Compressive layer Compressive layers B.C+30wt%sic Tensile layer e B C+30wtysiC 3 Figure I Schematic presentation of symmetric 3 layered and multilayered composite. stress components appear at or near the free surface of residual stress, and Kc is the intrinsic fracture toughness of a material in the layer. If a condition of a crack growth onsets fulfilled then Ka= Kc-K, is the apparent frac- ture toughness. If o, is compressive, then K, <0 and 3. Laminate design for enhanced Ka increases. The more rI, the more Ka. The more fracture toughness a, the more Ka. The largest value of a crack length in The schematic presentation of symmetric three-layered compressed layer is I1. The maximum apparent frac- and nine-layered composites are shown in Fig. l. The ture toughness can be obtained for such crackUnfor proposed design targeted a fracture toughness increase tunately, small cracks have Ka close to Ke B4C-SiC composites and was based on the prelimi A schematic presentation of factors that affect an ap- nary results both from our work [24-26]and from the parent fracture toughness is shown in Fig.2.Note, that work of others [9, 27-30] the contribution of a residual stress to the maximum ap- In case of non-homogeneous(particularly, layered) parent fracture toughness is K,=Y(,/w)o, 1/,where materials, So-called apparent fracture toughness should be considered. This is the fracture toughness of some .(i/w)is a geometrical factor. The factor Y(/w)//2 effective homogeneous specimen. If we measure frac increases as lI increases(Fig. 2a). The compressive residual stress decreases as li increases. It can be cal- ture toughness in bending, the effective sample param- culated using Equation 1. In addition, the residual stress eters should satisfy the following conditions:(1)the depends on the number of layers in the sample(Fig 2b) specimen has to have the same dimensions as a real The final dependences of Ka onI, for various numbers depth equal to that of the real layered specimen; (3) non-monotonic curves with a maximum that depends under the same loading conditions the specimen has on a number of layers in the laminate. The labels w/5 to demonstrate the same load to fracture as that of the real layered specimen. Under these considerations the w/4, w/3 and w/2 designate the maximum thickne parent fracture toughness is the fracture toughness of the top layer for symmetrical layered structures with 9, 7, 5 and 3 layers, respectively. It can be seen that the calculated from a testing data of the layered sample highest apparent fracture toughness can be obtained for approach does not meet the fracture mechanicA uch an the three-layer specimen. Thus, the study of the layers onsidering this specimen as"homogene ment of taking into account all features of stress dis- tribution near crack tip in layered media, but it is still a useful characteristic allowing an effective contribu- ion of such factors as residual stresses and a material inhomogeneity to be accounted for. The compressive residual stress or in the top lay- ers of a laminate shields natural and artificial cracks in the layer. Therefore, the effective(apparent) frac ture toughness of such a structure increases. The more oppressive residual stress induces, the more shielding occurs. Another important factor that contributes to the 3 layers apparent fracture toughness increase is a crack length a A longer crack promotes more shielding. A maximum length of a transverse crack in a top compressive layer is limited by the layer thickness I1. These two factors de- termine the apparent fracture toughness of the material. In general, a condition of a crack growth onset is Ka+kr=Kc. where Ka= Ka(da, a) is the applied stress intensity factor that can be measured, oa is the w/5w/4w/3w2 distribution of applied stress resulted from bending, Figure 2 Factors affecting laminate design for maximum apparent frac- Kr= k(or, a) is the stress intensity fac a ture toughness.Figure 1 Schematic presentation of symmetric 3 layered and multilayered composite. stress components appear at or near the free surface of a layer. 3. Laminate design for enhanced fracture toughness The schematic presentation of symmetric three-layered and nine-layered composites are shown in Fig. 1. The proposed design targeted a fracture toughness increase of B4C-SiC composites and was based on the prelimi￾nary results both from our work [24–26] and from the work of others [9, 27–30]. In case of non-homogeneous (particularly, layered) materials, so-called apparent fracture toughness should be considered. This is the fracture toughness of some effective homogeneous specimen. If we measure frac￾ture toughness in bending, the effective sample param￾eters should satisfy the following conditions: (1) the specimen has to have the same dimensions as a real layered specimen; (2) the notched sample has a notch depth equal to that of the real layered specimen; (3) under the same loading conditions the specimen has to demonstrate the same load to fracture as that of the real layered specimen. Under these considerations the apparent fracture toughness is the fracture toughness calculated from a testing data of the layered sample considering this specimen as “homogeneous”. Such an approach does not meet the fracture mechanics require￾ment of taking into account all features of stress dis￾tribution near crack tip in layered media, but it is still a useful characteristic allowing an effective contribu￾tion of such factors as residual stresses and a material inhomogeneity to be accounted for. The compressive residual stress σr in the top lay￾ers of a laminate shields natural and artificial cracks in the layer. Therefore, the effective (apparent) frac￾ture toughness of such a structure increases. The more compressive residual stress induces, the more shielding occurs. Another important factor that contributes to the apparent fracture toughness increase is a crack length a. A longer crack promotes more shielding. A maximum length of a transverse crack in a top compressive layer is limited by the layer thickness l1. These two factors de￾termine the apparent fracture toughness of the material. In general, a condition of a crack growth onset is Ka + Kr = Kc, where Ka = Ka(σa, a) is the applied stress intensity factor that can be measured, σa is the distribution of applied stress resulted from bending, Kr = Kr(σr, a) is the stress intensity factor due to a residual stress, and Kc is the intrinsic fracture toughness of a material in the layer. If a condition of a crack growth onset is fulfilled then Ka = Kc−Kr is the apparent frac￾ture toughness. If σr is compressive, then Kr < 0 and Ka increases. The more |σr|, the more Ka..The more a, the more Ka..The largest value of a crack length in compressed layer is l1. The maximum apparent frac￾ture toughness can be obtained for such crack. Unfor￾tunately, small cracks have Ka close to Kc. A schematic presentation of factors that affect an ap￾parent fracture toughness is shown in Fig. 2. Note, that the contribution of a residual stress to the maximum ap￾parent fracture toughness is Kr = Y (l1/w)σrl 1/2 1 , where Y (l1/w) is a geometrical factor. The factor Y (l1/w)l 1/2 1 increases as l1 increases (Fig. 2a). The compressive residual stress decreases as l1 increases. It can be cal￾culated using Equation 1. In addition, the residual stress depends on the number of layers in the sample (Fig. 2b). The final dependences of Ka on l1 for various numbers of layers are shown in Fig. 2c. These dependences are non-monotonic curves with a maximum that depends on a number of layers in the laminate. The labels w/5, w/4, w/3 and w/2 designate the maximum thickness of the top layer for symmetrical layered structures with 9, 7, 5 and 3 layers, respectively. It can be seen that the highest apparent fracture toughness can be obtained for the three-layer specimen. Thus, the study of the layers’ Figure 2 Factors affecting laminate design for maximum apparent frac￾ture toughness. 5485