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NASA NTRS1982

Advances and trends in plate buckling research

Advances and current trends in plate bucklin research are summarized. The field is divided into three parts: (1) classical buckling studies, including plates of rectangular, circular and other shapes; (2) classical complicating effects, including elastic foundation, anisotropic material, variable thickness, shear deformation and nonhomogeneous material; and (3) nonclassical considerations, including postbuckling, imperfections, parametric excitation, follower forces, magnetoelastic buckling and inelastic buckling.

Leissa, A.↗

NASA NTRS2000

Implementation of Laminate Theory Into Strain Rate Dependent Micromechanics Analysis of Polymer Matrix Composites

A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to impact loads. Previously, strain rate dependent inelastic constitutive equations developed to model the polymer matrix were implemented into a mechanics of materials based micromechanics method. In the current work, the computation of the effective inelastic strain in the micromechanics model was modified to fully incorporate the Poisson effect. The micromechanics equations were also combined with classical laminate theory to enable the analysis of symmetric multilayered laminates subject to in-plane loading. A quasi-incremental trapezoidal integration method was implemented to integrate the constitutive equations within the laminate theory. Verification studies were conducted using an AS4/PEEK composite using a variety of laminate configurations and strain rates. The predicted results compared well with experimentally obtained values.

Goldberg, Robert K.↗

NASA NTRS1982

Some inelastic effects of thermal cycling on ZrO2-Y2O3 materials

An analysis has been developed which relates the effects of inelastic behavior of Y2O3 stabilized ZrO2 (YSZ) materials. The results show these materials to be sensitive to small changes in temperature and are supported by measurements of inelastic behavior in disk and bar specimens at temperatures as low as 1010 C (1850 F). At higher thermomechanical loads, the test specimens can deform to strains greater than 1 percent and for bar specimens, with sufficient strength, to remain bonded to the metallic substrate.

Hendricks, R. C.↗

NASA NTRS1982

Some inelastic effects of thermal cycling on yttria-stabilized zirconia

The effects of inelastic behavior of yttria-stabilized zirconia (YSZ) materials were analyzed. The results show these materials to be sensitive to small changes in temperature and are supported by measurements of inelastic behavior in disc and bar specimens at temperatures as low as 1010 C (1850 F). At higher thermomechanical loadings, the test specimens can deform to strains above 1 percent.

Hendricks, R. C.↗

NASA NTRS2002

Deformation, Failure, and Fatigue Life of SiC/Ti-15-3 Laminates Accurately Predicted by MAC/GMC

NASA Glenn Research Center's Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) (ref.1) has been extended to enable fully coupled macro-micro deformation, failure, and fatigue life predictions for advanced metal matrix, ceramic matrix, and polymer matrix composites. Because of the multiaxial nature of the code's underlying micromechanics model, GMC--which allows the incorporation of complex local inelastic constitutive models--MAC/GMC finds its most important application in metal matrix composites, like the SiC/Ti-15-3 composite examined here. Furthermore, since GMC predicts the microscale fields within each constituent of the composite material, submodels for local effects such as fiber breakage, interfacial debonding, and matrix fatigue damage can and have been built into MAC/GMC. The present application of MAC/GMC highlights the combination of these features, which has enabled the accurate modeling of the deformation, failure, and life of titanium matrix composites.

Bednarcyk, Brett A.↗

NASA NTRS2004

Modeling the Nonlinear, Strain Rate Dependent Deformation of Shuttle Leading Edge Materials with Hydrostatic Stress Effects Included

An analysis method based on a deformation (as opposed to damage) approach has been developed to model the strain rate dependent, nonlinear deformation of woven ceramic matrix composites, such as the Reinforced Carbon Carbon (RCC) material used on the leading edges of the Space Shuttle. In the developed model, the differences in the tension and compression deformation behaviors have also been accounted for. State variable viscoplastic equations originally developed for metals have been modified to analyze the ceramic matrix composites. To account for the tension/compression asymmetry in the material, the effective stress and effective inelastic strain definitions have been modified. The equations have also been modified to account for the fact that in an orthotropic composite the in-plane shear response is independent of the stiffness in the normal directions. The developed equations have been implemented into LS-DYNA through the use of user defined subroutines (UMATs). Several sample qualitative calculations have been conducted, which demonstrate the ability of the model to qualitatively capture the features of the deformation response present in woven ceramic matrix composites.

