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NASA NTRS2006

Large Engine Technology (LET) Short Haul Civil Tiltrotor Contingency Power Materials Knowledge and Lifing Methodologies

This report documents the results of an experimental program conducted on two advanced metallic alloy systems (Rene' 142 directionally solidified alloy (DS) and Rene' N6 single crystal alloy) and the characterization of two distinct internal state variable inelastic constitutive models. The long term objective of the study was to develop a computational life prediction methodology that can integrate the obtained material data. A specialized test matrix for characterizing advanced unified viscoplastic models was specified and conducted. This matrix included strain controlled tensile tests with intermittent relaxtion test with 2 hr hold times, constant stress creep tests, stepped creep tests, mixed creep and plasticity tests, cyclic temperature creep tests and tests in which temperature overloads were present to simulate actual operation conditions for validation of the models. The selected internal state variable models where shown to be capable of representing the material behavior exhibited by the experimental results; however the program ended prior to final validation of the models.

Spring, Samuel D.↗

NASA NTRS2006

Using ABAQUS Scripting Interface for Materials Evaluation and Life Prediction

An ABAQUS script has been written to aid in the evaluation of the mechanical behavior of viscoplastic materials. The purposes of the script are to: handle complex load histories; control load/displacement with alternate stopping criteria; predict failure and life; and verify constitutive models. Material models from the ABAQUS library may be used or the UMAT routine may specify mechanical behavior. User subroutines implemented include: UMAT for the constitutive model; UEXTERNALDB for file manipulation; DISP for boundary conditions; and URDFIL for results processing. Examples presented include load, strain and displacement control tests on a single element model. The tests are creep with a life limiting strain criterion, strain control with a stress limiting cycle and a complex interrupted cyclic relaxation test. The techniques implemented in this paper enable complex load conditions to be solved efficiently with ABAQUS.

Powers, Lynn M.↗

NASA NTRS2006

Thermal Expansion of Polyurethane Foam

Closed cell foams are often used for thermal insulation. In the case of the Space Shuttle, the External Tank uses several thermal protection systems to maintain the temperature of the cryogenic fuels. A few of these systems are polyurethane, closed cell foams. In an attempt to better understand the foam behavior on the tank, we are in the process of developing and improving thermal-mechanical models for the foams. These models will start at the microstructural level and progress to the overall structural behavior of the foams on the tank. One of the key properties for model characterization and verification is thermal expansion. Since the foam is not a material, but a structure, the modeling of the expansion is complex. It is also exacerbated by the anisoptropy of the material. During the spraying and foaming process, the cells become elongated in the rise direction and this imparts different properties in the rise direction than in the transverse directions. Our approach is to treat the foam as a two part structure consisting of the polymeric cell structure and the gas inside the cells. The polymeric skeleton has a thermal expansion of its own which is derived from the basic polymer chemistry. However, a major contributor to the thermal expansion is the volume change associated with the gas inside of the closed cells. As this gas expands it exerts pressure on the cell walls and changes the shape and size of the cells. The amount that this occurs depends on the elastic and viscoplastic properties of the polymer skeleton. The more compliant the polymeric skeleton, the more influence the gas pressure has on the expansion. An additional influence on the expansion process is that the polymeric skeleton begins to breakdown at elevated temperatures and releases additional gas species into the cell interiors, adding to the gas pressure. The fact that this is such a complex process makes thermal expansion ideal for testing the models. This report focuses on the thermal expansion tests and the response of the microstructure. A novel optical method is described which is appropriate for measuring thermal expansion at high temperatures without influencing the thermal expansion measurement. Detailed microstructural investigations will also be described which show cell expansion as a function of temperature. Finally, a phenomenological model on thermal expansion will be described.

