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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 NTRS1985

Effects of a high mean stress on the high cycle fatigue life of PWA 1480 and correlation of data by linear elastic fracture mechanics

High-cycle fatigue tests using 5-mm-diameter smooth specimens were performed on the single crystal alloy PWA 1480 (001 axis) at 70F (room temperature) in air and at 100F (538C) in vacuum (10 to the -6 power torr). Tests were conducted at zero mean stress as well as at high tensile mean stress. The results indicate that, although a tensile mean stress, in general, reduces life, the reduction in fatigue strength, for a given mean stress at a life of one million cycles, is much less than what is predicted by the usual linear Goodman plot. Further, the material appears to be significantly more resistant to mean stress effects at 1000F than at 70F. Metallographic examinations of failed specimens indicate that failures in all cases are initiated from micropores of sizes of the order of 30 to 40 microns. Since the macroscopic stress-strain response in all cases was observed to be linear elastic, linear elastic fracture mechanics (LEFM) analyses were carried out to determine the crack growth curves of the material assuming that crack initiation from a micropore (a sub o = 40 microns) occurs very early in life. The results indicate that the calculated crack growth rates at an R (defined as the ratio between minimum stress to maximum stress) value of zero are approximately the same at 70F as at 1000F. However, the calculated crack growth rates at other R ratios, both positive and negative, tend to be higher at 70F than at 1000F. Calculated threshold effects at large R values tend to be independent of temperature in the temperature regime studied. They are relatively constant with increasing R ratio up to a value of about 0.6, beyond which the calculated threshold stress intensity factor range decreases rapidly with increasing R ratios.

Majumdar, S.↗
NASA NTRS2018

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

higher-order↗
NASA NTRS2017

A Review of the Proposed KIsi Offset-Secant Method for Size-Insensitive Linear-Elastic Fracture Toughness Evaluation

Recently proposed modifications to ASTM E399 would provide a new size-insensitive approach to analyzing the force-displacement test record. The proposed size-insensitive linear-elastic fracture toughness, KIsi, targets a consistent 0.5mm crack extension for all specimen sizes by using an offset secant that is a function of the specimen ligament length. The KIsi evaluation also removes the Pmax/PQ criterion and increases the allowable specimen deformation. These latter two changes allow more plasticity at the crack tip, prompting the review undertaken in this work to ensure the validity of this new interpretation of the force-displacement curve. This paper provides a brief review of the proposed KIsi methodology and summarizes a finite element study into the effects of increased crack tip plasticity on the method given the allowance for additional specimen deformation. The study has two primary points of investigation: the effect of crack tip plasticity on compliance change in the force-displacement record and the continued validity of linear-elastic fracture mechanics to describe the crack front conditions. The analytical study illustrates that linear-elastic fracture mechanics assumptions remain valid at the increased deformation limit; however, the influence of plasticity on the compliance change in the test record is problematic. A proposed revision to the validity criteria for the KIsi test method is briefly discussed.

James, Mark↗
NASA NTRS2017

A Review of the Proposed KIsi Offset-Secant Method for Size-Insensitive Linear-Elastic Fracture Toughness Evaluation

Recently proposed modifications to ASTM E399 would provide a new size-insensitive approach to analyzing the force-displacement test record. The proposed size-insensitive linear-elastic fracture toughness, KIsi, targets a consistent 0.5mm crack extension for all specimen sizes by using an offset secant that is a function of the specimen ligament length. The KIsi evaluation also removes the Pmax/PQ criterion and increases the allowable specimen deformation. These latter two changes allow more plasticity at the crack tip, prompting the review undertaken in this work to ensure the validity of this new interpretation of the force-displacement curve. This paper provides a brief review of the proposed KIsi methodology and summarizes a finite element study into the effects of increased crack tip plasticity on the method given the allowance for additional specimen deformation. The study has two primary points of investigation: the effect of crack tip plasticity on compliance change in the force-displacement record and the continued validity of linear-elastic fracture mechanics to describe the crack front conditions. The analytical study illustrates that linear-elastic fracture mechanics assumptions remain valid at the increased deformation limit; however, the influence of plasticity on the compliance change in the test record is problematic. A proposed revision to the validity criteria for the KIsi test method is briefly discussed.

