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NASA NTRS1990

Physical interpretation and application of principles of ultrasonic nondestructive evaluation of high-performance materials

An ultrasonic measurement system employed in the experimental interrogation of the anisotropic properties (through the measurement of the elastic stiffness constants) of the uniaxial graphite-epoxy composites is presented. The continuing effort for the development of improved visualization techniques for physical parameters is discussed. The background is set for the understanding and visualization of the relationship between the phase and energy/group velocity for propagation in high-performance anisotropic materials by investigating the general requirements imposed by the classical wave equation. The consequences are considered when the physical parameters of the anisotropic material are inserted into the classical wave equation by a linear elastic model. The relationship is described between the phase velocity and the energy/group velocity three dimensional surfaces through graphical techniques.

Miller, James G.↗

NASA NTRS1988

A hybrid-stress finite element for linear anisotropic elasticity

Standard assumed displacement finite elements with anisotropic material properties perform poorly in complex stress fields such as combined bending and shear and combined bending and torsion. A set of three dimensional hybrid-stress brick elements were developed with fully anisotropic material properties. Both eight-node and twenty-node bricks were developed based on the symmetry group theory of Punch and Atluri. An eight-node brick was also developed using complete polynomials and stress basis functions and reducing the order of the resulting stress parameter matrix by applying equilibrium constraints and stress compatibility constraints. Here the stress compatibility constraints must be formulated assuming anisotropic material properties. The performance of these elements was examined in numerical examples covering a broad range of stress distributions. The stress predictions show significant improvement over the assumed displacement elements but the calculation time is increased.

Fly, Gerald W.↗

NASA NTRS1991

Secondary orientation effects in a single crystal superalloy under mechanical and thermal loads

The nickel-base single crystal superalloy PWA 1480 is a candidate blading material for the advanced turbopump development program of the SSME. In order to improve thermal fatigue resistance of the turbine blades, the single crystal superalloy PWA 1480 is grown along the low modulus zone axes (001) crystal orientation by a directional solidification process. Since cubic single crystal materials such as PWA 1480 exhibit anisotropic elastic behavior, the stresses developed within the single crystal superalloy due to mechanical and thermal loads are likely to be affected by the exact orientation of the secondary crystallographic direction with respect to the geometry of the turbine blade. The effects of secondary crystal orientation on the elastic response of single crystal PWA 1480 superalloy were investigated.

Kalluri, Sreeramesh↗

NASA NTRS1991

Deformation and stress response of composite laminated shells under internal pressure

This paper presents a theoretical study of the response of filament wound composite shells under internal pressure. Each layer of the material is generally cylindrically anisotropic. By using cylindrically anisotropic elasticity field equations and Lekhnitskii's stress functions, a system of sixth-order ordinary differential equations is obtained. The general expressions for the stresses and displacements in the laminated composite shells under internal pressure are discussed. Two composite systems, graphite/epoxy and glass/epoxy, are selected to demonstrate the influence of degree of material anisotropy and fiber orientations on the axial and induced twisting deformation. Stress distributions of (45/-45)s symmetric angle-ply fiber-reinforced laminated shells are shown to illustrate the effect of radius-to-thickness ratio.