Lerch, Bradley A.↗

NASA NTRS2006

STRANAL-PMC Version 2.0

Version 2.0 of the Strain Rate Dependent Analysis of Polymer Matrix Composites (STRANAL-PMC) software has been released. A prior version was reported in Analyzing Loads and Strains in Polymer- Matrix Composites (LEW-17227), NASA Tech Briefs, Vol. 26, No. 11 (November 2002), page 36. To recapitulate: Modified versions of constitutive equations of viscoplasticity of metals are used to represent deformation of a polymeric matrix. The equations are applied in a micromechanical approach, proceeding upward from slices of unit cells, through the ply level, to the laminate level. The constitutive equations are integrated in time by a Runge- Kutta technique. To predict the ultimate strength of each composite ply, failure criteria are implemented within the micromechanics. The inputs to STRANAL-PMC are the laminate geometry, properties of the fiber and matrix materials, and applied stress or strain versus time. The outputs are time-dependent stresses and strains at the slice, ply, and laminate levels. The improvements in version 2.0 include more rigorous representation of hydrostatic- stress effects in the matrix, refinement and extension of ply failure models, and capabilities to analyze transverse shear stresses. Version 2.0 can be implemented as a material-model code within transient dynamic finite-element codes.

Goldberg, Robert↗

NASA NTRS2010

Phase Transformation and Creep Behavior in Ti50Pd30Ni20 High Temperature Shape Memory Alloy in Compression

The creep behavior and the phase transformation of Ti50Pd30Ni20 High Temperature Shape Memory Alloy (HTSMA) is investigated by standard creep tests and thermomechanical tests. Ingots of the alloy are induction melted, extruded at high temperature, from which cylindrical specimens are cut and surface polished. A custom high temperature test setup is assembled to conduct the thermomechanical tests. Following preliminary monotonic tests, standard creep tests and thermally induced phase transformation tests are conducted on the specimen. The creep test results suggest that over the operating temperatures and stresses of this alloy, the microstructural mechanisms responsible for creep change. At lower stresses and temperatures, the primary creep mechanism is a mixture of dislocation glide and dislocation creep. As the stress and temperature increase, the mechanism shifts to predominantly dislocation creep. If the operational stress or temperature is raised even further, the mechanism shifts to diffusion creep. The thermally induced phase transformation tests show that actuator performance can be affected by rate independent irrecoverable strain (transformation induced plasticity + retained martensite) as well as creep. The rate of heating and cooling can adversely impact the actuators performance. While the rate independent irrecoverable strain is readily apparent early in the actuators life, viscoplastic strain continues to accumulate over the lifespan of the HTSMA. Thus, in order to get full actuation out of the HTSMA, the heating and cooling rates must be sufficiently high enough to avoid creep.

Kumar, Parikshith K.↗

NASA NTRS2010

Experiment and Modeling of Simultaneous Creep, Plasticity and Transformation of High Temperature Shape Memory Alloys During Cyclic Actuation

The present work is focused on studying the cycling actuation behavior of HTSMAs undergoing simultaneous creep and transformation. For the thermomechanical testing, a high temperature test setup was assembled on a MTS frame with the capability to test up to temperatures of 600 C. Constant stress thermal cycling tests were conducted to establish the actuation characteristics and the phase diagram for the chosen HTSMA. Additionally, creep tests were conducted at constant stress levels at different test temperatures to characterize the creep behavior of the alloy over the operational range. A thermodynamic constitutive model is developed and extended to take into account a) the effect of multiple thermal cycling on the generation of plastic strains due to transformation (TRIP strains) and b) both primary and secondary creep effects. The model calibration is based on the test results. The creep tests and the uniaxial tests are used to identify the viscoplastic behavior of the material. The parameters for the SMA properties, regarding the transformation and transformation induced plastic strain evolutions, are obtained from the material phase diagram and the thermomechanical tests. The model is validated by predicting the material behavior at different thermomechanical test conditions.

