#### Date of Award

Fall 2013

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Aeronautics and Astronautics

#### First Advisor

R. Byron Pipes

#### Committee Chair

R. Byron Pipes

#### Committee Member 1

C. T. Sun

#### Committee Member 2

Michael Sangid

#### Committee Member 3

Marisol Koslowski

#### Abstract

The present work contains the solution of two problems in composite structures. In the first, an approximate elasticity solution for prediction of the displacement, stress and strain fields within the m-layer, symmetric and balanced angle-ply composite laminate of finite-width subjected anticlastic bending deformation is developed. The solution is shown to recover classical laminated plate theory predictions at interior regions of the laminate and thereby illustrates the boundary layer character of this interlaminar phenomenon. The results exhibit the anticipated response in congruence with the solutions for uniform axial extension and uniform temperature change, where divergence of the interlaminar shearing stress is seen to occur at the intersection of the free-edge and planes between lamina of +theta and -theta orientation. The analytical results show excellent agreement with the finite-element predictions for the same boundary-value problem and thereby provide an efficient and compact solution available for parametric studies of the influence of geometry and material properties. The solution is combined with previously developed solutions for uniform axial extension and uniform temperature change of the identical laminate and the combined solution is exercised to compare the relative magnitudes of free-edge phenomenon arising from the different loading conditions, to study very thick laminates and laminates where the laminate width is less than the laminate thickness. Significantly, it was demonstrated that the solution is valid for arbitrary stacking sequence and the solution was exercised to examine antisymmetric and non-symmetric laminates. Finally, the solution was exercised to determine the dimensions of the boundary layer for very large numbers of layers. It was found that the dimension of the boundary layer width in bending is approximately twice that in uniform axial extension and uniform temperature change.

In the second, the intrinsic flaw concept is extended to the determination of the intrinsic flaw length and the prediction of performance variability in the 10-degree off-axis specimen. The intrinsic flaw is defined as a fracture mechanics-type, through-thickness planar crack extending in the fiber direction from the failure initiation site of length, a. The distribution of intrinsic flaw lengths is postulated from multiple tests of 10-degree off-axis specimens by calculating the length of flaw that would cause fracture at each measured failure site and failure load given the fracture toughness of the material. The intrinsic flaw lengths on the homogeneous and micromechanical scales for unnotched (no hole) and specimens containing a centrally-located, through-thickness circular hole are compared. 8 hole-diameters ranging from 1.00 - 12.7 mm are considered. On the micromechanical scale, the intrinsic flaw ranges between approximately 10 and 100 microns in length, on the order of the relevant microstructural dimensions. The intrinsic flaw lengths on the homogeneous scale are determined to be an order of magnitude greater than that on the micromechanical scale. The effect of variation in the fiber volume fraction on the intrinsic flaw length is also considered.

In the strength predictions for the specimens, the intrinsic flaw crack geometry and probability density function of intrinsic flaw lengths calculated from the unnotched specimens allow fracture mechanics predictions of strength variability. The strength prediction is dependent on the flaw density, the number of flaws per unit length along the free-edge. The flaw density is established by matching the predicted strength with the experimental strength. The distribution of intrinsic flaw lengths is used with the strength variability of the unnotched and of open-hole specimens to determine the flaw density at each hole-size. The flaw density is shown to be related to the fabrication machining speed suggesting machining damage as a mechanism for the hole-size dependence of the flaw density.

The strength prediction methodology based on the distribution of intrinsic flaw lengths and flaw density and an examination of the intrinsic flaw lengths and failure sites in the open-hole specimens are used to address two questions about the failure-initiation site in the open-hole off-axis specimen. In the first, it is determined that the perimeter of the circular-hole is the likely site of failure initiation, as opposed to the lateral edge. In the second, it is determined that failure initiation likely occurs at a single site, rather than at multiple sites. This justifies investigation of the perimeter of the circular-hole in the determination of the intrinsic flaw length and suggests the set of the least intrinsic flaw length from each specimen to be the set of critical flaw lengths.

With the intrinsic flaw geometry, the set of critical intrinsic flaw lengths and the flaw density, the strength variability in the open-hole specimens may be predicted using the strength prediction methodology. The strength and failure-site variability in the 6.35 mm open-hole specimen is predicted. This is the specimen with the greatest number of experimental specimens tested. The predicted distributions of strength and failure-site are compared with the experimentally observed distributions and good agreement is observed. The Bayes factor and an area metric are introduced for quantitative comparison. Prediction results from methodologies employing different parameters, including constant or variable flaw length and constant or variable failure site, and considering the flaw length calculated from constant or variable fiber volume fraction, are compared. Finally, the strength dependence on hole-diameter, or the hole-size effect in the off-axis specimen is predicted. It is found that the intrinsic flaw strength prediction methodology yields a conservative prediction of the minimum strength at each hole-size.

#### Recommended Citation

Goodsell, Jonathan, "Solution to Certain Problems in the Failure of Composite Structures" (2013). *Open Access Dissertations*. 166.

http://docs.lib.purdue.edu/open_access_dissertations/166

#### Included in

Aerospace Engineering Commons, Materials Science and Engineering Commons, Mechanical Engineering Commons