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All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Notes and comments on computational elastoplasticity - Some new models and their numerical implementation

The following topics are discussed in this paper: (1) the basic interactive nature of classical elasto-plasticity and a redefinition of elastic and plastic processes that facilitates numerical calculations, (2) generalized mid-point or end-point algorithms to determine the stress increment in an elastic-plastic solid from a given strain increment, (3) an endochronic (internal time) rate theory of time-independent plasticity which encompasses various multiple-yield-surface theories and nonlinear kinematic hardening theories as its specializations, and (4) comments on finite element and boundary element methods for solving boundary value problems in elasto-plasticity.

Atluri, S. N.↗
NASA NTRS1990

A constitutive model for AS4/PEEK thermoplastic composites under cyclic loading

Based on the basic and essential features of the elastic-plastic response of the AS4/PEEK thermoplastic composite subjected to off-axis cyclic loadings, a simple rate-independent constitutive model is proposed to describe the orthotropic material behavior for cyclic loadings. A one-parameter memory surface is introduced to distinguish the virgin deformation and the subsequent deformation process and to characterize the loading range effect. Cyclic softening is characterized by the change of generalized plastic modulus. By the vanishing yield surface assumption, a yield criterion is not needed and it is not necessary to consider loading and unloading separately. The model is compared with experimental results and good agreement is obtained.

Rui, Yuting↗
NASA NTRS1991

Fluid volcanism on Miranda and Ariel - Flow morphology and composition

Several types of volcanic units have been recognized on the icy Uranian satellites Miranda and Ariel. On Miranda, ridges characterized by crest grooves are up to 10 km wide and 500 m high. A continuous flat-topped flow band also 10 km wide and 500 m high forms the outer southern margin of Elsinore Corona, which appears to comprise coalesced flow bands and ridges. On Ariel, in addition to at least one ridge unit similar to those on Miranda, flood plains material has covered the floors of deep chasmata (grabens) and an irregular depression. Flows on both satellites are characterized by linear vent geometries and distinct topographic margins, which indicate extrusion of a relatively viscous material. The topography of the flows can be used to estimate flow viscosity or yield strength using a Bingham plastic model. Extrusion viscosity estimates, incorporating plausible volcanologically based emplacement time scales and a rigid crust correction, range from 10 MP to 1 GP (10 TP in the unlikely absence of a chilled crust). Viscosity estimates are dependent on the assumed emplacement time scale, however, and could be as high as 10 PP, if a solid-state-based time scale is assumed.

Schenk, Paul M.↗
NASA NTRS1978

Yield strengths of flows on the earth, Mars, and moon

Dimensions of flows on the earth, Mars, and moon and their topographic gradients obtained from remote measurements are used to calculate yield strengths with a view to explore the validity of the Bingham plastic model and determine whether there is a relation between yield strengths and silica contents. Other factors are considered such as the vagaries of natural phenomena that might contribute to erroneous interpretations and measurements. Comparison of yield strengths of Martian and lunar flows with terrestrial flows suggests that the Martian and lunar flows are more akin to terrestrial basalts than they are to terrestrial andesites, trachytes, and rhyolites.

Moore, H. J.↗
NASA NTRS1984

Dugdale plastic zone size and CTOD equations for the compact specimen

With the aim of applying the Dugdale model to the compact specimen, the equations for stress intensity factor and crack surface displacement are obtained for a pair of pin loads and a uniform stress acting on a segment of the crack surface. The plastic zone size is calculated from the 'finiteness' condition of Dugdale, and the results agree well with collocation results from Terada (1983). The load that causes incipient yielding at the compression point of the compact specimen is calculated from a finite element strip yield analysis for an elastic-perfectly plastic material. The crack tip opening displacement for the compact specimen is calculated by adding the displacement at the tip of the physical crack length due to the pin load and due to the uniform stress. The results are within 1.5 percent of current collocation results.