Kumar, Parikshith K.↗

NASA NTRS2013

Viscoelastoplastic Deformation and Damage Response of Titanium Alloy, Ti-6Al-4V, at Elevated Temperatures

Time-dependent deformation and damage behavior can significantly affect the life of aerospace propulsion components. Consequently, one needs an accurate constitutive model that can represent both reversible and irreversible behavior under multiaxial loading conditions. This paper details the characterization and utilization of a multi-mechanism constitutive model of the GVIPS class (Generalized Viscoplastic with Potential Structure) that has been extended to describe the viscoelastoplastic deformation and damage of the titanium alloy Ti-6Al-4V. Associated material constants were characterized at five elevated temperatures where viscoelastoplastic behavior was observed, and at three elevated temperatures where damage (of both the stiffness reduction and strength reduction type) was incurred. Experimental data from a wide variety of uniaxial load cases were used to correlate and validate the proposed GVIPS model. Presented are the optimized material parameters, and the viscoelastoplastic deformation and damage responses at the various temperatures.

Arnold, Steven M.↗

NASA NTRS2017

Effects of Adiabatic Heating on the High Strain Rate Deformation of Polymer Matrix Composites

Polymer matrix composites (PMCs) are increasingly being used in aerospace structures that are expected to experience complex dynamic loading conditions throughout their lifetime. As such, a detailed understanding of the high strain rate behavior of the constituents, particularly the strain rate, temperature, and pressure dependent polymer matrix, is paramount. In this paper, preliminary efforts in modeling experimentally observed temperature rises due to plastic deformation in PMCs subjected to dynamic loading are presented. To this end, an existing isothermal viscoplastic polymer constitutive formulation is extended to model adiabatic conditions by incorporating temperature dependent elastic properties and modifying the components of the inelastic strain rate tensor to explicitly depend on temperature. It is demonstrated that the modified polymer constitutive model is capable of capturing strain rate and temperature dependent yield as well as thermal softening associated with the conversion of plastic work to heat at high rates of strain. The modified constitutive model is then embedded within a strength of materials based micromechanics framework to investigate the manifestation of matrix thermal softening, due to the conversion of plastic work to heat, on the high strain rate response of a T700Epon 862 (T700E862) unidirectional composite. Adiabatic model predictions for high strain rate composite longitudinal tensile, transverse tensile, and in-plane shear loading are presented. Results show a substantial deviation from isothermal conditions; significant thermal softening is observed for matrix dominated deformation modes (transverse tension and in-plane shear), highlighting the importance of accounting for the conversion of plastic work to heat in the polymer matrix in the high strain rate analysis of PMC structures.

polymer matrix composites↗

NASA NTRS2025

Physics-Based Modeling and Simulation of Self-Reacting Friction Stir Welding Using Computational Fluid Dynamics

A physics-based model was developed to simulate the behavior of material in a self-reacting friction stir welding (SR-FSW) process for the joining of metals. This steady-state model builds upon fundamental computational fluid dynamic (CFD) principles within Ansys Fluent to solve the discretized equations. The effective viscosity is calculated using a viscoplastic model using a Sheppard-Wright formulation of flow stress. Numerous advancements have been made in the incorporated physics including (1) temperature-dependent material properties; (2) locally adaptable flow and thermal boundary conditions; and (3) adapting material properties in nugget in response to microstructural changes. Simulation strategies to accelerate computation and improve numerical stability include adapting the mesh refinement and solver relaxation factors during simulation. The result is a highly robust and computationally efficient model capable of providing the material flow and temperature history across the domain. As material history determines the local microstructure and ultimately weld strength, an accurate and detailed physics-based model has the potential to accelerate SR-FSW process development. The model is highly adaptable to changes in process parameters, tool design, or alloy.

Process Modeling↗

DOE OSTI2023

Overview of a Versatile Loading System for Anisotropic Material Property Characterization

Additive manufacturing, cold rolling, and other thermomechanical treatments on metals, especially HCP, can cause texture and oriented grain structures resulting in anisotropic mechanical properties. This can lead to macroscopic response that significantly deviates from isotropic assumptions which motivates studying mechanical properties in multiple directions. In addition, multiaxial loading and complex stress states overlapping the above mentioned material anisotropy can lead to unexpected outcomes. Idaho National Laboratory developed an advanced mechanical testing system to study a range of uniaxial to multiaxial stress states while measuring the anisotropic response bringing insight into the overlap between material properties and stress states. High-temperature capability and stress- or strain-controlled loading is available to enable a variety of experiment types and conditions to measure elastic, plastic, and viscoplastic properties. This poster presents the design and capabilities of this system with preliminary results highlighting the benefits of multiaxial loading and anisotropic analysis in an integrated system.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

