, the cost would be around 32 k€ which is significantly cheaper. This difference, even without considering the reduction in possible damages during the transportation can justify transporting labor, equipment and etc. and producing in the destination point in case of receptors, the 200m length requirement, rationalizes the proposed transportation method even more. Hence, the concept of mobile factory is used in this project. As DesJardin presents, there are three major level of mobility for a factory; Fixed, transportable and portable. Various factors should be considered to make a factory in high level of portability such as size reduction, weight reduction and power source [START_REF] Desjardin | DOWNSIZING WITH VXIbus: Opportunities and Limitations in Factory, Field, and Portable environments[END_REF]. In this project, there are two aspects of mobility. First, because of the size and complexity of the product, it's not possible to move the finished goods. So, the idea is to move the material, equipment, labor, and energy source to the destination and then produce and install at site.

The concept of movable factory is not limited to solar plant. Offshore workshop, used in Navy, is a good example of movable production system which enables carrying the missions' maintenance system anywhere in the world. Movable assembly line is another example of using this concept in aerospace industry to have a leaner and more efficient production system.

Second aspect is to use portable factory. A portable factory which is also dubbed as "factory in a box" is a pre-assembled group of equipment which is transportable and can be used as plug-and-play in site. These kinds of buildings are just placed in the site and can be easily removed and transported to another place afterwards. In such buildings, features such as HVAC system, energy generators, etc. could be housed in a 20ft shipping container which can be shipped, trucked or airlifted to any location.

Thus, in the process of production and installation design for such project, movable factory based on the level of mobility, factory life cycle, interdependency of process and product, and other issues needs to be designed.

Before starting to design, the life cycle of the process to build the solar plant needs to be examined. This cycle includes preparation, storage, transportation, installation, use, and uninstallation. The transportation stage means either to move from the source to the project site or from one project to another. In this stage, three categories of human resource, machines and robots, and material need to be transported. In each category some elements could be used by local resources while others need to be transported. Table 2 is the summery of these elements and the way to utilize. The cycle starts from the preparation of equipment, materials, labors, etc.

The installation stage means to install the temporary factory (e.g. in 6 months) in order to build the solar plant and in "use" stage the factory is used to produce the components and install it.

Table 2. Using local resources vs. transporting resources

Because of the difficulty of components like receptor, and time shortage, these two stages need to be done in parallel with a proper scheduling. For fast establishment of large area foundation, machines such as concert slip forming machine, asphalt finisher, track renewal train and etc. could be occupied. These machines create a flat surface which makes it easy for equipment and labor to move in the project area especially for portable factories and also it can be used to install the solar plant components. After installation and use, with considering the concept of green factory, all the equipment of plant production must be collected from the site except those which are necessary for the utilizing the solar plant.

Conclusion and Discussions

This paper proposed an example and the starting elements of a methodology in order to deal with complexity in design of product and production/installation process with bearing in mind the cost, quality and time. The main complexity which is faced first in this project is the interaction of product with process which made it necessary for a concurrent designing. The next level that must be integrated is the adaptability and reliability requirements due to mobility.

To evaluate a design as a "good design", at first the goal has to be identified. So, this methodology is started from goal domain. This goal maps the functional requirement which maps the physical domain for product and process. Finally, in the process domain, the procedure needs to be divided properly and the three steps apply for each section.

After designing the product and processes, the solution needs to be evaluated by the "evaluation tool" which was proposed. By means of this tool, different solutions of product design would be examined and subsequently, the design of process is evaluated. Regarding the goal domain, the design decision is made based on the result which includes cost, scheduling, number of containers, etc.

After the conceptual design phases, other aspects such as movable factory are also integrated which according to the project, the level of movability needs to be chosen. This movability makes the process less expensive in transportation, more efficient for covering large area, and possible to be reused for at least five times. The reason of choosing "five" as reusability is that considering transportation time, inventory waiting time and production time, five times of implanting a solar power plant takes about 5 to 7 years. After this time most probably the product is no longer on top of technology and should be replaced by a competing product which gives a better performance.

Since the time is so limited in this project in comparison with size of the project, milestones are substantial to be scheduled and therefore each process needs to be illustrated as simogram. This Gaunt chart is fundamental as far as so many processes may happen in parallel in this project and it's crucial to have them all on time. This methodology, using the evaluation tool, works as a dynamic tool for "what-if" scenario. At any stage, one factor can be modified and the result is being observed. However, the discussion is for the early stage of design and the next developments will give more precise rules for evaluation (costs or time). These sharper equations can be easily integrated in the evaluation tool and use its final results (input/output data). After evaluation of the solutions, if the result is not satisfactory, the characteristics of domains change and then the method applies again until the desired result is achieved.

Fig. 5 .

 5 Fig. 5. Product/process elements interactions [5] After designing stage, regarding these links, each design solution need to be evaluated based on: 1) Process steps and sub-steps, 2) Cycle times, 3) Throughput time, 4) Human resource (number and skills), 5) Types and cost of material, 6) Type and cost of machines, 7) Number of container needed to move the factory, 8) Number of container needed to supply the materials, 9) Bottle necks, 10) Machines' efficiency, 11) Product mass and weight, as presented in Appendix A.For cost evaluation, reusability of the mobile factory needs to be considered. Assuming five times for reusability, the total cost will be calculated as;

Table 1 .

 1 cost of transportation for ready panels vs. materials from France to North Africa

		Size: 12m×2.35m×2.4m , Volume limit: 37 m 3 , Weight limit: 36500 kg
	40ft Container	transportation cost of each container: 340 €
		Fixed transportation cost: 2,300 €
			Required container	Estimated cost of transportation
	Prepared panels		2273	775 k€
	Materials (Glass & Aluminum)	88	32 k€

Product choices [START_REF] Babaeizadeh Malmiry | Product-Process Interaction Analysis: Design of Mobile Factory for Fresnel Thermodynamic Solar Plant[END_REF]


Yang Xu
email: yang.xu@pku.edu.cn

Alain Bernard
email: alain.bernard@irccyn.ec-nantes.fr

Nicolas Perry
email: n.perry@i2m.u-bordeaux1.fr

Florent Laroche

Improvement of product design process by knowledge value analysis

Nowadays, design activities remain the core issue for global product development. As knowledge is more and more integrated, effective analysis of knowledge value becomes very useful for the improvement of product design processes. This paper aims at proposing a framework of knowledge value analysis in the context of product design process. By theoretical analysis and case study, the paper illustrates how knowledge value can be calculated and how the results can help the improvement of product design process, such as deciding which knowledge to choose and what to do next.

Introduction

In this world of globalization, more and more enterprises consider knowledge management (KM) process as an important part, if not the only part, of their production activities [START_REF] Nonaka | The knowledge creating company[END_REF][START_REF] Bernard | Methods and tools for effective knowledge life-cyclemanagement[END_REF]. Meanwhile, how to pay deeper attention to the crucial competence "knowledge" is becoming a strategic approach in production management, and product design process is linked more and more tightly with knowledge [START_REF] Perry | Eco Global Evaluation: Cross Benefits of Economic and Ecological Evaluation[END_REF].

When considering knowledge management in product design activities, how to evaluate knowledge has always been a challenging problem. Which knowledge is more "useful" and thus can add more value to the product? What knowledge to be acquired in the next step of design? The answers of such questions may greatly improve design activities, so the following sections will focuses on this related issue: how to calculate and analyze knowledge value in product design processes and help them improve.

How to evaluate knowledge value

Product development process

We may describe the product development process as the following procedure: a product starts from its initial state and arrive to a required state (final state), and a task T is supposed to be accomplished to realize this product evolution from that initial state 0 P to the final state n P . The product development process can be described by a series of state changes. Given an initial state 0 P , the product development process can be characterized by a sequence of product states « Ω is a set of weights pq ω which are assigned to each arc pq α .

n P P P P → → → → L 2 1 0 »,
Particularly, the sub-tasks which do not have successors are named atom-tasks, noted as i at .

The reason that T is characterized by a graph, not a tree, is that there may be several sub-tasks which are not independent and they may have one or several sub-tasks in common.

Knowledge value

Supposing that knowledge K is necessary to accomplish the task T and knowledge fragment i k is needed to accomplish sub-task i t , thus, i k is the solution for the sub-task i t , and knowledge K can be considered as a set of solutions which together can accomplish the task T . Obviously, a knowledge fragment i k can be a person, a book, a plan or any type of solutions provided, and knowledge characterization in detail can be referred from the works of Xu and Bernard (2010a).

Based on this proposal, some questions may be raised. Is knowledge K can accomplish the task T completely? If knowledge K can only solve a part of the task T , which part is solved? What knowledge fragments i k have to be added in order to solve the remaining parts? How to choose the knowledge fragments i k to accomplish the unsolved sub-tasks?

