Charles E. Harris

Internal State Variable Approach for Predicting Stiffness Reductions in Fibrous Laminated Composites with Matrix Cracks

A mathematical model utilizing the Internal State Variable (ISV) concept is proposed for predicting the upper bound of the reduced axial stiffnesses in cross-ply lami nates with matrix cracks. The axial crack opening displacement is explicitly expressed in terms of the observable axial strain and the undamaged material properties. A crack parameter representing the effect of matrix cracks on the observable axial Youngs modulus is calculated for glass/epoxy and graphite/epoxy material systems. The results of the present study show that the matrix crack opening displacement and conse quently the effective Youngs modulus depends not on the crack length but on its ratio to the crack spacing. Comparisons of the present model with experimental data and other models in the litera ture show a good agreement, thus confirming direct applicability of the model to [0 p /90 r ] s type laminates.

Design and Manufacturing of Aerospace Composite Structures, State-of-the-Art Assessment

The results ofan assessment ofthe state of theartin the design and manufacturing of largecompositestructures are described. The focus of the assessment is on the use of polymeric matrix composite materials for large airframe structural components, such as thosein commercial and military aircraft and spacetransportation vehicles. Applications of composite materials for large commercial transport aircraft, general aviation aircraft, rotorcraft, military aircraft, and uninhabited rocket launch vehicles are reviewed. The results of the assessment of the state of the art include a summary of lessons learned, examples of current practice, and an assessment of advanced technologies under development. The results of the assessment conclude with an evaluation of the future technology challenges and advancements associated with applications of composite materials to the primary structures of commercial transport aircraft and advanced space transportation vehicles. These future technologies include breakthroughs in materials and process methods, next generation design tools, and nondestructive examination methods. I. Introduction A N assessment of the design and manufacturing practices for large composite structures has been conducted to determine the current state of the art for these technologies. The background that motivated the assessment was a series of unexpected manufacturing and design problems with the composite structures of several NASA experimental vehicles currently under development. The focus of the assessment is on the use of polymeric matrix composite materials for large airframe structural components such as those in commercial and military aircraft and space transportation vehicles. The baseline for the assessment is the historical evolution of the use of composite materials in actual aerospace vehicles. The assessment emphasizes the application of composite structures in moderately to heavily loaded aerospace vehicles. Applications of composite materials are reviewed for large commercial transport aircraft,generalaviation aircraft,rotorcraft, military e ghteraircraft, and military transport aircraft. The baseline also includes the application of composite materials for uninhabited rockets and space transportation vehicles. The assessment of the state of the art includes a summary of lessons learned, examples of current practice, and an assessment of advanced technologies under development. The assessment concludes with an evaluation of the future technology challenges associated with applications of composite materials to the primary structure of commercial aircraft and advanced space transportation vehicles. As a preamble to assessing the state of the art in the design and manufacturing of composite structures, the design requirements for aerospace vehicles are briee y reviewed. Because of the universal design requirement to minimize the gross takeoff weight of all aerospace vehicles, aerospace structural components are designed at or near zero margin of safety. Whereas the margin of safety is not

A cumulative damage model for continuous fiber composite laminates with matrix cracking and interply delaminations

Experimental evidence has shown that significant stiffness loss occurs in graphite/ epoxy laminates when matrix cracking and interply delaminations exist. Therefore, a cumulative damage model for predicting stiffness lossin graphite/epoxy laminates is proposed herein by applying a thermomechanical constitutive theory for elastic composites with distributed damage. The model proceeds from a continuum mechanics and thermodynamics approach wherein the distributed damage is characterized by a set of second-order tensor-valued internal state variables. The internal state variables represent locally averaged measures of matrix cracking and interply delaminations. The model formulation provides a set of damage dependent laminated plate equations. These are developed by modifying the classical Kirchhoff plate theory. The effect of the matrix cracking enters the formulation through alteration in the individual lamina constitution. The effect of interply delamination enters the formulation through modifications of the Kirchhoff displacements. The corresponding internal state variables are defined utilizing the kinematics of the interply delaminated region and the divergence theorem. These internal state variables depend on the components of the displacements created by the delamination.

Experimental Verification of a Progressive Damage Model for IM7/5260 Laminates Subjected to Tension-Tension Fatigue

The durability and damage tolerance of laminated composites are critical design considerations for airframe composite structures. Therefore, the ability to model damage initiation and growth and predict the life of laminated composites is necessary to achieve structurally efficient and economical designs. The purpose of this research is to experimentally verify the application of a continuum damage model to predict progressive damage development in a toughened material system. Damage due to monotonic and tension-tension fatigue was documented for IM7/5260 graphite/bismaleimide laminates. Crack density and delamination surface area were used to calculate matrix cracking and delamination internal state variables to predict stiffness loss in unnotched laminates. A damage dependent finite element code predicted the stiffness loss for notched laminates with good agreement to experimental data. It was concluded that the continuum damage model can adequately predict matrix damage progression in notched and unnotched laminates as a function of loading history and laminate stacking sequence.

