Solution to certain problems in the failure of composite structures

Johnathan Goodsell, Purdue University

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 +&thetas; and −&thetas; 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. (Abstract shortened by UMI.)

Degree

Ph.D.

Advisors

Pipes, Purdue University.

Subject Area

Aerospace engineering|Mechanical engineering|Materials science

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