Area under the tensile test curve, - Toughness

The area under the true stress-true strain curve up to fracture is known as the material’sToughness, that is, the amount of energy per unit volume that the material dissipatesprior to fracture. Note: that toughness involves both the height and width of the stress-strain curve of the material, Whereas, 1. Strength is related only to the height of the curve 2. Ductility is related only to the width of the curve.

The area under the, true stress-true strain curve at a particular strain is the energy per unit volume (specific energy) of the material deformed and indicates the work required to plastically deform a unit volume of the material to that strain.

When the curve shown in Fig. 2.5c is plotted on a log-log graph, it is found that the curve is approximately a straight line (Fig. 2.5 d). The slope of the curve is equal to the exponent “n”. Thus, the higher the slope, the greater is the strain-hardening capacity of the material--that is, the stronger and harder it becomes as it is strained.

How is a Load Vs Extension curve in a tensile test converted as Stress Vs Strain curve?

Construction of Engg Stress-Strain CurvesThe procedure for constructing an engineering stress-strain curve is to take theLoad - elongation curve (Fig. 2.5 a; also, Fig. 2.2), and then to divide the load (verticalaxis) by the original cross-sectional area, AO, and the elongation (horizontal axis) bythe original gage length, IO. Because AO and lO are constants, the engineering stress - strain curve obtained (shown in Fig. 2.5b) has the same shape as the load-elongation curve shown in Fig. 2.5a. (In this example, AO = 36.1 mm2 and AF= 10.3 mm2.)

Fig 2.5 “a” and “ b”

Calculation of Engg Ultimate tensile strength from True ultimate tensile strength

Engg strain Vs True Strain

For true strain, first consider the elongation of the specimen as consisting of increments of instantaneous change in length.

Then, using calculus, it can be shown that the true strain (natural or logarithmic strain) is calculated as

For small values of strain, the engineering strain “e” and true strains “ ” are approximately equal.

However, they diverge rapidly as the strain increases. For example, when e = 0.1, = 0.095 , and when e = 1, = 0.69.

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