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NASA NTRS1989

Noninteractive macroscopic reliability model for ceramic matrix composites with orthotropic material symmetry

A macroscopic noninteractive reliability model for ceramic matrix composites is presented. The model is multiaxial and applicable to composites that can be characterized as orthotropic. Tensorial invariant theory is used to create an integrity basis with invariants that correspond to physical mechanisms related to fracture. This integrity basis is then used to construct a failure function per unit volume (or area) of material. It is assumed that the overall strength of the composite is governed by weakest link theory. This leads to a Weibull type model similar in nature to the principle of independent action (PIA) model for isotropic monolithic ceramics. An experimental program to obtain model parameters is briefly discussed. In addition, qualitative features of the model are illustrated by presenting reliability surfaces for various model parameters.

Duffy, Stephen F.↗

NASA NTRS1989

Noninteractive macroscopic reliability model for ceramic matrix composites with orthotropic material symmetry

Duffy, Stephen F.↗

NASA NTRS1978

The displacement field associated with line forces in a cracked orthotropic body

An explicit result is presented for the two-dimensional Green function for an orthotropic body containing a crack along an orthotropic plane and with its tip in an orthotropic direction. A formal solution and a numerical program for its calculation are presented for a crack on a plane rotated about an orthotropic direction. The use of such Green functions to couple a finite element mesh to a surrounding elastic continuum, thereby shortening finite element calculations for composite bodies with macroscopic orthotropic symmetry, is discussed.

Gehlen, P. C.↗

NASA NTRS1984

Composite laminate optimization program suitable for microcomputers

The design of a composite panel requires some way of finding the minimum thickness laminate which will withstand the load requirements without failure. The mathematical complexity of this problem dictates the use of nonlinear optimization techniques. Specialized laminate optimization programs were developed which are compact and efficient enough to run on microcomputers. Only stresses at a point and inplane loads and deflections are considered. The programs are simple to use and require no knowledge of optimization. Techniques are developed which find minimum thickness laminates with either ply ratios or ply angles as design variables. A method is presented for finding the optimum orientation for the axis of symmetry of an orthotropic laminate. The orthotropic laminate program uses an approximate failure theory, which speed up computations dramatically.

Flanagan, G. V.↗

NASA NTRS1976

Symmetries in laminated composite plates

The different types of symmetry exhibited by laminated anisotropic fibrous composite plates are identified and contrasted with the symmetries of isotropic and homogeneous orthotropic plates. The effects of variations in the fiber orientation and the stacking sequence of the layers on the symmetries exhibited by composite plates are discussed. Both the linear and geometrically nonlinear responses of the plates are considered. A simple procedure is presented for exploiting the symmetries in the finite element analysis. Examples are given of square, skew and polygonal plates where use of symmetry concepts can significantly reduce the scope and cost of analysis.

Noor, A. K.↗

NASA NTRS1990

A New Approach to Fibrous Composite Laminate Strength Prediction

A method of predicting the strength of cross-plied fibrous composite laminates is based on expressing the classical maximum-shear-stress failure criterion for ductile metals in terms of strains. Starting with such a formulation for classical isotropic materials, the derivation is extended to orthotropic materials having a longitudinal axis of symmetry, to represent the fibers in a unidirectional composite lamina. The only modification needed to represent those same fibers with properties normalized to the lamina rather than fiber is a change in axial modulus. A mirror image is added to the strain-based lamina failure criterion for fiber-dominated failures to reflect the cutoffs due to the presence of orthogonal fibers. It is found that the combined failure envelope is now identical with the well-known maximum-strain failure model in the tension-tension and compression-compression quadrants but is truncated in the shear quadrants. The successive application of this simple failure model for fibers in the 0/90 degree and +/- 45 degree orientations, in turn, is shown to be the necessary and sufficient characterization of the fiber-dominated failures of laminates made from fibers having the same tensile and compressive strengths. When one such strength is greater than the other, the failure envelope is appropriately truncated for the lesser direct strain. The shear-failure cutoffs are now based on the higher axial strain to failure since they occur at lower strains than and are usually not affected by such mechanisms as microbuckling. Premature matrix failures can also be covered by appropriately truncating the fiber failure envelope. Matrix failures are excluded from consideration for conventional fiber/polymer composites but the additional features needed for a more rigorous analysis of exotic materials are covered. The new failure envelope is compared with published biaxial test data. The theory is developed for unnotched laminates but is easily shrunk to incorporate reductions to allow for bolt holes, cutouts, reduced compressive strength after impact, and the like.

Hart-Smith, L. J.↗

NASA NTRS1987

Exploiting symmetries in the modeling and analysis of tires

A simple and efficient computational strategy for reducing both the size of a tire model and the cost of the analysis of tires in the presence of symmetry-breaking conditions (unsymmetry in the tire material, geometry, or loading) is presented. The strategy is based on approximating the unsymmetric response of the tire with a linear combination of symmetric and antisymmetric global approximation vectors (or modes). Details are presented for the three main elements of the computational strategy, which include: use of special three-field mixed finite-element models, use of operator splitting, and substantial reduction in the number of degrees of freedom. The proposed computational stategy is applied to three quasi-symmetric problems of tires: linear analysis of anisotropic tires, through use of semianalytic finite elements, nonlinear analysis of anisotropic tires through use of two-dimensional shell finite elements, and nonlinear analysis of orthotropic tires subjected to unsymmetric loading. Three basic types of symmetry (and their combinations) exhibited by the tire response are identified.

