A COMPARISON OF THE MODELLING OF COMMINUTION AND LIBERATION IN MINERALS PROCESSING AND SHREDDING OF PASSENGER VEHICLES

EPD Congress 2005 Edited by Mark E. Schlesinger TMS (The Minerals, Metals & Materials Society), 2005 A COMPARISON OF THE MODELLING OF COMMINUTION AND LIBERATION IN MINERALS PROCESSING AND SHREDDING OF PASSENGER VEHICLES Alexandre Richard, Antoinette van Schaik and Markus Andreas Reuter Delft University of Technology, Mijnbouwstraat 120, Delft, The Netherlands. Keywords: Liberation performance, Recycling rates, Design for Recycling, Passenger Vehicles Abstract The material connections and combinations in the design of the car determine the particle size reduction and the degree of liberation of the product during shredding, which affects the composition of the intermediate recycling streams (composition and amount of the nonliberated particles) and the efficiency of physical separation. The quality of intermediate recycling products is of critical importance in order to optimize the material recovery in metallurgical processing, in order to achieve high recycling rates as imposed by legislation the European Union. Liberation during shredding is the natural link between design and recycling. Modeling of liberation is extensively applied in classical minerals processing. However, from previous work by the authors, it was learned that modeling of liberation for modern consumer goods differs fundamentally from minerals processing. This paper will therefore investigate in detail the fundamental differences and analogies between comminution and liberation in minerals processing and shredding modern consumer goods, such as the car. From this research, it will become clear to what extent classical minerals processing approaches and definitions can be used to model the design and shredding of the car. A clear direction will be given for future modeling and optimization work on the recycling of end-of-life vehicles. Introduction In Europe targets have been laid down by EU legislation for the recycling rate of end-of-life vehicles to be achieved within the nearby future (Directive 2000/53/EC, 2002). These strict recycling targets are one of the driving forces for more awareness on the importance of recycling in the product s life cycle as well as for the optimization of recycling systems. Often recycling is negated by the designer, but legislation makes recycling very important. The performance of a recycling system, as well as the effect of optimizing it, can be communicated based on the achieved recycling rate. This recycling performance can only be captured based on a fundamental understanding of recycling systems and their leading parameters (Van Schaik and Reuter, 2004a; Van Schaik et al, 2004). Van Schaik et al. (2004) and Castro, et al. (2004) have shown that the modeling of the liberation of the car during shredding is essential to define the link between product design and the performance of the recycling system. Although a first step has been made by the authors to model liberation in car shredding (Van Schaik, et al., 2004), more research is required to capture the relation between design characteristics such as joints and material combinations and the recycling rate in order to model 1039

the behavior of the car shredder in view of liberation. Therefore the objectives of this paper are the following: Determine to what extend minerals processing modeling and car shredding modeling can be compared theoretically; Investigate the fundamental differences between comminution and car shredding to determine how the work that already has been performed on the modeling of the influence of design on the recycling rate (Van Schaik, et al., 2004) has to be continued; Suggest a methodology to integrate car shredding and modeling in design for recycling as part of design for environment; in which experimental data is applied for calibration and verification of the modeling of car shredding as suggested in this work. Modeling of comminution for mineral processing systems It is known from traditional minerals processing technology that the behavior of ore dressing equipment depends on the nature of the individual particles processed (Heiskanen, 1993; King, 2001). King (2001) and Heiskanen (1993) discuss that the two most important fundamental properties for separation are the size of the particle and its mineralogical composition (after breakage), which are both determined by the comminution process. Mineral liberation is the natural link between comminution and mineral recovery operations. The same principles apply to the separation of artificial ores, such as modern consumer products, of which the mineralogy is determined by design. In order to investigate the possibilities to apply minerals processing modeling in the description of car shredding and liberation, the basic principles of comminution modeling in minerals processing and car shredding have to be investigated and compared with each other. Only the aspects of minerals processing theory which are relevant for the comparison will be considered here and are given in Table I. Table I Comparative elements between comminution modeling in minerals processing and car shredding modeling Minerals processing Car shredding Mineralogical Texture: Design: Size of mineral grains in the particles (grade), Materials choices, size and shape of the elements their shape, orientation and position. of the car, the joints between these different Minerals properties: Minerals are generally considered as brittle and hard materials. Liberation: Detachment by comminution (particle size reduction) of one or more species of mineral from the complex in which it is bound in a larger piece of ore (Pryor, 1963) elements. Materials properties: Since the large range of elements composing cars, different materials behaviours have to be considered, from brittleness to ductility. Liberation: To be defined Grain size: It is discussed by King (2001) that in spite of the differences between the sizes of the different grains from a same mineral in a particle, it is useful to define a characteristic grain size for minerals. King discusses that the concept of defining a characteristic grain size corresponding to a liberation size can be used. This concept could be introduced since for many real ore textures, the distribution of particles as a function of the grade range moves from an 1040

