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NASA NTRS1988

A virtual crack-closure technique for calculating stress intensity factors for cracked three dimensional bodies

A three-dimensional virtual crack-closure technique is presented which calculates the strain energy release rates and the stress intensity factors using only nodal forces and displacements from a standard finite element analysis. The technique is an extension of the Rybicki-Kanninen (1977) method, and it assumes that any continuous function can be approximated by a finite number of straight line segments. Results obtained by the method for surface cracked plates with and without notches agree favorably with previous results.

Shivakumar, K. N.↗

NASA NTRS1993

Role of secondary instability theory and parabolized stability equations in transition modeling

In modeling the laminar-turbulent transition region, the designer depends largely on benchmark data from experiments and/or direct numerical simulations that are usually extremely expensive. An understanding of the evolution of the Reynolds stresses, turbulent kinetic energy, and quantifies in the transport equations like the dissipation and production is essential in the modeling process. The secondary instability theory and the parabolized stability equations method are used to calculate these quantities, which are then compared with corresponding quantities calculated from available direct numerical simulation data for the incompressible boundary-layer flow of laminar-turbulent transition conditions. The potential of the secondary instability theory and the parabolized stability equations approach in predicting these quantities is discussed; results indicate that inexpensive data that are useful for transition modeling in the early stages of the transition region can be provided by these tools.

El-Hady, Nabil M.↗

NASA NTRS2009

Calculation of Stress Intensity Factors for Interfacial Cracks in Fiber Metal Laminates

Stress intensity factors for interfacial cracks in Fiber Metal Laminates (FML) are computed by using the displacement ratio method recently developed by Sun and Qian (1997, Int. J. Solids. Struct. 34, 2595-2609). Various FML configurations with single and multiple delaminations subjected to different loading conditions are investigated. The displacement ratio method requires the total energy release rate, bimaterial parameters, and relative crack surface displacements as input. Details of generating the energy release rates, defining bimaterial parameters with anisotropic elasticity, and selecting proper crack surface locations for obtaining relative crack surface displacements are discussed in the paper. Even though the individual energy release rates are nonconvergent, mesh-size-independent stress intensity factors can be obtained. This study also finds that the selection of reference length can affect the magnitudes and the mode mixity angles of the stress intensity factors; thus, it is important to report the reference length used with the calculated stress intensity factors.

Wang, John T.↗

NASA NTRS1981

Edge delamination in angle-ply composite laminates, part 5

A theoretical method was developed for describing the edge delamination stress intensity characteristics in angle-ply composite laminates. The method is based on the theory of anisotropic elasticity. The edge delamination problem is formulated using Lekhnitskii's complex-variable stress potentials and an especially developed eigenfunction expansion method. The method predicts exact orders of the three-dimensional stress singularity in a delamination crack tip region. With the aid of boundary collocation, the method predicts the complete stress and displacement fields in a finite-dimensional, delaminated composite. Fracture mechanics parameters such as the mixed-mode stress intensity factors and associated energy release rates for edge delamination can be calculated explicity. Solutions are obtained for edge delaminated (theta/-theta theta/-theta) angle-ply composites under uniform axial extension. Effects of delamination lengths, fiber orientations, lamination and geometric variables are studied.

Wang, S. S.↗

NASA NTRS1985

Dynamic fracture mechanics

Dynamic fracture and crack propagation concepts for ductile materials are reviewed. The equations for calculating dynamic stress integrity and the dynamic energy release rate in order to study dynamic crack propagation are provided. The stress intensity factor versus crack velocity relation is investigated. The uses of optical experimental techniques and finite element methods for fracture analyses are described. The fracture criteria for a rapidly propagating crack under mixed mode conditions are discussed; crack extension and fracture criteria under combined tension and shear loading are based on maximum circumferential stress or energy criteria such as strain energy density. The development and use of a Dugdale model and finite element models to represent crack and fracture dynamics are examined.

Kobayashi, A. S.↗

NASA NTRS1973

A method for calculating unsteady turbulent boundary layers in two- and three-dimensional flows.