Goldberg, Robert K.↗

NASA NTRS2001

General Multimechanism Reversible-Irreversible Time-Dependent Constitutive Deformation Model Being Developed

Since most advanced material systems (for example metallic-, polymer-, and ceramic-based systems) being currently researched and evaluated are for high-temperature airframe and propulsion system applications, the required constitutive models must account for both reversible and irreversible time-dependent deformations. Furthermore, since an integral part of continuum-based computational methodologies (be they microscale- or macroscale-based) is an accurate and computationally efficient constitutive model to describe the deformation behavior of the materials of interest, extensive research efforts have been made over the years on the phenomenological representations of constitutive material behavior in the inelastic analysis of structures. From a more recent and comprehensive perspective, the NASA Glenn Research Center in conjunction with the University of Akron has emphasized concurrently addressing three important and related areas: that is, 1) Mathematical formulation; 2) Algorithmic developments for updating (integrating) the external (e.g., stress) and internal state variables; 3) Parameter estimation for characterizing the model. This concurrent perspective to constitutive modeling has enabled the overcoming of the two major obstacles to fully utilizing these sophisticated time-dependent (hereditary) constitutive models in practical engineering analysis. These obstacles are: 1) Lack of efficient and robust integration algorithms; 2) Difficulties associated with characterizing the large number of required material parameters, particularly when many of these parameters lack obvious or direct physical interpretations.

Saleeb, A. F.↗

NASA NTRS2004

Implementation of Improved Transverse Shear Calculations and Higher Order Laminate Theory Into Strain Rate Dependent Analyses of Polymer Matrix Composites

A numerical procedure has been developed to investigate the nonlinear and strain rate dependent deformation response of polymer matrix composite laminated plates under high strain rate impact loadings. A recently developed strength of materials based micromechanics model, incorporating a set of nonlinear, strain rate dependent constitutive equations for the polymer matrix, is extended to account for the transverse shear effects during impact. Four different assumptions of transverse shear deformation are investigated in order to improve the developed strain rate dependent micromechanics model. The validities of these assumptions are investigated using numerical and theoretical approaches. A method to determine through the thickness strain and transverse Poisson's ratio of the composite is developed. The revised micromechanics model is then implemented into a higher order laminated plate theory which is modified to include the effects of inelastic strains. Parametric studies are conducted to investigate the mechanical response of composite plates under high strain rate loadings. Results show the transverse shear stresses cannot be neglected in the impact problem. A significant level of strain rate dependency and material nonlinearity is found in the deformation response of representative composite specimens.

Zhu, Lin-Fa↗

NASA NTRS2017

Effects of Adiabatic Heating on the High Strain Rate Deformation of Polymer Matrix Composites

Polymer matrix composites (PMCs) are increasingly being used in aerospace structures that are expected to experience complex dynamic loading conditions throughout their lifetime. As such, a detailed understanding of the high strain rate behavior of the constituents, particularly the strain rate, temperature, and pressure dependent polymer matrix, is paramount. In this paper, preliminary efforts in modeling experimentally observed temperature rises due to plastic deformation in PMCs subjected to dynamic loading are presented. To this end, an existing isothermal viscoplastic polymer constitutive formulation is extended to model adiabatic conditions by incorporating temperature dependent elastic properties and modifying the components of the inelastic strain rate tensor to explicitly depend on temperature. It is demonstrated that the modified polymer constitutive model is capable of capturing strain rate and temperature dependent yield as well as thermal softening associated with the conversion of plastic work to heat at high rates of strain. The modified constitutive model is then embedded within a strength of materials based micromechanics framework to investigate the manifestation of matrix thermal softening, due to the conversion of plastic work to heat, on the high strain rate response of a T700Epon 862 (T700E862) unidirectional composite. Adiabatic model predictions for high strain rate composite longitudinal tensile, transverse tensile, and in-plane shear loading are presented. Results show a substantial deviation from isothermal conditions; significant thermal softening is observed for matrix dominated deformation modes (transverse tension and in-plane shear), highlighting the importance of accounting for the conversion of plastic work to heat in the polymer matrix in the high strain rate analysis of PMC structures.

