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NASA NTRS1992

Laboratory experiments from the toy store

The following is a laboratory experiment designed to further understanding of materials science. This material could be taught to a typical student of materials science or manufacturing at the high school level or above. The objectives of this experiment are as follows: (1) to qualitatively demonstrate the concepts of elasticity, plasticity, and the strain rate and temperature dependence of the mechanical properties of engineering materials; (2) to qualitatively demonstrate the basics of extrusion including material flow, strain rate dependence of defects, lubrication effects, and the making of hollow shapes by extrusion (the two parts may be two separate experiments done at different times when the respective subjects are covered); and (3) to demonstrate the importance of qualitative observations and the amount of information which can be gathered without quantitative measurements.

Mcclelland, H. T.↗

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 NTRS1992

Environmental fatigue of an Al-Li-Cu alloy. Part 3: Modeling of crack tip hydrogen damage

Environmental fatigue crack propagation rates and microscopic damage modes in Al-Li-Cu alloy 2090 (Parts 1 and 2) are described by a crack tip process zone model based on hydrogen embrittlement. Da/dN sub ENV equates to discontinuous crack advance over a distance, delta a, determined by dislocation transport of dissolved hydrogen at plastic strains above a critical value; and to the number of load cycles, delta N, required to hydrogenate process zone trap sites that fracture according to a local hydrogen concentration-tensile stress criterion. Transgranular (100) cracking occurs for process zones smaller than the subgrain size, and due to lattice decohesion or hydride formation. Intersubgranular cracking dominates when the process zone encompasses one or more subgrains so that dislocation transport provides hydrogen to strong boundary trapping sites. Multi-sloped log da/dN-log delta K behavior is produced by process zone plastic strain-hydrogen-microstructure interactions, and is determined by the DK dependent rates and proportions of each parallel cracking mode. Absolute values of the exponents and the preexponential coefficients are not predictable; however, fractographic measurements theta sub i coupled with fatigue crack propagation data for alloy 2090 established that the process zone model correctly describes fatigue crack propagation kinetics. Crack surface films hinder hydrogen uptake and reduce da/dN and alter the proportions of each fatigue crack propagation mode.

Piascik, Robert S.↗

NASA NTRS2003

Implementation of an Associative Flow Rule Including Hydrostatic Stress Effects Into the High Strain Rate Deformation Analysis of Polymer Matrix Composites

A previously developed analytical formulation has been modified in order to more accurately account for the effects of hydrostatic stresses on the nonlinear, strain rate dependent deformation of polymer matrix composites. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical J2 plasticity theory definitions of effective stress and effective inelastic strain, along with the equations used to compute the components of the inelastic strain rate tensor, are appropriately modified. To verify the revised formulation, the shear and tensile deformation of two representative polymers are computed across a wide range of strain rates. Results computed using the developed constitutive equations correlate well with experimental data. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite for several fiber orientation angles across a variety of strain rates. The computed values compare well to experimentally obtained results.

Goldberg, Robert K.↗

NASA NTRS1983

A Unified Constitutive Relationship for the Time-dependent Behavior of Fast Breeder Alloys

Constitutive equations based on classical concepts of creep and plasticity generally rest on the assumption that the inelastic strain can be decomposed into two distinct and additive contributions, one time dependent (creep) and the other time dependent (plastic). It is suggested that an approach is to adopt a unified representation in which creep and plasticity are characterized as occurring simultaneously and interactively and time is an essential ingredient throughout. Examples of the inherent time dependency exhibited by some fast breeder alloys at elevated temperature are rate dependency under monotonic and cyclic straining, thermal recovery and strong creep-elasticity interaction. The stron influence of the recent history of plastic straining on stress relaxation is shown.

