Optimize the constituent properties.

In the first step of the MCT material characterization process, the in situ constituent properties are optimized so that the micro-mechanical finite element model predicts homogenized composite material properties that match measured properties of the actual composite material. It is assumed that each of the tensile moduli is equal to the corresponding compressive moduliCIR.

During the optimization of the in situ constituent properties discussed here, matrix and fiber constituents are assumed to be transversely isotropic materialsCIR. To begin the optimization process, the initial values of the in situ constituent properties are provided by the measured bulk constituent properties.

The in situ constituent properties are chosen so the homogenized composite properties (predicted by the micro-mechanical finite element model) agree with the eight measured composite properties in a weighted least-squares sense.

Example Problem: Determination of in situ properties for a glass fiber reinforced polyester (D155/CoRezyn®63-AX-051 OrthoPolyester)

For this example, our confidence in the measured value of is not high, so we exclude using this term in minimizing the error. To do this, set the "weight" of this term in the error calculation to zero.

Measured Composite Properties of D155/CoRezyn®63-AX-051 OrthoPolyester:

Fiber Volume Fraction = 0.36

= 28.3 GPa, = = 7.75 GPa

= = 3.3 GPa, = 2.55 GPa

= = 0.32, = 0.44

Measured bulk matrix properties for CoRezyn®63-AX-051 OrthoPolyester (or initial values of the in situ matrix properties):

= = = 3.8 GPa

= = = 1.407 GPa

= = = 0.35

Measured bulk fiber properties for D155 glass fiber (or initial values of the in situ fiber properties):

= = = 74.0 GPa

= = = 30.8 GPa

= = = 0.2

If the micro-mechanical finite element model is used in conjunction with the measured bulk constituent properties, the following composite properties are predicted:

The optimization procedure produces the following in situ constituent properties.

Optimized in situ matrix properties:

= 3.8 GPa, = = 3.75 GPa

= = 1.681 GPa, = 1.403 GPa

= = 0.393, = 0.335

Optimized in situ fiber properties:

= = = 72.1 GPa

= = = 31.2 GPa

= = = 0.219

Using optimized in situ constituent properties with the micro-mechanical finite element model yields the following predicted composite properties.

Generally speaking, the use of optimized in situ constituent properties (as opposed to measured bulk constituent properties) causes the micro-mechanical finite element model to predict homogenized composite properties that agree much more closely with the actual measured composite properties. Of the six measured composite properties (, = , = , , = , ), and are the only properties that exhibit less agreement with the measured values after completing the optimization process. This increased discrepancy between the measured and predicted values of and is simply caused by assigning them weight coefficients of zero. This prevents these two properties from participating in the optimization process. The reason for this choice was that the measured values of and for this particular composite material were considered to be significantly less accurate than the other composite properties (hence the reason for a weighted optimization).