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NASA NTRS1983

A nonlinear fracture mechanics approach to the growth of small cracks

An analytical model of crack closure is used to study the crack growth and closure behavior of small cracks in plates and at notches. The calculated crack opening stresses for small and large cracks, together with elastic and elastic plastic fracture mechanics analyses, are used to correlate crack growth rate data. At equivalent elastic stress intensity factor levels, calculations predict that small cracks in plates and at notches should grow faster than large cracks because the applied stress needed to open a small crack is less than that needed to open a large crack. These predictions agree with observed trends in test data. The calculations from the model also imply that many of the stress intensity factor thresholds that are developed in tests with large cracks and with load reduction schemes do not apply to the growth of small cracks. The current calculations are based upon continuum mechanics principles and, thus, some crack size and grain structure exist where the underlying fracture mechanics assumptions become invalid because of material inhomogeneity (grains, inclusions, etc.). Admittedly, much more effort is needed to develop the mechanics of a noncontinuum. Nevertheless, these results indicate the importance of crack closure in predicting the growth of small cracks from large crack data.

Newman, J. C., Jr.↗

NASA NTRS1987

A kinematic model for the evolution of the Gorda Plate

The magnetic lineation pattern produced by the Gorda Rise reflects a complex tectonic history marked by propagating ridges and nonrigid deformation of the Gorda plate. The Pacific-side lineation pattern is matched using a kinematic model which incorporates northward and southward propagating ridge segments and ridge rotation. By superimposing flexural-slip style deformation on the resulting Gorda-side lineations, and allowing convergent motion at the Mendocino Fracture Zone, the Gorda magnetic pattern is also successfully predicted. A similar model, but one which does not allow convergence at the Mendocino Fracture Zone, fails to produce the observed lineation pattern. Model predictions of the amount of material that would be 'obducted' at the Mendocino due to convergence between the Gorda and Pacific agree with bathymetric and density estimates of the amount of material located along the Mendocino Ridge.

Stoddard, Paul R.↗

NASA NTRSDate not supplied

Modeling the Stochastic Response of Fiber Reinforced Composites with Varied Representative Volume Element Sizes

Fiber reinforced composites are desirable in applications where low weight and high strength are needed, but are susceptible to variability and flaws during manufacturing, making failure predictions difficult. These flaws may occur at the microscale where mechanical properties vary locally due to regions of fiber clusters and matrix pockets. In this study, a multiscale approach was taken to model 3-point bend, 4-point bend, and tensile experiments of a unidirectional composite from only having microstructure scans of these samples and constituent properties from literature. These scans were sampled with different sized windows, and statistically equivalent microstructures were generated, then simulated for stiffness, strength, and fracture toughness using a reduced order micromechanical model and NASA’s Multiscale Analysis Tool (NASMAT). Mesoscale models were created with equivalent element sizes to microstructures and properties sampled from microscale simulation results. Results showed how microscale size affects certain mechanical properties. Also shown is how well mesoscale models agree to experiments when using stochastic element properties and varying element size.

microstructure↗

NASA NTRS1981

Lunar floor-fractured craters - Evidence for viscous relaxation of crater topography

Viscous relaxation is evaluated quantitatively as a possible mechanism to account for the observed topographical modification of floor-fractured lunar craters. On the basis of a model of the moon as a viscous material of uniform Newtonian viscosity, the ultimate topographic profiles of fresh craters predicted taking into account viscous relaxation effects are compared with the observed profiles of floor-fractured craters of similar diameter. It is found that for a number of crater pairs, the agreement of the observations with the predictions of the simple viscous relaxation model is good, suggesting that isostatic adjustment of craters in areas of anomalously high temperatures at shallow depth may be a more important source of deformation than previously realized.

Hall, J. L.↗

NASA NTRS2012

Simplified Models for the Study of Postbuckled Hat-Stiffened Composite Panels

The postbuckling response and failure of multistringer stiffened panels is analyzed using models with three levels of approximation. The first model uses a relatively coarse mesh to capture the global postbuckling response of a five-stringer panel. The second model can predict the nonlinear response as well as the debonding and crippling failure mechanisms in a single stringer compression specimen (SSCS). The third model consists of a simplified version of the SSCS that is designed to minimize the computational effort. The simplified model is well-suited to perform sensitivity analyses for studying the phenomena that lead to structural collapse. In particular, the simplified model is used to obtain a deeper understanding of the role played by geometric and material modeling parameters such as mesh size, inter-laminar strength, fracture toughness, and fracture mode mixity. Finally, a global/local damage analysis method is proposed in which a detailed local model is used to scan the global model to identify the locations that are most critical for damage tolerance.

