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                                                                                     Failures Resulting from Static Loading  245
                       Figure 5–28               3

                       Plate in tension containing a
                       circular hole with two cracks.       2a
                                                                                  r  = 0.5
                                                                                  b
                                                 2
                                                             r
                                                            2b      r  = 0.25
                                                                    b

                                                 1
                                                   r  = 0
                                                  b


                                                 0
                                                 0        0.2       0.4      0.6      0.8
                                                                    a b ratio


                       Figure 5–29               4.0

                       A cylinder loading in axial
                       tension having a radial crack of
                                                                             r  r  = 0
                       depth a extending completely   a           a          i  o
                                                 3.0
                       around the circumference of
                       the cylinder.                                             0.1

                                                                                   0.4

                                                 2.0
                                                                                      0.8
                                                         r i   r o

                                                 1.0
                                                  0        0.2       0.4      0.6       0.8
                                                                    a (r  – r ) ratio
                                                                      o  i

                                               Fracture Toughness
                                               When the magnitude of the mode I stress intensity factor reaches a critical value,
                                               K Ic , crack propagation initiates. The critical stress intensity factor K Ic is a material
                                               property that depends on the material, crack mode, processing of the material, temper-
                                               ature, loading rate, and the state of stress at the crack site (such as plane stress versus
                                               plane strain). The critical stress intensity factor K Ic is also called the fracture toughness
                                               of the material. The fracture toughness for plane strain is normally lower than that for
                                               plane stress. For this reason, the term K Ic is typically defined as the mode I, plane strain
                                               fracture toughness. Fracture toughness  K Ic for engineering metals lies in the range
                                                                  √
                                               20 ≤ K Ic ≤ 200 MPa ·  m; for engineering polymers and ceramics,  1 ≤ K Ic ≤
                                                      √
                                               5 MPa ·  m. For a 4340 steel, where the yield strength due to heat treatment ranges
                                                                                                √
                                               from 800 to 1600 MPa, K Ic decreases from 190 to 40 MPa ·  m.
                                                  Table 5–1 gives some approximate typical room-temperature values of  K Ic for
                                               several materials. As previously noted, the fracture toughness depends on many factors
                                               and the table is meant only to convey some typical magnitudes of K Ic . For an actual
                                               application, it is recommended that the material specified for the application be certi-
                                               fied using standard test procedures [see the American Society for Testing and Materials
                                               (ASTM) standard E399].
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