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Experimental Calibration of Flow Rule Coefficients for LS-Dyna Mat_213

Composite materials have become a popular choice in aerospace engineering applications due to their low weight, high specific stiffness, high specific energy absorption, and economic synthesis. As use of composite materials has proliferated, the need for accurate simulation under extreme loading conditions is of increasing importance. *MAT_213 is a tabulated plasticity and damage material model in LS-DYNA designed for such use cases. To account for the nonlinear material response, a plasticity algorithm is used, which employs a non-associative flow rule with coefficients requiring experimental calibration. This work outlines an experimental methodology for calibrating these coefficients using the macroscopic stress-strain response and microscopic in-plane strain measurements from coupon scale experiments. The model material used for the development and demonstration of this methodology is a plain weave woven fabric with T300 carbon fiber tows in the warp direction and Kevlar© 49 fiber tows in the weft direction, and an Epon© 828/Epikure© 3223 thermoset epoxy matrix. Coupon-scale tensile testing performed at multiple fiber angles (carbon fibers oriented 0º, 22.5º, 45º, 67.5º, and 90º relative to the loading axis) provides data for multiple calibration processes. The measured plastic strain increments in the principal material coordinate are used to set limits for ratios between flow rule coefficients. The identified ranges are used to bound the search for a set of coefficients, leading to convergence of different coupon responses in the effective stress – effective plastic strain space. Flow rule coefficients found by this methodology are then used as (i) input for LS-DYNA simulations of uniaxial tension coupon tests at varying fiber angles, and (ii) comparison of predicted values for the plastic Poisson’s ratio in global coordinates with the experimentally measured one for all off-axis orientations. These results are quantitatively and qualitatively compared to macroscopic stress-strain curves and experimental strain components. The conformity of the experimentally measured quantities with those derived from the simulations provide a means for assessing the quality of calibrated coefficients.

Polymer Matrix Composites↗

NASA NTRS1983

Some Recent Developments in the Endochronic Theory with Application to Cyclic Histories

Constitutive equations with only two easily determined material constants predict the stress (strain) response of normalized mild steel to a variety of general strain (stress) histories, without a need for special unloading-reloading rules. The equations are derived from the endochronic theory of plasticity of isotropic materials with an intrinsic time scale defined in the plastic strain space. Agreement between theoretical predictions and experiments are are excellent quantitatively in cases of various uniaxial constant amplitude histories, variable uniaxial strain amplitude histories and cyclic relaxation. The cyclic ratcheting phenomenon is predicted by the present theory.

Valanis, K. C.↗

NASA NTRS1988

Evaluation of structural analysis methods for life prediction

The utility of advanced constitutive models and structural analysis methods are evaluated for predicting the cyclic life of an air-cooled turbine blade for a gas turbine aircraft engine. Structural analysis methods of various levels of sophistication were exercised to obtain the cyclic stress-strain response at the critical airfoil location. Calculated strain ranges and mean stresses from the stress-strain cycles were used to predict crack initiation lives by using the total strain version of the strain range partitioning life prediction method. The major results are given and discussed.

Kaufman, A.↗

NASA NTRS2000

A Study of Influencing Factors on the Tensile Response of a Titanium Matrix Composite With Weak Interfacial Bonding

The generalized method of cells micromechanics model is utilized to analyze the tensile stress-strain response of a representative titanium matrix composite with weak interfacial bonding. The fiber/matrix interface is modeled through application of a displacement discontinuity between the fiber and matrix once a critical debonding stress has been exceeded. Unidirectional composites with loading parallel and perpendicular to the fibers are examined, as well as a cross-ply laminate. For each of the laminates studied, analytically obtained results are compared to experimental data. The application of residual stresses through a cool-down process was found to have a significant effect on the tensile response. For the unidirectional laminate with loading applied perpendicular to the fibers, fiber packing and fiber shape were shown to have a significant effect on the predicted tensile response. Furthermore, the interface was characterized through the use of semi-emperical parameters including an interfacial compliance and a "debond stress;" defined as the stress level across the interface which activates fiber/matrix debonding. The results in this paper demonstrate that if architectural factors are correctly accounted for and the interface is appropriately characterized, the macro-level composite behavior can be correctly predicted without modifying any of the fiber or matrix constituent properties.

Goldberg, Robert K.↗

NASA NTRS1991

Stirling engine: Available tools for long-life assessment

A review is presented for the durability approaches applicable to long-time life assessment of Stirling engine hot-section components. The crucial elements are experimental techniques for generating long-time materials property data (both monotonic and cyclic flow and failure properties); analytic representations of slow strain rate material stress-strain response characteristics (monotonic and cyclic constitutive relations) at high temperatures and low stresses and strains; analytic creep-fatigue-environmental interaction life prediction methods applicable to long lifetimes at high temperatures and small stresses and strains; and experimental verification of life predictions. Long-lifetime design criteria for materials of interest are woefully lacking. Designing against failures due to creep, creep-rupture, fatigue, environmental attack, and creep-fatigue-environmental interaction will require considerable extrapolation. Viscoplastic constitutive models and time-temperature parameters will have to be calibrated for the hot-section materials of interest. Analysis combined with limited verification testing in a short-time regime will be required to build confidence in long-lifetime durability models.