average grade to a distribution with dispersion towards the liberated ranges. This indicates that liberation occurs at a particle size, characteristic for the mineral texture. Randomness: As discussed by King (2001), comminution could be seen as the superposition of a fracture network on the mineralogical texture. That superposition determines the composition of the particles after breakage. In general there is no correlation between the mineralogical texture and the fracture network it implies. It means that comminution is a random process. On this basis, King discusses different models for liberation prediction. These models are specific to two components mineralogical textures and will be discussed below. Prediction of liberation using image analysis Since the mineralogical texture plays an important role in liberation, a model for liberation has to start with a quantitative description of that texture. Image analysis is an effective tool to do this. Image analysis permits the measurement of the distribution of linear grades from the linear samples. The combination with the linear intercept distribution density produces the distribution of linear grades in particles of size D from the equation D g L l P(g L l) p(l D) Pg ( L D) ( L Pg lpl ) ( Ddl ) 0 = mesh size, = linear grade = intercept length = conditional density for linear grades in intercepts of length l and = conditional density for intercepts length from particles of size D Eq. 1 implies that P(g L l,d) is independent of the particle size. This is true if the fracture process is random and independent of the texture. Converting the results of Eq. 1 by a stereological transformation, it is possible to obtain the predicted liberation as a function of particle size after comminution. It is discussed by King that these assumptions can only be used when no other process affects the distribution of particles. This is not the case in traditional ore equipment. Therefore a different method is required to describe minerals breakage in a suitable way. The Andrews-Mika diagram In the population balance models the effect of mineral liberation could be described using a breakage matrix bxx ( ; ')(King, 2001) (see Eq. 2). This matrix is difficult to model for any particular case since many material liberation characteristics are involved. However, useful models have already been developed e.g. using a graphical approach of the problem for example the Andrews-Mika diagram. bxx ( ; ') bgdg (, ; ', d') (2) x = coordinate vector in the product particle space x = coordinate vector in the parent particle space g = product particle grade d = product particle size g = parent particle d = parent particle size (1) 1041

Eq. 2 could be defined using the properties of conditional distributions (Eq. 3). bgdg (, ; ', d') bg ( \ dg ; ', d') bdg ( ; ', d') (3) In many cases, b(d;g,d ) is considered being independent of g. This is a realistic assumption, since most of the time the valuable component is present in a very low grade in the ore (g << 1). This implies that in view of breakage properties, particles could be regarded as single matrix particles and Eq. 3 could be simplified to Eq. 4: bgdg (, ; ', d') bg ( \ dg ; ', d') bdd ( ; ') (4) in which b(d;d ) gives the breakage function of a one component particle and b(g\d;g,d ) gives the distribution of the fracture products of a two components particle of size d and grade g. King (2001) discusses different patterns for the breakage function, considering the fracture of brittle and hard materials. b(g\d;g,d ) is described by Andrews and Mika (1975) with a geometrical model. An example of the boundaries of this diagram for three different parent particle sizes is given by Fig. 1. The internal structure of the diagram, which contains the information on how progeny particles are distributed when a parent particle of a given size and range is broken, has been modeled by King using the beta distribution that is widely used in mathematical statistics. Fig. 1 Boundaries of the Andrews-Mika diagram for the three cases: parent particle size > liberation size, parent particle size liberation size, parent particle size < liberation size. When the function b(g\d;g,d ) has been calculated it is possible to combine it with the breakage function b(d;d ) to use the simplified equation Eq. 4 and to obtain the breakage matrix. In the two models described above, comminution is regarded to be a random process. It means that the models do not consider any correlation between the mineralogical texture and the fracture pattern. Non-random breakage in minerals processing In some cases breakage cannot be considered as a random operation. These exceptions are listed below. Only the first three of these exceptions have been modeled successfully in minerals processing (King, 2001). 1042