In order to answer these questions, some hypotheses are firstly presented:

Hypothesis 1. The atom-tasks are noted as i at , and all atom-tasks correspond

to an explicit answer "yes" or "no" which shows whether it can be solved or not.

In other words, the atom-tasks cannot be solved partially. Hypothesis 2. The principles of task decomposition are as follows.

If the task T is decomposed into 1 T , 2 T , ..., n T , we have: a. (The weights indicate the importance of the sub-tasks to the original task, for example, if the design of a car focuses more on speed improvement, then the sub-task of speed improvement will have a higher weight than the sub-task of cost diminution)

The value of knowledge i K to the task i T is noted as ) , (

i i K T V
. This notation indicates that knowledge is always in context, in other words, knowledge evaluation is linked with specific tasks. Knowledge value thus varies according to different tasks. For example, given a same knowledge fragment "to adjust the height of a chair", it could have a high value to the task "to consider the ergonomics" and have a low value to the task "to control the cost". The value of knowledge K to the atom-task i at is defined as follows.

Based on the two hypotheses and Definition 2, knowledge value can be measured by the procedure as follow.

Procedure for knowledge value measurement:

Step 1: All the value of knowledge K to the atom-tasks is obtained according to Definition 2.

Step 2: For any

H h i ∈ , find all the ) , ( j i h h
and their associate ij ω , then: . During this process of knowledge addition, both explicit knowledge and tacit knowledge might be needed. Usually, explicit knowledge comes from databases, publications, rules, etc. and tacit knowledge comes from experience, expertise, wisdom, judgment, etc.

∑ ⋅ = j j ij i K h V K h V ) , ( ) , (
1 i i at i i m u u i K at V K at V K T V i ⋅ = ⋅ = ∏ = ω ω
This calculation process is realized by a calculator called CAL-KNOW, which is used in case study introduced latter.

If two knowledge fragment

   = , 0 , 1 ) , ( K at V i i
at can be solved by K i at can not be solved by K higher value is usually chosen. As collaborative networks is regarded as a critical success factor to achieve product innovation [START_REF] Perry | Collaborative Knowledge Networks Emergence for Innovation. Factors of Success Analysis and Comparison[END_REF], it is always useful to choose the most valuable knowledge to be exchanged and shared.

Knowledge evaluation in product design process

During product lifecycle design, which can be defined as a sequence of tasks [START_REF] Nacsa | Knowledge management support for machine tool designers using expert enablers[END_REF], both tacit and explicit knowledge may be required to accomplish the tasks i at , so these two kinds of knowledge can add value to the knowledge of design K and thus make knowledge evolution [START_REF] Bernard | An integrated knowledge reference system for product development[END_REF]Xu and Bernard, 2010b).

Here are the main steps to take during the procedure of knowledge evaluation in supporting product design. 1. To decompose of the product development process into simpler processes, in other words, to realize the decomposition of the task T into atom-tasks i at .

2. To evaluate the value of the existing knowledge using the evaluation model introduced in the previous section.

3.

If not all the atom-tasks are solved, find out which i at should be solved next.

4. To add appropriate knowledge, explicit and/or tacit, to accomplish i at .

Do Step 3 and

Step 4 repeatedly until all atom-tasks are solved.

In the product design process, knowledge mat add value to products and product may also make knowledge more valuable [START_REF] Xu | Quantifying the value of knowledge within the context of product development[END_REF], and such mutual value adding process can be explicitly describe and controlled using our knowledge evaluation model.

Case Study

This paper has chosen a case of chair design, which is a part extracted from the product lifecycle of a chair. The concentration is implemented on the phase of design as it is a key phase where major decisions are made concerning knowledge. In this example, the task « design a chair » should be accomplished in order to make the product (chair) evolves in the development process. Figure 1(1) and Figure 1(2) illustrate how the task is decomposed. Although the decomposition is lack of completeness, for example, several tasks such as market study, packaging and logistics matters, particular optimization, etc., are neglected, it can serve as an adequate demonstration.

Based on the criteria obtained from experience in product design, the principle task « design a chair » is decomposed into four sub-tasks.

The weights i ω are given by the experts of different roles who have different points of view in design activities. Table 1 shows the weights given to each subtask by experts of different roles. In order to determine a weight, we have taken into account the results given by a group of experts for each given role. How to improve the results of collecting and analyzing the weight values given by different people is another complicated topic, which needs further researches on statistical techniques, human behaviors, etc., and in this paper, we simply regard the weight value as is the average of the weights proposed by all the experts assigned in each group. Here are some illustrations about Figure 1.1: • « Perception test » and « To consider the psychological comfort issues » can be solved by questionnaire surveys.

•

« Ergonomic studies » mainly focus on examining the degree of fatigue of different parts of the body (muscle, bone, joint, etc.) of a person who sits in the chair for a period of time or by simulations.

•

« Tests of the material attributes » may include the thermal conductivity (in winter, people do not like to sit in a chair with a surface of iron, because it's too cold), the sensation of the material (for example, smooth or rough, soft or hard), etc. • « To consider the aesthetics of the chair » considers the intrinsic beauty of the chair, which depends on the cultural and social context. In other words, for a same chair, it may vary from beautiful to disgusting due to different tastes of people from different countries or groups.

Design a chair

Task B To consider the dimensional and mechanical design issues

Task A

To consider the comfort and the aesthetics issues

•

« To consider the adaptiveness in the context of use » considers whether the chair matches the environment of use. For example, in a fast-food restaurant, sofas are not suitable to the environment although they are very beautiful.

•

« Architectural design » is considered before the design in details.

•

For the assignments of the values of the weights

•

The tasks « To consider the mechanical holding issues » and « To consider the stability » have a same sub-task « To consider the positions of gravity centers ». Such situation that several tasks may have a same sub-task in common is acceptable according to Definition 1 which defined the Task T as a graph.

•

Here are two weights which have the value « 100% ». They mean that the tasks linked by an arrow of a weight of « 100% » are « equal ». In this case, when people have accomplished « to define a skeleton », they have accomplished the « architectural design » at the same time.

•

In order to determine the values of the weights 1 C ω and 2 C ω , the context of design should be considered, in other words, they depend on the amount of production of the chairs provided by customers. Table 3 gives two examples. In the condition that the chair is designed to be produced in large quantities, the cost of materials has a weight of greater importance. When it is a case of custom design, the weight of materials is lower. The client is willing to pay the extra cost for differentiation even if the materials used are more expensive.

broken leg, the interface between the leg and the body of the chair should be well designed. In such cases, the design of the interface should be given special attentions.

In real cases tested, each time a solution (knowledge fragment) with a higher value is chosen, and from the list of unaccomplished atom-tasks, we could find out easily which tasks should be accomplished next. Every time that K reaches a state that can solve one more task, its value increases.

When knowledge reaches its final state, its value may not always be 100%, but it is not critical if people are already satisfied with its current value. In the given example, if we do not have to accomplish the task of "To calculate the cost of labor", knowledge can remain in a state that its value is not 100%. In such cases, people have to take some risks when they are going to the next stage of the product lifecycle.

Conclusions

Knowledge evaluation is a key issue in knowledge management, and this paper has presented a knowledge evaluation model in product lifecycle design. The model integrates the process of knowledge evolution and product development, and the mutual effects between knowledge and product are analyzed. Based on the theoretical definitions and models, this paper illustrates how knowledge value can be assessed by studying a specific case. In the applications of product lifecycle design, knowledge values calculated by the model can serve as important factors in a decision making system that decides which knowledge to choose and what to do next. The model could serve as a framework to describe the knowledge related activities and could be a useful tool for managing knowledge in product lifecycle design and support.

Interesting perspectives may include deeper analysis about the optimization issues of weights and dynamic product development processes.

((

  The combination of the sub-tasks should cover the original task T ) Any sub-task i T cannot cover the original task T ) c. The task T is decomposed with weights, noted as:

ω

  The procedure shows that from Step 1 we can obtain all the

  and compared. Generally, knowledge that has a Definition 2.

Fig

  Fig. 1.1(1) The decomposition of the task « design a chair » (Part I)

  where 1 P is the product state when 2 t is accomplished, etc., and when task T is accomplished, the product comes to its final state n P . Task T can be defined as follow.H is a set of tasks, whose elements are the task T , the non-atom tasks m t

															P is the product state when 1 t is ac-
	complished, 2
		Definition 1. Task T is represented by a weighted directed graph
	G	( T	)	=	(	H	,	, A	Ω	)	, where:
			and the atom-tasks n at , i.e.,	H	=	{ h i	}	=	{ T	,	1 t	,	t	2	,...,	t	m	,	1 at	,	at	2	,...,	at	n	}	;
			A is a set of directed arcs pq α , i.e. p h and q h are linked by pq α , from
			p h to q h ;

Table 1 .

