Plastic strains and energy density in cracked plates. ii - comparison with elastic theory.
Plastic strain and energy density data for cracked plates compared with elastic theory, establishing ductile fracture criteria
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Dynamic fields near a crack tip growing in an elastic-perfectly-plastic solid
A full asymptotic solution is presented for the fields in the neighborhood of the tip of a steadily advancing crack in an incompressible elastic-perfectly-plastic solid. There are four findings for mode I crack growth in the plane strain condition. The first is that the entire crack tip in steady crack growth is surrounded by a plastic region and that no elastic unloading is predicted by the complete dynamic asymptotic solution. The second is that, in contrast to the quasi-static solution, the dynamic solution yields strain fields with a logarithmic singularity everywhere near the crack tip. The third is that whereas the stress field varies throughout the entire crack tip neighborhood, it does not exhibit behavior that can be approximated by a constant field followed by an essentially centered-fan field and then by another constant field, especially for small crack growth speeds. The fourth finding is that there are two shock fronts emanating from the crack tip across which certain stress and strain components undergo jump discontinuities. After reviewing the mode III steady-state crack growth, it is concluded that ductile fracture criteria for nonstationary cracks must be based on solutions that include the inertia effects and that for this purpose quasi-static solutions may be inadequate.
Nemat-Nasser, S.↗
FAA/NASA International Symposium on Advanced Structural Integrity Methods for Airframe Durability and Damage Tolerance
International technical experts in durability and damage tolerance of metallic airframe structures were assembled to present and discuss recent research findings and the development of advanced design and analysis methods, structural concepts, and advanced materials. The symposium focused on the dissemination of new knowledge and the peer-review of progress on the development of advanced methodologies. Papers were presented on: structural concepts for enhanced durability, damage tolerance, and maintainability; new metallic alloys and processing technology; fatigue crack initiation and small crack effects; fatigue crack growth models; fracture mechanics failure, criteria for ductile materials; structural mechanics methodology for residual strength and life prediction; development of flight load spectra for design and testing; and advanced approaches to resist corrosion and environmentally assisted fatigue.
Harris, Charles E.↗
FAA/NASA International Symposium on Advanced Structural Integrity Methods for Airframe Durability and Damage Tolerance, part 2
The international technical experts in the areas of durability and damage tolerance of metallic airframe structures were assembled to present and discuss recent research findings and the development of advanced design and analysis methods, structural concepts, and advanced materials. The principal focus of the symposium was on the dissemination of new knowledge and the peer-review of progress on the development of advanced methodologies. Papers were presented on the following topics: structural concepts for enhanced durability, damage tolerance, and maintainability; new metallic alloys and processing technology; fatigue crack initiation and small crack effects; fatigue crack growth models; fracture mechanics failure criteria for ductile materials; structural mechanics methodology for residual strength and life prediction; development of flight load spectra for design and testing; and corrosion resistance.