Newman, J. C., Jr.↗
NASA NTRS1993

On the development of constitutive relations for metallic powders

This article describes the development of elastic and plastic constitutive relations as functions of relative density for partially consolidated -100 mesh aluminum powder. First, measurements of yield stress as a function of stress state and relative density are described. Measurements of the plastic strain increments associated with yielding in unconstrained compression tests and elastic properties, both as functions of relative density, are also described. The experimental results are combined with the associated flow rule to show that the yield surface is asymmetric with respect to hydrostatic tension and compression. Second, it is shown that the yield stress results can be represented by a two-part (capped Drucker-Prager) yield surface. The consolidation yield surface moves along the hydrostatic stress axis during densification, while the shear yield surface approaches the Mises yield surface. For the Al powder used in the present investigation, superposition of shear stress on a hydrostatic stress state aids the densification process. However, the hydrostatic stress requirement was found to be reduced by only about 20 pct for relative densities below 0.98.

Watson, T. J.↗
NASA NTRS1975

Effect of crack initiation, stable crack growth and unstable crack propagation on the crack-tip plastic zone

A technique for measuring the plastic zones associated with initial crack-tip yielding, subcritical crack growth, and unstable fracture is discussed. The results of the measurement of the locus of these yield regions, on center-cracked sheet and compact tension specimens of 7075-T6, 7075-T651, and 2024-T3 aluminum, are reported in this paper. It was found that a very accurate representation of the strains was obtained by this method and that the results added significant insight into the fracture process. The plastic zones were found to be approximately eight times wider in 2024-T3 than in the 7075-T6 sheets. The yield zones approached a maximum value after unstable fracture was attained and maintained that size through the fast fracture region. As expected, the plastic zones in the compact tension specimen were associated only with the formation of the shear lips and no plastic zones were observed in the fatigue precracked regions of either the center-cracked or compact-tension specimens.

Poulose, P. K.↗
NASA NTRS1974

Small-scale yielding analysis of mixed mode plane-strain crack problems

The small-scale yielding analysis of an elastic-plastic body with a line crack under plane-strain conditions subject to combinations of Mode I and II loadings is examined. The analysis of the near-tip field follows the works of Hutchinson and Rice and Rosengren. Dominant singularity solutions governing the asymptotic behavior of the stresses and strains at the crack tip are obtained for the complete range of loadings between Mode I and II. The results of an accurate finite element technique, which imbeds the dominant singularity solutions, directly relates the near-tip behavior to the elastic stress intensity factors K(I) and K(II). Implications of this study to mixed mode fracture mechanics is also discussed, particularly with respect to the direction of crack initiation and the relation of fracture toughness under mixed modes to that in Mode I. Details of the mixed mode plastic zone sizes and shapes are also given.

Shih, C. F.↗
NASA NTRS1993

The origin of Venusian channels: Modelling of thermal erosion by lava

Magellan imagery has revealed that channels, apparently volcanic in origin, are abundant on the surface of Venus. There has been much debate about the origin of these channels. Are they the result of erosional (either thermal or mechanical) or constructional processes? A common characteristic of the simple sinuous channels is that they show evidence of erosion near their source and then become purely constructional, forming levees and in some cases roofing over completely. One method of showing that thermal erosion is capable of producing the type of channels seen is to use computer modeling incorporating the physical conditions on Venus and the physical characteristics of the different types of lava that may have been erupted. It is possible to calculate, relatively easily, two channel parameters. The first is the erosion rate, which combined with eruption duration, gives depth. The second is for how long after leaving the source the erupted lava will continue to be capable of thermal erosion before constructional processes dominate. Making assumptions about the rheology of the lava (e.g., assume it behaves as a Bingham plastic) along with the slope angle yields a flow velocity and therefore a distance over which thermal erosion will take place. Due to the resolution (both vertical and horizontal) of the Magellan altimetric data, the distance from the source that the channel is erosional can be much more accurately measured than the depth of the channel. This will remain the case until stereo imagery becomes available for large areas of the planet.

