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Planning of expert systems for materials selection
Planning of Expert Systems for Materials Selection
M Chiner, Professor of Engineering Design, Dept of Mechanical Engineering and Materials, Polytechnic University, Valence 22012, Spain
Abstract
This paper shows a methodology for materials selection structured in five steps: 1 definition of design, 2 analysis of material properties, 3 screening of candidate materials, 4 evaluation and decision for optimal solution and 5 verification tests. The steps are illustrated with actual practical examples. The aim of article is to supply a plan for building expert system of materials selection integrated into a CAD.CAM system.
Introduction Materials selection should contribute to every part of the whole design process. This is because it is hardly possible to proceed very far with a genuinely innovative design without taking into account all the materials and manufacturing methods that are available for use. To select the most suitable material for a product involves two important concepts, first, materials selection should be an integral part of the design process, and, second, materials selection should be as quantitative as Possible. It is therefore necessary first to examine the nature of the design process and the way in which it is carried out. Then it is necessary to consider at rather greater extent how the selection 6f materials can be made quantitative. We choose to do this by defining and describing all of the individually important properties that materials are required to have and then categorising the useful materials in terms of these properties. Not long ago, materials selection was considered a minor part of the design process. Materials were selected
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from handbooks with limited choice and on the basis of limited property data. Today, however, that is an unacceptable approach for all but the most routine and simple design. Also much material selection is based on past experience. What worked before is a solution, but will not necessarily give the optimum. There is a wide range of materials available for the designer to choose from and a correspondingly wide range of properties. It is important to realise that although a material may be chosen mainly because it is able to satisfy a predominant requirement for one property above all others, there must always be in addition certain supplementary properties. That is, every useful material must possess a combination of properties. The desired cluster of properties will not r=ecessadly be wide-ranging and the exact combination required will depend upon the given application. A useful reduction in the initial number of candidate materials can be obtained by establishing at the outset upper and lower bounds for the various design requirements. It is agreed that every design requirement must be
MATERIALS & DESIGN Vol. 9 No. 4 JULY/AUGUST 1988
met to an acceptable degree, but that costs must inevitably increase if it is present to a greater extent than is strictly necessary. Considerable knowledge and experience are required to reject a material at this stage, because materials properties can be varied widely during manufacture and processing, and so also can costs. A material would not necessarily be rejected because it was unsatisfactory in respect to a single secondary design requirement, or even a primary one, if there were scope for amelirorating the disadvantage during design and manufacture. In modern times the development of the computer has permitted the use of more sophisticated theory in the design process. This has given the designer more confidence; he is therefore more ready either to introduce new ideas or to work closer to the margin of failure. Recently, important computerised approaches have been carried out with respect to materials I(1),(2),(5),(6),(7),(9),(10)]. Background information on engineering and design is given in references 1(12)'(13).(14)1. Mlethodoloff)"
for
materiall
far from easy. The problem is not only often made difficult by insufficient or inaccurate property data but is typically one of decision making in the face of multiple constraints without a clear-cut objective function. Moreover, materials selection, like any other aspect of engineering design, is a problem-soMng process. Therefore, the methodology of materials selection (fig 1) can be constructed in five steps: - definition of design; identification of needs. - analysis of required material properties. - screening of candidate materials with a data base. - evaluation of and decision on optimal material by methods of uni- and -multi-criteria. - verification tests to obtain reliable measures of the material in service. These steps are now explained.
DEFINITION OF DESIGN
selection
The decision-making process of materials selection may be initiated for a variety of rea~sons; several situations may arise in which the need for a decision on materials use quickly becomes a key solution. Any given situation may itself modify both the approach to the decision and the decision itself. There are three main types of situation: • innovative. The introduction of a new product, component or plant which is being produced or built for the first time. • renovative. A desire for the improvement of an existing product, or a recogniQon of overdesign where economy can be affected, which may be considered as an evolutionary change. • exigent. A problem situation, due to the faliure of components leading to rejection by customers, failure either of supplies or in, manufacturing plant, necessitating a change in material use. The creation of completely new product should commence with a clearly defined objective, derived from market research and associated cost accountancy in the case of a component for sale, and with a time scale which should allow an optimum choice to be made. For such a venture to be successful a programme for market entry in relation to the costs of development and production must be fulfilled. However, markets will change, new competitors will arise and to some extent where known, competitors may also change their approach. However, for the maximum chance of success the choice of materials will be a key decision in terms of value for money in service and the impact on the market. Also, since the choice may well control the method of fabrication, it will influence the whole production line specification involving a very large capital investment, which cannot always accommodate a subsequent change of material. It generally is not possible to realise the full potential of a new material unless the product is redesigned to exploit both the properties and the manufacturing characteristics of material, in other words, a simple sub~tution of a new material without changing the design rarely provides optimum utilisation of the material. The selection of materials on a purely rational basis is
MATERIALS & DESIGN Vol. 9 No. 4 JULY/AUGUST 1988
I_
l-
ANALYSIS OF REQUIRED MATERIAL PROPERTIES
]
DATA BASE
_ --I
MATERIAL SCREENING
EVALUATION METHODS
_J
OPTIMAL
--I MATERIAL
~
SELECTION
_
I-PM~N.T
I FABR,CAT,°N I Fig 1
Diagramof materials selection process
Definition of design An exhaustive definition of the need for the design is essential to arrive at the right choice of the optimal material of a design. The requests demanded by the specific application must be analysed to choose the optimal design material. So, it will be the material that does at minimal cost what is required by an optimal commitment among all the requests. This definition is logical as a question to raise when searching for a solution but we will see that its application is complex. At this stage we suggest s o m e requirements that would be considered in the initial definition of a design. In the following stage we
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will justi~ that all the materials do not have the same weight for the choice of the material. In the initial assessment the requirements of design can emerge as the combination of human, aesthetic, functional, economic and use needs with associated technology as a determining factor in all the cases, in addition to all aspects connected with human factors, (eg safety, ergonomy), interface man-machine-environment (noise, vibration, pollutants, etc) must be studied. The requirements to consider in relation to shape and aesthetic aspect of the product are laws of composition, high finish, coiour, texture. The functional and use factors are related to the applications of the product. The functional factor imposes technological requirements in the materials and their manufacturing such as resistance, machining, reliability. Finally, the economic factor demands market information, that is, the price at which the product will sell when there is competition, the number of units that will be sold and the cycle of life of product to be able to define the useful life time that the product should have. The same material will not be necessarily used if the practical life" of product is fixed as five or ten years; this parameter affects the properties of the material, reliability and cost. It follows that we should foresee the advances of this product, the alternatives and if it gets obsolete to adjust the requirements to the real necessities of product.
