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1656_C006.fm  Page 284  Monday, May 23, 2005  5:50 PM





                       284                                 Fracture Mechanics: Fundamentals and Applications























                       FIGURE 6.29 The process-zone toughening mechanism usually results in a rising R curve.


                       case of uniaxial loading. Figure 6.28(b) compares the stress-strain curve of brittle and toughened
                       ceramics. The latter material is capable of higher strains, and absorbs more energy prior to failure.
                          Many toughened ceramics contain second-phase particles that are capable of nonlinear deformation,
                       and are primarily responsible for the elevated toughness. Figure 6.28(c) illustrates the process zone for
                       such a material. Assuming the particles provide all of the energy dissipation in the process zone, and
                       the strain-energy density in this region does not depend on y, the fracture toughness is given by

                                                                d
                                                    G =  R  hf ∫  ij ε  σε i  j  + 2  2γ s       (6.21)
                                                                i
                                                                j
                                                            0
                       where f is the volume fraction of second-phase particles. Thus the toughness is controlled by the
                       width of the process zone, the concentration of second-phase particles, and the area under the
                       stress-strain curve. Recall the delamination of composites with tough resins (Section 6.1.3), where
                       the fracture toughness of the composite was not as great as the neat resin because the fibers restricted
                       the size of the process zone (h).
                          The process zone mechanism often results in a rising R curve, as Figure 6.29 illustrates. The
                       material resistance increases with crack growth, as the width of the processes zone grows. Even-
                       tually, h and G  reach steady-state values.
                                   R
                          Figure 6.30 illustrates the crack bridging mechanism, where the propagating crack leaves fibers
                       or second-phase particles intact. The unbroken fibers or particles exert a traction force on the crack
                       faces, much like the Dugdale-Barenblatt strip-yield model [18, 19]. The fibers eventually rupture
                       when the stress reaches a critical value. According to Equation (3.42) and Equation (3.43), the
















                                                               FIGURE 6.30 The fiber bridging mechanism for
                                                               ceramic toughening.
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