A. Mukherjee, H.S. Rao/ Computational Materials Science 4(1995)249-262 trol elements exceeds the matrix cracking stress 1333. 3 MPa. In order to observe the crack deflec (700 MPa)this elements stiffness is reduced to tion and the slip the displacements are magnified zero thus simulating the occurrence of matrix by a factor of 25. This magnified deflected shape cracking. In the other 50 interface elements used of the CMC (see Fig. 11 (a)), clearly shows the to model the whisker /matrix interface the shear crack deflection mechanism. For the CMcs with stiffness(K is set to a high value initially to IFS ranging from 2200 to 3800 MPa, the debond limit any non-slip displacement. Once the inter- ing of the interface has not occurred even when face shear stress exceeds the interface shear he Matrix crack reaches the whisker. The whisker strength, the shear stiffness Ks is set to zero momentarily halts the further propagation of the allowing slip. Loads were applied incrementally crack, thus, bridging the matrix crack (i.e. the and stress-strain relationships have been ob- whisker bridging mechanism). The whisker bridg- tained. Stress-strain curves for five different in- ing continues till the interface starts debonding terface shear strengths of 800 MPa, 2200 MP or the whisker fractures, depending on the rela 2600 MPa, 3000 MPa and 3800 MPa have been tive strengths of the interface and the whisker. blaine fruil the finite elenent allalysis. In real cpicted in magnified dclc ity increase of interface strength increases the the CMcs in Figs. 11(b)and(c). Fig. 11(b)shows matrix cracking stress. In the present work this the deflected shape of the CMc with an IFS of effect has not been considered, simply to avoid 2200 MPa, at an applied stress of 1556 MPa. It is e problem. The em- seen from the figure that, the debonding of the phasis of this work is to numerically demonstrate nterface does not initiate at this stress, though, he effect of interface strength on the toughening the matrix cracks at 922 MPa. It can be further of the CMCs observed from Fig. 10 that at this stress level, the stress-strain relation is linear. The matrix crack 41. Results and discussion has been bridged by the strong whisker till the interface debonding initiated at a stress of 1611 Fig 10 shows the stress-strain curves obtained MPa, thus deflecting the crack along the inter from the finite element analysis of the chosen face. On the other hand in the case of Cmc with ceramic-matrix-composite, for different interface an IFS of 3800 MPa, whisker bridging continued strength parameters. The matrix crack originated till the whisker stress bccame ncarly cqual to its from the free end A(see Fig 9)at an applied fracture value, and finally the CMc failed with stress of 922.2 MPa, and the entire matrix portion whisker fracture, with very little debonding of the AB cracked at this stress level, thus transferring interface(see Fig. 11(d)). This figure depicts, the the load on to the whisker. when the interface magnified deflected shape of the composite with shear strength(IFS )is 800.0 MPa, the interface IFS= 3800 MPa at the instant of failure. It can started debonding readily thus deflecting the be seen from the figure, that very little debonding crack parallel to the whisker (crack deflection has taken place at the interface, bcforc the hanism). At this point, the stress-strain curve whisker fractured. This is due to the relatively leviates from the linear path with further in- trong whisker /matrix interface. crease in load, the crack continues to propagate With increasing interface strength, it can be along the whisker/matrix interface. This is indi- observed that the stress-strain curves(see Fig 10) cated in the present model by the failure of the deviated from the linear path at higher stress interface clements. The deviation of the stress- levels. This is due to the relatively stronger strain curve from the lincar path indicates the whisker/matrix interface not debonding readily, nitiation of the toughening exhibited by the Cmc. thus contributing to lesser toughening. when the This crack deflection mechanism is depicted in interface shear strength was increased to 3800.0 Fig. 11a. The figure shows the magnified de- MPa, very little debonding has occurred at the flected shape of the CMC with an interface shear whisker/matrix interface, resulting in a brittle strength(IFS)of &00 MPa, at an applied stress of failure, characterised by the near linear stress-258 A. Mukherjee, H.S. Rao /Computational