Halford, Gary R.↗

NASA NTRS1991

Stirling engine - Available tools for long-life assessment

A review is presented for the durability approaches applicable to long-time life assessment of Stirling engine hot-section components. The crucial elements are experimental techniques for generating long-time materials property data (both monotonic and cyclic flow and failure properties); analytic representations of slow strain rate material stress-strain response characteristics (monotonic and cyclic constitutive relations) at high temperatures and low stresses and strains; analytic creep-fatigue-environmental interaction life prediction methods applicable to long lifetimes at high temperatures and small stresses and strains; and experimental verification of life predictions. Long-lifetime design criteria for materials of interest are woefully lacking. Designing against failures due to creep, creep-rupture, fatigue, environmental attack, and creep-failure-environmental interaction will require considerable extrapolation. Viscoplastic constitutive models and time-temperature parameters will have to be calibrated for the hot-section materials of interest. Analysis combined with limited verification testing in a short-time regime will be required to build confidence in long-lifetime durability models.

Halford, Gary R.↗

NASA NTRS1991

Compression failure of angle-ply laminates

The present work deals with modes and mechanisms of failure in compression of angle-ply laminates. Experimental results were obtained from 42 angle-ply IM7/8551-7a specimens with a lay-up of ((plus or minus theta)/(plus or minus theta)) sub 6s where theta, the off-axis angle, ranged from 0 degrees to 90 degrees. The results showed four failure modes, these modes being a function of off-axis angle. Failure modes include fiber compression, inplane transverse tension, inplane shear, and inplane transverse compression. Excessive interlaminar shear strain was also considered as an important mode of failure. At low off-axis angles, experimentally observed values were considerably lower than published strengths. It was determined that laminate imperfections in the form of layer waviness could be a major factor in reducing compression strength. Previously developed linear buckling and geometrically nonlinear theories were used, with modifications and enhancements, to examine the influence of layer waviness on compression response. The wavy layer is described by a wave amplitude and a wave length. Linear elastic stress-strain response is assumed. The geometrically nonlinear theory, in conjunction with the maximum stress failure criterion, was used to predict compression failure and failure modes for the angle-ply laminates. A range of wave length and amplitudes were used. It was found that for 0 less than or equal to theta less than or equal to 15 degrees failure was most likely due to fiber compression. For 15 degrees less than theta less than or equal to 35 degrees, failure was most likely due to inplane transverse tension. For 35 degrees less than theta less than or equal to 70 degrees, failure was most likely due to inplane shear. For theta less than 70 degrees, failure was most likely due to inplane transverse compression. The fiber compression and transverse tension failure modes depended more heavily on wave length than on wave amplitude. Thus using a single parameter, such as a ratio of wave amplitude to wave length, to describe waviness in a laminate would be inaccurate. Throughout, results for AS4/3502, studied previously, are included for comparison. At low off-axis angles, the AS4/3502 material system was found to be less sensitive to layer waviness than IM7/8551-7a. Analytical predictions were also obtained for laminates with waviness in only some of the layers. For this type of waviness, laminate compression strength could also be considered a function of which layers in the laminate were wavy, and where those wavy layers were. Overall, the geometrically nonlinear model correlates well with experimental results.

Peel, Larry D.↗

NASA NTRS1982

Nonlinear structural and life analyses of a combustor liner

Three dimensional, nonlinear finite element structural analyses were performed for a simulated combustor liner specimen to assess the capability of nonlinear analyses using classical inelastic material models to represent the thermoplastic creep response of the one half scale component. Results indicate continued cyclic hardening and ratcheting while experimental data suggested a stable stress strain response after only a few loading cycles. The computed stress strain history at the critical location was put into two life prediction methods, strainrange partitioning and a Pratt and Whitney combustor life prediction method to evaluate their ability to predict cyclic crack initiation. It is found that the life prediction analyses over predicted the observed cyclic crack initiation life.

Moreno, V.↗

NASA NTRS1971

Theoretical frameworks for testing relativistic gravity: A review

Metric theories of gravity are presented, including the definition of metric theory, evidence for its existence, and response of matter to gravity with test body trajectories, gravitational red shift, and stressed matter responses. Parametrized post-Newtonian framework and interpretations are reviewed. Gamma, beta and gamma, and varied other parameters were measured. Deflection of electromagnetic waves, radar time delay, geodetic gyroscope precession, perihelion shifts, and periodic effects in orbits are among various studies carried out for metric theory experimentation.

