Materials - Engineering, Science, Processing and Design

Preface to 3rd edition

Science-led or design-led? Two approaches to materials teaching

What is different about this book?

And understanding phase diagrams and phase transformations relies on interpreting graphical displays of compositional and thermodynamic information. We have chosen to present crystallography and phase diagrams and phase transformations in this way here.

What’s new in the 3rd edition

Both topics can be packaged into self-contained guided learning units, with each new concept presented and immediately practiced with exercises, building confidence. The full Guided Learning Units follow later in the book and offer courses that require deeper understanding.

This book and the CES EduPack Materials and Process Information software

Thus, Crystallography, for example, includes ideas of symmetry and three-dimensional geometry, which are more easily grasped by drawing and problem solving. Their use to understand and predict microstructure follows procedures that are best learned from application.

Acknowledgements

Reviewers

Advisors

Resources that accompany this book

Introduction

Keywords

Materials, processes and choice

But our purpose here is not contention; rather, it is to give a vision of the universe of materials (since even on the most distant planets you will find the same elements) and of the universe of processes, and to provide methods and tools to select them for a happy, to ensure durable union. They present the properties of materials in ways that give a global view, that reveal relationships between properties and that enable selection.

Material properties

Software for the last of these - the selection of materials and processes - uses databases of the properties of materials and processes, documents their mutual compatibility and allows them to be searched and displayed in ways that enable choices that best suit the requirements of ' a design meets . This text presents a design-led approach to materials and manufacturing processes that makes use of such maps: new graphics to display the world of materials and processes in easily accessible ways.

Mechanical properties

The steel ruler bends elastically, but if it is a good one, it is difficult to give it a permanent bend. The resistance of materials to cracks and breakage is measured by the fracture toughness.

Thermal Properties

This feeling has to do with two thermal properties of the material: thermal conductivity and heat capacity. For a given thickness of the plate, time is inversely proportional to the thermal diffusivity, a, of the material of the plate.

Electrical, magnetic and optical properties

To be energy efficient, the pan must have a high thermal conductivity, λ, to transmit and spread heat well, and must resist corrosion from anything that might be cooked in it, including hot salt water , dilute acids (acetic acid, vinegar) and mild alkalis (baking soda). And it should be sweat-resistant and scratch-resistant enough to handle normal handling.

Chemical properties

Given this, a material that is cheap allows either a lower cost for the consumer or a higher profit margin for the manufacturer.

Environmental properties

Design-limiting properties

This means that, to achieve a desired level of performance, the values of design limiting properties must meet certain objectives and those that fail to do so are not suitable. Materials are selected by identifying limiting design properties, applying constraints to them, and examining those that do not meet the constraints (Chapter 3).

Summary and conclusions

In the design of power transmission lines, the electrical resistivity is design limiting; in the design of a camera lens it is optical quality and refractive index. These can also be design limiting, leading to a parallel scheme for selecting viable processes (Chapters 18 and 19).

The history and evolution of materials

Exercises

E1.5 In your opinion, what are the design-limiting properties of the material in an oven mitt. E1.6 In your opinion, what are the design-limiting properties of the material in an electric lamp filament.

Family trees

Introduction and synopsis

This is the subject of Section 2.3, which shows the differences between the different types of material information. However, this is not ultimately the material we are looking for; is a particular profile of properties – the one that best suits the needs of the design.

Getting materials organised: the materials tree

These are graphs with material properties as axes that show the location of the families and their members. The maps provide an overview of materials and their properties, reveal aspects of the science underlying the properties, and provide a powerful tool for material selection.

Classifying materials

Organising processes: the process tree

The choice for a given component depends on the material from which it will be made; on its form, dimensions and accuracy; and about how much should be made—in short, about the design requirements. Materials that melt at moderate temperatures to low-viscosity liquids can be cast; those that do not need to be processed by other routes.

Classifying processes

Process-property interaction
Material property charts
Computer-aided information management for materials and processes
Summary and conclusions
Further reading
Exercises
Exploring design using CES
Exploring the science with CES Elements

E2.13 Use the 'Browse' option on Level 1 of the CES software to find a record for copper. Use the "Browse" option on Level 1 of the CES software to find the entry for Phenolic Thermosetting Polymer.

