Key Words: average behavior, upper and lower bounds, Mori-Tanaka theory, composites, polycrystals

Key Words: average behavior, upper and lower bounds, Mori-Tanaka theory, composites, polycrystals

(Q)1=C1(E)1, (0)2=C2(E)2 (4) QQQ= fi(o)1+f2(2+(1-fi-f2)(o)m E=flIE1+12(6)2+(1-fl-f2)(E)D (5a) (5b) (E)i=1E/D+-y, 2=1,2 (6) {0}i=Ci{1ED+ii} (7) QM=CMEM, 01=C1i, Q2=C2E2 (1) (o)i=cm{1e/d+li-ei} (g) Eti={CM-(CM-Ca)Si}-1(CM-C2)(E)D (12) (Q)M=CM{E}D (3) (o)i=c11e/d+cisiea (10) 1/z=CM(E)D+CM(Sz-I)Es (11) Ei={CM-(CM-Cz)Sti}-1(CM-C)CMl(Q)M E=(E)D+flit+f2Y2 (14)

E=CMl(o)M+flSlE1+f2S2E2 (15) (O)i=(Q)M+CM(Sti-I)Ei (16) A=CM+f1CM(S1-I){CM BEI+f151{CM C=AB-1 (17) -(CM-C1)S1}(CM-C1) +f2cm(s2-i){cm -(CM-C2)52F(CM-C2) -(CM-C1)S1}(CM-C1) +12S2{CM -(CM-C2)S2}-1(CM-C2) (18a) (18b) AK=kM(1-fi-f2) BK=1-fi-f2 Au=12M(1-fi-f2) Bu=1-fi-f2 k=flk1+f2k2 (23)

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