## pcGina

__Summary of pcGINA© modeling capabilities__Our research group constructed mechanistic models, with a special focus on SiC/SiC composites, for many programs starting with the EPM program, to PRDA I and PRDA VII and ACE. We believe that in order to develop successful mechanistic models, the first step has to involve a clear characterization of the geometry of the reinforcing perform to allow for the delineation of its role in various stress/strain distributions as well as crack propagation and possible failure of the composite. This vision led us to develop a system of models based on a core technical capability embedded in the algorithm of pcGINA©. A short description of pcGINA© and some of the models based on its framework are detailed in the ensuing sections.

__The Graphical Integrated Numerical Analysis (pcGINA©)__is a two-part model. First, a processing-science approach is used to mathematically and geometrically model the fabric preform and evaluate the relative volume fraction and spatial orientation of each yarn in the composite space. Data acquired from the geometric model is used by a hybrid finite element analysis to calculate the mechanical and thermal properties of the composite. The geometric model follows the fabric forming process, weaving or braiding, to identify the location of a set of spatial points “knots” along the yarn center-line path. A B-spline function is utilized to approximate a smooth yarn centerline path relative to the identified knots and minimize the strain energy of the path. The final step in this model is carried out by constructing a 3-D object (i.e. yarn) by sweeping a cross section along the smooth centerline forming the yarn surface.

A repeat

**unit cell**of the modeled preform is identified from the geometric model and used to represent a complete yarn or tow pattern. The unit cell is divided into smaller subcells where each subcell is a hexahedral brick element with fibers and matrix around each integration point. A virtual work technique is applied within a hybrid finite element solution to calculate the properties of the repeat unit cell. The unit cell properties are considered to be representative of the composite properties. Currently, pcGINA© can calculate, with a good level of accuracy,__the elastic properties, thermal conductivities, thermal expansion coefficients for 2D wovens (e.g., plain weaves and n-HS), biaxial and triaxial braids, angle and layers interlock weaves, step weaves and orthogonal 3D weaves at room temperature and elevated temperatures.__It was experimentally observed and documented in literature that the value of the strain at yarn crossover points in a woven fabric composite is higher than that between crossover points. In order to quantify such strain variation within a single unit cell, pcGINA© core capability was utilized to map the stress and strain distributions at different points within a unit cell. This stress/strain mapping model was verified using ANSYS® for a unit cell of a plain weave SiC/SiC composites where yarns were meshed using SOLID45 elements and a sweep mesh with the material properties changing along their path to accommodate the change of angle with load direction. The total number of elements used in the ANSYS® model was 15,552 as compared to 225 in pcGINA©.

Modeling of the stress/strain distribution at a unit cell level was further refined to

The above mentioned models represent a short summary of our continuous activities and attempts to understand the instantaneous and long term behavior of PMCs. Many of these models were verified and published in refereed literature as well as presented at technical meetings.

__Stress/strain mapping at the unit cell level__was used to understand stress build-up and its role in crack development and failure and was also used to evaluate the effect of the size of strain gauges on the accuracy of their readings.Modeling of the stress/strain distribution at a unit cell level was further refined to

__calculate the stress and strain distribution in constituent materials (i.e., fiber, coat and matrix)__. The solution was formulated in the longitudinal direction of the fibers using a constant applied stress and an axisymmetric stress analysis. In the transverse direction, a general solution for the bi-harmonic equation of Kolosov-Mukhelishvili complex potential was used to obtain a set of equations to represent the stresses and displacements for each region of an n-phase material. The model was verified by comparing it to models from archived literature.The above mentioned models represent a short summary of our continuous activities and attempts to understand the instantaneous and long term behavior of PMCs. Many of these models were verified and published in refereed literature as well as presented at technical meetings.