Analysis of required material properties The identification of needs and definition of design realised at the first stage is a complete study of utility in the whole process of design. The object of this second stage is to separate from the initial list of requirements obtained for the design, those that affect directly properties of material and with method of analysis that we will describe in this section to arrive at definition of critical properties of material with weighting factors. Different procedures may be used for the identification of critical properties as a function of the degree of complexity of design. Here we describe the procedures of 'domination matrix' and 'analysis of sensitivity'. The method of domination matrix leads to good results if the design is simple or if the essential nature of the product is known. The method consists in building a matrix with the properties of materials that derive from requirements of design and to determine the grade of domination of each property in the product. This matrix is constituted by coefficients a,j that indicate the degree of the domination of the property (i) relative to the property (j). If the property (i) is more significant than the property 0) for the design then au> % The coefficients a,i take values between zero and one. If a few properties have been considered then the coetfidents au ought to take the values 0.25, 0.5 and 0.75. The matrix of domination exhibit the following properties:
V i=~j
Of-a, --/- 1
(1)
aj~ ----- 1 - a U The values of auover the diagonal (i < j) indicate that the property (i) dominates over the property (j). The values of a=i under the diagonal (i > j) indicate that the property (i) is dominated by the property (j).
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For example, a u= 0.75 mean that if only the properties (i) and (j) were needed for the choice of material, then the influence of the property (i) in the design would be the 75% and the influence of the property (j) would be the 25%. The weighting factor wi for the property (i) is attained from the following expression:
~n
a~
j=l w,=
(2) n i=1
~
n
a,
j=l
where n ---- number of properties
~;n a~j = m~ = weight of the property (i)
j----1 ~n
i=1
~n
a,j = N = n.(n-1)/2
j=l
For illustrating this procedure we present now an example, in the figure 2-a) we show a lever and a rod that opens and closes the gas valve of a heater. Fig 2-b) shows the operation of the system. When the lever (grooved cylinder) turns toward the right, the rod is pushed upward through the prominence. A piston that closes and opens a vent is attached to the rod. When the rod slides over the inclined plane, it suffers an abrasion in the prominence. If we analyse the behaviour system to choose the material of the lever or of the rod, the properties that must be considered infered by the functioning of the systems are: friction coefficient, resistance of compression, hardness and cost. In Table I the matrix of domination corresponding to these properties is shown. From this matrix we obtain the weighting factor of each property affecting the product. These weights will be used afterwards in the evaluation of the candidate materials for the lever.
Analysis of sensiUoi~j This method is more rigorous and requires preanalysis of product because of variations in the properties of materials. These must correspond to" real cases of materials to be able to evaluate the implied cost. The analysis of sensitivity will show the influence that each material property exerts on the product in a quantitative way; by comparing the analysis obtained for each material in the same units we can obtain a relation of priorities. This method permits us to extract more information from the material as we will see in the stage of evaluation. Another product studied is a metal cylindrical silo made of corrugated sheet for storage of cereals. The aim of this work is to obtain the optimal design of the silo, studying geometrical dimensions as well as the materials.
MATERIALS & DESIGN Vol. 9 No. 4 JULY/AUGUST 1988
The optimisation indudes work on sensitivity analysis(3~ of all the designing variables to determine the critical variables. A program of structural analysis has been developed to know the behaviour of the silo before different hypothesis of loading, of materials properties, of joint, etc. This program procures the stress on a net of discreet points and it makes an economic evaluation about the cost of the silo from the 41 data. The outcome of the program (the cost of the silo) is represented by a plotter for each one of the designing data. Fig 3 shows one of the results obtained corresponding to the total cost of silo per volume (m 3) for different alloys of sheet with different elastic limits, E. These curves give the sensitivity of the cost with the elastic limit. The cost per volume is given in ptas/m 3 (15 = 110.29 ptas, :30 November 1987). We get from the analysis that the elastic limit is a critical property and that the optimal material is given as a function of the dimensions of the silo.
Screening of candidate materials This stage consists of the development of a list of candidate materials formed from those that fulfil the properties defined in the previous stage with an admissible range of variation. Because of the great diversity of materials that have arisen in the past years the help of the computer in this job is growing stronger. The computer provides a quick answer for the search of materials to examine their properties through a wide data base in which the properties of a wide range of materials have been previously introduced. A data base that can be effective in the selection of materials must contain at least one hundred different
rig 2-a) Gas valve assembly
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Fig 2-b) Detail of operation. On the left the developed outline of the lever. Designation: I-lever 2.rod 3-prominence
MATERIALS & DESIGN Vol. 9 No. 4 JULY/AUGUST 1988
198
Table I Weighting factors, w, derived off the matrix of domination of properties
optimal material for the design. Depending on its complexity we can fall back on uni-or multi-criteria selection methods.
Uni-criteria methods
dominant r.~
4
r-
E
dominated
"~o ,._
friction
~ 1
hardness
0
resistance
0
cost
0
o o
t-
1
Unicriteria methods are most appropriate when there is a critical property clearly dominates over the others. Uni-criteria methods of wider application are those that take the cost of material as the most critical property. It seems logical to use as a reference factor the cost of the material and refer it to the most critical property.
mi
m,=z~aii j=l
wi= N N=6
1
1
"--" 3
0.5
1
o
-*
1
0.1 6
--*
1
0.16
--~
1
0.16
o
It is more suitable to consider the total life cycle of the product than to consider t h e initial inversion. This allows us to consider the cost of material plus the cost of manufacturing and installation plus the cost of operation and maintenance. Since material cost is directly related to the weight of material the determination of cost/property relation b e c o m e s a question of determining the structural equivalency of different materials. Typical problems are determination of the relative weight of each material for equal strength and the relative weight for equal stiffness. To illustrate the development of a cost/property ratio, consider the simplest case of the yielding of a bar in uniaxial tension as follows.
properties and more than one thousand materials. Besides it must be user-friendly and allow systems of graphic representation. Recently in Sweden an important data base for materials has been developed('). A data base is the first step in building expert system of materials. In this article we will c o m m e n t on other aspects that must include both a knowledge and data base.
Evaluation and decision of optimal material Finally a m o n g the candidate materials we must select the
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199
I
15
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20
25
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Sensitivity analysis of elastic limit, E (Kg/cm'), for different alloys. ASTM designation.
