Fracture

Typically as the yield strength of a material is increased, its ductility and toughness decrease. Toughness is the energy absorbed in fracturing. If a material has a high yield strength, it can be subjected to stresses high enough to cause fracture before there has been much plastic deformation to absorb energy. Factors that inhibit plastic flow lower ductility as schematically indicated in Figure 5.1. These factors include decreased temperatures, increased strain rates, and the presence of notches.

Engineers should be interested in ductility and fracture for two reasons. Ductility is required to form metals into useful parts by forging, rolling, extrusion, or other plastic working processes. Also, some plastic deformation is necessary to absorb energy so as to prevent failure in service.

Fractures can be classified several ways. A fracture may be described as being ductile or brittle, depending on the amount of deformation that precedes it. Failures may also be described as intergranular or transgranular, depending on the fracture path. The terms cleavage, shear, void coalescence, etc., are used to identify failure mechanisms. These descriptions are not mutually exclusive. A brittle fracture may be intergranular, or it may occur by cleavage.

The failure in a tensile test of a ductile material occurs well after the maximum load is reached and a neck has formed. In this case, fracture usually starts by nucleation of voids in the center of the neck where the hydrostatic tension is the greatest.

Bulk Forming

Processes for forming solid metals can be classified as bulk forming in which the forces are mostly compressive, and sheet forming in which the metal is stretched in tension. Bulk forming processes may be further classified as either hot working or cold working, depending on whether the work material leaves in a recrystallized state.

Figure 10.1 illustrates several important bulk forming processes. Compression is clearly the dominant force in rolling, extrusion, and forging. For rolling, extrusion, and forging, the reduction is usually limited by the capacity of the machinery to deliver forces. Although drawing involves pulling a rod or wire through a die, the pressure the die exerts on the rod or wire is the dominant force. In rod and wire draw-ing, the maximum reduction per pass is limited by the possibility of tensile failure of the drawn wire. Typically a maximum strain per pass is about ε = ln(A1/A2) = 0.65, which corresponds to a diameter reduction of 38%. Obviously many passes are required to make fine wire. Many rolling passes are used to make sheets and shapes. Forging uses repeated blows to achieve a final shape. In contrast, rods, tubes, and other shapes are extruded in a single operation to their final shape because high reductions are possible.

Fibers

Fibers of nylon, polyester, and other thermoplastics are made by extruding molten material through tiny holes in a spinneret. The resulting fibers are cooled before coiling. The strengths of nylon, polyester, polypropylene, and high-density polyethylene fibers are increased greatly by stretching them by 400 to 500% in tension (drawing) to orient the molecules parallel to the fiber axis.

Fiber strength is often quoted in terms of grams force per denier (g force/denier). A denier is defined as grams mass per 9000 m of fiber. Figure 19.1 shows the relative strengths of various fibers. Kevlar fibers are much stronger, having strengths of about 22 g force/denier.

Example Problem 19–1:

Develop an equation for converting tenacity in g force/denier to MPa.

Solution: Let T be the tenacity in g force/denier. Then T[g force/(g mass/9000 m)]ρ(g/cm3)(100 cm/m)(980.7 × 10-7N/g-force)(1002cm2/m2) = 883 × 103 (Tρ) Pa. Tensile strength is 0.883Tρ MPa.

Fabrication of Porous Foams

Natural cellular materials include sponges and wood. Foams of polymers, metals, and ceramics can be made by numerous methods. Many foams are produced by gas evolvution. Inert gasses such as CO2 and N2 may be dissolved under high pressure and released by decreasing the pressure. Gas bubbles may also be formed by chemical decomposition or chemical reaction. Polyurethane foam is made by reacting isocyanate with water to form CO2. Mechanical beating also will produce foams. Foamed materials such as styrofoam can be formed by bonding together spheres that have been previously foamed.

Two-dimensional Photolithography

The intricate circuits formed on semiconductor chips are patterned by photolithography. A photosensitive material (photoresist) is applied to a semiconductor surface and baked at a low temperature. The surface is then exposed to intense ultraviolet light. The exposed regions of the photoresist become soluble in a developer and are removed. The surface is then baked at a somewhat higher temperature to harden the remaining photoresist. The exposed regions are then acid etched.

