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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

ASME Code change proposal to implement new universal high temperature constitutive models for Section III, Division 5

This report completes work on a universal high temperature constitutive model suitable for use with the ASME Boiler & Pressure Vessel Code Section III, Division 5 rules for the design by inelastic analysis of Class A nuclear reactor components. The goals of this work are to provide a simple model form that adequately captures the high temperature response of materials and can be applied to any future Code material. Additionally, the report describes an automated process for calibrating a model against test data. The idea is to simplify the effort required to generate a constitutive model for an arbitrary material, provided test data is available. This will accelerate the process of qualifying new Code materials in the future. In addition, the report provides calibrated models and detailed validation comparisons to test data for five currently-qualified or soon-to-be qualified materials: 316H, Grade 91, Alloy 800H, Alloy 617, and Alloy 709. The report surveys the available data for the remaining two ASME Class Materials --- 2.25Cr-1Mo and 304H --- concluding that there is enough data data to generate a model for 2.25Cr-1Mo steel provided some additional sources of non-public data can be included in the test database, but that a dedicated cyclic test campaign would be needed for 304H. Supplemental material includes the full text of an ASME Code change proposal to incorporate the models for the four currently-qualified Class A material, detailed validation comparisons to test data for the five material models, and input files for reference implementations of the constitutive models in the NEML and NEML2 modeling frameworks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS2003

Development of a Pressure-Dependent Constitutive Model with Combined Multilinear Kinematic and Isotropic Hardening

The development of a pressure-dependent constitutive model with combined multilinear kinematic and isotropic hardening is presented. The constitutive model is developed using the ABAQUS user material subroutine (UMAT). First the pressure-dependent plasticity model is derived. Following this, the combined bilinear and combined multilinear hardening equations are developed for von Mises plasticity theory. The hardening rule equations are then modified to include pressure dependency. The method for implementing the new constitutive model into ABAQUS is given.

Allen Phillip A.↗
DOE OSTI2023

An assessment of Callahan's crushed salt constitutive model

This memorandum investigates the Callahan crushed salt constitutive model developed and used at Sandia National Laboratories for geomechanics applications. The formulation is reviewed, calibration against a novel long-term experiment with complex loading history is performed and validation against other experiments is attempted. Areas of improvement and deficiencies are identified that support the need for an alternative or updated constitutive model for crushed salt.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS2026

Development, Characterization, and Validation of Elevated-Temperature Constitutive Models: Deformation and Damage

This report provides a brief review of experimentally observed hereditary and nonhereditary material behavior along with background information on standard as well as advanced internal state variable constitutive modeling at elevated temperature. A description of exploratory, characterization, and validation testing is presented along with a detailed outline of what constitutes “sufficient” data content (i.e., quality and quantity) for developing or enhancing, characterizing, and validating a particular sophisticated nonlinear time- and history-dependent (hereditary) class of constitutive models known as GVIPS (generalized viscoplasticity with potential structure). The tests described are necessary to reveal a material’s behavior in the reversible (or viscoelastic) and irreversible (or viscoplastic) regimes, for the identification of both deformation and damage model parameters. Results presented are primarily for metallic materials. In all cases, both uniaxial and multiaxial tests are described, and the linkage between the specific tests and the parameters within the model that can be characterized from the results of these tests are also discussed. Discussion is also provided relative to the role information management must play relative to material data collection, analysis, maintenance, and dissemination. The need for such an information system is particularly important as both analyst and designer move toward utilizations of sophisticated, nonlinear time- and history dependent (hereditary) constitutive models. Lastly, the concept of state space and its utility in understanding and establishing constitutive models is addressed throughout. The intent behind this document is to help both the modeler and experimentalist understand each other’s specific points of view and provide guidance for both model development and characterization. Emphasis has been placed on providing the mechanician with information regarding how tests are performed and what issues to be aware of when interpreting results. It is hoped that experimentalists will take away a new perspective on the types of information that modelers and analysts are looking for from them.

Constitutive Modeling↗
NASA NTRS1986

Structural analysis of turbine blades using unified constitutive models

The utility of advanced constitutive models and structural analysis methods in predicting the cyclic life of an air-cooled turbine blade is assessed. Five structural analysis methods were exercised in calculating the cyclic stress-strain response at the airfoil critical location. The methods studied were a cyclic elastic finite-element analysis, nonlinear finite-element analyses based on classical inelastic models and the unified models of Bodner and Walker, and a simplified inelastic procedure. These analyses were compared in terms of computing times and of predicted crack initiation lives using the Strainrange Partitioning method.

