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NASA NTRS1996

Finite Element Analysis of Geodesically Stiffened Cylindrical Composite Shells Using a Layerwise Theory

Layerwise finite element analyses of geodesically stiffened cylindrical shells are presented. The layerwise laminate theory of Reddy (LWTR) is developed and adapted to circular cylindrical shells. The Ritz variational method is used to develop an analytical approach for studying the buckling of simply supported geodesically stiffened shells with discrete stiffeners. This method utilizes a Lagrange multiplier technique to attach the stiffeners to the shell. The development of the layerwise shells couples a one-dimensional finite element through the thickness with a Navier solution that satisfies the boundary conditions. The buckling results from the Ritz discrete analytical method are compared with smeared buckling results and with NASA Testbed finite element results. The development of layerwise shell and beam finite elements is presented and these elements are used to perform the displacement field, stress, and first-ply failure analyses. The layerwise shell elements are used to model the shell skin and the layerwise beam elements are used to model the stiffeners. This arrangement allows the beam stiffeners to be assembled directly into the global stiffness matrix. A series of analytical studies are made to compare the response of geodesically stiffened shells as a function of loading, shell geometry, shell radii, shell laminate thickness, stiffener height, and geometric nonlinearity. Comparisons of the structural response of geodesically stiffened shells, axial and ring stiffened shells, and unstiffened shells are provided. In addition, interlaminar stress results near the stiffener intersection are presented. First-ply failure analyses for geodesically stiffened shells utilizing the Tsai-Wu failure criterion are presented for a few selected cases.

Gerhard, Craig Steven↗

NASA NTRS1996

Mechanics of Granular Materials (MGM)

The constitutive behavior of uncemented granular materials such as strength, stiffness, and localization of deformations are to a large extend derived from interparticle friction transmitted between solid particles and particle groups. Interparticle forces are highly dependent on gravitational body forces. At very low effective confining pressures, the true nature of the Mohr envelope, which defines the Mohr-Coulomb failure criterion for soils, as well as the relative contribution of each of non-frictional components to soil's shear strength cannot be evaluated in terrestrial laboratories. Because of the impossibility of eliminating gravitational body forces on earth, the weight of soil grains develops interparticle compressive stresses which mask true soil constitutive behavior even in the smallest samples of models. Therefore the microgravity environment induced by near-earth orbits of spacecraft provides unique experimental opportunities for testing theories related to the mechanical behavior of terrestrial granular materials. Such materials may include cohesionless soils, industrial powders, crushed coal, etc. This paper will describe the microgravity experiment, 'Mechanics of Granular Materials (MGM)', scheduled to be flown on Space Shuttle-MIR missions. The paper will describe the experiment's hardware, instrumentation, specimen preparation procedures, testing procedures in flight, as well as a brief summary of the post-mission analysis. It is expected that the experimental results will significantly improve the understanding of the behavior of granular materials under very low effective stress levels.

Alshibli, Khalid A.↗

NASA NTRS1999

Design of Composite Structures for Reliability and Damage Tolerance

A summary of research conducted during the first year is presented. The research objectives were sought by conducting two tasks: (1) investigation of probabilistic design techniques for reliability-based design of composite sandwich panels, and (2) examination of strain energy density failure criterion in conjunction with response surface methodology for global-local design of damage tolerant helicopter fuselage structures. This report primarily discusses the efforts surrounding the first task and provides a discussion of some preliminary work involving the second task.

Rais-Rohani, Masoud↗

NASA NTRS2000

A Study of Single Crystal Fatigue Failure Criteria

This paper presents the results of a study whose objective was to study the applicability of different failure equations in modeling low cycle fatigue (LCF) test data for single crystal test specimens. A total of four failure criteria were considered in this study. One of the failure equations was developed by Pratt & Whitney and is based on normal and shear strains on the primary crystallographic slip planes of the single crystal material. Other failure equations considered are based on isotropic criteria. Because these failure equations were originally developed for isotropic materials such as structural steel, they were modified to be applicable to the single crystal slip systems of the LCF specimen material. By observing how closely the various equations were able to reduce the scatter in the LCF test data, the applicability of those equations in modeling the LCF test data was assessed. It is desired to subsequently use the failure equation with the highest correlation in the development of a new single crystal failure criterion for the Alternative Turbopump Development (ATD) for the space shuttle main engine (SSME) High Pressure Fuel Turbopump (HPFTP).

