Chapter 11 Designing Hybrid Materials Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Figure 11.1 Hybrid materials combine the properties of two (or more) monolithic materials or of one material and space. They include fibrous and particulate composites, foams and lattices, sandwiches, and almost all natural materials Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Figure 11.2 Four configurations for a bridge. The design variables describing the performance of each differ. Optimization of performance becomes possible only when a configuration has been chosen. Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Figure 11.3 All material property charts examined thus far have been populated with holes. One approach to filling these holes is by developing hybrid materials that have the desired property profile Figure 11.3 shows holes in modulus-density space. Material development that extended the occupied territory in the direction of the arrow allows components with greater stiffness to weight than any current material allows Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Figure 11.4 The possibilities of hybridization. The properties of the hybrid reflect those of its component materials, combined in one of several ways. Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Steps in designing a hybrid to meet given design requirements Figure 11.5 Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Four Types of Composites Figure 11.6 Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Properties of Composites Density ρm – density of matrix ρr – density of reinforcement f – volume fraction of reincforcement Modulus Upper Bound Er – Young’s modulus of reinforcement Em – Young’s modulus of matrix f – volume fraction of reinforcement Lower Bound Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Strength Tensile – loading parallel to fiber Tensile – transverse loading Compressive – axial Upper Limit Lower Limit Upper Limit Lower Limit Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Figure 11.7 Bounds for the moduli of hybrids made by mixing aluminum alloys, beryllium, and alumina are shown. Diagonal contours plot the criterion of excellence Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Failure Modes in Composites Figure 11.8 Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Figure 11.9 The limits for axial (a) and transverse (b) strength of a composite ply Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Figure 11.10 A part of expansion-coefficient/conductivity space showing aluminum alloys, boron nitride, and silicon carbide Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Figure 11.11 Polymer and metal matrix composites expand the occupied area of modulus-density space. Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Figure 11.12 Similarly, polymer and metal matrix composites expand the occupied area of strength-density space Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Sandwich Structures A sandwich panel combines two materials in a specified geometry and scale, configured such that one forms the faces and the other the core to give a structure of high bending stiffness Figure 11.13 Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Equivalent Properties of Sandwich Structures Density Figure 11.14 Stiffness B1, B2 are constant to describe modes of loading – specific values are found in Table 11.3 Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Face Yield Face Buckling Core Shear Sandwich panels can fail in many different ways. The failure mechanisms compete, meaning that the one at the lowest load dominates. We calculate an equivalent flexural strength for each mode, then seek the lowest. Figure 11.15 Face Yield Face Buckling Core Shear Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Face Buckling Core Shear Figure 11.16 Figure 11.17 Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

The optimization of a light, stiff sandwich panel: Figure 11.18 Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

The optimization of a strong and light sandwich panel: Figure 11.19 Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Figure 11.20 The sandwich data of Figure 11.18 superimposed on a modulus-density chart, showing the exceptional value of the flexural stiffness material index Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Figure 11.21 The sandwich data of Figure 11.19 superimposed on a strength-density chart, showing the exceptional value of the flexural strength index Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Cellular Structure of Foam Figure 11.22 A cell in a low-density foam. When the foam is loaded, the cell edges bend, giving a low-modulus structure. Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Figure 11.23 The plateau stress is determined by buckling, plastic bending, or fracturing of cell walls Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Foaming creates bending-dominated structures with lower modulus and density (a). Lattices that are stretch-dominated have moduli that are much greater than those of foams of the same density (b). Figure 11.24 Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Collapse of Foams Figure 11.25 When a foam made of a plastic material is loaded beyond its elastic limit, the cell edges bend plastically An elastomeric foam, by contrast, collapses by the elastic buckling of its cell edges A brittle foam collapses by successive fracturing of cell edges Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Lattice: Stretch-Dominated Structures Maxwell Stability Criterion b: struts j: frictionless joints M<0 – frame is a mechanism M>0 – stretch-dominated structure The pin-jointed frame at (a) is a mechanism. If its joints are welded together, the cell edges bend. The pin-jointed, triangulated frame at (b) is stiff when loaded because the transverse bar carries tension, preventing collapse. When the frame’s joints are welded, its stiffness and strength hardly change. The frame at (c) is over-constrained. If the horizontal bar is tightened, the vertical bar is put in tension even when there are no external loads. Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Figure 11.27 A micro-truss and its unit cell. this is a stretch-dominated structure and is over-constrained, meaning that it is possible for it to be in a state of self-stress. Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Figure 11.28 Foams and micro-truss structures are hybrids of material and space. Their mechanical response depends on their structure. Foams are usually bending-dominated and lie along a line of slope 2 on this chart. Micro-truss structures are stretch-dominated and lie on a line of slope 1. Both extend the occupied are of this chart by many decades. Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby

Materials For Long-Span Power Cables Figure 11.29 Materials Selection in Mechanical Design, 4th Edition © 2010 Michael Ashby