Yuan, F. G.↗

NASA NTRSDate not supplied

Recent Developments to the Porous Microstructure Analysis (PuMA) Software

Introduction The Porous Microstructure Analysis (PuMA) software is an open source framework for image-based simulation, primarily used to determine effective properties based on material microstructure. PuMA was originally developed for the study of NASA thermal protection materials; however, many of the solvers in PuMA have applicability to a broad range of materials science applications. PuMA version 3.2 computes material surface area, pore diameters, effective thermal conductivity, continuum and rarefied tortuosity, and permeability. For anisotropic materials, PuMA can estimate material orientation and compute anisotropic thermal conductivity and elasticity. In this talk, a brief overview of the PuMA software and underlying methods will be presented, as well as some recent and ongoing developments, including the use of immersed boundary methods for image-based simulation and the development of a new weave segmentation tool, called TomoSAM. Cut-Cell method for heat and mass transfer For simulations on complex microstructures, traditional unstructured meshing techniques often prove to be difficult and time-intensive. Voxel-based solvers, which represent the surface as a staircase structure, are relatively simple to implement but can lose accuracy when feature resolution is poor. In this work, we present a novel 3D cut-cell method for solving the variable coefficient Poisson equation on complex microstructures, suitable for the determination of effective thermal conductivity or tortuosity of a material. The method uses a Marching Cubes/Marching Squares surface reconstruction to create cut-cells and determine geometric quantities. A flux-correction method is extended to 3D, with least squares gradient reconstruction, to solve for the boundary fluxes in the cut-cells. Verification cases show the solver achieves globally 2nd order accuracy on complex microstructures. TomoSAM TomoSAM, a module of the PuMA software, has been developed as a plugin for 3D Slicer, a software platform used for 3D image processing and visualization. It utilizes the Segment Anything Model (SAM), a deep learning model capable of identifying objects and generating image masks based on minimal user input. This feature enables efficient segmentation of complex 3D datasets, particularly of woven materials, from tomography or similar imaging methods, reducing the need for manual segmentation.

Tomography↗

NASA NTRSDate not supplied

Recent Developments to the Porous Microstructure Analysis (PuMA) Software

The Porous Microstructure Analysis (PuMA) software is an open source framework for image-based simulation, primarily used to determine effective properties based on material microstructure. PuMA was originally developed for the study of NASA thermal protection materials; however, many of the solvers in PuMA have applicability to a broad range of materials science applications. PuMA version 3.2 computes material surface area, pore diameters, effective thermal conductivity, continuum and rarefied tortuosity, and permeability. For anisotropic materials, PuMA can estimate material orientation and compute anisotropic thermal conductivity and elasticity. In this talk, a brief overview of the PuMA software and underlying methods will be presented, as well as some recent and ongoing developments, including the use of immersed boundary methods for image-based simulation and the development of a new weave segmentation tool, called TomoSAM. Cut-Cell method for heat and mass transfer For simulations on complex microstructures, traditional unstructured meshing techniques often prove to be difficult and time-intensive. Voxel-based solvers, which represent the surface as a staircase structure, are relatively simple to implement but can lose accuracy when feature resolution is poor. In this work, we present a novel 3D cut-cell method for solving the variable coefficient Poisson equation on complex microstructures, suitable for the determination of effective thermal conductivity or tortuosity of a material. The method uses a Marching Cubes/Marching Squares surface reconstruction to create cut-cells and determine geometric quantities. A flux-correction method is extended to 3D, with least squares gradient reconstruction, to solve for the boundary fluxes in the cut-cells. Verification cases show the solver achieves globally 2nd order accuracy on complex microstructures. TomoSAM TomoSAM, a module of the PuMA software, has been developed as a plugin for 3D Slicer, a software platform used for 3D image processing and visualization. It utilizes the Segment Anything Model (SAM), a deep learning model capable of identifying objects and generating image masks based on minimal user input. This feature enables efficient segmentation of complex 3D datasets, particularly of woven materials, from tomography or similar imaging methods, reducing the need for manual segmentation.

Tomography↗

NASA NTRS1984

On constitutive relations at finite strain - Hypo-elasticity and elasto-plasticity with isotropic or kinematic hardening

Nagtegaal and de Jong (1982) have studied stresses generated by simple finite shear in the case of elastic-plastic and rigid-plastic materials which exhibit anisotropic hardening. They reported that the shear stress is oscillatory in time. It was found that the occurrence of such an 'anomaly' is not restricted to anisotropic plasticity. Similar behavior in finite shear may result even in the case of hypoelasticity and classical isotropic hardening plasticity theory. The present investigation is concerned with the central problem of 'generalizing' with respect to the finite strain case, taking into account the constitutive relations of infinitesimal strain theories of classical plasticity with isotropic or kinematic hardening. The problem of hypoelasticity is also considered. It is shown that current controversies surrounding the choice of stress rate in the finite-strain generalizations of the constitutive relations and the anomalies surrounding kinematic hardening plasticity theory are easily resolvable.