Strategic thinking

Introduction and synopsis

This chapter introduces some of the design vocabulary, the stages in its implementation, and the ways in which material selection relates to it. The choice of materials and the process evolve in parallel with this process, in the manner described in this chapter.

The design process

Our goal in this chapter is to develop a strategy for selecting materials and processes that is design-led; that is, the strategy uses the requirements for the design as input.

Original design

Redesign

Much of the cost of a mass-produced product comes from the materials it is made of and the processes chosen to make it. Much of the redesign has to do with detail—the last of the three boxes in the central window of Figure 3.1—but not all.

Devices to open corked bottles

Material and process information for design

The selection of the process follows a trajectory parallel to that of the material (Figure 3.1, right). The interaction between material, form and process is at the heart of the selection process.

The strategy: translation, screening, ranking and documentation

The interactions are two-way: specification of form limits choice of material and process; We will return to process selection in Chapters 18 and 19, but for now we will limit ourselves to materials.

Translation

The result of the translation step is a list of the design constraints and the constraints they must meet.

Screening

Ranking

Documentation

Examples of translation
Further reading
Exercises
Exploring design using CES

E3.8 A material is required for the windings of an electric air furnace capable of operating at temperatures up to 1000 °C. E3.12 State the constraints and objective you would associate with the choice of material to make the forks of a racing bicycle.

Stiffness and weight

Introduction and synopsis

Distortion—a change of form—is its response; it depends on the magnitude of the stress and the way it is applied—the way of loading. Shafts carry torsion, as in the drive shaft of cars or the propeller shaft of an airplane.

Density, stress, strain and moduli

Beams carry bending moments, such as aircraft wing spans or the horizontal beams of an airport roof. These properties are neatly summarized in a material property graph - the modulus - density graph - the first of many we will explore in this book.

Density

Stiffness is the resistance to change in shape that is elastic, meaning that the material returns to its original shape when the stress is removed. Stiffness (measured by the elastic modulus E, defined in a moment) and strength (measured by the elastic limit σy or tensile strength σts) are material properties.

Modes of loading

Stress

If the force instead lies parallel to the surface of the element, three other forces are required to maintain equilibrium (Figure 4.3, row (b)). Pressures are positive when they compress—the reverse of the convention for simple tension and compression.

Strain

Stress–strain curves and moduli

The tensile stress is proportional to the tensile stress:. and the same applies to compression. Young's modulus, the shear modulus, and the bulk modulus are related, but to relate them we need one more quantity, Poisson's 6 ratio.

Hooke’s Law in three dimensions

Therefore, the effect of the constraint is to induce a stress νσ1 in the constrained direction, perpendicular to the applied stress σ1. But this stress will itself contribute a Poisson strain in direction 1, so the strain vertically is.

Elastic energy

4.16) The effect is even more noticeable when there is restriction in both 2- and 3-directions (see Exercises at the end of the chapter), and the effect is most important for values of Poisson's ratio close to 0.5. As noted earlier, the solid material with the lowest modulus rubber exhibits the most significant stiffening effect when loaded in a constraint-imposing geometry.

Measurement of Young’s modulus

Stress-free strain

The big picture: material property charts

The modulus–density chart

This helps in the general problem of material selection for stiffness-constrained applications in which weight must be kept to a minimum.

The modulus–relative cost chart

Anisotropy

The science: what determines stiffness and density?

Introduction to Guided Learning Unit 1: Simple ideas of crystallography

Atom packing in metals and the unit cell

The atoms in the upper, lower, and central plane form tightly packed layers like those in Figure 4-10(b), with ABAB. The last cell, shown in Figure 4-13(c), is the characteristic unit of the square layer structure of Figure 4-11; it's a cube with an atom on each corner and one in the middle, and is aptly named Body-Centred Cubic (BCC).

Atom packing in ceramics

Atom packing in glasses

Atom packing in polymers

Weak thermoplastics, however, try to keep the bond lengths short by lining up the molecules, as shown in Figure 4.19(a). Thermosets such as epoxies and phenolics have many crosslinks, as in Figure 4.20(d), making them stiffer and stronger than thermoplastics.

