# Resilience

The ability of a material to absorb energy when deformed elastically and to return it when unloaded is called resilience. This is usually measured by the modulus of resilience, which is the strain energy per unit volume required to stress the material from, zero stress to the yield stress. The toughness of a material is its ability to absorb energy in the plastic range. The ability to withstand occasional, stresses above the yield stress without fracturing is particularly desirable in parts such as freight-car couplings, gears, chains, and crane hooks. Toughness is a commonly used concept, which is difficult to pin down and define.

The ability of a material to absorb energy when deformed elastically and to return it when unloaded is called resilience. This is usually measured by the modulus of resilience, which is the strain energy per unit volume required to stress the material from, zero stress to the yield stress s. The strain energy per unit volume for uniaxial tension is

 (1)

From the above definition the modulus of resilience is

 (2)

This equation indicates that the ideal material for resisting energy loads in applications where the material must not undergo permanent distortion, such as mechanical springs, is having a high yield stress and a low modulus of elasticity. Table 1 gives some values of modulus of resilience for different materials.

Table 1. Modulus of resilience for various materials

 Material E, psi s0, psi Modulus of resilience, Ur Medium-carbon steel 30×106 45000 33,7 High-carbon spring steel 30×106 140000 320 Duraluminium 10,5×106 18000 17,0 Cooper 16×106 4000 5,3 Rubber 150 300 300 Acrylic polymer 0,5×106 2000 4,0

### Toughness

The toughness of a material is its ability to absorb energy in the plastic range. The ability to withstand occasional, stresses above the yield stress without fracturing is particularly desirable in parts such as freight-car couplings, gears, chains, and crane hooks. Toughness is a commonly used concept, which is difficult to pin down and define. One way of looking at toughness is to consider that it is the total area under the stress-strain curve. This area is an indication of the amount of work per unit volume, which can be done, on the material without causing it to rupture. Figure 1.2 shows the stress-strain curves for high- and low-toughness materials. The high-carbon spring steel has a higher yield strength and tensile strength than the medium-carbon structural steel. However, the structural steel is more ductile and has a greater total elongation. The total area under the stresstrain curve is greater for the structural steel, and therefore it is a tougher material. This illustrates that toughness is a parameter that comprises both strength and ductility. The crosshatched regions in Fig. 1 indicate the modulus of resilience for each steel. Because of its higher yield strength, the spring steel has the greater resilience.
Several mathematical approximations for the area under the stress-strain curve have been suggested. For ductile metals that have a stress-strain curve like that of the structural steel, the area under the curve can be approximated by either of the following equations:

 (3)

 (4)

For brittle materials the stress-strain curve is sometimes assumed to be a parabola, and the area under the curve is given by

 (5)

Figure 1. Comparison of stress-strain curves

All these relations are only approximations to the area under the stress-strain curves. Further, the curves do not represent the true behavior in the plastic range, since they are all based on the original area of the specimen.

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The Total Materia Extended Range includes a unique collection of stress-strain curves and diagrams for calculations in the plastic range for thousands of metal alloys, heat treatments and working temperatures. Both true and engineering stress curves are given for various strain rates where applicable.

Finding a stress-strain graph in the database is simple and takes only seconds.

Enter the material of interest into the quick search field. You can optionally narrow your search by specifying the country/standard of choice in the designated field and click Search.

After selecting the material of interest to you, click on the Stress-Strain diagrams link to view data for the selected material. The number of available stress-strain diagrams is displayed in brackets next to the link.

Because Total Materia stress-strain curves are neutral across standard specifications, you can review stress-strain diagrams by clicking the appropriate link for any of the subgroups.

Besides the stress-strain curves at different temperatures, stress and strain data are given in a tabular format which is convenient for copying to, for example, a CAE software.

It is also possible to view stress-strain curves and data for other working temperatures.

To do this, simply insert a new temperature into the ‘Enter temperature’ field within the defined range.

After clicking the Calculate button, a new curve is plotted and values in the table now correspond to the temperature you have defined. See example below for 250°C.

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