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NASA NTRS1991

An equivalent domain integral method for three-dimensional mixed-mode fracture problems

A general formulation of the equivalent domain integral (EDI) method for mixed mode fracture problems in cracked solids is presented. The method is discussed in the context of a 3-D finite element analysis. The J integral consists of two parts: the volume integral of the crack front potential over a torus enclosing the crack front and the crack surface integral due to the crack front potential plus the crack face loading. In mixed mode crack problems the total J integral is split into J sub I, J sub II, and J sub III representing the severity of the crack front in three modes of deformations. The direct and decomposition methods are used to separate the modes. These two methods were applied to several mixed mode fracture problems, were analyzed, and results were found to agree well with those available in the literature. The method lends itself to be used as a post-processing subroutine in a general purpose finite element program.

Shivakumar, K. N.↗

NASA NTRS1992

An equivalent domain integral method for three-dimensional mixed-mode fracture problems

Shivakumar, K. N.↗

NASA NTRS1987

Evidence for divergent plate-boundary characteristics and crustal spreading on Venus

Detailed examination of the topography and morphology of western Aphrodite Terra reveals numerous features that are similar to terrestrial divergent plate-boundary characteristics. Individual domains between fracture-zone-like discontinuities contain a variety of bilaterally symmetrical topographic elements that suggest that topographic features have been created at rise crests, rifted and separated, and moved laterally to their present symmetrical positions. The topographic and morphologic similarities, together with strikingly similar mirror-image map patterns on both sides of the rise axis, suggest that western Aphrodite Terra shares the characteristics of oceanic divergent plate boundaries, and is the site of crustal spreading on Venus. Topographic profiles are consistent with spreading rates of the order of several centimeters per year.

Head, James W., III↗

NASA NTRS1992

Phase transformations in 40-60-GPa shocked gneisses from the Haughton Crater (Canada): An Analytical Transmission Electron Microscopy (ATEM) study

In order to better understand phase transformations, chemical migration, and isotopic disequilibrium in highly shocked rocks, we have performed a microprobe and an ATEM study on gneisses shocked up to 60 GPa from the Haughton Crater. This study reveals the following chemical and structural characteristics: (1) SiO2 dominant areas are formed by a mixture of pure SiO2 polycrystalline quartz identified by electron diffraction pattern and chemical analysis and a silica-rich amorphous phase containing minor amounts of aluminium, potassium, and iron; (2) Areas with biotitelike composition are formed by less than 200-nm grains of iron-rich spinels embedded in a silica-rich amorphous phase that is very similar to the one described above; (3) Layers with feldsparlike composition are constituted by 100-200-nm-sized alumina-rich grains (the indexation of the crystalline structure is under progress) and the silica-rich amorphous phase; (4) Zones characterized by the unusual Al/Si ratio close to 1 are formed by spinel grains (200-nm-sized) embedded in the same silica-rich amorphous phase; and (5) The fracturated sillimanites contain domains with a lamellar structure, defined by the intercalation of 100-nm-wide lamellae of mullite crystals and of a silica-rich amorphous phase. These mullite crystals preserved the crystallographical orientation of the preshock sillimanite. All compositional domains, identified at the microprobe scale, can thus be explained by a mixture in different proportion between the following phases: (1) a silica-rich amorphous phase, with minor Al and K; (2) quartz crystals; (3) spinel crystals and alumina-rich crystals; (4) sillimanite; and (5) mullite. Such mixtures of amorphous phases and crystals in different proportions explain disturbed isotope systems in these rocks and chemical heterogeneities observed on the microprobe.

Martinez, I.↗

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↗

NASA NTRS1991

A three-dimensional equivalent domain integral method for cracked solids

Three-dimensional FEM analysis is presently undertaken via the general formulation of the equivalent-domain integral method for mixed-mode fracture problems in general anisotropic and nonlinear materials. In mixed-mode integrals, the total J-integral is split into three separate modes of fracture; direct and decomposition methods are effective in this separation of the modes, as presently demonstrated by their application to several pure and mixed-mode fracture problems. The results are found to agree well with those reported in the literature, and suggest the usefulness of the method as a FEM-program postprocessing subroutines.

Shivakumar, K. N.↗

NASA NTRS1991

Structural design methodologies for ceramic-based material systems

One of the primary pacing items for realizing the full potential of ceramic-based structural components is the development of new design methods and protocols. The focus here is on low temperature, fast-fracture analysis of monolithic, whisker-toughened, laminated, and woven ceramic composites. A number of design models and criteria are highlighted. Public domain computer algorithms, which aid engineers in predicting the fast-fracture reliability of structural components, are mentioned. Emphasis is not placed on evaluating the models, but instead is focused on the issues relevant to the current state of the art.

