Approach of Calculating a Parameter of Ductility in Tensile Test

Ductility by the sum of longitudinal elongation ∆L and reduction of diameter ∆d which is the difference of initial diameter and necking diameter assumes that it is represented by the sum of the total longitudinal movement made by ∆L and transverse displacement of necking diameter.


Introduction
Ductility by the sum of the distributed elongation and necking with the difference of initial diameter and necking assumes that it is represented by the sum of the total longitudinal movement made by ΔL and transverse displacement Δd ( Figure 1).

Materials
To develop and analyze the second step of our work, we experiment tensile test on 03 different grades of carbon steel. For each grade we use 03 specimens test grades are XC18 carbon steel, XC38 and XC48. Ductility values of the above-mentioned steels is known because of the carbon content, in other words it is known that XC18 is more ductile than XC38 and XC48 because it contains less carbon, and XC38 is more ductile than XC48. Based on this fact we test the ductility approach and we have to prove this order of ductility values of XC18, XC38 and XC48.
We experiment the approach that we called D 2 obtained as we said by the sum of total longitudinal elongation ΔL and reduction of diameter Δd on XC18, XC38 and XC48 after that we compare results.
For proving the task of ductility approach D 2 , we must have linear deformation represented by D 2 of XC18 higher than XC38 and XC48; and also linear deformation of XC38 higher than XC48.

Methods
As the sum of the total elongation and the reduction in diameter is obtained: From a geometrical point of view the progress of this approach is performed in a linear geometry before starting the initial test point and extending over a right characterizing the uniform elongation in homogeneous deformation then it becomes a geometric form L as soon as appearance of necking.
From Figure 2, we note that the elongation and reduction of diameter whose intersection gives the L-geometric form are perfectly identical on both sides of the axis through the necking which leads us note that the final geometry of the ductility approach D 2 is inverted to T form on the left side in this case because it can also be reversed on the right side. This is the length (mm) of this geometric form which T represents is the ductility approach D 2 characterized by the sum of the total elongation with the difference of initial and necking diameter [41-58].
So we have:  So the linear deformation of XC18 symbolized physically by the parameter of ductility approach D 2 is higher than other steels wich is true (Tables 1-4). For a superplastic material ductility is very significant.
For a plastic material ductility is significant and positive, So D 2 > 0 Where: ∆L > 0 and ∆d > 0, which is true for a plastic material.
So the modeling approach of ductility D 2 offer us à good appreciation of ductility on the other hand its easy to use for calculus. D 2 also activates simultaneously as a summation key 02 variants influencing ductility: the elongation ∆L and the variation of the diameter ∆d. In Figure 3, there is no ductility, it is a brittle material. Finally we note that the ductility approac D 2 = ∆L + ∆d h is a measurable quantity of linear dimension (mm). And we can say that this parameter represent a linear deformation with dimension 1 (Figures 4-7).

Experimental study of the ductility approach D 2 of XC18
We notice that:

Conclusion
Finally the linear and monodimensional approach D 2 = ∆L + ∆d (mm) is intersting because it gives the measurement of deformation as a linear deformation easy to calculate. Valeur de D 2 en mm