True stress and strain

Tutorial Video Mechanical Property Calculations from Tensile Test Measurements 

Concept Check 6.2 Of those metals listed in Table 6.3, 

Material Yield Strength (MPa) Tensile Strength (MPa) Strain at Fracture Fracture Strength (MPa) Elastic Modulus (GPd) 

Sometimes it is more meaningful to use a true stress-true strain scheme. True stress cTf is defined as the load F divided by the instantaneous cross-sectional area At over which deformation is occurring (i.e., the neck, past the tensile point), or 

True stress-true strain relationship in the plastic region of deformation (to the point of necking) 

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Chapter 8 Nominal and True Stress and Strain, Energy of Deformation... 

Stress and strain, as computed here, are sometimes called "engineering stress and strain." They are not true stress and strain, which can be computed on the basis of the area and the gage length that exist for each increment of load and deformation. For example, true strain is the natural log of the elongation (In and true stress is P/A, where A is area. The latter values are usually... 

Relationship between true stress and strain for a given material undergoing plastic deformation. 

True stress and strain are calculated using the instantaneous (deformed at a particular load) values of the cross-sectional area. A, and the length of the rectangle, L,... 

An approximate sketch of the stress-strain diagram for mild steel is shown in Fig. 2.8(a). The numbers given for proportional limit, upper and lower yield points and maximum stress are taken from the literature, but are only approximations. Notice that the stress is nearly hnear with strain until it reaches the upper yield point stress which is also known as the elastic-plastic tensile instability point. At this point the load (or stress) decreases as the deformation continues to increase. That is, less load is necessary to sustain continued deformation. The region between the lower yield point and the maximum stress is a region of strain hardening, a concept that is discussed in the next section. Note that if true stress and strain are used, the maximum or ultimate stress is at the rupture point. 

Note Property values such as those listed in this table vary widely and should not be used for design purposes without validating by testing tbe exact polymer to be used. ASTM Standard testing procedures offer reliable experimental protocols for such experiments. Mechanical properties of polymers can also be found in reference handbooks such as The Polymer Handbook (2006) and other textbooks such as Rodriguez, 1996 (p. 696-710) as well as various online databases such as plasticsusa.com. Variability of polymer properties can be seen for example in Fig. 3.7, where the true stress and strain at rupture for polycarbonate differ from the values tabulated here. 

In Chapters 5-7 we discussed difficulties in getting true stress and strain values as a result of sample-related problems like inertia, flow instabilities, shear heating, and evaporation of matrix solvent. 

Until failure occurs true stress and strain are related to engineering stress and strain by Eqs. (1.14) and (1.15) ... 

Corrections to the engineering stress and strain (what is seen on the stress-strain diagram) can be made to obtain true stress and strain. True stress is simply a- — PjA, where A is the cross-sectional area at the neck of the sample. 

Eqnations 6.18a and 6.18b are valid only to the onset of necking beyond this point, true stress and strain shonld be computed from actual load, cross-sectional area, and gauge length measnrements. 

Using the appropriate data tabulated in Problem 6.30, make a plot of log o- versus log and determine the values of n and K. It will be necessary to convert engineering stresses and strains to true stresses and strains using Equations 6.18a and 6.18b. 

In the mathematical expression relating true stress and strain. Equation 6.19, the parameter n is called the strain-hardening exponent, which is a measure of the ability of a metal to strain harden the larger its magnitude, the greater is the strain hardening for a given amount of plastic strain. 

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