Sayyah, Tarek↗

NASA NTRS2000

Testing and Analysis of Composite Skin/Stringer Debonding Under Multi-Axial Loading

A consistent step-wise approach is presented to investigate the damage mechanism in composite bonded skin/stringer constructions under uniaxial and biaxial (in-plane/out-of-plane) loading conditions. The approach uses experiments to detect the failure mechanism, computational stress analysis to determine the location of first matrix cracking and computational fracture mechanics to investigate the potential for delamination growth. In a first step, tests were performed on specimens, which consisted of a tapered composite flange, representing a stringer or frame, bonded onto a composite skin. Tests were performed under monotonic loading conditions in tension, three-point bending, and combined tension/bending to evaluate the debonding mechanisms between the skin and the bonded stringer. For combined tension/bending testing, a unique servohydraulic load frame was used that was capable of applying both in-plane tension and out-of-plane bending loads simultaneously. Specimen edges were examined on the microscope to document the damage occurrence and to identify typical damage patterns. For all three load cases, observed failure initiated in the flange, near the flange tip, causing the flange to almost fully debond from skin. In a second step, a two dimensional plane-strain finite element model was developed to analyze the different test cases using a geometrically nonlinear solution. For all three loading conditions, computed principal stresses exceeded the transverse strength of the material in those areas of the flange where the matrix cracks had developed during the tests. In a third step, delaminations of various lengths were simulated in two locations where delaminations were observed during the tests. The analyses showed that at the loads corresponding to matrix ply crack initiation computed strain energy release rates exceeded the values obtained from a mixed mode failure criterion in one location, Hence. Unstable delamination propagation is likely to occur as observed in the experiments.

Krueger, Ronald↗

NASA NTRS2000

COSIM: A Finite-Difference Computer Model to Predict Ternary Concentration Profiles Associated with Oxidation and Interdiffusion of Overlay-Coated Substrates

A finite-difference computer program (COSIM) has been written which models the one-dimensional, diffusional transport associated with high-temperature oxidation and interdiffusion of overlay-coated substrates. The program predicts concentration profiles for up to three elements in the coating and substrate after various oxidation exposures. Surface recession due to solute loss is also predicted. Ternary cross terms and concentration-dependent diffusion coefficients are taken into account. The program also incorporates a previously-developed oxide growth and spalling model to simulate either isothermal or cyclic oxidation exposures. In addition to predicting concentration profiles after various oxidation exposures, the program can also be used to predict coating fife based on a concentration dependent failure criterion (e.g., surface solute content drops to two percent). The computer code, written in an extension of FORTRAN 77, employs numerous subroutines to make the program flexible and easily modifiable to other coating oxidation problems.

Nesbitt, James A.↗

NASA NTRS2001

Fracture Behavior of a Stitched Warp-Knit Carbon Fabric Composite

Tests were conducted on several types of fracture specimens made from a carbon/epoxy composite. The composite material was stitched prior to introducing epoxy resin. Boeing, used this material to develop a composite wing box for a transport aircraft in the NASA Advanced Composites Transport Program. The specimens included compact, extended compact, and center notched tension specimens. The specimens were cut from panels with three orientations in order to explore the effects of anisotropy. The panels were made with various thicknesses to represent a wing, skin from tip to root. All fractures were not self-similar depending on specimen type and orientation. Unnotched tension specimens were also tested to measure elastic constants and strengths. The normal and shear strains were calculated on fracture planes using a series representation of strain fields for plane anisotropic crack problems. The fracture parameters were determined using a finite element method. Characteristic distances for critical tension and shear strains were calculated for each specimen and a failure criterion based on the interaction of tension and shear strains was proposed.

Poe, Clarence C., Jr.↗

NASA NTRS2001

Effect of Load Rate on Ultimate Tensile Strength of Ceramic Matrix Composites at Elevated Temperatures

The strengths of three continuous fiber-reinforced ceramic composites, including SiC/CAS-II, SiC/MAS-5 and SiC/SiC, were determined as a function of test rate in air at 1100 to 1200 C. All three composite materials exhibited a strong dependency of strength on test rate, similar to the behavior observed in many advanced monolithic ceramics at elevated temperatures. The application of the preloading technique as well as the prediction of life from one loading configuration (constant stress-rate) to another (constant stress loading) suggested that the overall macroscopic failure mechanism of the composites would be the one governed by a power-law type of damage evolution/accumulation, analogous to slow crack growth commonly observed in advanced monolithic ceramics. It was further found that constant stress-rate testing could be used as an alternative to life prediction test methodology even for composite materials, at least for short range of lifetimes and when ultimate strength is used as the failure criterion.

