Composite Analysis Project

The Problem

The team was assigned a carbon/epoxy laminate with a symmetric layup of [90/45/0/-45]s and 0.005ib ply thickness. The objective was to use MATLAB code to determine whether the laminate could endure four distinct loading conditions without failure, perform different failure modes for each case, as well as identify which plies are most critical. 

The Approach

This analysis uses Classical Laminate Plate Theory which relates in-plane force and moment resultants to midplane strains and curvatures through ABD laminate stiffness matrices. A Extensional, B bending-extension coupling, and D bending. Due to the symmetric layout, the B matrix is zero. In the total the A, B, and D matrices were assembled by summing the transformed reduced stiffness terms of each ply through the thickness. 

A = extensional stiffness 348.9 ksi in on diagonal                        D = bending stiffness: 0.0274 ksi in^3 on diagonal

After the midplane strains and curvatures where established for each load case, the stresses and strains were recovered at the outermost coordinate of each ply, for both in global laminate coordinates and transformed into local coordinates. this ply by ply recover is essential as composite failure is caused by local fiber and matrix stresses. 

Specifically for load case 3, thermal effects were incorporated by calculating equivalent thermal force and moment resultants using given thermal expansion coefficients. Due to the carbon and epoxy matrix expanding at different rates, the mismatch created residual stress in the transvers direction often leading to warping. 

Failure was evaluated using four independent criteria, evaluation was done ply by ply and stops at first ply failure. 

• Maximum Stress

• Maximum Strain

• Hill-Tsai

• Tsai-Wu

Using all four criteria in parallel allows us to analyze the failure and ensure it is consistent across methods. 

The enitre analysis was implemented into a custom MATLAB code developed by the group. The code was structured to have the values inputed and automatically output stiffness matricies, laminate properties, midplane strains and curvates, ply level stress and strain, through thickness strain, and finally strain plots for all four criteria seen below. This code allows for any type of composite to be alayzed, demonstrating its versatility. Finally the code was discussed during a live oral exam, where several examples where run to verify the results and authenticity. 

Results

• Load Case 1  -  Combined in-plane + bending  -  No Failure

• Load Case 2  -  Pure Bending                               -  No Failure 

• Load Case 3  -  Combined in-plane + thermal   -  Failure at Ply 1 (90deg) Matrix Tension

• Load Case 4  -  Pure twisting                                -  Failure at Ply 1 (90deg) Matrix Shear

Load cases 1 and 2 showed no failure, however load cases 3 and 4 failed both at Ply 1, first due to matrix tension driven by thermal mismatch causing tension, and second due to matrix shear under pure twisting respectively. These failures where verified by all four criteria, all where indicated to be matrix dominated, meaning fiber orientation caused certain plies to carry disproportionate stress, causing failure. Therefore the recommended design changes involve improving stacking sequence and orientation to redistribute the load away from citical locations. 

Results Tables 

Takeaway

This capstone project proved valuable to me in learning the analysis and behavior of modern composites, as the use of composite laminates grow in the modern aerospace industry, it is becoming more and more important to understand how to analyze their behavior, implement it in MATLAB code, and interpret the failure. This project also connected to my composite manufacturing experience with Aztec Design Build Fly, in constructing a composite fuselage and wing for a UAV, learning why structures are designed the way they are.