Kaufman, A.↗
NASA NTRS1988

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.

Sherwood, J. A.↗
NASA NTRS1985

Constitutive modeling for single crystal superalloys

A crystallographic approach to constitutive modeling of single crystal superalloys is discussed. The approach is based on identifying the active slip planes and slip directions. The shear stresses are computed on each of the slip planes from applied stress components. The slip rate is then computed on each slip system and the microscopic inelastic strain rates are the sum of the slip in the individual slip systems. The constitutive model was implemented in a finite element code using twenty noted isoparametric solid elements. Constants were determined for octahedral and cube slip systems. These constants were then used to predict tension-compression asymmetry and fatigue loops. Other data was used to model the tensile and creep response.

Stouffer, Donald C.↗
NASA NTRSDate not supplied

A Nonlinear Viscoelastic-Viscoplastic Constitutive Model for Epoxy Polymers

The objective of this paper is to develop a nonlinear viscoelastic–viscoplastic constitutive model for epoxy polymers. The classic nonlinear viscoelasticity model is reformulated to yield a closed-form incremental constitutive relation, which relates the stress increments to the viscoelastic strain increments. A viscoplasticity model, which consists of the Drucker–Prager yield function, nonlinear isotropic and kinematic hardening laws, and the Perzyna viscosity function, is subsequently developed. The nonlinear viscoelasticity and the vis-coplasticity models are then implemented in a radial return algorithm. A closed-form algorithmic tangent operator is derived to facilitate model implementation. The nonlinear viscoelasticity model is validated by reproducing the test data for polymethyl methacrylate(PMMA). The present constitutive model’s capabilities are demonstrated through modeling viscoelastic–viscoplastic PMMA loaded at different strain rates. The mechanics of structure genome-based micromechanics approach, embedded with the present constitutive model, is used to homogenize a unidirectional fiber-reinforced composite with a PMMA matrix, subjected to uniaxial and shear loading at different strain rates. The viscoelastic characterization of PMT-F7 epoxy is evaluated by comparing the predicted creep–recovery responses by the present constitutive model with the experimental ones.

Liang Zhang↗
NASA NTRS1982

Life prediction and constitutive models for anisotropic materials

The intent of this program is to develop a basic understanding of cyclic creep-fatigue deformation mechanisms and damage accumulation, a capability for reliable life prediction, and the ability to model the constitutive behavior of anisotropic single crystal (SC) and directionally solidified or recrystallized (DSR) comprise the program, and the work breakdown for each option reflects a distinct concern for two classes of anisotropic materials, SC and DSR materials, at temperatures encountered in the primary gas path (airfoil temperatures), and at temperatures typical of the blade root attachment and shank area. Work directed toward the higher temperature area of concern in the primary gas path includes effects of coatings on the behavior and properties of the materials of interest. The blade root attachment work areas will address the effects of stress concentrations associated with attachment features.

Bill, R. C.↗
DOE OSTI2022

ASME Code Revisions to Incorporate 316H and Alloy 617 Viscoplastic Constitutive Models to Section III, Division 5 and Code Case N-898

This report provides a final status update on work to develop and implement two new constitutive models for 316H stainless steel and the Ni-based Alloy 617 in Nonmandatory Appendix Z to the Section III, Division 5, Subsection HB, Subpart B ASME Boiler & Pressure Vessel Code rules covering the design and construction of Class A high temperature nuclear reactor components. This report summarizes the objections of the overall project and provides the final versions of the constitutive models proposed for incorporation into the ASME Code. The report also provides an update on the balloting status at ASME of the two proposed constitutive models. As of the time of writing (July 2022) the models are on-track to be approved by ASME after the August 2022 Code Week. If so, this will mean the 316H model will be published in the 2023 edition of the Code and the A617 model available as part of a revised Code Case immediately

36 MATERIALS SCIENCE↗
DOE OSTI2025

Advancements in Constitutive Model Calibration: Leveraging the Power of Full‐Field DIC Measurements and In Situ Load Path Selection for Reliable Parameter Inference

