J. Ye, AK Kaw Theoretical and Applied Fracture Mechanics 32(1999)15-25 20 24 0.6 E ■BEM 羹言14 L EL=2 12 0.16 Coefficient of frictio ≡60.2 Fig. 9. Maximum pushout force as a function of coefficient of 0.0平14 friction for SLA and BEM models (Go=-75 MPa. AT=-3263 Fiber volume fraction Ve Fig. ll. Maximum pushout force as a function of fiber volume fraction for BEM and SLA models(oo=-75 MPa, H=0.12. L=L=218um,△T=-3263K) 0.8 4- BEM translate into less or more differences in the ex- tracted values of the two mechanical properties of the fiber-matrix interface. Based on the data ob Youngs modulus ratio E/E tained for Fig. 4, the difference between the bem and sla results r trix moduli ratio for sla and bem models (on -75 MPa. maximum pushout force as opposed to about 20% u=0.12,L=L=218um) for the extracted value of the coefficient of friction 00=-75 MPa, u=0. 12 for L=218 um for SLA 6 Conclusions and BEM models. Except for the Youngs modu- lus of the fiber, all other properties assumed are The adequacy of using SLA models to extract same as given in Table 1. The residual radial stress the two mechanical properties of the fiber-matrix in all the cases was assumed to be -75 MPa; interface is studied The following are the conclu hence, the temperature changes were recalculated sions of this study for BEM model. Again. there is about 20% dif-. The coefficient of friction of the fiber-matrix in- ference between beM and sla results. Similar terface extracted by using BEM and Sla differs magnitudes of difference were observed for longer by 15%. However, the difference is only 1% for specimens as well. the interfacial residual radial stress Fig. 1l shows the maximum pushout force as a Like the SLA model results, the interface function of fiber volume fraction vr with go stresses in bEM remain constant through the 75 MPa, u=0.12 for L=218 um. The temp thickness of the specimen except at the top ture changes for all fiber volume fractions were and the bottom surfaces of the specimen kept the same(-3263 K) and interfacial residual The maximum pushout force is independent of stresses for use in the sla model were calculated the indentor radius and type, and push from the infinite composite cylinder problem [15]as through-hole radius. This is important observa discussed in the beginning of this section. Again, tion for the experimentalist in conducting the there is about 20% difference between the results of pushout test. Also, the SLa model does not BEM and SLA. Similar magnitudes of difference need to account for these extrinsic factors were observed for longer specimens as well The parametric studies show that there is ap In Figs. 9-1l, although there is a 20%differenc proximately 20% difference between the maxi- between the maximum pushout force values cal- mum pushout force obtained by BEM and culated using Sla and BEM models, does it SLA when coefficient of friction fiber to matrixr0 ˆ ÿ75 MPa, l ˆ 0.12 for L ˆ 218 lm for SLA and BEM models. Except for the YoungÕs modu￾lus of the ®ber, all other properties assumed are same as given in Table 1. The residual radial stress in all the cases was assumed to be ÿ75 MPa; hence, the temperature changes were recalculated for BEM model. Again, there is about 20% dif￾ference between BEM and SLA results. Similar magnitudes of di€erence were observed for longer specimens as well. Fig. 11 shows the maximum pushout force as a function of ®ber volume fraction Vf with r0 ˆ ÿ75 MPa, l ˆ 0.12 for L ˆ 218 lm. The tempera￾ture changes for all ®ber volume fractions were kept the same (ÿ3263 K) and interfacial residual stresses for use in the SLA model were calculated from the in®nite composite cylinder problem [15] as discussed in the beginning of this section. Again, there is about 20% di€erence between the results of BEM and SLA. Similar magnitudes of di€erence were observed for longer specimens as well. In Figs. 9±11, although there is a 20% di€erence between the maximum pushout force values cal￾culated using SLA and BEM models, does it translate into less or more di€erences in the ex￾tracted values of the two mechanical properties of the ®ber±matrix interface. Based on the data ob￾tained for Fig. 4, the di€erence between the BEM and SLA results averaged about 16% for the maximum pushout force as opposed to about 20% for the extracted value of the coecient of friction. 6. Conclusions The adequacy of using SLA models to extract the two mechanical properties of the ®ber±matrix interface is studied. The following are the conclu￾sions of this study: · The coecient of friction of the ®ber±matrix in￾terface extracted by using BEM and SLA di€ers by 15%. However, the di€erence is only 1% for the interfacial residual radial stress. · Like the SLA model results, the interfacial stresses in BEM remain constant through the thickness of the specimen except at the top and the bottom surfaces of the specimen. · The maximum pushout force is independent of the indentor radius and type, and push￾through-hole radius. This is important observa￾tion for the experimentalist in conducting the pushout test. Also, the SLA model does not need to account for these extrinsic factors. · The parametric studies show that there is ap￾proximately 20% di€erence between the maxi￾mum pushout force obtained by BEM and SLA when coecient of friction, ®ber to matrix Fig. 9. Maximum pushout force as a function of coecient of friction for SLA and BEM models (r0 ˆ ÿ75 MPa, DT ˆ ÿ3263 K). Fig. 10. Maximum pushout force as a function of ®ber to matrix moduli ratio for SLA and BEM models (r0 ˆ ÿ75 MPa, l ˆ 0.12, Ls ˆ L ˆ 218 lm). Fig. 11. Maximum pushout force as a function of ®ber volume fraction for BEM and SLA models (r0 ˆ ÿ75 MPa, l ˆ 0.12, Ls ˆ L ˆ 218 lm, DT ˆ ÿ3263 K). 24 J. Ye, A.K. Kaw / Theoretical and Applied Fracture Mechanics 32 (1999) 15±25