Bussey, D. B. J.↗
NASA NTRS1999

Residual Strength Prediction of Fuselage Structures with Multiple Site Damage

This paper summarizes recent results on simulating full-scale pressure tests of wide body, lap-jointed fuselage panels with multiple site damage (MSD). The crack tip opening angle (CTOA) fracture criterion and the FRANC3D/STAGS software program were used to analyze stable crack growth under conditions of general yielding. The link-up of multiple cracks and residual strength of damaged structures were predicted. Elastic-plastic finite element analysis based on the von Mises yield criterion and incremental flow theory with small strain assumption was used. A global-local modeling procedure was employed in the numerical analyses. Stress distributions from the numerical simulations are compared with strain gage measurements. Analysis results show that accurate representation of the load transfer through the rivets is crucial for the model to predict the stress distribution accurately. Predicted crack growth and residual strength are compared with test data. Observed and predicted results both indicate that the occurrence of small MSD cracks substantially reduces the residual strength. Modeling fatigue closure is essential to capture the fracture behavior during the early stable crack growth. Breakage of a tear strap can have a major influence on residual strength prediction.

Chen, Chuin-Shan↗
NASA NTRS2006

The Equivalence of the Radial Return and Mendelson Methods for Integrating the Classical Plasticity Equations

The radial return and Mendelson methods for integrating the equations of classical plasticity, which appear independently in the literature, are shown to be identical. Both methods are presented in detail as are the specifics of their algorithmic implementation. Results illustrate the methods' equivalence across a range of conditions and address the question of when the methods require iteration in order for the plastic state to remain on the yield surface. FORTRAN code implementations of the radial return and Mendelson methods are provided in the appendix.

Bednarcyk, Brett A.↗
NASA NTRS2012

Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures

A research program has been developed to quantify the effects of the microstructure of a woven ceramic matrix composite and its variability on the effective properties and response of the material. In order to characterize and quantify the variations in the microstructure of a five harness satin weave, chemical vapor infiltrated (CVI) SiC/SiC composite material, specimens were serially sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source quantitative image analysis tools were then used to isolate the constituents, from which two dimensional finite element models were generated which approximated the actual specimen section geometry. A simplified elastic-plastic model, wherein all stress above yield is redistributed to lower stress regions, is used to approximate the progressive damage behavior for each of the composite constituents. Finite element analyses under in-plane tensile loading were performed to examine how the variability in the local microstructure affected the macroscopic stress-strain response of the material as well as the local initiation and progression of damage. The macroscopic stress-strain response appeared to be minimally affected by the variation in local microstructure, but the locations where damage initiated and propagated appeared to be linked to specific aspects of the local microstructure.

Mital, Subodh K.↗
NASA NTRS2005

Mechanical Behavior of Gamma-Met PX under Uniaxial Loading at Elevated Temperatures and High Strain Rates

Gamma titanium aluminides have received considerable attention over the last decade. These alloys are known to have low density, good high temperature strength retention and good oxidation and corrosion resistance. However, poor ductility and low fracture toughness have been the key limiting factors in the full utilization of these alloys. More recently, a new generation of gamma titanium aluminide alloys, commonly referred to as Gamma-met PX, has been developed by GKSS, Germany. These alloys have been observed to have superior strength and better oxidation resistance at elevated temperatures when compared with conventional gamma titanium aluminides. The present paper discusses results of a study to understand the uniaxial mechanical behavior in both compression and tension of Gamma-Met PX at elevated temperatures and high strain rates. The compression and tensile tests are conducted using a modified split-Hopkinson bar apparatus at test temperatures ranging from room temperature to 900 C and strain rates of up to 3500/s. Under uniaxial compression, in the temperature range from room to 600 C, the flow stress is observed to be nearly independent of test temperature. However, at temperatures higher than 600 C thermal softening is observed at all strain rates with the rate of thermal softening increasing dramatically between 800 C and 900 C. The room temperature tensile tests show negligible strain-rate dependence on both yield stress and flow stress. With an increase in test temperature from room to 900 C the material shows a drop in both yield and flow stress at all levels of plastic strain. However, the measured flow stress is still higher when compared to nickel based super-alloys and other gamma titanium aluminides under similar test conditions. Also, no anomaly in yield stress is observed up to 900 C.

