J. Ye, AK Kaw Theoretical and Applied Fracture Mechanics 32(1999)15-25 axial locations close to ends of the fiber. Note that BEM in SlA. axial stresses in the fiber and ma assumed to vary only along the length of the specimen and are independent of the radial loca -B0 tion Figs. 6 and 7 show the interfacial radial stresses and shear stresses along the length of the interface respectively. From Figs. 6 and 7, the shear stresses Location along the interface Z(mm) and radial stresses by SLa are almost constant Fig. 6. Radial stress along the fiber-matrix interface from SLa rough out the interface. The difference between and BEM models(up=10 un 675m,L=L=218pn results of BEM and Sla is about 20% away from u=0.12,00=-75MPa,△T=-3263K the two ends of the interface. The differences in the shear and radial stresses from sla and bem 16 models near the ends of the interface are due to Shear-lag two reasons. First, different loading conditions are used in the two analyses In bem, a uniform dis placement was used while in SLA a uniform pressure loading was used. Second, in SLA, the residual stress is assumed constant throughout the interface. but the residual radial stress is nonuni 200 form as found in bem models Location along the interface Z(mm) 5.3. Parametric studies to show difference between Fig. 7. Shear stress along the fiber-matri and BEM models(up =10 um, Ip=67.5 um, L=L=218 um bem and sla results μ=0.12,00=-75MPa,T=-3263K) Fig. 8 shows the maximum pushout force as a function of the radius of the indentor The maxi- mum pushout force does not change significantly L=2045 In fact, the largest difference is less than 0.01% This shows that the indentor radius does not affect =1014 the maximum pushout force vs specimen thick ness data. and hence the extraction of the two mechanical properties of the fiber-matrix inter face. Also, the radius of the hole has a negligible 0 0.2 0. 4 0.6 0.8 1 effect on the results of the test [8]. Since these two Loading radius /fiber radius a /r, parameters are not accounted for in the shear-la model, it is important for the experimentalist to Fig.8. Maximum pushout force as a function of loading radius know that these parameters do not influence the ratios for different specimen thicknesses using BEM(Go -75MPa,H=0.12,△T=-3263K) maximum pushout force vs specimen length data Fig.9 shows the maximum pushout force as a function of coefficient of friction of the interface Away from the loading end, the axial stress varies for oo=-75 MPa, L=218 um for SLA and BEM little along the radial coordinate. At the axial lo models. The difference between the results of bem cations close to the free end of the fiber, the axial and Sla is approximately 20%. Similar magni stress starts to increase from approximately half of tudes of difference were observed for longer spec- the fiber radius. a similar trend is also observed in imens as well for longer specimen lengths, but the axial stress Fig 10 shows the maximum pushout force as a changes less drastically along the fiber radius at function of Young's modulus ratio(Er/Em) withAway from the loading end, the axial stress varies little along the radial coordinate. At the axial lo￾cations close to the free end of the ®ber, the axial stress starts to increase from approximately half of the ®ber radius. A similar trend is also observed in for longer specimen lengths, but the axial stress changes less drastically along the ®ber radius at axial locations close to ends of the ®ber. Note that in SLA, axial stresses in the ®ber and matrix are assumed to vary only along the length of the specimen and are independent of the radial loca￾tion. Figs. 6 and 7 show the interfacial radial stresses and shear stresses along the length of the interface, respectively. From Figs. 6 and 7, the shear stresses and radial stresses by SLA are almost constant through out the interface. The di€erence between results of BEM and SLA is about 20% away from the two ends of the interface. The di€erences in the shear and radial stresses from SLA and BEM models near the ends of the interface are due to two reasons. First, di€erent loading conditions are used in the two analyses. In BEM, a uniform dis￾placement was used while in SLA a uniform pressure loading was used. Second, in SLA, the residual stress is assumed constant throughout the interface, but the residual radial stress is nonuni￾form as found in BEM models. 5.3. Parametric studies to show di€erence between BEM and SLA results Fig. 8 shows the maximum pushout force as a function of the radius of the indentor. The maxi￾mum pushout force does not change signi®cantly. In fact, the largest di€erence is less than 0.01%. This shows that the indentor radius does not a€ect the maximum pushout force vs. specimen thick￾ness data, and hence the extraction of the two mechanical properties of the ®ber±matrix inter￾face. Also, the radius of the hole has a negligible e€ect on the results of the test [8]. Since these two parameters are not accounted for in the shear±lag model, it is important for the experimentalist to know that these parameters do not in¯uence the maximum pushout force vs. specimen length data. Fig. 9 shows the maximum pushout force as a function of coecient of friction of the interface for r0 ˆ ÿ75 MPa, L ˆ 218 lm for SLA and BEM models. The di€erence between the results of BEM and SLA is approximately 20%. Similar magni￾tudes of di€erence were observed for longer spec￾imens as well. Fig. 10 shows the maximum pushout force as a function of YoungÕs modulus ratio (Ef/Em) with Fig. 6. Radial stress along the ®ber±matrix interface from SLA and BEM models (up ˆ 10 lm, rp ˆ 67.5 lm, Ls ˆ L ˆ 218 lm, l ˆ 0.12, r0 ˆ ÿ75 MPa, DT ˆ ÿ3263 K). Fig. 7. Shear stress along the ®ber±matrix interface from SLA and BEM models (up ˆ 10 lm, rp ˆ 67.5 lm, Ls ˆ L ˆ 218 lm, l ˆ 0.12, r0 ˆ ÿ75 MPa, T ˆ ÿ3263 K). Fig. 8. Maximum pushout force as a function of loading radius ratios for di€erent specimen thicknesses using BEM (r0 ˆ ÿ75 MPa, l ˆ 0.12, DT ˆ ÿ3263 K). J. Ye, A.K. Kaw / Theoretical and Applied Fracture Mechanics 32 (1999) 15±25 23