MATERIALS & DESIGN Vol. 9 No. 4 JULY/ AUG UST 1988
then:
where W.W2,...,Wn are weighting factors
Let:
cr~ P A ~, crb
= working stress = tensile yield strength = axial force
fl,f2....
Y,,Yb.... Y,
s e c t i o n area
= stress materials a,b
D°,D~ = diameter bar a,b
p W V
ma, mb
,C.,C~
= density = weight = volume ---- price per unit mass a,b = cost/strength elastic limit =
P A
,% e ~
(3) =
Ab • o'b
D.2 . ¢ .
=
D~-~(4)
m
(5)
D. /r
W=p
V=p
d
D~L
(6)
b
Wb
o'.
Wa
Orb ,
(7) Ca = W~rn. and Cb = Wd'nb Cb
or,p P'nb
Ca
(rb p.ma
(8) (9)
For this easy example it is possible to obtain the analytic cost/property relation. In other more complex designs this relation can be obtained in an implicit way by means of a computer program and finally we can represent graphically the results to make it easier to interpret. This procedure was used in the silo (fig 3) using the analysis of sensitivity facing the cost as a criterion for the selection of material. Multi-criteria methods Muiti-cdteda methods consider various factors for materiai selection with weighting factors that should have been obtained off the matrix of domination in stage (ii). The multi-criteria methods are the most used because the majority of the designs in practice demand that material must satisfy various requiremerits with similar priorities. A multi-criteria planning demands a rigorous formulation of multffactor objective function, F, to optimise: F -- w,f,(y,,y~,..)+w2f2(y,,y,..)+...+W,fn(y,,yb..)
MATERIALS & DESIGN Vol. 9 No. 4 JULY/AUGUST 1988
fn
(10)
are factors of design are variables of design, eg properties of material, dimensions, etc.
In this method it may be complicated to find the analytical function fo of some critical factor of design. The expression of the objective function is often a computer program that evaluates the cost from predimensioning of product. One can proceed by several ways to obtain the analytical expression that represents the factor fo, according to the available information and the degree of knowledge of the problem. F'u'stone can obtain analytical expression from a range of values obtained by experimental measures of trials performed modifying the variables associated with factor f, for several conditions and adjusting the points to an equation by regression. In the second place another way is to obtain an expression of L, dependent on a mathematical model from a computer program that integrates all the information associated to the factor fo. This second method is more complex and needs some intermediate mathematical equations which express the relations between the variables, in the application of this method to the design of silo (4)the program BMDP (Library mathematical and statistics of Fortran programme) (n) was used obtaining the mathematical expression of the cost functions by a statistical collection of points obtained of the program of analysis. For the resolution of the problem of optimisation the program SUMT (Sequential Unconstrained Minimisation Technique) was used obtaining the optimal materials for the silo and the optima] geometric dimensions. Finally another multi-criteria evaluation method consists of an adaptation of decision theory to obtain the value of the matedais. This is the scaled properties method. This method consists of building a matrix of scaled properties of materials. Since different properties have widely different numedcai values, each property must be so scaled that the largest value does not exceed 100. scaled property = value of property largest value under consideration x 100
11 1
(12) For properties such that it is more desirable to have ~ow values, eg., density, corrosion, wear, cost, the scale factor is formulated: scaled property = lowest value under consideration value of property
x 100
(12)
In this method the evaluation of the materials is carded out using the following expression:
Value =}~n scaled property x weighting factor
(13)
Table I! shows the matrix of scaled properties for the gas valve example. Low values for both the coefficient
200
Table il Matrix of scaled properties and values of materials for the rod of the gas ualue
property Coefficient of friction
Hardness
wl = 0.5
w2 = 0.16
Resistance to ** compressive stress w3 -- 0.16
Cost ***
value
w4 = 0.16
4 0.16
0.16 material
P1
S1 - - ~
S3 " - ~
S2--~
P1
P3
2000
P,
115 R 100
1600
80
615
P2
115
Polyamide PA 66 + GF 3 0 "
0.16
Therm. polyester PETP + GF 35
0.2
80
100 M
86.95
2000
100
Acetalic resin POM + GF 30
0.3
53
95 M
82.65
1500
75
* ** ***
100
GF 30 = glass fibre 30% Compressive stress Kg/cm 2 Cost ptas/kg
[]
S 4 --
570
P,
92.68
= w i x Si i=1
93.63
570 100
85.91
590
67.06
95.9
weighting factor of the matrix of domination, w~ (see Table I) P1, P2,..value of the property $1, $2,.. scaled property (x 100)
of friction and the cost are desirable. These scaled properties have been obtained with the expression<12). For the other properties, (hardness and resistance to compressive stress) expression<11>has been used. From the values obtained it is advisable to propose the polyamide PA66+GF30 for this application whilst lacking result of verification tests.
Verification tests The aim of this step is to obtain both experimentally the key material properties for the selected material and statistically reliable measures of the material performance under the specific conditions expected to be encountered in service and to find likely failure. The causes of failure in service can be from errors in design, inherent defects in a material properly selected, defects introduced during fabrication or deterioration in service. It is vital to know every feature of a material which in service could become a critical defect; the ability to inspect and evaluate such defects within the whole economic framework of the material use is also essential. Also, defects introduced during fabrication, defects in fastening and joining, poorly controlled heat treatment giving quench cracks and internal stresses, poor machining, incorrect assembly and misalignment producing unexpected stress levels, may result in subsequent failure in service. Ideally, the original design will anticipate and incorporate the effects of the fabrication route, on which the design may even depend, but the degree of modification of the intrinsic mechanical and chemical properties may sometimes go beyond that originally envisaged, wholly or locally. This is why field testing of a realistic prototype is so desirable. Finally, the resistance to environmental conditions of
201
0.16
chemical attack or corrosion and wear, or the stability of the microstructure on which mechanical properties depend, will have been part of the initial design context, but unusual conditions are sometimes encountered which give rise to a change in performance and premature failure. On the left side of the figure 4 we show a guide abraded in test laboratory after 10000 cycles of operation. The guide material was polyamide 66+GF30. In other tests carried out with acetal resin -I-GF30 the guide became useless after 5000 cycles: (10000 cycles of operation is equivalent to twelve years in service.) Since the useful life time in gas heater is approximately ten years the polyamide 66 is more appropriate for this application.