polymer matrix composites↗

NASA NTRS2004

Modeling the Nonlinear, Strain Rate Dependent Deformation of Woven Ceramic Matrix Composites With Hydrostatic Stress Effects Included

An analysis method based on a deformation (as opposed to damage) approach has been developed to model the strain rate dependent, nonlinear deformation of woven ceramic matrix composites with a plain weave fiber architecture. In the developed model, the differences in the tension and compression response have also been considered. State variable based viscoplastic equations originally developed for metals have been modified to analyze the ceramic matrix composites. To account for the tension/compression asymmetry in the material, the effective stress and effective inelastic strain definitions have been modified. The equations have also been modified to account for the fact that in an orthotropic composite the in-plane shear stiffness is independent of the stiffness in the normal directions. The developed equations have been implemented into a commercially available transient dynamic finite element code, LS-DYNA, through the use of user defined subroutines (UMATs). The tensile, compressive, and shear deformation of a representative plain weave woven ceramic matrix composite are computed and compared to experimental results. The computed values correlate well to the experimental data, demonstrating the ability of the model to accurately compute the deformation response of woven ceramic matrix composites.

Goldberg, Robert K.↗

NASA NTRS1985

On numerical integration and computer implementation of viscoplastic models

Due to the stringent design requirement for aerospace or nuclear structural components, considerable research interests have been generated on the development of constitutive models for representing the inelastic behavior of metals at elevated temperatures. In particular, a class of unified theories (or viscoplastic constitutive models) have been proposed to simulate material responses such as cyclic plasticity, rate sensitivity, creep deformations, strain hardening or softening, etc. This approach differs from the conventional creep and plasticity theory in that both the creep and plastic deformations are treated as unified time-dependent quantities. Although most of viscoplastic models give better material behavior representation, the associated constitutive differential equations have stiff regimes which present numerical difficulties in time-dependent analysis. In this connection, appropriate solution algorithm must be developed for viscoplastic analysis via finite element method.

Chang, T. Y.↗

NASA NTRS1988

MHOST: An efficient finite element program for inelastic analysis of solids and structures

An efficient finite element program for 3-D inelastic analysis of gas turbine hot section components was constructed and validated. A novel mixed iterative solution strategy is derived from the augmented Hu-Washizu variational principle in order to nodally interpolate coordinates, displacements, deformation, strains, stresses and material properties. A series of increasingly sophisticated material models incorporated in MHOST include elasticity, secant plasticity, infinitesimal and finite deformation plasticity, creep and unified viscoplastic constitutive model proposed by Walker. A library of high performance elements is built into this computer program utilizing the concepts of selective reduced integrations and independent strain interpolations. A family of efficient solution algorithms is implemented in MHOST for linear and nonlinear equation solution including the classical Newton-Raphson, modified, quasi and secant Newton methods with optional line search and the conjugate gradient method.

Nakazawa, S.↗

NASA NTRS1991

Inelastic Strain Analysis of Solder Joint in NASA Fatigue Specimen

The solder fatigue specimen designed by NASA-GSFC/UNISYS is analyzed in order to obtain the inelastic strain history during two different representative temperature cycles specified by UNISYS. In previous reports (dated July 25, 1990, and November 15, 1990), results were presented of the elastic-plastic and creep analysis for delta T = 31 C cycle, respectively. Subsequent results obtained during the current phase, from viscoplastic finite element analysis of the solder fatigue specimen for delta T = 113 C cycle are summarized. Some common information is repeated for self-completeness. Large-deformation continuum formulations in conjunction with a standard linear solid model is utilized for modeling the solder constitutive creep-plasticity behavior. Relevant material properties are obtained from the literature. Strain amplitudes, mean strains, and residual strains (as well as stresses) accumulated due to a representative complete temperature cycle are obtained as a result of this analysis. The partitioning between elastic strains, time-independent inelastic (plastic) strains, and time-dependent inelastic (creep) strains is also explicitly obtained for two representative cycles. Detailed plots are presented for two representative temperature cycles. This information forms an important input for fatigue damage models, when predicting the fatigue life of solder joints under thermal cycling