Atluri, S. N.↗

NASA NTRS1985

Orthotropic fracture using a singular isoparametric element

The six noded quarter point natural isoparametric triangular element is employed to obtain displacement and stress distributions in the vicinity of the crack tip in a center cracked tensile coupon of unidirectional graphite epoxy. The material is considered to be homogeneous, elastic and orthotropic. The finite element results are compared to the analytical solution of anisotropic elasticity. Convergence as a function of mesh parameters is studied for isotropic and orthotropic materials. It is shown that displacements converge faster than stresses and that meshes which are convergent for isotropic and orthotropic materials. It is shown that displacements converge faster than stresses and that meshes which are convergent for isotropic materials are not completely convergent for the highly orthotropic graphite epoxy.

Gregory, M. A.↗

NASA NTRS1988

Stress concentration around circular hole in a composite material specimen representative of the X-29A forward-swept wing aircraft

The theory of anisotropic elasticity was used to evaluate the anisotropic stress concentration factors of a composite laminated plate containing a small circular hole. This advanced composite material was used to manufacture the X-29A forward swept wing. Observe that the usual isotropic material stress concentration factor is three. However, for composite material, it was found that the anisotropic stress concentration factor is no longer constant, and that the locations of maximum tangential stress points could shift by changing the fiber orientation with respect to the loading axis. The analysis showed that through the lamination process, the stress concentration factor could be drastically reduced, and therefore the structural performance could be improved. Both the mixture rule approach and the constant strain approach were used to calculate the stress concentration factor. The results predicted by the mixture rule approach were about 20 percent deviate from the experimental data. However, the results predicted by the constant strain approach matched the testing data very well. This showed the importance of the inplane shear effect on the evaluation of stress concentration factor for the X-29A composite plate.

Yeh, Hsien-Yang↗

NASA NTRS1992

Failure analysis of thick composite cylinders under external pressure

Failure of thick section composites due to local compression strength and overall structural instability is treated. Effects of material nonlinearity, imperfect fiber architecture, and structural imperfections upon anticipated failure stresses are determined. Comparisons with experimental data for a series of test cylinders are described. Predicting the failure strength of composite structures requires consideration of stability and material strength modes of failure using linear and nonlinear analysis techniques. Material strength prediction requires the accurate definition of the local multiaxial stress state in the material. An elasticity solution for the linear static analysis of thick anisotropic cylinders and rings is used herein to predict the axisymmetric stress state in the cylinders. Asymmetric nonlinear behavior due to initial cylinder out of roundness and the effects of end closure structure are treated using finite element methods. It is assumed that local fiber or ply waviness is an important factor in the initiation of material failure. An analytical model for the prediction of compression failure of fiber composites, which includes the effects of fiber misalignments, matrix inelasticity, and multiaxial applied stresses is used for material strength calculations. Analytical results are compared to experimental data for a series of glass and carbon fiber reinforced epoxy cylinders subjected to external pressure. Recommendations for pretest characterization and other experimental issues are presented. Implications for material and structural design are discussed.

Caiazzo, A.↗

NASA NTRS1983

Fracture mechanics for delamination problems in composite materials

A fracture mechanics approach to the well-known delamination problem in composite materials is presented. Based on the theory of anisotropic laminate elasticity and interlaminar fracture mechanics concepts, the composite delamination problem is formulated and solved. The exact order of the delamination crack-tip stress singularity is determined. Asymptotic stress and displacement fields for an interlaminar crack are obtained. Fracture mechanics parameters such as mixed-mode stress intensity factors, KI, KII, KIII, and the energy release rate, G, for composite delamination problems are defined. To illustrate the fundamental nature of the delamination crack behavior, solutions for edge-delaminated graphite-epoxy composites under uniform axial extension are presented. Effects of fiber orientation, ply thickness, and delamination length on the interlaminar fracture are examined.

