IV. Tension Test Diagram and It’s Characteristic Points

The behaviour of materials in tension²⁶ is best understood from a consideration of a curve called a tension test diagram, which represents the stress-strain relation in tension. It is usually obtained from a diagram in the coordinates: tensile force P and absolute elongation of a specimen ΔL. A P–ΔL diagram is traced by a recording instrument or plotted from successive readings of the load and the corresponding increase in the length of the specimen. The forces measured at different instants during the testing are laid off to scale on the axis of ordinates, and the elongations on the axis of abscissas.

A diagram in these coordinates will, of course, depend on the dimensions of a specimen. The longer the specimen, the greater are the absolute elongations for one and the same force. In order to make these diagrams independent of the dimensions of test pieces and comparable for different materials, the ordinates should represent not forces but stresses obtained by dividing the tensile force by the original cross-sectional area of the specimen

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The abscissas should represent strains rather than absolute elongations.

The points of the tension test diagram thus obtained characterize the state of the specimen at different instants, and the entire diagram gives the stress-strain relation for the specimen over the duration of the test, shows a tension test diagram of mild steel. We proceed to consider its characteristic points.

Proportional limit. Up to a certain state characterized by point A in the diagram, the relation is represented by a straight line. This is an indication of the fact that here elongations of the specimen increase directly as stresses. This straight line makes a very small angle with the axis of ordinates, i. e., and the elongations of the specimen increase slowly in this portion. Point A corresponds to the stress known as the proportional limit. Up to the proportional limit Hooke’s law holds good. Consequently, the proportional limit is defined as the maximum stress to which strains increase directly as stresses in the material. The stress corresponding to the proportional limit is designated as .

If we consider any state of the specimen within the straight-line portion of the diagram, such as the state represented by point, the slope of the straight-line portion to the axis of abscissas is given by the ratio where is a concrete quantity and a pure number. On the other hand, according to Hooke’s law.

Consequently i. e., the numerical value of the modulus of elasticity of the first kind can be determined, with the proper use of scales for the diagram, as the slope of the straight-line portion to the axis of abscissas.

Elastic limit. In designing a structure it is sometimes important to know the stress at which the material first undergoes plastic action. Extremely precise measurements show that even highly elastic materials develop permanent deformations under very small stresses. But the magnitude of these permanent deformations is so small that they are of no practical significance. Permanent deformations increase with increasing stress. The elastic limit is defined as the stress at which the material develops a certain predetermined value of permanent strain (0,002 to 0,005 or 0,2 to 0,5 per cent of the original length of the specimen).

The elastic limit is designated as . The determination of the elastic limit presents great difficulties. It requires very precise and prolonged tests. In practice the magnitude of the elastic limit (for steel, for example) is very close to the proportional limit, and therefore point corresponding to the proportional limit is considered to be coincident with the point corresponding to the elastic limit. Further, as the stress increases, the tension test curve rises and departs from the straight line, turning smoothly to the right point.

Yield point (critical point). Some materials, such as mild steel, have a portion in the tension test diagram slightly above the proportional limit, from point on, in which elongations begin to increase without increase in stress. This phenomenon is called yielding. The yield point is defined as the stress at which a perceptible elongation occurs in the material without any increase of the stress. The yield point is designated as . The point of the diagram corresponding to the yield strength is called the critical point. Sometimes instead of a horizontal portion of the diagram there is even an inclined portion (sloping down to the right).

After passing the yield point the material recovers its ability to resist deformation but its elongation now begins to increase more rapidly than stresses, permanent deformations also increase rapidly. The yield point is a very important characteristic of the mechanical behavior of a material since stresses above the yield point produce impermissible permanent deformations.

Many materials, such as steel alloys, have no pronounced yield point. The tension test diagram of such materials passes smoothly from the elastic part to a part where large permanent deformations occur. The yield strength of such materials is established in a pure conventional manner. The yield strength for them is considered as the stress at which they develop a permanent set (offset) equal to a specified value. Therefore, when speaking of the yield strength of such materials it is necessary to indicate the corresponding permanent set. The yield strength is commonly taken as the stress corresponding to a permanent set of 0,2 per cent. When materials having a pronounced yield point are stretched, it is easy to observe the onset of yielding. If, for example, a tension testing machine is provided with a pointer indicating tensile forces, the pointer stops moving and remains on the same division for some time when the yield point of the material is reached though the deformations of the specimen continue to grow.

Also, the onset of yielding in the material can be noticed by observing the specimen itself. The polished surface of the specimen dulls²⁷ and gradually becomes lusterless when the yield point is reached. Under close examination the surface exhibits lines inclined at about 45⁰ to the axis of the specimen. The number of these lines, known as Luders lines, increases gradually and in consequence the surface of the specimen becomes dull. The occurrence of these lines and their propagation throughout the length of the specimen are evidence of the shears produced in crystals of the material.

Ultimate strength. Beyond the yield point the tension test diagram becomes curved (principally convex upward) and, as already stated, the deformations of the specimen begin to grow more rapidly than the stresses. Point corresponds to the maximum value of the tensile force. The stress equal to the ratio of the maximum tensile force to the original cross-sectional area of the specimen is called the ultimate strength. The ultimate strength is designated as . After the ultimate strength is reached, a local reduction of area of the specimen, called necking, begins to occur gradually. During necking the specimen elongates mainly at the necked-down portion while the remainder of the specimen elongates only slightly.

