Elementary engineering fracture mechanics
Borosilicate glasses or epoxy materials with several kinds of incorporated metallic inclusions such as Mo, V, Ni, Al, W or FeNiCo alloy can serve as an example of particle reinforced composites starting to be used in engineering design. Several kinds of toughening mechanisms induced by mismatch of elastic moduli and thermal expansion coefficients, by pulling out and bridging, by microcracking or by crack bowing and crack deflection can act in combination with each other to produce an overall
... ghening effect. This paper is focused on the shielding of the crack tip caused by crack deflection (tilting). When a crack under remote mode I loading approaches a secondary phase, the crack front can deflect to experience a mixed mode I+II (tilting). The ratio between the averaged strain energy release rates (or related stress intensity factors) at the deflected and the undeflected crack front expresses the relative amount of toughening (e.g. ). The susceptibility to the crack tip tilting can be assesses by using the well-proved criterion based on the minimization of the mode II affected crack growth . It can be easily shown  that, in case of a small kink, this criterion leads to the relative amount of toughening as expressed by the effective stress intensity factor K eff , normalized to the remote K Ifactor. Spherical particles of different size and interparticle spacing, having both the negligibly small (zero) and the very high (20 times higher than that of the matrix) Young moduli, are considered in the model. The analysis was performed by means of the code ANSYS based on the finite element method assuming the standard CT specimen employed in the fracture toughness testing. In the first step, the effective stress intensity factor K eff is calculated for many crack tip positions in front, and in between, two secondary particles of the same kind. According to the criterion based on the minimization of the mode II, the associated kink angles are computed as well. The averaged results have shown that the spherical holes induce, in spite of a significant crack tip tilting, a slight increase in the K eff factor (antishielding). On the other hand, the rigid particles cause a significant decrease in the K eff -value (shielding), while leaving the crack practically undeflected. These results qualitatively agree with those previously obtained for the crack interaction with a single secondary particle (e.g.  ). In the second step, the crack tip positions in between and behind the particles will be analyzed in order to assess the expected inverse effect of both types of particles. A summarized analysis should yield a comparison of global levels of crack tip shielding produced by particles of different elastic moduli.