Noor, Ahmed K.↗

NASA NTRS1989

Efficient Computation Of Behavior Of Aircraft Tires

NASA technical paper discusses challenging application of computational structural mechanics to numerical simulation of responses of aircraft tires during taxing, takeoff, and landing. Presents details of three main elements of computational strategy: use of special three-field, mixed-finite-element models; use of operator splitting; and application of technique reducing substantially number of degrees of freedom. Proposed computational strategy applied to two quasi-symmetric problems: linear analysis of anisotropic tires through use of two-dimensional-shell finite elements and nonlinear analysis of orthotropic tires subjected to unsymmetric loading. Three basic types of symmetry and combinations exhibited by response of tire identified.

Tanner, John A.↗

NASA NTRS2000

Crack Turning in Integrally Stiffened Aircraft Structures

Current emphasis in the aircraft industry toward reducing manufacturing cost has created a renewed interest in integrally stiffened structures. Crack turning has been identified as an approach to improve the damage tolerance and fail-safety of this class of structures. A desired behavior is for skin cracks to turn before reaching a stiffener, instead of growing straight through. A crack in a pressurized fuselage encounters high T-stress as it nears the stiffener--a condition favorable to crack turning. Also, the tear resistance of aluminum alloys typically varies with crack orientation, a form of anisotropy that can influence the crack path. The present work addresses these issues with a study of crack turning in two-dimensions, including the effects of both T-stress and fracture anisotropy. Both effects are shown to have relation to the process zone size, an interaction that is central to this study. Following an introduction to the problem, the T-stress effect is studied for a slightly curved semi-infinite crack with a cohesive process zone, yielding a closed form expression for the future crack path in an infinite medium. For a given initial crack tip curvature and tensile T-stress, the crack path instability is found to increase with process zone size. Fracture orthotropy is treated using a simple function to interpolate between the two principal fracture resistance values in two-dimensions. An extension to three-dimensions interpolates between the six principal values of fracture resistance. Also discussed is the transition between mode I and mode II fracture in metals. For isotropic materials, there is evidence that the crack seeks out a direction of either local symmetry (pure mode I) or local asymmetry (pure mode II) growth. For orthotropic materials the favored states are not pure modal, and have mode mixity that is a function of crack orientation.

Pettit, Richard Glen↗

NASA NTRS1981

Photoelastic techniques for the complete determination of stresses in composite structures

Three new methods are proposed for determining the individual values of the principal stresses or strains in an orthotropic birefringent model using transmission photoelastic analysis. One of the methods is an extension of the oblique incidence technique in which the model (or the light beam) is rotated about one of the material symmetry axes. In another method, transmission and reflection photoelastic responses are combined, while in the third method small circular holes are drilled at points of interest and the isochromatic fringe order is measured at selected points on the hole boundary. The three methods are applied to an orthotropic disc under diametral compression and results are compared with strain gage data.

Prabhakaran, R.↗

NASA NTRS1978

The problem of an inclined crack in an orthotropic strip

The elastostatic problem for an infinite orthotropic strip containing crack was considered. It was assumed that the orthogonal axes of material orthotropy may have an arbitrary angular orientation with respect to the orthogonal axes of geometric symmetry of the uncracked strip. The crack was located along an axis of orthotropy, hence, at an arbitrary angle with respect to the sides of the strip. The general problem was formulated in terms of a system of singular integral equations for arbitrary crack surface tractions. As examples Modes 1 and 2 stress intensity factors were calculated for the strip having an internal or an edge crack with various lengths and angular orientations.

Delale, F.↗

NASA NTRS1978

Stress intensity factors for an inclined crack in an orthotropic strip

The elastostatic problem for an infinite orthotropic strip containing a crack is considered. It is assumed that the orthogonal axes of material orthotropy may have an arbitrary angular orientation with respect to the orthogonal axes of geometric symmetry of the uncracked strip. The crack is located along an axis of orthotropy, hence at an arbitrary angle with respect to the sides of the strip. The general problem is formulated in terms of a system of singular integral equations for arbitrary crack surface tractions. As examples Modes I and II stress intensity factors are calculated for the strip having an internal or an edge crack with various lengths and angular orientations. In most calculations uniform tension or uniform bending away from the crack region is used as the external load. Limited results are also given for uniform normal or shear tractions on the crack surface.

Delale, F.↗

NASA NTRS1979

The problem of an inclined crack in an orthotropic strip

The elastostatic problem for an infinite orthotropic strip containing a crack is considered. It is assumed that the orthogonal axes of material orthotropy may have an arbitrary angular orientation with respect to the orthogonal axes of geometric symmetry of the uncracked strip. The crack is located along an axis of orthotropy, hence at an arbitrary angle with respect to the sides of the strip. The general problem is formulated in terms of a system of singular integral equations for arbitrary crack surface tractions. As examples Modes I and II stress-intensity factors are calculated for the strip having an internal or an edge crack with various lengths and angular orientations. In most calculations uniform tension or uniform bending away from the crack region is used as the external load. Limited results are also given for uniform normal or shear tractions on the crack surface.