Building an expert system After analysing the philosophy of material selection in the previous sections, where each stage of process has already been studied, in this last section we consider on planning expert system integrated into CAD-CAM systems that permit the choice of material for each piece of design. Since for complex designs, choice of material and predimensioned are usually obtained in parallel by an iterative stage of pre-analysis, the need for integration of the expert system in CAD-CAM is vital. Therefore the choice of material must be integrated in the process of design and must be fedback with the results of design so that several dimensions may be combined with different materials to evaluate all solutions. Development of an expert system comprises two main phases. The first phase involves identifying and conceptualising the problem. Identification includes selecting knowledge sources and clearly defining the problem.
MATERIALS & DESIGN Vol. 9 No. 4 JULY/AUGUST 1988
F g4
Wear in test/aboratory at the end of the rod when it pushes against the lever. 4.a) Initial rod 4-b) Abraded rod after 10000 cycles of operation
Conceptualisation includes uncovering the key concepts and relations needed to characterise the problem. The second phase then deals with the formalisation, implementation and testing of an appropriate architecture for the system, including constant reformulation of concepts, redesign of representations and refinement of the implemented system; revision results from the expert's criticisms and suggestions for improving the system's behaviour. Much time is spent in the latter phase as the system evolves but accurately defining the problem and carefully attending to the task types and strategies in the initial phase can dramatically affect the outcome. For problem identification, it is important to answer the following questions: • what class of problems will the expert system be expected to solve? • how can these problems be charactedsed or defined? • what are important subproblems and partitioning of tasks? • what are the data? • what are important terms and their interrelations? • what does a solution look like and what concepts are used in it? • what is the nature and extent of relevant knowledge that underlies the human solutions? • what situations are likely to impede solutions? • how will these impediments affect an expert system? The key concepts and relations, already mentioned during the identification stage, are made explicit during the conceptualisation stage. The following questions need to be answered before proceeding with the conceptualisation process:
MATERIALS & DESIGNVol. 9 No. 4 JULY/AUGUST 1988
• • • • •
what types of data are available? what is given and what is inferred? do the subtasks have names? do the strategies have names? are there identifiable partial hypotheses that are commonly used? • how are the objects in the domain related? • can a hierarchy and labelled casual relations, set inclusion, part~vhole relations, etc be put in a diagram? • what processes are involved in problem solution? • what are the constraints on these processes? • what is the information flow? • can the knowledge needed for solving a problem be identified and separated from that used to justify a solution? As far as the materials selection is concerned the knowledge base besides a data base of materials properties must contain data about reliability and failure in service for different applications and different dimensions. It includes the following categories: - types of materials - typical desirable properties - main applications - priorities a m o n g properties admissible bounds of variation This information must be brought up-to-date and amplified in the course of time with a dynamic knowledge base storing results of designs and verification tests of prototypes. The key concepts in materials selection have been explained in the first stages of methodology developed in the foregoing sections. -
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The inference process of expert systems must contain the evaluation and decision methods that have already been described in the selection process to make a quantitative decision. The formalisation process involves mapping the key concepts, subproblems and information flow characteristics isolated during conceptualisation into more formal representations. A variety of languages and tools can be used to build the expert system. One of the most variable c h a r a ~ " s is the way they search for solutions. The architecture of expert system of materials selection integrated in CAD-CAM systems must group the following abilities: • abstractions for each problem are composed from terms to fit the structure of the problem • during the problem-soMng process, these concepts represent partial solutions that are combined and evaluated • the concepts are assigned fixed and predetermined abstraction levels • the problem solution proceeds fiom the top downward, that is, from the most abstract to the most specific • solutions to the problem are completed at one level before moving down to the next more specific level • within each level sub-problems are solved in a problem-independent order • to know there is enough information to make a decision • to suspend problem-solving activity on a subproblem when the information is not available • to move between subproblems, restarting work as information becomes available • to combine information from different subproblems. Finally the expert system of materials selection must be graphically displayed on display units to represent the development of problem, making the pursuit and the interpretation easier while the time for errors detection is decreased.
203
Conclusion Modem materials for high-grade applications are often extremely complex and it is easy to overlook the significance of certain service conditions in relation to a particular material. The selection of the suitable material is a complex process that demands the management of a great amount of information about the materials properties and there are often several solutions for a specified application. The computer is a very useful aid. An expert system of materials selection integrated in CAD-CAM system is very necessary for engineering design. References (1)
Erik Ullman, Development of a National Materials Data Base in Sweden. Materials & Design Vol 8 No 6 (1987) p 346 (2) G L Bata, Computer Integrated Materials Processing - A Generic Application of CAD-CA/~ hlatedals & Design Vol 8 No 4 (1987) p 220 (3) M Chiner, Variables crlticas en el disan~o de silos mediante anAlisisde sensibilidad.VI Congreso Nacional Ingenieria Mec~nica 1987 (4) M Chiner, Criterios de optimizaci6n para el disen~o de silos mediante prograrnaci6n matem~.ica no lineal. Valencia 1987 (5) E J Wright, F_xpertSystems to aid Design Against Corrosion Materials & Design Vol 8 No 3 (1987) p 156 (6) Roll Sandstrom, An approach to systematic materials selection Materials & Design Vol 6 (1985) p 328 (7) Bernard Williams, Computer Program for Ferrous PM Materials Selection Materials & Design Vol 8 No 2 (1987) p 89 (8) h~rtini-Wedensky, Selection of Materials by Computer - What is Missing? h~tedals & Design Vol 6 No 3 (1985) p 134 (9) Jean-YvesDutour, Howto Choose Engineering Rastics Materials& Design Vol 7 No 1 (1986) p 14 (10) Roll SandsO'om,The Assessment and Evaluation of Property Data for Materials Selection purposes. Materials & Design Vol 7 No 4 1986 p 198 (11) W J Dixon, BMDP Statistical Software UCLA Report California 1981 (12) European Convention for Constructional Steelwork, European Recommendations for the Design of profiled sheeting. ECCS-TC71983, London. (13) M B Peterson & W Winer, Wear Con~ol Handbook. American Society of Mechanical Engineers, New York 1980. (14) T T Woodson, Introduction to Engineering Design McGraw Hill Book Company New York, 1966
MATERIALS & DESIGN Vot. 9 No. 4 JULY/AUGUST 1988
M Chiner, Professor of Engineering Design, Dept of Mechanical Engineering and Materials, Polytechnic University, Valence 22012, Spain
Abstract
This paper shows a methodology for materials selection structured in five steps: 1 definition of design, 2 analysis of material properties, 3 screening of candidate materials, 4 evaluation and decision for optimal solution and 5 verification tests. The steps are illustrated with actual practical examples. The aim of article is to supply a plan for building expert system of materials selection integrated into a CAD.CAM system.
