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- 2018
利用外方内圆模型预测单向连续纤维增强树脂基复合材料的横向弹性模量
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Abstract:
为了对连续纤维增强树脂基复合材料的横向弹性模量进行较高精度的解析计算，利用代表性体积单元横截面为正方形基体包裹圆形纤维的外方内圆模型，采用先并联后串联和先串联后并联的两种计算方式进行公式推导，借助于Mathematica软件进行符号积分运算，获得了横向弹性模量的2组解析解，将其中间值作为预测值，给出了预测值的近似公式，并与一组实验数据进行了比较。研究表明，外方内圆模型能较好地反映客观实际，利用Mathematica软件可以解决计算困难的问题；将解析解的中间值作为横向弹性模量的预测值，与一组实验数据比较，显示解析计算的相对误差基本在10%以内；给出的近似公式形式简单，且其曲线能较好地吻合中间值曲线，在纤维体积分数小于75%的范围内，近似公式与中间值公式计算结果之间的最大误差不超过7%。 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%.
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