From Well Log to Formation Model: A Novel Laboratory Calibrated Methodology with Demonstration

This work demonstrates how the characterization and modeling of both elastic and creep properties are essential to describe zones in layered rock formations as either low-stress targets for stimulation or high-stress barriers to fracture growth. Prediction of fracture height is critical for designing stimulation operations in oil and gas wells. Ideally, fractures are placed in target zones which will produce hydrocarbons and should not propagate into zones expected to be unproductive or to produce unwanted fluids such as water which in turn must be treated and/or disposed. The essential task in designing stimulation plans is predicting which zones have low horizontal stresses and which will be high-stress barriers to fracture growth. Despite this importance, there are gaps in current knowledge and a complete workflow from laboratory characterization to a finite element model which includes time dependent rock deformation is required. While the research and methodology presented here also have application to CO 2or hydrogen storage, wastewater injection, and geothermal applications, the focus will be on hydrocarbon extraction. This thesis presents the results of a characterization-to-prediction workflow for the Caney shale, which is an emerging hydrocarbon resource in Oklahoma, USA. It begins with an investigation to enable critical evaluation of the Caney zonation into nominally “brittle” and “ductile” zones based on properties observed from well logs. It shows none of the zones are consistently “brittle” or “ductile” mechanical behavior based on the variety of definitions of these terms. However, the nominally ductile zones are weaker and more prone to creep. A laboratory investigation of samples including strength, elastic, and creep properties, is then used in a finite element model of stress evolution. The model includes both elastic deformation and viscoplastic creep. Results predict the least creep-prone layers to have the lowest horizontal stresses, therefore comprising hydraulic fracturing targets. The most creep-prone layers attain a horizontal stress similar to the vertical stress and therefore are predicted to be high stress barriers to hydraulic fracture stimulation. In addition to defining stimulation target intervals, the model shows how as tectonic strain rate increases, there is a transition from creep-dominated stresses to stresses dominated by elasticity.

Benge, Margaret↗

DOE OSTI2021

Role of crystallographic orientation on intragranular void growth in polycrystalline FCC materials

In this study, we study the effect of crystallographic orientation and applied triaxiality on the growth of intragranular voids. Two 3D full-field micromechanics methods are used, the dilatational visco-plastic fast-Fourier transform (DVP-FFT) and the crystal plasticity Finite Elements (CP-FE), both of which incorporate a combination of crystalline plasticity and dilatational plasticity. We demonstrate with several select cases that predictions of void growth from both formulations agree qualitatively. With the more computationally efficient DVP-FFT, additional effects of polycrystalline microstructure and the influence of nearest neighborhood are investigated. Crystals bearing a single intracrystalline void are studied in three types of 3D microstructural environments: isolated single crystals, individual equal-sized grains within a regular polycrystal, and individual variable sized grains within a polycrystal with grains and voids randomly located. We show that loading type plays a significant role. In strain-rate controlled conditions, voids in the hardest [111]-crystals grow the fastest in time, whereas in stress-controlled conditions, voids in the softest [100]-crystal grow the fastest in time. The analysis reveals that on average void growth is slower for the same starting orientation in the polycrystal than in the single crystal. We find that at the highest triaxiality tested that the correlation between crystal orientation and void growth rate in the polycrystal strengthens, drawing closer to that seen in the isolated single crystals. These results and model can help guide the microstructural design of polycrystalline materials with high strength and damage-tolerance in high-rate deformation.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Long-term sinking of nuclear waste canisters in salt formations by low-stress creep at high temperature