Accurate material characterization and model calibration are essential for computationally supported high-consequence engineering decisions. Historically, characterization and calibration methods (1) use simplified test specimen geometries and global data, (2) cannot guarantee that sufficient characterization data are collected for a specific model of interest, (3) use deterministic methods that provide best-fit parameter values with no uncertainty quantification, and (4) are sequential, inflexible, and time-consuming. This work brings together several recent advancements into an improved workflow called interlaced characterization and calibration (ICC) that advances the state-of-the-art in constitutive model calibration. The ICC paradigm (1) employs tools to efficiently use full-field data to calibrate high-fidelity material models, (2) aligns the data needed with the data collected by adopting an optimal experimental design protocol, (3) quantifies parameter uncertainty through Bayesian inference and (4) incorporates these advancements into a quasi real-time feedback loop. The ICC framework is demonstrated here on the calibration of a material model using simulated full-field data for an aluminium cruciform specimen being deformed biaxially. The cruciform is actively driven through the myopically preferred load path using Bayesian optimal experimental design, which selects load steps that yield the maximum expected information gain (EIG). Principal component analysis (PCA) is performed on the model predictions of full-field displacements, and fast surrogate models are built to approximate the input-output relationships of the expensive finite element model. Furthermore, the tools developed and demonstrated here show that high-fidelity constitutive models can be efficiently and reliably calibrated with quantified uncertainty, thus supporting credible decision-making and potentially increasing the agility of solid mechanics modelling by enabling utilization of computational simulations at earlier stages of the design cycle.

Bayesian optimal experimental design↗
NASA NTRS1995

Requirements for energy based constitutive modeling in tire mechanics

The history, requirements, and theoretical basis of a new energy based constitutive model for (rubber) material elasticity, hysteresis, and failure are presented. Energy based elasticity is handled by many constitutive models, both in one dimension and in three dimensions. Conversion of mechanical energy to heat can be modeled with viscoelasticity or as structural hysteresis. We are seeking unification of elasticity, hysteresis, and failure mechanisms such as fatigue and wear. An energy state characterization for failure criteria of (rubber) materials may provide this unification and also help explain the interaction of temperature effects with failure mechanisms which are described as creation of growth of internal crack surface. Improved structural modeling of tires with FEM should result from such a unified constitutive theory. The theory will also guide experimental work and should enable better interpretation of the results of computational stress analyses.

Luchini, John R.↗
DOE OSTI2026

A finite viscoelastic constitutive model for low to high strain rate response of elastomers with application of strain rate-induced glass transition

Amorphous elastomers exhibit significant rate-stiffening and unique viscous flow characteristics across a wide range of strain rates, often undergoing glass transition above a strain rate threshold. We have developed a thermodynamically-consistent and micromechanically-inspired constitutive model for soft elastomeric materials to capture the rate-dependent stress-strain behavior and hysteresis when subjected to low to high strain rates. Here, our proposed constitutive model encapsulates the viscous flow of materials through molecular motion at low strain rates and local rearrangement and alignment of the molecules trying to overcome the intermolecular resistance at high strain rates, essentially covering the glass transition. We applied our constitutive model to uniaxial compression experiments performed at low and high strain rates for polyborosiloxane (PBS) to identify the material parameters, and subsequently, performed numerical simulations of single and multi-cycle compression, stress relaxation, and small amplitude oscillatory tension-compression. Our analyses indicate that the model predicts higher total energy dissipation with increasing strain rate; however, dissipation associated with molecular relaxation decreases (forming a cusp) because, beyond a crossover strain rate, intermolecular rearrangement and alignment become dominant, which is consistent with the onset of the glass transition. For cyclic loading-unloading, we observed that dissipation over a cycle remains constant at low strain rates but decreases non-monotonically at high strain rates before becoming constant, with the peak stress over the cycle becoming higher, which can be interpreted as more loading being carried elastically by the polymer network as the intermolecular rearrangement process occurs. Additionally, our model was able to predict the qualitative nature of the storage modulus and loss modulus in the limit of small strain over a wide range of frequency sweeps.

36 MATERIALS SCIENCE↗
NASA NTRS1984

Constitutive modeling for isotropic materials

A state-of-the-art review of applicable constitutive models with selection of two for detailed comparison with a wide range of experimental tests was conducted. The experimental matrix contained uniaxial and biaxial tensile, creep, stress relaxation, and cyclic fatigue tests at temperatures to 1093 C and strain rates from .0000001 to .001/sec. Some nonisothermal cycles will also be run. The constitutive models will be incorporated into the MARC finite element structural analysis program with a demonstration computation made for advanced turbine blade configuration. In the code development work, particular emphasis is being placed on developing efficient integration algorithms for the highly nonlinear and stiff constitutive equations. Another area of emphasis is the appropriate and efficient methodology for determing constitutive constants from a minimum extent of experimental data.