Choi, Sung R.↗

NASA NTRS2001

COSIM: A Finite-Difference Computer Model to Predict Ternary Concentration Profiles Associated With Oxidation and Interdiffusion of Overlay-Coated Substrates

A finite-difference computer program (COSIM) has been written which models the one-dimensional, diffusional transport associated with high-temperature oxidation and interdiffusion of overlay-coated substrates. The program predicts concentration profiles for up to three elements in the coating and substrate after various oxidation exposures. Surface recession due to solute loss is also predicted. Ternary cross terms and concentration-dependent diffusion coefficients are taken into account. The program also incorporates a previously-developed oxide growth and spalling model to simulate either isothermal or cyclic oxidation exposures. In addition to predicting concentration profiles after various oxidation exposures, the program can also be used to predict coating life based on a concentration dependent failure criterion (e.g., surface solute content drops to 2%). The computer code is written in FORTRAN and employs numerous subroutines to make the program flexible and easily modifiable to other coating oxidation problems.

Nesbitt, James A.↗

NASA NTRS2002

Generalized Reliability Methodology Applied to Brittle Anisotropic Single Crystals

A generalized reliability model was developed for use in the design of structural components made from brittle, homogeneous anisotropic materials such as single crystals. The model is based on the Weibull distribution and incorporates a variable strength distribution and any equivalent stress failure criteria. In addition to the reliability model, an energy based failure criterion for elastically anisotropic materials was formulated. The model is different from typical Weibull-based models in that it accounts for strength anisotropy arising from fracture toughness anisotropy and thereby allows for strength and reliability predictions of brittle, anisotropic single crystals subjected to multiaxial stresses. The model is also applicable to elastically isotropic materials exhibiting strength anisotropy due to an anisotropic distribution of flaws. In order to develop and experimentally verify the model, the uniaxial and biaxial strengths of a single crystal nickel aluminide were measured. The uniaxial strengths of the <100> and <110> crystal directions were measured in three and four-point flexure. The biaxial strength was measured by subjecting <100> plates to a uniform pressure in a test apparatus that was developed and experimentally verified. The biaxial strengths of the single crystal plates were estimated by extending and verifying the displacement solution for a circular, anisotropic plate to the case of a variable radius and thickness. The best correlation between the experimental strength data and the model predictions occurred when an anisotropic stress analysis was combined with the normal stress criterion and the strength parameters associated with the <110> crystal direction.

Salem, Jonathan A.↗

NASA NTRS2004

Design/Analysis of Metal/Composite Bonded Joints for Survivability at Cryogenic Temperatures

A major design and analysis challenge for the JWST ISM structure is the metal/composite bonded joints that will be required to survive down to an operational ultra-low temperature of 30K (-405 F). The initial and current baseline design for the plug-type joint consists of a titanium thin walled fitting (1-3mm thick) bonded to the interior surface of an M555/954-6 composite truss square tube with an axially stiff biased lay-up. Metallic fittings are required at various nodes of the truss structure to accommodate instrument and lift-point bolted interfaces. Analytical experience and design work done on metal/composite bonded joints at temperatures below liquid nitrogen are limited and important analysis tools, material properties, and failure criteria for composites at cryogenic temperatures are virtually nonexistent. Increasing the challenge is the difficulty in testing for these required tools and parameters at 30K. A preliminary finite element analysis shows that failure due to CTE mismatch between the biased composite and titanium or aluminum is likely. Failure is less likely with Invar, however an initial mass estimate of Invar fittings demonstrates that Invar is not an automatic alternative. In order to gain confidence in analyzing and designing the ISM joints, a comprehensive joint development testing program has been planned and is currently running. The test program is designed for the correlation of the analysis methodology, including tuning finite element model parameters, and developing a composite failure criterion for the effect of multi-axial composite stresses on the strength of a bonded joint at 30K. The testing program will also consider stress mitigation using compliant composite layers and potential strength degradation due to multiple thermal cycles. Not only will the finite element analysis be correlated to the test data, but the FEA will be used to guide the design of the test. The first phase of the test program has been completed and the preliminary analysis has been revisited based on the test data In this work, we present an overview of the test plan, results today, and resulting design improvements.

