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All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

On finite deformation elasto-plasticity

Lee (1969) has proposed a theory based on the decomposition of the total deformation gradient to an elastic and plastic part, and from it has concluded that the additive decomposition of the strain rates holds only approximately. Lubarda and Lee (1981) have declared that Lee's 'exact finite-deformation kinematics shows the almost universal assumption that the total velocity strain or rate of deformation is the sum of elastic and plastic rates to be in error'. Hence questions are raised regarding the validity of essentially all finite deformation elasto-plasticity theories. The present investigation is concerned with these questions. It is shown that the additive decomposition of the strain rates follows from all common finite elasto-plasticity concepts. Lee's theory is examined, and it is shown that this theory also leads to an additive strain rate decomposition, and therefore, his conclusion stems from misinterpretation. It is found that the elastic and the plastic strain rates considered by Lee do not correspond to the same configuration. They are, therefore, not compatible measures.

Nemat-Nasser, S.↗
NASA NTRS1983

Micromechanically Based Constitutive Relations for Polycrystalline Solids

A basic method to estimate the overall mechanical response of solids which contain periodically distributed defects is presented. The method estimates the shape and growth pattern of voids periodically distributed over the grain boundaries in a viscous matrix. The relaxed moduli are obtained for a polycrytalline solid that undergoes relaxation by grain boundary sliding which accounts for the interaction effects. The overall inelastic nonlinear response at elevated temperatures in terms of a model which considers nonlinear power law creep within the grains, and linear viscous flow in the grain boundaries is discussed.

Nemat-Nasser, S.↗
NASA NTRS1982

On composites with periodic structure

The overall moduli of a composite with an isotropic elastic matrix containing periodically distributed (anisotropic) inclusions or voids, can be expressed in terms of several infinite series which only depend on the geometry of the inclusions or voids, and hence can be computed once and for all for given geometries. For solids with periodic structures these infinite series play exactly the same role as does Eshelby's tensor for a single inclusion or void in an unbounded elastic medium. For spherical and circular-cylindrical geometries, the required infinite series are calculated and the results are tabulated. These are then used to estimate the overall elastic moduli when either the overall strains or the overall stresses are prescribed, obtaining the same results. These results are compared with other estimates and with experimental data. It is found that the model of composites with periodic structure yields estimates in excellent agreement with the experimental observations.

Nemat-Nasser, S.↗
NASA NTRS1983

Composites with periodic microstructure

For an elastic body containing periodically distributed inhomogeneities, a general procedure is developed for estimating the overall properties of the composite in terms of several infinite series which, for the isotropic matrix (but anisotropic inclusions), depend only on the geometry of the inhomogeneities and hence can be calculated once and for all for each geometry. These infinite series are obtained and tabulated for ellipsoidal inhomogeneities, and the results are used to estimate the overall elastic moduli of composites which contain spherical or ellipsoidal voids or elastic inclusions.

Iwakuma, T.↗
NASA NTRS1983

Growth and stability of interacting surface flaws of arbitrary shape

Growth regimes of interacting surface flaws of arbitrary shape are analyzed with the aid of the body force method, and the stability of the process is assessed on the basis of the variation of the load during the growth. It is shown that irregularly shaped flaws are often associated with very high stress intensity factors locally, which tend to change as the flaws grow into more regular shapes. Several examples of various flaw shapes are worked out for illustration, and it is shown that a simple formula seems to provide an accurate estimate of the maximum stress intensity factor for surface flaws of various shapes, which are not very slender. The formula involves the overall maximum tension, as well as the area of the projection of the flaw on the plane normal to the maximum tension.

Murakami, Y.↗
NASA NTRS1983

Dynamic fields near a crack tip growing in an elastic-perfectly-plastic solid

A full asymptotic solution is presented for the fields in the neighborhood of the tip of a steadily advancing crack in an incompressible elastic-perfectly-plastic solid. There are four findings for mode I crack growth in the plane strain condition. The first is that the entire crack tip in steady crack growth is surrounded by a plastic region and that no elastic unloading is predicted by the complete dynamic asymptotic solution. The second is that, in contrast to the quasi-static solution, the dynamic solution yields strain fields with a logarithmic singularity everywhere near the crack tip. The third is that whereas the stress field varies throughout the entire crack tip neighborhood, it does not exhibit behavior that can be approximated by a constant field followed by an essentially centered-fan field and then by another constant field, especially for small crack growth speeds. The fourth finding is that there are two shock fronts emanating from the crack tip across which certain stress and strain components undergo jump discontinuities. After reviewing the mode III steady-state crack growth, it is concluded that ductile fracture criteria for nonstationary cracks must be based on solutions that include the inertia effects and that for this purpose quasi-static solutions may be inadequate.

Nemat-Nasser, S.↗
NASA NTRS1984

Finite elastic-plastic deformation of polycrystalline metals

Applying Hill's self-consistent method to finite elastic-plastic deformations, the overall moduli of polycrystalline solids are estimated. The model predicts a Bauschinger effect, hardening, and formation of vertex or corner on the yield surface for both microscopically non-hardening and hardening crystals. The changes in the instantaneous moduli with deformation are examined, and their asymptotic behavior, especially in relation to possible localization of deformations, is discussed. An interesting conclusion is that small second-order quantities, such as shape changes of grains and residual stresses (measured relative to the crystal elastic moduli), have a first-order effect on the overall response, as they lead to a loss of the overall stability by localized deformation. The predicted incipience of localization for a uniaxial deformation in two dimensions depends on the initial yield strain, but the orientation of localization is slightly less than 45 deg with respect to the tensile direction, although the numerical instability makes it very difficult to estimate this direction accurately.

Iwakuma, T.↗
NASA NTRS1984

On stress field near a stationary crack tip

It is well known that the stress and elastic-plastic deformation fields near a crack tip have important roles in the corresponding fracture process. For elastic-perfectly-plastic solids, different solutions are given in the literature. In this work several of these solutions are examined and compared for Mode I (tension), Mode II (shear), and mixed Modes I and II loading conditions in plane strain. By consideration of the dynamic solution, it is shown that the assumption that the material is yielding all around a crack tip may not be reasonable in all cases. By admitting the existence of some elastic sectors, continuous stress fields are obtained even for mixed Modes I and II.

Nemat-Nasser, S.↗
NASA NTRS2020

Roman Space Telescope Coronagraph Engineering Design and Operating Concept

NASA’s Nancy Grace Roman Space Telescope (formerly known as WFIRST) is a flagship astrophysics mission planned for launch in 2025. The coronagraph instrument (CGI) on Roman will demonstrate the technology for direct imaging and spectroscopy of exoplanets around nearby stars. It will work with the obscured 2.4 meter diameter telescope and demonstrate starlight suppression that is up to 3 orders of magnitude deeper than the preceding space-based and ground-based coronagraphs by using active wavefront control in space with deformable mirrors. CGI has passed its Preliminary Design Review (PDR) in September 2019 and is working toward the instrument Critical Design Review (CDR) in the spring of 2021. We will describe the flow down of key and driving CGI requirements from high level performance to the instrument hardware and software, current instrument configuration and engineering design, operational concept planned for CGI observations, integrated modeling status, and performance predictions.

Tanga, Hong↗