Page 375 - Mechanics Analysis Composite Materials
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360                 Mechanics and analysis of composite materials
                 &T_-e2T--aoAT,                                                (7.79)
                  I

             where a0  is the CTE of the mandrel material and A T = TO- T,. On the other hand,
             if the layer is cooled being preliminary removed from the mandrel, its strains can be
             calculated as




             The first terms in the right-hand sides of these equations are free temperature strains
             along and across the fibers (see Fig. 7.51), while E(: and E!  correspond to the possible
             layer shrinkage in these directions.
               Using Eqs. (7.79) and (7.80) we can determine the strains that appear in the layer
             when it is removed from the mandrel, i.e.


                                                                               (7.81)


             These strains can be  readily found if  we  measure the layer diameter and  length
              before and after it is removed from the mandrel. Then, the shrinkage strains can be
             determined as






              For a glass-epoxy composite with the following thermo-mechanical properties:

                 EI = 37.24 GPa,   E2  = 2.37 GPa,   Gl2 = 1.2 GPa,
                  ltl2 =0.26,   = 3.1 x  lo-‘  1/”C,   ~12= 25 x   I/OC  ,

              Morozov and Popkova (1987) found  8:  = -93.6  x    = -64. IO?   Further
              experiments performed for different winding tensions and materials of the mandrel
              have shown that, while strain E(:  strongly depends on these parameters, strain e!  -
              practically does not change. This supports the assumption that strain 6; is caused by
              the chemical shrinkage of the resin and depends only on its properties.
                For  a cylinder in  which fibers make angle 4 with  the x-axis in  Fig. 7.51, the
              strains induced by  the removal of the mandrel can be found from Eqs. (4.70),i.e.
                  EX  = 11  cos24 + ~2 sin26,
                  E,,  = 11  sin24 +  cos24,                                    (7.82)
                  jJxy  = (El  - E2) sin 24 ,

              where El  and E2  are specified by  Eqs. (7.81). Dependencies of E,,  E.”,  and +,,  on 4
              plotted with the aid of Eqs. (7.82) are shown in Fig. 7.52 together with expenmental
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