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NASA NTRS1989

Fracture mechanics applied to elevated temperature crack growth

Twenty-six isothermal crack growth tests were performed on Hastelloy-X tubular specimens at a variety of temperatures and strain ranges. Conditions were selected to include nominally elastic and nominally plastic conditions. A number of parameters including the stress intensity factor, strain intensity factor, J-integral, Crack Opening Displacement, and Tompkins model were examined for their ability to correlate the data. Test conditions were selected such that growth rates at a single value of the parameter were obtained at radially different crack lengths, thus exploring the geometry independence of the correlating parameter. None of the parameters were fully satisfactory. However, COD calculated from J-integral appeared to be the most successful.

Jordan, E. H.↗

NASA NTRS1994

Microstructurally based model of fatigue initiation and growth

A model to calculate fatigue life is developed based on the assumption that fatigue life is entirely composed of crack growth from an initial microstructural inhomogeneity. Specifically, growth is considered to start from either an ellipsoidal void, a cracked particle, or a debonded particle. The capability of predicting fatigue life from material microstructure is based on linear elastic fracture mechanics principles, the sizes of the crack-initiating microstructural inhomogeneities, and an initiation parameter that is proportional to the cyclic plastic zone size. A key aspect of this modeling approach is that it is linked with a general purpose probability program to analyze the effect of the distribution of controlling microstructural features within the material. This enables prediction of fatigue stress versus life curves for various specimen geometries using distributional statistics obtained from characterizations of the microstructure. Results are compared to experimental fatigue data from an aluminum alloy.

Brockenbrough, J. R.↗

NASA NTRSDate not supplied

Comparing Analysis of Hydrogen Concentration in Astromaterials Nominally Anhydrous Minerals by Multiple SIMS

Secondary Ion Mass Spectrometry (SIMS) is utilized to determine hydrogen (H) concentration in astromaterials nominally anhydrous minerals (NAMs) and their inclusions [e.g., 1]. This data is interpreted to refine the volatile history of planetary bodies. Four instruments are being used to compare H concentration analysis: a large geometry SIMS (The University of Hawaiʻi Cameca IMS 1280), a compact SIMS (Arizona State University (ASU) Cameca IMS 6f), and two Cameca NanoSIMS 50L at ASU and NASA-Johnson Space Center (JSC). Results on the first three instruments are available. Although fundamentally similar, SIMS instruments and their modifications [2] may produce different values or pose advantages for H analysis, especially for shocked samples that are susceptible to contamination filling their fractures. New data from the IMS 1280 is reported, using its microchannel plate (MCP) to image high H signals in grain fractures during pre-sputtering to avoid them as much as possible. Between fractures, 16 OH/ 30 Si was measured with a Cs + 4 nA primary beam, 30 micron spot size, and central ~5x5 micron collection area. First order comparison of H concentration (reported in ppm H 2 O) is achieved on a terrestrial gem quality clinopyroxene (SLP114, 162±12 ppm H 2 O [3]), with 157±7 and 215±40 ppm H 2 O by the IMS 1280 and 6f respectively. SIMS comparison is then extended to analysis of two Martian shergottites: RBT 04262 and NWA 5789. Due to a dense fracture network (< 20 micron) in RBT 04262, only one clinopyroxene hosted glassy inclusion was analyzed (n=6, ≤1 ppm H 2 O), while six olivine grains in NWA 5789 (n=12, ≤ 2 ppm H 2 O) (1s ±0.21) were analyzed. Higher concentrations were obtained for RBT 04262 olivine by the ASU NanoSIMS 50L (up to 350 ppm H 2 O [4]), and IMS 6f (300+ ppm H 2 O, [5]), for which contamination in fractures could not be avoided. Work on the JSC NanoSIMS 50L will further develop the SIMS comparison.