Duffy, Stephen F.↗

NASA NTRS1992

Structural design methodologies for ceramic-based material systems

Duffy, Stephen F.↗

NASA NTRS1995

Detecting gear tooth fracture in a high contact ratio face gear mesh

This paper summarized the results of a study in which three different vibration diagnostic methods were used to detect gear tooth fracture in a high contact ratio face gear mesh. The NASA spiral bevel gear fatigue test rig was used to produce unseeded fault, natural failures of four face gear specimens. During the fatigue tests, which were run to determine load capacity and primary failure mechanisms for face gears, vibration signals were monitored and recorded for gear diagnostic purposes. Gear tooth bending fatigue and surface pitting were the primary failure modes found in the tests. The damage ranged from partial tooth fracture on a single tooth in one test to heavy wear, severe pitting, and complete tooth fracture of several teeth on another test. Three gear fault detection techniques, FM4, NA4*, and NB4, were applied to the experimental data. These methods use the signal average in both the time and frequency domain. Method NA4* was able to conclusively detect the gear tooth fractures in three out of the four fatigue tests, along with gear tooth surface pitting and heavy wear. For multiple tooth fractures, all of the methods gave a clear indication of the damage. It was also found that due to the high contact ratio of the face gear mesh, single tooth fractures did not significantly affect the vibration signal, making this type of failure difficult to detect.

Zakrajsek, James J.↗

NASA NTRS1989

Three-dimensional analysis of surface crack-Hertzian stress field interaction

The results are presented of a stress intensity factor analysis of semicircular surface cracks in the inner raceway of an engine bearing. The loading consists of a moving spherical Hertzian contact load and an axial stress due to rotation and shrink fit. A 3-D linear elastic Boundary Element Method code was developed to perform the stress analysis. The element library includes linear and quadratic isoparametric surface elements. Singular quarter point elements were employed to capture the square root displacement variation and the inverse square root stress singularity along the crack front. The program also possesses the capability to separate the whole domain into two subregions. This procedure enables one to solve nonsymmetric fracture mechanics problems without having to separate the crack surfaces a priori. A wide range of configuration parameters was investigated. The ratio of crack depth to bearing thickness was varied from one-sixtieth to one-fifth for several different locations of the Hertzian load. The stress intensity factors for several crack inclinations were also investigated. The results demonstrate the efficiency and accuracy of the Boundary Element Method. Moreover, the results can provide the basis for crack growth calculations and fatigue life prediction.

Ballarini, R.↗

NASA NTRS1991

Modeling the growth and interaction of fractures

The research objectives are to develop accurate, efficient numerical tool for fracture mechanics analysis with the capabilities of the method including the modeling of multiple site damage and the simulation of crack propagation. The fracture is modeled using a distribution of edge dislocations. Fundamental solutions for dislocations in an infinite medium, in the neighborhood of a circular inhomogeneity, and near a bi-material interface are incorporated into the procedure to allow exceptionally accurate modeling of fracture geometries involving these types of inhomogeneities. To model arbitrary (finite) domains under general boundary conditions, a combination of the dislocation methodology and boundary element techniques is used. The dislocation scheme is a natural means to model the crack(s), and the boundary element method is an effective way to model the region in which the crack is embedded. The hybrid scheme is relatively easy to use and is very accurate. The research accomplishments are presented.

Mear, Mark E.↗

NASA NTRS1981

Problems encountered with conventional fiber-reinforced composites

Preparational, computational, and operational problems associated with fiber-reinforced composites (FRC) are reviewed. Initial preparation of FRCs is shown to involve consideration of the type of prepreg, the setting time, cure conditions and cycles, and cure temperatures. The effects of the choice of bonding agents, the fiber transfer length, and individual fiber responses to bonding agents are noted to have an impact on fiber strength, moisture uptake, and fatigue resistance. The deformation prior to failure and the failure region are modeled through models of mini-, micro- and macro mechanics formulations employing a stiffness matrix, failure criterion, or fracture mechanics. The detection, evaluation, and repair of defects comprises the operational domain, and it is stressed that no good repair techniques exist for FRCs.

Landel, R. F.↗

NASA NTRS1993

Analysis of local delaminations caused by angle ply matrix cracks

Two different families of graphite/epoxy laminates with similar layups but different stacking sequences, (0,theta,-theta) sub s and (-theta/theta/0) sub s were analyzed using three-dimensional finite element analysis for theta = 15 and 30 degrees. Delaminations were modeled in the -theta/theta interface, bounded by a matrix crack and the stress free edge. The total strain energy release rate, G, along the delamination front was computed using three different techniques: the virtual crack closure technique (VCCT), the equivalent domain Integral (EDI) technique, and a global energy balance technique. The opening fracture mode component of the strain energy release rate, Gl, along the delamination front was also computed for various delamination lengths using VCCT. The effect of residual thermal and moisture stresses on G was evaluated.

