Search NASA⌕ Search

SEARCH · Search NASA

Results for “SHEAR LAG”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5

Predictions of the critical strain for matrix cracking of ceramic matrix composites

The critical strain for matrix cracking of ceramic matrix composites has been studied; emphasis is placed on the effects of the fiber/matrix debonding length and interfacial debonding energy. Based on a modified shear-lag model, stresses in the fiber and matrix have been found for both the bonded and debonded regions. An energy-balance approach, based upon the stress field, is then adopted to evaluate the critical strain for matrix cracking. From the general equation for the critical strain, close form solutions have been deduced for two limiting cases: complete debonding and perfect bonding. Numerical solutions are given for the cases of nonzero debonding energy and partial fiber debonding. The results show that the interfacial debonding energy, which has been ignored by most of the investigators, is an important factor in determining both the critical strain and the debonding length.

Kuo, Wen-Shyong↗

Modeling of crack bridging in a unidirectional metal matrix composite

The effective fatigue crack driving force and crack opening profiles were determined analytically for fatigue tested unidirectional composite specimens exhibiting fiber bridging. The crack closure pressure due to bridging was modeled using two approaches: the fiber pressure model and the shear lag model. For both closure models, the Bueckner weight function method and the finite element method were used to calculate crack opening displacements and the crack driving force. The predicted near crack tip opening profile agreed well with the experimentally measured profiles for single edge notch SCS-6/Ti-15-3 metal matrix composite specimens. The numerically determined effective crack driving force, Delta K(eff), was calculated using both models to correlate the measure crack growth rate in the composite. The calculated Delta K(eff) from both models accounted for the crack bridging by showing a good agreement between the measured fatigue crack growth rates of the bridged composite and that of unreinforced, unbridged titanium matrix alloy specimens.

Ghosn, Louis J.↗

Matrix fatigue crack development in a notched continuous fiber SCS-6/Ti-15-3 composite

In this study the extensive matrix fatigue cracking that has been observed in notched SCS-6/Ti-15-3 composites is investigated. Away from the notch uniform spacing of the fatigue cracks develops. Closer to the notch, fiber-matrix debonding which occurs increases the crack spacing. Crack spacing and debond length determined from shear-lag cylinder models compare favorably with experimental observations. Scanning electron microscope (SEM) fractography showed that the principal fatigue crack initiation occurred around the zero degree fibers. Interface failure in the 90 degree plies does not lead to the development of the primary fatigue cracking.

Hillberry, B. M.↗

The optimal fiber volume fraction and fiber-matrix property compatibility in fiber reinforced composites

Although the question of minimum or critical fiber volume fraction beyond which a composite can then be strengthened due to addition of fibers has been dealt with by several investigators for both continuous and short fiber composites, a study of maximum or optimal fiber volume fraction at which the composite reaches its highest strength has not been reported yet. The present analysis has investigated this issue for short fiber case based on the well-known shear lag (the elastic stress transfer) theory as the first step. Using the relationships obtained, the minimum spacing between fibers is determined upon which the maximum fiber volume fraction can be calculated, depending on the fiber packing forms within the composites. The effects on the value of this maximum fiber volume fraction due to such factors as fiber and matrix properties, fiber aspect ratio and fiber packing forms are discussed. Furthermore, combined with the previous analysis on the minimum fiber volume fraction, this maximum fiber volume fraction can be used to examine the property compatibility of fiber and matrix in forming a composite. This is deemed to be useful for composite design. Finally some examples are provided to illustrate the results.

Pan, Ning↗

Prediction of thermal cycling induced matrix cracking

Thermal fatigue has been observed to cause matrix cracking in laminated composite materials. A method is presented to predict transverse matrix cracks in composite laminates subjected to cyclic thermal load. Shear lag stress approximations and a simple energy-based fracture criteria are used to predict crack densities as a function of temperature. Prediction of crack densities as a function of thermal cycling is accomplished by assuming that fatigue degrades the material's inherent resistance to cracking. The method is implemented as a computer program. A simple experiment provides data on progressive cracking of a laminate with decreasing temperature. Existing data on thermal fatigue is also used. Correlations of the analytical predictions to the data are very good. A parametric study using the analytical method is presented which provides insight into material behavior under cyclical thermal loads.