The etched regions may then be treated differently from the rest of the surface. They may be doped by exposure to plasma containing n- or p-type impurities, or they may be plated to form conducting circuits. Integrated circuits are composed of many overlapping layers (Figure 24.1), each defined by photolithography. Dopants are diffused into the substrate, and additional ions are implanted into some layers. Metal and polycrystalline silicon are deposited on others to form conductive circuits.

Transistors can be formed where there are n-p-n or p-n-p diffusion layers. Resistors are formed by meandering stripes of varying lengths. Capacitors are formed by parallel conductors separated by insulating material. The most common integrated circuits and those with the highest density are random access memories.

Photo-stereolithography

Three-dimensional parts can be made by photo-stereolithography using a liquid that polymerizes on exposure to ultraviolet light. A substrate platform is lowered into a bath and a desired portion of the surface of the liquid is exposed to a beam of ultraviolet light, causing it to polymerize.

The importance of materials to civilization is attested to by the names we give to various eras (Stone Age, Bronze Age, and Iron Age). We do not consider present times in terms of one specific material because so many are vital, including steel. The computer age would not be possible without silicon in computer chips.

Most introductory texts on materials science and engineering start with topics that are not of great interest to most engineers: atomic bonding, crystal structures, Miller indices. This introductory materials text differs from others because it is written primarily for engineers. It is shorter than most other materials texts so that it can easily be covered in one term. Emphasis is on mechanical and electrical properties of interest to most engineers. Thermal, optical, and magnetic behaviors are also covered. In addition, processing is treated in some detail.

Topics like X-ray diffraction, Miller indices, dislocations and coordination in compounds, surfaces, average molecular weights, Avrami kinetics, and Weibull analysis, which are of great interest to materials scientists but of little interest to most engineers, are covered only in the appendices. There is also an appendix on wood. There is no treatment of crystal systems, the Hall effect, or ferroelectricity.

After an introductory chapter, the text starts with phases and phase diagrams. This is followed by a chapter on diffusion, which treats diffusion in multiphase as well as single-phase systems. The next several chapters on mechanical behavior and failure should be of particular interest to mechanical engineers.

Edge and Screw Dislocations

Plastic deformation of crystalline solids occurs primarily by slip, which is the sliding of atomic planes over one another. An entire plane does not slide over another at one time. Rather it occurs by the motion of imperfections called dislocations. Dislocations are line imperfections in a crystal. The lattice around a dislocation is distorted so the atoms are displaced from their normal lattice sites. The lattice distortion is greatest near a dislocation and decreases with distance from it. One special form of a dislocation is an edge dislocation that is sketched in Figure A5.1. The geometry of an edge dislocation can be visualized by cutting into a perfect crystal and then inserting an extra half-plane of atoms. The dislocation is the bottom edge of this extra half-plane. An alternative way of visualizing dislocations is illustrated in Figure A5.2.

An edge dislocation is created by shearing the top half of the crystal by one atomic distance perpendicular to the end of the cut (Figure A5.3B). This produces an extra half-plane of atoms, the edge of which is the center of the dislocation. The other extreme form of a dislocation is the screw dislocation. This can be visualized by cutting into a perfect crystal and then shearing half of it by one atomic distance in a direction parallel to the end of the cut (Figure A5.3C). The end of the cut is the dislocation.

Carbon can occur in several different forms including diamond, graphite, amorphous carbon, and fullerenes. None of these forms fit into the classification of materials as metals, ceramics, or polymers. Figure 18.1 shows the equilibrium between graphite, diamond, and liquid.

Diamond

Each carbon atom in diamond is covalently bonded to four other carbon atoms as shown in Figure 18.2. Very strong bonding makes diamond the hardest material known (10,000 kg/mm2). Diamond is used for cutting very hard materials. Diamond has an extremely high Young's modulus (1,050 GPa) and a very low coefficient of thermal expansion (1 × 10−6/K). It has the highest thermal conductivity of all materials (2 kW/m-K compared with 401W/m-K for copper), making it useful for dissipating heat. Its density (3.52 Mg/m3) is considerably greater than that of graphite (2.25 Mg/m3).

