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The fiber length determined by optical microscopy has been used for the determination of the theoretical elastic moduli of a unidirectional (UD) short fiber composite and a quasi-isotropic (QI) completely random short fiber composite. In the hypothesis of a complete alignment of the fibers in the injection direction, the elastic modulus Ej, of a lamina with UD aligned short fibers has been determined from the modified Halpin Tsai equations [66]: where dg is the fiber diameter, obtained experimentally from HeIM analysis, Eg and E, are the elastic moduli of the fiber and matrix, respectively, and Vs the fiber volume content. The values of d¢, Ex, Em and Ve are reported in Table 1. Finally, l¢is the mean value of the fiber length measured by optical microscopy and modeled by the Weibull distribu- tion. As reported in Table 2, a mean value of 118.4 ym has been adopted.

Table 1 The fiber length determined by optical microscopy has been used for the determination of the theoretical elastic moduli of a unidirectional (UD) short fiber composite and a quasi-isotropic (QI) completely random short fiber composite. In the hypothesis of a complete alignment of the fibers in the injection direction, the elastic modulus Ej, of a lamina with UD aligned short fibers has been determined from the modified Halpin Tsai equations [66]: where dg is the fiber diameter, obtained experimentally from HeIM analysis, Eg and E, are the elastic moduli of the fiber and matrix, respectively, and Vs the fiber volume content. The values of d¢, Ex, Em and Ve are reported in Table 1. Finally, l¢is the mean value of the fiber length measured by optical microscopy and modeled by the Weibull distribu- tion. As reported in Table 2, a mean value of 118.4 ym has been adopted.

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Material properties. Table 1
Material properties. Table 1
Fig. 1. Flow chart of the research.
Fig. 1. Flow chart of the research.
Fig. 2. a) Injection molded sample; b) broken tensile specimen; c) sample region considered for micro-CT analysis. X-axis is parallel to the injection direction in all pictures.
Fig. 2. a) Injection molded sample; b) broken tensile specimen; c) sample region considered for micro-CT analysis. X-axis is parallel to the injection direction in all pictures.
Equation (1) fitting parameters for the basalt fiber reinforced PP. Table 2 3.2. Fiber orientation distribution by micro-CT analysis
Equation (1) fitting parameters for the basalt fiber reinforced PP. Table 2 3.2. Fiber orientation distribution by micro-CT analysis
Fig. 3. Fiber length distribution of BFPP composites obtained by injection molding. Fitting line according to eq. (1). where k and d are the shape and scale parameter, respectively. The fitting parameters are summarized in Table 2.
Fig. 3. Fiber length distribution of BFPP composites obtained by injection molding. Fitting line according to eq. (1). where k and d are the shape and scale parameter, respectively. The fitting parameters are summarized in Table 2.
Fig. 4. a) 3D tomographic image of the injection molded sample obtained by stacking the 2D slices along the Z-axis; b,c,d) Reconstructed cross-sections (2D slices) of the injection molded sample.
Fig. 4. a) 3D tomographic image of the injection molded sample obtained by stacking the 2D slices along the Z-axis; b,c,d) Reconstructed cross-sections (2D slices) of the injection molded sample.
Fig. 5. 3D rose diagrams of a) MIL; b) VO; c) SLD and d) SVD methods; e) diagonal components of the fabric tensor
Fig. 5. 3D rose diagrams of a) MIL; b) VO; c) SLD and d) SVD methods; e) diagonal components of the fabric tensor
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Fabric tensors and eigenvalues obtained from the four morphometric methods. Table 3
Mechanical properties of tested samples. Table 4 partitioning the integration domain in different material regions depending on the orientation of fibers as predicted by numerical simu- lation of injection molding. The model has been obtained by combining
Mechanical properties of tested samples. Table 4 partitioning the integration domain in different material regions depending on the orientation of fibers as predicted by numerical simu- lation of injection molding. The model has been obtained by combining
Fig. 6. a) XY slice cross section with the boundaries of the six subdomains indicated; b), c) and d) average value in each layer of the diagonal components of the tensors, txx, tyy and tzz, respectively.
Fig. 6. a) XY slice cross section with the boundaries of the six subdomains indicated; b), c) and d) average value in each layer of the diagonal components of the tensors, txx, tyy and tzz, respectively.
Fig. 7. Equivalent composite lay-up sketch (not in scale) used for the mechanical model. As simplest case, a laminate of only three plies (laminate #1) has been considered. As reported in Fig. 7, the diagonal components of the tensor have been assumed directly proportional to the thickness of the
Fig. 7. Equivalent composite lay-up sketch (not in scale) used for the mechanical model. As simplest case, a laminate of only three plies (laminate #1) has been considered. As reported in Fig. 7, the diagonal components of the tensor have been assumed directly proportional to the thickness of the
Fig. 8. Comparison between the experimental elastic modulus and the values obtained from the micro-macro mechanical approach for laminates 1 (3 plies), 2 (21 plies) and 3 (18 plies).
Fig. 8. Comparison between the experimental elastic modulus and the values obtained from the micro-macro mechanical approach for laminates 1 (3 plies), 2 (21 plies) and 3 (18 plies).
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