The governing equations for an unsteady turbulent boundary layer on a swept infinite cylinder, composed of a continuity equation, a pair of momentum equations and a pair of rate equations for the shear stress, based on the turbulent kinetic-energy equation, are solved numerically. These rate equations for the shear-stress express a balance between the convection, production, dissipation and diffusion of the turbulent shear stress components. Due to the physical model of turbulence employed, this system of equations is hyperbolic. An explicit, second-order accurate, conditionally stable difference scheme for this system, together with appropriate boundary and initial conditions, is formulated and developed into a computer program. Calculations for oscillating free stream flows with no pressure gradient show significant unsteady effects on the turbulent boundary layer.

Singleton, R. E.↗

NASA NTRS1993

A numerical study of confined turbulent jets

A numerical investigation is reported of turbulent incompressible jets confined in two ducts, one cylindrical and the other conical with a 5 degree divergence. In each case, three Craya-Curtet numbers are considered which correspond, respectively, to flow situations with no moderate and strong recirculation. Turbulence closure is achieved by using the k-epsilon model and a recently proposed realizable Reynolds stress algebraic equation model that relates the Reynolds stresses explicitly to the quadratic terms of the mean velocity gradients and ensures the positiveness of each component of the turbulent kinetic energy. Calculations are carried out with a finite-volume procedure using boundary-fitted curvilinear coordinates. A second-order accurate, bounded convection scheme and sufficiently fine grids are used to prevent the solutions from being contaminated by numerical diffusion. The calculated results are compared extensively with the available experimental data. It is shown that the numerical methods presented are capable of capturing the essential flow features observed in the experiments and that the realizable Reynolds stress algebraic equation model performs much better than the k-epsilon model for this class of flows of great practical importance.

Zhu, J.↗

NASA NTRS1982

Separated trailing-edge flow at a transonic Mach number

Results from an experimental investigation of a small-scale separated flow at a sharp trailing edge are presented. The separated flow was a result of sustained adverse pressure gradients. Experiments were carried out at a transonic Mach number, without any shock wave in the flow, and at a high Reynolds number. Measurements include surface pressure distributions, mean velocity, turbulent shear stress, turbulent kinetic energy, and some streamwise turbulence intensity profiles in the region from just upstream of separation to downstream into the near-wake, following wake-closure. The results show noticeable changes in the mean and turbulent quantities in the separated region although the wall adverse pressure gradients are relatively weak. Turbulent normal stress becomes important in the vicinity of separation and in the separated zone with regard to both mean-flow development and turbulence-energy production. The experimental data are used to assess the performance of two boundary-layer calculation methods.

Viswanath, P. R.↗

NASA NTRS1994

VAPEPS Management Center

A VibroAcoustic Payload Environment Prediction System (VAPEPS) Management Center is established and being maintained at JPL. VAPEPS is a computer program that utilizes statistical energy analysis (SEA) theory and SEA extrapolation methods to predict the vibroacoustic environments of complex systems. The program is commonly utilized to establish random vibration and acoustic test requirements for aerospace components exposed to launch environments. It can also be used in the payload or launch vehicle design process for control or mitigation of the launch or on-orbit vibration and acoustic environments, as well as to calculate acoustically induced stresses in structures such as solar panels and reflectors.

VAPEPS↗

NASA NTRS1986

Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite volume, time marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier Stokes equations. The entire calculation is performed in the physical domain. The method is currently limited to the calculation of attached flows. The features of the current method can be summarized as follows. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is now needed. Different time steps are used in the different governing equations to improve the convergence speed of the viscous calculations. A new pressure interpolation scheme is introduced which improves the shock capturing ability of the method. A multi-volume method for pressure changes in the boundary layer allows calculations which use very long and thin control volumes. A special discretization technique is also used to stabilize these calculations. A special formulation of the energy equation is used to provide improved transient behavior of solutions which use the full energy equation. The method is then compared with a wide variety of test cases. The freestream Mach numbers range from 0.075 to 2.8 in the calculations. Transonic viscous flow in a converging diverging nozzle is calculated with the method; the Mach number upstream of the shock is approximately 1.25. The agreement between the calculated and measured shock strength and total pressure losses is good. Essentially incompressible turbulent boundary layer flow in a adverse pressure gradient is calculated and the computed distribution of mean velocity and shear stress are in good agreement with the measurements. At the other end of the Mach number range, a flat plate turbulent boundary layer with a freestream Mach number of 2.8 is calculated using the full energy equation; the computed total temperature distribution and recovery factor agree well with the measurements when a variable Prandtl number is used through the boundary layer.

