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NASA NTRS1993

Analysis of the anisotropic viscoplastic-damage response of composite laminates - Continuum basis and computational algorithms

The mathematical structure underlying the rate equations of a recently-developed constitutive model for the coupled viscoplastic-damage response of anisotropic composites is critically examined. In this regard, a number of tensor projection operators have been identified, and their properties were exploited to enable the development of a general computational framework for their numerical implementation using the Euler fully-implicit integration method. In particular, this facilitated (i) the derivation of explicit expressions of the (consistent) material tangent stiffnesses that are valid for both three-dimensional as well as subspace (e.g. plane stress) formulations, (ii) the implications of the symmetry or unsymmetry properties of these tangent operators from a thermodynamic standpoint, and (iii) the development of an effective time-step control strategy to ensure accuracy and convergence of the solution. In addition, the special limiting case of inviscid elastoplasticity is treated. The results of several numerical simulations are given to demonstrate the effectiveness of the schemes developed.

Saleeb, A. F.↗

NASA NTRS2013

Unit-Sphere Anisotropic Multiaxial Stochastic-Strength Model Probability Density Distribution for the Orientation of Critical Flaws

Models that predict the failure probability of monolithic glass and ceramic components under multiaxial loading have been developed by authors such as Batdorf, Evans, and Matsuo. These "unit-sphere" failure models assume that the strength-controlling flaws are randomly oriented, noninteracting planar microcracks of specified geometry but of variable size. This report develops a formulation to describe the probability density distribution of the orientation of critical strength-controlling flaws that results from an applied load. This distribution is a function of the multiaxial stress state, the shear sensitivity of the flaws, the Weibull modulus, and the strength anisotropy. Examples are provided showing the predicted response on the unit sphere for various stress states for isotropic and transversely isotropic (anisotropic) materials--including the most probable orientation of critical flaws for offset uniaxial loads with strength anisotropy. The author anticipates that this information could be used to determine anisotropic stiffness degradation or anisotropic damage evolution for individual brittle (or quasi-brittle) composite material constituents within finite element or micromechanics-based software

Nemeth, Noel↗

NASA NTRS1986

Design of anisotropic plates for improved damage tolerance

An analytical study is presented showing the effects of the notch tip geometry on the location and direction of crack growth from an existing notch in a unidirectional fibrous composite modeled as a homogeneous, anisotropic, elastic material. Anisotropic elasticity and the normal stress ratio theory are used to study crack growth from elliptical notches in unidirectional composites. Sharp cracks, circular holes, and ellipses are studied under far-field tension and shear loading. The capabilities of a previously developed design code was upgraded to handle more generalized plate geometries and laminates under a more generalized loading and boundary conditions. Discussion of the developments of the design code is presented.

Guerdal, Zafer↗

NASA NTRS2016

Multiscale Static Analysis of Notched and Unnotched Laminates Using the Generalized Method of Cells

The generalized method of cells (GMC) is demonstrated to be a viable micromechanics tool for predicting the deformation and failure response of laminated composites, with and without notches, subjected to tensile and compressive static loading. Given the axial [0], transverse [90], and shear [+45/-45] response of a carbon/epoxy (IM7/977-3) system, the unnotched and notched behavior of three multidirectional layups (Layup 1: [0,45,90,-45](sub 2S), Layup 2: [0,60,0](sub 3S), and Layup 3: [30,60,90,-30, -60](sub 2S)) are predicted under both tensile and compressive static loading. Matrix nonlinearity is modeled in two ways. The first assumes all nonlinearity is due to anisotropic progressive damage of the matrix only, which is modeled, using the multiaxial mixed-mode continuum damage model (MMCDM) within GMC. The second utilizes matrix plasticity coupled with brittle final failure based on the maximum principle strain criteria to account for matrix nonlinearity and failure within the Finite Element Analysis--Micromechanics Analysis Code (FEAMAC) software multiscale framework. Both MMCDM and plasticity models incorporate brittle strain- and stress-based failure criteria for the fiber. Upon satisfaction of these criteria, the fiber properties are immediately reduced to a nominal value. The constitutive response for each constituent (fiber and matrix) is characterized using a combination of vendor data and the axial, transverse, and shear responses of unnotched laminates. Then, the capability of the multiscale methodology is assessed by performing blind predictions of the mentioned notched and unnotched composite laminates response under tensile and compressive loading. Tabulated data along with the detailed results (i.e., stress-strain curves as well as damage evolution states at various ratios of strain to failure) for all laminates are presented.