The first synthetic diamonds were made by subjecting carbon to very high pressures at high temperatures. Diamond can also be grown by chemical vapor deposition (CVD) under low pressure (1 to 27 kPa). Gasses include a carbon source and typically hydrogen heated in a pressurized chamber and broken down, depositing diamond on exposed surfaces. Large areas (> 150 mm2) can be coated on a substrate. This allows CVD diamond films to be used as heat sinks in electronics and to be used in wear-resistant surfaces.

Graphite

The structure of graphite consists of sheets of carbon atoms arranged in a hexagonal pattern (Figure 18.3). The bonding in the hexagonal sheets is like that in a benzene ring.

It is often convenient to identify a plane or direction in a crystal by its indices. Note that all parallel planes have the same indices.

Planar Indices

The rules for determining the Miller indices of planes are as follows:

1. Write the intercepts of the plane on the three axes in order (a1, a2, and a3).

2. Take the reciprocals of these.

3. Reduce to the lowest set of integers with the same ratios.

4. Enclose in parentheses (hkl).

Commas are not used except in the rare case that one of the integers is larger than one digit. (This is rare because we are normally interested only in planes with low indices.) If a plane is parallel to an axis, its intercept is taken as ∞ and its reciprocal as 0. If the plane contains one of the axes or the origin, either analyze a parallel plane or translate the axes before finding indices. This is permissible since all parallel planes have the same indices. A negative index is indicated by a bar over the index rather than a negative sign, e.g., (11). Figure A2.1 shows several examples.

Direction Indices

The indices of a direction are the translations parallel to the three axes that produce the direction under consideration. The rules for finding direction indices are as follows:

1. Write the components of the direction parallel to the three axes in order.

2. Reduce to the lowest set of integers with the same ratios.

3. Enclose in brackets [uvw].

Polymer is the technical term for what are commonly called plastics. Polymers consist of very large molecules. In fact, the word polymer comes from poly (for many) and mer (for parts). There are two main groups of polymers: thermoplastics, which are composed of linear molecules and will soften and melt when heated, and thermosetting polymers, whose molecules form three-dimensional framework structures. Thermosetting polymers will not melt or even soften appreciably when heated. The basic organic chemistry of bonding in polymers is treated in Appendix 7.

Thermoplastics

Thermoplastics consist of long chain molecules. The simplest of these have carbon-carbon backbones. The structure of polyethylene is illustrated schematically in Figure 11.1. Other linear polymers with carbon-carbon backbones are listed in Table 11.1.

Other thermoplastics have more complex backbones. Among these are nylon, polyester (PET), polycarbonate, cellulose, and poly(paraphenylene terephthalamide) or PPTA (also known as Kevlar®). Figure 11.2 illustrates the molecular structure of these.

Elastomers are rubber-like polymers. They have carbon backbones that include carbon-carbon double bonds. Figure 11.3 shows the repeating unit. The radicals, R, are listed in Table 11.2.

Silicones are polymers with -Si-O-Si-O- backbones.

Degree of Polymerization

The degree of polymerization is the average number of mer units per molecule. It is the molecular weight of the polymer divided by the molecular weight of the mer. There are two ways of describing the molecular weight: the number-average molecular weight, and the weight-average molecular weight. They are usually not very different but the weight average is always somewhat larger.

What Is a Phase?

A phase is a state of aggregation of matter that has a distinctive structure. Phases may be solid, liquid, or gaseous. A phase may be a pure material or a solution of several components. A solid phase is either amorphous or has a characteristic crystal structure and definite composition range. A physical system may contain more than one solid phase with different crystal structures, or different ranges of possible compositions – one or more mutually insoluble liquid phases (for example oil and water) and a gas phase. All gasses are mutually soluble, and therefore only one gaseous phase is possible.

