Stress is defined as the load per unit area

In countries using the English system of measurement stress is always given in pounds per square inch (lbs per sq in.). Where the metric system is used, stress is given in newtons per square milli­meter (N/mm2), where 1 lb is 4.44822 newtons.

1000 L8S. ЮОО UBS. ,’OOOIBS.

Stress is defined as the load per unit area


I000LBS. 1000 LBS.


Stress is defined as the load per unit area

1000 LBS.

Stress is defined as the load per unit area


Fig. И-I. Stresses in metals. A. Compressive; B, Tensile; C. Shear; D. Torsional


There are several ways in which stresses act inside a piece of metal. In Fig. 11-1 A, the stress is a compressive stress and, in addition to the bearing plate, every particle of the metal inside the column is subjected to a compressive stress. Usually other kinds of stresses in combination are also present; however, for simplification, it can be said that the stress in the column is compressive.

In Fig, 11 -1B, a round rod is shown being pulled at each end by a 1,000 lb load. If the cross-sectional area of the rod is 1 sq in., the stress in the rod is 1,000 lbs per sq in., and it is in tension. If we can imagine a disc-shaped slice anywhere in the rod, this slice is being pulled by the metal to which it is attached on each side. The stress on the slice (any slice in the rod) is 1,000 lbs per sq in. tension.

Figure И-1C shows another kind of stress, a “shear” stress. Each section of the metal in the area of the punch and the die is resisting the severance of the metal by the internal shear stresses that are set up by the load. When the internal shear strength of the metal is exceeded, it will fail or shear off.

When a shaft, such as the crankshaft in Fig. 11 -1D, is subjected to a torsional load, internal torsional stresses are set up to resist the external load. Torsional stresses are not distributed uniformly across the entire cross section of the part carrying the load. They are greatest at the outside and are zero at the center of the round bar. Actually, the torsional stresses are shear stresses; however, the torsional strength is often reported separately and it is important in design.

Strain. All metals behave elastically, like a rubber band, up to a certain limit of stress. That is, they deform slightly when the load is applied and when the load is released they snap back to their original length. Technically, strain is the distance each unit length of the metal is changed as a load is applied. In the English system it is given in terms of inch elongation per inch length and in the metric system it is millimeter per millimeter. Strain then alludes to the elastic movement of the metal when a load is applied, whereas stress alludes to the resistance to this movement

Strength. The strength of the metal from which a part is made depends on the load it must carry, its size, and its shape. Each size and shape of a given metal can carry a different maximum load; therefore a standard size and shape are necessary in order to be able to compare the strengths of different metals. Thus, a standard size is established for test pieces and the strength of these test pieces is reported in lbs per sq in. stress. This value can then, in many instances, be used to calculate loads non-standard sizes and shapes will stand.

The strength of the metal is usually given in tables and often is shown in stress-strain diagrams, such as Fig. 11 -2. One must be careful in reading strength values in handbooks because there are two different values that can be reported, the ultimate strength and the yield strength.

Stress is defined as the load per unit area

Fig* I 1-2. Stress-strain diagram. Curve A is for ductile materials and curve 8 is

for brittle materials.

Ultimate Tensile Strength. Most published figures on the tensile strength of metals refer to the ultimate tensile strength. It is the maximum tensile strength that the metal can withstand before failure by rupture occurs. One difficulty is that this stress occurs in the region of plastic deformation (see Fig. 11 -2) and when the metal reaches this stress level, it has already been permanently deformed. For this reason an adequate factor of safety is required when using the ultimate tensile strength in design calculations.

Yield Strength. In machines and structures the metal must not deform permanently when subjected to a load. For this reason, the yield strength is often reported. The yield strength is the stress to which a metal can be subjected without permanent deformation. In ductile materials the yield strength is at a lower stress level than the ultimate tensile strength, as shown for curve A in Fig. 11-2.

A typical plot of the stress-strain characteristic of a very hard and brittle metal, such as hardened tool steel, is shown by curve В in Fig.

11-2. Such metals exhibit little or no permanent deformation before breaking. For this reason, the yield strength has no meaning for very hard brittle materials and the ultimate strength or breaking strength is used.

Hardness. Hardness is defined as the resistance to penetration. It is also sometimes defined as the resistance of the metal to plastic deformation. Both definitions are essentially correct. Most methods of measuring hardness do so by measuring the indentation made when a specified load is placed on a small penetrator. This measure­ment is then converted to a suitable hardness scale or reading.

Hardness is related closely to strength. Both properties involve the ability of a metai to resist permanent deformation beyond the elastic range.

Hardenability. This property is related to the depth below the surface to which a metal can be hardened. It does not relate to the maximum hardness that can 1эе achieved in a given metal. There are several standard tests for hardenability with, perhaps, the Jominy End Quench Hardenability Test being the most popular.

Ductility. The relative amount that a metal will deform without breaking is what is meant by ductility. As shown by curve A in Fig.

