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

A Study of the Artifacts of the Post-Columbian Indian Culture of the Southeastern United States

This paper is an effort to study and analyze some of the culture objects of the early American Indians of the Southeastern United States. The source of these is the A. J. Powers Collection which is presently on exhibit in the Museum of Cornell College, Mt. Vernon, Iowa

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

Political Content And Political Behavior: Using Functional Theory To Test The Ability Of Political Content To Stimulate Political Interest

The health of the American democracy is up for debate. Digital natives will decide the future of this democracy. Fewer digital natives--those who have grown up with Internet access--are engaging in formal political participation, compared to their parents. Digital natives lack the information needed to participate. This study examined the effects of interactive political content on digital natives\u27 political information efficacy (PIE) through an experiment. The results revealed a decrease in the participants\u27 political confidence and a decrease in the likelihood they would vote. Exposure to political information harmed most digital natives\u27 PIE and reinforced political attitudes in some. The results are troubling for the future health of the American democracy. The results call attention to the need for further research on the relationship between digital natives\u27 use of new communication technologies and its effect on political participation

Network Growth with Preferential Attachment for High Indegree and Low Outdegree

We study the growth of a directed transportation network, such as a food web, in which links carry resources. We propose a growth process in which new nodes (or species) preferentially attach to existing nodes with high indegree (in food-web language, number of prey) and low outdegree (or number of predators). This scheme, which we call inverse preferential attachment, is intended to maximize the amount of resources available to each new node. We show that the outdegree (predator) distribution decays at least exponentially fast for large outdegree and is continuously tunable between an exponential distribution and a delta function. The indegree (prey) distribution is poissonian in the large-network limit

Synthesis, Structure, Spectroscopy, and Reactivity of Azapentadienyl-Ruthenium-Phosphine Complexes

This dissertation focuses on the systematic synthesis of ¬bis-azapentadienyl-ruthenium-phosphine complexes. The synthetic approach involves the treatment of Cl2Ru(PPh3)3 with potassium tert-butylazapentadienide reagent. The reactivity of this parent compound with other 2e- donor ligands is investigated. These resultant complexes\u27 reactivity with triflic acid is also studied. Treatment of Cl2Ru(PPh3)3 with potassium tert-butylazapentadienide produces [(1,2,3-η3)-5-tert-butylazapentadienyl]2Ru(PPh3)2 (1). Compound 1 undergoes single substitution of one of the triphenylphosphines when treated with PMe3, dmpe, P(OMe)3, CNCMe3, CO, and PEt3 at room temperature, resulting in [(1,2,3-η3)-5-tert-butylazapentadienyl]2Ru(PPh3)(L) (2, L = PMe3; 3, L= dmpe; 4, L = P(OMe)3; 5, L = CNCMe3; 6, L = CO; 7, L = PEt3). By increasing the reaction time of 1 with PEt3, double substitution of both triphenylphosphines occurs, resulting in [(1,2,3-η3)-5-tert-butylazapentadienyl]2Ru(PEt3)2 (8). Compounds 1 - 8 possess a pseudo-octahedral geometry where both ancillary ligands sit trans to the C3\u27s of the azapentadienyl ligands. Compounds 1 - 4, 7 and 8 exhibit a ligand orientation in which both ancillary ligands sit in the mouth of each azapentadienyl ligand, denoted as mC3/mC3. In contrast, 5 exhibits a ligand arrangement where the PPh3 sits in the mouth of one azapentadienyl ligand while CNCMe3 sits on the backbone of the other azapentadienyl ligand. Other double substitution reactions occur when 1 is treated with PMe3, P(OMe)3, and dmpe in THF at reflux, resulting in [(1,2,3-η3)-5-tert-butylazapentadienyl]2Ru(L)x (9, L = PMe3, x = 2; 10, L = P(OMe3), x = 2; 11, L = dmpe, x = 1). Compounds 9 and 10 exist in solution as an equilibrium mixture of two structural isomers. The two isomers in solution have either a mC3/mC3 or mC3/bC1 ligand orientation. Treatment of 8, 9 and 10 with triflic acid results in dicationic products, {[(1,2,3-η3)-(CH2CHCHCH=N(H)(CMe3)]2Ru(L)2}2+(-O3SCF3)2 (12, L = PEt3; 13, L = PMe3; 14, L = P(OMe)3), in which both azapentadienyl nitrogen atoms have been protonated. The protonated product, 12, shows a ligand conversion from mC3/mC3 (seen in 8) to mC3/bC3. Upon protonation, 9 and 10 each convert to a single isomer, 12 and 13, respectively. Like 12, compound 13 possesses a mC3/bC3 orientation while 14 has a ligand orientation in which the azapentadienyl ligands appear to be mC3/mC3. Treatment of 2, 4 and 5 with triflic acid results in multiple isomers of the diprotonated {[(1,2,3-η3)-CH2CHCHCH=N(H)(CMe3)]2Ru(PPh3)(L)}2+(-O3SCF3)2 (15, L = PMe3; 16, L = P(OMe)3; 17, L = CNCMe3). All of the compounds have been characterized, in part, by NMR spectroscopy, and the structures of 2, 4, 5, 7, 8, and 12 have been confirmed by single-crystal X-ray diffraction