Selective breakage: This phenomenon is the result of the unequal brittleness of the different mineral phases. Particles that have an important proportion of the more brittle phase will have a more important rate of breakage. The difference between the properties of the materials that are connected in a car implies that this phenomenon will occur in car shredding. Differential breakage: This is happens when the breakage function b(d;d ) depends on the composition of the parent particle. Since few elements can be regarded as invaluable in ELV s the breakage of the car depends on its composition. Preferential breakage: If crack branching is more frequently in one of the mineral phases it is called preferential breakage. Because of the differences between the properties of the different elements of the ELV s that are shredded this phenomenon can occur in car shredding. Phase-boundary fracture: Cracks have a tendency to move along the grain joints rather than across the phases. This could occur in car shredding when the joint between two elements is weaker than the elements that are connected. Liberation by detachment: Since minerals grains are relatively loosely bonded they become detached from the ore matrix during comminution. It can occur for some connection types in car shredding (insertion for example). Boundary-region fracture: The boundary highly stressed region in the area of the boundary between two dissimilar minerals is preferentially fractured. The joint between two elements in a car will be destroyed preferentially during breakage if it is highly stressed. Car shredding modeling As indicated by Van Schaik et al. (2004), the comminution behavior of man-made products such as cars differs fundamentally from minerals processing. In this section, the different parameters that can be defined to explain the differences are presented at the backdrop of the discussion in the previous section. Design: Design in car shredding modeling could be defined as the comparative element of the mineralogical texture described in minerals processing. Designers define the materials associations, their shape, position, orientation and the types of connection involved in each association (see Table II). All these elements could be captured by the definition of the mineralogy of the input product of the shredder (Van Schaik, et al., 2004). From the theory on minerals processing as discussed above it can be concluded that the following elements can be considered illustrating a fundamental difference in minerals processing and car shredding: Grain size: Grain size is an important parameter in the modeling of minerals comminution. In car shredding, due to the mineralogy, some connections cannot be broken and some materials will remain associated (incomplete liberation) (Van Schaik, et al., 2004). Designers could use materials in several and very different scales. It is much very difficult to define a grain size that could be used as an indication corresponding to a liberation size as is the case in minerals processing. 1043

Table II Possible connection types in car design Connections types Before shredding After shredding Bolting/riveting Gluing Insertion Coating / Painting Grade: In ore processing the assumption is made that the grade of the valuable component in the ore is low (g <<1 in b(d;g,d ) in Eq. 3), based on which the breakage function could be simplified. It is not possible to describe car breakage as a single particle breakage. The car breakage modeling has to consider materials behavior differences in car (ductile, brittle) and also connections behavior during breakage. This implies that the simplifications made for minerals processing modeling are not valid for car shredding. The breakage function for car shredding has to be defined for this specific problem. Materials choices and associations: Opposite to what is generally found in minerals processing, the difference of materials behavior (ductility, brittleness) between the components in particle will play an essential role in car shredding. Moreover materials applied in the car are, in general, not as brittle as mineralogical materials. This will significantly influence the patterns used to describe comminution. The fracture patterns have to be adapted to all materials types and also joint types occurring in the car. The Griffith theory, used to describe fracture pattern of a single particle in minerals processing (King, 2001), is applied for brittle materials. The particle breakage modeling used in minerals processing has to be adapted to semi-brittle and ductile materials to consider the plastic deformation that could occur during shredding. Tenacity is the material property used to describe the tendency to cracking of materials. Breakage will be strongly influence by the composition of the particles. Flaws: Materials breakage properties depend also on the history of the materials. It s a similar to the role of the flaws described by King (2001) in minerals processing. A particle made of the same material will not always break in the same way if it has been used very intensively or not. The distribution of cracks inside the materials will change depending on its use. Mechanical fatigue could be taken in consideration since a material could be used in different ways depending on it location in the car. At least, mechanical fatigue could give some indications on the breakage behavior of the different areas of the car, as a function of the use. 1044

(Non) randomness in car shredding: The comminution operation in minerals processing is a random process, except for some cases discussed above. In order to determine whether the probability theory for prediction of liberation in minerals processing can be applied to car shredding systems, it is necessary to investigate if the shredding operation is a random process. This will be discussed below using some examples. High randomness in shredding: Although the materials combinations and combinations defined in the design do influence the composition of the shredder product, the randomness of the shredding operation is affecting the composition of the output (see Fig. 2).? Fig. 2 High randomness in shredding Low randomness shredding: The particles formed after shredding will have the same composition as the starting fragment. The composition of the output will not be affected by the randomness of the shredding operation itself (see Fig. 3). In this example, the connection strength between rubber and steel is strong, and involves a preferential shredding direction. Fig. 3 Low randomness in shredding. Very low randomness in shredding: Fig. 4 illustrates that the particles after shredding will have a composition very similar to the input particle. The composition is not affected by the shredding operation. This could occur in case of e.g. surface joining of materials. Fig. 4 Very low randomness in shredding. From these examples the assumption can be made that design significantly determines the degree of randomness of the shredding operation. As in minerals processing, the shredding 1045