Lindholm, U. S.↗
NASA NTRS2001

The Constitutive Modeling of Thin Films with Randon Material Wrinkles

Material wrinkles drastically alter the structural constitutive properties of thin films. Normally linear elastic materials, when wrinkled, become highly nonlinear and initially inelastic. Stiffness' reduced by 99% and negative Poisson's ratios are typically observed. This paper presents an effective continuum constitutive model for the elastic effects of material wrinkles in thin films. The model considers general two-dimensional stress and strain states (simultaneous bi-axial and shear stress/strain) and neglects out of plane bending. The constitutive model is derived from a traditional mechanics analysis of an idealized physical model of random material wrinkles. Model parameters are the directly measurable wrinkle characteristics of amplitude and wavelength. For these reasons, the equations are mechanistic and deterministic. The model is compared with bi-axial tensile test data for wrinkled Kaptong(Registered Trademark) HN and is shown to deterministically predict strain as a function of stress with an average RMS error of 22%. On average, fitting the model to test data yields an RMS error of 1.2%

Murphey, Thomas W.↗
NASA NTRS1990

Application of symbolic computations to the constitutive modeling of structural materials

In applications involving elevated temperatures, the derivation of mathematical expressions (constitutive equations) describing the material behavior can be quite time consuming, involved and error-prone. Therefore intelligent application of symbolic systems to faciliate this tedious process can be of significant benefit. Presented here is a problem oriented, self contained symbolic expert system, named SDICE, which is capable of efficiently deriving potential based constitutive models in analytical form. This package, running under DOE MACSYMA, has the following features: (1) potential differentiation (chain rule), (2) tensor computations (utilizing index notation) including both algebraic and calculus; (3) efficient solution of sparse systems of equations; (4) automatic expression substitution and simplification; (5) back substitution of invariant and tensorial relations; (6) the ability to form the Jacobian and Hessian matrix; and (7) a relational data base. Limited aspects of invariant theory were also incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet pre-defined order and simplify expressions so as to limit expression growth. Results are displayed, when applicable, utilizing index notation. SDICE was designed to aid and complement the human constitutive model developer. A number of examples are utilized to illustrate the various features contained within SDICE. It is expected that this symbolic package can and will provide a significant incentive to the development of new constitutive theories.

Arnold, Steven M.↗
NASA NTRS1986

Anisotropic constitutive model for nickel base single crystal alloys: Development and finite element implementation

A tool for the mechanical analysis of nickel base single crystal superalloys, specifically Rene N4, used in gas turbine engine components is developed. This is achieved by a rate dependent anisotropic constitutive model implemented in a nonlinear three dimensional finite element code. The constitutive model is developed from metallurigical concepts utilizing a crystallographic approach. A non Schmid's law formulation is used to model the tension/compression asymmetry and orientation dependence in octahedral slip. Schmid's law is a good approximation to the inelastic response of the material in cube slip. The constitutive equations model the tensile behavior, creep response, and strain rate sensitivity of these alloys. Methods for deriving the material constants from standard tests are presented. The finite element implementation utilizes an initial strain method and twenty noded isoparametric solid elements. The ability to model piecewise linear load histories is included in the finite element code. The constitutive equations are accurately and economically integrated using a second order Adams-Moulton predictor-corrector method with a dynamic time incrementing procedure. Computed results from the finite element code are compared with experimental data for tensile, creep and cyclic tests at 760 deg C. The strain rate sensitivity and stress relaxation capabilities of the model are evaluated.

Dame, L. T.↗
NASA NTRS2002

Constitutive Modeling of Nanotube-Reinforced Polymer Composites

In this study, a technique is presented for developing constitutive models for polymer composite systems reinforced with single-walled carbon nanotubes (SWNT). Because the polymer molecules are on the same size scale as the nanotubes, the interaction at the polymer/nanotube interface is highly dependent on the local molecular structure and bonding. At these small length scales, the lattice structures of the nanotube and polymer chains cannot be considered continuous, and the bulk mechanical properties can no longer be determined through traditional micromechanical approaches that are formulated by using continuum mechanics. It is proposed herein that the nanotube, the local polymer near the nanotube, and the nanotube/polymer interface can be modeled as an effective continuum fiber using an equivalent-continuum modeling method. The effective fiber serves as a means for incorporating micromechanical analyses for the prediction of bulk mechanical properties of SWNT/polymer composites with various nanotube lengths, concentrations, and orientations. As an example, the proposed approach is used for the constitutive modeling of two SWNT/polyimide composite systems.

Odegard, G. M.↗