Vescovini, Riccardo↗

NASA NTRS2004

A Hierarchical Approach to Fracture Mechanics

Recent research conducted under NASA LaRC's Creativity and Innovation Program has led to the development of an initial approach for a hierarchical fracture mechanics. This methodology unites failure mechanisms occurring at different length scales and provides a framework for a physics-based theory of fracture. At the nanoscale, parametric molecular dynamic simulations are used to compute the energy associated with atomic level failure mechanisms. This information is used in a mesoscale percolation model of defect coalescence to obtain statistics of fracture paths and energies through Monte Carlo simulations. The mathematical structure of predicted crack paths is described using concepts of fractal geometry. The non-integer fractal dimension relates geometric and energy measures between meso- and macroscales. For illustration, a fractal-based continuum strain energy release rate is derived for inter- and transgranular fracture in polycrystalline metals.

Saether, Erik↗

NASA NTRS1992

Microstructure-failure mode correlations in braided composites

Explication of the fracture processes of braided composites is needed for modeling their behavior. Described is a systematic exploration of the relationship between microstructure, loading mode, and micro-failure mechanisms in carbon/epoxy braided composites. The study involved compression and fracture toughness tests and optical and scanning electron fractography, including dynamic in-situ testing. Principal failure mechanisms of low sliding, buckling, and unstable crack growth are correlated to microstructural parameters and loading modes; these are used for defining those microstructural conditions which are strength limiting.

Filatovs, G. J.↗

NASA NTRS1979

Origin of Valles Marineris

The purpose of the paper is to propose an origin of Valles Marineris and contiguous features such as Noctis Labyrinthus, chaotic terrain, and the large channels of Mars. These are found to: (1) be continuous to each other, (2) have gradual transition between the morphologies, (3) be related by tectonic fracturing, and associated with features of possible magmatic origin. A model is presented in which the geological process is a magmatic process, and after initial uplift and fracturing, Valles Marineris, Noctis Labyrinthus and some chaotic terrain were produced by subsidence caused by lava withdrawal.

Schonfeld, E.↗

NASA NTRS1984

An elastic-plastic finite element analysis of crack initiation, stable crack growth, and instability

Studies have been conducted to develop efficient techniques to simulate crack extension and to examine various local and global fracture criteria. Of the considered criteria, the crack-tip-opening angle (CTOA) or displacement (CTOD) at a specified distance from the crack tip was shown to be most suited for modeling stable crack growth and instability during the fracture process. The results obtained in a number of studies show the necessity for studying different crack configurations when assessing the validity of any fracture criteria. One of the objectives of the present investigation is related to a critical evaluation of the CTOD growth criterion using an elastic-plastic finite element analysis under monotonic loading to failure. The analysis was found to predict three stages of crack growth behavior under monotonic loading to failure. Calculated CTOD values agreed well with experimental values for crack growth initiation.

Newman, J. C., Jr.↗

NASA NTRS1974

Model for thermal stress resistance of truly elastic materials containing more than one crack

The model was developed upon the physical properties of surface energy and intrinsic modulus of elasticity of a material containing a number of equal sized microcracks which are independent of one another. The effect of these cracks upon the strain energy per unit volume of material necessary to continue simultaneous crack growth as well as the measured physical properties was established, and the thermal stress resistance is developed in terms of this energy. The model is expressed in its final form in terms of the measured physical properties of fracture strength, effective modulus of elasticity, and coefficient of thermal expansion. The model was applied to existent thermal stress data of ceramic materials for which these physical properties had been measured. On the basis of these data it was concluded that the thermal stress resistance of a material may be improved by increasing the fracture strength.