equipment will also influence this. Breakage in the shredder is determined by the impact energy; the wearing of the hammers; as well as the feeding and pre-treatment of the cars (e.g. all cars are not flattened and put on the conveyor belt in the same way). Shredding: liberation or creation? In order to compare car shredding and minerals processing modeling it is essential to investigate if shredding could be regarded as a liberation operation as defined by Pryor (1963) for minerals processing (see Table I). In minerals processing a prediction model proposed by King (2001) indicates that the presence of two components particles is decreasing with the size reduction, indicating that the two elements composing the particle are mostly liberated after comminution. The formation of different progeny particles could be described using the liberation prediction model of King. Considering two components particles, shredding is clearly a liberation operation as is indicated by Table III. The difference is, however, that after shredding, the smallest particle size class may contain more un-liberated elements than the comminution product. However, cars are multi-components parent particles. If the shredding input is described as an entire car, most of the elements will be liberated from the car, but some multi-components particles remaining after shredding will not have the same composition than the car in the input. New products will be found, and it is difficult to say that these products are liberated from the car since there are still multi-components particles. Thus, shredding appears to be a creation process (see Table III). Table III Different descriptions of car shredding as determined from industrial scale experimental work. Liberation operation Liberation operation Creation/Liberation but non-realistic Output Input + + 2 components particles shredding: Liberation could be defined similar to minerals processing systems Multi-components particles shredding: Output is composed by liberated elements and the same multi-components particle as in the input: Multi-components particles shredding: Output is composed by liberated elements and new multi-components particles. New multi-components particles are created; they contain, at least, one element in a more important proportion than in the input. So, the creation of these particles is involved in the liberation of the elements. 1046

Input-output description in minerals processing and car shredding Considering shredding as creation and liberation, the objective of the model is to predict the presence of liberated elements in the output, but also to determine the probability of the creation of new particles. However, considering an entire car as the input could make modeling very difficult because of the very complex structure of man-made products. Since input and output descriptions seem to play an important role, a proper description of the input (car) and output (shredded particles) have to be found to set up the car shredding model. Minerals processing: The input and output of the comminution operation have almost the same structure (valuable mineral in the ore matrix and liberated mineral), which allows a similar inand output description. A first description type is a description using only 1 particle type including all the elements. King (2001) uses that description for two-component particles. The output contains liberated elements and two-component particles. Each non-liberated particle is composed of all the elements, as defined in the input description. For multi-components particles description a different approach is developed. As discussed by Gay (2003) and Mehta et al. (1989), different particles types compose the ore. Their models on liberation of multicomponents systems have been developed using these particles types. Therefore, liberation is seen as a transformation of parent particles types in progeny particles types. Using this description, the objective of the models is to determine the probability that each parent particles forms a progeny particle. The description using one particle type including the two elements for a two-component system could be seen as a specific case of the multi-components description. Car shredding: The description of cars as the input of a shredder is difficult, because of the complexity of their structure. However, the input has to be defined in a suitable way to give all the information needed in the model and to define its link to shredded particles and recycling performance. The input may for example be described as being the entire car; however it would be very difficult to consider all the associations of materials in only one input particle. This implies that a particle type description is needed. The first option to describe all these combinations would be to dismantle the car by to define the particle types from the different elements found. This definition does not take in consideration the associations of the materials in the car. Another solution is to divide the car in several volumes, in order to define the different particle types in these volumes. The choice of the parent particle types has to be made considering the parts that can be isolated in a car (e.g. engine, body, bumper). The knowledge of the particle types present in the output could be helpful to define these. A parent particle type could be defined as a function of its size; the elements the particle contains, their ratios, and the type of joint between the different elements (see Table II). The particle type could also be called design type or a joint type. The importance of connections is discussed above; indicating that a proper indication for the selection of these volumes could be to focus on these connections (see Fig. 5). Interesting Volumes Connections/joints Fig. 5 Example of volume selection for the definition of particle types 1047