Single-phase materials include brass (a solid solution of zinc in copper with zinc atoms occupying lattice sites), sodium chloride crystals, glass, and polyethylene. Most plain carbon steels are two-phase materials, consisting of an iron-rich solid solution and iron carbide. A glass of ice water consists of two phases: liquid water and ice. In a glass of tonic water there may be three phases: liquid, ice, and gas bubbles.

The composition of a single phase may vary from place to place, but composition change is always gradual and without abrupt changes. In multiple-phase systems, however, there are discontinuities of composition and structure at phase boundaries. The compositions on each side of the boundary are usually in equilibrium. For example, the oxygen concentration changes abruptly between copper with some oxygen dissolved in it and copper oxide.

Properties

One material is chosen over another for a particular application because its properties are better suited for the intended use. Among the important properties are strength, corrosion resistance, electrical conductivity, weight, material cost, processing costs, and appearance. Usually several properties are important.

In many applications, stiffness is important. Materials deform when a stress is applied to them. If the stress is low, the deformation will be elastic. In this case the deformation will disappear and the material will regain its original shape when the stress is removed. Good examples are elastic bands and paper clips. With greater stress, a material may deform plastically. In this case the deformation does not disappear when the stress is removed, so the shape change is permanent. This happens when the stress exceeds the yield strength of the material. With a still higher stress, the material may reach its tensile strength and fail. Ductility and toughness are also important. The ductility of a material is the amount of deformation a material may undergo before breaking. Toughness is a measure of how much energy a material absorbs per area before fracture.

Electrical properties are of paramount importance in some applications. Electrical conductors should have high conductivities and insulators very low conductivities. Integrated circuits for computers require semiconductors. The dielectric constant may be important in applications involving high frequencies. Piezoelectric behavior is required for sonar transmitters and receivers.

Glasses are amorphous so they have no long-range order and no symmetry. There is, however, a great deal of short-range order. If crystallization is prevented during cooling, an amorphous glass will form with short-range order inherited from the liquid. The critical cooling rate to prevent crystallization varies greatly from one material to another. Silicate glasses cannot crystallize unless the cooling rates are extremely slow. On the other hand, extremely rapid cooling is required to prevent crystallization of metals.

Structure of Silicate Glasses

The basic structural units of silicate glasses are tetrahedra with Si4+ ions in the center bonded covalently to O2− ions at each corner. In pure silica all corner oxygen ions are shared by two tetrahedra (Figure 13.1). The result is a covalently bonded glass with a very high viscosity at elevated temperatures.

The compositions of typical commercial glasses are quite complex. Soda-lime glasses may contain 72% SiO2, 14% Na2O, 11% CaO, and 3% MgO. The Na+, Ca2+, and Mg2+ ions are bonded ionically to some of the corner O2− ions (Figure 13.2). With these alkali and alkaline earth oxides, not all of the oxygen ions are covalently bonded to two tetrahedra. This lowers the viscosity at high temperatures.

Steels

Steels are iron-base alloys usually containing carbon. Figure 7.1 shows the iron-carbon phase diagram. Below 911°C and between 1410°C and the melting point, iron has a bcc crystal structure called ferrite. Between 1410°C and 911°C it has an fcc crystal structure called austenite. Austenite dissolves much more carbon interstitially than ferrite. On slow cooling below 727°C, the austenite transforms by a eutectoid reaction into ferrite and iron carbide or cementite (which contains 6.7%C). The ferrite and cementite form alternating platelets called the eutectoid temperature. The resulting microstucture is called pearlite (see Figure 7.2).

Pearlite Formation

When a steel containing less than 0.77%C (hypo-eutectoid steel) is slowly cooled, some ferrite forms before any pearlite. A steel containing more than 0.77%C (hyper-eutectoid steel) will form some cementite before any pearlite. The formation of pearlite from austenite on cooling requires diffusion of carbon from ahead of the advancing ferrite platelets to the advancing carbide platelets as indicated in Figure 7.3. Because diffusion takes time, pearlite formation is not instantaneous. The rate at which pearlite forms depends on how much the temperature is below 717°C. The rate of diffusion increases with temperature, but the driving force for the transformation increases as the temperature is lowered. The result is that the rate of transformation is fastest between 500 and 600°C, as indicated schematically in Figure 7.4.