Nicholson, S.↗

NASA NTRSDate not supplied

Testing the Efficacy of Laser Sterilization as A Spacecraft Bioburden Reduction Alternative

As NASA continues to put forth efforts in seeking out life in the solar system with missions like Europa Clipper, Mars Sample Return, and Dragonfly, reducing the bioburden (number of living microbes) on spacecraft is required by NASA policy for the protection of potentially habitable worlds. In this project, we are testing the efficacy of a novel method for laser sterilization on stress tolerant bacterial spores (Bacillus subtilis) using a high energy femtosecond laser. To test the laser, we inoculate metal coupons with Bacillus subtilis spores. After laser treatment, we do a PVA (polyvinyl acetate) peel to recover the spores then we calculate to find the number of spores that survived the treatment. Our results show that within a certain pulse count range, increasing fluence increases sterilization effectiveness. We have demonstrated the ability to reduce viable microbial counts by at least 10-4. By studying laser sterilization, we could change the way spacecraft are sterilized by making the process more efficient and cost-effective.

Planetary protection↗

NASA NTRS1996

Element Library for Three-Dimensional Stress Analysis by the Integrated Force Method

The Integrated Force Method, a recently developed method for analyzing structures, is extended in this paper to three-dimensional structural analysis. First, a general formulation is developed to generate the stress interpolation matrix in terms of complete polynomials of the required order. The formulation is based on definitions of the stress tensor components in term of stress functions. The stress functions are written as complete polynomials and substituted into expressions for stress components. Then elimination of the dependent coefficients leaves the stress components expressed as complete polynomials whose coefficients are defined as generalized independent forces. Such derived components of the stress tensor identically satisfy homogenous Navier equations of equilibrium. The resulting element matrices are invariant with respect to coordinate transformation and are free of spurious zero-energy modes. The formulation provides a rational way to calculate the exact number of independent forces necessary to arrive at an approximation of the required order for complete polynomials. The influence of reducing the number of independent forces on the accuracy of the response is also analyzed. The stress fields derived are used to develop a comprehensive finite element library for three-dimensional structural analysis by the Integrated Force Method. Both tetrahedral- and hexahedral-shaped elements capable of modeling arbitrary geometric configurations are developed. A number of examples with known analytical solutions are solved by using the developments presented herein. The results are in good agreement with the analytical solutions. The responses obtained with the Integrated Force Method are also compared with those generated by the standard displacement method. In most cases, the performance of the Integrated Force Method is better overall.

Kaljevic, Igor↗

NASA NTRS1973

Turbulent kinetic energy equation and free mixing

Calculation of free shear flows was carried out to investigate the usefulness of several concepts which were previously successfully applied to wall flows. The method belongs to the class of differential approaches. The turbulence is taken into account by the introduction of one additional partial differential equation, the transport equation for the turbulent shear stress. The structure of turbulence is modeled after Bradshaw et al. This model was used successfully in boundary layers and its applicability to other flows is demonstrated. The work reported differs substantially from that of an earlier attempt to use this approach for calculation of free flows. The most important difference is that the region around the center line is treated by invoking the interaction hypothesis (concerning the structure of turbulence in the regions separated by the velocity extrema). The compressibility effects on shear layer spreading at low and moderate Mach numbers were investigated. In the absence of detailed experiments in free flows, the evidence from boundary layers that at low Mach numbers the structure of turbulence is unaffected by the compressibility was relied on. The present model was tested over a range of self-preserving and developing flows including pressure gradients using identical empirical input. The dependence of the structure of turbulence on the spreading rate of the shear layer was established.

Morel, T.↗

NASA NTRS1940

The Torsion of Box Beams with One Side Lacking

The torsion of box beams of rectangular section, the edges of which are strengthened by flanges, and of which one side is lacking, is analyzed by the energy method. The torsional stresses are generally taken up by the bending of the two parallel walls, the rigidity of which is augmented by the third wall. The result was checked experimentally on duralumin and plywood boxes. The torsion recorded was 10 to 30 percent less than that given by the calculation, owing to self-stiffening.

