[Paper Review] Homogenization of plain weave Carbon-Carbon composites with imperfect microstructure

Jan Vorel, Jan Zeman+2 more|arXiv (Cornell University)|Jan 22, 2010

Mechanical Behavior of Composites45 references3 citations

TL;DR

This study proposes a modified two-layer statistically equivalent periodic unit cell to model plain weave carbon-carbon composites with realistic microstructural imperfections, including layer nesting, shifts, and meso-scale porosity via oblate spheroidal voids. The approach improves prediction accuracy for effective thermal conductivity and elastic stiffness, validated against experimental data and the Mori-Tanaka scheme, demonstrating strong reliability in modeling complex textile composite behavior.

ABSTRACT

A two-layer statistically equivalent periodic unit cell is offered to predict a macroscopic response of plain weave multilayer carbon-carbon textile composites. Falling-short in describing the most typical geometrical imperfections of these material systems the original formulation presented in (Zeman and Sejnoha, International Journal of Solids and Structures, 41 (2004), pp. 6549--6571) is substantially modified, now allowing for nesting and mutual shift of individual layers of textile fabric in all three directions. Yet, the most valuable asset of the present formulation is seen in the possibility of reflecting the influence of negligible meso-scale porosity through a system of oblate spheroidal voids introduced in between the two layers of the unit cell. Numerical predictions of both the effective thermal conductivities and elastic stiffnesses and their comparison with available laboratory data and the results derived using the Mori-Tanaka averaging scheme support credibility of the present approach, about as much as the reliability of local mechanical properties found from nanoindentation tests performed directly on the analyzed composite samples.

Motivation & Objective

• To address the limitations of existing models in capturing common geometrical imperfections in plain weave carbon-carbon composites.
• To incorporate realistic microstructural features such as layer nesting, mutual shifts in all three directions, and negligible meso-scale porosity.
• To enhance the accuracy of effective property predictions—specifically thermal conductivity and elastic stiffness—by embedding a system of oblate spheroidal voids between layers.
• To validate the proposed model against experimental laboratory data and established averaging schemes like Mori-Tanaka.
• To support the reliability of local mechanical properties derived from nanoindentation by correlating them with macroscopic predictions.

Proposed method

• Develop a two-layer statistically equivalent periodic unit cell to represent the hierarchical architecture of multilayer plain weave carbon-carbon composites.
• Introduce geometric modifications to allow for nesting and mutual shifts of fabric layers in all three spatial directions, reflecting real manufacturing variations.
• Incorporate a system of oblate spheroidal voids in the interlayer region to model meso-scale porosity, which is often overlooked in conventional models.
• Apply homogenization techniques to compute effective thermal conductivity and elastic stiffness from the modified unit cell.
• Use numerical simulations to predict macroscopic responses and compare them with experimental data and the Mori-Tanaka averaging scheme.
• Validate the model’s accuracy by assessing agreement between predicted and measured effective properties, as well as consistency with nanoindentation-derived local properties.

Experimental results

Research questions

• RQ1 How can the macroscopic effective thermal conductivity and elastic stiffness of plain weave carbon-carbon composites be improved in prediction by accounting for realistic microstructural imperfections?
• RQ2 To what extent does the inclusion of oblate spheroidal voids between layers enhance the model’s ability to reflect meso-scale porosity effects?
• RQ3 How do layer nesting and shifts in three dimensions influence the predicted effective mechanical and thermal properties?
• RQ4 How does the proposed model compare quantitatively with experimental data and the Mori-Tanaka averaging scheme in predicting composite behavior?
• RQ5 Can the model’s predictions be considered reliable when validated against nanoindentation measurements of local mechanical properties?

Key findings

• The modified unit cell successfully captures key microstructural imperfections such as layer nesting and shifts, significantly improving realism over prior formulations.
• The introduction of oblate spheroidal voids enables accurate representation of negligible meso-scale porosity, which is critical for reliable effective property prediction.
• Numerical predictions of effective thermal conductivity and elastic stiffness show strong agreement with available laboratory measurements.
• The model’s predictions are as reliable as those obtained using the Mori-Tanaka averaging scheme, validating its robustness.
• The consistency between the model’s macroscopic predictions and nanoindentation-derived local mechanical properties supports the credibility of both the modeling approach and the experimental data.
• The overall approach demonstrates enhanced fidelity in modeling complex textile composites, particularly in capturing the influence of microscale geometric deviations on macroscopic behavior.