Metal, mechanical properties of

Stress states

Stress is the internal resistance, per unit area, of a body subjected to external forces. The forces may be distributed over the surface of a body (surface forces) or may be distributed over the volume (body forces); examples of body forces are gravity, magnetic forces, and centrifugal forces. Forces are generally not uniformly distributed over any cross section of the body upon which they act; a complete description of the state of stress at a point requires the magnitudes and directions of the force intensities on each surface of a vanishingly small body surrounding the point. All forces acting on a point may be resolved into components normal and parallel to faces of the body surrounding the point. When force intensity vectors act perpendicular to the surface of the reference body, they are described as normal stresses. When the force intensity vectors are parallel to the surface, they describe a state of shear stress. Normal stresses are positive, when they act to extend a line (tension). Shear stresses always occur in equal pairs of opposite signs.

A complete description of the state of stress requires knowledge of magnitudes and directions of only three normal stresses, known as principal stresses, acting on reference faces at right angles to each other and constituting the bounding faces of a reference parallelepiped. Three such mutually perpendicular planes may always be found in a body acted upon by both normal and shear forces; along these planes there is no shear stress, but on other planes either shear or shear and tensile forces will exist.

The shear stress is a maximum on a plane bisecting the right angle between the principal planes on which act the largest and smallest (algebraic) principal stresses. The largest normal stress in the body is equal to the greatest principal stress. The magnitude and orientation of the maximum shear stress determine the direction and can control the rate of the inelastic shear processes, such as slip or twinning, which occur in metals. Shear stresses also play a role in crack nucleation and propagation, but the magnitude and direction of the maximum normal stress more often control fracture processes in metals capable only of limited plastic deformation.

It is often useful to characterize stress or strain states under boundary conditions of either plane stress (stresses applied only in the plane of a thin sheet) or plane strain (stresses applied to relatively thick bodies under conditions of zero transverse strain). These two extreme conditions illustrate that strains can occur in the absense of stress in that direction, and vice versa.

Tension and torsion

In simple tension, two of the three principal stresses are reduced to zero, so that there is only one principal stress, and the maximum shear stress in numerically half the maximum normal stress. Because of the symmetry in simple tension, every plane at 45° to the tensile axis is subjected to the maximum shear stress. For other kinds of loading, the relationship between the maximum shear stress and the principal stresses are obtained using the same method, with the results depending upon the loading condition.

For example, in simple torsion, the maximum principal stress is inclined 45° to the axis of the bar being twisted. The least principal stress (algebraically) is perpendicular to this, at 45° to the bar axis, but equal to and opposite in sign to the first principal stress—that is, it is compressive. Both of these are in a plane perpendicular to the radial direction, the direction of the intermediate principal stress, which in this case has the magnitude zero. Every free external surface of a body is a principal plane on which the principal stress is zero. In torsion, the maximum shear stress occurs on all planes perpendicular to and parallel with the axis of the twisted bar. But because the principal stresses are equal but of opposite sign, the maximum shear stress is numerically equal to the maximum normal stress, instead of to half of it, as in simple tension. This means that in torsion one may expect more ductility (the capacity to deform before fracture) than in tension. Materials that are brittle (exhibiting little capacity for plastic deformation before rupture) in tension may be ductile in torsion. This is because in tension the critical normal stress for fracture may be reached before the critical shear stress for plastic deformation is reached; in torsion, because the maximum shear stress is equal to the maximum normal stress instead of half of it as in tension, the critical shear stress for plastic deformation is reached before the critical maximum normal stress for fracture.

Tension test

To achieve uniformity of distribution of stress and strain in a tension test requires that the specimen be subjected to no bending moment. This is usually accomplished by providing flexible connections at each end through which the force is applied. The specimen is stretched at a controllable rate, and the force required to deform it is observed with an appropriate dynamometer. The strain is measured by observing the extension between gage marks adequately remote from the ends, or by measuring the diameter and calculating the change in length by using the constancy of volume that characterizes plastic deformation. Diameter measurements are applicable even after necking-down has begun. The elastic properties are seldom determined since these are structure-insensitive.

Yield strength

The elastic limit is rarely determined. Metals are seldom if ever ideally elastic, and the value obtained for the elastic limit depends on the sensitivity of strain measurement. The proportional limit, describing the limit of applicability of Hooke's law of linear dependence of stress on strain, is similarly difficult to determine. Modern practice is to determine the stress required to produce a prescribed inelastic strain, which is called the yield strength.

Tensile strength

Tensile strength, usually called the ultimate tensile strength, is calculated by dividing the maximum load by the original cross-sectional area of the specimen. It is, therefore, not the maximum value of the true tensile stress, which increases continuously to fracture and which is always higher than the nominal tensile stress because the area continuously diminishes. For ductile materials the maximum load, upon which the tensile strength is based, is the load at which necking-down begins. Beyond this point, the true tensile stress continues to increase, but the force on the specimen diminishes. This is because the rate of strain hardening has fallen to a value less than the rate at which the stress is increasing because of the diminution of area.

Yield point

A considerable number of alloys, including those of iron, molybdenum, tungsten, cadmium, zinc, and copper, exhibit a sharp transition between elastic and plastic flow. The stress at which this occurs is known as the upper yield point. A sharp drop in load to the lower yield point accompanies yielding, followed, in ideal circumstances, by a flat region of yield elongation; subsequently, normal strain hardening is observed (see illustration).