Lineback, L. D.↗

NASA NTRS1974

Numerical modelling of instantaneous plate tectonics

Assuming lithospheric plates to be rigid, 68 spreading rates, 62 fracture zones trends, and 106 earthquake slip vectors are systematically inverted to obtain a self-consistent model of instantaneous relative motions for eleven major plates. The inverse problem is linearized and solved iteratively by a maximum-likelihood procedure. Because the uncertainties in the data are small, Gaussian statistics are shown to be adequate. The use of a linear theory permits (1) the calculation of the uncertainties in the various angular velocity vectors caused by uncertainties in the data, and (2) quantitative examination of the distribution of information within the data set. The existence of a self-consistent model satisfying all the data is strong justification of the rigid plate assumption. Slow movement between North and South America is shown to be resolvable.

Minster, J. B.↗

NASA NTRS1990

Characterization of the tensile and microstructural properties of an aluminum metal matrix composite

This study examines a powder metallurgy aluminum alloy in the unreinforced state and with a discontinuous reinforcement of 15 v/o or 30 v/o SiC whisker or 15 v/o SiC particulate. The materials were extruded and then hot-rolled to three plate thicknesses of 6.35, 3.18 and 1.8 mm and were investigated in the as-fabricated and peak aged conditions. The influence of mechanical working on the reinforcement morphology and distribution were examined. A comparison of the mechanical properties was made and the elastic moduli of the reinforced materials were predicted using a micromechanics model. Fractography of tensile specimens revealed that the fracture process was dominated by the presence of microstructural inhomogeneities which were related to both the matrix alloy and to the reinforcement type. An analysis of these microstructural features and a description of the micromechanics model are presented in the paper.

Birt, M. J.↗

NASA NTRS1999

Crack Growth Prediction Methodology for Multi-Site Damage: Layered Analysis and Growth During Plasticity

A finite element program has been developed to perform quasi-static, elastic-plastic crack growth simulations. The model provides a general framework for mixed-mode I/II elastic-plastic fracture analysis using small strain assumptions and plane stress, plane strain, and axisymmetric finite elements. Cracks are modeled explicitly in the mesh. As the cracks propagate, automatic remeshing algorithms delete the mesh local to the crack tip, extend the crack, and build a new mesh around the new tip. State variable mapping algorithms transfer stresses and displacements from the old mesh to the new mesh. The von Mises material model is implemented in the context of a non-linear Newton solution scheme. The fracture criterion is the critical crack tip opening displacement, and crack direction is predicted by the maximum tensile stress criterion at the crack tip. The implementation can accommodate multiple curving and interacting cracks. An additional fracture algorithm based on nodal release can be used to simulate fracture along a horizontal plane of symmetry. A core of plane strain elements can be used with the nodal release algorithm to simulate the triaxial state of stress near the crack tip. Verification and validation studies compare analysis results with experimental data and published three-dimensional analysis results. Fracture predictions using nodal release for compact tension, middle-crack tension, and multi-site damage test specimens produced accurate results for residual strength and link-up loads. Curving crack predictions using remeshing/mapping were compared with experimental data for an Arcan mixed-mode specimen. Loading angles from 0 degrees to 90 degrees were analyzed. The maximum tensile stress criterion was able to predict the crack direction and path for all loading angles in which the material failed in tension. Residual strength was also accurately predicted for these cases.

James, Mark Anthony↗

NASA NTRS2006

Multiscale Analysis of Delamination of Carbon Fiber-Epoxy Laminates with Carbon Nanotubes

A multi-scale analysis is presented to parametrically describe the Mode I delamination of a carbon fiber/epoxy laminate. In the midplane of the laminate, carbon nanotubes are included for the purposes of selectively enhancing the fracture toughness of the laminate. To analyze carbon fiber epoxy carbon nanotube laminate, the multi-scale methodology presented here links a series of parameterizations taken at various length scales ranging from the atomistic through the micromechanical to the structural level. At the atomistic scale molecular dynamics simulations are performed in conjunction with an equivalent continuum approach to develop constitutive properties for representative volume elements of the molecular structure of components of the laminate. The molecular-level constitutive results are then used in the Mori-Tanaka micromechanics to develop bulk properties for the epoxy-carbon nanotube matrix system. In order to demonstrate a possible application of this multi-scale methodology, a double cantilever beam specimen is modeled. An existing analysis is employed which uses discrete springs to model the fiber bridging affect during delamination propagation. In the absence of empirical data or a damage mechanics model describing the effect of CNTs on fracture toughness, several tractions laws are postulated, linking CNT volume fraction to fiber bridging in a DCB specimen. Results from this demonstration are presented in terms of DCB specimen load-displacement responses.

