Please construct a Matlab Program that converts the true stress vs true strain c

Question

Please construct a Matlab Program that converts the true stress vs true strain chart below and computes and plots ENGINEERING stress vs ENGINEERING strain for a tension test of hot rolled steel. (Please dont copy a program for a load vs displacement chart)

Take the minimum and maximum true strains to be 0.0001 and 0.92. Assume that the initial cylindrical sample dimensions are: radius = 1.0 in., length = 5.0 in

Here is the true stress vs strain chart to convert.

Elastic region Transition region Plastic strain-strengthening region . 200 = 0.92 115 100 80 115 KS 60 30 10 3 4 5 6 780.1 2 3 4 56 78 1.0 2 3 4 56 78 10 2 3 4 5678100 True strain ET1% (log) FIGURE 3.3 True-stress-true-strain curve-hot-rolled 1020 steel (corresponds to Figs. 3.1 and 3.2).

Explanation / Answer

The context of this lesson is written with respect to the tensile test. Sometimes the stress plotted in stress-strain diagrams is obtained by dividing the load, P, by the cross-sectional area, A0 of the specimen measured before any deformation has taken place. Since the cross-sectional area of the specimen decreases as P increases, the stress plotted in the diagram may not represent the actual stress in the specimen. The difference between the engineering stress:

and the true stress:

obtained by dividing P by the cross-sectional area A of the deformed specimen becomes apparent in ductile materials after yield has started. While the engineering stress, , which is directly proportionalto the load, P, decreases with P during the necking phase, the true stress t, which is proportional to P and inversely proportional to A, is observed to keep increasing until rupture of the specimen occurs.

Many scientists also use a definition of strain different from that of the engineering strain:

Instead of using the total elongation and the original value L0 of the gage length, all the successive values of L are used that have been recorded. Dividing each increment L of the distance between the gage marks, by the corresponding value of L, the elementary strain is obtained:

Adding the successive values of , the true strain, t, is defined:

With the summation replaced by an integral, the true strain can also be expressed as follows:

or:

The diagram obtained by plotting true stress versus true strain reflects more accurately the behavior of the material. There is no decrease in true stress during the necking phase. Also, the results obtained from tensile and from compressive tests will produce essentially the same plot when true stress and true strain are used. This is not the case for large values of the strain when the engineering stress is plotted versus the engineering strain. However, engineers, whose responsibility is to determine whether a load, P, will produce an acceptable stress and an acceptable deformation in a given member, will want to use a diagram based on the engineering stress and the engineering strain, since their respective expressions involve data that are available to them, namely the cross-sectional area A0 and the length L0 of the member in its undeformed state.

(Eq1)     = P A0

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