Abstract Rock salt has a self-sealing capacity, low permeability, and high thermal conductivity, making it a potential host for heat-generating nuclear waste. The feasibility of nuclear waste disposal within salt formations has been investigated mostly for small-sized canisters. Geologic disposal of larger-sized canisters originally designed for spent fuel storage and transportation has lately been examined as a cost-effective alternative. This raises questions about their long-term vertical movement due to their weight and high decay heat. Low-stress creep governs this movement; however, most salt constitutive models do not incorporate it. In this paper, the Norton and the WIPP creep models are compared with the Lux/Wolters/Lerche (LWL) model and a simpler model that combines linear and Norton creep laws (named combined creep model). The LWL and combined creep models consider pressure solution creep, though all incorporate dislocation creep. The models are first applied to creep tests under various stress levels. The LWL and the combined creep models results fit the experimental data well in both high and low stress ranges, whereas the Norton and WIPP models results only fit in higher-stress ranges. The different models are further applied for analyzing long-term canister movement. A sinking rate of $$-4.4\times 10^{-7}$$ - 4.4 × 10 - 7 mm/year was predicted using the Norton and WIPP models versus $$-2.1\times 10^{-2}$$ - 2.1 × 10 - 2 mm/year and $$-3.1\times 10^{-2}$$ - 3.1 × 10 - 2 mm/year using the LWL and the combined creep models, respectively. This comparative study confirms that creep models calibrated exclusively against high-deviatoric stress data might result in an inaccurate estimation of waste packages sinking rate in salt formations.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Anisotropic thermal-conductivity degradation in the phase-field method accounting for crack directionality

Dynamic loads applied to metals may lead to brittle or ductile fracture depending on the imposed strain rates, material properties, and specimen geometry. With an increase in the applied velocity, brittle to ductile failure mode transition may also be observed. Furthermore, at high strain rates, ductile fracture may be preceded by shear bands, which are narrow bands of intense plastic deformation, typically accompanied by a significant rise in temperature. Reliable models are needed to predict the response of metals subject to dynamic loads. In particular, capturing the interplay between heat conduction and crack propagation using the phase-field fracture method is still an open research field. To accurately capture the heat transfer physics across crack surfaces, damage models degrading thermal-conductivity are necessary. While isotropic thermal-conductivity degradation models were proposed, they may lead to errors as they are indifferent to crack directionality. In our current work, a new anisotropic approach is proposed in which thermal-conductivity, which depends on the phase-field gradient, is degraded solely across the crack. Here, it is shown that this approach improves the near-field approximation of temperature and heat flux compared with isotropic degradation, when taking the discontinuous crack solutions as reference. Additionally, the anisotropic degradation approach is implemented in a unified dynamic fracture model and a couple of examples demonstrate the viability of this approach.

42 ENGINEERING↗

DOE OSTI2021

A crystal plasticity finite element model embedding strain-rate sensitivities inherent to deformation mechanisms: Application to alloy AZ31

We report the fundamental power-law relationship representing the flow rule in crystal visco-plasticity ensures uniqueness in the selection of slip systems accommodating imposed plastic strain-rates. The power-law relationship also introduces an artificially high strain-rate sensitivity in crystal plasticity simulations, unless a high value of the power-law exponent is used. However, the use of high values for the exponent is limited by numerical tractability. This paper presents a numerical method implemented in a crystal plasticity finite element (CPFE) model for embedding any value of the power-law exponent reflecting the true material strain-rate sensitivity. Importantly, the method does not increase computation time involved in the simulations. The enhanced CPFE model is used to interpret and predict a complex strain-rate sensitive response and microstructural evolution of AZ31 Mg alloy. Measured values of strain-rate sensitivity for slip and twinning modes are used in the simulations. Calculations show that the model successfully captures the phenomena pertaining to the effect of changing applied strain-rate on the mechanical response including flow stress and evolution of texture and twinning for a broad range of strain-rates ranging from 10 -3 s -1 to 10 3 s -1 and loading orientations in tension and compression. It is shown that such predictions are a consequence of not only relative amounts of slip and twinning activities driven by a set of accurately characterized hardening law parameters but also values of the strain-rate sensitivities inherent to individual deformation mechanisms. Besides, the model validates the measured strain-rate dependency of deformation mechanisms while accurately reproducing the mechanical data. Hence, the model can be used to verify and further refine or infer measured strain-rate sensitivity per deformation mechanism by reproducing experimental data.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Training material models using gradient descent algorithms