 1

	1 The values of weights
	Experts of dif-				ω	D
	ferent roles			Costs	End of life
	Client	50%	10	30%	10%
	Designer	10%	50%	30%	10%
	Manufacturer	0	30%	50%	20%
	Seller	30%	10%	40%	20%
	Transporter	0	60%	30%	10%
	Recycler	0	0	30%	70%

A ω Comfort/aesthetics B ω Dimension/Mechanics C ω

Author's Initial(s) Author's Last Name ("Running head -left" style) Why the arrow from the task "Single-criterion optimization" to the task "Multi-criteria optimization" has a weight of "100%"? Obviously, when people can perform the task of "Multi-criteria optimization", they are able to accomplish the task of "Single-criterion optimization". In other words, these two tasks have a containment relationship. In case when two tasks have a containment relationship, an arrow of a weight of "100%" is used. Optimizations of the design are often made retrospectively, taking new knowledge into account, [START_REF] Del Prete | Design optimization application in accordance with product and process requirements[END_REF].

•

Management of product end-of-life and recycling are critical issues in environment treatment for manufacturing enterprises so they should be considered in product lifecycle design [START_REF] Bufardi | Multiple criteria decision aid for selecting the best product end of life scenario[END_REF][START_REF] Ueda | Decision Making and Institutional Design for Product Lifecycle Management[END_REF]. The task « To consider the recycling issues» needs knowledge about the possibilities of recycling the materials used.

•

The number of materials to be considered is not limited to three, and it may differ from case to case. In other words, this number depends on how many principal types of materials are used to build the chair.

•

The three weights of the chair, for example, the proportion of each material used, the cost of each material used, etc.

•

The task « To consider the disassembly issues » evaluate whether the designed chair can be disassembled. The easy disassembly of a product will facilitate the recycling of material used and the reuse of different parts of the chair.

•

The task « To consider the interface issues » mainly considers the reuse issues of different parts of the chair. For example, if a chair has a leg broken, instead of throw away the chair and replace it by a new one, people can simply substitute the broken leg. But in order to realize the substitution of the


M Prinçaud
email: m.princaud@ism.u-bordeaux1.fr

S Pompidou

H Andriankaja

G Sonnemann

N Perry

MAKING VIABLE THE RECYCLING OF CARBON FIBER/THERMOSET MATRIX COMPOSITES. FIRST ELEMENTS OF STUDY

Keywords: C/epoxy composite, LCA, aqueous solvolysis, recycled carbon fiber

Originally developed for high-tech applications, carbon/epoxy composites have been increasingly used in leisure and sports industries, for several years. Nevertheless, the carbon reinforcement is an expensive constituent, and it has been recently shown that it is also the most environmentally impacting in a composite part manufacturing. In this way, recycling these materials (even restricted to the reinforcement recovery) could lead to reduce economic and environmental inadequacies, while satisfying legislative requirements for their end-of-life. This article is the basis for a life cycle analysis that assesses benefits and environmental challenges of this recycling loop. The recovery of the carbon reinforcement (based on the solvolysis of the matrix by water under supercritical conditions) offers an average gain of 70% for all ecoindicators.

INTRODUCTION

Carbon fiber/thermoset matrix composites were originally developed for high-tech applications in aeronautic and aerospace fields. However for several years, these materials have been increasingly used in automotive and leisure and sports industries. In these sectors, one may seek aesthetic criterions or a simple feeling of high technology, more than high technical properties. Thus, constituents' characteristics, and specifically reinforcement's (e.g. Young's modulus, tensile strength, etc.), are considered as a secondary matter and may be oversized regarding the function of the product. This is particularly true for non-structural decorative parts (e.g. with a carbon look finish), for which the reinforcement is the most expensive constituent, and where glass fibers, very much cheaper, cannot be used.

As a consequence for these scopes, alternative solutions to technical and economic inadequacies have to be found, but kept in line with the environmental impact of the product. Indeed, it has been shown that the carbon reinforcement is environmentally the most impacting constituent in a carbon/epoxy composite's elaboration process [START_REF] Duflou | Environmental impact analysis of composite use in car manufacturing[END_REF] (cf. analysis Figure 1). First, recycling end-of-life composites (even restricted to the reinforcement recovery) could lead to reduce some anthropogenic impacts, by decreasing the use of first-generation raw materials (mainly petroleum) for their production. Besides, it would help design engineers to balance energy efficiency and cost, by opening new opportunities for developing second-generation composites, firstly dedicated to the manufacture of medium or low loaded parts. Lastly, recycled carbon fabric could widen the range of reinforcements on the marketplace, between first-generation carbon and glass fibers.

All this has to be led in line with European directives that already force industries to improve their products' recyclability (e.g. in automotive industry (European Parliament & Council of the European Union, 2000, p. 53)). However, making viable this new recycling sector requires overcoming users' reluctances by ensuring the second-generation semi-product's validity from economic and environmental aspects. Therefore, we carried out a life cycle assessment (LCA), in which the resource efficiency and potential environmental challenges of the carbon/epoxy composites' recycling process are analyzed.

MATERIALS AND METHODS

To assess a LCA, every stage of the life cycle of the composite part has to be modeled, from its manufacture to its end-of-life treatment, following the usual steps defined by the ISO 14040 standards (ISO, 2006).

Materials, goal and scope

As previously mentioned, we focus on carbon/epoxy composites. The deposit of materials to be recycled consists possibly in end-of-life aeronautic parts, but most likely to date, in composite offcuts. The composite part chosen for the LCA is assumed to be processed in Europe, with a Japanese carbon reinforcement. Its mass is supposed to be 1 kg. Thus, we aim at studying the interest of recycling such materials, that is to say more generally, the viability of the recycling process.

Life cycle inventory

The following analysis is based on Duflou et al.'s data (Duflou et al., 2009), who assessed the manufacturing of composite semi-structural panels in automotive industry. All these data have been recalculated relative to the mass of the chosen product (i.e. 1 kg).

In our case study, the use phase is not taken into account. Indeed, the only input data concern transport operations. Like so, as rather classically, the present simulation led to show that this factor did not contribute much to the overall impacts (less than 5%).

Regarding the product's end-of-life, two scenarios have been modeled:

-the first one consists in burying the composite part, that is what is currently done; -the second one consists in the recovery of the carbon reinforcement. The recycling process we focus on has been developed at laboratory scale (ICMCB, Bordeaux). It consists in (i) an aqueous solvolysis of the matrix by water under supercritical conditions (temperature around 400°C and pressure about 250 bar); (ii) and a hydrothermal oxidation of the effluent to clear matrix components from water, at the end of the solvolysis process. This technology is the only one that allows the fiber to be recovered. Therefore, it is a real (but partial) recycling, and not a simple material valorization [START_REF] Morin | Near-and supercritical solvolysis of carbon fibre reinforced polymers (CFRPs) for recycling carbon fibers as a valuable resource: State of the art[END_REF]. Lastly, the device uses energy, water and oxygen, and only emits water and carbon dioxide.

Lastly, O. Mantaux and A. Gillet from the MPI Department of the Mechanics Institute of Bordeaux, have developed a prototype for packaging these second-generation fibers in an attractive form for users (i.e. designers). Data matching the remanufacturing stage have not been taken into account yet in this very first LCA. However, this energy input is assumed to be very weak, compared to those involved in the first-generation reinforcement process. As a consequence, the life cycle only loops after the manufacturing of the first-generation carbon reinforcement, with no specific additional remanufacturing.

Method

The LCA is led with the SimaPro software and the ReCiPe Midpoint (H) method [START_REF] Goedkoop | ReCiPe 2008. A life cycle impact assessment method which comprises harmonised category indicators at the midpoint and the endpoint level[END_REF]. As previously mentioned, in the recycling stage, the skipped material is the reinforcement. In other words, the production of a new raw material with non-renewable resources (i.e. first-generation carbon reinforcement), is avoided.

RESULTS AND DISCUSSION

Environmental validation

The LCA of a 1 kg composite part that takes into account the recycling of the reinforcement, clearly shows the interest of this end-of-life option. Actually, it almost offsets the whole environmental impacts of the composite manufacturing (cf. Figure 2). For example, emission of greenhouse gases may be divided by 10, compared to the landfill option, despite electricity consumption in the recycling process. The environmental gain is on average about 70%, according to the ReCiPe Midpoint (H) method.

