- The section on mechanical properties and tests discusses all the hardness tests and includes a detailed explanation of the tensile test and tensile properties. - A study of the mechanical properties of materials must begin with an understanding of the structure of solid materials. - The definitions of the mechanical properties given in the following sections are on the basis of the crys- talline structure of material. - For example, strength (and hardness) is defined as the ability of the material to resist slip along its crystallographic planes. - The crystal structure and the type of interatomic bonding forces determine the strength and ductility of the material.. - The number of protons in the nucleus determines the nuclear charge of the atom and is called the atomic number. - The atomic weight of an atom is the sum of the number of protons and neutrons. - The maximum number of electrons in any shell is 2n 2 , where n is the quantum number of the shell. - This is one of the most important distinctions between ionic (or covalent) bonding and metallic bonding and is discussed later.. - Of the three primary bonding forces, the metallic bond is by far the most important for an understanding of the mechanical properties of the materials with which the practicing engineer is concerned. - The metallic bond is a special type of covalent bond wherein the positively charged nuclei of the metal atoms are attracted by electro- static forces to the valence electrons that surround them. - The mean radius of the valence electrons in a free (isolated) metal atom is larger than the interatomic distance of that metal in the solid crystalline state. - Thus the structure of the solid metal is a close- packed arrangement of positive ion "cores". - This ability of the valence electrons to move freely through the solid explains the high thermal and electrical conductivities of metals. - That is, the center of the positive charge and the center of the negative charge do not coincide, and it is this dipole that creates molecular bonding.. - Whereas the electrical properties of a material depend on the internal structure of the atoms, the mechanical properties depend on the types of structures that groups of atoms form. - Amorphous materials are those whose structure has no repetitive arrangement of the atoms of which it is comprised. - A given mass of hot glass, like any liq- uid, takes the shape of the container in which it is placed.. - When hot liquid glass is cooled to some temperature T g , called the glass transition temperature, there is an abrupt change in the slope of the specific volume versus temperature curve. - Figure 7.2 shows some of the more common monomers or unsaturated molecules that are used in the building of macromolecules. - It is the base of the group of hydrocarbons called olefins. - Because of the shape of the molecule, it is described as a ring molecule or compound. - Figure 7.3 illustrates the addition polymerization of the ethylene monomer. - 1.2b, is similar to ethylene except that one of the hydrogen atoms is replaced with a chlorine atom. - The styrene monomer is made from the benzene ring (CeH 6 ) with one of the hydrogen atoms replaced with a CH=CH 2 molecule, as shown in Fig.. - That is, the long axes of the chains of all the molecules tend to be parallel. - the degree of orientation being a measure of the crystallinity. - The strength of an aligned polymeric material is stronger along the axis of the chains and much lower in the perpendicular directions. - This is due to the fact that only weak van der Waals forces hold the individual, aligned macromolecules together, whereas the atoms along the axes of the chains are held together by strong and covalent bonds. - The intermolecu- lar strength of linear polymers can be increased by the addition of polar (dipole) groups along the length of the chain. - A space lattice is the three-dimensional network of straight lines that connects the centers of the atoms along three axes. - The intersec- tions of the lines are lattice points, and they designate the locations of the atoms.. - Although the atoms vibrate about their centers, they occupy the fixed positions of the lattice points. - Figure 7.6 is a sketch of a space lattice, with the circles represent- ing the centers of the atoms. - Most of the metals belong to three of the space-lattice types: face-centered cubic, body- centered cubic, and hexagonal close-packed. - Most of the common metals (see Table 7.1) have face-centered cubic structures. - Fig- ure 7.7 shows the arrangement of the atoms, represented by spheres, in the face- centered cubic (FCC) structure as well as that fraction or portion of each atom associated with an individual unit cell. - A quan- titative measure of how efficiently the atoms are packed in a structure is the atomic packing factor (APF), which is the ratio of the volume of the atoms in a cell to the total volume of the unit cell. - This means that 26 percent of the FCC unit cell is "void". - Many of the stronger metals (Cr, Fe, Mo, W) have body-centered cubic (BCC) lattice structures, whereas the softer, more ductile metals (Ag, Al, Au, Cu, Ni) have the FCC structure (see Table 7.1). - There are two atoms per unit cell: one in the center (body center) and 1 A in each of the eight corners. - The Miller indices are used to designate specific crystallographic planes with respect to the axes of the unit cell. - The Miller indices are determined from the three intercepts that the plane makes with the three axes of the crystal. - Actually it is the reciprocal of the distances between the intercepts with. - (b) one half of the front face showing the relationship between the lattice parameter a and the atomic radius r.. - FIGURE 7.8 Unit cell of body-centered cubic structure, (a) The unit cell has 1 A atom at each of 8 corners and 1 atom at the geometric center of the cell, for a total of 2 atoms. - (b) the relationship of the lattice parameter a and atomic radius r.. - the axis and the origin measured in terms of multiples or fractions of the unit cell lengths a, b, and c used in the determination. - Figure 1.9a identifies the front face of the crystal with the Miller indices (100).. - The commas are not included because they are simply part of the sentence structure.. - Figure 7.95 shows the (110) plane that is parallel to the z axis and is a face diago- nal on the top and bottom faces of the unit cell. - spaces of the lat-. - Thus the lattice lines joining the centers of the atoms are not straight in the vicinity of the vacancy. - Vacancies have no effect on the metallurgical control of the mechanical properties discussed in later sections. - However, it does not lie in the