J. Ye, AK Kaw Theoretical and Applied Fracture Mechanics 32(1999)15-25 of friction and less than 2% difference for the re- the two major sources -thermal expansion mis- sidual radial stress. Fig. 4 shows the regressio match and roughness are given by: curves obtained using sla and bem models. For interfacial residual radial stresses. note that (oo)hema=k(x-xm)△T th he input to the BEM model is the temperature (oo)rouch=ky (34) change and not directly the residual stress at the fiber-matrix interface as used in the SLA model. where(oo)thermal is the thermal exe sig acial re- nsion mismatch How is the appropriate temperature change cal induced interfacial residual radial stress and culated for use in the BEM model? A residual (oo)rough is the roughness induced stress is first calculated for a temperature change of sidual radial stress. In Eq.(34), AT=-l K for the problem of a perfectly bonded composite cylinder [15] same properties and ge- k1 EmEt ometry(except the cylinders are infinitely long) Er(1+vm)+Em(1-ve (35) were used as given in Table 1. Then after calcula- The coefficient of thermal expansion of fiber and tion of the residual stress for AT=-l K, and since matrix, are given by af and om, respectively. The there is a linear relationship between AT and oo, temperature change is AT and Us is the fiber-ma- the appropriate AT can be found to develop the trix gap due to amplitude of roughness of surfaces required interfacial residual stress. For example, no distinction will be made between the two for Go=-75 MPa in the present this calc residual stresses. The total residual radial stress is lated temperature change is AT=-3263 K. simulated through a temperature change because But this temperature change AT=-3263 K is this study is focussed on addressing the adequacy different from the processing temperatures change of using SLa in extracting mechanical properties △T==700K K [14]. Then how could a of the fiber-matrix interface, and not on hot temperature change of only -3263 K justified? mechanical behavior of fiber-matrix interface First but secondary, the Sic fibers are coated with should be modeled. a carbon layer of 3 um thickness that affects the Figs. 5-8 show trends of fiber, matrix and in- thermal stresses [6] facial stresses in the composite specimen. Fig. 5 Second but more importantly [14] the roughness shows the distribution of the axial stress along the induced interfacial residual stresses is higher than radial coordinate for different distances from the the thermal expansion mismatch induced interfa loading end for a short fiber length (Ls=L cial residual stress. The approximate residual ra- 218 um). The axial stress changes drastically at the dial stress calculated in SLA [13, 16] where from edge of the indentor on the top of the fiber(==0) z=213 mm · Experimental da Shear-lag SLA亿z=0mm) Specimen thickness(mm) Fig. 5. Axial stress in fiber along the interfac Inction of Fig. 4. Comparison of extraction of interface properties from radius with distance from the loaded end(up=10 um, Ip=67.5 experimental data using SLA and BEM models m,L=L=218pm,H=0.12,00=-75MPa,△T=-3263K)of friction and less than 2% di€erence for the re￾sidual radial stress. Fig. 4 shows the regression curves obtained using SLA and BEM models. For interfacial residual radial stresses, note that the input to the BEM model is the temperature change and not directly the residual stress at the ®ber±matrix interface as used in the SLA model. How is the appropriate temperature change cal￾culated for use in the BEM model? A residual stress is ®rst calculated for a temperature change of DT ˆ ÿ1 K for the problem of a perfectly bonded composite cylinder [15] same properties and ge￾ometry (except the cylinders are in®nitely long) were used as given in Table 1. Then after calcula￾tion of the residual stress for DT ˆ ÿ1 K, and since there is a linear relationship between DT and r0, the appropriate DT can be found to develop the required interfacial residual stress. For example, for r0 ˆ ÿ75 MPa in the present case, this calcu￾lated temperature change is DT ˆ ÿ3263 K. But this temperature change DT ˆ ÿ3263 K is di€erent from the processing temperatures change of only DT@ ÿ700 K [14]. Then how could a temperature change of only ÿ3263 K justi®ed? First but secondary, the SiC ®bers are coated with a carbon layer of 3 lm thickness that a€ects the thermal stresses [6]. Second but more importantly [14] the roughness induced interfacial residual stresses is higher than the thermal expansion mismatch induced interfa￾cial residual stress. The approximate residual ra￾dial stress calculated in SLA [13,16] where from the two major sources ± thermal expansion mis￾match and roughness are given by: …r0†thermal ˆ k1…af ÿ am†DT ; …r0†rough ˆ k1 Us rf ; …34† where (r0)thermal is the thermal expansion mismatch induced interfacial residual radial stress and (r0)rough is the roughness induced interfacial re￾sidual radial stress. In Eq. (34), k1 ˆ EmEf Ef…1 ‡ mm† ‡ Em…1 ÿ mf† : …35† The coecient of thermal expansion of ®ber and matrix, are given by af and am, respectively. The temperature change is DT and Us is the ®ber±ma￾trix gap due to amplitude of roughness of surfaces. No distinction will be made between the two residual stresses. The total residual radial stress is simulated through a temperature change because this study is focussed on addressing the adequacy of using SLA in extracting mechanical properties of the ®ber±matrix interface, and not on how mechanical behavior of ®ber±matrix interface should be modeled. Figs. 5±8 show trends of ®ber, matrix and in￾terfacial stresses in the composite specimen. Fig. 5 shows the distribution of the axial stress along the radial coordinate for di€erent distances from the loading end for a short ®ber length (Ls ˆ L ˆ 218 lm). The axial stress changes drastically at the edge of the indentor on the top of the ®ber (z ˆ 0). Fig. 4. Comparison of extraction of interface properties from experimental data using SLA and BEM models. Fig. 5. Axial stress in ®ber along the interface as a function of radius with distance from the loaded end (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). 22 J. Ye, A.K. Kaw / Theoretical and Applied Fracture Mechanics 32 (1999) 15±25