MATERIALS SELECTION FOR SPECIFIC USE

Transcription

1 MATERIALS SELECTION FOR SPECIFIC USE -2 Sub-topics 1 Material indices for elastic design Design problems - 2

2 METHOD FOR EARLY TECHNOLOGY SCREENING Design performance is determined by the combination of: Shape Materials Process Performance isn't just about materials - shape can also play an important role Shape can be optimized to maximize performance for a given loading condition Simple cross-sectional geometries are not always optimal Shape is limited by material Goal is to optimize both shape and material for a given loading condition do not underestimate impact of shape or the limitation of process 2

3 LOADING CONDITIONS AND SHAPE Different loading conditions are enhanced by maximizing different geometric properties 3

4 MINIMIZING WEIGHT OF BEAM Beams come in many shapes; Let s firstly consider beam of square cross-section 4

5 SHAPES AND MOMENTS 5

6 A LIGHT, STIFF BEAM A design calls for a rectangular beam of specified length Lto carry a bending moment M; it is to be of minimum mass 6

7 Elastic deflection of the beam Stiffness of a beam under transverse loading C 1 is the only value that depends on the distribution of the load 7

8 Objective function: Stiffness constraint and second moment of inertia: Eliminating the free variable A from the objective function and identifying the unspecified variables 8

9 SHAPE FACTOR DEFINITION Shape factor measures efficiency: For a given loading condition, section uses as little material as possible. Defined as 1 for a solid cross-section Higher number is better, more efficient 9

10 SHAPE FACTOR By reshaping the crosssection of a beam, it is possible to increase I thus increasing stiffness without increasing the total area Shaping is used to make structures lighter; it is a way to achieve the same stiffness with less material 10

11 The effect of shaping on stiffness and mass of beams in different structural materials The factor by which a beam can be made stiffer, for the same mass, by shaping The factor by which a beam can be made lighter, for the same stiffness, by shaping Shaping could increase the value of I by 64X if steel is used in the construction of a beam with a square cross-section; if wood was used, the maximum increase would 11 be 9X

12 SHAPE FACTOR FOR ELASTIC BENDING Compare sections of same area A 0 = A Notice that shape factor is dimensionless 12

13 I-BEAM ELASTIC BENDING SHAPE FACTOR 13

14 BEAM For these dimensions, the shape increased stiffness over 13 times while using the same amount of material!

15 MINIMIZING MATERIALS COST Material indices change as the objective changes; the objective function for minimizing cost of the tie rod, panel, or beam would be: With A and L being specified, the goal of a material selection would be to minimize C m ρor maximize 1/ C m ρ 15

16 PLOTTING LIMITS AND INDICES ON CHARTS Screening: attribute limits on charts Constraints can be plotted as horizontal or vertical lines on material property charts Constraints : E > 10 GPa Relative Cost < 3 All materials in the search region meet both constraints Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

17 DESIGNFORALIGHT, STIFFBEAM Many structures require that a beam or rod sustains a certain force F without deflecting more than a given amount, l. If, in addition, the beam or rod forms part of a transport system -a plane or rocket, or a train -or something which has to be carried or moved -a rucksack for instance -then it is desirable, also, to minimise the weight. 17

18 DESIGNOFALIGHTSTIFFBEAM l The square-section beam of length L (determined by the design of the structure, and thus fixed) and thickness t(a variable) is held rigidly at one end while a force F(the maximum service force) is applied to the other b b Design requirements: Function Beam Constraints Objective Free variables Minimize mass Materials Area of cross-section 18

19 DESIGNOFALIGHTSTIFFBEAM- SOLUTION 19

20 THE MODULUS DENSITY CHART 1000 Ceramics 100 Young s modulus E, (GPa) Composites Woods Foams Polymers Metals 0.01 Elastomers Density (Mg/m 3 ) Source: M. Ashby, H. Shercliff, D. Cebon. Materials eng., processing and design, ISBN: , 2008

21 EXAMPLE OF MATERIAL SELECTION 21

22 EXAMPLE: MATERIALS EVOLUTION The Camera Roughly 140 years ago, when the camera was invented, changes in the design came slowly. Early cameras were made from wood, brass, leather, and, of course, glass. The materials chosen for the cameras were mostly metal they were durable and put an emphasis on engineered quality. But as the market for the standard product started to saturate new variants appeared: the disposable camera (made of paper), the miniature spy camera (metalized polymers) and waterproof cameras (elastomers overmolded on a range of polymers) differentiation through technical innovation is often coupled with changes in material. 22

23 CASE STUDIES: STRUCTURAL MATERIALS A stiff beam with minimum cost is required