Thorne, K. S.↗

NASA NTRS1986

Ultrasonic characterization of plastic deformation in metals

Acoustic tone burst spectroscopy is used to examine the effect of plastic deformation on higher order elastic properties of specimens of AISI 1016, 1045, 1095 and 8620 steel rods by measuring the stress acoustic constants (SACs). The SAC is found to be influenced by prestraining, and prestrain SAC measurements on 8620 steel demonstrate similar behavior to previously measured steels even though the composition of 8620 steel is significantly different. It is suggested from bias stress measurements that the stress acoustic response of prestrained 8620 steel is sensitive to the sign of the applied stress due to the different directions is which dislocations move under tension as opposed to compression, providing an approach to nondestructive testing of residual stress in steels.

Allison, S. G.↗

NASA NTRS1988

Anisotropic constitutive modeling for nickel-base single crystal superalloys

An anisotropic constitutive model was developed based on crystallographic slip theory for nickel base single crystal superalloys. The constitutive equations developed utilizes drag stress and back stress state variables to model the local inelastic flow. Specially designed experiments were conducted to evaluate the existence of back stress in single crystal superalloy Rene N4 at 982 C. The results suggest that: (1) the back stress is orientation dependent; and (2) the back stress state variable is required for the current model to predict material anelastic recovery behavior. The model was evaluated for its predictive capability on single crystal material behavior including orientation dependent stress-strain response, tension/compression asymmetry, strain rate sensitivity, anelastic recovery behavior, cyclic hardening and softening, stress relaxation, creep and associated crystal lattice rotation. Limitation and future development needs are discussed.

Sheh, Michael Y.↗

NASA NTRS1990

Effect of tensile mean stress on fatigue behavior of single-crystal and directionally solidified superalloys

Two nickel base superalloys, single crystal PWA 1480 and directionally solidified MAR-M 246 + Hf, were studied in view of the potential usage of the former and usage of the latter as blade materials for the turbomachinery of the space shuttle main engine. The baseline zero mean stress (ZMS) fatigue life (FL) behavior of these superalloys was established, and then the effect of tensile mean stress (TMS) on their FL behavior was characterized. At room temperature these superalloys have lower ductilities and higher strengths than most polycrystalline engineering alloys. The cycle stress-strain response was thus nominally elastic in most of the fatigue tests. Therefore, a stress range based FL prediction approach was used to characterize both the ZMS and TMS fatigue data. In the past, several researchers have developed methods to account for the detrimental effect of tensile mean stress on the FL for polycrystalline engineering alloys. However, the applicability of these methods to single crystal and directionally solidified superalloys has not been established. In this study, these methods were applied to characterize the TMS fatigue data of single crystal PWA 1480 and directionally solidified MAR-M 246 + Hf and were found to be unsatisfactory. Therefore, a method of accounting for the TMS effect on FL, that is based on a technique proposed by Heidmann and Manson was developed to characterize the TMS fatigue data of these superalloys. Details of this method and its relationship to the conventionally used mean stress methods in FL prediction are discussed.

Kalluri, Sreeramesh↗

NASA NTRS1982

Experimental verification of the Neuber relation at room and elevated temperatures

The accuracy of the Neuber equation at room temperature and 1,200 F as experimentally determined under cyclic load conditions with hold times. All strains were measured with an interferometric technique at both the local and remote regions of notched specimens. At room temperature, strains were obtained for the initial response at one load level and for cyclically stable conditions at four load levels. Stresses in notched members were simulated by subjecting smooth specimens to he same strains as were recorded on the notched specimen. Local stress-strain response was then predicted with excellent accuracy by subjecting a smooth specimen to limits established by the Neuber equation. Data at 1,200 F were obtained with the same experimental techniques but only in the cyclically stable conditions. The Neuber prediction at this temperature gave relatively accurate results in terms of predicting stress and strain points.

Lucas, L. J.↗

NASA NTRS1983

Development of a simplified analytical method for representing material cyclic response

Development of a simplified method for estimating structural inelastic stress and strain response to cyclic thermal loading is presented. The method assumes that high temperature structural response is the sum of time independent plastic and time dependent elastic/creep components. The local structural stress and strain response predicted by linear elastic analysis is modified by the simplified method to predict the inelastic response. The results with simulations by a nonlinear finite element analysis and used time independent plasticity and unified time dependent material model are compared.