Introduction Materials selection should contribute to every part of the whole design process. This is because it is hardly possible to proceed very far with a genuinely innovative design without taking into account all the materials and manufacturing methods that are available for use. To select the most suitable material for a product involves two important concepts, first, materials selection should be an integral part of the design process, and, second, materials selection should be as quantitative as Possible. It is therefore necessary first to examine the nature of the design process and the way in which it is carried out. Then it is necessary to consider at rather greater extent how the selection 6f materials can be made quantitative. We choose to do this by defining and describing all of the individually important properties that materials are required to have and then categorising the useful materials in terms of these properties. Not long ago, materials selection was considered a minor part of the design process. Materials were selected
195
from handbooks with limited choice and on the basis of limited property data. Today, however, that is an unacceptable approach for all but the most routine and simple design. Also much material selection is based on past experience. What worked before is a solution, but will not necessarily give the optimum. There is a wide range of materials available for the designer to choose from and a correspondingly wide range of properties. It is important to realise that although a material may be chosen mainly because it is able to satisfy a predominant requirement for one property above all others, there must always be in addition certain supplementary properties. That is, every useful material must possess a combination of properties. The desired cluster of properties will not r=ecessadly be wide-ranging and the exact combination required will depend upon the given application. A useful reduction in the initial number of candidate materials can be obtained by establishing at the outset upper and lower bounds for the various design requirements. It is agreed that every design requirement must be
MATERIALS & DESIGN Vol. 9 No. 4 JULY/AUGUST 1988
met to an acceptable degree, but that costs must inevitably increase if it is present to a greater extent than is strictly necessary. Considerable knowledge and experience are required to reject a material at this stage, because materials properties can be varied widely during manufacture and processing, and so also can costs. A material would not necessarily be rejected because it was unsatisfactory in respect to a single secondary design requirement, or even a primary one, if there were scope for amelirorating the disadvantage during design and manufacture. In modern times the development of the computer has permitted the use of more sophisticated theory in the design process. This has given the designer more confidence; he is therefore more ready either to introduce new ideas or to work closer to the margin of failure. Recently, important computerised approaches have been carried out with respect to materials I(1),(2),(5),(6),(7),(9),(10)]. Background information on engineering and design is given in references 1(12)'(13).(14)1. Mlethodoloff)"
for
materiall
far from easy. The problem is not only often made difficult by insufficient or inaccurate property data but is typically one of decision making in the face of multiple constraints without a clear-cut objective function. Moreover, materials selection, like any other aspect of engineering design, is a problem-soMng process. Therefore, the methodology of materials selection (fig 1) can be constructed in five steps: - definition of design; identification of needs. - analysis of required material properties. - screening of candidate materials with a data base. - evaluation of and decision on optimal material by methods of uni- and -multi-criteria. - verification tests to obtain reliable measures of the material in service. These steps are now explained.
DEFINITION OF DESIGN
selection
The decision-making process of materials selection may be initiated for a variety of rea~sons; several situations may arise in which the need for a decision on materials use quickly becomes a key solution. Any given situation may itself modify both the approach to the decision and the decision itself. There are three main types of situation: • innovative. The introduction of a new product, component or plant which is being produced or built for the first time. • renovative. A desire for the improvement of an existing product, or a recogniQon of overdesign where economy can be affected, which may be considered as an evolutionary change. • exigent. A problem situation, due to the faliure of components leading to rejection by customers, failure either of supplies or in, manufacturing plant, necessitating a change in material use. The creation of completely new product should commence with a clearly defined objective, derived from market research and associated cost accountancy in the case of a component for sale, and with a time scale which should allow an optimum choice to be made. For such a venture to be successful a programme for market entry in relation to the costs of development and production must be fulfilled. However, markets will change, new competitors will arise and to some extent where known, competitors may also change their approach. However, for the maximum chance of success the choice of materials will be a key decision in terms of value for money in service and the impact on the market. Also, since the choice may well control the method of fabrication, it will influence the whole production line specification involving a very large capital investment, which cannot always accommodate a subsequent change of material. It generally is not possible to realise the full potential of a new material unless the product is redesigned to exploit both the properties and the manufacturing characteristics of material, in other words, a simple sub~tution of a new material without changing the design rarely provides optimum utilisation of the material. The selection of materials on a purely rational basis is
MATERIALS & DESIGN Vol. 9 No. 4 JULY/AUGUST 1988
I_
l-
ANALYSIS OF REQUIRED MATERIAL PROPERTIES
]
DATA BASE
_ --I
MATERIAL SCREENING
EVALUATION METHODS
_J
OPTIMAL
--I MATERIAL
~
SELECTION
_
I-PM~N.T
I FABR,CAT,°N I Fig 1
Diagramof materials selection process
Definition of design An exhaustive definition of the need for the design is essential to arrive at the right choice of the optimal material of a design. The requests demanded by the specific application must be analysed to choose the optimal design material. So, it will be the material that does at minimal cost what is required by an optimal commitment among all the requests. This definition is logical as a question to raise when searching for a solution but we will see that its application is complex. At this stage we suggest s o m e requirements that would be considered in the initial definition of a design. In the following stage we
196
will justi~ that all the materials do not have the same weight for the choice of the material. In the initial assessment the requirements of design can emerge as the combination of human, aesthetic, functional, economic and use needs with associated technology as a determining factor in all the cases, in addition to all aspects connected with human factors, (eg safety, ergonomy), interface man-machine-environment (noise, vibration, pollutants, etc) must be studied. The requirements to consider in relation to shape and aesthetic aspect of the product are laws of composition, high finish, coiour, texture. The functional and use factors are related to the applications of the product. The functional factor imposes technological requirements in the materials and their manufacturing such as resistance, machining, reliability. Finally, the economic factor demands market information, that is, the price at which the product will sell when there is competition, the number of units that will be sold and the cycle of life of product to be able to define the useful life time that the product should have. The same material will not be necessarily used if the practical life" of product is fixed as five or ten years; this parameter affects the properties of the material, reliability and cost. It follows that we should foresee the advances of this product, the alternatives and if it gets obsolete to adjust the requirements to the real necessities of product.
