EChem 1 Module 6 - Mechanical Properties of Metals PDF

EChem 1 Module 6 Mechanical Properties of Metals  WHY STUDY The Mechanical Properties of Metals? It is incumbent on engineers to understand how the various mechanical properties are measured and what these properties represent; they may be called upon to design structures/component...

EChem 1 Module 6 Mechanical Properties of Metals  WHY STUDY The Mechanical Properties of Metals? It is incumbent on engineers to understand how the various mechanical properties are measured and what these properties represent; they may be called upon to design structures/components using predetermined materials such that unacceptable levels of deformation and/or failure will not occur. ▪ It is necessary to know the characteristics of the material and to design the member from which it is made such that any resulting deformation will not be excessive and fracture will not occur. ▪ The mechanical behavior of a material reflects the relationship between its response or deformation to an applied load or force. ▪ Important mechanical properties are strength, hardness, ductility, and stiffness.  Important mechanical properties ▪ Strength ▪ Hardness ▪ Ductility ▪ Stiffness  CONCEPTS OF STRESS AND STRAIN If a load is static or changes relatively slowly with time and is applied uniformly over a cross section or surface of a member, the mechanical behavior may be ascertained by a simple stress–strain test; these are most commonly conducted for metals at room temperature. There are three principal ways in which a load may be applied: namely, tension, compression, and shear  CONCEPTS OF STRESS AND STRAIN Three principal ways in which a load may be applied: ▪ Tension ▪ Compression ▪ Shear There are three principal ways in which a load may be applied: namely, tension, compression, and shear  Tension Tests One of the most common mechanical stress–strain tests is performed in tension. The tension test can be used to ascertain several mechanical properties of materials that are important in design. Standard tensile specimen ▪ The tensile testing machine is designed to elongate the specimen at a constant rate, and to continuously and simultaneously measure the instantaneous applied load (with a load cell) and the resulting elongations (using an extensometer). ▪ A stress–strain test typically takes several minutes to perform and is destructive; that is, the test specimen is permanently deformed and usually fractured. ▪ Gauge length is used in ductility computations; the standard value is 50 mm (2.0 in.). The specimen is mounted by its ends into the holding grips of the testing apparatus.  To minimize the geometrical factors, load and elongation are normalized to the respective parameters of engineering stress and engineering strain. Engineering stress is defined by the relationship ▪ Engineering strain is defined according to  Compression Tests Compression stress–strain tests may be conducted if in-service forces are of this type.A compression test is conducted in a manner similar to the tensile test,except that the force is compressive and the specimen contracts along the direction of the stress. These equations are utilized to compute compressive stress and strain Compressive tests are used when a material’s behavior under large and permanent (i.e., plastic) strains is desired, as in manufacturing applications, or when the material is brittle in tension.  Shear and Torsional Tests Shear stress is computed according to  Torsion is a variation of pure shear, wherein a structural member is twisted; torsional forces produce a rotational motion about the longitudinal axis of one end of the member relative to the other end. Examples of torsion are found for machine axles and drive shafts, and also for twist drills. Torsional tests are normally performed on cylindrical solid shafts or tubes. ▪ Shear stress is a function of the applied torque T ▪ Shear strain is related to the angle of twist  Geometric Considerations of the Stress State Stresses that are computed from the tensile, compressive, shear, and torsional force states act either parallel or perpendicular to planar faces of the bodies represented in these illustrations. The stress state is a function of the orientations of the planes upon which the stresses are taken to act.  Stresses that are computed from the tensile, compressive, shear, and torsional force states act either parallel or perpendicular to planar faces of the bodies represented in these illustrations.  STRESS–STRAIN BEHAVIOR The degree to which a structure deforms or strains depends on the magnitude of an imposed stress. For most metals that are stressed in tension and at relatively low levels, stress and strain are proportional to each other through the relationship known as Hooke’s Law, and the constant of proportionality E (GPa or psi) is the modulus of elasticity, or Young’s modulus. Modulus of elasticity values for several metals at room temperature Elastic Deformation - deformation in which stress and strain are proportional; a plot of stress (ordinate) versus strain (abscissa) results in a linear relationship. ▪ The slope of this linear segment corresponds to the modulus of elasticity E. ▪ This modulus may be thought of as stiffness, or a material’s resistance to elastic deformation. ▪ The greater the modulus, the stiffer the material, or the smaller the elastic strain that results from the application of a given stress. ▪ The modulus is an important design parameter used for computing elastic deflections. ▪ Elastic deformation is nonpermanent, which means that when the applied load is released, the piece returns to its original shape. There are some materials (e.g., gray cast iron, concrete, and many polymers) for which this elastic portion of the stress–strain curve is not linear; hence, it is not possible to determine a modulus of elasticity. For this nonlinear behavior, either tangent or secant modulus is normally used. Tangent modulus is taken as the slope of the stress–strain curve at some specified level of stress, while secant modulus represents the slope of a secant drawn from the