Robinson, D. N.↗

NASA NTRS2022

Impact Simulation of Composite Panels for Aerospace Applications

The aerospace research community has been working towards the development of a comprehensive framework for the design of composite structures at the component, subassembly, assembly, and system levels. Such a framework requires accurate, efficient and easy-to-use mathematical and computational models that are in sync with physical reality. The research work in this paper is designed to help an aerospace structural engineer move towards this goal by simulating dynamic impact to composite panels. First, the existing orthotropic visco-elastic visco-plastic material model in LS-DYNA commercial finite element program, MAT_COMPOSITE_TABULATED_PLASTICITY_DAMAGE (MAT_213) is enhanced with the development and use of rate-dependent damage data. Using state-of-the-art experimental procedures, impact validation test data are created. Second, the versatility of the constitutive model is examined by its ability to simulate a low velocity (27 ft/s, 8 m/s) impact test, and two high velocity impact tests (385–417 ft/s, 117–127 m/s) that straddle the ballistic limit of the projectile and the composite panels. Third, these impact events are modeled using three different finite element types – under-integrated and fully-integrated solid elements, and fully-integrated thin shell elements. Insight into accuracy versus numerical efficiency is gained by comparing the performance of solid versus thin shell elements. The numerical results show that accurate predictions of these impact events can be obtained with reasonable effort and care.

Simulations↗

NASA NTRS1987

Rate-dependent mode I interlaminar crack growth mechanisms in graphite/epoxy and graphite/PEEK

In this paper the mode I fracture behavior of graphite/epoxy and graphite/PEEK composites is examined over four decades of crosshead rates (0.25-250 mm/min). Straight-sided double-cantilever-beam specimens consisting of unidirectional laminates were tested at room temperature. For graphite/epoxy the load-deflection response was linear to fracture, and stable slow crack growth initiating at the highest load level was observed for all rates tested. In contrast, mode I crack growth in the graphite/PEEK material was often unstable and showed stick-slip behavior. Subcritical crack growth occurring prior to the onset of fracture was observed at intermediate displacement rates. A mechanism for the fracture behavior of the graphite/PEEK material (based on viscoelastic, plastic, and microcrack coalescence in the process zone) is proposed and related to the observed rate-dependent phenomena.

Gillespie, J. W., Jr.↗

NASA NTRS1978

Tensile and creep properties of the experimental oxide dispersion strengthened iron-base sheet alloy MA-956E at 1365 K

A study of the 1365 K tensile properties, creep characteristics and residual room temperature properties after creep testing of the experimental oxide dispersion strengthened iron-base alloy MA-956E (Fe-20Cr-4.5Al-0.5Ti-0.5Y2O3) was conducted. The 1365 K tensile properties, particularly ductility, are strongly dependent on strain rate. It appears that MA-956E does not easily undergo slow plastic deformation. Rather than deform under creep loading conditions, the alloy apparently fails by a crack nucleation and growth mechanism. Fortunately, there appears to be a threshold stress below which crack nucleation and/or growth does not occur.

Whittenberger, J. D.↗

NASA NTRS2002

Computational Nanomechanics of Carbon Nanotubes and Composites

Nanomechanics of individual carbon and boron-nitride nanotubes and their application as reinforcing fibers in polymer composites has been reviewed with interplay of theoretical modeling, computer simulations and experimental observations. The emphasis in this work is on elucidating the multi-length scales of the problems involved, and of different simulation techniques that are needed to address specific characteristics of individual nanotubes and nanotube polymer-matrix interfaces. Classical molecular dynamics simulations are shown to be sufficient to describe the generic behavior such as strength and stiffness modulus but are inadequate to describe elastic limit and nature of plastic buckling at large strength. Quantum molecular dynamics simulations are shown to bring out explicit atomic nature dependent behavior of these nanoscale materials objects that are not accessible either via continuum mechanics based descriptions or through classical molecular dynamics based simulations. As examples, we discus local plastic collapse of carbon nanotubes under axial compression and anisotropic plastic buckling of boron-nitride nanotubes. Dependence of the yield strain on the strain rate is addressed through temperature dependent simulations, a transition-state-theory based model of the strain as a function of strain rate and simulation temperature is presented, and in all cases extensive comparisons are made with experimental observations. Mechanical properties of nanotube-polymer composite materials are simulated with diverse nanotube-polymer interface structures (with van der Waals interaction). The atomistic mechanisms of the interface toughening for optimal load transfer through recycling, high-thermal expansion and diffusion coefficient composite formation above glass transition temperature, and enhancement of Young's modulus on addition of nanotubes to polymer are discussed and compared with experimental observations.