Analysis of required material properties The identification of needs and definition of design realised at the first stage is a complete study of utility in the whole process of design. The object of this second stage is to separate from the initial list of requirements obtained for the design, those that affect directly properties of material and with method of analysis that we will describe in this section to arrive at definition of critical properties of material with weighting factors. Different procedures may be used for the identification of critical properties as a function of the degree of complexity of design. Here we describe the procedures of 'domination matrix' and 'analysis of sensitivity'. The method of domination matrix leads to good results if the design is simple or if the essential nature of the product is known. The method consists in building a matrix with the properties of materials that derive from requirements of design and to determine the grade of domination of each property in the product. This matrix is constituted by coefficients a,j that indicate the degree of the domination of the property (i) relative to the property (j). If the property (i) is more significant than the property 0) for the design then au> % The coefficients a,i take values between zero and one. If a few properties have been considered then the coetfidents au ought to take the values 0.25, 0.5 and 0.75. The matrix of domination exhibit the following properties:
V i=~j
Of-a, --/- 1
(1)
aj~ ----- 1 - a U The values of auover the diagonal (i < j) indicate that the property (i) dominates over the property (j). The values of a=i under the diagonal (i > j) indicate that the property (i) is dominated by the property (j).
197
For example, a u= 0.75 mean that if only the properties (i) and (j) were needed for the choice of material, then the influence of the property (i) in the design would be the 75% and the influence of the property (j) would be the 25%. The weighting factor wi for the property (i) is attained from the following expression:
~n
a~
j=l w,=
(2) n i=1
~
n
a,
j=l
where n ---- number of properties
~;n a~j = m~ = weight of the property (i)
j----1 ~n
i=1
~n
a,j = N = n.(n-1)/2
j=l
For illustrating this procedure we present now an example, in the figure 2-a) we show a lever and a rod that opens and closes the gas valve of a heater. Fig 2-b) shows the operation of the system. When the lever (grooved cylinder) turns toward the right, the rod is pushed upward through the prominence. A piston that closes and opens a vent is attached to the rod. When the rod slides over the inclined plane, it suffers an abrasion in the prominence. If we analyse the behaviour system to choose the material of the lever or of the rod, the properties that must be considered infered by the functioning of the systems are: friction coefficient, resistance of compression, hardness and cost. In Table I the matrix of domination corresponding to these properties is shown. From this matrix we obtain the weighting factor of each property affecting the product. These weights will be used afterwards in the evaluation of the candidate materials for the lever.
Analysis of sensiUoi~j This method is more rigorous and requires preanalysis of product because of variations in the properties of materials. These must correspond to" real cases of materials to be able to evaluate the implied cost. The analysis of sensitivity will show the influence that each material property exerts on the product in a quantitative way; by comparing the analysis obtained for each material in the same units we can obtain a relation of priorities. This method permits us to extract more information from the material as we will see in the stage of evaluation. Another product studied is a metal cylindrical silo made of corrugated sheet for storage of cereals. The aim of this work is to obtain the optimal design of the silo, studying geometrical dimensions as well as the materials.
MATERIALS & DESIGN Vol. 9 No. 4 JULY/AUGUST 1988
The optimisation indudes work on sensitivity analysis(3~ of all the designing variables to determine the critical variables. A program of structural analysis has been developed to know the behaviour of the silo before different hypothesis of loading, of materials properties, of joint, etc. This program procures the stress on a net of discreet points and it makes an economic evaluation about the cost of the silo from the 41 data. The outcome of the program (the cost of the silo) is represented by a plotter for each one of the designing data. Fig 3 shows one of the results obtained corresponding to the total cost of silo per volume (m 3) for different alloys of sheet with different elastic limits, E. These curves give the sensitivity of the cost with the elastic limit. The cost per volume is given in ptas/m 3 (15 = 110.29 ptas, :30 November 1987). We get from the analysis that the elastic limit is a critical property and that the optimal material is given as a function of the dimensions of the silo.
Screening of candidate materials This stage consists of the development of a list of candidate materials formed from those that fulfil the properties defined in the previous stage with an admissible range of variation. Because of the great diversity of materials that have arisen in the past years the help of the computer in this job is growing stronger. The computer provides a quick answer for the search of materials to examine their properties through a wide data base in which the properties of a wide range of materials have been previously introduced. A data base that can be effective in the selection of materials must contain at least one hundred different
rig 2-a) Gas valve assembly
rtn /
{
i
\
\\.
I
I ! J i i I
I
!, L
I
Fig 2-b) Detail of operation. On the left the developed outline of the lever. Designation: I-lever 2.rod 3-prominence
MATERIALS & DESIGN Vol. 9 No. 4 JULY/AUGUST 1988
198
Table I Weighting factors, w, derived off the matrix of domination of properties
optimal material for the design. Depending on its complexity we can fall back on uni-or multi-criteria selection methods.
Uni-criteria methods
dominant r.~
4
r-
E
dominated
"~o ,._
friction
~ 1
hardness
0
resistance
0
cost
0
o o
t-
1
Unicriteria methods are most appropriate when there is a critical property clearly dominates over the others. Uni-criteria methods of wider application are those that take the cost of material as the most critical property. It seems logical to use as a reference factor the cost of the material and refer it to the most critical property.
mi
m,=z~aii j=l
wi= N N=6
1
1
"--" 3
0.5
1
o
-*
1
0.1 6
--*
1
0.16
--~
1
0.16
o
It is more suitable to consider the total life cycle of the product than to consider t h e initial inversion. This allows us to consider the cost of material plus the cost of manufacturing and installation plus the cost of operation and maintenance. Since material cost is directly related to the weight of material the determination of cost/property relation b e c o m e s a question of determining the structural equivalency of different materials. Typical problems are determination of the relative weight of each material for equal strength and the relative weight for equal stiffness. To illustrate the development of a cost/property ratio, consider the simplest case of the yielding of a bar in uniaxial tension as follows.
properties and more than one thousand materials. Besides it must be user-friendly and allow systems of graphic representation. Recently in Sweden an important data base for materials has been developed('). A data base is the first step in building expert system of materials. In this article we will c o m m e n t on other aspects that must include both a knowledge and data base.
Evaluation and decision of optimal material Finally a m o n g the candidate materials we must select the
HLBSTI
6000
C
LIHIT
® ®
5500
\, 4500
/ \
E-3600
(~)
E-5500
Q
E-2000
/
/
/
03 ,~
A167
(~)
5000
E-2200 kg/cm 2
.