Shazly, Mostafa↗
NASA NTRS1976

Ductile fracture of cylindrical vessels containing a large flaw

The fracture process in pressurized cylindrical vessels containing a relatively large flaw is considered. The flaw is assumed to be a part-through or through meridional crack. The flaw geometry, the yield behavior of the material, and the internal pressure are assumed to be such that in the neighborhood of the flaw the cylinder wall undergoes large-scale plastic deformations. Thus, the problem falls outside the range of applicability of conventional brittle fracture theories. To study the problem, plasticity considerations are introduced into the shell theory through the assumptions of fully-yielded net ligaments using a plastic strip model. Then a ductile fracture criterion is developed which is based on the concept of net ligament plastic instability. A limited verification is attempted by comparing the theoretical predictions with some existing experimental results.

Erdogan, F.↗
NASA NTRS1976

Finite element solutions for crack-tip behavior in small-scale yielding

The subject considered is the stress and deformation fields in a cracked elastic-plastic power law hardening material under plane strain tensile loading. An incremental plasticity finite element formulation is developed for accurate analysis of the complete field problem including the extensively deformed near tip region, the elastic-plastic region, and the remote elastic region. The formulation has general applicability and was used to solve the small scale yielding problem for a set of material hardening exponents. Distributions of stress, strain, and crack opening displacement at the crack tip and through the elastic-plastic zone are presented as a function of the elastic stress intensity factor and material properties.

Tracey, D. M.↗
NASA NTRS2008

Elastic-Plastic Fracture Mechanics Analysis of Critical Flaw Size in ARES I-X Flange-to-Skin Welds

NASA's Ares 1 Upper Stage Simulator (USS) is being fabricated from welded A516 steel. In order to insure the structural integrity of these welds it is of interest to calculate the critical initial flaw size (CIFS) to establish rational inspection requirements. The CIFS is in turn dependent on the critical final flaw size (CFS), as well as fatigue flaw growth resulting from transportation, handling and service-induced loading. These calculations were made using linear elastic fracture mechanics (LEFM), which are thought to be conservative because they are based on a lower bound, so called elastic, fracture toughness determined from tests that displayed significant plasticity. Nevertheless, there was still concern that the yield magnitude stresses generated in the flange-to-skin weld by the combination of axial stresses due to axial forces, fit-up stresses, and weld residual stresses, could give rise to significant flaw-tip plasticity, which might render the LEFM results to be non-conservative. The objective of the present study was to employ Elastic Plastic Fracture Mechanics (EPFM) to determine CFS values, and then compare these values to CFS values evaluated using LEFM. CFS values were calculated for twelve cases involving surface and embedded flaws, EPFM analyses with and without plastic shakedown of the stresses, LEFM analyses, and various welding residual stress distributions. For the cases examined, the computed CFS values based on elastic analyses were the smallest in all instances where the failures were predicted to be controlled by the fracture toughness. However, in certain cases, the CFS values predicted by the elastic-plastic analyses were smaller than those predicted by the elastic analyses; in these cases the failure criteria were determined by a breakdown in stress intensity factor validity limits for deep flaws (a greater than 0.90t), rather than by the fracture toughness. Plastic relaxation of stresses accompanying shakedown always increases the calculated CFS values compared to the CFS values determined without shakedown. Thus, it is conservative to ignore shakedown effects.

Chell, G. Graham↗
NASA NTRS1986

Constitutive modeling of cyclic plasticity and creep, using an internal time concept

Using the concept of an internal time as related to plastic strains, a differential stress-strain relation for elastoplasticity is rederived, such that (1) the concept of a yield-surface is retained; (2) the definitions of elastic and plastic processes are analogous to those in classical plasticity theory; and (3) its computational implementation, via a 'tangent-stiffness' finite element method and a 'generalized-midpoint-radial-return' stress-integration algorithm, is simple and efficient. Also, using the concept of an internal time, as related to both the inelastic strains as well as the Newtonian time, a constitutive model for creep-plasticity interaction, is discussed. The problem of modeling experimental data for plasticity and creep, by the present analytical relations, as accurately as desired, is discussed. Numerical examples which illustrate the validity of the present relations are presented for the cases of cyclic plasticity and creep.

Watanabe, O.↗