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NASA NTRS1990

Interfacial sliding near a free surface in a fibrous or layered composite during thermal cycling

This paper presents a simple shear lag model of interfacial sliding at a free surface in a layered or continuous fiber composite. The interface is characterized by a critical interfacial shear stress, tau0, which might represent the critical stress for frictional sliding at a weakly bonded interface, or the shear flow stress of a thin ductile interface layer at a well bonded interface. The history, during heating and cooling, of the relative normal displacement of the reinforcing inclusions and the matrix on a free surface cut normal to the inclusions is calculated and shown to depend on both the absolute value and the temperature dependence of tau0, as well as on the magnitudes of the bulk residual stresses. The variety of possible displacement histories suggests that they are a rich source of information about tau0 and the residual stresses.

Cox, B. N.↗

NASA NTRS1985

Longitudinal splitting in unidirectional composites, analysis and experiments

An experimental study is conducted to determine the fracture behavior of center notched, unidirectional graphite/epoxy laminates when subjected to tensile loading. The actual behavior is compared to the behavior predicted by a mathematical model based on classical shear-lag assumptions. The model allows for damage to occur in the form of longitudinal matrix yielding and splitting with the matrix assumed to fail in pure shear. Results indicate that the model is capable of predicting split initiation stress levels accurately, but does not describe the subsequent split growth adequately. The model predicts rapid split growth following split initiation due to shear failure, while the actual behavior involves a slow split growth region prior to the rapid growth region. It is suggested that transverse matrix normal stresses are responsible for split initiation and the early, slow split growth. The model predicts the actual initiation stress levels reliably, and also appears to be able to predict the point at which the shear failure mode begins to dominate. The shear failure mode does eventually dominate, but at a slower rate than predicted. The nonuniform structure of the graphite/epoxy laminates is thought to be responsible for decreasing the split growth rate due to shear failure.

Goree, J. G.↗

NASA NTRS1991

Variational mechanics analysis of the stresses in microdrop debond specimens

A recently derived variational mechanics analysis of stresses in single-fiber model composites has been applied to the analysis of the stresses in the microdrop debond specimen. The new analysis is more accurate than the commonly applied shear-lag or elastic-plastic analyses. The results from a sample stress state calculation suggest that interfacial failure between the fiber and the microdrop is by mode I or opening mode failure at the beginning of the microdrop. The opening mode failure is caused by a large tensile radial stress at the fiber/matrix interface. Previous analyses of microdrop debond data have been in terms of a shear strength. It is suggested that these analyses misrepresent microdrop debond results and recommend instead a failure analysis based on energy release rate and interfacial fracture toughness. A procedure for calculating the energy release rate for the growth of an interfacial crack is described.

Scheer, Robert J.↗

NASA NTRS2021

Analytical Simulation of Effects of Local Mechanisms on Tensile Response of Ceramic Matrix Minicomposites

A micromechanics-based method based on a fiber shear lag analysis was developed to analyze the fast fracture response of uncoated ceramic matrix minicomposites. The model was applied to two SiCf/SiC minicomposite systems that were fabricated by Rolls-Royce and the University of Connecticut. The analysis approach accounts in an average sense for the fact that the cracks in an actual minicomposite often have an irregular geometry. The effects of local variations in the fiber volume ratio on the composite response was also investigated. Parametric studies were performed to investigate the effect of the interfacial shear stress, global fiber volume fraction and percentage of the composite that remains uncracked on the proportional limit stress and the composite secondary modulus. This work will facilitate an increased understanding of the key material mechanisms that take place during fast fracture loading.