4000
\ j~
3500
© U
3000
.~--
2500
0
A36
f" i
l
/
2000
O A242
/
® A51,,
1500
1OOO
I
0
I
5
I
10
OlnMEITER
Fig 3
199
I
15
I
20
25
30
M
Sensitivity analysis of elastic limit, E (Kg/cm'), for different alloys. ASTM designation.
MATERIALS & DESIGN Vol. 9 No. 4 JULY/ AUG UST 1988
then:
where W.W2,...,Wn are weighting factors
Let:
cr~ P A ~, crb
= working stress = tensile yield strength = axial force
fl,f2....
Y,,Yb.... Y,
s e c t i o n area
= stress materials a,b
D°,D~ = diameter bar a,b
p W V
ma, mb
,C.,C~
= density = weight = volume ---- price per unit mass a,b = cost/strength elastic limit =
P A
,% e ~
(3) =
Ab • o'b
D.2 . ¢ .
=
D~-~(4)
m
(5)
D. /r
W=p
V=p
d
D~L
(6)
b
Wb
o'.
Wa
Orb ,
(7) Ca = W~rn. and Cb = Wd'nb Cb
or,p P'nb
Ca
(rb p.ma
(8) (9)
For this easy example it is possible to obtain the analytic cost/property relation. In other more complex designs this relation can be obtained in an implicit way by means of a computer program and finally we can represent graphically the results to make it easier to interpret. This procedure was used in the silo (fig 3) using the analysis of sensitivity facing the cost as a criterion for the selection of material. Multi-criteria methods Muiti-cdteda methods consider various factors for materiai selection with weighting factors that should have been obtained off the matrix of domination in stage (ii). The multi-criteria methods are the most used because the majority of the designs in practice demand that material must satisfy various requiremerits with similar priorities. A multi-criteria planning demands a rigorous formulation of multffactor objective function, F, to optimise: F -- w,f,(y,,y~,..)+w2f2(y,,y,..)+...+W,fn(y,,yb..)
MATERIALS & DESIGN Vol. 9 No. 4 JULY/AUGUST 1988
fn
(10)
are factors of design are variables of design, eg properties of material, dimensions, etc.
In this method it may be complicated to find the analytical function fo of some critical factor of design. The expression of the objective function is often a computer program that evaluates the cost from predimensioning of product. One can proceed by several ways to obtain the analytical expression that represents the factor fo, according to the available information and the degree of knowledge of the problem. F'u'stone can obtain analytical expression from a range of values obtained by experimental measures of trials performed modifying the variables associated with factor f, for several conditions and adjusting the points to an equation by regression. In the second place another way is to obtain an expression of L, dependent on a mathematical model from a computer program that integrates all the information associated to the factor fo. This second method is more complex and needs some intermediate mathematical equations which express the relations between the variables, in the application of this method to the design of silo (4)the program BMDP (Library mathematical and statistics of Fortran programme) (n) was used obtaining the mathematical expression of the cost functions by a statistical collection of points obtained of the program of analysis. For the resolution of the problem of optimisation the program SUMT (Sequential Unconstrained Minimisation Technique) was used obtaining the optimal materials for the silo and the optima] geometric dimensions. Finally another multi-criteria evaluation method consists of an adaptation of decision theory to obtain the value of the matedais. This is the scaled properties method. This method consists of building a matrix of scaled properties of materials. Since different properties have widely different numedcai values, each property must be so scaled that the largest value does not exceed 100. scaled property = value of property largest value under consideration x 100
11 1
(12) For properties such that it is more desirable to have ~ow values, eg., density, corrosion, wear, cost, the scale factor is formulated: scaled property = lowest value under consideration value of property
x 100
(12)
In this method the evaluation of the materials is carded out using the following expression:
Value =}~n scaled property x weighting factor
(13)
Table I! shows the matrix of scaled properties for the gas valve example. Low values for both the coefficient
200
Table il Matrix of scaled properties and values of materials for the rod of the gas ualue
property Coefficient of friction
Hardness
wl = 0.5
w2 = 0.16
Resistance to ** compressive stress w3 -- 0.16
Cost ***
value
w4 = 0.16
4 0.16
0.16 material
P1
S1 - - ~
S3 " - ~
S2--~
P1
P3
2000
P,
115 R 100
1600
80
615
P2
115
Polyamide PA 66 + GF 3 0 "
0.16
Therm. polyester PETP + GF 35
0.2
80
100 M
86.95
2000
100
Acetalic resin POM + GF 30
0.3
53
95 M
82.65
1500
75
* ** ***
100
GF 30 = glass fibre 30% Compressive stress Kg/cm 2 Cost ptas/kg
[]
S 4 --
570
P,
92.68
= w i x Si i=1
93.63
570 100
85.91
590
67.06
95.9
weighting factor of the matrix of domination, w~ (see Table I) P1, P2,..value of the property $1, $2,.. scaled property (x 100)
of friction and the cost are desirable. These scaled properties have been obtained with the expression<12). For the other properties, (hardness and resistance to compressive stress) expression<11>has been used. From the values obtained it is advisable to propose the polyamide PA66+GF30 for this application whilst lacking result of verification tests.
Verification tests The aim of this step is to obtain both experimentally the key material properties for the selected material and statistically reliable measures of the material performance under the specific conditions expected to be encountered in service and to find likely failure. The causes of failure in service can be from errors in design, inherent defects in a material properly selected, defects introduced during fabrication or deterioration in service. It is vital to know every feature of a material which in service could become a critical defect; the ability to inspect and evaluate such defects within the whole economic framework of the material use is also essential. Also, defects introduced during fabrication, defects in fastening and joining, poorly controlled heat treatment giving quench cracks and internal stresses, poor machining, incorrect assembly and misalignment producing unexpected stress levels, may result in subsequent failure in service. Ideally, the original design will anticipate and incorporate the effects of the fabrication route, on which the design may even depend, but the degree of modification of the intrinsic mechanical and chemical properties may sometimes go beyond that originally envisaged, wholly or locally. This is why field testing of a realistic prototype is so desirable. Finally, the resistance to environmental conditions of
201
0.16
chemical attack or corrosion and wear, or the stability of the microstructure on which mechanical properties depend, will have been part of the initial design context, but unusual conditions are sometimes encountered which give rise to a change in performance and premature failure. On the left side of the figure 4 we show a guide abraded in test laboratory after 10000 cycles of operation. The guide material was polyamide 66+GF30. In other tests carried out with acetal resin -I-GF30 the guide became useless after 5000 cycles: (10000 cycles of operation is equivalent to twelve years in service.) Since the useful life time in gas heater is approximately ten years the polyamide 66 is more appropriate for this application.