High temperature design requires accurate constitutive models to describe material inelastic deformation and failure behavior. Oftentimes, calibrating accurate models devolves into the problem of fitting the model parameters against experimental test data. Here, we present the pyopmat package, an open source framework for calibrating constitutive models against experiment data subjected to various loading conditions using machine learning techniques. The package calculates the exact gradient of the model response with respect to the parameters using a combination of automatic differentiation and the adjoint method. Given this exact gradient, we compare the performance of several gradient-based optimization techniques in fitting realistic constitutive models against data. Here, we demonstrate the efficiency and accuracy of our package through example problems using both synthetic data, generated using known parameter sets, under monotonic and cyclic loading conditions and also with an example applying the techniques developed here to actual high temperature creep-fatigue test data.

36 MATERIALS SCIENCE↗

DOE OSTI2022

A reinvestigation into Munson’s model for room closure in bedded rock salt

Accurate predictions of room closure are important for hazardous waste repositories in rock salt formations, such as the Waste Isolation Pilot Plant (WIPP). When Munson and co-workers simulated several room closure experiments conducted at the WIPP during the 1980’s and 1990’s, their simulated closure curves closely agreed with the closure measurements. A careful review of their work, however, raised concerns and prompted the reinvestigation in this paper. Here, to begin the reinvestigation, Munson’s legacy Room D closure simulation was reasonably recreated in a current-day finite element code. Next, special care was taken to obtain numerically converged results, re-introduce the anhydrite strata intermittently ignored by Munson, and calibrate the Munson–Dawson (M–D) constitutive model for salt as much as possible from laboratory test measurements. When this new model was used to simulate Room D’s closure, it under-predicted the horizontal and vertical closure rates by 2.34x and 3.10x, respectively, at 5.7 years after room excavation. As a result, the M–D model was extended to capture the newly established creep behavior at low equivalent stresses (<8 MPa) and replace the Tresca with the Hosford equivalent stress. Simulations using the new M–D model over-predicted the horizontal closure rate by 1.15x and under-predicted the vertical closure rate by 1.08x at 5.7 years, averaged over three room closure experiments. Although further improvements could be made, the new model has a stronger scientific foundation than Munson’s legacy model and appears ready for careful engineering use.

58 GEOSCIENCES↗

DOE OSTI2026

Low-stress creep behavior of multiple salt caverns under cyclic operations

Here, the use of multiple salt caverns for large-scale underground hydrogen storage offers a strategic solution to the growing demand for efficient and flexible energy storage, due to the inherent low permeability, high mechanical strength, and self-healing properties of the salt formation. Despite these advantages, the long-term geomechanical response of salt caverns under cyclic injection and withdrawal remains a significant challenge for ensuring operational stability. This mechanistic study highlights the critical role of low-stress creep, also known as pressure solution creep, in governing deformation of salt caverns during cyclic operations. Unlike conventional creep mechanisms that dominate under high-stress conditions, low-stress creep becomes particularly relevant under the moderate stress changes induced by repeated injection and withdrawal, which provides a previously underexplored control on cavern closure. Our three-dimensional computational model integrates the low-stress creep mechanism into the Munson–Dawson creep equation across a spectrum of operational scenarios including variations in cavern pressure cycles, injection-withdrawal frequencies, and caprock mechanical property. The low-stress creep components accelerate the cavern creep closure, which is amplified with shorter cycle frequency and larger pressure difference. Sensitivity analyses capture the complex interactions between multiple caverns and surround formations at the field scale that allows for a quantitative assessment of deformation patterns and closure rates over time and thereby informs the design and operation of sustainable underground hydrogen storage system.

Cyclic operation↗