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          64      Chapter 2  Mechanical Behavior, Testing, and Manufacturing Properties of Materials

           The true area at the onset of necking is obtained from        P = 0-Aneck = 0-A050-5,



                            Aneck  = n = ()_5_              where cr is the true ultimate tensile strength. Hence,
                                                                                              .. g
           Thus,                                                    P == 488 0.606 A  ..>  = 2900A k  .
                                                                            ><
                                                                                  ><
                                                                        <
                           A  ck 2 A e-0.5,                 Since UTS = P/Ao.
                            DE     O
                                                                            UTS = 296 MPa.
           and the maximum load, P, is

                                                                                    200   leo
                                                    Siren#iii;
                                              ;_E/astic m
                                                    -‘ Od  I
                                         600-  Tensile           ‘\`\                   .5    A
                                                                                        V -40 $
                                       'ni                                    ~    -150  Q5
                                       Q.                                               U9    "’
                                       2 400 -                                          -§     ‘5
                                       jg      Y                                   -100 <3    sg
                                       Q        leld  strength                          E      §>
                                       5                                                ,g -20 _
                                         200-                                      _50 3      U1
                                               E\or\Qa‘\0“                              Lu

                                           0 _J                                     O      _I 0
                                             0        200       400       600
                                                         Temperature (°C)



                                   FIGURE 2.1  Effect of temperature on mechanical properties of a carbon steel. Most
                                   materials display similar temperature sensitivity for elastic modulus, yield strength, ultimate
                                   strength, and ductility.


                                   2.2.6 Temperature Effects

                                   Increasing the temperature generally has the following effects on stress-strain curves
                                   (Fig. 2.7>¢
                                     a. The ductility and toughness incease, and
                                     b. The yield stress and the modulus of elasticity decrease.

                                   Temperature also affects the strain-hardening exponent of most metals, in that n
                                   decreases with increasing temperature. The influence of temperature is, however,
                                   best described in conjunction with the rate of deformation.

                                   2.2.7 Rate-of-deformation Effects
                                   just as we can blow up a balloon or stretch a rubber band at different rates, we can
                                   shape a piece of material in a manufacturing process at different speeds. Some
                                   machines, such as hydraulic presses, form materials at low speeds; others, such as
                                   mechanical presses, form materials at high speeds. To incorporate such effects, it is
                                   common practice to strain a specimen at a rate corresponding to that which will be
                                   experienced in the actual manufacturing process.
                                        The deformation rate is defined as the speed at which a tension test is being
                                   carried out, in units of, say, mfs. The strain rate, on the other hand, is a function of
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