Economic validation

In 2010, a market study led by Alcimed has shown that there will always be relevant uses for recycled reinforcements or for semi-products based on second-generation fiber, whatever their mechanical characteristics are, and as long as the price remains reasonable [START_REF] Alcimed | Evaluation du gisement de fibres de carbone à recycler et de leur valorisation pour le consortium RECCO[END_REF]. The integration of recycled carbon fiber is only interesting if the mechanical performances/price ratio is higher than glass fiber's. Therefore, in light of excellent secondgeneration reinforcement's mechanical properties [START_REF] Mantaux | Recycling of Carbon Fibre Reinforced Composite Materials with Supercritical Water Dissolution[END_REF], this ratio should be much higher than for new carbon fibers. Thus, the viability of the recycling will be provided if the second-generation semi-products price does not exceed 70-80% of the new ones.

CONCLUSIONS

In the present context, the use of carbon/epoxy composite is ever increasing. Now, it is well known that those composites can be recycled [START_REF] Morin | Near-and supercritical solvolysis of carbon fibre reinforced polymers (CFRPs) for recycling carbon fibers as a valuable resource: State of the art[END_REF], keeping good mechanical properties [START_REF] Mantaux | Recycling of Carbon Fibre Reinforced Composite Materials with Supercritical Water Dissolution[END_REF]. Taking right now into account that they will be soon subjected to regulation, it is essential to show that the composite recycling network will be viable, both economically and environmentally.

The recovery of the carbon reinforcement (which is the most environmentally impacting constituent in the composite manufacturing) by an aqueous solvolysis of the composite's matrix, leads to an average gain of about 70% for all eco-indicators compared to the landfill end-of-life option.

Lastly, the remanufacturing process developed by the Mechanics Institute of Bordeaux allows obtaining a semi-product easily usable. Consequently, from an economic point of view, the mechanical performances/price ratio of the second-generation carbon fiber should be higher than the virgin carbon fiber's, or the glass reinforcement's one.

Figure 1 .

 1 Figure 1. Environmental impacts due to the carbon reinforcement (red), the epoxy matrix (green) and the injection molding process (yellow), while processing a 1 kg carbon/epoxy composite part. The analysis is based on Duflou et al. (2009) data and on the ReCiPe Midpoint (H) method.

Figure 2 .

 2 Figure 2. Life-cycle impact assessment of the landfill of a 1 kg carbon/epoxy composite part (red), compared with the reinforcement's recycling (green). The analysis is based on the ReCiPe Midpoint (H) method.

ACKNOWLEDGEMENTS

The authors would like to express their thanks to the stakeholders of the RECCO Project.


B Vieille
email: benoit.vieille@insa-rouen.fr

V M Casado

C Bouvet

Influence of matrix toughness and ductility on the compressionafter-impact behavior of woven-ply thermoplastic-and thermosettingcomposites: A comparative study

Keywords:

This study was aimed at comparing the residual compressive strength and behavior of TS-based (epoxy) and TP-based (PPS or PEEK) laminates initially subjected to low velocity impacts. Provided that the impact energy is not too low, the permanent indentation is instrumental in initiating laminates local buckling under compressive loadings. CAI tests revealed that matrix toughness is not the primary parameter ruling the damage tolerance of the studied materials. However, matrix ductility seems to slow down the propagation of transverse cracks during compression thanks to plastic micro-buckling which preferentially takes place at the crimps in woven-ply laminates. It could therefore justify why the matrix toughness of TP-based laminates does not result in significantly higher CAI residual strengths. Finally, the compressive failure mechanisms of impacted laminates are discussed depending on matrix nature, with a particular attention paid to the damage scenario (buckling and propagation of 0°fibers failure).

Introduction

Low velocity impact is one of the most detrimental solicitations for laminates because it drastically reduces the residual mechanical properties of the structure [START_REF] Cantwell | The impact resistance of composite materials -a review[END_REF][START_REF] Jang | Impact behavior and impact-fatigue testing of polymer composites[END_REF][START_REF] Abrate | Impact on composites structures[END_REF]. It is well established that polymer matrix composite laminates are prone to delamination when impacted, resulting in low damage tolerance, which is of great concern for load carrying applications. To discuss the damage tolerance of polymer matrix composites it is initially helpful to consider the nature of constitutive materials and the reinforcement type [START_REF] Hancox | An overview of the impact behavior of fibre-reinforced composites[END_REF]. Thus, high-performance thermoplastic (denoted TP) resins (e.g. polyetheretherketone -PEEK -and polyphenylenesulfide -PPS) are increasingly considered in composite structures mainly for damage tolerance reasons. Semi-crystalline TPs resins offer a number of advantages over conventional thermosetting (denoted TS) resins (such as epoxies): a high degree of chemical resistance, excellent damage and impact resistances, and they may be used over a wide range of temperatures.

About damage tolerance of TS-and TP-based laminates

Very few authors have compared the impact behavior of TS-and TP-based composite structures, and their effects on residual strength [START_REF] Bibo | High-temperature damage tolerance of CRFP: Part 1: impact characteristics[END_REF][START_REF] Bibo | High-temperature damage tolerance of CRFP: 2. Post-impact compression characteristics[END_REF][START_REF] Jang | Repeated impact failure of continuous fiber reinforced thermoplastic and thermoset composites[END_REF][START_REF] Ishikawa | Some experimental findings in CAI tests of CF/PEEK and conventional CF/Epoxy flat plates[END_REF][START_REF] Davies | Thermoplastic composite cylinders for underwater applications[END_REF][START_REF] Schrauwen | Influence of matrix ductility and fibre architecture on the repeated impact response of glass-fibre-reinforced laminated composites[END_REF], as well as the damage tolerance of UD-ply and woven-ply laminates [START_REF] Schrauwen | Influence of matrix ductility and fibre architecture on the repeated impact response of glass-fibre-reinforced laminated composites[END_REF][START_REF] Kim | Impact and delamination failure of woven-fabric composites[END_REF][START_REF] Bibo | Review: the role of reinforcement architecture in impact damage mechanisms and post-impact compression behavior[END_REF]. From a general standpoint, it appears from literature that TP-based composites display a better resistance to the impact damage than epoxy-based composites. The brief literature review, herein, is not aimed at giving a general overview of the impact behavior of TS-based laminates for which a great number of references are available in the literature [START_REF] Cantwell | The impact resistance of composite materials -a review[END_REF][START_REF] Mili | Impact behavior of cross-ply laminated composite plates under low velocities[END_REF][START_REF] Aktas ß | An experimental investigation of the impact response of composite laminates[END_REF][START_REF] Reis | Impact response of Kevlar composites with filled epoxy matrix[END_REF]. In the early 90s, the impact performance and damage tolerance of TP-based composites had been studied in order to understand why such materials were often more damage tolerant than TS-based composite materials [START_REF] Morton | Impact response of tough carbon fibre composites[END_REF][START_REF] Prevorsek | Damage tolerance: design for structural integrity and penetration[END_REF]. To this aim, a few authors have investigated the influence of matrix type and morphology on the ability of TP-based composites to withstand penetration [START_REF] Bartus | Performance of long fiber reinforced thermoplastics subjected to transverse intermediate velocity blunt object impact[END_REF][START_REF] Reyes | Modeling and damage repair of woven thermoplastic composites subjected to low velocity impact[END_REF], absorb energy, and sustain damage at different temperature levels. Most of the studies about the impact performance, and damage tolerance of TP-based composites deal with PEEK-based composites [START_REF] Ishikawa | Some experimental findings in CAI tests of CF/PEEK and conventional CF/Epoxy flat plates[END_REF][START_REF] Davies | Thermoplastic composite cylinders for underwater applications[END_REF][START_REF] Nejhad | Impact behaviour and damage tolerance of woven carbon fibre-reinforced TP composites[END_REF][START_REF] Wang | Damage extension in carbon fiber/PEEK cross ply laminates under low velocity impact[END_REF][START_REF] Gao | Cooling rate influence in carbon fibre/PEEK composites. Part III: impact damage performance[END_REF][START_REF] Aymerich | Static loading and low-velocity impact characterization of graphite/PEEK Laminates[END_REF][START_REF] Chaudhuri | Impact characterization of graphite fiber reinforced thermoplastic laminates[END_REF]. However, only very few references report the impact behavior of PPS-based laminates [START_REF] Jang | Repeated impact failure of continuous fiber reinforced thermoplastic and thermoset composites[END_REF][START_REF] Nejhad | Impact behaviour and damage tolerance of woven carbon fibre-reinforced TP composites[END_REF][START_REF] Vedula | Impact resistance of cross-plied polyphenylene sulfide composites[END_REF][START_REF] Spamer | Investigation of the CAI properties of C/PPS and C/APC-2 TP materials[END_REF][START_REF] Ma | Effect of physical aging on the toughness of CFR PEEK and PPS composites[END_REF][START_REF] Davies | Design methodology to improve damage tolerance in composites[END_REF]. The impact energy adversely affects the impact performance of the laminates, whereas the effect of impact velocity is found to be insignificant. Among the properties governing the impact behavior of laminated composites, the mode I and mode II critical energy release rates G IC and G IIC (see Table 1) are of the utmost importance [START_REF] De Baere | Study of the Mode I and Mode II interlaminar behavior of a carbon fabric reinforced TP[END_REF][START_REF] Davies | The delamination behavior of carbon fiber reinforced PPS[END_REF][START_REF] Lachaud | Experimental and numerical study of delamination caused by local buckling of TP and TS composites[END_REF][START_REF] O'brien | Composite Interlaminar Shear Fracture Toughness GIIc: shear measurement or sheer myth?[END_REF]. In addition, higher Compression After Impact (CAI) strengths are generally observed in C/PEEK compared to C/Epoxy (see Fig. 1a), and the reason has already been explained [START_REF] Ishikawa | Some experimental findings in CAI tests of CF/PEEK and conventional CF/Epoxy flat plates[END_REF][START_REF] Davies | Design methodology to improve damage tolerance in composites[END_REF].

