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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Correlations Between Metallurgical Characterization Studies, Exploratory Mechanical Tests, and Continuum Mechanics Approaches to Constitutive Equations

Austenitic stainless steels, such as types 316 and 304, are widely used as pressure vessel materials in the temperature range of 425 to 650 C. Stainless steel specimens were tested to rupture at two different stress levels sigma and sigma 2 sigma 1 sigma 2) to establish the normal stain-time behavior. A subsequent test was performed in which the specimen was crept at the higher stress (sigma 1) to the beginning of the secondary stage of creep, presumed to be the strain/time conditions at which a steady state microstructure is developed, and then the stress was reduced to the lower level (sigma 2). The associated microstructure, and significance of this microstructure on the creep strain-hardening model for variable uniaxial loads were assesed and found to be consistent with the use of creep-recovery models at high stresses and temperatures and strain-hardening models at low stresses and tempertures.

Moteff, J.↗
NASA NTRS1988

The einstein equivalence principle, intrinsic spin and the invariance of constitutive equations in continuum mechanics

The invariance of constitutive equations in continuum mechanics is examined from a basic theoretical standpoint. It is demonstrated the constitutive equations which are not form invariant under arbitrary translational accelerations of the reference frame are in violation of the Einstein equivalane principle. Furthermore, by making use of an analysis based on statistical mechanics, it is argued that any frame-dependent terms in constitutive equations must arise from the intrinsic spin tensor and are negligible provided that the ratio of microscopic to macroscopic time scales is extremely small. The consistency of these results with existing constitutive theories is discussed in detail along with possible avenues of future research.

Speziale, Charles G.↗
NASA NTRS1973

A highly stable explicit integration technique for computational continuum mechanics

A user-oriented subroutine package is built around a highly stable explicit integration algorithm for solution of large order systems of ordinary differential equations, as result from discretization of initial-boundary value problems in continuum mechanics. Fast and accurate solutions, for problems in laminar and turbulent, two and three-dimensional viscous flow fields and multi-dimensional transient heat transfer, are presented using this algorithm, as embodied within a general purpose finite element computer program.

Baker, A. J.↗
NASA NTRS1982

Post-instability in continuous systems. I - Failure of differentiability of solutions in continuum mechanics

It is pointed out that mathematical models of continua are based on certain assumptions regarding functions which must be at least piece-wise differentiable. The assumption about smoothness of the functions makes it possible to use the mathematical technique of differentiable equations. However, this artificial mathematical limitation follows neither from the principles of mechanics nor from the definition of a continuum. The price paid for such a mathematical convenience is instability (in the class of smooth functions) of the solutions to the corresponding governing equations in some regions of the parameters. A new mathematical technique should, therefore, be developed to describe the solutions which are not necessarily differentiable. The present investigation is concerned with the criteria of applicability of the classical models of continua from the view point of stability of the corresponding solutions, postinstability models derived by reformulation of the original models, and postinstability models in enlarged classes of functions.

Zak, M.↗
NASA NTRS1976

A space-time tensor formulation for continuum mechanics in general curvilinear, moving, and deforming coordinate systems

Tensor methods are used to express the continuum equations of motion in general curvilinear, moving, and deforming coordinate systems. The space-time tensor formulation is applicable to situations in which, for example, the boundaries move and deform. Placing a coordinate surface on such a boundary simplifies the boundary condition treatment. The space-time tensor formulation is also applicable to coordinate systems with coordinate surfaces defined as surfaces of constant pressure, density, temperature, or any other scalar continuum field function. The vanishing of the function gradient components along the coordinate surfaces may simplify the set of governing equations. In numerical integration of the equations of motion, the freedom of motion of the coordinate surfaces provides a potential for enhanced resolution of the continuum field function. An example problem of an incompressible, inviscid fluid with a top free surface is considered, where the surfaces of constant pressure (including the top free surface) are coordinate surfaces.

Avis, L. M.↗
NASA NTRS1980

A mathematical model of post-instability in continuum mechanics

The post-instability can appear in the form of failure of hyperbolicity or in the form of cascade instability (stretching of vorticity in an inviscid fluid or instability of the Navier-Stokes equations). All the cases are characterized by an unlimited decrease of the scale of the motions, in the course of which the derivatives of the corresponding functions tend to infinity, though the functions themselves remain finite. Such an instability shows that the corresponding state of a continuum cannot be properly simulated by smooth functions. Hence, the original model must be corrected by giving up the requirement about differentiability and enlarging the class of functions. Applications to a model of an inviscid fluid and to a model of turbulence are discussed.