Bartoszyk, Andrew E.↗

NASA NTRS2000

Testing and Analysis of Composite Skin/Stringer Debonding under Multi-Axial Loading

A consistent step-wise approach is presented to investigate the damage mechanism in composite bonded skin/stringer constructions under uniaxial and biaxial (in-plane/out-of-plane) loading conditions. The approach uses experiments to detect the failure mechanism, computational stress analysis to determine the location of first matrix cracking and computational fracture mechanics to investigate the potential for delamination growth. In a first step, tests were performed on specimens, which consisted of a tapered composite flange, representing a stringer or frame, bonded onto a composite skin. Tests were performed under monotonic loading conditions in tension, three-point bending, and combined tension/bending to evaluate the debonding mechanisms between the skin and the bonded stringer. For combined tension/bending testing, a unique servohydraulic load frame was used that was capable of applying both in-plane tension and out-of-plane bending loads simultaneously. Specimen edges were examined on the microscope to document the damage occurrence and to identify typical damage patterns. For all three load cases, observed failure initiated in the flange, near the flange tip, causing the flange to almost fully debond from the skin. In a second step, a two-dimensional plane-strain finite element model was developed to analyze the different test cases using a geometrically nonlinear solution. For all three loading conditions, computed principal stresses exceeded the transverse strength of the material in those areas of the flange where the matrix cracks had developed during the tests. In a third step, delaminations of various lengths were simulated in two locations where delaminations were observed during the tests. The analyses showed that at the loads corresponding to matrix ply crack initiation computed strain energy release rates exceeded the values obtained from a mixed mode failure criterion in one location. Hence, unstable delamination propagation is likely to occur as observed in the experiments.

Krueger, Ronald↗

NASA NTRS1990

Design/Analysis of the JWST ISIM Bonded Joints for Survivability at Cryogenic Temperatures

A major design and analysis challenge for the JWST ISIM structure is thermal survivability of metal/composite bonded joints below the cryogenic temperature of 30K (-405 F). Current bonded joint concepts include internal invar plug fittings, external saddle titanium/invar fittings and composite gusset/clip joints all bonded to M55J/954-6 and T300/954-6 hybrid composite tubes (75mm square). Analytical experience and design work done on metal/composite bonded joints at temperatures below that of liquid nitrogen are limited and important analysis tools, material properties, and failure criteria for composites at cryogenic temperatures are sparse in the literature. Increasing this challenge is the difficulty in testing for these required tools and properties at cryogenic temperatures. To gain confidence in analyzing and designing the ISIM joints, a comprehensive joint development test program has been planned and is currently running. The test program is designed to produce required analytical tools and develop a composite failure criterion for bonded joint strengths at cryogenic temperatures. Finite element analysis is used to design simple test coupons that simulate anticipated stress states in the flight joints; subsequently the test results are used to correlate the analysis technique for the final design of the bonded joints. In this work, we present an overview of the analysis and test methodology, current results, and working joint designs based on developed techniques and properties.

Bartoszyk, Andrew↗

NASA NTRS2006

Analysis of Composite Panel-Stiffener Debonding Using a Shell/3D Modeling Technique

Interlaminar fracture mechanics has proven useful for characterizing the onset of delaminations in composites and has been used with limited success primarily to investigate onset in fracture toughness specimens and laboratory size coupon type specimens. Future acceptance of the methodology by industry and certification authorities however, requires the successful demonstration of the methodology on structural level. For this purpose a panel was selected that was reinforced with stringers. Shear loading cases the panel to buckle and the resulting out-of-plane deformations initiate skin/stringer separation at the location of an embedded defect. For finite element analysis, the panel and surrounding load fixture were modeled with shell element. A small section of the stringer foot and the panel in the vicinity of the embedded defect were modeled with a local 3D solid model. A failure index was calculated by correlating computed mixed-mode failure criterion of the graphite/epoxy material.

Krueger, Ronald↗

NASA NTRS2007

Design and Optimization of Composite Gyroscope Momentum Wheel Rings

Stress analysis and preliminary design/optimization procedures are presented for gyroscope momentum wheel rings composed of metallic, metal matrix composite, and polymer matrix composite materials. The design of these components involves simultaneously minimizing both true part volume and mass, while maximizing angular momentum. The stress analysis results are combined with an anisotropic failure criterion to formulate a new sizing procedure that provides considerable insight into the design of gyroscope momentum wheel ring components. Results compare the performance of two optimized metallic designs, an optimized SiC/Ti composite design, and an optimized graphite/epoxy composite design. The graphite/epoxy design appears to be far superior to the competitors considered unless a much greater premium is placed on volume efficiency compared to mass efficiency.