Wang, S. S.↗

NASA NTRS1988

Temperature effect on stress concentration around circular hole in a composite material specimen representative of X-29A forward-swept wing aircraft

The theory of anisotropic elasticity was used to evaluate the anisotropic stress concentration factors of a composite laminated plate containing a small circular hole. This advanced composite was used to manufacture the X-29A forward-swept wing. It was found for composite material, that the anisotropic stress concentration is no longer a constant, and that the locations of maximum tangential stress points could shift by changing the fiber orientation with respect to the loading axis. The analysis showed that through the lamination process, the stress concentration factor could be reduced drastically, and therefore the structural performance could be improved. Both the mixture rule approach and the constant strain approach were used to calculate the stress concentration factor of room temperature. The results predicted by the mixture rule approach were about twenty percent deviate from the experimental data. However, the results predicted by the constant strain approach matched the testing data very well. This showed the importance of the inplane shear effect on the evaluation of the stress concentration factor for the X-29A composite plate.

Yeh, Hsien-Yang↗

NASA NTRS1992

Exact solutions for laminated composite cylindrical shells in cylindrical bending

Analytic elasticity solutions for laminated composite cylindrical shells under cylindrical bending are presented. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity, coupled governing partial differential equations are developed. The general expressions for the stresses and displacements in the laminated composite cylinders are discussed. The closed form solutions based on Classical Shell Theory (CST) and Donnell's (1933) theory are also derived for comparison purposes. Three examples illustrate the effect of radius-to-thickness ratio, coupling and stacking sequence. The results show that, in general, CST yields poor stress and displacement distributions for thick-section composite shells, but converges to the exact elasticity solution as the radius-to-thickness ratio increases. It is also shown that Donnell's theory significantly underestimates the stress and displacement response.

Yuan, F. G.↗

NASA NTRS1983

The mechanics of delamination in fiber-reinforced composite materials. Part 2: Delamination behavior and fracture mechanics parameters

Based on theories of laminate anisotropic elasticity and interlaminar fracture, the complete solution structure associated with a composite delamination is determined. Fracture mechanics parameters characterizing the interlaminar crack behavior are defined from asymptotic stress solutions for delaminations with different crack-tip deformation configurations. A numerical method employing singular finite elements is developed to study delaminations in fiber composites with any arbitrary combinations of lamination, material, geometric, and crack variables. The special finite elements include the exact delamination stress singularity in its formulation. The method is shown to be computationally accurate and efficient, and operationally simple. To illustrate the basic nature of composite delamination, solutions are shown for edge-delaminated (0/-0/-0/0) and (+ or - 0/+ or - 0/90/90 deg) graphite-epoxy systems under uniform axial extenstion. Three-dimensional crack-tip stress intensity factors, associated energy release rates, and delamination crack-closure are determined for each individual case. The basic mechanics and mechanisms of composite delamination are studied, and fundamental characteristics unique to recently proposed tests for interlaminar fracture toughness of fiber composite laminates are examined.

Wang, S. S.↗

NASA NTRS1983

The mechanics of delamination in fiber-reinforced composite materials. II - The delamination behavior and fracture mechanics parameters

