A.2 RESIDUAL STRESSES IN FIBERS AND MATRIX IN A LAMINA DUE TO COOLING [1] The following equations,derived on the basis of a composite cylinder model (Figure A.2.1),can be used to calculate the residual stresses in fibers and matrix in a unidirectional composite lamina developed due to differential thermal shrinkage as it cools down from the high processing temperature to the ambient temperature: =40+) 0m=A2, ==4-》 =4(-》 where =radial distance from the center of the fiber rr =fiber radius Im =matrix radius in the composite cylinder model,which is equal to (ri/ve) m,f =subscripts for matrix and fiber,respectively r,0,z=subscripts for radial,tangential (hoop),and longitudinal directions, respectively. Radial Fiber Matrix FIGURE A.2.1 Cross section of a composite cylinder model. 2007 by Taylor Francis Group.LLC.A.2 RESIDUAL STRESSES IN FIBERS AND MATRIX IN A LAMINA DUE TO COOLING [1] The following equations, derived on the basis of a composite cylinder model (Figure A.2.1), can be used to calculate the residual stresses in fibers and matrix in a unidirectional composite lamina developed due to differential thermal shrinkage as it cools down from the high processing temperature to the ambient temperature: srm ¼ A1 1
r2 m r2
, sum ¼ A1 1 þ r2 m r2
, szm ¼ A2, srf ¼ suf ¼ A1 1
r2 m r2 f
, szf ¼ A2 1
r2 m r2 f
, where r ¼ radial distance from the center of the fiber rf ¼ fiber radius rm ¼ matrix radius in the composite cylinder model, which is equal to (rf=vf 1 2) m,f ¼ subscripts for matrix and fiber, respectively r,u,z ¼ subscripts for radial, tangential (hoop), and longitudinal directions, respectively. Fiber Matrix rf r m Radial Tangential q FIGURE A.2.1 Cross section of a composite cylinder model.
2007 by Taylor & Francis Group, LLC.