Since during necking the cross section at the neck becomes smaller and smaller, the deformation of the specimen occurs with decreasing load. The ultimate strength is a very important strength characteristic of a material, particularly important for brittle materials, such as cast iron, hardened and cold-drawn steel, etc., which undergo relatively small deformations at fracture. At a stress corresponding to point the specimen ruptures. The stress at rupture lies below the ultimate strength in the tension test diagram. This is due to the fact that we agreed to calculate the stresses on the basis of the original cross-sectional area of the specimen. Actually, however, at the time of rupture the material develops the maximum stress since the area of the section becomes a minimum at that time. This stress is sometimes called the true ultimate strength.

The diagram considered above is termed an ordinary stress and strain diagram since the stresses are related to the original cross-sectional area and the elongations, to the original length. The cross section and length of the specimen vary continuously during the test. However, the ordinary diagram closely coincides with the true one up to the yield point. In the true diagram the ordinate is the stress obtained by dividing the force by the corresponding value of the minimum cross-sectional area of the specimen and the abscissa is the true unit elongation of the specimen, i. e., and the change in length divided by the length of the specimen at the current instant.

Ductility of material. Besides the yield point and the ultimate strength characterizing the mechanical properties of a material, a very important characteristic is ductility of the material. The ductility of the material is characte­rized by the magnitude of the percentage elongation and the percentage reduction of the cross-sectional area at rupture.

The percentage elongation at rupture is expressed as where is the length of the specimen after rupture and is the original length.

The percentage reduction of the cross-sectional area is found from the expression where the cross-sectional area at the neck is after rupture and is the original cross-sectional area of the specimen.

It is customary to distinguish between ductile and brittle materials depending on whether permanent deformations occurring in the specimen at rupture are large or small, shows, for comparison, tension test diagrams of a ductile material (mild steel) and a brittle material (cast iron). It is seen that the brittle material fractures at a small strain and has no yield point. It should be noted, however, that the ductility of a material varies with the state of stress, strain rate, temperature and other conditions. A material exhibiting brittleness under tension at normal temperature may behave as a ductile material under other conditions, and conversely.

Consider the deformation of the specimen beyond the elastic limit. If the specimen is unloaded at some point of the diagram lying above the elastic limit, the line of unloading will be a straight line parallel to line. The segment represents the overall unit elongation of the specimen at the stress corresponding to point. The segment equal to represents the amount of plastic deformation which remains in the specimen after unloading. The strain beyond the elastic limit is made up of two parts; the elastic strain which disappears after removal of the load and the plastic strain which remains after unloading the specimen.

The elastic part of the strain beyond the elastic limit is proportional to the stress defined by segment.

Based on a so-called law of unloading, the elastic part of the strain can be determined beyond the elastic limit. Just before the rupture of the specimen its overall elongation is represented in the diagram by segment. After rupture the elastic part of the strain is recovered and only the permanent strain remains. The larger the permanent deformation, the more ductile is the material.

The Mechanical properties of metals as revealed in tests depend on the chemical composition of the material, temperature, heat treatment, speed of testing, etc.

The effects of chemical composition and heat treatment on mechanical properties are studied in metallographic analysis; here we shall briefly outline the effect of other factors on the mechanical properties of materials.

Temperature effect. The results of mechanical testing of materials usually relate to room temperatures (15-200⁰C) at which tests are conducted in laboratories. However, many parts even of one and the same machine operate in widely different temperature conditions. Thus, the exhaust valves of an automobile engine operate at 500 to 800⁰C while engine parts which are in direct contact with the environment sometimes operate at very low temperatures. For most materials the strength decreases and the ductility increases with increasing temperature. Mild steel behaves somewhat differently: at a temperature of about 250-300 ⁰C the ultimate strength of the steel attains a maximum value but falls off sharply with further increase in temperature, diagrams showing the variation of the ultimate strength and ductility of steel with temperature. At high temperature, from 300-400 ⁰C, metals continue to deform, though very slowly, at constant load. Strain rate increases with increasing load or temperature. This property of metals to deform continually at constant load and high temperature is called creep.²⁸

Gas turbine blades operating at high temperature and subjected to centrifugal loads continually elongate with time. This elongation may cause the fracture of blades or dangerous brushing of these against the body, which sometimes happens in practice. Therefore, special steels and heat-resistant alloys exhibiting a small amount of creep are employed under these conditions.

At elevated temperatures the ultimate strength of a material depends also on the duration of testing. In these cases the strength of a material is referred to as creep-rupture strength, shows the creep-rupture strengths of a heat-resistant alloy at 700 ⁰C, as is seen, the strength of the material falls with increasing time of testing.

As the temperature drops off, the strength of steel increases but the ductility sharply decreases. At low temperature steel is very sensitive to all kinds of vibrations and blows (cold brittleness of steel). An addition of nickel increases its resistance to impact loads at low temperatures.

Speed of testing. The mechanical characteristics of a material are also affected by the testing procedure. Therefore, to make the test results comparable it is necessary to follow a definite established testing procedure. Thus, for example, all metals possess the property of increasing their resistance to plastic deformation with increasing strain rate. Therefore, the more rapidly the specimen is loaded during testing, the higher are the resulting mechanical characteristics (proportional limit, yield point and ultimate strength) and the smaller the deformations. Steel possesses this property to a considerably lesser degree than more ductile metals such as zinc, lead, copper, etc.

The strain rate has its greatest effect on the yield point of a material. Under very rapid loading the yield stress may turn out to be higher than the ultimate strength obtained under slow loading. In view of this property of metals the rate of increase of stresses up to the yield point is usually not higher than 1000 N/cm² per second under normal conditions of testing.