Srivastava, Deepak↗

NASA NTRS1990

Elevated temperature crack growth in aluminum alloys: Tensile deformation of 2618 and FVS0812 aluminum alloys

Understanding the damage tolerance of aluminum alloys at elevated temperatures is essential for safe applications of advanced materials. The objective of this project is to investigate the time dependent subcritical cracking behavior of powder metallurgy FVS0812 and ingot metallurgy 2618 aluminum alloys at elevated temperatures. The fracture mechanics approach was applied. Sidegrooved compact tension specimens were tested at 175, 250, and 316 C under constant load. Subcritical crack growth occurred in each alloy at applied stress intensity levels (K) of between about 14 and 25 MPa/m, well below K (sub IC). Measured load, crack opening displacement and displacement rate, and crack length and growth rate (da/dt) were analyzed with several continuum fracture parameters including, the C-integral, C (sub t), and K. Elevated temperature growth rate data suggest that K is a controlling parameter during time dependent cracking. For FVS0812, da/dt is highest at 175 C when rates are expressed as a function of K. While crack growth rate is not controlled by C (sub t) at 175 C, da/dt appears to better correlate with C (sub t) at higher temperatures. Creep brittle cracking at intermediate temperatures, and perhaps related to strain aging, is augmented by time dependent transient creep plasticity at higher temperatures. The C (sub t) analysis is, however, complicated by the necessity to measure small differences in the elastic crack growth and creep contributions to the crack opening displacement rate. A microstructural study indicates that 2618 and FVS0812 are likely to be creep brittle materials, consistent with the results obtained from the fracture mechanics study. Time dependent crack growth of 2618 at 175 C is characterized by mixed transgranular and intergranular fracture. Delamination along the ribbon powder particle boundaries occurs in FVS0812 at all temperatures. The fracture mode of FVS0812 changes with temperature. At 175 C, it is characterized as dimpled rupture, and at 316 C as mixed matrix superplastic rupture and matrix-dipersoid debonding.

Leng, Yang↗

NASA NTRS2003

Analytical Modeling of the High Strain Rate Deformation of Polymer Matrix Composites

The results presented here are part of an ongoing research program to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric matrix materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical 5 plasticity theory definitions of effective stress and effective plastic strain are modified by applying variations of the Drucker-Prager yield criterion. To verify the revised formulation, the shear and tensile deformation of a representative toughened epoxy is analyzed across a wide range of strain rates (from quasi-static to high strain rates) and the results are compared to experimentally obtained values. For the analyzed polymers, both the tensile and shear stress-strain curves computed using the analytical model correlate well with values obtained through experimental tests. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. In the micromechanics, the unit cell is divided up into a number of independently analyzed slices, and laminate theory is then applied to obtain the effective deformation of the unit cell. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite (composed using the representative polymer analyzed for the correlation of the polymer constitutive equations) for several fiber orientation angles across a variety of strain rates. The computed values compare favorably to experimentally obtained results.

Goldberg, Robert K.↗

NASA NTRS2015

Impact and Penetration of Thin Aluminum 2024 Flat Panels at Oblique Angles of Incidence