Mcmanus, Hugh L.↗

Progressive matrix cracking in off-axis plies of a general symmetric laminate

A generalized shear-lag model is derived to determine the average through-the-thickness stress state present in a layer undergoing transverse matrix cracking, by extending the method of Lee and Daniels (1991) to a general symmetric multilayered system. The model is capable of considering cracking in layers of arbitrary orientation, states of general in-plane applied loading, and laminates with a general symmetric stacking sequence. The model is included in a computer program designed for probabilistic laminate analysis, and the results are compared to those determined with the ply drop-off technique.

Thomas, David J.↗

Transverse cracking and stiffness reduction in composite laminates

A study of transverse cracking mechanism in composite laminates is presented using a singular hybrid finite element model. The model provides the global structural response as well as the precise local crack-tip stress fields. An elasticity basis for the problem is established by employing Lekhnitskii's complex variable potentials and method of eigenfunction expansion. Stress singularities associated with the transverse crack are obtained by decomposing the deformation into the symmetric and antisymmetric modes and proper boundary conditions. A singular hybrid element is thereby formulated based on the variational principle of a modified hybrid functional to incorporate local crack singularities. Axial stiffness reduction due to transverse cracking is studied. The results are shown to be in very good agreement with the existing experimental data. Comparison with simple shear lag analysis is also given. The effects of stress intensity factors and strain energy density on the increase of crack density are analyzed. The results reveal that the parameters approach definite limits when crack densities are saturated, an evidence of the existence of characteristic damage state.

Yuan, F. G.↗

Recommendations for numerical solution of reinforced-panel and fuselage-ring problems

Procedures are recommended for solving the equations of equilibrium of reinforced panels and isolated fuselage rings as represented by the external loads and the operations table established according to Southwell's method. From the solution of these equations the stress distribution can be easily determined. The method of systematic relaxations, the matrix-calculus method, and several other methods applicable in special cases are discussed. Definite recommendations are made for obtaining the solution of reinforced-panel problems which are generally designated as shear lag problems. The procedures recommended are demonstrated in the analysis of a number of panels. In the case of fuselage rings it is not possible to make definite recommendations for the solution of the equilibrium equations for all rings and loadings. However, suggestions based on the latest experience are made and demonstrated on several rings.

Hoff, N J↗

Effects of ply thickness on thermal cycle induced damage and thermal strain

An experimental study was conducted to determine the effects of ply thickness in composite laminates on thermally induced cracking and changes in the coefficient of thermal expansion, CTE. A graphite-epoxy composite material, P75/ERL 1962, in thin (1 mil) and thick (5 mils) prepregs was used to make cross-ply laminates, ((0/90)(sub n))s, with equal total thickness (n=2, n=10) and cross-ply laminates with the same total number of plies (n=2). Specimens of each laminate configuration were cycled up to 1500 times between -250 and 250 F. Thermally induced microdamage was assessed as a function of the number of cycles as was the change in CTE. The results showed that laminates fabricated with thin-plies microcracked at significantly different rates and reached significantly different equilibrium crack densities than the laminate fabricated with thick-ply and n=2. The CTE of thin-ply laminates was less affected by thermal cycling and damage than the CTE of thick-ply laminates. These differences are attributed primarily to differences in interply constraints. Observed effects of ply thickness on crack density was qualitatively predicted by a combined shear-lag stress/energy method.

Tompkins, Stephen S.↗

Quantitative characterization of the small-scale fracture patterns on the plains of Venus

The objectives of this research project were to (1) compile a comprehensive database of the occurrence of regularly spaced kilometer scale lineations on the volcanic plains of Venus in an effort to verify the effectiveness of the shear-lag model developed by Banerdt and Sammis (1992), and (2) develop a model for the formation of irregular kilometer scale lineations such as typified in the gridded plains region of Guinevere Planitia. Attached to this report is the paper 'A Tectonic Model for the Formation of the Gridded Plains on Guinevere Planitia, Venus, and Implications for the Elastic Thickness of the Lithosphere'.