The model has to predict the liberation of the elements and the creation of the progeny particles from the parent particles defined (depending on the materials used, their properties, their connections types, their size). This partially virtual description of the input must allow the presence of the real particles in the output. The particle types for the output have to be defined using similar characteristics as for the input; the size, the elements the particle contains, their proportions, and the type of association between the different elements. Gay (2004) models the link between parent and progeny using probability theory. In the case of car shredding the link between parent and progeny particle types is still to be found and will be a function of connections behavior, materials properties, connection dimension, as investigated in this work. Experimental work was used to verify the suggestions made in this paper (see some results in Table II). Finite Elements Method The breakage matrix b(x;x ) can be determined by the use of Finite Element Method for modeling, which is extensively used for car crash test simulation. An important difference with crash test in car shredding is that the objective would be to see how cracks move in the materials to determine the way particles break. It does not only concern deformation. Modeling crack growth in FEM could imply problems of re-meshing, however, solutions have been developed to achieve that modeling (Dolbow, et al., 2001). In future models, FEM could be a solution for the breakage matrix modeling. At least it could give interesting (and quantitative) information on connections behavior during shredding. Liberation performance in car shredding The final objective of models on recycling rate optimization is to link design and the recycling rate. The discussion above will help to value liberation and, as a consequence, to calculate the recycling rate, which is the interesting performance parameter for designers. Therefore, liberation can be seen as a liberation performance involved in the recycling performance. Ashby (2003), Ashby, et al. (2004) and Landru (2001) have discussed methods for aided design that could be helpful for the integration of liberation performance in design. Ashby defines performance indexes that are the basis of a quantitative analysis of aided materials and processes selection. As discussed by Ashby, et al. (2004) the value function of design defined by Landru (2001) is applicable for multi-objective problems. To integrate car shredding modeling, the quantification of car shredding product could lead to the calculation of the recycling rate, which could be used within traditional design specifications in a value function of design. Discussion and conclusions Based on the work discussed above the following conclusions can be drawn. Similarities with minerals processing theory Car shredding could (partially) be described as a liberation operation; Particle type definition of the parent (car) and progeny (shredded car) particles can be defined in both minerals processing and car shredding as a basis for modeling liberation behavior; 1048

The exceptions defined for minerals processing modeling (such as the correlation between the mineralogical texture and the fracture network with non-random fracture) could be used as a basis to model the shredding of cars. For example, it is possible to compare the detachment of loosely bonded grains in the ore matrix and the detachment of loosely bonded materials in the shredder. Fundamental differences Comminution modeling uses a characteristic grain size as liberation size; this cannot be defined for a complex structure as the car; Materials associations and connections types play a very important role in car shredding. The modeling of the input particle breakage as defined in minerals processing has to change from a single brittle particle breakage empirical modeling (being valid since g << 1) to that of modeling of particles with many different connected materials all present in various ratios. This makes the above simplification of the breakage matrix of minerals processing invalid for car shredding modeling. In that case, it is still possible to start modeling from the breakage matrix, which has however to be adapted to car shredding. Due to the diversity of materials used in the car (semi-brittle, ductile), modeling of car shredding cannot be performed using minerals processing models defined for brittle materials. Design has a very important influence on the degree of randomness of the shredding operation and on the composition of the shredded product. Car shredding can therefore not be modeled on the same basis as minerals processing, being a predominantly random operation. Shredding modeling has to take in consideration that beside liberation of particles, new unliberated particles are created during shredding. As a consequence, the description of the input and output of the shredding operation has to be adapted. Useful particle types for both the description of design and shredded particles have to be derived based on the size of particles, material combinations and connections, etc. Recommendations From the discussions and conclusions of this work different recommendations can be made with regard to car shredding modeling and its introduction in computer aided design. Recommendations concerning car shredding modeling The Finite Element Method provides a possibility to model the breakage matrix for car shredding. At least, it could be interesting to model the behavior of the different connection types and materials combinations to obtain quantitative information on the liberation of the different elements in a particle as a function of the connection type and materials associations. Extensive experimental work and data collection (in addition to what has been done for this paper) could be helpful to capture the behavior of the different connection types found in car design. Particle type description seems to be a suitable method to give all the information with regard to the behavior of materials and joints during shredding. The integration of this description in the recycling models and dynamic models as developed by Van Schaik, et al. (2004) and Van Schaik and Reuter (2004b) is a suitable development for modeling the liberation behavior and its role in the recycling and resource cycle of cars. 1049