GMC↗

NASA NTRS2015

Investigation of Micro-Scale Architectural Effects on Damage of Composites

This paper presents a three-dimensional, energy based, anisotropic, stiffness reduction, progressive damage model for composite materials and composite material constituents. The model has been implemented as a user-defined constitutive model within the Abaqus finite element software package and applied to simulate the nonlinear behavior of a damaging epoxy matrix within a unidirectional composite material. Three different composite microstructures were considered as finite element repeating unit cells, with appropriate periodicity conditions applied at the boundaries. Results representing predicted transverse tensile, longitudinal shear, and transverse shear stress-strain curves are presented, along with plots of the local fields indicating the damage progression within the microstructure. It is demonstrated that the damage model functions appropriately at the matrix scale, enabling localization of the damage to simulate failure of the composite material. The influence of the repeating unit cell geometry and the effect of the directionality of the applied loading are investigated and discussed.

damage↗

NASA NTRS1998

Isothermal Fatigue, Damage Accumulation, and Life Prediction of a Woven PMC

This dissertation focuses on the characterization of the fully reversed fatigue behavior exhibited by a carbon fiber/polyimide resin, woven laminate at room and elevated temperatures. Nondestructive video edge view microscopy and destructive sectioning techniques were used to study the microscopic damage mechanisms that evolved. The residual elastic stiffness was monitored and recorded throughout the fatigue life of the coupon. In addition, residual compressive strength tests were conducted on fatigue coupons with various degrees of damage as quantified by stiffness reduction. Experimental results indicated that the monotonic tensile properties were only minimally influenced by temperature, while the monotonic compressive and fully reversed fatigue properties displayed noticeable reductions due to the elevated temperature. The stiffness degradation, as a function of cycles, consisted of three stages; a short-lived high degradation period, a constant degradation rate segment composing the majority of the life, and a final stage demonstrating an increasing rate of degradation up to failure. Concerning the residual compressive strength tests at room and elevated temperatures, the elevated temperature coupons appeared much more sensitive to damage. At elevated temperatures, coupons experienced a much larger loss in compressive strength when compared to room temperature coupons with equivalent damage. The fatigue damage accumulation law proposed for the model incorporates a scalar representation for damage, but admits a multiaxial, anisotropic evolutionary law. The model predicts the current damage (as quantified by residual stiffness) and remnant life of a composite that has undergone a known load at temperature. The damage/life model is dependent on the applied multiaxial stress state as well as temperature. Comparisons between the model and data showed good predictive capabilities concerning stiffness degradation and cycles to failure.

Gyekenyesi, Andrew L.↗

NASA NTRS1992

A differential CDM model for fatigue of unidirectional metal matrix composites

A multiaxial, isothermal, continuum damage mechanics (CDM) model for fatigue of a unidirectional metal matrix composite volume element is presented. The model is phenomenological, stress based, and assumes a single scalar internal damage variable, the evolution of which is anisotropic. The development of the fatigue damage model, (i.e., evolutionary law) is based on the definition of an initially transversely isotropic fatigue limit surface, a static fracture surface, and a normalized stress amplitude function. The anisotropy of these surfaces and function, and therefore the model, is defined through physically meaningful invariants reflecting the local stress and material orientation. This transversely isotropic model is shown, when taken to it's isotropic limit, to directly simplify to a previously developed and validated isotropic fatigue continuum damage model. Results of a nondimensional parametric study illustrate (1) the flexibility of the present formulation in attempting to characterize a class of composite materials, and (2) the capability of the formulation in predicting anticipated qualitative trends in the fatigue behavior of unidirectional metal matrix composites. Also, specific material parameters representing an initial characterization of the composite system SiC/Ti 15-3 and the matrix material (Ti 15-3) are reported.