Based on theories of laminate anisotropic elasticity and interlaminar fracture, the complete solution structure associated with a composite delamination is determined. Fracture mechanics parameters characterizing the interlaminar crack behavior are defined from asymptotic stress solutions for delaminations with different crack-tip deformation configurations. A numerical method employing singular finite elements is developed to study delaminations in fiber composites with any arbitrary combinations of lamination, material, geometric, and crack variables. The special finite elements include the exact delamination stress singularity in its formulation. The method is shown to be computationally accurate and efficient, and operationally simple. To illustrate the basic nature of composite delamination, solutions are shown for edge-delaminated (0/-0/-0/0) and (+ or - 0/+ or - 0/90/90 deg) graphite-epoxy systems under uniform axial extension. Three-dimensional crack-tip stress intensity factors, associated energy release rates, and delamination crack-closure are determined for each individual case. The basic mechanics and mechanisms of composite delamination are studied, and fundamental characteristics unique to recently proposed tests for interlaminar fracture toughness of fiber composite laminates are examined. Previously announced in STAR as N84-13222

Wang, S. S.↗

NASA NTRSDate not supplied

Computing the effective elasticity of anisotropic porous media from X-ray computed micro-tomography images

Development and optimization of composite materials designed for thermal protection of NASA’s spacecraft requires the understanding of their physical response to high-enthalpy environments. To predict their macro-scale properties and behavior, high-fidelity 3D simulations are performed at the micro-scale on realistic representations of these composites. The digital micro-structures are generated either synthetically or through X-ray micro-tomography reconstructions. One of the main challenges in the prediction of heatshield material structural response is the computation of the effective elasticity of the fibrous composite, as well as the understanding of the deformation and stresses generated at the micro-scale. These are driven by the fiber layout within the micro-structure and the distribution of the infused matrix. In this effort, the micro-mechanical linear elastic behavior of fibrous ablators is modeled through the use of a numerical method based on the Multi-Point Stress Approximation (MPSA) finite volume scheme. The MPSA, a generalization of the more commonly used Multi-Point Flux Approximation (MPFA), was discussed in a previous presentation at the 15th USCCN and in reference. To predict the behavior of fibrous and woven architectures, algorithms that compute the local fiber orientation are used. The implementation of the MPSA was verified using analytical solutions, engineering test cases and compared against legacy Finite Element Analysis (FEA) software. The stress analysis models were then applied to real geometries used by NASA in thermal protection systems such as fibrous preforms and woven materials and the results were compared to experimental data.

Federico Semeraro↗

NASA NTRS1975

Fundamental analysis of the failure of polymer-based fiber reinforced composites

A mathematical model predicting the strength of unidirectional fiber reinforced composites containing known flaws and with linear elastic-brittle material behavior was developed. The approach was to imbed a local heterogeneous region surrounding the crack tip into an anisotropic elastic continuum. This (1) permits an explicit analysis of the micromechanical processes involved in the fracture, and (2) remains simple enough to be useful in practical computations. Computations for arbitrary flaw size and orientation under arbitrary applied loads were performed. The mechanical properties were those of graphite epoxy. With the rupture properties arbitrarily varied to test the capabilities of the model to reflect real fracture modes, it was shown that fiber breakage, matrix crazing, crack bridging, matrix-fiber debonding, and axial splitting can all occur during a period of (gradually) increasing load prior to catastrophic failure. The calculations also reveal the sequential nature of the stable crack growth process proceding fracture.

Kanninen, M. F.↗

NASA NTRS1974

Elastic moduli of precompressed pyrophyllite used in ultrahigh pressure research

The propagation of ultrasonic pulses in pyrophyllite specimens was studied to determine the effect of specimen precompression on the measured elastic moduli. Measurements were made at room pressure and, for the precompressed specimens, to pressures of 3 kbar. Pyrophyllite was found to be elastically anisotropic, apparently the result of the fabric present in our material. The room pressure adiabatic bulk modulus as measured on specimens made of isostatically compacted powered pyrophyllite was determined to be 96.1 kbar. The wave speeds of ultrasonic pulses in pyrophyllite were found to decrease with increasing specimen precompression. A limiting value of precompression was found, above which no further decrease in wave speed was observed. For the shear wave speeds this occurs at 10 kbar while for the longitudinal wave at 25 kbar. In the limit, the shear waves propagate 20% slower than in the unprecompressed samples; for the longitudinal wave the difference is 30%.

Sachse, W.↗