The U.S. Federal Aviation Administration (FAA) and the National Aeronautics and Space Administration (NASA) are actively involved in improving the predictive capabilities of transient finite element computational methods for application to safety issues involving unintended impacts on aircraft and aircraft engine structures. One aspect of this work involves the development of an improved deformation and failure model for metallic materials, known as the Tabulated Johnson-Cook model, or MAT224, which has been implemented in the LS-DYNA commercial transient finite element analysis code (LSTC Corp., Livermore, CA) (Ref. 1). In this model the yield stress is a function of strain, strain rate and temperature and the plastic failure strain is a function of the state of stress, temperature and strain rate. The failure criterion is based on the accumulation of plastic strain in an element. The model also incorporates a regularization scheme to account for the dependency of plastic failure strain on mesh size. For a given material the model requires a significant amount of testing to determine the yield stress and failure strain as a function of the three-dimensional state of stress, strain rate and temperature. In addition, experiments are required to validate the model. Currently the model has been developed for Aluminum 2024 and validated against a series of ballistic impact tests on flat plates of various thicknesses (Refs. 1 to 3). Full development of the model for Titanium 6Al-4V is being completed, and mechanical testing for Inconel 718 has begun. The validation testing for the models involves ballistic impact tests using cylindrical projectiles impacting flat plates at a normal incidence (Ref. 2). By varying the thickness of the plates, different stress states and resulting failure modes are induced, providing a range of conditions over which the model can be validated. The objective of the study reported here was to provide experimental data to evaluate the model under more extreme conditions, using a projectile with a more complex shape and sharp contacts, impacting flat panels at oblique angles of incidence.

Ruggeri, Charles R.↗

NASA NTRS1983

Development of constitutive models for cyclic plasticity and creep behavior of super alloys at high temperature

An uncoupled constitutive model for predicting the transient response of thermal and rate dependent, inelastic material behavior was developed. The uncoupled model assumes that there is a temperature below which the total strain consists essentially of elastic and rate insensitive inelastic strains only. Above this temperature, the rate dependent inelastic strain (creep) dominates. The rate insensitive inelastic strain component is modelled in an incremental form with a yield function, blow rule and hardening law. Revisions to the hardening rule permit the model to predict temperature-dependent kinematic-isotropic hardening behavior, cyclic saturation, asymmetric stress-strain response upon stress reversal, and variable Bauschinger effect. The rate dependent inelastic strain component is modelled using a rate equation in terms of back stress, drag stress and exponent n as functions of temperature and strain. A sequence of hysteresis loops and relaxation tests are utilized to define the rate dependent inelastic strain rate. Evaluation of the model has been performed by comparison with experiments involving various thermal and mechanical load histories on 5086 aluminum alloy, 304 stainless steel and Hastelloy X.

Haisler, W. E.↗

NASA NTRS1994

Patterns of brittle deformation under extension on Venus

The development of fractures at regular length scales is a widespread feature of Venusian tectonics. Models of lithospheric deformation under extension based on non-Newtonian viscous flow and brittle-plastic flow develop localized failure at preferred wavelengths that depend on lithospheric thickness and stratification. The characteristic wavelengths seen in rift zones and tessera can therefore provide constraints on crustal and thermal structure. Analytic solutions were obtained for growth rates in infinitesimal perturbations imposed on a one-dimensional, layered rheology. Brittle layers were approximated by perfectly-plastic, uniform strength, overlying ductile layers exhibiting thermally-activated power-law creep. This study investigates the formation of faults under finite amounts of extension, employing a finite-element approach. Our model incorporates non-linear viscous rheology and a Coulomb failure envelope. An initial perturbation in crustal thickness gives rise to necking instabilities. A small amount of velocity weakening serves to localize deformation into planar regions of high strain rate. Such planes are analogous to normal faults seen in terrestrial rift zones. These 'faults' evolve to low angle under finite extension. Fault spacing, orientation and location, and the depth to the brittle-ductile transition, depend in a complex way on lateral variations in crustal thickness. In general, we find that multiple wavelengths of deformation can arise from the interaction of crustal and mantle lithosphere.

Neumann, G. A.↗

NASA NTRS1997

Transient Finite Element Analyses Developed to Model Fan Containment Impact Events