Cambilargiu, E↗

NASA NTRS1984

A comparison of several methods of calculating fracture toughness from composite laminate test data

Critical fracture toughness was determined by two different techniques for graphite/epoxy laminates of three stacking sequences and several thicknesses. Critical fracture toughness was determined by a finite element stress analysis of a center-cracked tension specimen which yielded the stress intensity factor as a function of specimen thickness and applied load. As an alternative approach the critical strain energy release rate was determined from the compliance calibration technique. Test results from both procedures are compared and discussed.

Harris, C. E.↗

NASA NTRS1986

Analysis of mixed-mode crack propagation using the boundary integral method

Crack propagation in a rotating inner raceway of a high speed roller bearing is analyzed using the boundary integral equation method. The method consists of an edge crack in a plate under tension, upon which varying Hertzian stress fields are superimposed. A computer program for the boundary integral equation method was written using quadratic elements to determine the stress and displacement fields for discrete roller positions. Mode I and Mode II stress intensity factors and crack extension forces G sub 00 (energy release rate due to tensile opening mode) and G sub r0 (energy release rate due to shear displacement mode) were computed. These calculations permit determination of that crack growth angle for which the change in the crack extension forces is maximum. The crack driving force was found to be the alternating mixed-mode loading that occurs with each passage of the most heavily loaded roller. The crack is predicted to propagate in a step-like fashion alternating between radial and inclined segments, and this pattern was observed experimentally. The maximum changes DeltaG sub 00 and DeltaG sub r0 of the crack extension forces are found to be good measures of the crack propagation rate and direction.

Mendelson, A.↗

NASA NTRS1982

Three dimensional flow field inside compressor rotor, including blade boundary layers

The Reynolds stress equation, pressure strain correlation, and dissipative terms and diffusion are discussed in relation to turbulence modelling using the Reynolds stress model. Algebraic modeling of Reynolds stresses and calculation of the boundary layer over an axial cylinder are examined with regards to the kinetic energy model for turbulence modelling. The numerical analysis of blade and hub wall boundary layers, and an experimental study of rotor blade boundary layer in an axial flow compressor rotor are discussed. The Patankar-Spalding numerical method for two dimensional boundary layers is included.

Galmes, J. M.↗

NASA NTRSDate not supplied

Derivation and Testing of Consumptive Water Use Fraction for Specialty Crops

The Crop Consumptive Use Fraction (CCUF) expresses beneficial water use in the form of seasonal evapotranspiration of applied water (ETAW), relative to total irrigation volume. The metric is an indicator of the efficiency of agricultural water use and is a recommended component for preparation of agricultural water management plans in California. An FAO-56 based web application has been developed to facilitate retrospective evaluation of ETAW, and hence CCUF, at field level. The current application is optimized for prevailing climate in four of the state’s main growing regions: San Joaquin Valley, Sacramento Valley, Central Coast, and North Coast. User inputs include crop type, soil texture, irrigation method, daily irrigation volume, daily rainfall, and seasonal start/stop dates to define the analysis period. Time series of fractional green canopy cover (Fc), based on Landsat and Sentinel-2 Earth-resource satellite observations, are imported from NASA’s Satellite Irrigation Management Support (SIMS) system. Grass reference evapotranspiration (ETo) time series are accessed from Spatial CIMIS (California Irrigation Management Information System). Daily crop height (h) is estimated as a simple function of typical maximum height for the given crop type (from FAO-56) and Fc. A vegetation density coefficient (Kd) is derived from Fc and h. Stomatal control factors during mid-and late-season are applied to tree and vine crops. Typical values for minimum daily relative humidity and mean daily windspeed, derived from historical CIMIS weather data, are used to correct for regional deviations from standard climate (defined as RHmin=45%, windspeed =2m/s). The resulting daily basal crop coefficient (Kcb) represents the ET of a well-watered crop with minimal soil evaporation, relative to ETo. A soil water balance sub-model for the top 0.1 m is used to calculate daily evaporation coefficients (Ke). A second sub-model applies to the root zone to calculate crop water stress coefficients (Ks) and effective precipitation (Pe), which is the fraction of rainfall that is available for crop use. Those coefficients are combined with Kcb and ETo to calculate daily ETc. ETAW is then derived as cumulative ETc less cumulative Pe. For verification purposes, sensor installations were used to measure seasonal ETc in commercial fields for several annual and perennial specialty crops by soil water balance and energy balance methods. Model estimates of seasonal ETc show mean absolute error of <10% compared to the ground measurements.

Derivation↗