Recommendations concerning the introduction of car shredding modeling in computer aided design Car shredding modeling evaluates the liberation performance of wrecks. One of the issues is to use this knowledge during design to help designers to improve the recycling rate of cars. Material and connection type choices for improving the recycling rate is a multi-criteria design problem. To include recycling optimization in design methods, the recycling rate has to be added to the traditional materials and processes selection criteria and have to become part of already developed methodologies concerning computer-aided design for multicriteria problems. Recycling rate can be included in a value function in existing design methods if liberation is modeled as a function of the connection type and materials. The liberation performance is determined by design and influences the recycling rate (Figure 6). The Liberation Performance - LP of the connections is, for the moment, only described in a qualitative way (as the majority of the existing eco-indicators). Further work is required to determine the expression of the liberation performance for which a start is given in Eq. 6 as a function of intrinsic material properties and connection types. i j C i j C LP f,,, K, K, K, GEOMETRY,... (6) r r r 1c 1c 1c i r, j r, C r K K i 1c j 1c C 1c = Mechanical properties of connected Material i = Mechanical properties of connected Material j, K = Mechanical properties of the connection GEOMETRY = Geometry of the connection FEM could also help to determine the liberation performance of the connections and to set up a database with regard to the behavior of material during shredding (depending on materials associations and connection types). Introduction of the liberation performance in computer aided design: the liberation performance is one of the parameters for the calculation of the recycling rate and, as a consequence, could be a quantitative recycling indicator for designers. Fig. 6 shows how shredding modeling and the determination of the liberation performance could be introduced in recycling modeling and dynamic modeling of the resource cycle of product and could be applied as a metric for Design for Recycling or Design for Environment. 1050

Primary metal/ material= p(t) Product Manufacture Losses Stockpile Losses m(t) Car inflow x(t) Car outflow Market Losses Secondary metal/ material= s(t-) z(t) Metallurgy & Thermal Treatment Losses (flue dusts/slags) (1-a) Physical Separation a b d Product Design Computer Aided Design (CAD) z(t-) Delay Specifications, material selection Design for environment c Shredding Modelling Valuation of the Liberation Performance (LP) of design Design LP i j C r, r,, r i j C LP f K, K, K, 1 c 1 c 1 c GEOMETRY,... Modelling Connections Behaviour with Finite Element Modelling (e.g. Export) Losses Optimisation Model Design for nano-/bio materials & products Linking product (car) design and Liberation Performance (LP) via fundamental product properties to the losses to the environment in the dynamic Design for environment model. This model also uses an Optimization model for recycling based on physics, thermodynamics and chemistry of the separation technology. No MFA, LCA, SFA model can do this, therefore making the use of these models in Design for Recycling obsolete! The losses in the block left interact dynamically with the environment and are hence the link to natural cycles such as water. This dynamic link is the other innovative part of the proposed approach, linking dynamically industrial and natural systems. This has never been done i.e. linking the Physics of a car design to losses to nature fundamentally at Endof-Life. ELV input - y m,p,l 0 Dismantled materials - z m,p,l Dismantling 1 i=1 Spare parts - x m,p,l 1 ELV - y m,p,l 1 Shredding i=2 Shredded ELV y m,p,l 2 Air suction i=3 ASR light - x m,p,l 3 Optimization Model Model Parameters Separation is a function of physics and thermodynamics Unit operation = i Elements/materials = k Major Element = m Particle size classes p Liberation classes l Structural coefficients = i, i, i, i Material strength properties Shredded y m,p,l 3 Waste fraction NF 1 z m,p,l y m,p,l 7 Al fraction 6 Non- Magnetic Eddy y m,p,l Mixer 1 ferrous 1 Mix fraction NF 1 x m,p,l 7 5 separation X X i=6 current i=7 NF i=4 i=5 Al fraction NF 1 y m,p,l y m,p,l 4 Mixer 3 10 y m,p,l 7 NF fraction Waste z m,p,l i=10 4 x m,p,l 5 y m,p,l 8 Nonferrous 2 y m,p,l Ferrous x m,p,l i=8 9 4 i=9 Steel y k 14 Waste fraction - z m,p,l Al fraction NF 2 X Mixer 2 Steel Waste fraction 9 Slag x k plant 14 z m,p,l 5 Landfill/ i=14 Flue dust z k 14 X Mixer 4 Incineration i=12 i=15 Mix fraction NF 2 x m,p,l 9 Alloy y k 11 Salt slag melting Salt slag x k 11 i=11 Flue dust z k 11 Cu plant i=13 Copper y k 13 Slag x k 13 Flue dust z k 13 Fig. 6 Linking product (car) design and Liberation Performance (LP) to the optimization of the recycling system and a dynamic Design for Environment/Design for Recycling model 1051

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