Building an expert system After analysing the philosophy of material selection in the previous sections, where each stage of process has already been studied, in this last section we consider on planning expert system integrated into CAD-CAM systems that permit the choice of material for each piece of design. Since for complex designs, choice of material and predimensioned are usually obtained in parallel by an iterative stage of pre-analysis, the need for integration of the expert system in CAD-CAM is vital. Therefore the choice of material must be integrated in the process of design and must be fedback with the results of design so that several dimensions may be combined with different materials to evaluate all solutions. Development of an expert system comprises two main phases. The first phase involves identifying and conceptualising the problem. Identification includes selecting knowledge sources and clearly defining the problem.
MATERIALS & DESIGN Vol. 9 No. 4 JULY/AUGUST 1988
F g4
Wear in test/aboratory at the end of the rod when it pushes against the lever. 4.a) Initial rod 4-b) Abraded rod after 10000 cycles of operation
Conceptualisation includes uncovering the key concepts and relations needed to characterise the problem. The second phase then deals with the formalisation, implementation and testing of an appropriate architecture for the system, including constant reformulation of concepts, redesign of representations and refinement of the implemented system; revision results from the expert's criticisms and suggestions for improving the system's behaviour. Much time is spent in the latter phase as the system evolves but accurately defining the problem and carefully attending to the task types and strategies in the initial phase can dramatically affect the outcome. For problem identification, it is important to answer the following questions: • what class of problems will the expert system be expected to solve? • how can these problems be charactedsed or defined? • what are important subproblems and partitioning of tasks? • what are the data? • what are important terms and their interrelations? • what does a solution look like and what concepts are used in it? • what is the nature and extent of relevant knowledge that underlies the human solutions? • what situations are likely to impede solutions? • how will these impediments affect an expert system? The key concepts and relations, already mentioned during the identification stage, are made explicit during the conceptualisation stage. The following questions need to be answered before proceeding with the conceptualisation process:
MATERIALS & DESIGNVol. 9 No. 4 JULY/AUGUST 1988
• • • • •
what types of data are available? what is given and what is inferred? do the subtasks have names? do the strategies have names? are there identifiable partial hypotheses that are commonly used? • how are the objects in the domain related? • can a hierarchy and labelled casual relations, set inclusion, part~vhole relations, etc be put in a diagram? • what processes are involved in problem solution? • what are the constraints on these processes? • what is the information flow? • can the knowledge needed for solving a problem be identified and separated from that used to justify a solution? As far as the materials selection is concerned the knowledge base besides a data base of materials properties must contain data about reliability and failure in service for different applications and different dimensions. It includes the following categories: - types of materials - typical desirable properties - main applications - priorities a m o n g properties admissible bounds of variation This information must be brought up-to-date and amplified in the course of time with a dynamic knowledge base storing results of designs and verification tests of prototypes. The key concepts in materials selection have been explained in the first stages of methodology developed in the foregoing sections. -
202
The inference process of expert systems must contain the evaluation and decision methods that have already been described in the selection process to make a quantitative decision. The formalisation process involves mapping the key concepts, subproblems and information flow characteristics isolated during conceptualisation into more formal representations. A variety of languages and tools can be used to build the expert system. One of the most variable c h a r a ~ " s is the way they search for solutions. The architecture of expert system of materials selection integrated in CAD-CAM systems must group the following abilities: • abstractions for each problem are composed from terms to fit the structure of the problem • during the problem-soMng process, these concepts represent partial solutions that are combined and evaluated • the concepts are assigned fixed and predetermined abstraction levels • the problem solution proceeds fiom the top downward, that is, from the most abstract to the most specific • solutions to the problem are completed at one level before moving down to the next more specific level • within each level sub-problems are solved in a problem-independent order • to know there is enough information to make a decision • to suspend problem-solving activity on a subproblem when the information is not available • to move between subproblems, restarting work as information becomes available • to combine information from different subproblems. Finally the expert system of materials selection must be graphically displayed on display units to represent the development of problem, making the pursuit and the interpretation easier while the time for errors detection is decreased.
203
Conclusion Modem materials for high-grade applications are often extremely complex and it is easy to overlook the significance of certain service conditions in relation to a particular material. The selection of the suitable material is a complex process that demands the management of a great amount of information about the materials properties and there are often several solutions for a specified application. The computer is a very useful aid. An expert system of materials selection integrated in CAD-CAM system is very necessary for engineering design. References (1)
Erik Ullman, Development of a National Materials Data Base in Sweden. Materials & Design Vol 8 No 6 (1987) p 346 (2) G L Bata, Computer Integrated Materials Processing - A Generic Application of CAD-CA/~ hlatedals & Design Vol 8 No 4 (1987) p 220 (3) M Chiner, Variables crlticas en el disan~o de silos mediante anAlisisde sensibilidad.VI Congreso Nacional Ingenieria Mec~nica 1987 (4) M Chiner, Criterios de optimizaci6n para el disen~o de silos mediante prograrnaci6n matem~.ica no lineal. Valencia 1987 (5) E J Wright, F_xpertSystems to aid Design Against Corrosion Materials & Design Vol 8 No 3 (1987) p 156 (6) Roll Sandstrom, An approach to systematic materials selection Materials & Design Vol 6 (1985) p 328 (7) Bernard Williams, Computer Program for Ferrous PM Materials Selection Materials & Design Vol 8 No 2 (1987) p 89 (8) h~rtini-Wedensky, Selection of Materials by Computer - What is Missing? h~tedals & Design Vol 6 No 3 (1985) p 134 (9) Jean-YvesDutour, Howto Choose Engineering Rastics Materials& Design Vol 7 No 1 (1986) p 14 (10) Roll SandsO'om,The Assessment and Evaluation of Property Data for Materials Selection purposes. Materials & Design Vol 7 No 4 1986 p 198 (11) W J Dixon, BMDP Statistical Software UCLA Report California 1981 (12) European Convention for Constructional Steelwork, European Recommendations for the Design of profiled sheeting. ECCS-TC71983, London. (13) M B Peterson & W Winer, Wear Con~ol Handbook. American Society of Mechanical Engineers, New York 1980. (14) T T Woodson, Introduction to Engineering Design McGraw Hill Book Company New York, 1966
MATERIALS & DESIGN Vot. 9 No. 4 JULY/AUGUST 1988