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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Analysis of Large Quasistatic Deformations of Inelastic Solids by a New Stress Based Finite Element Method

A new hybrid stress finite element algorithm suitable for analyses of large quasistatic deformation of inelastic solids is presented. Principal variables in the formulation are the nominal stress rate and spin. The finite element equations which result are discrete versions of the equations of compatibility and angular momentum balance. Consistent reformulation of the constitutive equation and accurate and stable time integration of the stress are discussed at length. Examples which bring out the feasibility and performance of the algorithm conclude the work.

Reed, Kenneth W.↗
NASA NTRS1983

Analyses of large quasistatic deformations of inelastic bodies by a new hybrid-stress finite element algorithm - Applications

A new hybrid-stress finite element algorithm suitable for analyzing large quasistatic deformations of inelastic solids is presented and its feasibility and performance are demonstrated with examples. The algorithm provides extremely accurate bifurcation analysis which is stable with respect to variation in the finite element mesh, so long as the same type of element is used in every mesh. When the mesh element is varied, the result changes in a predictable manner. The method does not necessarily lead to an upper or lower bound for the critical load. An explicit forward gradient scheme is used to improve stability and is shown to be useful also for elongation-dominated deformations. The application of the method to the onset of necking in plane extension and to deformation and stress in plane extension of an elasticoviscous fluid with an array of cylindrical voids is given in detail.

Reed, K. W.↗
NASA NTRS1984

Hybrid stress finite elements for large deformations of inelastic solids

A new hybrid stress finite element algorithm, based on a generalization of Fraeijs de Veubeke's complementary energy principle is presented. Analyses of large quasistatic deformation of inelastic solids (hypoelastic, plastic, viscoplastic) are within its capability. Principle variables in the formulation are the nominal stress rate and spin. A brief account is given of the boundary value problem in these variables, and the 'equivalent' variational principle. The finite element equation, along with initial positions and stresses, comprise an initial value problem. Factors affecting the choice of time integration schemes are discussed. Results found by application of the new algorithm are compared to those obtained by a velocity based finite element algorithm.

Reed, K. W.↗
NASA NTRS1997

A Viscoplastic Constitutive Theory for Monolithic Ceramic Materials

With increasing use of ceramic materials in high temperature structural applications such as advanced heat engine components, the need arises to accurately predict thermomechanical behavior. This paper, which is the first of two in a series, will focus on inelastic deformation behavior associated with these service conditions by providing an overview of a viscoplastic constitutive model that accounts for time-dependent hereditary material deformation (e.g., creep, stress relaxation, etc.) in monolithic structural ceramics. Early work in the field of metal plasticity indicated that inelastic deformations are essentially unaffected by hydrostatic stress. This is not the case, however, for ceramic-based material systems, unless the ceramic is fully dense. The theory presented here allows for fully dense material behavior as a limiting case. In addition, ceramic materials exhibit different time-dependent behavior in tension and compression. Thus, inelastic deformation models for ceramics must be constructed in a fashion that admits both sensitivity to hydrostatic stress and differing behavior in tension and compression. A number of constitutive theories for materials that exhibit sensitivity to the hydrostatic component of stress have been proposed that characterize deformation using time-independent classical plasticity as a foundation. However, none of these theories allow different behavior in tension and compression. In addition, these theories are somewhat lacking in that they are unable to capture creep, relaxation, and rate-sensitive phenomena exhibited by ceramic materials at high temperature. When subjected to elevated service temperatures, ceramic materials exhibit complex thermomechanical behavior that is inherently time-dependent, and hereditary in the sense that current behavior depends not only on current conditions, but also on thermo-mechanical history. The objective of this work is to present the formulation of a macroscopic continuum theory that captures these time-dependent phenomena. Specifically, the overview contained in this paper focuses on the multiaxial derivation of the constitutive model, and examines the scalar threshold function and its attending geometrical implications.

Janosik, Lesley A.↗
DOE OSTI2024

Phase-field modeling of thermally-grown oxide and damage evolution in environmental barrier coatings