James, Mark↗
NASA NTRS2017

A Review of the Proposed K (sub Isi) Offset-Secant Method for Size-Independent Linear-Elastic Toughness Evaluation

The proposed size-independent linear-elastic fracture toughness, K (sub Isi), for potential inclusion in ASTM E399 targets a consistent 0.5 millimeters crack extension for all specimen sizes through an offset secant that is a function of the specimen ligament length. The K (sub Isi) method also includes an increase in allowable deformation, and the removal of the P (sub max)/P (sub Q) criterion. A finite element study of the K (sub Isi) test method confirms the viability of the increased deformation limit, but has also revealed a few areas of concern. Findings: 1. The deformation limit, b (sub o) greater than or equal to 1.1 times (K (sub I) divided by delta (sub ys) squared) maintains a K-dominant crack tip field with limited plastic contribution to the fracture energy; 2. The three dimensional effects on compliance and the shape of the force versus CMOD (Crack-Mouth Opening Displacement) trace are significant compared to a plane strain assumption; 3. The non-linearity in the force versus CMOD trace at deformations higher than the current limit of 2.5 times (K (sub I) divided by delta (sub ys) squared) is sufficient to introduce error or even "false calls" regarding crack extension when using a constant offset secant line. This issue is more significant for specimens with W (width) greater than or equal to 2 inches; 4. A non-linear plasticity correction factor in the offset secant may improve the viability of the method at deformations between 2.5 times (K (sub I) divided by delta (sub ys) squared) and 1.1 times (K (sub I) divided by delta (sub ys) squared).

James, Mark↗
NASA NTRS1994

Principles Of Linear Elastic Fracture Mechanics

NASA technical memorandum discusses principles of linear elastic fracture mechanics. Emphasis on practical problems; intended especially to help structural engineers understand fracture-mechanics software.

Wilson, Christopher D.↗
DOE OSTI2022

A coupling approach for linear elasticity problems with spatially non-coincident discretized interfaces

Here we present a new method for coupled linear elasticity problems whose finite element discretization may lead to spatially non-coincident discretized interfaces. Our approach combines the classical Dirichlet–Neumann coupling formulation with a new set of discretized interface conditions obtained through Taylor series expansions. We show that these conditions ensure linear consistency of the coupled finite element solution. We then formulate an iterative solution method for the coupled discrete system and apply the new coupling approach to two representative settings for which we also provide several numerical illustrations. The first setting is a mesh-tying problem in which both coupled structures have the same Lamé parameters whereas the second setting is an interface problem for which the Lamé parameters in the two coupled structures are different.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A New Proof That the Number of Linear Elastic Symmetries in Two Dimensions Is Four

In this work, we present an elementary and self-contained proof that there are exactly four symmetry classes of the elasticity tensor in two dimensions: oblique, rectangular, square, and isotropic. In two dimensions, orthogonal transformations are either reflections or rotations. The proof is based on identification of constraints imposed by reflections and rotations on the elasticity tensor, and it simply employs elementary tools from trigonometry, making the proof accessible to a broad audience. For completeness, we identify the sets of transformations (rotations and reflections) for each symmetry class and report the corresponding equations of motions in classical linear elasticity.

42 ENGINEERING↗
NASA NTRS2023

Unconservatism of Linear-Elastic Fracture Mechanics (LEFM) Analysis Post Autofrettage

The scope of the NASA Engineering and Safety Center (NESC) Unconservatism of Linear-Elastic Fracture Mechanics (LEFM) Analysis Post Autofrettage assessment was to evaluate the influence of the elastic-plastic autofrettage cycle on elastic cycles post autofrettage and generate data to support damage tolerance life analysis verification approach. The decision to include an elastic-plastic autofrettage cycle is informed by other factors beyond damage tolerance, including manufacturing and fatigue crack initiation. The results of the NESC assessment are contained in this report.

Linear-Elastic Fracture Mechanics↗
DOE OSTI2024

An intrinsic ductility parameter derived from anisotropic linear elasticity theory

A new indicator of intrinsic ductility (κ) is introduced based on linear elasticity. In the limit of elastic isotropy this parameter is equal to the Pugh ratio ( B / G ) plus a constant; but unlike the Pugh ratio, κ incorporates anisotropy and crystallography to improve predictive value. We identify a single ductile-to-brittle transition setpoint for κ that predicts crack-tip plasticity in atomistic simulations, experimental elongation to failure of polycrystalline elemental metals pulled in tension, and fracture energy measurements of glasses, suggesting commonality in the relationship between plasticity and fracture across all three of these cases. Statistical analysis supports the superiority of κ over B / G at predicting crack-tip plasticity in atomistic simulations and elongation to failure of polycrystalline elemental metals.

