Prediction of transverse elastic modulus of unidirectional continuous fiber reinforced resin composites using the model of circle-in-square

In order to calculate the transverse elastic modulus of continuous fiber reinforced resin composites with high precision, two analytical solutions of the transverse elastic modulus were obtained, by using the model of circle-in-square, which is the cross-section shape of a representative volume unit that the square matrix wraps a circle fiber, and by derivating formulas using two kinds of calculation method in parallel after series and in series after parallel by means of Mathematica software. The median value of the two analytical solutions was treated as the predictive value, and the approximate formula of the predictive value was given. The research results show that, the model of circle-in-square can better reflect the objective reality, and the Mathematica software can be used to solve the problem of difficult calculation in this project; The median value of the two analytical solutions can be used as the predictive value of the transverse elastic modulus. Compared with a set of experimental data, the relative errors of the median values are basically less than 10%; The form of the approximate formula is simple, and its curve can well fit the median value curve. In the range that the fiber volume fraction is less than 75%, the maximum error between the calculation results of approximate formula and the median value formula is not more than 7%.