The process of delamination propagation in the final stage of C/ Epoxy CAI tests is well understood: delamination causes buckling deflection reverse in the impact side and reduces the load carrying capacity of the delaminated plates. Due to the ability to arrest delamination, the CAI strain of C/PEEK laminates is almost twice that of C/epoxy (see Fig. 1b), whereas the CAI residual strength is 70% reduced in TS-based laminates and 50% reduced in TP-based laminates at higher impact energy [START_REF] Spamer | Proceedings of the 33rd International SAMPE Symposium[END_REF].

About damage tolerance of woven-ply laminates

In addition to the contribution of the matrix toughness to the impact performance of a composite system, the impact behavior and the damage tolerance are also importantly influenced by the reinforcement architecture. The issue of the specific impact behaviors of UD-ply laminates and woven-ply laminates has been well addressed in [START_REF] Schrauwen | Influence of matrix ductility and fibre architecture on the repeated impact response of glass-fibre-reinforced laminated composites[END_REF][START_REF] Kim | Impact and delamination failure of woven-fabric composites[END_REF][START_REF] Bibo | Review: the role of reinforcement architecture in impact damage mechanisms and post-impact compression behavior[END_REF][START_REF] Reyes | Modeling and damage repair of woven thermoplastic composites subjected to low velocity impact[END_REF][START_REF] Nejhad | Impact behaviour and damage tolerance of woven carbon fibre-reinforced TP composites[END_REF][START_REF] Spamer | Proceedings of the 33rd International SAMPE Symposium[END_REF][START_REF] Kim | Impact performance of a woven fabric CFRP laminate[END_REF][START_REF] Funk | The interlaminar fracture toughness of woven graphite/ epoxy composites[END_REF][START_REF] Siow | An experimental study of low velocity impact damage in woven fiber composites[END_REF][START_REF] Jegley | Compression behavior of graphite-thermoplastic and graphiteepoxy panels with circular holes or impact damage[END_REF][START_REF] Baker | Mechanical property characterization and impact resistance of selected graphite/PEEK composite materials[END_REF][START_REF] Atas | An overall view on impact response of woven fabric composite plates[END_REF][START_REF] Hongkarnjanakul | Validation of low velocity impact modelling on different stacking sequences of CFRP laminates and influence of fibre failure[END_REF]. An illustration of the significant contribution of fiber reinforcement to impact behavior is given by Ghasemi Nejhad and Parvizi-Majidi who studied the impact behavior and damage tolerance of carbon-fiber woven-ply TP-based (PEEK and PPS) laminates [START_REF] Nejhad | Impact behaviour and damage tolerance of woven carbon fibre-reinforced TP composites[END_REF]. The CAI strength of PEEK-based composite remained at 47% of the value for virgin material even after sustaining an impact of 29 J. The features and failure mechanisms are identified [START_REF] Karaog ˘lan | Frictional contact/impact response of textile composite structures[END_REF][START_REF] Akkerman | Impact damage in woven fabric reinforced composites[END_REF]: inherent toughness of the fabric; the availability of matrix-rich regions at the fiber bundles crimps where plastic deformation can develop along with micro-buckling; crack propagation along the undulating pattern of the yarns creating a large fracture surface area; and multiple crack delaminations on the impacted side [START_REF] Bibo | Review: the role of reinforcement architecture in impact damage mechanisms and post-impact compression behavior[END_REF]. Thus, woven-ply laminates generally exhibit a lower peak load, a smaller damage area, a higher ductility index, and a higher residual CAI strength than UD cross-ply laminates [START_REF] Kim | Impact performance of a woven fabric CFRP laminate[END_REF], because they show much higher G IC values (often more than 4-5 times) than the UD counter-parts. As a result, the damage tolerance of woven-ply laminates is better, but the overall mechanical properties of non-impacted UD-ply laminates are higher. From this brief literature review, it seemed necessary to look further into matrix's specific contribution (toughness and ductility) to the impact performance, and damage tolerance of different types of woven-ply laminates. To this aim, low velocity impact tests have been conducted at different impact energies [START_REF] Vieille | About the impact behavior of woven-ply carbon fiber-reinforced thermoplastic-and thermosetting-composites: a comparative study[END_REF]. In this work dealing only with the impact behavior, C-scan inspections and a fractography analysis showed that C/TP laminates are characterized by reduced damage (C/PPS laminates in particular), confirming that a tougher matrix can possibly be associated with better impact performance. In addition, the reinforcement weave structure limits extensive growth of delamination, but fiber breakages are more common and appear at lower impact energies because of fiber crimps. The permanent indentation (representative of local matrix crushing or plasticization, and local fiber breakage) can be ascribed to specific mechanisms. In TP-based laminates, the matrix plasticization seems to play an important role in matrix-rich areas by locally promoting permanent deformations. Fiber-bridging also prevents the plies from opening in mode I, and slows down the propagation of interlaminar and intralaminar cracks. Both mechanisms seem to reduce the extension of damages, in particular, the subsequent delamination for a given impact energy. In epoxybased laminates, the debris of broken fibers and matrix get stuck in the cracks and the adjacent layers, and create a sort of blocking system that prevents the cracks and delamination from closing after impact [START_REF] Hongkarnjanakul | Permanent indentation characterization for low-velocity impact modelling using three-point bending test[END_REF].

Objectives of the study

In order to assess the severity of damage on the compressive residual strength and behavior, CAI tests were carried out on specimens impacted in [START_REF] Vieille | About the impact behavior of woven-ply carbon fiber-reinforced thermoplastic-and thermosetting-composites: a comparative study[END_REF]. To the authors' knowledge, most of the previous studies focused on the values of residual strength, but do not shed light on a detailed understanding of damage mechanisms leading to the final failure under compressive loading. In general, the compressive residual strength is determined by the G Ic (kJ/m 2 ) neat resin 4 0.5-0.9 0.1 G Ic,initiation (kJ/m 2 ) carbon fiber woven-ply polymer 1.1-2.1 0.85-1 0.35-0.5 G IIc,initiation (kJ/m 2 ) carbon fiber woven-ply polymer 2-4.9 1.8 1.5

Fig. 1. Comparison of the CAI properties of TP-and TS-based laminates as a function of the impact energy: (a) normalized strength [START_REF] Spamer | Proceedings of the 33rd International SAMPE Symposium[END_REF] -compressive strain to failure [START_REF] Ishikawa | Some experimental findings in CAI tests of CF/PEEK and conventional CF/Epoxy flat plates[END_REF].

resistance to buckling of the sub-laminates rather than their inplace resistance [START_REF] Ishikawa | Some experimental findings in CAI tests of CF/PEEK and conventional CF/Epoxy flat plates[END_REF][START_REF] Aktas ß | An experimental investigation of the impact response of composite laminates[END_REF][START_REF] Reis | Impact response of Kevlar composites with filled epoxy matrix[END_REF]. The buckling of sub-laminates, called ''local buckling'', is mainly influenced by delamination which depends on the level of impact energy [START_REF] Freitas | Failure mechanisms on composite specimens subjected to compression after impact[END_REF][START_REF] Sanchez-Saez | Compression after impact of thin composite laminates[END_REF]. Ply clustering has potential to increase delamination which splits the laminate into sub-laminates, but it results in a lower damage resistance [START_REF] González | Effects of ply clustering in laminated composite plates under low-velocity impact loading[END_REF]. However, this phenomenon is not sufficient to explain the final failure of the laminates, since in most cases the delamination does not propagate over the entire width of the plate, and the compressive failure is due to the propagation of a crack transversely to the loading direction, from the impact zone to the specimen's edges. In woven-ply laminates, the onset of the final failure is assumed to be induced by local compression failure at the edge of the damage [START_REF] Yan | Compression-after-impact response of woven fiber-reinforced composites[END_REF][START_REF] Aktas | Compression-after impact behavior of laminated composite plates subjected to low velocity impact in high temperatures[END_REF], but transversal cracks may appear before 80% of the final failure load during CAI tests [START_REF] Kinsey | Post-impact compressive behaviour of low temperature curing woven CFRP laminates[END_REF]. These cracks may result from micro-buckling of fibers in the 0°plies. However, the nature and the origin of these cracks (fiber failure in compression, or fiber failure due to buckling) are not discussed in these references. As a result, the objective of the present work is to further investigate the mechanisms leading to the compressive failure of impact-damaged laminates. From multi-instrumented CAI tests (Digital Image Stereo-Correlation), the role of initial damage (delamination, post-impact cracks, permanent indentation, etc.) on the onset of buckling and cracks development during CAI loadings is analyzed.