Sammis, Charles G.↗

Prediction of microcracking in composite laminates under thermomechanical loading

Composite laminates used in space structures are exposed to both thermal and mechanical loads. Cracks in the matrix form, changing the laminate thermoelastic properties. An analytical methodology is developed to predict microcrack density in a general laminate exposed to an arbitrary thermomechanical load history. The analysis uses a shear lag stress solution in conjunction with an energy-based cracking criterion. Experimental investigation was used to verify the analysis. Correlation between analysis and experiment is generally excellent. The analysis does not capture machining-induced cracking, or observed delayed crack initiation in a few ply groups, but these errors do not prevent the model from being a useful preliminary design tool.

Maddocks, Jason R.↗

Thermally induced damage in composite space structure: Predictive methodology and experimental correlation

A general analysis method is presented to predict matrix cracks in all plies of a composite laminate, and resulting degraded laminate properties, as functions of temperature or thermal cycles. A shear lag solution of the stresses in the vicinity of cracks and a fracture mechanics crack formation criteria are used to predict cracks. Damage is modeled incrementally, which allows the inclusion of the effects of temperature dependent material properties and softening of the laminate due to previous cracking. The analysis is incorporated into an easy-to-use computer program. The analysis is correlated with experimentally measured crack densities in a variety of laminates exposed to monotonically decreasing temperatures. Crack densities are measured at the edges of specimens by microscopic inspection, and throughout the specimen volumes by x-ray and sanding down of the edges. Correlation between the analytical results and the crack densities in the interiors of the specimens was quite good. Crack densities measured at specimen edges did not agree with internal crack densities (or analyses) in some cases. A free-edge stress analysis clarified the reasons for these discrepancies.

Park, Cecelia↗

Microcracking in composite laminates under thermal and mechanical loading

Composites used in space structures are exposed to both extremes in temperature and applied mechanical loads. Cracks in the matrix form, changing the laminate thermoelastic properties. The goal of the present investigation is to develop a predictive methodology to quantify microcracking in general composite laminates under both thermal and mechanical loading. This objective is successfully met through a combination of analytical modeling and experimental investigation. In the analysis, the stress and displacement distributions in the vicinity of a crack are determined using a shear lag model. These are incorporated into an energy based cracking criterion to determine the favorability of crack formation. A progressive damage algorithm allows the inclusion of material softening effects and temperature-dependent material properties. The analysis is implemented by a computer code which gives predicted crack density and degraded laminate properties as functions of any thermomechanical load history. Extensive experimentation provides verification of the analysis. AS4/3501-6 graphite/epoxy laminates are manufactured with three different layups to investigate ply thickness and orientation effects. Thermal specimens are cooled to progressively lower temperatures down to -184 C. After conditioning the specimens to each temperature, cracks are counted on their edges using optical microscopy and in their interiors by sanding to incremental depths. Tensile coupons are loaded monotonically to progressively higher loads until failure. Cracks are counted on the coupon edges after each loading. A data fit to all available results provides input parameters for the analysis and shows them to be material properties, independent of geometry and loading. Correlation between experiment and analysis is generally very good under both thermal and mechanical loading, showing the methodology to be a powerful, unified tool. Delayed crack initiation observed in a few cases is attributed to a lack of preexisting flaws assumed by the analysis. Some interactions between adjacent ply groups are attributed to local stress concentrations. These two effects are not captured by the analysis due to its global nature. The analysis is conservative in these cases and agrees well with data after the observed onset of cracking.

Maddocks, Jason R.↗

Fatigue Crack Growth and Crack Bridging in SCS-6/Ti-24-11

Interfacial damage induced by relative fiber/matrix sliding was found to occur in the bridged zone of unidirectional SCS-6/Ti-24Al-11Nb intermetallic matrix composite specimens subjected to fatigue crack growth conditions. The degree of interfacial damage was not uniform along the bridged crack wake. Higher damage zones were observed near the machined notch in comparison to the crack tip. The interfacial friction shear strength tau(sub f) measured in the crack wake using pushout testing revealed lower values than the as-received interface. Interfacial wear also reduced the strength of the bridging fibers. The reduction in fiber strength is thought to be a function of the magnitude of relative fiber/matrix displacements ind the degree of interfacial damage. Furthermore, two different fiber bridging models were used to predict the influence of bridging on the fatigue crack driving force. The shear lag model required a variable tau(sub f) in the crack wake (reflecting the degradation of the interface) before its predictions agreed with trends exhibited by the experimental data. The fiber pressure model did an excellent job in predicting both the FCG data and the DeltaCOD in the bridged zone even though it does not require a knowledge of tau(sub f).