origin to some given point of the curve. On an atomic scale, macroscopic elastic strain is manifested as small changes in the interatomic spacing and the stretching of interatomic bonds. As a consequence, the magnitude of the modulus of elasticity is a measure of the resistance to separation of adjacent atoms, that is, the interatomic bonding forces. Furthermore,this modulus is proportional to the slope of the interatomic force–separation curve at the equilibrium spacing: Figure shows the force–separation curves for materials having both strong and weak interatomic bonds; the slope at is indicated for each. Values of the modulus of elasticity for ceramic materials are about the same as for metals; for polymers they are lower. These differences are a direct consequence of the different types of atomic bonding in the three materials types. Furthermore, with increasing temperature, the modulus of elasticity diminishes, as is shown for several metals in Figure.  The imposition of compressive, shear, or torsional stresses also evokes elastic behavior. The stress–strain characteristics at low stress levels are virtually the same for both tensile and compressive situations, to include the magnitude of the modulus of elasticity. Shear stress and strain are proportional to each other through the expression where G is the shear modulus, the slope of the linear elastic region of the shear stress–strain curve  ANELASTICITY ▪ Time-dependent elastic behavior and it is due to time-dependent microscopic and atomistic processes that are attendant to the deformation. ▪ Elastic deformation will continue after the stress application, and upon load release some finite time is required for complete recovery. ▪ For metals the anelastic component is normally small and is often neglected. However, for some polymeric materials its magnitude is significant; in this case it is termed viscoelastic behavior. ELASTIC PROPERTIES OF MATERIALS  For isotropic materials, shear and elastic moduli are related to each other and to Poisson’s ratio according to In most metals G is about 0.4E; thus, if the value of one modulus is known, the other may be approximated. Many materials are elastically anisotropic; that is, the elastic behavior (e.g.,the magnitude of E) varies with crystallographic direction.  Plastic Deformation For most metallic materials, elastic deformation persists only to strains of about 0.005. As the material is deformed beyond this point, the stress is no longer proportional to strain (Hooke’s law, Equation 6.5, ceases to be valid), and permanent, nonrecoverable, or plastic deformation occurs.  Figure 6.10a plots schematically the tensile stress–strain behavior into the plastic region for a typical metal. The transition from elastic to plastic is a gradual one for most metals; some curvature results at the onset of plastic deformation, which increases more rapidly with rising stress. ▪ From an atomic perspective, plastic deformation corresponds to the breaking of bonds with original atom neighbors and then reforming bonds with new neighbors as large numbers of atoms or molecules move relative to one another; upon removal of the stress they do not return to their original positions. ▪ The mechanism of this deformation is different for crystalline and amorphous materials. ▪ For crystalline solids, deformation is accomplished by means of a process called slip, which involves the motion of dislocations. ▪ Plastic deformation in noncrystalline solids (as well as liquids) occurs by a viscous flow mechanism.  TENSILE PROPERTIES ▪ Yielding and Yield Strength ▪ It is desirable to know the stress level at which plastic deformation begins, or where the phenomenon of yielding occurs. For metals that experience this gradual elastic– plastic transition, the point of yielding may be determined as the initial departure from linearity of the stress–strain curve; this is sometimes called the proportional limit, as indicated by point P in Figure 6.10a. ▪ The stress corresponding to the intersection of this line and the stress–strain curve as it bends over in the plastic region is defined as the yield strength ▪ The units of yield strength are MPa or psi ▪ Some steels and other materials exhibit the tensile stress–strain behavior as shown in Figure 6.10b. The elastic–plastic transition is very well defined and occurs abruptly in what is termed a yield point phenomenon. At the upper yield point, plastic deformation is initiated with an actual decrease in stress. ▪ The magnitude of the yield strength for a metal is a measure of its resistance to plastic deformation. Yield strengths may range from 35 MPa (5000 psi) for a low strength aluminum to over 1400 MPa (200,000 psi) for high-strength steels.  Tensile Strength ▪ The tensile strength TS (MPa or psi) is the stress at the maximum on the engineering stress–strain curve. ▪ After yielding, the stress necessary to continue plastic deformation in metals increases to a maximum, point M in Figure  Tensile Strength ▪ This corresponds to the maximum stress that can be sustained by a structure in tension; if this stress is applied and maintained, fracture will result. ▪ However, at this maximum stress, a small constriction or neck begins to form at some point, and all subsequent deformation is confined at this neck. ▪ This phenomenon is termed “necking,” and fracture ultimately occurs at the neck. The fracture strength corresponds to the stress at fracture.  Ductility ▪ Ductility is another important mechanical property. It is a measure of the degree of plastic deformation that has been sustained at fracture. ▪ A material that experiences very little or no plastic deformation upon fracture is termed brittle. ▪ The tensile stress–strain behaviors for both ductile and brittle materials are schematically illustrated in Figure.  