Cohesive energy and elastic moduli

4.20) muscular covalent C-C bonds, as in Figure 4.19(b), making the entire series into one large multiply-linked network. But as the graph (Figure 4.8) shows, materials exist that have moduli much lower than this limit.

The elastic moduli of elastomers

4.21) be aligned enough to stretch the covalent bonds, giving a much higher modulus (see the right end of the polymer stress-strain curve in Figure 4.4). This is exploited in the production of polymer fibers, giving properties far superior to bulk polymers.

Temperature-dependence of polymer moduli: the glass transition temperature

Elastomers and thermosets have a glass transition, but do not melt when heated - due to cross-linking, they decompose and burn instead. Since the stretching of the material can be accompanied by some sliding of the molecules next to each other, the stiffness is particularly sensitive to the loading rate.

Origin of density

This affects the amorphous regions, but in semi-crystalline thermoplastics the crystallites melt at a higher temperature, typically 1.5 × , due to the tighter packing of the chains. Semi-crystalline thermoplastics show a significant drop in modulus across the glass transition, of the order of 100 to 1000 times, but with a plateau in modulus that is sometimes, somewhat misleadingly, referred to as 'rubbery' behaviour.

Density and modulus of metallic alloys

Manipulating the modulus and density

The underlying science of atomic packing and bonding shows that changing the composition offers little scope for manipulating the modulus and density of a given class of metal alloys (steel, Al alloys and so on). But to produce new combinations of modulus and density across the range of materials, mixtures must be made on a more macroscopic scale, to make a hybrid material.

Composites

Estimate the Young's modulus and density of the composite: (i) if the glass is in the form of long parallel fibers (calculate the parallel-to-fiber properties); (ii) if the glass is in the form of small particles. That of the particle-reinforced composite is slightly lower than that of the matrix alone.

Foams

Acoustic properties

The wavelength is related to the frequency at. 4.31) where is the speed of sound in the medium in which it travels. The vibrations that cause sound produce a change in air pressure in the range 10−4 Pa (low-amplitude sound) to 10 Pa (the threshold for pain).

Sound velocity and wavelength

The range of acoustic frequency is much greater than this (Figure 4.27) with wavelengths extending into the nano range. It is usual to measure it on a relative, logarithmic scale, with units of decibels (dB).

Sound management

Sound wave impedance and radiation of sound energy

The decibel scale compares two sound intensities using the hearing threshold as a reference level (0 dB). 4.34) where is the impedance in the medium in which the sound originates and is that of the material in which it is transmitted. Thus, if the two impedances are roughly equal, most of the sound is transmitted, but if they differ greatly, most of the sound is reflected.

Visualising acoustic properties

Further reading
Exercises
Exploring design with CES

A practical approach to soundwood selection in instruments of the violin family. Make a copy of the modulus-density plot of Figure 4.8 and draw on it a set of contours showing the radiation factor.

Flex, sag and wobble

Introduction and synopsis

The result was visually striking: a sleek, slim, span like a 'light shaft' (the architect's words). You don't need to know how to derive all of these - these are standard results - but you do need to know where to find them.

Standard solutions to elastic problems

The models can be simple because the selection criteria that emerge are insensitive to the details of shape and load. So it makes sense to have a catalog of solutions for the default modes, where the response of the components is related to the load.

Elastic extension or compression

The stress σ varies linearly from tension to compression, changing sign on the neutral axis, resulting in a bending moment M. c) Shaft of circular cross-section, torsionally loaded. Note that the shape of the cross-sectional area is not important because the stress is uniform across the cross-section.

Elastic bending of beams

We find in Section 5.3 that the best choice of material is independent of the value of C1 with the happy result that the best choice for a complex distribution of loads is the same as for a simple one. a) The ruler in example 5.1 is made of stainless steel with a Young's modulus of 200 GPa. Calculate the vertical deflection of the free end if the ruler is mounted with: (i) the X-X axis horizontal; (ii) Y-Y axis horizontal.

Torsion of shafts

Its length and width must be the same as the stainless steel ruler, but its thickness can be changed by the designer. The polystyrene ruler must be mounted with its X-X axis horizontal and its deflection must not be greater than that of the stainless steel ruler under the 10 N end load.