Zak, M.↗
DOE OSTI2025

Green's function fast multipole method for continuum mechanics (SM-FMM)

Solid Mechanics Fast Multipole Method based on elastic Green's function and accelerated using FFTs The code calculates the mechanical fields (stress and strain) for a heterogeneous elasto-plastic material unit cell under quasi-static conditions (no dynamic effects). The fields are calculated using a Green's function method, where the strain field is given by a discrete convolution of Green's operator with an auxiliary stress field. The convolution is calculated using the fast multipole method.

Zecevic, Miroslav↗
NASA NTRS2015

3D Progressive Damage Modeling for Laminated Composite Based on Crack Band Theory and Continuum Damage Mechanics

A simple continuum damage mechanics (CDM) based 3D progressive damage analysis (PDA) tool for laminated composites was developed and implemented as a user defined material subroutine to link with a commercially available explicit finite element code. This PDA tool uses linear lamina properties from standard tests, predicts damage initiation with an easy-to-implement Hashin-Rotem failure criteria, and in the damage evolution phase, evaluates the degradation of material properties based on the crack band theory and traction-separation cohesive laws. It follows Matzenmiller et al.'s formulation to incorporate the degrading material properties into the damaged stiffness matrix. Since nonlinear shear and matrix stress-strain relations are not implemented, correction factors are used for slowing the reduction of the damaged shear stiffness terms to reflect the effect of these nonlinearities on the laminate strength predictions. This CDM based PDA tool is implemented as a user defined material (VUMAT) to link with the Abaqus/Explicit code. Strength predictions obtained, using this VUMAT, are correlated with test data for a set of notched specimens under tension and compression loads.

Wang, John T.↗
NASA NTRS2018

Implementation of a Matrix Crack Spacing Parameter in a Continuum Damage Mechanics Finite Element Model

Continuum Damage Mechanics (CDM) based progressive damage and failure analysis (PDFA) methods have demonstrated success in a variety of finite element analysis (FEA) implementations. However, the technical maturity of CDM codes has not yet been proven for the full design space of composite materials in aerospace applications. CDM-based approaches represent the presence of damage by changing the local material stiffness definitions and without updating the original mesh or element integration schemes. Without discretely representing cracks and their paths through the mesh, damage in models with CDM-based materials is often distributed in a region of partially damaged elements ahead of stress concentrations. Having a series of discrete matrix cracks represented by a softened region may affect predictions of damage propagation and, thus, structural failure. This issue can be mitigated by restricting matrix damage development to discrete, fiber-aligned rows of elements; hence CDM-based matrix cracks can be implemented to be more representative of discrete matrix cracks. This paper evaluates the effect of restricting CDM matrix crack development to discrete, fiber-aligned rows where the spacing of these rows is controlled by a user-defined crack spacing parameter. Initially, the effect of incrementally increasing matrix crack spacing in a unidirectional center notch coupon is evaluated. Then, the lessons learned from the center notch specimen are applied to open-hole compression finite element models. Results are compared to test data, and the limitations, successes, and potential of the matrix crack spacing approach are discussed.

Hyder, Imran↗
NASA NTRS1991

Differential continuum damage mechanics models for creep and fatigue of unidirectional metal matrix composites

Three multiaxial isothermal continuum damage mechanics models for creep, fatigue, and creep/fatigue interaction of a unidirectional metal matrix composite volume element are presented, only one of which will be discussed in depth. Each model is phenomenological and stress based, with varying degrees of complexity to accurately predict the initiation and propagation of intergranular and transgranular defects over a wide range of loading conditions. The development of these models is founded on the definition of an initially transversely isotropic fatigue limit surface, static fracture surface, normalized stress amplitude function and isochronous creep damage failure surface, from which both fatigue and creep damage evolutionary laws can be obtained. The anisotropy of each model is defined through physically meaningful invariants reflecting the local stress and material orientation. All three transversely isotropic models have been shown, when taken to their isotropic limit, to directly simplify to previously developed and validated creep and fatigue continuum damage theories. Results of a nondimensional parametric study illustrate (1) the flexibility of the present formulation when attempting to characterize a large class of composite materials, and (2) its ability to predict anticipated qualitative trends in the fatigue behavior of unidirectional metal matrix composites. Additionally, the potential for the inclusion of various micromechanical effects (e.g., fiber/matrix bond strength, fiber volume fraction, etc.), into the phenomenological anisotropic parameters is noted, as well as a detailed discussion regarding the necessary exploratory and characterization experiments needed to utilize the featured damage theories.

