30 3 Elastic Constants Based on Micromechanics This function uses the simple rule-of-mixtures 名 formula of equation (3.3) Vm =1-Vf; y Vf*NU12f Vm*NUm; function y E2(Vf,E2f,Em,Eta,NU12f,NU21f,NUm,Eif,p) %E2 This function returns Young's modulus in the % transverse direction.Its input are nine values: % Vf fiber volume fraction 名 E2f- transverse Young's modulus of the fiber ” Em - Young's modulus of the matrix % Eta stress-partitioning factor % NU12f Poisson's ratio NU12 of the fiber % NU21f Poisson's ratio NU21 of the fiber % NUm -Poisson's ratio of the matrix % Eif -longitudinal Young's modulus of the fiber % ? parameter used to determine which equation to use: % p =1 -use equation (3.4) % p =2-use equation (3.9) % p =3 -use equation (3.10) % Use the value zero for any argument not needed % in the calculations. Vm 1-Vf; if p ==1 y 1/(Vf/E2f Vm/Em) elseif p ==2 y 1/((Vf/E2f Eta*Vm/Em)/(Vf Eta*Vm)); elseif p =3 deno Eif*Vf Em*Vm; etaf (E1f*Vf ((1-NU12f*NU21f)*Em NUm*NU21f*E1f)*Vm)/deno; etam =(((1-NUm*NUm)*E1f -(1-NUm*NU12f)*Em)*Vf Em*Vm)/deno; y =1/(etaf*Vf/E2f etam*Vm/Em); end function y =G12(Vf,G12f,Gm,EtaPrime,p) %G12 This function returns the shear modulus G12 Its input are five values: 名 Vf fiber volume fraction % G12f -shear modulus G12 of the fiber % Gm shear modulus of the matrix EtaPrime-shear stress-partitioning factor % P parameter used to determine which equation to use: % p=1-use equation (3.5) % p=2-use equation (3.13) % p=3-use equation (3.14) % Use the value zero for any argument not needed % in the calculations. Vm 1 Vf;
30 3 Elastic Constants Based on Micromechanics % This function uses the simple rule-of-mixtures % formula of equation (3.3) Vm = 1 - Vf; y = Vf*NU12f + Vm*NUm; function y = E2(Vf,E2f,Em,Eta,NU12f,NU21f,NUm,E1f,p) %E2 This function returns Young’s modulus in the % transverse direction. Its input are nine values: % Vf - fiber volume fraction % E2f - transverse Young’s modulus of the fiber % Em - Young’s modulus of the matrix % Eta - stress-partitioning factor % NU12f - Poisson’s ratio NU12 of the fiber % NU21f - Poisson’s ratio NU21 of the fiber % NUm - Poisson’s ratio of the matrix % E1f - longitudinal Young’s modulus of the fiber % p - parameter used to determine which equation to use: % p = 1 - use equation (3.4) % p = 2 - use equation (3.9) % p = 3 - use equation (3.10) % Use the value zero for any argument not needed % in the calculations. Vm = 1 - Vf; if p == 1 y = 1/(Vf/E2f + Vm/Em); elseif p == 2 y = 1/((Vf/E2f + Eta*Vm/Em)/(Vf + Eta*Vm)); elseif p == 3 deno = E1f*Vf + Em*Vm; etaf = (E1f*Vf + ((1-NU12f*NU21f)*Em + NUm*NU21f*E1f)*Vm) /deno; etam = (((1-NUm*NUm)*E1f - (1-NUm*NU12f)*Em)*Vf + Em*Vm) /deno; y = 1/(etaf*Vf/E2f + etam*Vm/Em); end function y = G12(Vf,G12f,Gm,EtaPrime,p) %G12 This function returns the shear modulus G12 % Its input are five values: % Vf - fiber volume fraction % G12f - shear modulus G12 of the fiber % Gm - shear modulus of the matrix % EtaPrime - shear stress-partitioning factor % p - parameter used to determine which equation to use: % p = 1 - use equation (3.5) % p = 2 - use equation (3.13) % p = 3 - use equation (3.14) % Use the value zero for any argument not needed % in the calculations. Vm = 1 - Vf;