Buckling of columns and plates

The ratio of torque to twist, T/θ, per unit length, is equal to GK, which is called the torsional rigidity. a) Derive an expression for the second polar moment of area of a tube with a hollow circular section with inner radius ri and outer radius ro. A copper rod of shear modulus 40 GPa, length 200 mm, and with a solid circular cross-section of diameter 10 mm, is twisted with a torque of 10 Nm.

Vibrating beams and plates

Material indices for elastic design

Minimising weight: a light, stiff tie-rod

The lightest tie that will provide a stiffness S∗ is that made of the material with the smallest value of ρ/E. We can define it as the material index of the problem, find the material with a minimum value, but it is more common to express indices in a form for which a maximum is sought.

Minimising weight: a light, stiff panel

The length of the panel was specified, but we were free to change the area of the section. Then read the combination of material properties that appear in the objective function - the equation for mass.

Minimising weight: a light, stiff beam

So we need to get an idea of the effect of shape on bending performance. To have the same amount of material, the cross-sectional area of the pipe must be equal to that of the solid bar πR2.

Minimising material cost

Plotting limits and indices on charts

The brass rod in Example 5.3 is formed into a hollow tube with an outer radius of 25 mm and the same length, using the same amount of material. Therefore the hollow shaft, which has the same mass as the solid one, has about 11 times the torsional stiffness (T/θ).

Screening: attribute limits on charts

So if you compare materials for light, rigid beams using the index in equation (5.26), the performance of wood is not as good as it seems because other materials can be made into more efficient shapes. Shaping provides exactly the same benefits under torsional loading: a tube of the same mass has greater resistance to torsion (or alternatively, a lighter tube can do the same job as a solid round bar).

Ranking: indices on charts

It is now easy to read the subset of materials that maximize performance for any loading geometry. For example, all materials that lie on a line with constant M = E1/3/ρ perform equally well as a light and stiff panel; those above the line perform better, those below less well.

Computer-aided selection

Case studies

In most cases, little is lost by this: the best choice of material for a simple case is the same as for a more complex one.

Light levers for corkscrews

Cost: structural materials for buildings

Concrete, stone and brick have strength only in compression; the form of the building must use them in this way (walls, columns, arches). Wood, steel, and reinforced concrete have strength in both tension and compression, and steel, in addition, can be given efficient shapes (I-sections, box sections, tubes) that can carry bending and tensile loads as well as compression , allowing greater freedom of the shape of the building.

Cushions and padding: the modulus of foams

Wood, steel and reinforced concrete have strength in both tension and compression, and steel can also be given effective shapes (I-profiles, box profiles, tubes) that can withstand bending and tensile loads and compression, allowing greater freedom of form buildings. 5.35) where the density of the foam and ρs is the density of the solid from which it is made. This force bends the edge of the cell to which it connects, as on the right side of Figure 4.23.

Vibration: avoiding resonance when changing material

5.35) where the density of the foam and ρs is the density of the solid from which it is made. Thus, the edge of the cell is just a beam embedded at both ends that carries the centripetal force F.

Bendy design: part-stiff, part-flexible structures

Further reading
Exercises

Stiffness is affected by the size and shape of the cross-section and the material from which it is made. Use the material properties in the table below. d) Write an expression for the mass m of the ribbon and determine the mass of each of the ribbons in (c).

Beyond elasticity

Introduction and synopsis

But the unplanned yielding of the span of a bridge or the wing spar of an airplane or the forks of your bicycle is a disaster. For that reason, it is mainly (but not exclusively) about metals: it is the plasticity of iron and steel that made them the structural materials on which the Industrial Revolution was built, enabling the technical achievements of Telford1 and Brunel2, among others.

Strength, plastic work and ductility: definition and measurement

In Chapter 4, the area under the elastic part of the stress-strain curve was identified as the stored elastic energy per volume unit. For now, it is useful to have a practical measure of the strength of ceramics to allow their comparison with other materials.

True stress and true strain

The big picture: charts for yield strength

The strength–density chart

Because density changes very little (Chapter 4), strength bubbles for metals are long and thin. The wide ranges for metals reflect the fundamental physics of yielding and give designers the opportunity to manipulate strength by changing composition and process history.