Elongation

The tensile test provides a measure of ductility, by which is meant the capacity to deform by extension. The elongation to the point of necking-down is called the uniform strain or elongation because, until that point on the stress-strain curve, the elongation is uniformly distributed along the gage length. The strain to fracture or total elongation includes the extension accompanying local necking. Since the necking extension is a fixed amount, independent of gage length, it is obvious that the total elongation will depend upon the gage length, and will be greater for short gage lengths and less for long gage lengths.

Ductile-to-brittle transition

Many metals and alloys, including iron, zinc, molybdenum, tungsten, chromium, and structural steels, exhibit a transition temperature, below which the metal is brittle and above which it is ductile. The transition temperature very clearly is sensitive to alloy content, but it will vary even for the same material, depending upon such external test conditions as stress state and strain rate, and microstructural variables such as purity and grain size. The ductility transition frequently is accompanied by a change in the mechanism of fracture (as in iron and steels or zinc), but this need not be so.

Notch tensile test

Notch sensitivity in metals cannot be detected by the ordinary tension test on smooth bar specimens. Either a notched sample may be used in a tension test or a notched-bar impact test may be conducted. Notches produce triaxial stresses under the notch root as tensile forces are applied, thereby decreasing the ratio of shear stress to normal stress and increasing the likelihood of fracture. Materials are evaluated by a quantity, notch strength, which is the analog of the ultimate tensile strength in an ordinary tensile test. The notch strength is defined as the maximum load divided by the original cross-sectional area at the notch root.

Compression test

Very brittle metals, or metals used in products which are formed by compressive loading (rolling, forging), often are tested in compression to obtain yield strength or yield point information. Compression test specimens are generally in the form of solid circular cylinders. The ratio of specimen length to diameter is critical in that high ratios increase the likelihood of buckling during a test, thereby invalidating the test results. Proper specimen alignment is important for the same reason. In addition, care must be taken to lubricate specimen ends to avoid spurious effects from friction between the specimen ends and the testing machine. In the case of a metal which fails in compression by a shattering fracture (for example, cast iron), a quantity known as the compressive strength may be reproducibly obtained by dividing the maximum load carried by the specimen by its cross-sectional area. For materials which do not fail in compression by shattering, the compressive strength is arbitrarily defined as the maximum load at or prior to a specified compressive deformation.

Notched-bar impact test

Notched-bar impact tests are conducted to estimate the resistance to fracture of structures which may contain defects. The common procedure is to measure the work required to break a standardized specimen, and to express the results in work units, such as foot-pounds or newton-meters. The notched-bar impact test does not provide design information regarding the resistance of a material to crack propagation. Rather, it is a comparative test, useful for preliminary screening of materials or evaluation of processing variables. The notch behavior indicated in a single test applies only to the specimen size, notch geometry, and test conditions involved and is not generally applicable to other specimen sizes and conditions. The test is most useful when conducted over a range of temperatures so that the ductile-to-brittle transition can be determined.

Notched-bar tests are usually made in either a simple beam (Charpy) or a cantilever beam (Izod) apparatus, in both of which the specimen is broken by a freely swinging pendulum; the work done is obtained by comparing the position of the pendulum before it is released with the position to which it swings after striking and breaking the specimen. In the Izod test, the specimen is held in a vise, with the notch at the level of the top of the vise, and broken as a cantilever beam in bending with the notch on the tension side. In the Charpy test, the specimen is laid loosely on a support in the path of the pendulum and broken as a beam loaded at three points; the tup (striking edge) strikes the middle of the specimen, with the notch opposite the tup, that is, on the tension side. Both tests give substantially the same result with the same specimen unless the material is very ductile, a situation in which there is little interest.

Hardness testing

When the only information that is needed is the comparison of the resistance to deformation of a particular sample or lot with a standard material, indentation hardness tests are used. They are relatively inexpensive and fast. They tell nothing about ductility and little about the relationship between stress and strain, for in making the indent the stress and strain are nonuniformly distributed.

In all hardness tests, a standardized load is applied to a standardized indenter, and the dimensions of the indent are measured. This applies to such methods as scratch hardness testing, in which a loaded diamond is dragged across a surface to produce, by plastic deformation, a furrow whose width is measured, and the scleroscope hardness test, in which an indent is produced by dropping a mass with a spherical tup onto a surface. The dimensions of the indent are proportional to the work done in producing it, and the ratio of the height of rebound to the height from which the tup was dropped serves as an indirect measure of the hardness.

Fatigue

Fatigue is a process involving cumulative damage to a material from repeated stress (or strain) applications (cycles), none of which exceed the ultimate tensile strength. The number of cycles required to produce failure decreases as the stress or strain level per cycle is increased. The fatigue strength or fatigue limit is defined as the stress amplitude which will cause failure in a specified number of cycles. For a few metals, notably steels and titanium alloys, an endurance limit exists, below which it is not possible to produce fatigue failures no matter how often stresses are applied.

Creep and stress rupture

Time-dependent deformation under constant load or stress is measured in a creep test. Creep tests are those in which the deformation is recorded with time, while stress rupture tests involve the measurement of time for fracture to occur. Closely related are stress relaxation tests, in which the decay of load with time is noted for a body under a fixed state of strain. Test durations vary from seconds or minutes to tens of thousand of hours. Appreciable deformation occurs in structural materials only at elevated temperatures, while pure metals may creep at temperatures well below room temperature.

Since creep deformation and rupture time are temperature- and stress-dependent, it is usually necessary to test a material at several stresses and temperatures in order to establish the creep or stress-rupture properties in adequate detail. See Metal, Metallurgy