Constitutive modeling of inelastic anisotropic material response

A constitutive equation was developed to predict the inelastic thermomechanical response of single crystal turbine blades. These equations are essential for developing accurate finite element models of hot section components and contribute significantly to the understanding and prediction of crack initiation and propagation. The method used was limited to unified state variable constitutive equations. Two approaches to developing an anisotropic constitutive equation were reviewed. One approach was to apply the Stouffer-Bodner representation for deformation induced anisotropy to materials with an initial anisotropy such as single crystals. The second approach was to determine the global inelastic strain rate from the contribution of the slip in each of the possible crystallographic slip systems. A three dimensional finite element is being developed with a variable constitutive equation link that can be used for constitutive equation development and to predict the response of an experiment using the actual specimen geometry and loading conditions

A Potential Function Derivation of a Constitutive Equation for Inelastic Material Response

Physical and thermodynamic concepts are used to develop a potential function for application to high temperature polycrystalline material response. Inherent in the formulation is a differential relationship between the potential function and constitutive equation in terms of the state variables. Integration of the differential relationship produces a state variable evolution equation that requires specification of the initial value of the state variable and its time derivative. It is shown that the initial loading rate, which is directly related to the initial hardening rate, can significantly influence subsequent material response. This effect is consistent with observed material behavior on the macroscopic and microscopic levels, and may explain the wide scatter in response often found in creep testing

A constitutive model with damage for high temperature superalloys

A unified constitutive model is searched for that is applicable for high temperature superalloys used in modern gas turbines. Two unified inelastic state variable constitutive models were evaluated for use with the damage parameter proposed by Kachanov. The first is a model (Bodner, Partom) in which hardening is modeled through the use of a single state variable that is similar to drag stress. The other (Ramaswamy) employs both a drag stress and back stress. The extension was successful for predicting the tensile, creep, fatigue, torsional and nonproportional response of Rene' 80 at several temperatures. In both formulations, a cumulative damage parameter is introduced to model the changes in material properties due to the formation of microcracks and microvoids that ultimately produce a macroscopic crack. A back stress/drag stress/damage model was evaluated for Rene' 95 at 1200 F and is shown to predict the tensile, creep, and cyclic loading responses reasonably well

Finite element analysis of notch behavior using a state variable constitutive equation

The state variable constitutive equation of Bodner and Partom was used to calculate the load-strain response of Inconel 718 at 649 C in the root of a notch. The constitutive equation was used with the Bodner-Partom evolution equation and with a second evolution equation that was derived from a potential function of the stress and state variable. Data used in determining constants for the constitutive models was from one-dimensional smooth bar tests. The response was calculated for a plane stress condition at the root of the notch with a finite element code using constant strain triangular elements. Results from both evolution equations compared favorably with the observed experimental response. The accuracy and efficiency of the finite element calculations also compared favorably to existing methods

Anisotropic constitutive modeling for nickel base single crystal superalloy Rene N4 at 982 C

A back stress/drag stress constitutive model based on a crystallographic approach to model single crystal anisotropy is presented. Experimental results demonstrated the need for the back stress variable in the inelastic flow equations. Experimental findings suggested that back stress is orientation dependent and controls both strain hardening and recovery characteristics. Due to the observed stable fatigue loops at 1800 F, drag stress is considered constant for this temperature. The constitutive model operated with constraints determined only from tensile data was extensively tested from simple tensile and fatigue to complicated strain hold tests. The model predicted very well under those conditions

Development and Testing of a Variable Conductance Thermal Acquisition, Transport, and Switching System

This paper describes the development and testing of a scalable thermal control architecture for instruments, subsystems, or systems that must operate in severe space environments with wide variations in sink temperature. The architecture is comprised by linking one or more hot-side variable conductance heat pipes (VCHPs) in series with one or more cold-side loop heat pipes (LHPs). The VCHPs provide wide area heat acquisition, limited distance thermal transport, modest against gravity pumping, concentrated LHP startup heating, and high switching ratio variable conductance operation. The LHPs provide localized heat acquisition, long distance thermal transport, significant against gravity pumping, and high switching ratio variable conductance operation. Combining two variable conductance devices in series ensures very high switching ratio isolation from severe environments like the Earth's moon, where each lunar day spans 15 Earth days (270 K sink, with a surface-shielded/space viewing radiator) and each lunar night spans 15 Earth days (80-100 K radiative sink, depending on location). The single VCHP-single LHP system described herein was developed to maintain thermal control of International Lunar Network (ILN) anchor node lander electronics, but it is also applicable to other variable heat rejection space missions in severe environments. The LHPVCHP system utilizes a stainless steel wire mesh wick ammonia VCHP, a Teflon wick propylene LHP, a pair of one-third square meter high radiators (one capillary-pumped horizontal radiator and a second gravity-fed vertical radiator), a half-meter of transport distance, and a wick-bearing co-located flow regulator (CLFR) to allow operation with a hot (deactivated) radiator. The VCHP was designed with a small reservoir formed by extending the length of its stainless steel heat pipe tubing. The system was able to provide end-to-end switching ratios of 300-500 during thermal vacuum testing at ATK, including 3-5 W/K ON conductance and 0.01 W/K OFF conductance. The test results described herein also include an in-depth analysis of VCHP condenser performance to explain VCHP switching operation in detail. Future multi-VCHP/multi-LHP thermal management system concepts that provide scalability to higher powers/longer transport lengths are also discussed in the paper

