Secant Chord

A chord of a circle (or sphere) is a line segment whose end points lie on the circle (or sphere). A line which intersects the circle (or sphere) in two points is a secant of the circle (or sphere). A diameter of a circle (or sphere) is a chord containing the center and a radius is a line segment from the center to a point on the circle (or sphere). 

The modulus is the slope of the initial portion of the stress-strain curve. Its measurement is complicated by the fact that, unlike metals, most plastics do not have a linear relationship between stress and strain. This means that the modulus decreases with increasing strain, and the measured value depends on the strain region used as well as whether the slope is taken as a secant, a chord, or a tangent to this region. There is justification for each of these methods, and the choice depends on the application of the data. In order to ensure comparability, standards are used to define criteria for modulus measurement. 

To determine the tangent modulus, a straight line is drawn tangent to the curve the slope of which is reported. Typically, the steepest part of the eurve is selected this is invariably the initial slope, in which case it is reported as the initial modulus. When the tangent is taken at a specific strain level, this value must also be reported. To determine the chord modulus, two points on the eurve are selected and the slope of the line connecting them is calculated. When the initial point chosen is 0% strain, the value is reported as the secant modulus of the upper level, e.g., 1% or 2% secant modulus. In all modulus calculations it is assumed that deformation is homogeneous at low strains and that deformation... 

Figure 26 Schematic illustration of four of the principal methods used to ealeulate elastic modulus, (a) Initial modulus (b) tangent (1%) (c) chord, (1-2%) (d) secant (1%).

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