Winter, Ian S.↗
NASA NTRS1983

An investigation of the accuracy of finite difference methods in the solution of linear elasticity problems

The accuracy of the finite difference method in the solution of linear elasticity problems that involve either a stress discontinuity or a stress singularity is considered. Solutions to three elasticity problems are discussed in detail: a semi-infinite plane subjected to a uniform load over a portion of its boundary; a bimetallic plate under uniform tensile stress; and a long, midplane symmetric, fiber reinforced laminate subjected to uniform axial strain. Finite difference solutions to the three problems are compared with finite element solutions to corresponding problems. For the first problem a comparison with the exact solution is also made. The finite difference formulations for the three problems are based on second order finite difference formulas that provide for variable spacings in two perpendicular directions. Forward and backward difference formulas are used near boundaries where their use eliminates the need for fictitious grid points.

Bauld, N. R., Jr.↗
NASA NTRS1973

Energy-like Liapunov functionals for linear elastic systems on a Hilbert space.

An approach is presented for generating energy-like functionals for linear elastic dynamic systems on a Hilbert space. The objective is to obtain a family of functionals which may be used for stability analysis of the equilibrium, i.e., Liapunov functionals. Although the energy functional, when one exists, is always a member of this family, the family is shown to exist even when an energy functional does not. Several discrete and distributed-parameter examples are presented, as are certain specific techniques for utilizing this approach.

Walker, J. A.↗
NASA NTRS1996

First-Order System Least Squares for Velocity-Vorticity-Pressure Form of the Stokes Equations, with Application to Linear Elasticity

In this paper, we study the least-squares method for the generalized Stokes equations (including linear elasticity) based on the velocity-vorticity-pressure formulation in d = 2 or 3 dimensions. The least squares functional is defined in terms of the sum of the L(exp 2)- and H(exp -1)-norms of the residual equations, which is weighted appropriately by by the Reynolds number. Our approach for establishing ellipticity of the functional does not use ADN theory, but is founded more on basic principles. We also analyze the case where the H(exp -1)-norm in the functional is replaced by a discrete functional to make the computation feasible. We show that the resulting algebraic equations can be uniformly preconditioned by well-known techniques.

Cai, Zhiqiang↗
NASA NTRS1992

Linear elastic fracture mechanics primer

This primer is intended to remove the blackbox perception of fracture mechanics computer software by structural engineers. The fundamental concepts of linear elastic fracture mechanics are presented with emphasis on the practical application of fracture mechanics to real problems. Numerous rules of thumb are provided. Recommended texts for additional reading, and a discussion of the significance of fracture mechanics in structural design are given. Griffith's criterion for crack extension, Irwin's elastic stress field near the crack tip, and the influence of small-scale plasticity are discussed. Common stress intensities factor solutions and methods for determining them are included. Fracture toughness and subcritical crack growth are discussed. The application of fracture mechanics to damage tolerance and fracture control is discussed. Several example problems and a practice set of problems are given.

Wilson, Christopher D.↗
NASA NTRS1996

A Conforming Multigrid Method for the Pure Traction Problem of Linear Elasticity: Mixed Formulation

A multigrid method using conforming P-1 finite element is developed for the two-dimensional pure traction boundary value problem of linear elasticity. The convergence is uniform even as the material becomes nearly incompressible. A heuristic argument for acceleration of the multigrid method is discussed as well. Numerical results with and without this acceleration as well as performance estimates on a parallel computer are included.

Lee, Chang-Ock↗
NASA NTRS2010

Relating Cohesive Zone Model to Linear Elastic Fracture Mechanics

The conditions required for a cohesive zone model (CZM) to predict a failure load of a cracked structure similar to that obtained by a linear elastic fracture mechanics (LEFM) analysis are investigated in this paper. This study clarifies why many different phenomenological cohesive laws can produce similar fracture predictions. Analytical results for five cohesive zone models are obtained, using five different cohesive laws that have the same cohesive work rate (CWR-area under the traction-separation curve) but different maximum tractions. The effect of the maximum traction on the predicted cohesive zone length and the remote applied load at fracture is presented. Similar to the small scale yielding condition for an LEFM analysis to be valid. the cohesive zone length also needs to be much smaller than the crack length. This is a necessary condition for a CZM to obtain a fracture prediction equivalent to an LEFM result.

Wang, John T.↗