Experimental setup

Materials

The composite materials studied in this work are carbon fabricreinforced prepreg laminated plates consisting of different matrix systems: TP (PPS or PEEK) and TS (Epoxy). The PPS resin (Fortron 0214) is supplied by Ticona, the PEEK resin (grade 150) is supplied by Victrex, and the epoxy resin (914) is supplied by Hexcel. The woven-ply prepreg laminate consists of 5-harness satin weave carbon fiber fabrics whose reference is T300 3K 5HS, and is supplied by SOFICAR. The volume fraction of fibers is 50%. The prepreg plates are hot pressed according to a Quasi-Isotropic lay-up: [(0,90)/(±45)/(0,90)/(±45)/(0,90)/(±45)/(0,90)] in TP-based laminates, and [(0,90)/(±45)/(±45)/(0,90)/(0,90)/(±45)/(±45)/(0,90)] in C/Epoxy. The lay-up slightly differs in order to get similar laminates' thicknesses. The laminates' thickness was averaged from measurements at different points: 2.24 mm in C/PEEK, 2.31 mm in C/PPS, and 2.4 mm in C/Epoxy laminates. The 100 Â 150mm 2 specimens were cut from 600 * 600 mm 2 flat panels using a water-cooled diamond saw, and comply with the standard Airbus AITM 1-0010, except for the recommended thickness (4 mm).

The main mechanical properties (see Table 2) of the three composite systems investigated in this work have been evaluated in previous works [START_REF] De Baere | Study of the Mode I and Mode II interlaminar behavior of a carbon fabric reinforced TP[END_REF][START_REF] Aucher | Influence de la température sur le comportement mécanique de stratifiés tissés thermoplastique ou thermodurcissable[END_REF][START_REF] Vieille | Woven ply thermoplastic laminates under severe conditions: notched laminates and bolted joints[END_REF].

Experimental procedure 2.2.1. Compression-after-impact testing

Low velocity impact tests have been conducted at room temperature on the three composite materials for different impact energies: 2 J, 6 J, 10.5 J, 17 J, 25 J. The experimental set-up is described in [START_REF] Vieille | About the impact behavior of woven-ply carbon fiber-reinforced thermoplastic-and thermosetting-composites: a comparative study[END_REF]. Once the specimens have been impacted, their residual strength is evaluated by means of CAI (Compression after impact) tests, commonly used in the aerospace industry. All the CAI tests were performed using a 100 kN capacity load cell of a Schenk servo-hydraulic testing machine at room moisture (50%). The specimen is placed within a special fixture originally designed by Boeing, which incorporates adjustable side plates to accommodate for both variations in thickness and overall dimension, as well as to prevent specimen buckling (see Fig. 3). Such a compression after impact fixture is placed between the compression platens of the testing machine. The specimens were therefore subjected to compressive loadings at a constant displacement rate V = 0.2 mm/min. The objectives of the CAI tests are usually twofold: to evaluate the critical buckling stress and to assess the compressive failure strength. On the front side of the impacted specimen, an extensometer is positioned on a corner of the plate, as far as possible of the expected buckling zone. This extensometer measures the strain in the longitudinal direction e x . The out-of plane deflection w LVDT is measured thanks to one LVDT sensor, positioned perpendicularly to the laminates surface and at the center of the specimen, where the largest out-of plane displacement due to compressive loading should be observed. Another LVDT sensor is used to measure the longitudinal displacement u machine of the machine's lower grip. The experimental set-up monitors four different signals: longitudinal strain e x , displacement and force, as well as the out-of plane deflection w.

3D Digital Image Correlation technique

As impact leads to local damage, a 3D Digital Image Correlation technique can be used to detect singularities of the strain field for impacted plates subjected to compressive loads [START_REF] Kim | Local stiffness reduction in impacted composite plates from full-field measurement[END_REF][START_REF] Yu | Full field strain characteristics of composite laminate with impact damage under in-plane load[END_REF]. From CAI tests, it is indeed possible to follow the propagation of impactinduced transversal cracks and the changes in the strain fields (compressive and flexural strains) on both sides of the impacted specimen. Thereby, a video system consisting of two CCD cameras can be used in order to follow the propagation of cracks, and the 3D heterogeneous strains fields can be evaluated during compressive tests. Thanks to the observation of every point from two different vantage points (where the cameras are placed), the device gives the coordinates (x, y, z) of points in a Cartesian coordinate system whose origin is approximately the impact point (see Fig. 2a). Before performing the CAI tests, the spatial arrangement of the cameras is unknown. In order to make the calibration and set up the parameters, a series of pictures of a black and white pattern is taken. As the software is capable of determining the geometry of the pattern, the spatial arrangement of the cameras can be calculated. Once the device is calibrated, the cameras are able to correlate a random pattern. The software used for handling the cameras is supplied by the Society Correlated Solutions. During CAI tests, a pair of digital pictures was taken with Vic-Snap software every 5 kN until laminates failure. On the impacted side of the laminates, the relative displacements (u, v, w) of every point can be measured with respect to its original position, by using the Vic-3D software (see Fig. 2a). The different strains fields (e x , e y , e z ) can therefore be obtained from the displacement fields.

Results

Impact initiates damages and permanent indentation in laminates, which are instrumental in driving the compressive behavior (and residual strength) of impacted specimens. More particularly, transverse cracks and diamond-shaped fracture patterns (associated with permanent indentation) may lead to premature buckling of specimens. The Barely Visible Damage BVID (0.6 mm) is reached at about 13 J (C/PPS) and 16 J (C/PEEK) in TP-based laminates, whereas it is reached at about 11 J in C/epoxy (see Fig. 2b). Macroscopic views of the front (impacted side) and the back (nonimpacted side) of specimens give first information about the onset of damage as a function of the impact energy (see Fig. 4).

The theoretical buckling strength of non-impacted laminates under compression (see Fig. 5) can be classically obtained from the plates theory [START_REF] Xiang | Exact buckling solutions for composite laminates: propers free edge conditions under in-plane loading[END_REF]. The value is virtually the same for the three materials (see Table 2). According to the values of ultimate compressive strengths, the compressive stress in 0°layers at failure is much higher than the theoretical buckling strength. It therefore suggests that buckling occurs very early during the compressive loading of non-impacted specimens. In impacted laminates, the compressive residual strength gradually decreases as impact energy increases (see Fig. 5). At low impact energy (e.g. 2 J), the residual strength of PEEK-based laminates is about 10% and 40% higher than C/Epoxy and C/PPS laminates respectively. At intermediate impact energies, CAI strength of C/PEEK is about 20-30% higher than the one of C/Epoxy and C/PPS. At high impact energy (e.g. 25 J), the residual strength is virtually the same for the three composite systems. Another way to analyze these results is to consider the permanent indentation induced by impact. Such an indentation is ascribed to specific impact damage mechanisms discussed in [START_REF] Vieille | About the impact behavior of woven-ply carbon fiber-reinforced thermoplastic-and thermosetting-composites: a comparative study[END_REF], and is represented by the dent depth which seems to be of the utmost importance from the residual strength standpoint, as it may facilitate local buckling (see Fig. 6). The dent depth is associated with the blistering of the plate [START_REF] Vieille | About the impact behavior of woven-ply carbon fiber-reinforced thermoplastic-and thermosetting-composites: a comparative study[END_REF], from which buckling can be induced. From the results presented in Fig. 6, it appears that the residual strength decreases dramatically for very small values of dent depth (about 0.1 mm at 5 J) and for low impact energies. In addition, the ultimate compressive strengths tend to saturate to reach a minimum value for dent depths higher than the BVID. The observation of the impacted side of specimens reveals the presence of large transversal cracks along the 90°direction (see crack #1 in Fig. 4) which are induced by impact and associated with the failure of 0°fibers. Depending on the impact energy, these cracks may propagate more or less rapidly (depending on matrix nature) due to buckling or to compressive loading, ultimately resulting in the failure of specimens. The question is therefore to know which one of the buckling or the compressive loading drives the damage mechanism leading to the propagation of transversal cracks and the subsequent compressive failure of impacted laminates?