3.2 MATLAB Functions Used 吧 if p==1 y =1/(Vf/G12f Vm/Gm); elseif p ==2 y =1/((Vf/G12f EtaPrime*Vm/Gm)/(Vf EtaPrime*Vm)); elseif p ==3 y Gm*((Gm +G12f)-Vf*(Gm -G12f))/((Gm G12f)+ Vf*(Gm G12f)) end function y Alpha1(Vf,Eif,Em,Alphaif,Alpham) lpha1 This function returns the coefficient of thermal % expansion in the longitudinal direction. Its input are five values: Vf -fiber volume fraction 名 E1f longitudinal Young's modulus of the fiber Em - Young's modulus of the matrix % Alphalf -coefficient of thermal expansion in the % 1-direction for the fiber % Alpham coefficient of thermal expansion for the matrix Vm 1-Vf; y (Vf+E1f+Alpha1f Vm*Em*Alpham)/(E1f*Vf Em*Vm); function y Alpha2(Vf,Alpha2f,Alpham,E1,E1f,Em,NU1f,NUm, Alphaif,p) %Alpha2 This function returns the coefficient of thermal % expansion in the transverse direction. % Its input are ten values: Vf fiber volume fraction % Alpha2f coefficient of thermal expansion in the % 2-direction for the fiber % Alpham -coefficient of thermal expansion for the matrix % E1 -longitudinal Young's modulus of the lamina E1f -longitudianl Young's modulus of the fiber 名 Em -Young's modulus of the matrix % NU1f -Poisson's ratio of the fiber NUm -Poisson's ratio of the matrix % Alphaif -coefficient of thermal expansion in the 名 1-direction p parameter used to determine which equation to use % p =1 -use equation (3.8) p =2 -use equation (3.7) Use the value zero for any argument not needed in % the calculation Vm 1 Vf; 1fp=1 y Vf*Alpha2f Vm*Alpham; elseif p ==2 y =(Alpha2f -(Em/E1)*NU1f*(Alpham -Alphalf)+Vm)*Vf+ (Alpham (Eif/E1)*NUm*(Alpham Alphaif)*Vf)*Vm; end
3.2 MATLAB Functions Used 31 if p == 1 y = 1/(Vf/G12f + Vm/Gm); elseif p == 2 y = 1/((Vf/G12f + EtaPrime*Vm/Gm)/(Vf + EtaPrime*Vm)); elseif p == 3 y = Gm*((Gm + G12f) - Vf*(Gm - G12f))/((Gm + G12f) + Vf*(Gm - G12f)); end function y = Alpha1(Vf,E1f,Em,Alpha1f,Alpham) %Alpha1 This function returns the coefficient of thermal % expansion in the longitudinal direction. % Its input are five values: % Vf - fiber volume fraction % E1f - longitudinal Young’s modulus of the fiber % Em - Young’s modulus of the matrix % Alpha1f - coefficient of thermal expansion in the % 1-direction for the fiber % Alpham - coefficient of thermal expansion for the matrix Vm = 1 - Vf; y = (Vf*E1f*Alpha1f + Vm*Em*Alpham)/(E1f*Vf + Em*Vm); function y = Alpha2(Vf,Alpha2f,Alpham,E1,E1f,Em,NU1f,NUm, Alpha1f,p) %Alpha2 This function returns the coefficient of thermal % expansion in the transverse direction. % Its input are ten values: % Vf - fiber volume fraction % Alpha2f - coefficient of thermal expansion in the % 2-direction for the fiber % Alpham - coefficient of thermal expansion for the matrix % E1 - longitudinal Young’s modulus of the lamina % E1f - longitudianl Young’s modulus of the fiber % Em - Young’s modulus of the matrix % NU1f - Poisson’s ratio of the fiber % NUm - Poisson’s ratio of the matrix % Alpha1f - coefficient of thermal expansion in the % 1-direction % p - parameter used to determine which equation to use % p = 1 - use equation (3.8) % p = 2 - use equation (3.7) % Use the value zero for any argument not needed in % the calculation Vm = 1 - Vf; if p == 1 y = Vf*Alpha2f + Vm*Alpham; elseif p == 2 y = (Alpha2f - (Em/E1)*NU1f*(Alpham - Alpha1f)*Vm)*Vf + (Alpham + (E1f/E1)*NUm*(Alpham - Alpha1f)*Vf)*Vm; end