Moreno, V.↗

NASA NTRS1985

Longitudinal splitting in unidirectional composites, analysis and experiments

An experimental study is conducted to determine the fracture behavior of center notched, unidirectional graphite/epoxy laminates when subjected to tensile loading. The actual behavior is compared to the behavior predicted by a mathematical model based on classical shear-lag assumptions. The model allows for damage to occur in the form of longitudinal matrix yielding and splitting with the matrix assumed to fail in pure shear. Results indicate that the model is capable of predicting split initiation stress levels accurately, but does not describe the subsequent split growth adequately. The model predicts rapid split growth following split initiation due to shear failure, while the actual behavior involves a slow split growth region prior to the rapid growth region. It is suggested that transverse matrix normal stresses are responsible for split initiation and the early, slow split growth. The model predicts the actual initiation stress levels reliably, and also appears to be able to predict the point at which the shear failure mode begins to dominate. The shear failure mode does eventually dominate, but at a slower rate than predicted. The nonuniform structure of the graphite/epoxy laminates is thought to be responsible for decreasing the split growth rate due to shear failure.

Goree, J. G.↗

NASA NTRS2001

The catecholamine response to spaceflight: role of diet and gender

Compared with men, women appear to have a decreased sympathetic nervous system (SNS) response to stress. The two manifestations where the sexual dimorphism has been the most pronounced involve the response of the SNS to fluid shifts and fuel metabolism during exercise. The objectives of this study were to investigate whether a similar sexual dimorphism was found in the response to spaceflight. To do so, we compared catecholamine excretion by male and female astronauts from two similar shuttle missions, Spacelab Life Sciences 1 (SLS1, 1991) and 2 (SLS2, 1993) for evidence of sexual dimorphism. To evaluate the variability of the catecholamine response in men, we compared catecholamine excretion from the two SLS missions against the 1996 Life and Microgravity Sciences Mission (LMS) and the 1973 Skylab missions. RESULTS: No gender- or mission-dependent changes were found with epinephrine. Separating out the SLS1/2 data by gender shows that norepinephrine excretion was essentially unchanged with spaceflight in women (98 +/- 10%; n = 3) and substantially decreased with the men (41 +/- 9%; n = 4, P < 0.05). Data are a percentage of mean preflight value +/- SE. Comparisons among males demonstrated significant mission effects on norepinephrine excretion. After flight, there was a transient increase in norepinephrine but no evidence of any gender-specific effects. We conclude that norepinephrine excretion during spaceflight is both mission and gender dependent. Men show the greater response, with at least three factors being involved, a response to microgravity, energy balance, and the ratio of carbohydrate to fat in the diet.

NASA Discipline Regulatory Physiology↗

NASA NTRS2003

The Human Sympathetic Nervous System Response to Spaceflight

The sympathetic nervous system is an important part of the autonomic (or automatic) nervous system. When an individual stands up, the sympathetic nervous system speeds the heart and constricts blood vessels to prevent a drop in blood pressure. A significant number of astronauts experience a drop in blood pressure when standing for prolonged periods after they return from spaceflight. Difficulty maintaining blood pressure with standing is also a daily problem for many patients. Indirect evidence available before the Neurolab mission suggested the problem in astronauts while in space might be due partially to reduced sympathetic nervous system activity. The purpose of this experiment was to identify whether sympathetic activity was reduced during spaceflight. Sympathetic nervous system activity can be determined in part by measuring heart rate, nerve activity going to blood vessels, and the release of the hormone norepinephrine into the blood. Norepinephrine is a neurotransmitter discharged from active sympathetic nerve terminals, so its rate of release can serve as a marker of sympathetic nervous system action. In addition to standard cardiovascular measurements (heart rate, blood pressure), we determined sympathetic nerve activity as well as norepinephrine release and clearance on four crewmembers on the Neurolab mission. Contrary to our expectation, the results demonstrated that the astronauts had mildly elevated resting sympathetic nervous system activity in space. Sympathetic nervous system responses to stresses that simulated the cardiovascular effects of standing (lower body negative pressure) were brisk both during and after spaceflight. We concluded that, in the astronauts tested, the activity and response of the sympathetic nervous system to cardiovascular stresses appeared intact and mildly elevated both during and after spaceflight. These changes returned to normal within a few days.

Ertl, Andrew C.↗

NASA NTRS1985

Two simplified procedures for predicting cyclic material response from a strain history

Simplified inelastic analysis procedures were developed at NASA Lewis and Pratt & Whitney Aircraft for predicting the stress-strain response at the critical location of a thermomechanically cycled structure. These procedures are intended primarily for use as economical structural analysis tools in the early design stages of aircraft engine hot section components where nonlinear finite-element analyses would be prohibitively expensive. Both simplified methods use as input the total strain history calculated from a linear elastic analysis. The elastic results are modified to approximate the characteristics of the inelastic cycle by incremental solution techniques. A von Mises yield criterion is used to determine the onset of active plasticity. The fundamental assumption of these methods is that the inelastic strain is local and constrained from redistribution by the surrounding elastic material.

Kaufman, A.↗