Johnathan Goodsell

Generalized Free-Edge Stress Analysis Using Mechanics of Structure Genome

This work reveals the potential of mechanics of structure genome (MSG) for the free-edge stress analysis of composite laminates. First the cross-sectional analysis specialized from MSG is formulated for solving a generalized free-edge problem of composite laminates. Then, MSG and the companion code SwiftCompTM are applied to the free-edge stress analysis of several composite laminates with arbitrary layups and general loads including extension, torsion, in-plane and out-of-plane bending and their combinations. The results of MSG are compared with various existing solutions for symmetric angle-ply laminates. New results are presented for the free-edge stress fields in general la minates for combined mechanical loads and compared with three dimensional (3D) finite element analysis (FEA) results, which agree very well.

Interlaminar Stresses in Composite Laminates Subjected to Anticlastic Bending Deformation

Approximate elasticity solutions for prediction of the displacement, stress, and strain fields within the m-layer, symmetric and balanced angle-ply composite laminate of finite-width and subjected to uniform axial extension and uniform temperature change were developed earlier by the authors. In the present paper, the authors have extended these solutions to treat bending deformation. Bending and torsion moments are combined to yield a deformation state without twisting curvature and with transverse curvature due only to the laminate Poisson effect. This state of deformation is termed anticlastic bending. The approximate elasticity solution for this bending deformation is shown to recover 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 +θ and –θ 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. Finally, the solution was exercised to determine the dimensions of the boundary layer in bending for very large numbers of layers.

Challenge problems for the benchmarking of micromechanics analysis: Level I initial results

Because of composite materials’ inherent heterogeneity, the field of micromechanics provides essential tools for understanding and analyzing composite materials and structures. Micromechanics serves two purposes: homogenization or prediction of effective properties and dehomogenization or recovery of local fields in the original heterogeneous microstructure. Many micromechanical tools have been developed and codified, including commercially available software packages that offer micromechanical analyses as stand-alone tools or as part of an analysis chain. With the increasing number of tools available, the practitioner must determine which tool(s) provides the most value for the problem at hand given budget, time, and resource constraints. To date, simple benchmarking examples have been developed in an attempt to address this challenge. The present paper presents the benchmark cases and results from the Micromechanical Simulation Challenge hosted by the Composites Design and Manufacturing HUB. The challenge is a series of comprehensive benchmarking exercises in the field of micromechanics against which such tools can be compared. The Level I challenge problems consist of six microstructure cases, including aligned, continuous fibers in a matrix, with and without an interphase; a cross-ply laminate; spherical inclusions; a plain-weave fabric; and a short-fiber microstructure with “random” fiber orientation. In the present phase of the simulation challenge, the material constitutive relations are restricted to linear thermoelastic. Partial results from DIGIMAT-MF, ESI VPS, MAC/GMC, finite volume direct averaging method, Altair MDS, SwiftComp, and 3D finite element analysis are reported. As the challenge is intended to be ongoing, the full results are hosted and updated online at www.cdmHUB.org.

Three-dimensional thermoelastic properties of general composite laminates:

This paper presents a hybrid rule of mixtures for calculating the complete set of effective three-dimensional thermoelastic properties of a composite laminate when it is approximated as an equivalent, homogeneous, anisotropic solid. The laminate can be made of generally anisotropic layers with arbitrary layup sequence. This hybrid rule of mixtures is based on the exact solution obtained using the recently discovered mechanics of structure genome. Since mechanics of structure genome minimizes the loss of accuracy for homogenization, the three-dimensional thermoelastic properties obtained using the mechanics of structure genome-based hybrid rule of mixtures will be the most accurate one could obtain for composite laminates. The results of the hybrid rule of mixtures are compared with several other representative methods for predicting thermoelastic properties of composite laminates.

Free-Edge Interlaminar Stresses in Angle-Ply Laminates: A Family of Analytic Solutions

A family of analytic solutions for the prediction of interlaminar stresses in angle-ply laminates has been developed and is presented in a unified form and as a unique set of solutions. The uniqueness of the formulation is demonstrated for the class of thermomechanical states of deformation for which the solutions are valid. These are shown to be limited to the specific cases wherein only two in-plane stress components and one interlaminar stress components are nonzero. Interlaminar shear stress in the angle-ply laminate subjected to thermomechanical loading conditions of uniaxial extension, uniform temperature change, and anticlastic bending is shown to make up the family of solutions in the unified formulation. Further, these are shown to comprise the complete set of the solutions and the conditions which control the limitations of this family of solutions are articulated.

Multi-scale Intrinsic Flaws in Composite Materials

In the present, the intrinsic flaw concept introduced by Waddoups is extended to determination of the intrinsic flaw length in the 10-degree off-axis specimen. The intrinsic flaw will be defined as a fracture mechanics-type planar crack. The experimental testing procedures for fabricating, testing and examining the off-axis specimen are overviewed. A fracture mechanics-based methodology is introduced for calculation of the intrinsic flaw length. The intrinsic flaw length on the homogeneous scale and on the micromechanical scale will be determined and compared for unnotched (no hole) specimens and specimens containing a circular-hole. Variation in fiber volume fraction influences the micromechanical stress field; hence the effect of fiber volume fraction variation on the intrinsic flaw length is determined through a multi-scale, integrated computational approach. The effect of the spatial variation in fiber volume fraction, as observed in micrographs of the free-edge, is discussed. The intrinsic flaw lengths on the homogeneous and micromechanical scales, with and without fiber volume fraction variation are compared. The approach not only quantifies the length scale of critical flaws on multiple-scales but demonstrates an approach for treating the stochastic variation in fiber volume fraction.