Micromechanics Ceramic Matrix Composites Damage↗

NASA NTRS2012

Nonlinear Analysis of Bonded Composite Tubular Lap Joints

The present study describes a semi-analytical solution method for predicting the geometrically nonlinear response of a bonded composite tubular single-lap joint subjected to general loading conditions. The transverse shear and normal stresses in the adhesive as well as membrane stress resultants and bending moments in the adherends are determined using this method. The method utilizes the principle of virtual work in conjunction with nonlinear thin-shell theory to model the adherends and a cylindrical shear lag model to represent the kinematics of the thin adhesive layer between the adherends. The kinematic boundary conditions are imposed by employing the Lagrange multiplier method. In the solution procedure, the displacement components for the tubular joint are approximated in terms of non-periodic and periodic B-Spline functions in the longitudinal and circumferential directions, respectively. The approach presented herein represents a rapid-solution alternative to the finite element method. The solution method was validated by comparison against a previously considered tubular single-lap joint. The steep variation of both peeling and shearing stresses near the adhesive edges was successfully captured. The applicability of the present method was also demonstrated by considering tubular bonded lap-joints subjected to pure bending and torsion.

E. Oterkus↗

NASA NTRSDate not supplied

Analytical Simulation of the Effects of Local Mechanisms on the Tensile Response of CMC Minicomposites

A micromechanics-based method based on a fiber shear lag analysis was developed to analyze the fast fracture response of uncoated ceramic matrix minicomposites under room temperature conditions. The model was applied to two SiCf/SiC minicomposite systems that were fabricated by Rolls-Royce and the University of Connecticut. The analysis approach does not require the assumption that matrix cracks propagate along the entire width of the minicomposite. The ratio of the fiber slip length to the crack spacing was found to be a key parameter driving the stress level at which the proportional limit takes place and the secondary modulus. Parametric studies were performed to investigate the effect of interfacial shear stress, fiber volume fraction and percentage of the composite that remains uncracked on the proportional limit stress and the composite secondary modulus. This work will allow increased understanding of the key material mechanisms that take place during the fast fracture loading and can be expanded to provide improved analysis methods for full macro composites. simulations to simulations of a flat panel impact test, have been performed to fully exercise and evaluate the capabilities of the developed model.

Micromechanics↗

DOE OSTI2023

Tailoring the Toughening Effects in Two-Dimensional Nanomaterial-Reinforced Ceramic Matrix Composites

Abstract Ceramic matrix composites (CMCs) reinforced by two-dimensional (2D) nanomaterials have shown extraordinary load-carrying capacities, even in the harsh environments required by emerging applications. Their exceptional mechanical performance, especially fracture toughness, primarily arises from their heterogeneous microstructures. The deliberate dispersion of 2D reinforcements enables toughening mechanisms that are extrinsic to the matrix and thus endows the composites with substantial resistance to catastrophic failure. However, the incomplete understanding of the fracture behavior of such nanocomposites, especially the complex energy dissipation process of the matrix/reinforcement interface, limits the development of stronger and tougher CMCs. To overcome these limitations, we investigate crack deflection and energy dissipation in nanocomposites using an extended cohesive shear-lag model. This new model accounts for interfacial debonding and friction, which critically control the toughening of nanocomposites. Our analysis provides mechanistic insights for optimizing the toughening effects of CMCs.

Mechanics↗

NASA NTRS1974

Theory to test comparisons for selected aerospace multishell structures and their interfaces under thermomechanical loadings

Guidelines for structural shell analyses were obtained on the basis of theory-to-test comparisons made on two large-scale aerospace structures subject to thermomechanical loads. The first structural test was the cylindrical aluminum skin-stringer-ring construction of the S-IC forward skirt and S-II interstage. The second structural test included the truncated, cone-shaped, bonded honeycomb sandwich shell of the Spacecraft Lunar Module Adapter; the cylindrical bonded aluminum honeycomb sandwich construction of the Instrument Unit; and the skin-stringer construction with rings and intercostals of the S-IVB forward skirt. Analyses were made for loadings simulating the flight environment. Elementary shear lag theory was superimposed on shell analysis for interface junctions between stages to obtain favorable theory-to-test stress comparisons.

