True strain

To compare nominal strain and true strain, we investigate two different deformation processes of two rods The first rod is strained in two steps A/i and A/2, the second in a single step A/i 2 = A/i - - A/2- 

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This equation is given in terms of true stress and true strain. As we said in Chapter 8, tensile data are usually given in terms of nominal stress and strain. From Chapter 8 ... 

To see what is going on physically, it is easier to return to our first condition. At low stress, if we make a little neck, the material in the neck will work-harden and will be able to carry the extra stress it has to stand because of its smaller area load will therefore be continuous, and the material will be stable. At high stress, the rate of workhardening is less as the true stress-true strain curve shows i.e. the slope of the o/e curve is less. Eventually, we reach a point at which, when we make a neck, the workhardening is only just enough to stand the extra stress. This is the point of necking, with... 

True strain differs from nominal strain in that each increment in strain is expressed in terms of the actual length of the member at the time of the increment rather than in terms of the increment of the original length. The instantaneous nominal strain is given by... 

True strain, , is defined in such a way that the increment resulting from an increase in length by dL is based on the instantaneous length, L ... 

It follows that s = In Aq/A for large plastic strains. The quantity A0/A is a measure of the reduction in area due to deformation. One can define a quantity the true reduction in area (f), in a manner analogous to the definition of true strain ... 

It could be seen that for large plastic strains the true strain and the true reduction in area are identical. 

The rate of strain hardening, do /ds, at any given value of the true stain is given by the slope of the true stress-true strain plot at that strain and is called the modulus of strain hardening. 

A plot of log o against log s should thus yield a straight line whose slope is n and which makes an intercept equal to log fej on the log o axis (at s = 1). Thus the constant kj represents the true stress at unit true strain and is termed the strength coefficient. The exponent n is known as the strain hardening exponent. 

This relationship implies that the value of the true strain at which plastic instability sets in, i.e., necking starts to occur, is equal to the strain hardening exponent. 

Figure 5.25 Comparison of engineering stress-engineering strain and true stress-true strain plots. Reprinted, by permission, from J. F. Shackelford, Introduction to Materials Science for Engineers, 5th ed., p. 192. Copyright 2000 by Prentice HaU, Inc.

Person 2 Calculate the true strain Person 3 Calculate the % elongation. 

Person 2, 4 Determine the true stress. Use this value and the true strain to estimate the elastic modulus. 

In tests such as the tensile test it is necessary to differentiate between two basic ways of measuring strain. "Conventional strain" is the increase in length of the gage section divided by the original gage length, whereas the "true strain" is live natural logarithm... 

But true stress (load/actual section) and true strain, calculated as the natural logarithm of the relative height, n(L/L0), must be used to obtain better information on the material. The accuracy of strain measurements may be improved by the use of extensometers or strain gauges and actual cross section determination needs the use of double extensometers or stiffness correction of the machine and rigs (Cook et al., 1998). 

From the relationship between flow stress at a true strain of 0.1 and the strain... 

In the cases where L changes appreciably from its initial value, the method for so-called true strain should be used instead of the nominal strain method. The true strain is calculated by... 

The IR apparatus and dichroism methods used in this work have been previously described (11,12). In the differential dichroism experiment, the samples were stretched from both ends simultaneously at a true strain rate of approximately 30% per min. A motorized stretching jig was used which fits inside the instrument in the path of the common beam at a 45° angle. Wire grid polarizers were set at 45° in the reference and sample beams, and the instantaneous dichroic difference A A — AM — Aj was recorded with the instrument operating in constant, wave-number mode. 

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