Delale, F.↗

NASA NTRS1997

Effect of a growth hormone treatment on bone orthotropic elasticity in dwarf rats

A refinement of the current ultrasonic elasticity technique was used to measure the orthotropic elastic properties of rat cortical bone as well as to quantify changes in elastic properties, density, and porosity of the dwarf rat cortex after a treatment with recombinant human growth hormone (rhGH). The ultrasonic elasticity technique was refined via optimized signal management of high-frequency wave propagation through cubic cortical specimens. Twenty dwarf rats (37 days old) were randomly assigned to two groups (10 rats each). The dwarf rat model (5-10% of normal GH) was given subcutaneous injections of either rhGH or saline over a 14-day treatment period. Density was measured using Archimedes technique. Porosity and other microstructural characteristics were also explored via scanning electron microscopy and image analysis. Statistical tests verified significant decreases in cortical orthotropic Young's (-26.7%) and shear (-16.7%) moduli and density (-2.42%) concomitant with an increase in porosity (+125%) after rhGH treatments to the dwarf model (p < 0.05). A change in material symmetry from orthotropy toward planar isotropy within the radial-circumferential plane after GH treatments was also noted. These results demonstrate some alteration in bone properties at this time interval. Structural implications of these changes throughout physiological loading regimens should be explored.

NASA Discipline Musculoskeletal↗

NASA NTRS1989

Exploiting symmetries in the modeling and analysis of tires

A computational procedure is presented for reducing the size of the analysis models of tires having unsymmetric material, geometry and/or loading. The two key elements of the procedure when applied to anisotropic tires are: (1) decomposition of the stiffness matrix into the sum of an orthotropic and nonorthotropic parts; and (2) successive application of the finite-element method and the classical Rayleigh-Ritz technique. The finite-element method is first used to generate few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh-Ritz technique. The proposed technique has high potential for handling practical tire problems with anisotropic materials, unsymmetric imperfections and asymmetric loading. It is also particularly useful for use with three-dimensional finite-element models of tires.

Noor, Ahmed K.↗

NASA NTRS1990

Local stresses in metal matrix composites subjected to thermal and mechanical loading

An elasticity solution has been used to analyze matrix stresses near the fiber/matrix interface in continuous fiber-reinforced metal-matrix composites, modeling the micromechanics in question in terms of a cylindrical fiber and cylindrical matrix sheath which is embedded in an orthotropic medium representing the composite. The model's predictions for lamina thermal and mechanical properties are applied to a laminate analysis determining ply-level stresses due to thermomechanical loading. A comparison is made between these results, which assume cylindrical symmetry, and the predictions yielded by a FEM model in which the fibers are arranged in a square array.

Highsmith, Alton L.↗

NASA NTRS1981

Photoelastic techniques for the complete determination of stresses in composite structures

Three methods of photoelastic analysis are examined. The first method is an extension of the oblique incidence technique in which the model (or the light beam) is rotated about one of the material symmetry axes. In the second method, transmission and reflection photoelastic responses are combined. The third method requires the drilling of small holes and the determination of the fringe orders at selected points on the hole boundary. The three methods are applied to an orthotropic circular disk under diametral compression. Results are compared with strain gage data.

Prabhakaran, R.↗

NASA NTRS2000

Determination of the Fracture Parameters in a Stiffened Composite Panel

A modified J-integral, namely the equivalent domain integral, is derived for a three-dimensional anisotropic cracked solid to evaluate the stress intensity factor along the crack front using the finite element method. Based on the equivalent domain integral method with auxiliary fields, an interaction integral is also derived to extract the second fracture parameter, the T-stress, from the finite element results. The auxiliary fields are the two-dimensional plane strain solutions of monoclinic materials with the plane of symmetry at x(sub 3) = 0 under point loads applied at the crack tip. These solutions are expressed in a compact form based on the Stroh formalism. Both integrals can be implemented into a single numerical procedure to determine the distributions of stress intensity factor and T-stress components, T11, T13, and thus T33, along a three-dimensional crack front. The effects of plate thickness and crack length on the variation of the stress intensity factor and T-stresses through the thickness are investigated in detail for through-thickness center-cracked plates (isotropic and orthotropic) and orthotropic stiffened panels under pure mode-I loading conditions. For all the cases studied, T11 remains negative. For plates with the same dimensions, a larger size of crack yields larger magnitude of the normalized stress intensity factor and normalized T-stresses. The results in orthotropic stiffened panels exhibit an opposite trend in general. As expected, for the thicker panels, the fracture parameters evaluated through the thickness, except the region near the free surfaces, approach two-dimensional plane strain solutions. In summary, the numerical methods presented in this research demonstrate their high computational effectiveness and good numerical accuracy in extracting these fracture parameters from the finite element results in three-dimensional cracked solids.

Lin, Chung-Yi↗