Ferdie, R. D.↗

NASA NTRS1978

Fracture and crack growth in orthotropic laminates

Goree, J. G.↗

NASA NTRS1978

Planar scarf joints in composite repair

This study examined the effects of varying certain important geometric parameters on the stresses in an adhesive repair of a thin composite laminate. The repair, a planar scarf joint with a doubler, was studied using finite element methods at scarf angles of 6 deg and 12 deg, damage lengths between 2.5 mm and 25 mm and doubler overlaps between 10 mm and 40 mm. Finite element models also showed that significant stress peaks occur at the ends of the scarf joint adhesive, similar to shear lag phenomena in lap joints. A bending model of the planar scarf joint with a doubler, based on mechanics of materials theory, was also developed.

Adkins, D. W.↗

NASA NTRS1979

Analysis of a unidirectional composite containing broken fibers and matrix damage

An analytical solution is developed for the determination of the stresses and displacements in a unidirectional fiber-reinforced composite containing an arbitrary number of broken fibers as well as longitudinal yielding and splitting of the matrix. The solution is developed using a materials-modeling approach which is based on a shear-lag stress transfer mechanism. The equilibrium equation in the axial direction gives a pair of integral equations which are solved numerically. Excellent agreement is shown to exist between the solution and experimental results for notched unidirectional boron/aluminum laminates without splitting. For brittle matrix composites (i.e. epoxy) equally good results are indicated for both matrix yielding and splitting. For yielding without splitting the fracture strength depends on crack length while for large splitting it is crack length independent.

George, J. G.↗

NASA NTRS1980

Effects of moisture, residual thermal curing stresses and mechanical load on the damage development in quasi-isotropic laminates

Classical laminate theory and a finite element model were used to predict stress states prior to the first formation of damage in laminates fabricated from T/300/5208. Crack patterns characteristic of the laminate in a wet or dry condition were also predicted using a shear lag model. Development of edge damage was recorded and observed during the test by transferring an image of the damage from the edge surface on to a thin acetate sheet such that the damage imprinted could be immediately viewed on a microfiche card reader. Moisture was shown to significantly alter the interior and edge dry stress states due to swelling and a reduction of elastic properties and to reduce the transverse strength in 90 deg plies. A model was developed in order to predict changes in first ply failure laminate loads due to differences in stacking sequence together with a wet or dry environmental condition.

Kriz, R. D.↗

NASA NTRS1980

Stresses in a three-dimensional unidirectional composite containing broken fibers

An approximate solution is developed for the determination of the interlaminar normal and shear stresses in the vicinity of a crack in a three dimensional composite containing unidirectional linearly elastic fibers in an infinite linearly elastic matrix. In order to reduce the complexity of the formulation, certain assumptions are made as to the physically significant stresses to be retained. These simplifications reduce the partial differential equations of elasticity to differential-difference equations which are tractable using Fourier transform techniques. This 'material modeling' approach is in contrast with solutions developed by considering each lamina as a homogeneous, orthotropic layer. The resulting solution does not contain the classical singular stress field for the fibers and the influence of broken fibers on unbroken fibers is felt by a change in stress concentration factors. The matrix stresses however, are unbounded as the fiber spacing vanishes and an equivalent fiber-matrix geometry is proposed which gives the correct singular behavior. The numerical solution is considered in detail and several specific examples are presented. The potential for damaged or debonded zones to be generated by an embedded crack is discussed, and stress concentration factors for fibers near the crack are given. Detailed comparisons are made between the present solution, the analogous two-dimensional problem, and corresponding shear-lag models.