Materials Science 4 (1995) 249-262 trol elements exceeds the matrix cracking stress (700 MPa) this elements stiffness is reduced to zero thus simulating the occurrence of matrix cracking. In the other 50 interface elements used to model the whisker/matrix interface the shear stiffness (K,) is set to a high value initially to limit any non-slip displacement. Once the inter￾face shear stress exceeds the interface shear strength, the shear stiffness K, is set to zero allowing slip. Loads were applied incrementally and stress-strain relationships have been ob￾tained. Stress-strain curves for five different in￾terface shear strengths of 800 MPa, 2200 MPa, 2600 MPa, 3000 MPa and 3800 MPa have been obtained from the finite element analysis. In real￾ity increase of interface strength increases the matrix cracking stress. In the present work this effect has not been considered, simply to avoid too many parameters in the problem. The em￾phasis of this work is to numerically demonstrate the effect of interface strength on the toughening of the CMCs. 4.1. Results and discussion Fig. 10 shows the stress-strain curves obtained from the finite element analysis of the chosen ceramic-matrix-composite, for different interface strength parameters. The matrix crack originated from the free end A (see Fig. 9) at an applied stress of 922.2 MPa, and the entire matrix portion AB cracked at this stress level, thus transferring the load on to the whisker. When the interface shear strength (IFS) is 800.0 MPa, the interface started debonding readily thus deflecting the crack parallel to the whisker (crack deflection mechanism). At this point, the stress-strain curve deviates from the linear path. With further in￾crease in load, the crack continues to propagate along the whisker/matrix interface. This is indi￾cated in the present model by the failure of the interface elements. The deviation of the stress￾strain curve from the linear path indicates the initiation of the toughening exhibited by the CMC. This crack deflection mechanism is depicted in Fig. lla. The figure shows the magnified de￾flected shape of the CMC with an interface shear strength (IFS) of 800 MPa, at an applied stress of 1333.3 MPa. In order to observe the crack deflec￾tion and the slip, the displacements are magnified by a factor of 25. This magnified deflected shape of the CMC (see Fig. 11(a)), clearly shows the crack deflection mechanism. For the CMCs with IFS ranging from 2200 to 3800 MPa, the debond￾ing of the interface has not occurred even when the matrix crack reaches the whisker. The whisker momentarily halts the further propagation of the crack, thus, bridging the matrix crack (i.e. the whisker bridging mechanism). The whisker bridg￾ing continues till the interface starts debonding or the whisker fractures, depending on the rela￾tive strengths of the interface and the whisker. This is depicted in magnified deflected shapes of the CMCs in Figs. 11(b) and cc>. Fig. 11(b) shows the deflected shape of the CMC with an IFS of 2200 MPa, at an applied stress of 1556 MPa. It is seen from the figure that, the debonding of the interface does not initiate at this stress, though, the matrix cracks at 922 MPa. It can be further observed from Fig. 10 that at this stress level, the stress-strain relation is linear. The matrix crack has been bridged by the strong whisker, till the interface debonding initiated at a stress of 1611 MPa, thus deflecting the crack along the inter￾face. On the other hand, in the case of CMC with an IFS of 3800 MPa, whisker bridging continued till the whisker stress became nearly equal to its fracture value, and finally the CMC failed with whisker fracture, with very little debonding of the interface (see Fig. 11(d)). This figure depicts, the magnified deflected shape of the composite with IFS = 3800 MPa at the instant of failure. It can be seen from the figure, that very little debonding has taken place at the interface, before the whisker fractured. This is due to the relatively strong whisker/matrix interface. With increasing interface strength, it can be observed that the stress-strain curves (see Fig. 10) deviated from the linear path at higher stress levels. This is due to the relatively stronger whisker/matrix interface not debonding readily, thus contributing to lesser toughening. When the interface shear strength was increased to 3800.0 MPa, very little debonding has occurred at the whisker/matrix interface, resulting in a brittle failure, characterised by the near linear stress-