J.-M. Dudley↗

NASA NTRS1977

Biaxial load effects in fracture mechanics

It is found that the standard expressions for elastic stress and displacement in the crack-tip region (i.e., the so-called singular solution) cannot be considered to be approximations that are acceptable in a completely general sense. This conclusion is best illustrated by the instance of a biaxially loaded infinite sheet with a flat horizontal central crack, where the effect of load applied parallel to the plane of the crack appears entirely in the second terms of the series representations for local stresses and displacements. An elastoplastic finite-element analysis of the same biaxially loaded finite specimen geometry shows that the global energy release rate, the J-integral, the plastic stress and strain intensity factors (in the sense of Hilton and Hutchinson), and the size of the crack border region plastic yield, all have pronounced biaxial load dependence.

Liebowitz, H.↗

NASA NTRS1989

Predicting The Propagation Of Cracks

Advanced Crack Propagation Predictive Analysis Program, FLAGR04, developed as aid in predicting growth of preexisting flaws and cracks in structural components. Provides fracture-mechanics analyst with computerized method of evaluation of "safe crack-growth life" capabilities of structural components. Also used to evaluate tolerance-to-damage aspects of given structural design. Predicts growth of crack by use of two-dimensional model independently predicting growth of flaw in two directions based on calculation of stress-intensity factors. Input to FLAGR04 consists of initial definition of crack, type of rate solution, type and geometry of flaw, properties of material, data on load spectrum, load-stress functions, and design-limit stress levels. Output includes echo of input with any error or warning message and history of propagation of crack. Written in FORTRAN IV.

Tianlai, HU↗

NASA NTRS2021

Newmark-Type Pseudo-Three-Dimensional Back-Analysis of Co-Seismic Landslides in Egkremnoi, Lefkada, Greece

A pseudo-three-dimensional (pseudo-3D) methodology to back-analyze coseismic landslides was developed and applied to 68mapped landslides, which occurred over approximately 1 km2area in Egkremnoi, Greece, during the 2015 Mw6.5 Lefkada earthquake. The methodology is based on a one-dimensional (1D) Newmark-type sliding block model to assess instability and a spatial projection in 3D topography to derive landslide geometry. The strength parameters for modeled landslides that best match the landslide location, area, and volume were derived through an iterative scheme that optimizes the match using predefined matching criteria. The range of different-sized landslides produced shear strength estimates from ~10 to 300 kPa and led to the derivation of a regionally averaged strength envelope characterized by a cohesion of 6 kPa and a friction angle of 53°for the highly fractured limestones that are encountered in this area. Compared to previous full 3Dslope stability analyses in this area, the friction angle using this methodology was found to be generally consistent, but the cohesion was lower. The presented methodology can provide a computationally efficient method to estimate the average shear strength of a geologic unit over large areas, especially where extensive field and laboratory tests on the materials are unavailable or difficult to conduct.

Weibing Gong↗

NASA NTRS1990

Micromechanical model of crack growth in fiber reinforced ceramics

A model based on the micromechanical mechanism of crack growth resistance in fiber reinforced ceramics is presented. The formulation of the model is based on a small scale geometry of a macrocrack with a bridging zone, the process zone, which governs the resistance mechanism. The effect of high toughness of the fibers in retardation of the crack advance, and the significance of the fiber pullout mechanism on the crack growth resistance, are reflected in this model. The model allows one to address issues such as influence of fiber spacing, fiber flexibility, and fiber matrix friction. Two approaches were used. One represents the fracture initiation and concentrated on the development of the first microcracks between fibers. An exact closed form solution was obtained for this case. The second case deals with the development of an array of microcracks between fibers forming the bridging zone. An implicit exact solution is formed for this case. In both cases, a discrete fiber distribution is incorporated into the solution.