Research is underway to establish an increased level of confidence in existing numerical techniques for predicting transient behavior when the fan of a jet engine is released and impacts the fan containment system. To evaluate the predictive accuracy that can currently be obtained, researchers at the NASA Lewis Research Center used the DYNA 3D computer code to simulate large-scale subcomponent impact tests that were conducted at the University of Dayton Research Institute (UDRI) Impact Physics Lab. In these tests, 20- by 40-in. flat metal panels, contoured to the shape of a typical fan case, were impacted by the root section of a fan blade. The panels were oriented at an angle to the path of the projectile that would simulate the conditions in an actual blade-out event. The metal panels were modeled in DYNA 3D using a kinematic hardening model with the strain rate dependence of the yield stress governed by the Cowper-Simons rule. Failure was governed by the effective plastic strain criterion. The model of the fan blade and case just after impact is shown. By varying the maximum effective plastic strain, we obtained good qualitative agreement between the model and the experiments. Both the velocity required to penetrate the case and the deflection during impact compared well. This indicates that the failure criterion and constitutive model may be appropriate, but for DYNA 3D to be useful as a predictive tool, methods to determine accurate model parameters must be established. Simple methods for measuring model parameters are currently being developed. In addition, alternative constitutive models and failure criteria are being investigated.

Pereira, J. Michael↗

NASA NTRS2020

An Improved Plastically Dilatant Unified Viscoplastic Constitutive Formulation for Multiscale Analysis of Polymer Matrix Composites Under High Strain Rate Loading

Polymer matrix composites are commonly used to fabricate energy-absorbing structures expected to experience impact loading. As such, a detailed understanding of the dynamic response of the constituent materials is necessary. Since the rate, temperature, and pressure dependence of carbon fiber reinforced polymer matrix composites are primarily manifestations of the rate, temperature, and pressure dependence of the polymer matrix, it is crucial that the constitutive behavior of the matrix be accurately characterized. In this work, an existing unified viscoplastic constitutive formulation is extended to ensure thermodynamic consistency and to more accurately account for the tension-compression asymmetry observed in the response of polymeric materials. A new plastic potential function is proposed, and elementary loading conditions are utilized to determine relations between model constants to ensure nonnegative plastic dissipation, a necessary thermodynamic requirement. Expressions for plastic Poisson’s ratios are derived and are bounded by enforcing nonnegative plastic dissipation. The model is calibrated against available experimental data from tests conducted over a range of strain rates, temperatures, and loading cases on a representative thermoset epoxy; good correlation between simulations and experimental data is obtained. Temperature rises due to the conversion of plastic work to heat are computed via the adiabatic heat energy equation. The viscoplastic polymer model is then used as a constitutive model in the generalized method of cells micromechanics theory to investigate the effects of matrix adiabatic heating on the high strain rate response of a unidirectional composite. The thermodynamic consistency of the model ensures plastic dissipation can only cause an increase in temperature. Simulation results indicate that significant thermal softening due to the conversion of plastic work to heat is observed in the composite for matrix dominated deformation modes.

Impact loading↗

NASA NTRS1993

Incident angle dependence of proton response of CR-39 (TS-16) track detector

The proton response of the TS-16 type of CR-39 plastic nuclear track detector has been studied with accelerated and fast neutron induced protons in vacuum and in air. The diameters of etched tracks were measured as a function of etching time and the etch rate ratio and the etch induction layer were determined from the growth curve of the diameter using a variable etch rate ratio model. In the case of the accelerated protons in vacuum an anomalous incident angle dependence of the response is observed.

Radiation Monitoring/instrumentation↗

NASA NTRS1984

Surface property modification of silicon

The main emphasis of this work has been to determine the wear rate of silicon in fluid environments and the parameters that influence wear. Three tests were carried out on single crystal Czochralski silicon wafers: circular and linear multiple-scratch tests in fluids by a pyramidal diamond simulated fixed-particle abrasion; microhardness and three-point bend tests were used to determine the hardness and fracture toughness of abraded silicon and the extent of damage induced by abrasion. The wear rate of (100) and (111) n and p-type single crystal Cz silicon abraded by a pyramidal diamond in ethanol, methanol, acetone and de-ionized water was determined by measuring the cross-sectional areas of grooves of the circular and linear multiple-scratch tests. The wear rate depends on the loads on the diamond and is highest for ethanol and lowest for de-ionized water. The surface morphology of the grooves showed lateral and median cracks as well as a plastically deformed region. The hardness and fracture toughness are critical parameters that influence the wear rate. Microhardness tests were conducted to determine the hardness as influenced by fluids. Median cracks and the damage zone surrounding the indentations were also related to the fluid properties.

Danyluk, S.↗