Discussion

Compressive response of impact-damaged laminates

The experimental investigations clearly show the presence of two impact-induced cracks along the warp and weft directions on the non-impacted side (see Fig. 4). The CAI tests suggest that the cracks along the 90°direction propagate transversely to the loading direction, whereas the cracks along the 0°direction remains unaltered upon compression in agreement with the conclusions drawn in [START_REF] Yu | Full field strain characteristics of composite laminate with impact damage under in-plane load[END_REF]. At 17 J, the largest delamination under impact loading is observed between the 6th and 7th plies. It is reasonable to consider that the size of the delamination zone between plies increases as a function of thickness as it is represented by the delamination pyramid in [START_REF] Vieille | About the impact behavior of woven-ply carbon fiber-reinforced thermoplastic-and thermosetting-composites: a comparative study[END_REF]. A few prior investigations considered a complete lack of load carrying capacity of the plies within the damaged area [START_REF] Naik | Impact and compression after impact characteristics of plain weave fabric composites: effect of plate thickness[END_REF], resulting in a negligible residual strength in the 5-6-7 plies within the pyramidal damage zone after high impact energy (e.g. 17 J). After low energy impacts (e.g. 2 J), C-scan inspections reveal no visible delamination or cracks [START_REF] Vieille | About the impact behavior of woven-ply carbon fiber-reinforced thermoplastic-and thermosetting-composites: a comparative study[END_REF], hence suggesting that the compressive response of specimens will not be driven by impact-induced damage. Thus, the initial damage (depending on impact energy) is instrumental in governing the CAI response of laminates.

Local and micro-buckling

As it is mentioned in Section 1.3, classical global buckling of the plate and local buckling of the delaminated sub-laminates are accompanied by the propagation of transverse cracks on the impacted surface of laminates provided that the impact energy is not too low. Local buckling is facilitated by permanent indentation at high impact energy. Micro-buckling is primary due to the misaligned structure of the weave pattern at the crimps (see Fig. 7a). Both mechanisms are combined during CAI loadings. One of the main purposes of this study is therefore to identify the critical stress at which buckling occurs in impacted laminates. Two different methods can be used:

The first one consists in evaluating the plate's out-of plane deflection w until the onset of buckling, although most of the specimens actually suffered a reduced increase in their outof-plane deflection right from the beginning of the tests, because of the impact-induced damage (dent depth). When the critical stress is reached, the deflection suddenly and significantly increases (see Fig. 8). However, it is hard to identify the exact transition point. The second method is based on the observation of the longitudinal strain e x . Its behavior is linear under pure compression, and the linearity is lost when the plate starts buckling. Normally, this transition point can be more easily determined by observing the changes in the longitudinal strain than in the out-of-plane deflection (see Fig. 8). Thus, it is quite complicated to determine a precise value of this critical stress, and that is the reason why the corresponding value has been estimated from the curves representing longitudinal strain e x vs compressive stress.

For each method, the out-of-plane deflection w or the longitudinal strain e x can be obtained either from the LVDT sensors or from the CCD cameras (thanks to the 3D Digital Image Correlation). Thus, the second method based on the changes in e xCCD gives an experimental critical buckling strength (see Fig. 8) which can be compared to the ultimate compressive strength for every impact energy (see Fig. 9). During compressive loading, local buckling appears lately, and the buckling strength significantly decreases as impact-induced damage increases. In TP-based laminates, the buckling strength is about 20% lower than the CAI strength as impact energy increases (see Fig. 9a-b). In TS-based laminates, the values of both residual compressive strength and buckling strength tend to be the same as impact energy (initial damage) increases (see Fig. 9c). It suggests that the initial damage induced by impact (associated with the specimens' blistering and dent depth) makes local buckling a primary compressive failure mode at high impact energy.

Propagation of transversal cracks

Once the buckling strength is estimated, it is necessary to evaluate the compressive stress from which the transversal cracks associated with the failure of 0°fibers propagate (see crack #1 in Fig. 4). The initial length of transversal cracks only depends on the impact and permanent indentation. During CAI tests, the propagation of these impact-induced cracks can be locally observed by using the longitudinal displacement field resulting from the DIC analysis. Indeed, the curve representing the axial displacement as a function of the axial position is virtually continuous along line 1 drawn far from the crack (see Fig. 10). The transversal crack tip can be detected when a discontinuity is observed on the curve (see line 2 in Fig. 10), because such discontinuity indicates that the displacement of the upper part is higher than the lower part's one. One digital image being taken every 5 kN during compressive loading, the crack tip can be located from discontinuities appearing on each displacement field. Thus, this method can be used to investigate the propagation of transversal cracks as compressive stress increases for the three materials and every impact energy (see Fig. 11). It is worth noticing that the initial length of these cracks increases as the impact energy increases. For all impacted C/PPS laminates, the length of the crack remains constant (no propagation) until the compressive stress reaches the experimental critical buckling strength where the crack propagates suddenly (see Fig. 11b). It therefore suggests that buckling is instrumental in driving compressive failure in PPS-based composites at any impact energy. On the contrary, slow crack propagation can be observed in PEEK-and Epoxybased laminates under low compressive stresses (see Fig. 11a andc), suggesting that compressive load governs the compressive failure of 0°fibers of specimens initially subjected to impact energies ranging from 6 to 25 J. The crack propagation becomes therefore accelerates as compressive stress reaches the estimated buckling strength. At low impact energy (e.g. 2 J), cracks propagate suddenly once the compressive stress is higher than the estimated buckling strength, suggesting that buckling drives the compressive failure. A particular attention has been paid to the CAI tests carried out on specimens impacted at 17 J, because such impact energy is higher than the energy level for which the BVID is reached: 16 J in C/PEEK, 13 J in C/PPS, and 11 J in C/Epoxy. As it was indicated in Section 4, a 17 J impact promotes permanent indentation which is closely associated with local buckling. On such specimens, the observations of longitudinal strain fields along with the compressive stress and the crack propagation confirm the previous failure mechanisms: transversal cracks start propagating for compressive stress lower than the estimated buckling strength (at about 111 MPa and 100 MPa, for C/PEEK and C/Epoxy respectively). The propagation is slow until the compressive stress reaches r buckling x where the propagation becomes rapider as local buckling accelerates the propagation in C/Epoxy (see Fig. 12). The contribution of local buckling to the rapid crack propagation ultimately leads to the failure of these specimens. The main difference between C/Epoxy and C/PEEK is that PEEK matrix intrinsic toughness may counter-balance the effect of local buckling, resulting in relatively slow crack propagation (see Fig. 13). It therefore explains a better damage tolerance as the residual compressive strength is 30% higher in C/PEEK than in C/Epoxy laminates. It is also worth noticing that, comparatively to Epoxy-based laminates, cracks start propagating earlier in C/ PEEK during compressive loading, probably due to significantly different initial damage (more extensive delamination and less 0°fibers breakage in C/Epoxy). As 0°fibers breakage is instrumental in driving the CAI behavior, it is reasonable to consider that more impact-induced fiber breakage in C/PEEK laminates results in an earlier propagation. Finally, in C/PPS specimens, the crack length remains virtually unchanged (see Fig. 14), until the compressive stress reaches the estimated buckling strength (at about 125 MPa) where the propagation becomes rapider due to buckling. The highly ductile behavior of PPS matrix may contribute to plastic deformation due to micro-buckling at the crimps, which can delay the cracks onset and subsequent propagation. However, it appears that the previous scenario may differ from one material to another, depending on the contribution of matrix ductility [START_REF] Vieille | Woven ply thermoplastic laminates under severe conditions: notched laminates and bolted joints[END_REF] and toughness (see Table 1) to the CAI failure of the studied woven-ply laminates. The compressive failure is usually governed by three primary mechanisms in composite laminates [START_REF] Fleck | Compressive failure of fiber composites[END_REF]: (i) Buckle delamination is associated with low toughness matrix (typically in Epoxy-based laminates), and the presence of local delamination -(ii) Out-of-plane shearing leading to the fragmentation of the plies and local buckling of 0°fiber bundles. Such a mechanism is mostly based on the breakage of 0°fi bers -(iii) Splaying of external plies. Such a mechanism is associated with a longitudinal splitting between 0°fibers bundles in low ductility matrix (typically in Epoxy-based laminates).

