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128                          Chapter 4  Mechanical Testing: Tension Test and Other Basic Tests




                           σ u  = σ ou  or σ f
                                               σ , ε , fracture
                                                f
                                                  f
                  σ, Stress  σ ou , yield         (d)      (a)    (b)     (c)    (d)

                      (a)  (b)       (c)


                  0
                                 ε, Strain




            Figure 4.10 Engineering stress–strain curve and geometry of deformation typical of
            some polymers.

            in the laboratory measurements, and other such statistical errors.) The use of strain ε similarly
            removes the effect of sample length. For a given stress, specimens with greater length L will exhibit
            a proportionately larger length change  L, but the strain ε corresponding to the yield, ultimate, and
            fracture points is expected to be the same for any length of sample. Hence, the stress–strain curve is
            considered to give a fundamental characterization of the behavior of the material.


            4.3 ENGINEERING STRESS–STRAIN PROPERTIES

            Various quantities obtained from the results of tension tests are defined as materials properties.
            Those obtained from engineering stress and strain will now be described. In a later portion of this
            chapter, additional properties obtained on the basis of different definitions of stress and strain, called
            true stress and strain, will be considered.

            4.3.1 Elastic Constants

            Initial portions of stress–strain curves from tension tests exhibit a variety of different behaviors for
            different materials as shown in Fig. 4.11. There may be a well-defined initial straight line, as for
            many engineering metals, where the deformation is predominantly elastic. The elastic modulus, E,
            also called Young’s modulus, may then be obtained from the stresses and strains at two points on
            this line, such as A and B in (a):
                                                  σ B − σ A
                                              E =                                      (4.3)
                                                  ε B − ε A
            For accuracy, the two points should be as far apart as possible, and it may be convenient to
            locate them on an extrapolation of the straight-line portion. Where laboratory stress–strain data
            are recorded at short intervals with the use of a digital computer, values judged to be on the linear
            portion may be fitted to a least-squares line to obtain the slope E.
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