Silicon carbide-based ceramic matrix composites protected by environmental barrier coatings (EBCs) present a promising materials solution for next-generation gas turbines. Developing more robust and efficient EBCs is therefore of significant technological importance. During the service in high-temperature oxidative environments, there is a thermally grown oxide (TGO) layer, spontaneously formed in the EBC system. TGO is recognized as a critical factor for the degradation and failure of EBCs, yet the detailed mechanisms of TGO growth and its effect on EBC failure remain unclear. In this study we develop a comprehensive chemo-mechano-phase-field model to simulate growth of the TGO in EBCs, factoring in creep and deformation, and especially the cracking behaviors. The volume expansion due to TGO growth and the resulting large inelastic deformation are addressed by using our recently developed, so-called incremental realization of inelastic deformation (IRID) algorithm, in combination with an adapted Hu-Chen spectral solver for elasticity. Simulations of TGO growth are performed considering different growth modes of TGOs determined mainly by the ratio of oxidant permeability in the topcoat to that in the TGO itself. Large-scale three-dimensional (3D) simulations are performed to model the formation of interconnecting vertical/channel cracks (often called ‘mud cracks’). The simulated crack morphology are in excellent agreement with the experimental observations from the literature. The simulations also provide insights into the cracking of EBCs and its dependence on the structure and constituent properties of the coating system. Furthermore, these results demonstrate the developed damage model can be a useful tool for design of more durable EBCs.

Cracking↗
NASA NTRS1984

Inelastic and Dynamic Fracture and Stress Analyses

Large deformation inelastic stress analysis and inelastic and dynamic crack propagation research work is summarized. The salient topics of interest in engine structure analysis that are discussed herein include: (1) a path-independent integral (T) in inelastic fracture mechanics, (2) analysis of dynamic crack propagation, (3) generalization of constitutive relations of inelasticity for finite deformations , (4) complementary energy approaches in inelastic analyses, and (5) objectivity of time integration schemes in inelastic stress analysis.

Atluri, S. N.↗
NASA NTRS2013

Macroscopic and Microstructural Aspects of the Transformation Behavior in a Polycrystalline NiTi Shape Memory Alloy

The mechanical and microstructural behavior of a polycrystalline Ni(49.9)Ti(50.1) (at.%) shape memory alloy was investigated as a function of temperature around the transformation regime. The bulk macroscopic responses, measured using ex situ tensile deformation and impulse excitation tests, were compared to the microstructural evolution captured using in situ neutron diffraction. The onset stress for inelastic deformation and dynamic Young's modulus were found to decrease with temperature, in the martensite regime, reaching a significant minimum at approximately 80 C followed by an increase in both properties, attributed to the martensite to austenite transformation. The initial decrease in material compliance during heating affected the ease with which martensite reorientation and detwinning could occur, ultimately impacting the stress for inelastic deformation prior to the start of the reverse transformation.

Benafan, Othmane↗
DOE OSTI2025

Phase-Field Modeling of Damage Evolution in Ceramic Matrix Composite (CMC) and Environmental Barrier Coating (EBC)

Ceramic matrix composites (CMCs) protected by environmental barrier coatings (EBCs) present a promising materials solution for next generation gas turbines. Developments of more robust and efficient EBCs and mechanically tougher CMCs are thus of significant technological importance. Here we develop a phase-field modeling framework that incorporates the thermally grown oxide (TGO), recognized as a critical factor for degradation and failure of EBCs. We simulate crack growth in the TGO and the potential extension into the bond coat / CMC substrate. The model efficiently takes account of the large inelastic deformation induced by the severe volume expansion of TGO, thanks to our recently developed, so-called incremental realization of inelastic deformation (IRID) algorithm. A phase-field model is built for damage evolution in CMCs including crack growth and interfacial sliding. The effects of fiber layout and interfacial sliding on the macroscopic toughness of CMCs are revealed by large-scale simulations and compared to experiments.

advanced energy systems and materials↗
NASA NTRS1988

A theory of viscoplasticity accounting for internal damage

A constitutive theory for use in structural and durability analyses of high temperature isotropic alloys is presented. Constitutive equations based upon a potential function are determined from conditions of stability and physical considerations. The theory is self-consistent; terms are not added in an ad hoc manner. It extends a proven viscoplastic model by introducing the Kachanov-Rabotnov concept of net stress. Material degradation and inelastic deformation are unified; they evolve simultaneously and interactively. Both isotropic hardening and material degradation evolve with dissipated work which is the sum of inelastic work and internal work. Internal work is a continuum measure of the stored free energy resulting from inelastic deformation.

Freed, A. D.↗
NASA NTRS1980

Wear particles of single-crystal silicon carbide in vacuum

Sliding friction experiments, conducted in vacuum with silicon carbide /000/ surface in contact with iron based binary alloys are described. Multiangular and spherical wear particles of silicon carbide are observed as a result of multipass sliding. The multiangular particles are produced by primary and secondary cracking of cleavage planes /000/, /10(-1)0/, and /11(-2)0/ under the Hertzian stress field or local inelastic deformation zone. The spherical particles may be produced by two mechanisms: (1) a penny shaped fracture along the circular stress trajectories under the local inelastic deformation zone, and (2) attrition of wear particles.

