In Situ Constituent Properties

Learn the difference between bulk and in situ constituent properties and why in situ constituent properties are necessary in the MCT material characterization process.

Bulk constituent properties are simply properties measured using homogeneous test specimens composed of a single constituent material. Generally speaking, a micro-mechanical finite element model that uses bulk constituent properties will not yield accurate homogenized properties for the composite material. The inability of the micro-mechanical finite element model to predict accurate homogenized properties for the composite material is caused by several different factors described below.

1. The micro-mechanical finite element model represents an idealized microstructure, not the actual microstructure.
   • In an actual composite material with a fiber volume fraction of φf, the fibers exhibit a somewhat random distribution with local regions where fibers are actually touching each other and other regions where the distance between fibers is relatively large. Even if we attempt to use a micro-mechanical finite element model with random fiber spacing, it is doubtful the model correctly reflects the same degree of randomness exhibited in the actual composite material.
   • The actual composite material typically has a characteristic distribution of various defects at the micro-structural level caused by manufacturing and curing processes. In practice, the micro-mechanical finite element model is assumed to be completely free of these micro-defects.
2. Knowledge of the mechanical and thermal properties of the fiber/matrix interphase region is most often completely lacking. Therefore, the strength and stiffness of the interphase is not explicitly accounted for in the micro-mechanical finite element model.
3. Even if the bulk matrix properties are based on precise measurements performed on bulk matrix material, it is unlikely the bulk matrix material has been subjected to identical cure conditions (e.g., temperature, pressure, deformation, chemical environment) as the same matrix material experiences in a fiber-reinforced composite laminate. Therefore, we expect these differences in curing conditions will cause the resin in the composite material to behave somewhat differently from the bulk resin material.
4. Knowledge of the bulk mechanical and thermal properties of the fiber and matrix constituents is typically incomplete. In practice, some of the bulk constituent properties are actually measured, some are estimated based on measurements from similar materials, and some are simply guessed.
5. Since fiber tows undulate in woven composites, their properties in a global coordinate system are not the same as the properties in their local material coordinates.

One way of collectively accounting for all of the discrepancies and uncertainties listed above in items 1 through 4 is to use altered constituent properties (instead of measured bulk constituent properties). These altered constituent properties cause the micro-mechanical finite element model to produce the elastic properties that were actually measured for the composite material (e.g., stiffness, Poisson effect, and thermal expansion). These altered constituent properties are referred to as in situ constituent properties to emphasize they are purposefully chosen to function correctly in a specific micro-mechanical finite element model of a specific composite material. This causes the finite element model to yield the measured composite properties. Thus, the concept of developing in situ constituent properties can be thought of as purposefully tuning one aspect of the micro-mechanical finite element model (i.e., the material properties) to compensate for all other errors and unknowns in the micro-mechanical finite element model. The process of determining the in situ constituent properties is a mathematical optimization problem. We iteratively adjust the bulk constituent properties to minimize the error between the measured composite properties and the predicted composite properties of the micro-mechanical finite element model. Consequently, standard optimization routines are utilized to determine the in situ constituent properties. This optimization is currently performed using the method of steepest descent.