Arnold, S. M.↗

NASA NTRS1997

Robust Integration Schemes for Generalized Viscoplasticity with Internal-State Variables

The scope of the work in this presentation focuses on the development of algorithms for the integration of rate dependent constitutive equations. In view of their robustness; i.e., their superior stability and convergence properties for isotropic and anisotropic coupled viscoplastic-damage models, implicit integration schemes have been selected. This is the simplest in its class and is one of the most widely used implicit integrators at present.

Saleeb, Atef F.↗

NASA NTRS1989

A simple element for aeroelastic analysis of undamaged and damaged wings

The effects of material damage on the aeroelastic response of an anisotropic composite wing are investigated analytically. The wing is modeled as a Timoshenko beam of arbitrary cross section, applying a 24-DOF one-dimensional beam element and Cartesian coordinates. The formulations for the element stiffness matrix, the strain-displacement relations, the box-beam constitutive relations, the contributions of stringers and web, and the warping correction factor are outlined; the application of strip theory in deriving the aerodynamic model is briefly explained; and numerical results are presented in extensive graphs. It is shown that asymmetry and damage can induce bending-stretching coupling phenomena and thereby affect the stability of the aircraft either positively or negatively. The need to take such effects into account in the design of advanced composite wings is stressed.

Kapania, Rakesh K.↗

NASA NTRS1982

Life prediction and constitutive models for anisotropic materials

The intent of this program is to develop a basic understanding of cyclic creep-fatigue deformation mechanisms and damage accumulation, a capability for reliable life prediction, and the ability to model the constitutive behavior of anisotropic single crystal (SC) and directionally solidified or recrystallized (DSR) comprise the program, and the work breakdown for each option reflects a distinct concern for two classes of anisotropic materials, SC and DSR materials, at temperatures encountered in the primary gas path (airfoil temperatures), and at temperatures typical of the blade root attachment and shank area. Work directed toward the higher temperature area of concern in the primary gas path includes effects of coatings on the behavior and properties of the materials of interest. The blade root attachment work areas will address the effects of stress concentrations associated with attachment features.

Bill, R. C.↗

NASA NTRS1994

Lamb Wave Response of Fatigued Composite Samples

Composite materials are being more widely used today by aerospace, automotive, sports equipment, and a number of other commercial industries because of their advantages over conventional metals. Composites have a high strength-to-weight ratio and can be constructed to meet specific design needs. Composite structures are already in use in secondary parts of the Douglas MD-11 and are planned to be used in the new MD-12X. Plans also exist for their use in primary and secondary structures on the Boeing 777. Douglas proposed MD-XX may also incorporate composite materials into primary structures such as the wings and tail. Use of composites in these structures offers weight savings, corrosion resistance, and improved aerodynamics. Additionally, composites have been used to repair cracks in many B-1Bs where traditional repair techniques were not very effective. Plans have also been made to reinforce all of the remaining B-1s with composite materials. Verification of the structural integrity of composite components is needed to insure safe operation of these aerospace vehicles. One aspect of the use of these composites is their response to fatigue. To track this progression of fatigue in aerospace structures, a convenient method to nondestructively monitor this damage needs to be developed. Traditional NDE techniques used on metals are not easily adaptable to composites due to the inhomogeneous and anisotropic nature of these materials. Finding an effective means of nondestructively monitoring fatigue damage is extremely important to the safety and reliability of such structures. Lamb waves offer one method of evaluating these composite materials. As a material is fatigued, the modulus degrades. Since the Lamb wave velocity can be related to the modulus of the material, an effective tool can be developed to monitor fatigue damage in composites by measuring the velocity of these waves. In this work, preliminary studies have been conducted which monitor fatigue damage in composite samples using strain gage measurements as well as Lamb wave velocity measurements. A description of the test samples is followed by the results of two different measurements of Lamb wave velocity. The first technique is a contact measurement done at a single frequency, while the second involves an immersion study of Lamb waves in which dispersion curves are obtained. The results of the Lamb wave monitoring of fatigue damage is compared to the damage progression measured by strain gages. The final section discusses the results and conclusions.

