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NASA NTRS1988

Unified constitutive models for high-temperature structural applications

Unified constitutive models are characterized by the use of a single inelastic strain rate term for treating all aspects of inelastic deformation, including plasticity, creep, and stress relaxation under monotonic or cyclic loading. The structure of this class of constitutive theory pertinent for high temperature structural applications is first outlined and discussed. The effectiveness of the unified approach for representing high temperature deformation of Ni-base alloys is then evaluated by extensive comparison of experimental data and predictions of the Bodner-Partom and the Walker models. The use of the unified approach for hot section structural component analyses is demonstrated by applying the Walker model in finite element analyses of a benchmark notch problem and a turbine blade problem.

Lindholm, U. S.↗

DOE OSTI2020

Biaxial steel plated concrete constitutive models for composite structures: Implementation and validation

The Steel-plated Concrete (SC) technique is an alternative construction technique with faster onsite construction speed, reduced construction time, and increased structural performance. Aiming to predict the force transfer mechanism of SC elements, an innovative constitutive model package is proposed by implementing experimental-based biaxial steel plate concrete models into the nonlinear finite element (FE) model “Membrane Model of SC (MM-CS).” First, the formulation and implementation of the MM-SC is illustrated in detail, including the equilibrium and compatibility equations and the implementation of constitutive models. Next, various experimental data of SC members are selected and simulated using the proposed MM-SC model. In this research, two types of structures, SC panels and framed SC shear walls, and three types of loading conditions, including uniaxial compression, pure shear, and combined axial-flexural-shear tests, are analyzed respectively. Good agreements were obtained between the reported results and the FE simulation results in terms of yield capacity and ultimate capacity, proving the reliability of the implemented analytical constitutive material models and the biaxial membrane model formulations.

42 ENGINEERING↗

DOE OSTI2024

Constitutive model development of aluminum alloy 1100 for elevated temperature forming process

Commercially pure aluminum alloy, AA1100, presents good electrical and thermal conductivity, high formability, and low cost. Those favorable characteristics have the potential to enable bipolar plates with improved economics and enhanced performance compared to current stainless steel bipolar plates for proton exchange membrane fuel cells. An accurate constitutive model is essential to develop and optimize processing parameters and effectively control the forming process. Here, the objective of this work is to develop a constitutive model of AA1100 that is able to simulate stress-strain relation, formed geometry, and predict the onset of fracture strain to avoid forming failure. Initially, a set of tensile tests at temperature between 300 and 500°C and strain rate between 0.005 and 1.0/s were conducted to examine the deformation behavior. Then, a set of damage-based unified visco-plastic constitutive equations is proposed and calibrated based on the results of stress-strain data. A genetic algorithm optimization method is applied to search for best fitting material constants in constitutive equations. The proposed model shows good predictability of both the stress-strain relation and fracture strain at low strain rate and high temperature conditions. The accuracy of proposed model is also evaluated statistically. A comparison of the proposed model with three popular models (Arrhenius-type mode, Johnson-Cook model and Zerilli-Armstrong model) was made. The proposed model shows the best experimental agreement with correlation coefficient of 0.96 in contrast to 0.25, 0.38 and 0.75 for the popular models, respectively. The proposed model can help to optimize the elevated temperature forming process and guide die design to enable optimal geometric features in the formed components.

08 HYDROGEN↗

NASA NTRS1983

An uncoupled viscoplastic constitutive model for metals at elevated temperature

An uncoupled constitutive model for predicting the transient response of thermal and rate dependent, inelastic material behavior is presented. 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 modeled in an incremental form with a yield function, flow 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 modeled 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 is 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.↗

DOE OSTI2025

Towards machine-learning a fully-coupled constitutive model for thermal-hydraulic fracture in geothermal systems: phase I (Final Report)

This project, entitled “Towards machine-learning a fully-coupled constitutive model for thermal-hydraulic fracture in geothermal systems: phase I,” addresses challenges in understanding and controlling subsurface fracture networks, which are crucial for applications like deep geothermal heat mining and deep-crustal minerals/metals/hydrogen extraction. The research focuses on advancing the understanding of coupled thermal-hydro-mechanical-chemical (THMC) processes in geologic materials, particularly under the high temperature and pressure conditions found in the deep crust. This seed grant focused specifically on thermal cracking and the development of new constitutive models. Significant progress was made in both experimental and theoretical domains. To study micro-scale fracture formation, the project demonstrated the ability to create thermal cracking under stress in granite samples using a Paterson Gas-medium Deformation Apparatus.