The modulus–strength chart

Drilling down: the origins of strength and ductility

Perfection: the ideal strength

Crystalline imperfection: defects in metals and ceramics

The solute atoms or solute are rarely the same size as those of the host material, so they distort the surrounding lattice. The top part of the crystal has one more double layer of atoms than the bottom part (the double layer is needed to get the top-to-bottom register right).

Dislocations and plastic flow

At the end of the process, the upper part has slipped by b, the slip vector (or Burger's vector) with respect to the lower part. The passage of the dislocation through the slip plane, shown in the sequence (b), (c) and (d), cuts the upper part of the crystal above the lower part by the slip vector b.

Why does a shear stress make a dislocation move?

In real crystals it is easier to make and move dislocations in some planes than in others. A slip plane is shown in gray and a slip direction as an arrow in the FCC and BCC unit cells of Figure 4.13.

Line tension

The lattice resistance

Plastic flow in polymers

Manipulating strength

Strengthening metals

Thus, the added contribution to the shear stress τ needed to make the dislocation move is (from equation (6.14)). The shear stress τ required to force the displacement through the obstacle field then has the form

Solution hardening

Each individual obstacle exerts a pinning force p on the dislocation line—a resistive force per unit length of dislocation—. The pinning is an elastic effect—it arises from the fact that both the dislocation and the obstacle deform the lattice elastically, although, when the dislocation moves, it causes plastic deformation.

Dispersion and precipitate strengthening

They differ only in the degree to which the solute deforms the crystal, described by the constant α. A polycrystalline aluminum alloy contains a dispersion of hard particles with a diameter of 10−8 m and an average center-to-center spacing of 6 × 10−8 m, measured in the slip planes.

Work hardening

Grain boundary hardening

Relationship between dislocation strength and yield strength

Strength and ductility of alloys

Strengthening polymers

Further reading
Exercises

Record the actual stresses ε1 and ε2, respectively, for each of the two elongation processes considered separately. Make a bar graph of the energy stored in the form of dislocations for a dislocation density of 1014 m/m3.

Bend and crush

Introduction and synopsis

Standard solutions to plastic problems

Yielding of ties and columns

Yielding of beams and panels

In the first, the maximum moment is M FL, in the second FL/4 and in the third FL/8. Plastic hinges are formed at the positions marked in red when the maximum moment reaches the collapse moment.

Yielding of shafts

Helical springs are a special case of torsional loading (Figure 7.4): when the spring is axially loaded, the individual rotates. If the spring has n turns of wire of shear modulus G, each of diameter d, wound to give a spring of radius R, the stiffness is.

Spinning disks (flywheels)

This is the principle of the Kinetic Energy Recovery Systems (KERS), which was introduced in Formula I racing cars in 2009.

Contact stresses

This is a significant fraction of the yield strength of the surface, indicating that fatigue failure under cyclic loading may be a concern (Chapter 9).

Stress concentrations

Material indices for yield-limited design

Minimising weight: a light, strong tie-rod

Minimising weight: light, strong panels

Light, strong beams: the effect of shape

If you want to support bending loads, it is better to choose a shape that uses less material to provide the same strength. Remember from Chapter 5 that materials are not all equally easy to shape; if they were, they could all be given the same efficient form and the index in equation (7.18) would be sufficient.

Minimising material cost or volume

Case studies

Carrying loads safely is not only a matter of strength, but also of toughness - the resistance of the material to breaking. Strength and toughness are not the same thing—we explain why in the next chapter.

Corkscrew levers again: strength

For now, it is enough to know that some materials may appear to be good options for strength-limited design, but are impractical because they are too brittle under tension or impact loading.

Elastic hinges and couplings

High strength steel, CFRP and some polymers and elastomers are the best choice for the latter.

Materials for springs

Although it is less obvious, the index is the same for leaf springs, torsion springs and coil springs - the best choice for one is the best choice for all. The best choices are a high strength steel that lies near the top end of the line.

Full plasticity: metal forming

Further reading
Exercises

The forces and strength they require scale with the yield strength of the material being formed. Indicate that this design specification places a lower limit on the specific strength of the material used for the cable.