Rubinstein, Asher A.↗

NASA NTRS1990

Micromechanical model of crack growth in fiber reinforced brittle materials

Rubinstein, Asher A.↗

NASA NTRSDate not supplied

Simulation of Dynamic Crushing Behavior of Simulated Carbon/Epoxy Stanchions Using MAT58 and MAT213 in LS-DYNA

Carbon fiber-reinforced polymer (CFRP) composites have shown promise as a material for structures designed to absorb energy in crush-style impact loading. In complementing the lightweight and tailorable characteristics of CFRP structures, the benefits of impact energy absorption are particularly interesting in aerospace vehicles that require excellent crashworthiness performance. However, simulating the behavior of CFRP structures in dynamic, crushing-style impact loading is challenging because of the many damage and failure modes that are essential to capture in the model. For the present investigation, CFRP stanchions were tested using a crash sled experimental test rig. The stanchions were designed by the Composite Materials Handbook-17 (CMH-17) Crashworthiness Working Group for the purpose of comparing experimental crash sled tests to corresponding simulations of the tests. The stanchions are C-channel shaped and represent a geometry common in the interior of aerospace vehicle structures. Explicit simulations in LSDYNA were performed using a well-established composite material model (MAT58) and a next-generation material model (MAT213). Fully integrated shell elements were utilized instead of 3D solid elements to limit computation time. In all models, each of the sixteen plies were represented with individual layers of shell elements with tiebreak contact between each adjacent ply pair to simulate interlaminar fracture. Simulating the crushing of the stanchions occurred in two phases. First, the material models were calibrated using flat specimens that were manufactured with the same layup as the stanchions. While the original goal was calibration of material-related properties, meshdependent behavior was observed in simulations with either material model, and an unstructured mesh was selected to remediate undesirable mesh-dependent failure modes. Additionally, for both the MAT58 and MAT213 models, it was found that either the crush force or the failure mode could be modeled accurately, but no set of parameters could be identified to attain both results in the same model. Once satisfactory calibration was achieved, the same material parameters were applied to the stanchion crush simulations. The stanchion simulations showed that MAT213 more accurately predicted the experimentally determined crush force, and both material models predicted key aspects of the experimentally observed failure modes.

Composite Materials↗

NASA NTRS1990

Effect of interleaves on fracture of laminated composites. I - Analysis. II - Solution and results

The effect of interleaves placed between the fiber-reinforced plies of multilayered composite laminates is investigated analytically, with the composite approximated by linearly elastic isotropic media consisting of half-planes separated from a finite-width layer by thin interleaves of low extensional and shear moduli. Integral equations are derived which describe the effect of interleaves on damage growth. Numerical solutions are then developed which are based on Gaussian integration techniques and Hadamard's concept of differentiation of Cauchy integrals. Critical stresses and displacements are calculated to investigate the influence of relative elastic properties and geometry of the interleafed composite on interface debonding, extent and suppression and delamination, and stress relieving in the undamaged plies.

Kaw, A. K.↗

NASA NTRSDate not supplied

Simulations of Yarn Micro-Mechanics of Woven Heat Shield Materials (3MDCP)

Carbon and phenolic fibers are commonly used in ablative thermal protection materials, such as 3-dimensional Mid-Density Carbon Phenolic (3MDCP), a 3D-woven composite comprised of mixed-fiber yarn bundles. Predicting the micro-mechanical response and fracture of twisted yarns composed of brittle and ductile fibers requires a modeling approach that captures per-fiber yielding, fiber fracture, and inter-fiber friction and contact. This work presents an extended bonded particle model (BPM) for discrete element method (DEM) simulation of fiber and yarn mechanics, implemented in LAMMPS. The model builds on the incremental bond formulation of Guo et al. and introduces a piecewise elasto-plastic constitutive law for axial extension, enabling representation of fibers that yield before failure. 3MDCP yarns were constructed using measured fiber radius distributions and helical twist geometry. Tensile simulations of single-ply 3MDCP yarns show good agreement with vender stress–strain results. Fiber breakage models also show details on yarn breakage propagration, centered radially in the yarn. Yarn breakage of multi-ply 3MDCP also matched experimental observations in per-ply breakage; however, predicted yarn breakage strength were found higher than experimental observations.