Effects of a regenerating matrix on the survival of birds in tropical forest fragments

Background Vast areas of lowland neotropical forest have regenerated after initially being cleared for agricultural purposes. The ecological value of regenerating second growth to forest-dwelling birds may largely depend on the age of the forest, associated vegetative structure, and when it is capable of sustaining avian demographics similar to those found in pristine forest. Methods To determine the influence of second growth age on bird demography, we estimated the annual survival of six central Amazonian bird species residing in pristine forest, a single 100 and a single 10 ha forest fragment, taking into consideration age of the surrounding matrix (i.e. regenerating forest adjacent to each fragment) as an explanatory variable. Results Study species exhibited three responses: arboreal, flocking and ant-following insectivores (Willisornis poecilinotus, Thamnomanes ardesiacus and Pithys albifrons) showed declines in survival associated with fragmentation followed by an increase in survival after 5 years of matrix regeneration. Conversely, Percnostola rufifrons, a gap-specialist, showed elevated survival in response to fragmentation followed by a decline after 5 years of regeneration. Lastly, facultative flocking and frugivore species (Glyphorynchus spirurus and Dixiphia pipra, respectively) showed no response to adjacent clearing and subsequent regeneration. Conclusions Our results in association with previous studies confirm that the value of regenerating forest surrounding habitat patches is dependent on two factors: ecological guild of the species in question and second growth age. Given the rapid increase in survival following succession, we suggest that the ecological value of young tropical forest should not be based solely on a contemporary snapshot, but rather, on the future value of mature second growth as well

The effects of luteinizing hormone ablation/replacement versus steroid ablation/replacement on gene expression in the primate corpus luteum

This study was designed to provide a genome-wide analysis of the effects of luteinizing hormone (LH) versus steroid ablation/replacement on gene expression in the developed corpus luteum (CL) in primates during the menstrual cycle. On Days 9–11 of the luteal phase, female rhesus monkeys were left untreated (control) or received a GnRH antagonist Antide (A), A + LH, A + LH + the 3β-hydroxysteroid dehydrogenase inhibitor Trilostane (TRL) or A + LH + TRL + a progestin R5020. On Day 12 of the luteal phase, CL were removed and samples of RNA from individual CL were hybridized to Affymetrix™ rhesus macaque total genome microarrays. The greatest number of altered transcripts was associated with the ablation/replacement of LH, while steroid ablation/progestin replacement affected fewer transcripts. Replacement of LH during Antide treatment restored the expression of most transcripts to control levels. Validation of a subset of transcripts revealed that the expression patterns were similar between microarray and real-time PCR. Analyses of protein levels were subsequently determined for two transcripts. This is the first genome-wide analysis of LH and steroid regulation of gene transcription in the developed primate CL. Further analysis of novel transcripts identified in this data set can clarify the relative role for LH and steroids in CL maintenance and luteolysis

A universal model for mobility and migration patterns

Introduced in its contemporary form by George Kingsley Zipf in 1946, but with roots that go back to the work of Gaspard Monge in the 18th century, the gravity law is the prevailing framework to predict population movement, cargo shipping volume, inter-city phone calls, as well as bilateral trade flows between nations. Despite its widespread use, it relies on adjustable parameters that vary from region to region and suffers from known analytic inconsistencies. Here we introduce a stochastic process capturing local mobility decisions that helps us analytically derive commuting and mobility fluxes that require as input only information on the population distribution. The resulting radiation model predicts mobility patterns in good agreement with mobility and transport patterns observed in a wide range of phenomena, from long-term migration patterns to communication volume between different regions. Given its parameter-free nature, the model can be applied in areas where we lack previous mobility measurements, significantly improving the predictive accuracy of most of phenomena affected by mobility and transport processes.Comment: Main text and supplementary informatio

Mesoscopic structure and social aspects of human mobility

The individual movements of large numbers of people are important in many contexts, from urban planning to disease spreading. Datasets that capture human mobility are now available and many interesting features have been discovered, including the ultra-slow spatial growth of individual mobility. However, the detailed substructures and spatiotemporal flows of mobility - the sets and sequences of visited locations - have not been well studied. We show that individual mobility is dominated by small groups of frequently visited, dynamically close locations, forming primary "habitats" capturing typical daily activity, along with subsidiary habitats representing additional travel. These habitats do not correspond to typical contexts such as home or work. The temporal evolution of mobility within habitats, which constitutes most motion, is universal across habitats and exhibits scaling patterns both distinct from all previous observations and unpredicted by current models. The delay to enter subsidiary habitats is a primary factor in the spatiotemporal growth of human travel. Interestingly, habitats correlate with non-mobility dynamics such as communication activity, implying that habitats may influence processes such as information spreading and revealing new connections between human mobility and social networks.Comment: 7 pages, 5 figures (main text); 11 pages, 9 figures, 1 table (supporting information