During CAI tests, other compressive failure modes are possible, and usually result from a combination of the previous mechanisms. It is also known that carbon fibers under compressive loadings are prone to global instabilities [START_REF] Soutis | Compressive failure of notched carbon fiber composites[END_REF], and the initial alignment of fibers in reinforced composites has a large influence on their compressive response [START_REF] Avery | Compression strength of carbon fiber laminates containing flaws with fiber waviness[END_REF]. Thus, the crimp region plays a significant role in controlling the onset of failure in woven-ply laminates, mostly because of the undulating structure of carbon fabrics (see Fig. 7a), and the presence of matrix-rich areas at the crimps [START_REF] Naik | Impact and compression after impact characteristics of plain weave fabric composites: effect of plate thickness[END_REF][START_REF] Grape | The effect of temperature on the strength and failure mechanisms of a woven carbon/polyimide laminate under compression[END_REF][START_REF] Osada | Initial fracture behavior of satin woven fabric composites[END_REF]. Both matrix toughness and ductility contribute to specific failure mechanisms within a fiber network. In wovenply misaligned structures, micro-buckling at the crimps is found to cause fiber crushing and the possible onset of highly deformed inclined kink-band formation. In Epoxy-based specimens, the micro-buckling is combined with local buckling of the sub-laminates resulting from permanent indentation. Micro-buckling leads to the interlaminar cracking at the crimps, whereas local buckling promotes the growth of delamination, and ultimately the failure of 0°fibers in the [(0,90)] plies of the laminates (see Fig. 7c). In TP-based laminates, local and micro-buckling also operate even though the effect of local buckling is more significant in C/PEEK than in C/PPS because the dent depth is higher. In addition, micro-buckling comes along with a plastic deformation of the matrix in highly ductile matrix systems (such as PPS-based laminates), resulting in the formation of plastic kink-bands, also called plastic buckling (see Fig. 7b) [START_REF] Grape | The effect of temperature on the strength and failure mechanisms of a woven carbon/polyimide laminate under compression[END_REF][START_REF] Pinho | Fracture toughness of the tensile and compressive fibre failure modes in laminated composites[END_REF]. Such plastic buckling may delay the onset and subsequent propagation of transversal cracks during compressive loadings, whereas the local buckling of the delaminated sub-laminates is instrumental in accelerating the propagation of transverse cracks (failure of 0°fibers) in the [(0,90)] plies of the laminates. PEEK-based composite have a less ductile behavior than the one observed in C/PPS [START_REF] Kinsey | Post-impact compressive behaviour of low temperature curing woven CFRP laminates[END_REF], ultimately leading to the formation of less plastic kink-bands. In addition and as far the mode II interlaminar fracture is concerned (see Table 1), C/PEEK laminates are about 3 times tougher than C/PPS and C/Epoxy [START_REF] Vieille | About the impact behavior of woven-ply carbon fiber-reinforced thermoplastic-and thermosetting-composites: a comparative study[END_REF]. The CAI results suggest that the matrix toughness of TPbased resins (particularly C/PEEK) is not completely transferred to the reinforced polymer. As indicated in Section 4.3, the matrix toughness should counter-balance the effect of local buckling. However, the significant permanent indentation facilitates local buckling, which becomes a primary compressive failure mode at high impact energy. It could therefore justify why the much higher toughness of TP-based laminates (particularly C/PEEK) does not result in significantly higher CAI residual strengths in relation to the one obtained in C/Epoxy laminates.

Conclusion

The present work was aimed at investigating the mechanisms leading to the compressive failure of impact-damaged laminates consisting of a more or less tough and ductile matrix. From CAI tests combined with Digital Image Stereo-Correlation, the role of initial damage (delamination, post-impact cracks, permanent indentation, etc.) on the onset of buckling and transversal cracks (failure of 0°fiber bundles) development during CAI loadings is analyzed. At low impact energy, the CAI residual strength of PEEK-based laminates is about 10% and 40% higher than C/Epoxy and C/PPS laminates respectively, whereas it is virtually the same for the three composite systems at high impact energy.

During CAI loadings, local buckling is a primary compressive failure mode particularly at high impact energy. Buckling appears in a combination of local buckling of sub-laminates resulting from permanent indentation, and a micro-buckling at the crimps. Provided that the impact energy is not too low, the permanent indentation is associated with the blistering of the plate after impact, which seems to be of the utmost importance from the residual strength standpoint, as it may facilitate local buckling. Micro-buckling seems to be primarily ascribed to the misaligned structure of the weave pattern at the crimps.

In Epoxy-based laminates, micro-buckling leads to the interlaminar cracking at the crimps, whereas local buckling promotes the growth of delamination, and ultimately the failure of 0°fibers in the [(0,90)] plies of the laminates. In TP-based laminates, microbuckling comes along with a plastic deformation of the matrix in highly ductile matrix systems (such as PPS-based laminates), resulting in plastic buckling. Such plastic buckling may delay the onset and subsequent propagation of transversal cracks during compressive loadings, whereas local buckling is instrumental in accelerating the propagation of transverse cracks in the [(0,90)] plies of the laminates. The matrix toughness should counter-balance the effect of local buckling. However, the latter effect becomes a primary compressive failure mode at high impact energy, as it is facilitated by a significant permanent indentation. It could therefore justify why the much higher toughness of TP-based laminates (particularly C/PEEK) does not result in significantly higher CAI residual strengths in relation to the one obtained in C/Epoxy laminates.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Dent depth: (a) contour plot and corresponding 3-D image of damaged specimen -(b) Changes in dent depth as a function of the impact energy on the impacted side of specimens.

Fig. 4 .

 4 Fig. 4. Observations of impact damage patterns on front and back sides of impacted specimens as a function of the impact energy [43]: (a) 6 J -(b) 10.5 J -(c) 17 J -(d) 25 J.

Fig. 5 .

 5 Fig. 5. Ultimate compressive strength as a function of impact energy.

Fig. 6 .

 6 Fig. 6. Ultimate compressive strength as a function of dent depth.

Fig. 7 .

 7 Fig. 7. Mechanisms of compressive failure in woven-ply laminates: (a) micro-buckling of fiber bundles at the crimps in a 5-harness satin weave -(b) formation of plastic kink-bands in TP-based laminates -(c) interlaminar cracking and delamination growth in Epoxy-based laminates.

Fig. 8 .

 8 Fig. 8. Transversal deflection and longitudinal strain vs compressive stress during CAI tests on specimens impacted at different impact energies: (a) C/PEEK -(b) C/PPS -(c) C/ Epoxy.

Fig. 9 .

 9 Fig. 9. Comparison of ultimate and experimental critical buckling strength as a function of the impact energy: (a) C/PEEK -(b) C/PPS -(c) C/Epoxy.

Fig. 10 .

 10 Fig. 10. Method for detecting the tip of transversal cracks associated with 0°fibers failure.

Fig. 11 .

 11 Fig. 11. Propagation of transversal cracks during CAI tests on specimens impacted at different impact energies: (a) C/PEEK -(b) C/PPS -(c) C/Epoxy.

Fig. 12 .

 12 Fig. 12. CAI response of C/Epoxy laminates after a 17 J impact: correspondence of the crack propagation with transversal displacement w and longitudinal strain ex fields at different compressive stresses.

Fig. 13 .

 13 Fig. 13. CAI response of C/PEEK laminates after a 17 J impact: correspondence of the crack propagation with transversal displacement w and longitudinal strain ex fields at different compressive stresses.

Fig. 14 .

 14 Fig. 14. CAI response of C/PPS laminates after a 17 J impact: correspondence of the crack propagation with transversal displacement w and longitudinal strain ex fields at different compressive stresses.

Table 1

 1 Interlaminar fracture toughness of tested materials[START_REF] Vieille | About the impact behavior of woven-ply carbon fiber-reinforced thermoplastic-and thermosetting-composites: a comparative study[END_REF].

	C/PEEK	C/PPS	C/Epoxy (914)

Table 2

 2 Material properties of the different composite systems and buckling theoretical strength of non-impacted specimens[START_REF] Vieille | About the impact behavior of woven-ply carbon fiber-reinforced thermoplastic-and thermosetting-composites: a comparative study[END_REF].

			C/PEEK	C/PPS	C/Epoxy
	Ply thickness (mm)	0.32	0.33	0.30
	E xx (GPa)	59.1	56.5	63.3
	E yy (GPa)	59.4	58.2	63.7
	G xy (GPa)	4.04	4.08	5.1
	r ult comp ðMPaÞ [0] 7	716	710	731
	Stacking sequence	[0/45/0/45/0/45/0]	[0/45/À45/0] S
	r ult comp ðMPaÞ	491	479	513
	r buckling x	ðMPaÞ	318	323	330