Fracture and fracture toughness

Abstract

Introduction and synopsis

Toughness—resistance to fracture—requires a new material property, the fracture toughness developed in Section 8.3, to describe it. This new property is explored in Section 8.4 using diagrams like those we have already seen for modulus and strength.

Strength and toughness

The underlying scientific mechanisms (section 8.5) provide insight into ways in which toughness can be manipulated (section 8.6).

Strength and toughness? Why both? What’s the difference?

Tests for toughness

The mechanics of fracture

The stress intensity factor is thus a measure of the elastic stress field near the tip of a sharp crack, equation (8.2). From equation (8.4), the stress at quick fracture for stainless steel is 8.7) This is much greater than its yield strength - meaning the visor will yield before breaking.

The crack tip plastic zone

Material property charts for toughness

The fracture toughness–modulus chart

The fracture toughness–strength chart

Drilling down: the origins of toughness

Surface energy

The graph of figure 8.8 shows the contours of Gc; for most materials its value is hundreds of times greater than 2γ.

Brittle ‘cleavage’ fracture

Tough ‘ductile’ fracture

The stress still increases as the crack tip is approached, but at the point where it exceeds the yield point, the material yields and a plastic zone is formed. Cavities form within it that sprout, grow and connect, propelling the crack in a ductile manner, absorbing energy in the process.

The ductile-to-brittle transition

Within the plastic zone the same sequence as that of Figure 8.12 occurs: voids form, grow and connect to give a ductile fracture. Plasticity dampens the crack, and the stress concentration effect of a sharp crack is less strong than that of a sharp crack, so at the crack tip the stress is sufficient to sustain the plastic deformation of the material there.

Embrittlement of other kinds

Compressive and tensile failure of ceramics

Compressive failure of ceramics

Tensile failure of ceramics—Weibull statistics

Manipulating properties: the strength–toughness trade-off

Metals

Separation within the plastic zone, which allows crack propagation, is the result of the growth of voids formed at the inclusions (Figure 8.13). Pure steels, superalloys, and aluminum alloys produced by filtering the molten metal prior to casting have significantly higher toughness than those produced by conventional casting methods.

Polymers and composites

Further reading
Exercises

What is the new stress concentration factor at the corner of the window and what is the maximum stress. Show that the maximum tensile stress at the surface of the beam is given by.

Shake, rattle and roll

Introduction and synopsis

So when your pen clip breaks or your office chair topples over, fatigue is probably to blame (cover photo). We then turn to the accumulation of damage and cracking associated with appropriate fatigue loading.

Vibration and resonance: the damping coefficient

Fatigue

The problem of fatigue

Fatigue failure is insidious - there is little sign that anything is happening until it happens. There is then no initiation stage – the crack is already there – and the fatigue life is propagation controlled, that is, it depends on the rate at which the crack grows.

High-cycle fatigue and the S–N curve

The component is cyclically loaded with a zero-mean sinusoidal stress of amplitude 100 MPa (stress range 200 MPa) and has a fatigue life of 200,000 cycles. What will be the fatigue life if the stress amplitude is increased to 120 MPa (stress range = 240 MPa).

Low-cycle fatigue

High-cycle fatigue: mean stress and variable amplitude

Basquin's law expresses the number of cycles to failure if each amplitude is maintained throughout the life of the part. Thus, if N1 cycles are spent at a voltage amplitude Δσ1, a fraction of N1/Nf1 of the available lifetime is used up, where Nf1 is the number of cycles before it fails at that voltage amplitude.

Fatigue loading of cracked components

Charts for endurance limit

The most important single property characterizing fatigue strength is the endurance limit, σe, at 107 cycles and zero mean load (R-value -1). The strongest correlation is with the tensile strength σts, shown in the diagram in Figure 9.8.

Drilling down: the origins of damping and fatigue

Material damping: the mechanical loss coefficient

Fatigue damage and cracking

Manipulating resistance to fatigue

Choosing materials that are strong

Making sure they contain as few defects as possible

Providing a compressive surface stress

Further reading
Exercises

How many cycles will the material tolerate at a stress amplitude of 70 MPa and zero mean stress. Approximate S–N data for the material used are given in the figure, for zero mean stress.