Analytical Methodology for Predicting Widespread Fatigue Damage Onset in Fuselage Structure

A comprehensive analytical methodology has been developed for predicting the onset of widespread fatigue damage (WFD) in fuselage structure. The determination of the number of e ights and operational hours of aircraft service life that are related to the onset of WFD includes analyses for crack initiation, fatigue crack growth, and residual strength. Therefore, the computational capability required to predict analytically the onset of WFD must be able to represent a wide range of crack sizes, from the material (microscale) level to the global (structural-scale ) level. The results of carefully conducted teardown examinations of aircraft components indicate that fatigue crack behavior can be represented conveniently by the following three analysis scales: 1 ) small three-dimensional cracks at the microscale level, 2 ) through-the-thickness two-dimensional cracks at the local structural level, and 3 ) long cracks at the global structural level. The computational requirements for each of these three analysis scales are described in this paper.

A Continuum Model for Damage Evolution in Laminated Composites

The accumulation of matrix cracking is examined using continuum damage mechanics lamination theory. A phenomenologically based damage evolutionary relationship is proposed for matrix cracking in continuous fiber reinforced laminated composites. The use of material dependent properties and damage dependent laminate averaged ply stresses in this evolutionary relationship permits its application independently of the laminate stacking sequence. Several load histories are applied tocrossply laminates using this model and the results are compared to published experimental data. The stress redistribution among the plies during the accumulation of matrix damage is also examined. It is concluded that characteristics of the stress redistribution process could assist in the analysis of the progressive failure process in laminated composites.

The upper bounds of reduced axial and shear moduli in cross-ply laminates with matrix cracks

The present study proposes a mathematical model utilizing the internal state variable concept for predicting the upper bounds of the reduced axial and shear stiffnesses in cross-ply laminates with matrix cracks. The displacement components at the matrix crack surfaces are explicitly expressed in terms of the observable axial and shear strains and the undamaged material properties. The reduced axial and shear stiffnesses are predicted for glass/epoxy and graphite/epoxy laminates. Comparison of the model with other theoretical and experimental studies is also presented to confirm direct applicability of the model to angle-ply laminates with matrix cracks subjected to general in-plane loading.

A deformation-formulated micromechanics model of the effective Young's modulus and strength of laminated composites containing local ply curvature

A mathematical model based on the Euler-Bermoulli beam theory is proposed for predicting the effective Youngs moduli of piecewise isotropic composite laminates with local ply curvatures in the main load-carrying layers. Strains in corrugated layers, in-phase layers, and out-of-phase layers are predicted for various geometries and material configurations by assuming matrix layers as elastic foundations of different spring constants. The effective Youngs moduli measured from corrugated aluminum specimens and aluminum/epoxy specimens with in-phase and out-of-phase wavy patterns coincide very well with the model predictions. Moire fringe analysis of an in-phase specimen and an out-of-phase specimen are also presented, confirming the main assumption of the model related to the elastic constraint due to the matrix layers. The present model is also compared with the experimental results and other models, including the microbuckling models, published in the literature. The results of the present study show that even a very small-scale local ply curvature produces a noticeable effect on the mechanical constitutive behavior of a laminated composite.

Overview of NASA research related to the aging commercial transport fleet

This paper describes the research activities of the NASA Airframe Structural Integrity Program for the aging commercial transport fleet. Advanced analysis methods are under development to predict the fatigue crack growth in complex built-up shell structures. Innovative nondestructive examination technologies are under development to provide large area inspection capability to detect corrosion, disbonds, and fatigue cracks. The ultimate goal of this interdisciplinary program is to develop and transfer advanced technology to the airline operators and airframe manufacturers. The program is being conducted cooperatively with the FAA and the U.S. industry.

Recent Advances in Durability and Damage Tolerance Methodology at NASA Langley Research Center

Durability and damage tolerance (D&DT) issues are critical to the development of lighter, safer and more efficient aerospace vehicles. 1 Durability is largely an economic life-cycle design consideration whereas damage tolerance directly addresses the structural airworthiness (safety) of the vehicle. Both D&DT methodologies must address the deleterious effects of changes in material properties and the initiation and growth of damage that may occur during the vehicle’s service lifetime. The result of unanticipated D&DT response is often manifested in the form of catastrophic and potentially fatal accidents. As such, durability and damage tolerance requirements must be rigorously addressed for commercial transport aircraft and NASA spacecraft systems. This paper presents an overview of the recent and planned future research in durability and damage tolerance analytical and experimental methods for both metallic and composite aerospace structures at NASA Langley Research Center (LaRC).