Dasgupta, Abhijit↗

NASA NTRS1981

The accommodation of relative motion at depth on the San Andreas fault system in California

Plate motion below the seismogenic layer along the San Andreas fault system in California is assumed to form by aseismic slip along a deeper extension of the fault or may result from lateral distribution of deformation below the seismogenic layer. The shallow depth of California earthquakes, the depth of the coseismic slip during the 1906 San Francisco earthquake, and the presence of widely separated parallel faults indicate that relative motion is distributed below the seismogenic zone, occurring by inelastic flow rather than by aseismic slip on discrete fault planes.

Prescott, W. H.↗

NASA NTRS1991

Nonlinear structural analysis of cylindrical thrust chambers using viscoplastic models

The results are presented of a viscoplastic stress-strain analysis of a cylindrical thrust chamber used in experiments that were designed to simulate the SSME operating conditions. The inelastic strain was calculated by using a viscoplastic model, and a quasi-three-dimensional structural analysis was performed by using a finite element program MARC. The temperatures and pressures were calculated by using the loading cycles of experiments, and these temperatures and pressures were used in the computations. The deformed shape of the component was predicted after the end of each loading cycle. The predicted shape qualitatively replicated the deformed shape of the component as observed in experiments. The results indicate that the use of viscoplastic models for structural analysis may lead to more realistic life assessments of experimental thrust chambers.

Arya, Vinod K.↗

NASA NTRS1983

Nonlinear damage analysis: Postulate and evaluation

The objective of this program is to assess the viability of a damage postulate which asserts that the fatigue resistance curve of a metal is history dependent due to inelastic action. The study focusses on OFE copper because this simple model material accentuates the inelastic action central to the damage postulate. Data relevant to damage evolution and crack initiation are developed via a study of surface topography. The effects of surface layer residual stresses are explored via comparative testing as were the effects in initial prestraining. The results of the study very clearly show the deformation history dependence of the fatigue resistance of OFE copper. Furthermore the concept of deformation history dependence is shown to qualitatively explain the fatigue resistance of all histories considered. Likewise quantitative predictions for block cycle histories are found to accurately track the observed results. In this respect the assertion that damage per cycle for a given level of the damage parameter is deformation history dependent appears to be physically justified.

Leis, B. N.↗

NASA NTRS1974

Lunar seismicity, structure, and tectonics

Natural seismic events have been detected by the long-period seismometers at Apollo stations 16, 14, 15, and 12 at annual rates of 3300, 1700, 800, and 700, respectively, with peak activity at 13- to 14-day intervals. The data are used to describe magnitudes, source characteristics, and periodic features of lunar seismicity. In a present model, the rigid lithosphere overlies an asthenosphere of reduced rigidity in which present-day partial melting is probable. Tidal deformation presumably leads to critical stress concentrations at the base of the lithosphere, where moonquakes are found to occur. The striking tidal periodicities in the pattern of moonquake occurrence and energy release suggest that tidal energy is the dominant source of energy released as moonquakes. Thus, tidal energy is dissipated by moonquakes in the lithosphere and probably by inelastic processes in the asthenosphere.

Lammlein, D. R.↗

NASA NTRS1988

Relationship between fatigue life in the creep-fatigue region and stress-strain response

On the basis of mechanical tests and metallographic studies, strainrange partitioned lives were predicted by introducing stress-strain materials parameters into the Universal Slopes Equation. This was the result of correlating fatigue damage mechanisms and deformation mechanisms operating at elevated temperatures on the basis of observed mechanical and microstructural behavior. Correlation between high temperature fatigue and stress strain properties for nickel base superalloys and stainless steel substantiated the method. Parameters which must be evaluated for PP- and CC- life are the maximum stress achievable under entirely plastic and creep conditions respectively and corresponding inelastic strains, and the elastic modulus. For plasticity/creep interaction conditions (PC and CP) two more pairs of stress strain parameters must be ascertained.

Berkovits, A.↗