Riddick, Jaret C.↗

NASA NTRS1976

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

A mathematical model is described which will permit predictions of the strength of fiber reinforced composites containing known flaws to be made from the basic properties of their constituents. The approach was to embed a local heterogeneous region (LHR) surrounding the crack tip into an anisotropic elastic continuum. The model should (1) permit an explicit analysis of the micromechanical processes involved in the fracture process, and (2) remain simple enough to be useful in practical computations. Computations for arbitrary flaw size and orientation under arbitrary applied load combinations were performed from unidirectional composites with linear elastic-brittle constituent behavior. The mechanical properties were nominally those of graphite epoxy. With the rupture properties arbitrarily varied to test the capability of the model to reflect real fracture modes in fiber composites, 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 fracture. The computations reveal qualitatively the sequential nature of the stable crack process that precedes fracture.

Kanninen, M. F.↗

NASA NTRS1995

Failure models for textile composites

The goals of this investigation were to: (1) identify mechanisms of failure and determine how the architecture of reinforcing fibers in 3D woven composites controlled stiffness, strength, strain to failure, work of fracture, notch sensitivity, and fatigue life; and (2) to model composite stiffness, strength, and fatigue life. A total of 11 different angle and orthogonal interlock woven composites were examined. Composite properties depended on the weave architecture, the tow size, and the spatial distributions and strength of geometrical flaws. Simple models were developed for elastic properties, strength, and fatigue life. A more complicated stochastic model, called the 'Binary Model,' was developed for damage tolerance and ultimate failure. These 3D woven composites possessed an extraordinary combination of strength, damage tolerance, and notch insensitivity.

Cox, Brian↗

NASA NTRS1993

NASA-UVA Light Aerospace Alloy and Structures Technology Program (LA2ST)

The NASA-UVA Light Aerospace Alloy and Structures Technology (LA2ST) Program continues a high level of activity. Progress achieved between 1 Jan. and 30 Jun. 1993 is reported. The objective of the LA2ST Program is to conduct interdisciplinary graduate student research on the performance of next generation, light weight aerospace alloys, composites, and thermal gradient structures in collaboration with NASA-Langley researchers. The following projects are addressed: environmental fatigue of Al-Li-Cu alloys; mechanisms of localized corrosion and environmental fracture in Al-Cu-Li-Mg-Ag alloy X2095 and compositional variations; the effect of zinc additions on the precipitation and stress corrosion cracking behavior of alloy 8090; hydrogen interactions with Al-Li-Cu alloy 2090 and model alloys; metastable pitting of aluminum alloys; cryogenic fracture toughness of Al-Cu-Li + In alloys; the fracture toughness of Weldalite (TM); elevated temperature cracking of advanced I/M aluminum alloys; response of Ti-1100/SCS-6 composites to thermal exposure; superplastic forming of Weldalite (TM); research to incorporate environmental effects into fracture mechanics fatigue life prediction codes such as NASA FLAGRO; and thermoviscoplastic behavior.

Gangloff, Richard P.↗

NASA NTRS1986

Convection beneath young oceanic lithosphere - Implications for thermal structure and gravity

Small-scale convection under the oceanic lithosphere which begins in the first 5 m.y. of cooling can produce a gravity signal with the amplitude and wavelength observed for large areas of the central Pacific and southern Indian oceans using Seasat altimeter data. The trend of the observed anomalies is parallel to the direction of plate motion as might be expected if they were produced by small-scale convection. Models predict that the wavelengths of gravity anomalies increase more rapidly with age than is observed. The persistence of short relatively uniform wavelength anomalies (less than 200 km) to crustal ages of 50 Ma may indicate that they were produced when the lithosphere was very young and thin and were 'frozen in' as cooling thickened the elastic lithosphere. Small-scale convection which begins under very young lithosphere does not violate other geophysical data such as the rate of seafloor subsidence and variations of geoid height with age. After convection has begun, the subsidence due to thermal contraction within the lithosphere varies linearly with age, in the absence of mantle heat sources, although the rate of change of these quantities is affected by convection. Much of the variation of the geoid height across fracture zones can be fit by a model which includes small-scale convection.

Buck, W. R.↗