Miyoshi, K.↗
DOE OSTI2025

Towards a multiscale approach for understanding irradiation induced swelling and creep in 316 stainless steels - A coupled cluster dynamics and crystal plasticity approach

Structural materials undergo mechanical degradation, in part due to irradiation-induced swelling and creep, under nuclear reactor conditions. While swelling results from the migration and clustering of irradiation-induced atomic-scale mobile defects, the interaction of mesoscale dislocations with these defects causes creep deformation. A coupled crystal plasticity (CP) and mean-field cluster dynamics (CD) approach is presented to investigate the effect of irradiation on the long-term mechanical behavior of 316 stainless steel, which are under consideration for use in nuclear reactors. The temporal evolution of Frenkel pairs and extended defect population, under a chosen irradiation flux and temperature, is predicted using the CD model. The impact of the irradiation defects on the stress state, and the resulting dislocation-mediated inelastic deformation, is modeled concurrently with the CP model. The inelastic deformation is irradiation flux dependent, and early-stage defect evolution determines the later-stage mechanical behavior in 316 stainless steel.

36 - MATERIALS SCIENCE↗
DOE OSTI2024

Anomalous temperature dependence of elastic limit in metallic glasses

Abstract Understanding the atomistic mechanisms of inelastic deformation in metallic glasses (MGs) remains challenging due to their amorphous structure, where local carriers of plasticity cannot be easily defined. Using molecular dynamics (MD) simulations, we analyzed the onset of inelastic deformation in CuZr MGs, specifically the temperature dependence of the elastic limit, in terms of localized shear transformation (ST) events. We find that although the ST events initiate at lower strain with increasing temperature, the elastic limit increases with temperature in certain temperature ranges. We explain this anomalous behavior through the framework of an energy-strain landscape (ESL) constructed from high-throughput strain-dependent energy barrier calculations for the ST events identified in the MD simulations. The ESL reveals that the anomalous behavior is caused by the transition of ST events from irreversible to reversible with increasing temperature. An analytical formulation is developed to predict this transition and the temperature dependence of the elastic limit.

36 MATERIALS SCIENCE↗
NASA NTRS1981

The generation and morphology of single-crystal silicon carbide wear particles under adhesive conditions

Sliding friction experiments were performed in vacuum at room temperature on a plane-type SiC surface in contact with iron-based binary alloys. Multiangular and spherical wear particles were found to form as a result of multipass sliding. The multiangular particles were produced by primary and secondary cracking of the 0001, 10(-)10, and 11(-)20 plane-type cleavage planes under the Hertzian stress field or local inelastic deformation zone. When alloy surfaces are in contact with silicon carbide under a load of 0.2 N, the alloy around the contact area is subjected to stresses that are close to the elastic limit in the elastic deformation region and/or exceed it. It was also found that spherical wear particles may be produced by two mechanisms: a penny-shaped fracture along the circular stress trajectories under the local inelastic deformation zone, and the attrition and fatigue of wear particles.

Miyoshi, K.↗
NASA NTRS1998

Constitutive Theory Developed for Monolithic Ceramic Materials

With the increasing use of advanced ceramic materials in high-temperature structural applications such as advanced heat engine components, the need arises to accurately predict thermomechanical behavior that is inherently time-dependent and that is hereditary in the sense that the current behavior depends not only on current conditions but also on the material's thermomechanical history. Most current analytical life prediction methods for both subcritical crack growth and creep models use elastic stress fields to predict the time-dependent reliability response of components subjected to elevated service temperatures. Inelastic response at high temperatures has been well documented in the materials science literature for these material systems, but this issue has been ignored by the engineering design community. From a design engineer's perspective, it is imperative to emphasize that accurate predictions of time-dependent reliability demand accurate stress field information. Ceramic materials exhibit different time-dependent behavior in tension and compression. Thus, inelastic deformation models for ceramics must be constructed in a fashion that admits both sensitivity to hydrostatic stress and differing behavior in tension and compression. A number of constitutive theories for materials that exhibit sensitivity to the hydrostatic component of stress have been proposed that characterize deformation using time-independent classical plasticity as a foundation. However, none of these theories allow different behavior in tension and compression. In addition, these theories are somewhat lacking in that they are unable to capture the creep, relaxation, and rate-sensitive phenomena exhibited by ceramic materials at high temperatures. The objective of this effort at the NASA Lewis Research Center has been to formulate a macroscopic continuum theory that captures these time-dependent phenomena. Specifically, the effort has focused on inelastic deformation behavior associated with these service conditions by developing a multiaxial viscoplastic constitutive model that accounts for time-dependent hereditary material deformation (such as creep and stress relaxation) in monolithic structural ceramics. Using continuum principles of engineering mechanics, we derived the complete viscoplastic theory from a scalar dissipative potential function.