15 GEOTHERMAL ENERGY↗

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.↗

DOE OSTI2022

Initial development of viscoplastic constitutive model of Alloy 800H in support of the use of inelastic analysis methods for ASME Section III, Division 5, Class A applications

This report describes the development of a preliminary inelastic constitutive model for the thermomechanical behavior of Alloy 800H. The objective is to develop a model suitable for incorporating into Nonmandatory Appendix Z to Section III, Division 5 of the ASME Boiler & Pressure Vessel Code, which provides guidance and reference constitutive models for the ASME design by inelastic analysis rules for Class A components. The report describes the process of collecting experimental data, developing a mathematical form for the model, and training the model against the test data. The initial version of the model captures most of the relevant material deformation mechanisms, including dynamic strain aging effects. However, further development of the model form will be required to develop a final model suitable for ASME use.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

A mixed formulation of the plane-stress problem to facilitate reuse of constitutive models in finite-element programs

Here, the plane-stress assumption can be challenging to support in a finite element program because it traditionally requires separate implementations of constitutive models than those intended for three-dimensional or two-dimensional plane-strain simulations. As a solution to this issue, this paper presents a method to solve the plane-stress problem using a mixed formulation. In this formulation, the out-of-plane strain is treated as a field variable that is solved for in addition to the standard in-plane displacement variables, in a manner that weakly enforces the condition that the out-of-plane stress is zero. The proposed formulation is non-intrusive, requiring no modifications to the constitutive models in contrast to the conventional plane-stress formulation. The proposed mixed formulation has been benchmarked against analytical solutions and numerical solutions, with good performance and accuracy.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1984

Constitutive modeling for isotropic materials (HOST)

The results of the first year of work on a program to validate unified constitutive models for isotropic materials utilized in high temperature regions of gas turbine engines and to demonstrate their usefulness in computing stress-strain-time-temperature histories in complex three-dimensional structural components. The unified theories combine all inelastic strain-rate components in a single term avoiding, for example, treating plasticity and creep as separate response phenomena. An extensive review of existing unified theories is given and numerical methods for integrating these stiff time-temperature-dependent constitutive equations are discussed. Two particular models, those developed by Bodner and Partom and by Walker, were selected for more detailed development and evaluation against experimental tensile, creep and cyclic strain tests on specimens of a cast nickel base alloy, B19000+Hf. Initial results comparing computed and test results for tensile and cyclic straining for temperature from ambient to 982 C and strain rates from 10(exp-7) 10(exp-3) s(exp-1) are given. Some preliminary date correlations are presented also for highly non-proportional biaxial loading which demonstrate an increase in biaxial cyclic hardening rate over uniaxial or proportional loading conditions. Initial work has begun on the implementation of both constitutive models in the MARC finite element computer code.

Lindholm, Ulric S.↗

NASA NTRS1988

A constitutive model for an overlay coating

Coatings are frequently applied to gas turbine blades and vanes to provide protection against oxidation and corrosion. The results of an experimental and analytical study to develop a constitutive model for an overlay coating is presented. Specimens were machined from a hot isostatically pressed billet of PWA 286. The tests consisted of isothermal stress relaxation cycles with monotonically increasing maximum strain and were conducted at various temperatures. The results were used to calculate the constants for various constitutive models, including the classical, the Walker isotropic, a simplified Walker, and Stowell models. A computerized regression analysis was used to calculate model constants from the data. The best fit was obtained for the Walker model, with the simplified Walker and classical models close behind.

Nissley, D. M.↗

NASA NTRS1983

Application of an Uncoupled Elastic-plastic-creep Constitutive Model to Metals at High Temperature

A uniaxial, uncoupled constitutive model to predict the response of thermal and rate dependent elastic-plastic material behavior is presented. The model is based on an incremental classicial plasticity theory extended to account for thermal, creep, and transient temperature conditions. Revisions to he combined hardening rule of the theory allow for better representation of cyclic phenomenon including the high rate of strain hardening upon cyclic reyield and cyclic saturation. An alternative approach is taken to model the rate dependent inelastic deformation which utilizes hysteresis loops and stress relaxation test data at various temperatures. The model is evaluated and compared to experiments which involve various thermal and mechanical load histories on 5086 aluminum alloy, 304 stainless steel and Hastelloy-X.

Haisler, W. E.↗

NASA NTRS2007

A Constitutive Model for Creep Lifetime of PBO Braided Cord

A constitutive model to describe the creep lifetime of PBO braided cord has been developed and fit to laboratory data. The model follows an approach proposed for p-aramid cord in similar applications, and has a Boltzman-type representation that arises from consideration of the failure phenomenon mechanism. The data were obtained using a hydraulic-type universal testing machine, and were analyzed according to Weibull statistics using commercially-available software. The application of concern to the author is NASA's Ultra- Long Duration Balloon and other gossamer spacecraft, but the motivations for the related p-aramid works suggest broader interest.

Sterling, W. J.↗

NASA NTRS2004

Constitutive Modeling of Crosslinked Nanotube Materials

A non-linear, continuum-based constitutive model is developed for carbon nanotube materials in which bundles of aligned carbon nanotubes have varying amounts of crosslinks between the nanotubes. The model accounts for the non-linear elastic constitutive behavior of the material in terms of strain, and is developed using a thermodynamic energy approach. The model is used to examine the effect of the crosslinking on the overall mechanical properties of variations of the crosslinked carbon nanotube material with varying degrees of crosslinking. It is shown that the presence of the crosslinks has significant effects on the mechanical properties of the carbon nanotube materials. An increase in the transverse shear properties is observed when the nanotubes are crosslinked. However, this increase is accompanied by a decrease in axial mechanical properties of the nanotube material upon crosslinking.