Seale, Michael↗

NASA NTRS1999

Semiconductor etching by hyperthermal neutral beams

An at-least dual chamber apparatus and method in which high flux beams of fast moving neutral reactive species are created, collimated and used to etch semiconductor or metal materials from the surface of a workpiece. Beams including halogen atoms are preferably used to achieve anisotropic etching with good selectivity at satisfactory etch rates. Surface damage and undercutting are minimized.

Minton, Timothy K.↗

NASA NTRS1991

Effect of damage on elastically tailored composite laminates

A variationally consistent theory is derived in order to predict the response of anisotropic thin-walled closed sections subjected to axial load, torsion and bending. The theory is valid for arbitrary cross-sections made of laminated composite materials with variable thickness and stiffness. Closed form expressions for the stiffness coefficients are provided as integrals in terms of lay-ups parameters and cross-sectional geometry. A comparison of stiffness coefficients and response with finite element predictions and a closed form solution is performed. The theory is applied to the investigation of the effect of damage on the extension-twist coupling in a thin-walled closed section beam. The damage is simulated as a progressive ply-by-ply failure. Results show that damage can have a significant effect on the extension-twist coupling.

Armanios, Erian↗

NASA NTRSDate not supplied

Least Squares Reverse Time Migration (LSRTM) for Damage Imaging in Composite Laminates

A method for adapting least squares reverse time migration (LSRTM) for ultrasonic guided wave imaging of composite laminates is proposed in this paper. As composites become more widely used in fields such as the aerospace industry, the need for high-resolution imaging in structural health monitoring (SHM) and nondestructive evaluation (NDE) is also growing. For instance, delamination is a common problem in composite laminates, which has led to a certain degree of apprehension in the use of composite materials for load-bearing structures. Although the solver-based imaging techniques using conventional reverse time migration (RTM) methods illuminate damage with a wide range of damage-scattering effects, the resulting images do not fully define the damage regions due to the limited data acquisition aperture, sensor density, frequencies/wavelengths, and incompleteness of adjoint reconstruction. Previously, the LSRTM theory was derived by incorporating a least squares migration (LSM) algorithm into RTM, and benchmarked its high-resolution damage imaging performance for isotropic plates. To improve damage imaging in composite laminates, a process to create an ultrasonic guided wave-based LSRTM method for anisotropic materials is proposed in this paper. The derivation of the forward modeling operator and the adjoint operator is presented. Numerical case studies were conducted to show the improvement of LSRTM over RTM in mapping damage in composite plates. Multiple damage sites or damage with a complex shape were created in the numerical studies based on 1) Born approximation-based modeling or 2) reduction of the plate stiffness-based modeling. LSRTM begins by using a forward modeling process. The forward modeling accuracy for the flexural wave solver used in this study for LSRTM was also compared with the results from a three-dimensional rotated staggered grid (RSG) elastodynamic finite difference solver, previously open-sourced by NASA Langley Research Center. These benchmarking studies have shown that the LSRTM method is more effective in reducing artifacts, improving resolution, and enhancing damage model reconstruction compared to RTM in composite laminates.