Arnold, S. M.↗
NASA NTRS2007

Prediction of Size Effects in Notched Laminates Using Continuum Damage Mechanics

This paper examines the use of a continuum damage model to predict strength and size effects in notched carbon-epoxy laminates. The effects of size and the development of a fracture process zone before final failure are identified in an experimental program. The continuum damage model is described and the resulting predictions of size effects are compared with alternative approaches: the point stress and the inherent flaw models, the Linear-Elastic Fracture Mechanics approach, and the strength of materials approach. The results indicate that the continuum damage model is the most accurate technique to predict size effects in composites. Furthermore, the continuum damage model does not require any calibration and it is applicable to general geometries and boundary conditions.

Camanho, D. P.↗
NASA NTRS2011

Continuum Damage Mechanics Models for the Analysis of Progressive Failure in Open-Hole Tension Laminates

The performance of a state-of-the-art continuum damage mechanics model for interlaminar damage, coupled with a cohesive zone model for delamination is examined for failure prediction of quasi-isotropic open-hole tension laminates. Limitations of continuum representations of intra-ply damage and the effect of mesh orientation on the analysis predictions are discussed. It is shown that accurate prediction of matrix crack paths and stress redistribution after cracking requires a mesh aligned with the fiber orientation. Based on these results, an aligned mesh is proposed for analysis of the open-hole tension specimens consisting of different meshes within the individual plies, such that the element edges are aligned with the ply fiber direction. The modeling approach is assessed by comparison of analysis predictions to experimental data for specimen configurations in which failure is dominated by complex interactions between matrix cracks and delaminations. It is shown that the different failure mechanisms observed in the tests are well predicted. In addition, the modeling approach is demonstrated to predict proper trends in the effect of scaling on strength and failure mechanisms of quasi-isotropic open-hole tension laminates.

Song, Kyonchan↗
NASA NTRS2015

Representing Matrix Cracks Through Decomposition of the Deformation Gradient Tensor in Continuum Damage Mechanics Methods

A method is presented to represent the large-deformation kinematics of intraply matrix cracks and delaminations in continuum damage mechanics (CDM) constitutive material models. The method involves the additive decomposition of the deformation gradient tensor into 'crack' and 'bulk material' components. The response of the intact bulk material is represented by a reduced deformation gradient tensor, and the opening of an embedded cohesive interface is represented by a normalized cohesive displacement-jump vector. The rotation of the embedded interface is tracked as the material deforms and as the crack opens. The distribution of the total local deformation between the bulk material and the cohesive interface components is determined by minimizing the difference between the cohesive stress and the bulk material stress projected onto the cohesive interface. The improvements to the accuracy of CDM models that incorporate the presented method over existing approaches are demonstrated for a single element subjected to simple shear deformation and for a finite element model of a unidirectional open-hole tension specimen. The material model is implemented as a VUMAT user subroutine for the Abaqus/Explicit finite element software. The presented deformation gradient decomposition method reduces the artificial load transfer across matrix cracks subjected to large shearing deformations, and avoids the spurious secondary failure modes that often occur in analyses based on conventional progressive damage models.

Leone, Frank A., Jr.↗
DOE OSTI2024

A FFT-based mesoscale continuum dislocation mechanics with defect energy: Applications to composites and polycrystals

A crystal plasticity elastoviscoplastic FFT (fast Fourier transform) formulation with a mesoscale continuum field dislocation mechanics model is presented, which incorporates a defect energy density that depends on GND densities and an associated material length scale. This allows to thermodynamically derive internal length scale dependent intra-crystalline backstress and Peach–Koehler force acting on GND densities. The model considers GND density evolution through a filtered numerical spectral approach, which is coupled with stress equilibrium through the elastoviscoplastic FFT algorithm. The discrete Fourier transform (DFT) method together with finite difference (FD) schemes is applied to solve both the backstress tensor and the Fourier–Green operator. Numerical results are first reported for two-phase laminate composites with plastic single crystal channels and elastic precipitates for shear loadings. Channel size effects are simulated and analyzed on the overall and local hardening behaviors during monotonous loadings. In addition, the evolutions of GND densities and the role of their associated backstress on size effects are examined during reversible shear loading. In a second part, the role of the defect energy internal length scale on polycrystal’s hardening during tension–compression is discussed. The results are compared to those obtained using FFT-based continuum field dislocation mechanics without defect energy.