11-2, ductile metals tend to stretch considerably before they break. This property enables metals to be bent, twisted, drawn out, or otherwise changed in shape without breaking.

Ductility is generally defined as percent elongation or percent reduction in area. However, these values provide only a rough indication of ductility and cannot be used in design calculations. Another rough measure of ductility is the bend test, whereby a specimen is bent, either to fracture or through a complete 180-degree arc.

Toughness. The ability of a metal to withstand a sudden shock is called toughness. This property is determined by the energy absorbed when a notched specimen is struck by a hammer blow delivered by a swinging pendulum.

Brittleness. This property refers to the ease with which a metal will crack or break without appreciable deformation. Brittleness is related to hardness, As a metal gets harder its brittleness also increases, and as the metal is made softer, its brittleness decreases. An example of the stress-strain curve of a brittle metal is shown in curve B, Fig. 11-2.

Malleability. Malleability is the property that relates to the ability of metal to be permanently deformed by compression, usually by rolling or hammering. Most ductile metals are also malleable.

Fatigue. This property refers to the ability of a metal to withstand repeated or fluctuating loads. Fatigue failures always occur at a stress level that is below the yield strength of the metal. Several standard tests are used to measure this property. From these tests the endurance limit of a metal can be determined, which is defined as the stress below which the metal will withstand an indefinitely large number of cycles of stresses without failure. Fractures due to fatigue are often the result of sharp corners, scratches on the surface of the metal, or tool marks.

Grain Structure

In the solid state, metals are in the form of crystals called grains. Some of the grains can be quite large and can be seen by the naked eye. However, most grains are very small and require powerful magnification to be seen.

These crystals are composed of a more or less orderly arrange­ment of atoms called a lattice structure. Each atom is in a fixed position; that is, it oscillates about a fixed position.

Although the atoms cannot actually be seen, if it were possible to magnify a crystal about 35 million times, it would be possible to see the space lattice. Each lattice structure is composed of a number of unit cells that are repeated over and over again to form the lattice.

Metals are composed of four basic unit cells which are shown in Fig. 11-3. The lines between the atoms do not actually exist; they are drawn to illustrate the geometrical arrangement of the atoms.

For example, chromium and tungsten have a body-centered cubic structure. Iron, when below about 1666F, and steel, when below 1660 to 1333F, also have a body-centered cubic structure. Alumi­num, copper, nickel, silver, and gold have a face-centered cubic structure. When iron is above 1666F and plain carbon steel is above 1333 to 1666F, they have a face-centered cubic structure. Depend­ing on its composition, steel may be partially face-centered cubic and partially body-centered cubic between 1333 and 1666F. The hard component of steel called martensite, that has been formed by heating and quenching, has a body-centered tetragonal structure. Actually martensite is iron which has carbon atoms trapped in its structure to elongate the body-centered cubic structure into a body-centered tetragonal structure. Indium and tin have a body- centered tetragonal structure. Magnesium and zinc have a close - packed hexagonal structure.

It will be noted from the above that iron and steel have two structures or phases, depending on their temperature. This impor­tant fact makes it possible to harden steel by heat treatment. When steel is cooled slowly it will transpose from one structure to another without difficulty, and is called “phase change.” However, when this is done rapidly» carbon atoms interfere with this change, and the structure cannot assume its natural configuration at room tempera* ture. As already mentioned, it is body-centered tetragonal (marten­site) instead of body-centered cubic. This distorts the orderly arrangement of atoms, producing internal stresses which cause it to harden.

Anything that can be done to a metal that will disturb or distort the lattice structure will cause it to harden. In the case of steel, the lattice is distorted by a phase change brought about by heat treat­ment. Cold working a metal distorts the structure and thereby hardens it. Note that cold working does not crystallize the metal; it is always in the crystalline form. Inserting foreign atoms in the struc­ture by alloy additions distorts the structure and hardens it. When atoms are dissolved in a structure in the solid state and are then precipitated out, the structure is distorted and hardened. This is the mechanism used to harden aluminum. It is called age hardening or precipitation hardening.

Metals are actually an aggregate of crystals, or grains, as shown in Fig. 11-4. Each grain is surrounded by other grains, except at the surface of the metal. When polished and etched with a suitable reagent and then viewed under a microscope, the grains can clearly be seen.

Stress is defined as the load per unit area

Fig. і 1-4. The grain structure in metals.

Depending on the heat treatment received by the metal, the grains can have different sizes. Often the grains will be either large or small throughout the entire structure of a piece of metal. In some cases, where metal has been welded, for example, regions of large and small grains will exist side-by-side. When a metal has been cold- worked, the grains will appear distorted or flattened in the direction of the cold-working (see Fig. 11-17).

The grains in an alloy may or may not appear to be identical. In many alloys, different kinds of grains exist side-by-side in a struc­ture, The structure of a metal, when viewed under the microscope, is called its “microstructure,”

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