Goree, J. G.↗

NASA NTRS1980

Analysis of a unidirectional composite containing broken fibers and matrix damage

An analytical solution is developed for the determination of the stresses and displacements in a unidirectional fiber-reinforced composite containing an arbitrary number of broken fibers as well as longitudinal yielding and splitting of the matrix. The solution is developed using a 'materials-modeling' approach which is based on a shear-lag stress transfer mechanism. The equilibrium equation in the axial direction gives a pair of integral equations which are solved numerically. Excellent agreement is shown to exist between the solution and experimental results for notched unidirectional boron/aluminum laminates without splitting. For brittle matrix composites (i.e., epoxy) equally good results are indicated for both matrix yielding and splitting. For yielding without splitting the fracture strength is found to depend on crack length while for large splitting it is crack length independent.

Goree, J. G.↗

NASA NTRS1981

An assessment of buffer strips for improving damage tolerance

Graphite/epoxy panels with buffer strips were tested in tension to measure their residual strength with crack-like damage. Panels were made with 45/0/-45/90(2S) and 45/0/450(2S) layups. The buffer strips were parallel to the loading directions. They were made by replacing narrow strips of the 0 deg graphite plies with strips of either 0 deg S-Glass/epoxy or Kevlar-49/epoxy on either a one for one or a two for one basis. In a third case, O deg graphite/epoxy was used as the buffer material and thin, perforated Mylar strips were placed between the 0 deg piles and the cross-plies to weaken the interfaces and thus to isolate the 0 deg plies. Some panels were made with buffer strips of different widths and spacings. The buffer strips arrested the cracks and increased the residual strengths significantly over those plain laminates without buffer strips. A shear-lag type stress analysis correctly predicted the effects of layups, buffer material, buffer strip width and spacing, and the number of plies of buffer material.

Poe, C. C., Jr.↗

NASA NTRS1981

Mathematical modeling of damage in unidirectional composites

A review of some approximate analytical models for damaged, fiber reinforced composite materials is presented. Using the classical shear lag stress displacement assumption, solutions are presented for a unidirectional laminate containing a notch, a rectangular cut-out, and a circular hole. The models account for longitudinal matrix yielding and splitting as well as transverse matrix yielding and fiber breakage. The constraining influence of a cover sheet on the unidirectional laminate is also modeled.

Goree, J. G.↗

NASA NTRS1980

An assessment of buffer strips for improving damage tolerance of composite laminates

Graphite/epoxy panels with buffer strips were tested in tension to measure their residual strength with crack-like damage. Panels were made with (45/0/-45/90)2S and (45/0/-45/0)2S layups. The buffer strips were parallel to the loading direction. They were made by replacing narrow strips of the 0 deg graphite plies with strips of either 0 deg S-Glass/epoxy or Kevlar-90/epoxy on either a one-for-one or a two-for-one basis. In a third case, 0 deg graphite/epoxy was used as the buffer material and thin, perforated Mylar strips were placed between the 0 deg plies and the cross-plies to weaken the interfaces and thus to isolate the 0 deg plies. Some panels were made with buffer strips of different width and spacings. The buffer strips arrested the cracks and increased the residual strengths significantly over those of plain laminates without buffer strips. A shear-lag type stress analysis correctly predicted the effects of layup, buffer material, buffer strip width and spacing, and the number of plies of buffer material

Poe, C. C., Jr.↗

NASA NTRS1982

Fracture and crack growth in orthotropic laminates. Part 1: Analysis of a hybrid, unidirectional laminate with damage

The fracture behavior of unifirectional hybrid (buffer strip) composite laminates is studied. Three particular solutions are discussed: (1) broken fibers in a unidirectional half plane; (2) adjoined half planes of different fiber and matrix properties and (3) the solution of two half planes bounding a third distinct region of finite width. This finite width region represents a buffer strip and the potential of this strip to arrest a crack that originates in one of the half planes is investigated. The analysis is based on a materials modeling approach using the classical shear lag assumption to described the stress transfer between fibers. Explicit fiber and matrix properties of the three regions are retained and changes in the laminate behavior as a function of the relative material properties, buffer strip width and initial crack length are discussed.

Goree, J. G.↗