Ductility may be expressed quantitatively as either percent elongation or percent reduction in area. The percent elongation %EL is the percentage of plastic strain at fracture, or Percent reduction in area %RA is defined as  A knowledge of the ductility of materials is important for at least two reasons. ▪ First, it indicates to a designer the degree to which a structure will deform plastically before fracture. ▪ Second, it specifies the degree of allowable deformation during fabrication operations. Several important mechanical properties of metals may be determined from tensile stress– strain tests. ▪ Resilience is the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading, to have this energy recovered. The associated property is the modulus of resilience, which is the strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding. ▪ Computationally, the modulus of resilience for a specimen subjected to a uniaxial tension test is just the area under the engineering stress–strain curve taken to yielding Assuming a linear elastic region, Incorporation of the equations, yields ▪ Toughness is a mechanical term that is used in several contexts; loosely speaking, it is a measure of the ability of a material to absorb energy up to fracture.  TRUE STRESS AND STRAIN ▪ True stress is defined as the load F divided by the instantaneous cross-sectional area over which deformation is occurring ▪ True strain defined by Schematic comparison of engineering and true stress–strain behaviors For some metals and alloys the region of the true stress–strain curve from the onset of plastic deformation to the point at which necking begins may be approximated by  ELASTIC RECOVERY AFTER PLASTIC DEFORMATION Upon release of the load during the course of a stress–strain test, some fraction of the total deformation is recovered as elastic strain. This behavior is demonstrated in Figure 6.17, a schematic engineering stress–strain plot.  COMPRESSIVE, SHEAR, AND TORSIONAL DEFORMATION ▪ For compression, there will be no maximum, since necking does not occur; furthermore, the mode of fracture will be different from that for tension. ▪ HARDNESS which is a measure of a material’s resistance to localized plastic deformation (e.g., a small dent or a scratch).  Hardness tests are performed more frequently than any other mechanical test for several reasons: 1) They are simple and inexpensive—ordinarily no special specimen need be prepared, and the testing apparatus is relatively inexpensive. 2) The test is nondestructive—the specimen is neither fractured nor excessively deformed; a small indentation is the only deformation. 3) Other mechanical properties often may be estimated from hardness data, such as tensile strength  Rockwell Hardness Test The Rockwell tests constitute the most common method used to measure hardness because they are so simple to perform and require no special skills. Several different scales may be utilized from possible combinations of various indenters and different loads, which permit the testing of virtually all metal alloys (as well as some polymers).  Brinell Hardness Tests In Brinell tests, as in Rockwell measurements, a hard, spherical indenter is forced into the surface of the metal to be tested. The diameter of the hardened steel (or tungsten carbide) indenter is 10.00 mm (0.394 in.). Standard loads range between 500 and 3000 kg in 500-kg increments; during a test, the load is maintained constant for a specified time (between 10 and 30 s).  Knoop and Vickers Microindentation Hardness Tests15 Two other hardness-testing techniques are Knoop (pronounced ) and Vickers (sometimes also called diamond pyramid). For each test a very small diamond indenter having pyramidal geometry is forced into the surface of the specimen.Applied loads are much smaller than for Rockwell and Brinell,ranging between 1 and 1000 g.The resulting impression is observed under a microscope and measured;this measurement is then converted into a hardness number  Hardness Conversion The facility to convert the hardness measured on one scale to that of another is most desirable. However, since hardness is not a well-defined material property, and because of the experimental dissimilarities among the various techniques, a comprehensive conversion scheme has not been devised. Hardness conversion data have been determined experimentally and found to be dependent on material type and characteristics. The most reliable conversion data exist for steels, some of which are presented in Figure 6.18 for Knoop, Brinell, and two Rockwell scales; the Mohs scale is also included. Correlation Between Hardness and Tensile Strength Both tensile strength and hardness are indicators of a metal’s resistance to plastic deformation. Consequently, they are roughly proportional for tensile strength as a function of the HB for cast iron, steel, and brass. The same proportionality relationship does not hold for all metalsAs a rule of thumb for most steels, the HB and the tensile strength are related according to 1. A cylindrical specimen of a nickel alloy having an elastic modulus of 207 Gpa (30 x 106 psi) and an original diameter of 10.2 mm (0.40 in.) will experience only elastic deformation when a tensile load of 8900 N (2000 lbf) is applied. Compute the maximum length of the specimen before deformation if the maximum allowable elongation is 0.25 mm 90.010 in) 2. A cylindrical rod of steel (E = 207 Gpa, 30 x 106 psi) having a yield strenght of 310 MPa (45,000 psi) is to be subjected to a load of 11,100 N (2500 lbf). If the length of the rod is 500 mm (20.0 in.), what must be the diameter to allow an elongation of 0.38 mm (0.015 in.)? 3. A cylindrical specimen of a hypothetical metal alloy is stressed in compression. If its original and final diameters are 30.00 and 30.04 mm, respectively, and its final length is 105.20 mm, compute its original length if the deformation is totally elastic. The elastic and shear moduli for this alloy are 65.5 and 25.4 GPa, respectively. 4. A cylindrical metal specimen having an original diameter of 12.8 mm (0.505 in.) and gauge length of 50.80 mm (2.000 in.) is pulled in tension until fracture occurs.The diameter at the point of fracture is 8.13 mm (0.320 in.), and the fractured gauge length is 74.17 mm (2.920 in.). Calculate the ductility in terms of percent reduction in area and percent elongation. Reference: Materials Science and Engineering: An Introduction by William Calister, Jr.