Janosik, Lesley A.↗
NASA NTRS2001

Viscoplastic Model Development to Account for Strength Differential: Application to Aged Inconel 718 at Elevated Temperature

The magnitude of yield and flow stresses in aged Inconel 718 are observed to be different in tension and compression. This phenomenon, called the Strength differential (SD), contradicts the metal plasticity axiom that the second deviatoric stress invariant alone is sufficient for representing yield and flow. Apparently, at least one of the other two stress invariants is also significant. A unified viscoplastic model was developed that is able to account for the SD effect in aged Inconel 718. Building this model involved both theory and experiments. First, a general threshold function was proposed that depends on all three stress invariants and then the flow and evolution laws were developed using a potential-based thermodynamic framework. Judiciously chosen shear and axial tests were conducted to characterize the material. Shear tests involved monotonic loading, relaxation, and creep tests with different loading rates and load levels. The axial tests were tension and compression tests that resulted in sufficiently large inelastic strains. All tests were performed at 650 C. The viscoplastic material parameters were determined by optimizing the fit to the shear tests, during which the first and the third stress invariants remained zero. The threshold surface parameters were then fit to the tension and compression test data. An experimental procedure was established to quantify the effect of each stress invariant on inelastic deformation. This requires conducting tests with nonproportional three-dimensional load paths. Validation of the model was done using biaxial tests on tubular specimens of aged Inconel 718 using proportional and nonproportional axial-torsion loading. These biaxial tests also helped to determine the most appropriate form of the threshold function; that is, how to combine the stress invariants. Of the set of trial threshold functions, the ones that incorporated the third stress invariant give the best predictions. However, inclusion of the first stress invariant does not significantly improve the model predictions. The model shows excellent predictive capability for nonproportional load paths. Additionally, it reduces to the well-known models of Mises Drucker and Drucker-Prager. The requisite experiments involve reasonably simple load paths in the axial-shear stress plane and hence can be performed on a variety of different materials: be they metallic, geological. polymeric, ceramic or granular. The general form of the threshold function allows representation of inelastic deformation in a range of materials.

Iyer, Saiganesh↗
NASA NTRS1989

Elevated temperature crack growth

Alloy 718 crack growth experiments were conducted to assess the ability of the selected path-independent (P-I) integrals to describe the elevated temperature crack growth behavior. These tests were performed on single edge notch (SEN) specimens under displacement control with multiple extensometers to monitor the specimen and crack mouth opening displacement (CMOD). The displacements in these tests were sufficiently high to induce bulk cyclic inelastic deformation of the specimen. Under these conditions, the linear elastic fracture mechanics (LEFM) parameter K does not correlate the crack growth data. The experimentally measured displacement gradients at the end of specimen gage length were used as the boundary conditions in elastic-plastic finite element method (FEM) analyses. These analyses were performed with a node release approach using CYANIDE, a GEAE FEM code, which included a gap element which is capable of efficiently simulating crack closure. Excellent correlation was obtained between the experimentally measured and predicted variation of stress and CMOD with crack length and the stress-CMOD loops for Alloy 718 tests conducted at 538 C. This confirmed the accuracy of the FEM crack growth simulation approach. The experimentally measured crack growth rate data correlated well the selected P-I integrals. These investigations have produced significant progress in developing P-I integrals as non-linear fracture mechanics parameters. The results suggest that this methodology has the potential of accurately describing elevated temperature crack growth behavior under the combined influence of thermal cycling and bulk elastic-inelastic deformation states.

Kim, K. S.↗
DOE OSTI2023

Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach

The finite element method (FEM) is widely used to simulate a variety of physics phenomena. Approaches that integrate FEM with neural networks (NNs) are typically leveraged as an alternative to conducting expensive FEM simulations in order to reduce the computational cost without significantly sacrificing accuracy. However, these methods can produce biased predictions that deviate from those obtained with FEM, since these hybrid FEM-NN approaches rely on approximations trained using physically relevant quantities. In this work, an uncertainty estimation framework is introduced that leverages ensembles of Bayesian neural networks to produce diverse sets of predictions using a hybrid FEM-NN approach that approximates internal forces on a deforming solid body. The uncertainty estimator developed herein reliably infers upper bounds of bias/variance in the predictions for a wide range of interpolation and extrapolation cases using a three-element FEM-NN model of a bar undergoing plastic deformation. This proposed framework offers a powerful tool for assessing the reliability of physics-based surrogate models by establishing uncertainty estimates for predictions spanning a wide range of possible load cases.

42 ENGINEERING↗