plane of the solvent lattice but lies either above or below the sketched plane. - The third type of point defect, the presence of a foreign atom at one of the lattice points, is referred to as a substitutional defect. - Figure 7.1Oc and d shows the substitution of a smaller and a larger atom S at one of the lattice points. - Unlike the interstitial atom, the substitutional one is in the plane of the solvent matrix. - The crystallographic planes are also warped in the vicinity of the substitutional defect, inward for the smaller atom and outward for the larger atom. - The distortion of the crystallographic planes is very important to an under- standing of control of the strength of materials, which is presented later.. - Examinations of crystals under the electron microscope have shown interruptions in the periodicity of the lattice structure in certain directions. - Actually, it is the edge of this extra plane of atoms and runs from one end of the crystal to the other.. - When looking at the crystalline plane that is perpendicular to the dislocation line, the imperfection appears as an extra row of atoms in a part of the crystal.. - When the extra plane of atoms is in the bottom portion of the crystal, the vertical leg is placed below the horizontal one and the dislocation is said to be negative. - The part of the crystal containing the extra plane of atoms is in compression, whereas that portion on the other side of the dis- location line is in tension. - Shear stresses are set up in the lat- tice surrounding a screw dislocation as a result of the distortion in atomic array that the defect causes.. - The Burgers vector is the distance, measured in multiples of the lattice parameter, that is needed to close a straight-sided loop around a dislocation when going the same number of lattice distances in all four directions. - The material in the grain boundary is at a higher energy level than the material near the center of the grain because of the increased elastic strain energy of the atoms that are forced from their normal (lowest-energy) sites in a perfect lattice.. - The distortion of the twinned lattice is low in comparison to that at a grain boundary. - A third planar defect is the low-angle grain boundary or low-angle tilt boundary, where the angular misalignment of the two grains is very small, on the order of a few degrees. - The angular mismatch of the crystal planes is due to a row of dislocations piled above each other.. - The lattice on both sides of the defect is normal. - Slip can be defined as the massive sliding movement of one large body of atoms with respect to the remaining body of atoms of the crystal along crystallographic planes.. - The displacements of the individual atoms are very small during elastic deformation. - only the outline or exterior shape of the single crystal has changed. - It is believed, on the basis of the theories of elasticity, that the shear stress must be equal to the value of G/2n, where G is the shear modulus of elasticity.. - FIGURE 7.11 Two-dimensional sketch of the slip mechanism, (a) A perfect crystal. - shear strength of the other pure metals is also 400 to 500 times larger than the actual shear strength. - Experimental study of the spacings of the slip planes and the sizes of the jog have been made on some of the common metals. - The spacing of the parallel planes along which slip occurs varies randomly, with an average distance between slip planes of about 2000 atom diameters. - The length of the step or jog at the surface of the grain is approximately 200 to 700 atom diameters.. - The slip lines are the intersection of the crys- tallographic planes along which slip occurred with the etched surface of the speci- men. - Slip results in a narrow band on either side of the slip plane within which the lattice structure is severely distorted. - The metal in the higher energy level dissolves into the reagent much more rapidly than the rest of the crys- tal, leaving a narrow groove where the severely distorted band intersects the surface.. - Although the specific mechanical properties of real materials are discussed in detail in the material that follows, it is very appropriate at this time to relate the concepts of the strengthening mechanisms to the previously described crystalline structures. - These three principles are stated here because they involve the distortion of the lattice structure that has just been discussed.. - The second principle of mechanical strength is this: Slip is retarded by inducing mechanical strains, or distortions, in the lattice structure of the material These distor- tions were discussed previously as lattice imperfections or defects. - Local distortion of the lattice structure at the grain boundaries induces substantial strain energy in those regions. - This distortion impedes slip, or causes the dislocations to pile up, and consequently, the grain-boundary material is stronger than the mate- rial at the central portions of the crystal. - However, as additional energy is added to a polycrystalline material by raising the temperature, the grain-boundary material softens (and also melts) sooner or at a lower temperature than the bulk of the grain. - Above the equicohesive temperature, the grain-boundary material is the weaker of the two.. - Also, since the surface area of a sphere is proportional to the square of its diameter, it can be assumed as a first approximation that the yield strength is proportional to the reciprocal of the square of the grain diameter.. - tion of one grain intrudes into the space that was previously occupied by another grain, with a resulting distortion of the lattice in both grains.. - Alloying (single- and multiple-phase) is the most important of the methods avail- able to control or manipulate the mechanical properties of materials. - Figure 7.130 shows the effect on the strength of the material of adding a foreign element B or C to the lattice structure of element A. - That is, some of the added element goes into solution in the solvent lat- tice and thus has a strengthening effect. - the remainder of the added element forms a second phase (either another solid solution or a compound) that is present as small grains or crystals.. - On slow cooling, the second phase precip- itates as a massive network in the grain-boundary regions of the solvent matrix. - Hardness is used more frequently than any other of the mechanical properties by the design engineer to specify the final condition of a structural part. - The Rockwell hardnesses are hardness numbers obtained by an indentation type of test based on the depth of the indentation due to an increment of load
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