Abstract

The tensile machine test assumes that the cross-sectional area of the sample does not change by applying the force. Therefore, the apparent stress-strain diagram differs from the real stress-strain diagram. So the real yield point on apparent diagram is not an accurate point. in this article we try to calculate the real stress-strain diagram and real yield point form apparent diagram.

Keywords: True Stress, Real Stress, Nominal Stress, Engineering Stress, Apparent Stress, Tensile Test, ductile, yield point, plastic, deformation

 Introduction

The tensile test is used for measuring of variation of strain-stress ratio in a sample of material. For this purpose, the tensile machine pulls a dumbbell-shaped sample at a constant rate and records the amount of force applied to the sample. The device calculates the amount of stress by dividing the force on the cross section area of the sample:

 A₀ is the amount of surface area at zero moment.The problem is that the cross-section area is reduced by applying tension. Thus, the amount of stress recorded by the device is different from the real stress. Actually, the recorded stress (apparent stress) is always less than the real stress:

The following is a schematic diagram of the real (r) and apparent (a) stresses:

The relationship between real Area and zero stress

Assuming, the density of matter does not change due to the force; we can calculate the relationship between A and A₀ as:

So that λ is stretch ratio: the length of the sample at any moment divide by the sample length at zero time (λ=1 at t=0).

The relationship between real stress and apparent stress

Yield point

The condition of yield is:

By applying this condition on * equation we get:

So, yield point on the apparent diagram is the point that on it, the slope of the tangent to the curve is opposite to the slope of the line between the curve and the origin of the coordinates:

It is necessary to pay attention to this point that accorindg to ** equation:

Thus the real yield point is after maximum point of the apparent stress-strain diagram.