Keeping it all together

Introduction and synopsis

Cracks will not propagate if this K1 is kept below the fracture toughness K1c of the construction material. Cracks will not propagate if the cyclic stress intensity range, ΔK, is below the threshold range ΔKth.

Standard solutions to fracture problems

This would suggest that the best material to resist fracture is the material with the highest K1c, and this is also the case in a limited load design. Stress intensities under cyclic loading are given by the same standard solutions as for static loading.

Material indices for fracture-safe design

Energy-limited design

Displacement-limited design

Plotting indices on charts

Case studies

As he drank his coffee, the tank exploded, causing significant property damage and one death. The failure occurred through the longitudinal welding, which caused the tank to burst (see chapter opening image).

Fail-safe design

The pressure that can be borne increases with wall thickness, but there is an upper limit to the thickness determined by the leak-before-failure criterion, equation (10.12). From equation (10.7), the thickness is inversely proportional to the yield strength, so we also look for a reasonably high value.

Materials to resist fatigue: con-rods for high-performance engines

10.15) Both and could be made large by using a material with low yield stress, : for example, lead has high values of both and , but you would not choose it for a pressure vessel. 10.16), where σe is the endurance limit of the material from which the control rod is made.

Rail cracking

They use a compression strut (a CFRP tube) with an outer wrap of filament wound fibers to attach the bearing housings (made of titanium or aluminum) to the ends of the strut. So even though the rail head is compressed, at the tip of the crack there is tension - enough to drive the crack forward.

Fatigue crack growth: living with cracks

As the wheel passes the mouth of the crack, it is forced closed, trapping the water, which is compressed to a high pressure. This means increasing the test voltage, but there is a practical limit to this: it cannot exceed the yield stress of the material.

Designing for fracture

Further reading
Exercises

The figure also shows the S–N curve of the material from which it will be made. Before use, it was determined that the length of the largest crack in the steel was 1 mm.

Rub, slither and seize

Introduction and synopsis

It is certainly true that, if friction could be eliminated, the efficiency of engines, gearboxes, drivetrains and the like would be enormously increased; and if wear and tear could be eradicated, they would also last much longer. This experience is captured in reference sources (for which, see 'Further reading'); in the end it is they who must be consulted.

Tribological properties

But it helps to get a feel for the magnitude of the coefficients of friction and the rate of wear, and an idea of how these relate to the grade of material. If the bearing is used continuously for a year, how much will the surfaces have worn.

Charting friction and wear

The coefficient of friction

The wear rate–hardness chart

The physics of friction and wear 3

Friction

But even small loads produce large contact stresses sufficient to cause plastic deformation, as shown in Figure 11.5(a). The contacts can carry a higher stress than the uniaxial yield stress because the deformation of the asperities is limited by the surrounding material – the peaks in Figure 11.5 are enlarged for clarity.

Wear

Friction in design and metal processing

If the drivetrain bearings of your car had a μ of this size, negligible force would reach the wheels—almost all of it would be lost as heat in the bearing surfaces. In fact, about 15% of the power of the engine is lost in friction due to two innovations: lubrication and the replacement of sliding by roller bearings.

Lubrication

Solid lubricants - PTFE, molybdenum disulfide (MoS2) and graphite (a form of carbon) - extend the operating temperature to 500 °C. Moly-disulfide (up to 300 °C) and graphite (up to 500 °C) rely on their lamellar (layer-like) crystal structure, able to easily shear into several crystal planes, to provide much higher friction coefficients lower than 0.1.

Plane bearings

Rolling bearings

When the loads are very light, the races can be made of thermoplastic—polypropylene or acetal—with the advantage that no lubrication is needed (cheap bicycle pedals sometimes have such bearings). When rolling element bearings fail, it is usually due to fatigue - the repeated loading and unloading of ball and race as the bearing rotates, causing cracks to nucleate, split the balls, or pit the races.

High friction: materials for brakes and clutches

If the environment is corrosive or the temperature is high, stainless steel or ceramic (silicon carbide or silicon nitride) is used. Inclusions in the material are sources of fatigue cracking, so rolling bearing steels are processed to be as clean and inclusion-free as possible by processing under vacuum.

Waging war on wear

Friction in metal processing

Summary and conclusions