Page 347 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)
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1656_C007.fm  Page 327  Monday, May 23, 2005  5:54 PM





                       Fracture Toughness Testing of Metals                                        327


                       where r  is the plastic rotational factor, a constant between 0 and 1 that defines the relative position
                             p
                       of the apparent hinge point. The mouth-opening displacement is measured with a clip gage. In the
                       case of an SE(B) specimen, knife edges are often attached in order to hold the clip gage, so that
                       Equation (7.21) must take account of the knife-edge height z. The compact specimen is usually
                       designed such that z = 0. The plastic component of V is obtained from the load-displacement curve
                       by constructing a line parallel to the elastic loading line, as illustrated in Figure 3.6. The plastic
                       rotational factor is given by

                                                               .
                                                           r = 044                              (7.22a)
                                                           p
                       for the SE(B) specimen and

                                                                                  
                                                       a  2  a   12 /   a   
                                          r =  p  .    + 04 1 2    o   +  o  +    −05 .    o  + 2  05 .    (7.22b)
                                                
                                                        b   b o      b o  
                                                        o
                                                
                                                                                  
                       for the compact specimen. The original British standard for CTOD tests, BS 5762:1979, applied
                       only to SE(B) specimens and specified r  = 0.40.
                                                        p
                          The crack-mouth-opening displacement V on an SE(B) specimen is not the same as the load-
                       line displacement ∆. The latter displacement measurement is required for J estimation because A pl
                       in Figure 7.23 represents the plastic energy absorbed by the specimen. The CTOD standard utilizes
                       V  because this displacement is easier to measure in SE(B) specimens. If r  is known, however, it
                                                                                   p
                        p
                       is possible to infer J from a P-V curve or CTOD from a P-∆ curve [5, 6]. The compact specimen
                       simplifies matters somewhat because V = ∆ as long as z = 0.
                          When using the resistance curve procedure in  ASTM E 1820, the CTOD equation must
                       continually be updated with the current crack size. For the ith measurement point in the test, CTOD
                       is given by


                                                  K 2  ( − ν ) [  2  r  ( W  a −  ) ∆ a+  i]  V
                                                     1
                                            δ   =  () i    +  pi ()   i      pi ()               (7.23)
                                              i
                                              ()    σ E         () [       i ]
                                                   2  YS      r  pi  ( W  a −  i ) a +  z +
                       where a  is the current crack length and  ∆ a  i  a =  i  a −  o  . The stress-intensity factor  K  i ()  is computed
                             i
                       using the current crack length. For compact specimens, the rotational factor must also be continually
                       updated to account for crack growth:


                                                       a   2  a   12 /   a   
                                                                                  
                                          r pi ()  =  .    + 04 1 2    i   +  i  +    − 05 .    i  + 2  05   (7.24)
                                                  
                                                                               .
                                                         b   b i      b i  
                                                         i
                                                  
                                                                                  
                       Equation (7.23) and Equation (7.24) do not appear in ASTM E 1290.
                          When the material exhibits ductile crack extension, the above procedure can be used to generate
                       a d -R curve. The CTOD near the onset of ductile crack extension, d , can be inferred from the
                                                                               Ic
                       resistance curve in a manner very similar to the J  measurement (Figure 7.24). The slope of the
                                                               Ic
                       blunting line and exclusion lines for a d -R curve is M , where M  is assumed to equal 1.4 unless
                                                                            δ
                                                                   δ
                       an experimental measurement of the blunting line slope has been made. The provisional initiation
                       toughness d  is defined at the intersection between the d -R curve, defined by a power-law fit within
                                Q
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