Homogenized modeling approach for effective property prediction of 3D-printed short fibers reinforced polymer matrix composite material

AbstractQuery

The objective of this paper is to present the modeling approach for homogenizing the 3D-printed composite parts for the accurate prediction of effective mechanical properties. The Mori–Tanaka (MT) approach associated with two-step homogenization is applied to partially oriented short carbon fiber (SCF)-reinforced polycarbonate (SCF/PC)-based composites and compared with the experimental results. Detailed microstructural analysis was performed to investigate the variation in fiber length and bead dimensions that occurred due to change in fiber percentage (3%, 5%, 7.5%, and 10% by vol.). A two-step homogenization framework was performed in this research. Change in fiber length was considered in the first-step homogenization and change in bead dimensions was considered in the second step of homogenization approach to find the microscale and mesoscale constitutive properties of SCF/PC 3D-printed composite samples using the MT method respectively. Results of this study revealed that the stiffness of the composite samples increases with the increase in fiber percentage. As we increase the SCF, significant variations were observed in the fiber length and bead dimensions which also significantly affect the mechanical properties of 3D-printed composite parts. Results obtained after considering the fiber length and bead dimensions in mathematical calculation helps in reducing the error gap between the homogenized numerical and experimental results. It was also concluded that the prediction of Young’s modulus using higher fiber percentage has relatively low errors. Eventually, the properties attained from the respective approach help to find out the macro fields (average stress and average strain) in the 3D-printed composite samples.

Graphical abstract

Appendix

This section shows the Eshelby’s S tensors used in this study [43]. The local coordinate system used in this study may not match with the global coordinate system used in other computations.

For fiber-like inclusions

$$l=\mathrm{Fiber length}$$

$$d=\mathrm{fiber diameter}$$

$$a=\frac{l}{d} (\mathrm{aspect ratio})$$

$$a2={a}^{2}$$

$$y=\left(\frac{a}{{\left(a2-1\right)}^{3/2}}\right)\times \left(a{\left(a2-1\right)}^{2}-\mathrm{acosh}(a)\right)$$

$$b=\frac{1}{1-nu0}$$

$$c=1-2*nu0$$

$$e=\frac{1}{a2-1}$$

$$S1111=0.5*b(c+e*\left(3*a2-1\right)-\left(c+3*e*a2\right)*g)$$

$$S2222=\left(\frac{3}{8}\right)*b*e*a2+0.25*b*\left(c-\left(\frac{9}{4}\right)*e\right)*g$$

$$S1111=S2222$$

$$S3322=0.25*b*(0.5*e*a2-c-0.75*e*g)$$

$$S2211=-0.5*b*e*a2+0.25*b*\left(3*e*a2-c\right)*g$$

$$S1111=0.5*b(c+e*\left(3*a2-1\right)-\left(c+3*e*a2\right)*g)$$

$$S3311=S2211$$

$$S1122=-0.5*b*\left(c+e\right)+0.5*b*\left(c+1.5*e\right)*g$$

$$S1133=S1122$$

$$S2323=0.125*b*a2*e+0.0625*b*\left(4*c-3*e\right)*g$$

$$S1212=0.125*b*(2*c-2*e*\left(a2+1\right)+3*g*(-1+2nu0+3*e*\left(a2+1\right)))$$

$$S3131=S1212$$

Elliptic cylinder with c goes to infinity

$$a2={d}^{2}$$

$$b=\frac{1}{1-2*nu0}$$

$$c=2-2*nu0$$

$$S1111=\left(\frac{1}{c}\right)*(\left(\frac{a2+2*a2}{\left(d+d\right)}\right)+\left(b\right)*(\frac{d}{2*d}))$$

$$S1111=S2222$$

$$S1111=0$$

$$S2233=\left(\frac{1}{c}\right)*(\frac{2*nu0*d}{\left(d+d\right)})$$

$$S2211=S1122$$

$$S3311=0$$

$$S3322=0$$

$$S1111=\left(\frac{1}{c}\right)*\left(\left(\frac{a2}{d+d}*\left(d+d\right)\right)\right)-\left(b\right)*(\frac{d}{2*d})$$

$$S1133=S2233$$

$$S2323=\frac{d}{4*d}$$

$$S3131=S2323$$

$$S1212=\left(\frac{1}{c}\right)*(\left(\frac{a2+a2}{2*\left(d+d\right)*\left(d+d\right)}\right)+\frac{b}{2})$$