36 MATERIALS SCIENCE↗
NASA NTRS2020

Analysis of Open Hole Compression Specimens Using the CompDam Continuum Damage Mechanics Model

This report documents a validation study on the standard Open Hole Compression (OHC) laminate test specimen conducted as part of the NASA Advanced Composites Project (ACP). Tests were conducted on OHC specimens with hard, quasi-isotropic, and soft layups using digital image correlation and X-Ray computed tomography to capture the structural response and damage evolution. Progressive damage models were constructed for use with the CompDam continuum damage mechanics code following the best practices established during the ACP. Detailed interrogation of the analysis results and comparison with experimental measurements provide a basis for assessing the capability of the modeling approach for OHC. The structural response is found to be captured well, with strengths predicted within 3\% of the experimental values for hard and quasi-isotropic laminates. In the soft laminate, the model predicts failure to be more brittle than the nonlinear, ductile response that was measured. Damage states extracted from the models at the same load level as test measurements are overlaid to show directly the similarities and differences between test and analysis results. Studying the damage evolution predicted by the analysis reveals that the failure process is a competition between fiber damage and delamination/sub-laminate buckling, with fiber damage dominating the collapse in the hard laminate and sub-laminate buckling governing in the soft laminate. Finally, a series of parametric studies varying numerical solution parameters (mesh size, mass scaling) and physical properties (fiber direction compressive strength and toughness) reveal sensitivities and deficiencies of the model. To the authors' knowledge, this study is the first for OHC specimens to include detailed evaluation of damage mode interactions, direct overlay of predicted and measured damage states, and sensitivity of the predicted results to difficult-to-measure fiber direction material properties.

Continuum damage mechanics↗
NASA NTRS2017

Fracture-Based Mesh Size Requirements for Matrix Cracks in Continuum Damage Mechanics Models

This paper evaluates the ability of progressive damage analysis (PDA) finite element (FE) models to predict transverse matrix cracks in unidirectional composites. The results of the analyses are compared to closed-form linear elastic fracture mechanics (LEFM) solutions. Matrix cracks in fiber-reinforced composite materials subjected to mode I and mode II loading are studied using continuum damage mechanics and zero-thickness cohesive zone modeling approaches. The FE models used in this study are built parametrically so as to investigate several model input variables and the limits associated with matching the upper-bound LEFM solutions. Specifically, the sensitivity of the PDA FE model results to changes in strength and element size are investigated.

Leone, Frank A.↗
NASA NTRS2016

A Continuum Damage Mechanics Model to Predict Kink-Band Propagation Using Deformation Gradient Tensor Decomposition

A new model is proposed that represents the kinematics of kink-band formation and propagation within the framework of a mesoscale continuum damage mechanics (CDM) model. The model uses the recently proposed deformation gradient decomposition approach to represent a kink band as a displacement jump via a cohesive interface that is embedded in an elastic bulk material. The model is capable of representing the combination of matrix failure in the frame of a misaligned fiber and instability due to shear nonlinearity. In contrast to conventional linear or bilinear strain softening laws used in most mesoscale CDM models for longitudinal compression, the constitutive response of the proposed model includes features predicted by detailed micromechanical models. These features include: 1) the rotational kinematics of the kink band, 2) an instability when the peak load is reached, and 3) a nonzero plateau stress under large strains.

Bergan, Andrew C.↗
NASA NTRS1994

Experimental verification of a progressive damage model for composite laminates based on continuum damage mechanics

Progressive failure is a crucial concern when using laminated composites in structural design. Therefore the ability to model damage and predict the life of laminated composites is vital. The purpose of this research was to experimentally verify the application of the continuum damage model, a progressive failure theory utilizing continuum damage mechanics, to a toughened material system. Damage due to tension-tension fatigue was documented for the IM7/5260 composite laminates. Crack density and delamination surface area were used to calculate matrix cracking and delamination internal state variables, respectively, to predict stiffness loss. A damage dependent finite element code qualitatively predicted trends in transverse matrix cracking, axial splits and local stress-strain distributions for notched quasi-isotropic laminates. The predictions were similar to the experimental data and it was concluded that the continuum damage model provided a good prediction of stiffness loss while qualitatively predicting damage growth in notched laminates.

Coats, Timothy William↗