Woven↗

NASA NTRSDate not supplied

Simulations of Yarn Micro-Mechanics of Woven Heat Shield Materials

Discrete Element Method↗

NASA NTRS2014

Recent Developments and Challenges Implementing New and Improved Stress Intensity Factor (K) Solutions in NASGRO for Damage Tolerance Analyses

Fatigue crack growth analysis software has been available to damage tolerance analysts for many years in either commercial products or via proprietary in-house codes. The NASGRO software has been publicly available since the mid-80s (known as NASA/FLAGRO up to 1999) and since 2000 has been sustained and further developed by a collaborative effort between Southwest Research Institute® (SwRI®), the NASA Johnson Space Center (JSC), and the members of the NASGRO Industrial Consortium. Since the stress intensity factor (K) is the foundation of fracture mechanics and damage tolerance analysis of aircraft structures, a significant focus of development efforts in the past fifteen years has been geared towards enhancing legacy K solutions and developing new and efficient numerical K solutions that can handle the complicated stress gradients computed by today’s analysts using detailed finite element models of fatigue critical locations. This paper provides an overview of K solutions that have been recently implemented or improved for the analysis of geometries such as two unequal through cracks at a hole and two unequal corner cracks at a hole, as well as state-of-the-art weight function models capable of computing K in the presence of univariant and/or bivariant stress gradients and complicated residual stress distributions. Some historical background is provided to review how common K solutions have evolved over the years, including selective examples from the literature and from new research. Challenges and progress in rectifying discrepancies between older legacy solutions and newer models are reviewed as well as approaches and challenges for verification and validation of K solutions. Finally, a summary of current challenges and future research and development needs is presented. A key theme throughout the presentation of this paper will be how members of the aerospace industry have collaborated with software developers to develop a practical analysis tool that is used world-wide to support new design as well as the ongoing sustainment and airworthiness of commercial and military aircraft.

Cardinal, Joseph W.↗

NASA NTRS1973

Growth characteristics of a plane crack subjected to three-dimensional loading

The closed form expressions for the stress intensity factors due to concentrated forces applied to the surfaces of a half plane crack in an infinite body are used to generate solutions for distributed loads in this geometry. The stress intensity factors for uniformly distributed loads applied over a rectangular portion of the crack surface are given in closed form. An example of non-uniformly distributed loads which can be treated numerically is also included. In particular, combinations of normal and shear stresses on the crack which simulate the case of loading at an angle to the crack front are considered. The resulting stress intensity factors are combined with the strain energy density fracture criterion for the purpose of predicting the most likely direction of crack propagation. The critical value of the energy density factor can then be used for determining the allowable load on a specimen with a crack front not perpendicular to the tensile axis.

Hartranft, R. J.↗

NASA NTRS1976

Crack problems in cylindrical and spherical shells

Standard plate or shell theories were used as a starting point to study the fracture problems in thin-walled cylindrical and spherical shells, assuming that the plane of the crack is perpendicular to the surface of the sheet. Since recent studies have shown that local shell curvatures may have a rather considerable effect on the stress intensity factor, the crack problem was considered in conjunction with a shell rather than a plate theory. The material was assumed to be isotropic and homogeneous, so that approximate solutions may be obtained by approximating the local shell crack geometry with an ideal shell which has a solution, namely a spherical shell with a meridional crack, a cylindrical shell with a circumferential crack, or a cylindrical shell with an axial crack. A method of solution for the specially orthotropic shells containing a crack was described; symmetric and skew-symmetric problems are considered in cylindrical shells with an axial crack.