Salpekar, Satish A.↗

NASA NTRS1989

Analysis of whisker-toughened ceramic components: A design engineer's viewpoint

The use of ceramics components in gas turbines, cutting tools, and heat exchangers has been limited by the relatively low flaw tolerance of monolithic ceramics. The development of whisker toughened ceramic composites offers the potential for considerable improvement in fracture toughness as well as strength. However, the variability of strength is still too high for the application of deterministic design approaches. Several phenomenological reliability theories proposed for this material system are reviewed and the development is reported of a public domain computer algorithm. This algorithm, when coupled with a general purpose finite element program, predicts the fast fracture reliability of a structural component under multiaxial loading conditions.

Duffy, Stephen F.↗

NASA NTRS1982

Fracture mechanics in fiber reinforced composite materials, taking as examples B/A1 and CRFP

The validity of linear elastic fracture mechanics and other fracture criteria was investigated with laminates of boron fiber reinforced aluminum (R/A1) and of carbon fiber reinforced epoxide (CFRP). Cracks are assessed by fracture strength Kc or Kmax (critical or maximum value of the stress intensity factor). The Whitney and Nuismer point stress criterion and average stress criterion often show that Kmax of fiber composite materials increases with increasing crack length; however, for R/A1 and CFRP the curve showing fracture strength as a function of crack length is only applicable in a small domain. For R/A1, the reason is clearly the extension of the plastic zone (or the damage zone n the case of CFRP) which cannot be described with a stress intensity factor.

Peters, P. W. M.↗

NASA NTRS1985

Nonlinear quasi-fracture behavior of polymers

This paper deals with the nonlinear quasi-fracture behavior of polymers. Using the finite element method, the quasi-fracture model composed of an isolated craze opening with a nonlinear boundary envelope forces represented by oriented fibril domains is analyzed in simply-stressed rectangular plate. The stress distribution, the displacement profile, as well as the yield or plastic or flow zone adjacent to the craze tips are obtained. It is found that the variation of the stress distribution near the craze tip is not as sharp as that for an elastic crack. The initial load required for yielding or flowing is greater for the quasifracture as compared with that for a classical fracture. Under the same load the yield or flow zone is somewhat smaller as compared with that obtained on the basis of linear elastic-plastic fracture mechanics theory.

Sun, B. N.↗

NASA NTRS1993

CCARES: A computer algorithm for the reliability analysis of laminated CMC components

Structural components produced from laminated CMC (ceramic matrix composite) materials are being considered for a broad range of aerospace applications that include various structural components for the national aerospace plane, the space shuttle main engine, and advanced gas turbines. Specifically, these applications include segmented engine liners, small missile engine turbine rotors, and exhaust nozzles. Use of these materials allows for improvements in fuel efficiency due to increased engine temperatures and pressures, which in turn generate more power and thrust. Furthermore, this class of materials offers significant potential for raising the thrust-to-weight ratio of gas turbine engines by tailoring directions of high specific reliability. The emerging composite systems, particularly those with silicon nitride or silicon carbide matrix, can compete with metals in many demanding applications. Laminated CMC prototypes have already demonstrated functional capabilities at temperatures approaching 1400 C, which is well beyond the operational limits of most metallic materials. Laminated CMC material systems have several mechanical characteristics which must be carefully considered in the design process. Test bed software programs are needed that incorporate stochastic design concepts that are user friendly, computationally efficient, and have flexible architectures that readily incorporate changes in design philosophy. The CCARES (Composite Ceramics Analysis and Reliability Evaluation of Structures) program is representative of an effort to fill this need. CCARES is a public domain computer algorithm, coupled to a general purpose finite element program, which predicts the fast fracture reliability of a structural component under multiaxial loading conditions.

Duffy, Stephen F.↗

NASA NTRS1989

Designing ceramic components with the CARES computer program

NASA-Lewis has developed a public-domain computer program, designated 'Ceramic Analysis and Reliability Evaluation of Structures' (CARES) for calculating the fast-fracture reliability of macroscopically isotropic ceramic components subjected to the complex thermomechanical loadings typical of heat engines. The design methodology employed by CARES encompasses linear elastic fracture mechanics theory, extreme value statistics, and material microstructures; component integrity is conceived as a function of the entire field solution of the stresses, rather than being based solely on the most highly stressed point.

Nemeth, Noel N.↗