Ghosn, Louis J.↗

Microcracking of Materials for Space

The effect of thermal-cycling-induced microcracking in fiber-reinforced polymer matrix composites is studied. Specific attention is focused on microcrack density as a function of the number of thermal cycles, and the effect of microcracking on the dimensional stability of composite materials. Changes in laminate coefficient of thermal expansion (CTE) and laminate stiffness are of primary concern. Included in the study are materials containing four different Thornel fiber types: a PAN-based T50 fiber and three pitch-based fibers, P55, P75, and P120. The fiber stiffnesses range from 55 Msi to 120 Msi. The fiber CTE's range from -0.50 x 1O(exp -6)/degrees F to -0.80 x 10(exp -6)/degrees F. Also included are three matrix types: Fiberite's 934 epoxy, Amoco's ERL1962 toughened epoxy, and YLA's RS3 cyanate ester. The lamination sequences of the materials considered include a cross-ply configuration, [0/90](sub 2s), and two quasi-isotropic configurations, [0/+45/-45/90](sub s), and [0/+45/90/-45](sub s). The layer thickness of the materials range from a nominal 0.001 in. to 0.005 in. In addition to the variety of materials considered, three different thermal cycling temperature ranges are considered. These temperature ranges are +/-250 degrees F, +/-l5O degrees F, and +/-50 degrees F. The combination of these material and geometric parameters and temperature ranges, combined with thermal cycling to thousands of cycles, makes this one of the most comprehensive studies of thermal-cycling-induced microcracking to date. Experimental comparisons are presented by examining the effect of layer thickness, fiber type, matrix type, and thermal cycling temperature range on microcracking and its influence on the laminates. Results regarding layer thickness effects indicate that thin-layer laminates microcrack more severely than identical laminates with thick layers. For some specimens in this study, the number of microcracks in thin-layer specimens exceeds that in thick-layer specimens by more than a factor of two. Despite the higher number of microcracks in the thin-layer specimens, small changes in CTE after thousands of cycles indicate that the thin-layer specimens are relatively unaffected by the presence of these cracks compared to the thick-layer specimens. Results regarding fiber type indicate that the number of microcracks and the change in CTE after thousands of cycles in the specimens containing PAN-based fibers are less than in the specimens containing comparable stiffness pitch-based fibers. Results for specimens containing the different pitch-based fibers indicate that after thousands of cycles, the number of microcracks in the specimens does not depend on the modulus or CTE of the fiber. The change in laminate CTE does, however, depend highly on the stiffness and CTE of the fiber. Fibers with higher stiffness and more negative CTE exhibit the lowest change in laminate CTE as a result of thermal cycling. The overall CTE of these specimens is, however, more negative as a result of the more negative CTE of the fiber. Results regarding matrix type based on the +/-250 degree F temperature range indicate that the RS3 cyanate ester resin system exhibits the greatest resistance to microcracking and the least change in CTE, particularly for cycles numbering 3000 and less. Extrapolations to higher numbers of cycles indicate, however, that the margin of increased performance is expected to decrease with additional thermal cycling. Results regarding thermal cycling temperature range depend on the matrix type considered and the layer thickness of the specimens. For the ERL1962 resin system, microcrack saturation is expected to occur in all specimens, regardless of the temperature range to which the specimens are exposed. By contrast, the RS3 resin system demonstrates a threshold effect such that cycled to less severe temperature ranges, microcracking does not occur. For the RS3 specimens with 0.005 in. layer thickness, no microcracking or changes in CTE are observed in specimens cycled between +/-150 degree F or +/- 50 degree F. For the RS3 specimens with 0.002 in. layer thickness, no microcracking or changes in CTE are observed in specimens cycled between +/-50 degree F. Results regarding laminate stiffness indicate negligible change in laminate stiffness due to thermal cycling for the materials and geometries considered in this investigation. The study includes X-ray examination of the specimens, showing that cracks observed at the edge of the specimens penetrate the entire width of the specimen. Glass transition temperatures of the specimens are measured, showing that resin chemistry is not altered as a result of thermal cycling. Results are also presented based on a one-dimensional shear lag analysis developed in the literature. The analysis requires material property information that is difficult to obtain experimentally. Using limited data from the present investigation, material properties associated with the analysis are modified to obtain reasonable agreement with measured microcrack densities. Based on these derived material properties, the analysis generally overpredicts the change in laminate CTE. Predicted changes in laminate stiffness show reasonable correlation with experimentally measured values.