Erdogan, F.↗

NASA NTRS2011

Improved Rare-Earth Emitter Hollow Cathode

An improvement has been made to the design of the hollow cathode geometry that was created for the rare-earth electron emitter described in Compact Rare Earth Emitter Hollow Cathode (NPO-44923), NASA Tech Briefs, Vol. 34, No. 3 (March 2010), p. 52. The original interior assembly was made entirely of graphite in order to be compatible with the LaB6 material, which cannot be touched by metals during operation due to boron diffusion causing embrittlement issues in high-temperature refractory materials. Also, the graphite tube was difficult to machine and was subject to vibration-induced fracturing. This innovation replaces the graphite tube with one made out of refractory metal that is relatively easy to manufacture. The cathode support tube is made of molybdenum or molybdenum-rhenium. This material is easily gun-bored to near the tolerances required, and finish machined with steps at each end that capture the orifice plate and the mounting flange. This provides the manufacturability and robustness needed for flight applications, and eliminates the need for expensive e-beam welding used in prior cathodes. The LaB6 insert is protected from direct contact with the refractory metal tube by thin, graphite sleeves in a cup-arrangement around the ends of the insert. The sleeves, insert, and orifice plate are held in place by a ceramic spacer and tungsten spring inserted inside the tube. To heat the cathode, an insulating tube is slipped around the refractory metal hollow tube, which can be made of high-temperature materials like boron nitride or aluminum nitride. A screw-shaped slot, or series of slots, is machined in the outside of the ceramic tube to constrain a refractory metal wire wound inside the slot that is used as the heater. The screw slot can hold a single heater wire that is then connected to the front of the cathode tube by tack-welding to complete the electrical circuit, or it can be a double slot that takes a bifilar wound heater with both leads coming out the back. This configuration replaces the previous sheathed heater design that limited the cycling-life of the cathode.

Goebel, Dan M.↗

NASA NTRSDate not supplied

Next Generation Durability and Damage Tolerance to Support Certification of Flight Hardware

Durability and Damage Tolerance (D&DT), as currently applied to flight hardware throughout the Agency, is based on continuum and similitude assumptions and does not consider local material properties, environments and responses. These limitations impact our ability to support certification of new component designs, material systems and manufacturing approaches. The primary concern in this Engineering R&A plan is related to the imminent proliferation of parts produced by additive manufacturing (AM). These parts are being advocated by NASA’s suppliers for use on a myriad of flight hardware because of their design flexibility and cost advantages. AM provides opportunities to reduce part counts through complex geometry and reduce manufacturing costs of low volume parts. However, AM materials have some notable metallurgical and microstructural differences compared to traditionally fabricated materials. One of the challenges for the acceptance of AM is the greater tendency for a deleterious defect state, most commonly in the form of porosity, to exist in AM parts. Though this defect state is typically reduced through a hot isostatic pressing (HIP) processing step, the structural performance risks associated with the remaining defects and HIP-healed features is not known. Potential fracture control issues that must be resolved stem from the real possibility that an unhealed defect or a closed defect with less than pristine strength remains at a fracture critical location after HIP. As a result, NASA and the entire aerospace community have been confronted with the need to develop a robust and relevant certification methodology to enable safe implementation of these components. The present work is an important step toward positioning NASA to credibly respond to vendors’ push to implement this new AM materials technology by improving our understanding of AM processing and performance and transitioning that research-based understanding to next-generation engineering capabilities.

Edward H Glaessgen↗

NASA NTRS1986

Finite element analysis of the end notched flexure specimen for measuring Mode II fracture toughness

The paper presents a finite element analysis of the end-notched flexure (ENF) test specimen for Mode II interlaminar fracture testing of composite materials. Virtual crack closure and compliance techniques employed to calculate strain energy release rates from linear elastic two-dimensional analysis indicate that the ENF specimen is a pure Mode II fracture test within the constraints of small deflection theory. Furthermore, the ENF fracture specimen is shown to be relatively insensitive to process-induced cracks, offset from the laminate midplane. Frictional effects are investigated by including the contact problem in the finite element model. A parametric study investigating the influence of delamination length, span, thickness, and material properties assessed the accuracy of beam theory expressions for compliance and strain energy release rate, GII. Finite element results indicate that data reduction schemes based upon beam theory underestimate GII by approximately 20-40 percent for typical unidirectional graphite fiber composite test specimen geometries. Consequently, an improved data reduction scheme is proposed.

Gillespie, J. W., Jr.↗