Odegard, G. M.↗

DOE OSTI2021

A constitutive model for glass–ceramic materials

Glass–ceramics have received recent attention for use in glass–ceramic to metal hermetic seals. Due to their heterogeneous microstructure, these materials exhibit a number of advantageous responses over conventional glass based seals. Key amongst them is the possibility of a controllable thermal strain response and apparent coefficient of thermal expansion which may be used to minimize thermally induced residual stresses for aforementioned seals. Furthermore, these behaviors result from an inorganic glass matrix and variety of crystalline ceramic phases including silica polymorph(s) that may undergo reversible solid-to-solid transformations with associated inelastic strain. Correspondingly, these materials exhibit complex thermomechanical responses associated with multiple inelastic mechanisms (viscoelasticity and phase transformation). While modeling these behaviors is essential for developing and analyzing the corresponding applications, no such model exists. Therefore, in this work a three-dimensional continuum constitutive model for glass–ceramic materials combining these various inelastic mechanisms is developed via an internal state variable approach. A corresponding fully implicit three dimensional numerical formulation is also proposed and implemented. The model is used to simulate existing experiments and validate the proposed formalism. As an example, the simple seal problem of a glass–ceramic seal inside a concentric metal shell is explored. Finally, the impact of the cooling rates, viscoelastic shift factors, and inelastic strain on final residual stress state are all investigated and the differing contributions highlighted.

36 MATERIALS SCIENCE↗

NASA NTRS1985

Constitutive modeling for isotropic materials

The objective is to develop a unified constitutive model for finite element structural analysis of turbine engine hot-section components. This effort constitutes a different approach for non-linear finite-element computer codes which have heretofore been based on classical inelastic methods. The unified constitutive theory to be developed will avoid the simplifying assumptions of classical theory and should more accurately represent the behavior of superalloy materials under cyclic loading conditions and high temperature environments. During the first two years of the program, extensive experimental correlations were made with two representative unified models. The experiments were both uniaxial and biaxial at temperatures up to 1093 C (2000 F). In addition, the unified models were adopted to the MARC finite element code and used for stress analysis of notched bar and turbine blade geometries.

Lindholm, Ulric S.↗

DOE OSTI2023

A constitutive model for sheared dense fiber suspensions

Here we propose a constitutive model to predict the viscosity of fiber suspensions, which undergoes shear thinning, at various volume fractions, aspect ratios, and shear stresses/rates. We calibrate the model using the data from direct numerical simulation and prove the accuracy by predicting experimental measurements from the literature. We use a friction coefficient decreasing with the normal load between the fibers to quantitatively reproduce the experimentally observed shear thinning in fiber suspensions. In this model, the effective normal contact force, which is directly proportional to the bulk shear stress, determines the effective friction coefficient. A rise in the shear stress reduces the effective friction coefficient in the suspension. As a result, the jamming volume fraction increases with the shear stress, resulting in a shear thinning in the suspension viscosity. Moreover, we extend the model to quantify the effects of fiber volume fraction and aspect ratio in the suspension. We calibrate this model using the data from numerical simulations for the rate-controlled shear flow. Once calibrated, we show that the model can be used to predict the relative viscosity for different volume fractions, shear stresses, and aspect ratios. The model predictions are in excellent agreement with the available experimental measurements from the literature. The findings of this study can potentially be used to tune the fiber size and volume fraction for designing the suspension rheology in various applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1995

On the Finite Element Implementation of the Generalized Method of Cells Micromechanics Constitutive Model

The Generalized Method of Cells (GMC), a micromechanics based constitutive model, is implemented into the finite element code MARC using the user subroutine HYPELA. Comparisons in terms of transverse deformation response, micro stress and strain distributions, and required CPU time are presented for GMC and finite element models of fiber/matrix unit cell. GMC is shown to provide comparable predictions of the composite behavior and requires significantly less CPU time as compared to a finite element analysis of the unit cell. Details as to the organization of the HYPELA code are provided with the actual HYPELA code included in the appendix.

Wilt, T. E.↗

NASA NTRS1982

Constitutive model development for isotropic materials

The objective is to develop a unified constitutive model for finite-element structural analysis of turbine engine hot section components. This effort constitutes a different approach for nonlinear finite-element computer codes which were heretofore based on classical inelastic methods. A unified constitutive theory will avoid the simplifying assumptions of classical theory and should more accurately represent the behavior of superalloy materials under cyclic loading conditions and high temperature environments. Model development will be directed toward isotropic, cast nickel-base alloys used for aircooled turbine blades and vanes. The contractor will select a base material for model development and an alternate material for verification purposes from a list of three alloys specified by NASA. The candidate alloys represent a cross-section of turbine blade and vane materials of interest to both large and small size engine manufacturers. Material stock for the base and alternate materials will be supplied to the Contractor by the government.

Kaufman, A.↗