Bednarcyk, Brett A.↗

NASA NTRS2007

Mesh Deformation Based on Fully Stressed Design: The Method and Two-Dimensional Examples

Mesh deformation in response to redefined boundary geometry is a frequently encountered task in shape optimization and analysis of fluid-structure interaction. We propose a simple and concise method for deforming meshes defined with three-node triangular or four-node tetrahedral elements. The mesh deformation method is suitable for large boundary movement. The approach requires two consecutive linear elastic finite-element analyses of an isotropic continuum using a prescribed displacement at the mesh boundaries. The first analysis is performed with homogeneous elastic property and the second with inhomogeneous elastic property. The fully stressed design is employed with a vanishing Poisson s ratio and a proposed form of equivalent strain (modified Tresca equivalent strain) to calculate, from the strain result of the first analysis, the element-specific Young s modulus for the second analysis. The theoretical aspect of the proposed method, its convenient numerical implementation using a typical linear elastic finite-element code in conjunction with very minor extra coding for data processing, and results for examples of large deformation of two-dimensional meshes are presented in this paper. KEY WORDS: Mesh deformation, shape optimization, fluid-structure interaction, fully stressed design, finite-element analysis, linear elasticity, strain failure, equivalent strain, Tresca failure criterion

Hsu, Su-Yuen↗

NASA NTRS2010

Determining Shear Stress Distribution in a Laminate

A "simplified shear solution" method approximates the through-thickness shear stress distribution within a composite laminate based on an extension of laminated beam theory. The method does not consider the solution of a particular boundary value problem; rather, it requires only knowledge of the global shear loading, geometry, and material properties of the laminate or panel. It is thus analogous to lamination theory in that ply-level stresses can be efficiently determined from global load resultants at a given location in a structure and used to evaluate the margin of safety on a ply-by-ply basis. The simplified shear solution stress distribution is zero at free surfaces, continuous at ply boundaries, and integrates to the applied shear load. The method has been incorporated within the HyperSizer commercial structural sizing software to improve its predictive capability for designing composite structures. The HyperSizer structural sizing software is used extensively by NASA to design composite structures. In the case of through-thickness shear loading on panels, HyperSizer previously included a basic, industry-standard, method for approximating the resulting shear stress distribution in sandwich panels. However, no such method was employed for solid laminate panels. The purpose of the innovation is to provide an approximation of the through-thickness shear stresses in a solid laminate given the through-thickness shear loads (Qx and Qy) on the panel. The method was needed for implementation within the HyperSizer structural sizing software so that the approximated ply-level shear stresses could be utilized in a failure theory to assess the adequacy of a panel design. The simplified shear solution method was developed based on extending and generalizing bi-material beam theory to plate-like structures. It is assumed that the through-thickness shear stresses arise due to local bending of the laminate induced by the through-thickness shear load, and by imposing equilibrium both vertically and horizontally, the through-thickness shear stress distribution can be calculated. The resulting shear stresses integrate to the applied shear load, are continuous at the ply interfaces, and are zero at the laminate-free surfaces. If both Qx and Qy shear loads are present, it is assumed that they act independently and that their effects can be superposed. The calculated shear stresses can be rotated within each ply to the principal material coordinates for use in a ply-level failure criterion. The novelty of the simplified shear solution method is its simplicity and the fact that it does not require solution of a particular boundary value problem. The advantages of the innovation are that an approximation of the though-thickness shear stress distribution can be quickly determined for any solid laminate or solid laminate region within a stiffened panel.

Bednarcyk, Brett A.↗

NASA NTRS2011

Development of Benchmark Examples for Delamination Onset and Fatigue Growth Prediction

An approach for assessing the delamination propagation and growth capabilities in commercial finite element codes was developed and demonstrated for the Virtual Crack Closure Technique (VCCT) implementations in ABAQUS. The Double Cantilever Beam (DCB) specimen was chosen as an example. First, benchmark results to assess delamination propagation capabilities under static loading were created using models simulating specimens with different delamination lengths. For each delamination length modeled, the load and displacement at the load point were monitored. The mixed-mode strain energy release rate components were calculated along the delamination front across the width of the specimen. A failure index was calculated by correlating the results with the mixed-mode failure criterion of the graphite/epoxy material. The calculated critical loads and critical displacements for delamination onset for each delamination length modeled were used as a benchmark. The load/displacement relationship computed during automatic propagation should closely match the benchmark case. Second, starting from an initially straight front, the delamination was allowed to propagate based on the algorithms implemented in the commercial finite element software. The load-displacement relationship obtained from the propagation analysis results and the benchmark results were compared. Good agreements could be achieved by selecting the appropriate input parameters, which were determined in an iterative procedure.

Krueger, Ronald↗