Brown, Timothy L.↗

The Applicability of the Generalized Method of Cells for Analyzing Discontinuously Reinforced Composites

The paper begins with a short overview of the recent work done in the field of discontinuous reinforced composites, focusing on the different parameters which influence the material behavior of discontinuous reinforced composites, as well as the various analysis approaches undertaken. Based on this overview it became evident, that in order to investigate the enumerated effects in an efficient and comprehensive manner, an alternative approach to the computationally intensive finite-element based micromechanics approach is required. Therefore, an investigation is conducted to demonstrate the utility of utilizing the generalized method of cells (GMC), a semi-analytical micromechanics-based approach, to simulate the elastic and elastoplastic material behavior of aligned short fiber composites. The results are compared with (1) simulations using other micromechanical based mean field models and finite element (FE) unit cell models found in the literature given elastic material behavior, as well as (2) finite element unit cell and a new semianalytical elastoplastic shear lag model in the inelastic range. GMC is shown to definitely have a window of applicability when simulating discontinuously reinforced composite material behavior.

Pahr, D. H.↗

The Applicability of the Generalized Method of Cells for Analyzing Discontinuously Reinforced Composites

The paper begins with a short overview of the recent work done in the field of discontinuous reinforced composites, focusing on the different parameters which influence the material behavior of discontinuous reinforced composites, as well as the various analysis approaches undertaken. Based on this overview it became evident that in order to investigate the enumerated effects in an efficient and comprehensive manner, an alternative approach to the computationally intensive finite-element based micromechanics approach is required. Therefore, an investigation is conducted to demonstrate the utility of utilizing the generalized method of cells (GMC), a semi-analytical micromechanics-based approach, to simulate the elastic and elastoplastic material behavior of aligned short fiber composites. The results are compared with simulations using other micromechanical based mean field models and finite element (FE) unit cell models found in the literature given elastic material behavior, as well as finite element unit cell and a new semianalytical elastoplastic shear lag model in the inelastic range. GMC is shown to definitely have a window of applicability when simulating discontinuously reinforced composite material behavior.

Pahr, D. H.↗

Nonlinear Analysis of Bonded Composite Single-LAP Joints

This study presents a semi-analytical solution method to analyze the geometrically nonlinear response of bonded composite single-lap joints with tapered adherend edges under uniaxial tension. The solution method provides the transverse shear and normal stresses in the adhesive and in-plane stress resultants and bending moments in the adherends. The method utilizes the principle of virtual work in conjunction with von Karman s nonlinear plate theory to model the adherends and the shear lag model to represent the kinematics of the thin adhesive layer between the adherends. Furthermore, the method accounts for the bilinear elastic material behavior of the adhesive while maintaining a linear stress-strain relationship in the adherends. In order to account for the stiffness changes due to thickness variation of the adherends along the tapered edges, their in-plane and bending stiffness matrices are varied as a function of thickness along the tapered region. The combination of these complexities results in a system of nonlinear governing equilibrium equations. This approach represents a computationally efficient alternative to finite element method. Comparisons are made with corresponding results obtained from finite-element analysis. The results confirm the validity of the solution method. The numerical results present the effects of taper angle, adherend overlap length, and the bilinear adhesive material on the stress fields in the adherends, as well as the adhesive, of a single-lap joint

Oterkus, E.↗