Jiaze He↗

NASA NTRS1992

Stability of generally stiffened anisotropic noncircular cylinders

Continuous filament grid-stiffened structure is a stiffening concept that combines structural efficiency and damage tolerance. However, finite element design of such structures against buckling is expensive due to the complexities of the structure. An analytical model of such a structure is developed using a penalty method (artificial springs) with a first order shear deformation theory (FSDT). The buckling analysis under combined loadings is done using energy method with a penalty/Rayleigh-Ritz technique. The penalty/Rayleigh-Ritz approach is computationally less demanding when compared to the finite element solution and mesh generation. Apart from the published research works on buckling of stiffened plates and shells by finite element and finite strips, research works on buckling of stiffened plates and shells utilize three different approaches; smeared, column, and discrete approaches. The discrete approach considers the discrete effects of the stiffeners in the buckling behavior by modeling stiffeners as line of bending (EI) and torsion (GJ) stiffnesses on panel skin. Some local deformations are lost when stiffeners are modeled as (EI) and (GJ) stiffeners. This approach becomes difficult in the case of plate stiffened in more than two directions. Most of the work done using the discrete approach involved the Classical Plate Theory (CLPT) rather than the FSDT. We report on our formulation of a discrete approach coupled with a penalty formulation and FSDT.

Sobh, Nahil Atef↗

NASA NTRS1976

Impact of composite plates: Analysis of stresses and forces

The foreign object damage resistance of composite fan blades was studied. Edge impact stresses in an anisotropic plate were first calculated incorporating a constrained layer damping model. It is shown that a very thin damping layer can dramatically decrease the maximum normal impact stresses. A multilayer model of a composite plate is then presented which allows computation of the interlaminar normal and shear stresses. Results are presented for the stresses due to a line impact load normal to the plane of a composite plate. It is shown that significant interlaminar tensile stresses can develop during impact. A computer code was developed for this problem using the fast Fourier transform. A marker and cell computer code were also used to investigate the hydrodynamic impact of a fluid slug against a wall or turbine blade. Application of fluid modeling of bird impact is reviewed.

Moon, F. C.↗

NASA NTRS1992

Ultrasonic and micromechanical study of damage and elastic properties of SiC/RBSN ceramic composites

Ultrasonic techniques are employed to develop methods for nondestructive evaluation of elastic properties and damage in SiC/RBSN composites. To incorporate imperfect boundary conditions between fibers and matrix into a micromechanical model, a model of fibers having effective anisotropic properties is introduced. By inverting Hashin's (1979) microstructural model for a composite material with microscopic constituents the effective fiber properties were found from ultrasonic measurements. Ultrasonic measurements indicate that damage due to thermal shock is located near the surface, so the surface wave is most appropriate for estimation of the ultimate strength reduction and critical temperature of thermal shock. It is concluded that bonding between laminates of SiC/RBSN composites is severely weakened by thermal oxidation. Generally, nondestructive evaluation of thermal oxidation effects and thermal shock shows good correlation with measurements previously performed by destructive methods.

Chu, Y. C.↗

NASA NTRS1988

Fatigue life prediction modeling for turbine hot section materials

A major objective of the fatigue and fracture efforts under the Hot Section Technology (HOST) program was to significantly improve the analytic life prediction tools used by the aeronautical gas turbine engine industry. This was achieved in the areas of high-temperature thermal and mechanical fatigue of bare and coated high-temperature superalloys. The cyclic crack initiation and propagation resistance of nominally isotropic polycrystalline and highly anisotropic single crystal alloys were addressed. Life prediction modeling efforts were devoted to creep-fatigue interaction, oxidation, coatings interactions, multiaxiality of stress-strain states, mean stress effects, cumulative damage, and thermomechanical fatigue. The fatigue crack initiation life models developed to date include the Cyclic Damage Accumulation (CDA) and the Total Strain Version of Strainrange Partitioning (TS-SRP) for nominally isotropic materials, and the Tensile Hysteretic Energy Model for anisotropic superalloys. A fatigue model is being developed based upon the concepts of Path-Independent Integrals (PII) for describing cyclic crack growth under complex nonlinear response at the crack tip due to thermomechanical loading conditions. A micromechanistic oxidation crack extension model was derived. The models are described and discussed.

Halford, G. R.↗