Harris, Charles E.↗
The Relationship Between Constraint and Ductile Fracture Initiation as Defined by Micromechanical Analyses
The use of small laboratory specimens to predict the integrity of large, complex structures relies on the validity of single parameter fracture mechanics. Unfortunately, the constraint loss associated with large scale yielding, whether in a laboratory specimen because of its small size or in a structure because it contains shallow flaws loaded in tension, can cause the breakdown of classical fracture mechanics and the loss of transferability of critical, global fracture parameters. Although the issue of constraint loss can be eliminated by testing actual structural configurations, such an approach can be prohibitively costly. Hence, a methodology that can correct global fracture parameters for constraint effects is desirable. This research uses micromechanical analyses to define the relationship between global, ductile fracture initiation parameters and constraint in two specimen geometries (SECT and SECB with varying a/w ratios) and one structural geometry (circumferentially cracked pipe). Two local fracture criteria corresponding to ductile fracture micromechanisms are evaluated: a constraint-modified, critical strain criterion for void coalescence proposed by Hancock and Cowling and a critical void ratio criterion for void growth based on the Rice and Tracey model. Crack initiation is assumed to occur when the critical value in each case is reached over some critical length. The primary material of interest is A516-70, a high-hardening pressure vessel steel sensitive to constraint; however, a low-hardening structural steel that is less sensitive to constraint is also being studied. Critical values of local fracture parameters are obtained by numerical analysis and experimental testing of circumferentially notched tensile specimens of varying constraint (e.g., notch radius). These parameters are then used in conjunction with large strain, large deformation, two- and three-dimensional finite element analyses of the geometries listed above to predict crack initiation loads and to calculate the associated (critical) global fracture parameters. The loads are verified experimentally, and microscopy is used to measure pre-crack length, crack tip opening displacement (CTOD), and the amount of stable crack growth. Results for A516-70 steel indicate that the constraint-modified, critical strain criterion with a critical length approximately equal to the grain size (0.0025 inch) provides accurate predictions of crack initiation. The critical void growth criterion is shown to considerably underpredict crack initiation loads with the same critical length. The relationship between the critical value of the J-integral for ductile crack initiation and crack depth for SECT and SECB specimens has been determined using the constraint-modified, critical strain criterion, demonstrating that this micromechanical model can be used to correct in-plane constraint effects due to crack depth and bending vs. tension loading. Finally, the relationship developed for the SECT specimens is used to predict the behavior of circumferentially cracked pipe specimens.
Panontin, Tina L.↗
Implementation of J-A Methodology Elastic-Plastic Crack Instability Analysis Capability into the WARP-3D Code
Characterization of the near crack-tip stress/strain fields is the foundation of fracture mechanics. The description of the near tip stress field and the prediction of when fracture occurs is well established for brittle materials that exhibit linear elastic behavior. However, in ductile materials or conditions that violate linear elastic assumptions (Aluminum alloys, Al 2024-T3, Al 2024- T351 etc.), the elastic-plastic crack-tip stress fields are characterized by the Hutchison-Rice-Rosengren (HRR) field. The J-integral is commonly used to characterize amplitude of the HRR field under elastic-plastic conditions. The J-integral has been demonstrated for crack-tip fields that are under high constraint conditions (i.e., small-scale plasticity where the J-dominance is maintained). However, as the external load increases, yielding changes from small- to largescale plasticity and usually a loss of constraint (i.e., reduction in the triaxial stress field along the crack front). The loss of constraint leads to the deviation of the crack-tip stress fields from that given by the HRR field. Hence, the J-dominance will be gradually lost and additional parameter(s) are required to quantify the crack-tip stress fields and predict fracture behavior. The assessment objectives were to: 1) implement a two-parameter (i.e., J-A) fracture criterion into an elastic-plastic three-dimensional (3D) finite element analysis (FEA), 2) validate the implementation by comparison with the A parameter from literature data, 3) conduct material characterization tests to quantify the material behavior and provide fracture data for validation of the J-A fracture criteria, and (4) perform evaluations to establish if the J-A criteria can be used to predict fracture in a ductile metallic material (e.g., aluminum alloys). The A parameter in these criteria is the second parameter in a three-term elastic-plastic asymptotic expansion of the neartip stress behavior. A series of extensive FEAs were performed using WARP3D software package to obtain solutions for the A parameter for different specimen configurations. The methodology needed for the estimation of the A parameter in the asymptotic expansion was developed and implemented using Matlab®. A user material (UMAT) routine was used to model the material stress-strain response using a Ramberg-Osgood power law with a hardening exponent (n) and a material coefficient (alpha). This UMAT routine was successfully implemented in WARP3D software and validated through comparison with the experimental data. Three configurations were extracted from published results: 1) center cracked plate (CCP), 2) single edge-cracked plate (SECP), and 3) double edge-cracked plate (DECP). These configurations and four other configurations (three-hole tension (THT)), three-point bend (3PTB), three-hole compact tension (3PCT), and compact tension (CT)) were analyzed to verify the methodology that was developed and implemented into WARP3D. Solutions of the A parameter were obtained for remote tension loading conditions that started with small-scale yielding and continued into the large-scale plasticity regime. The results indicate that the methodology developed can be used to calculate the elastic-plastic J-A parameters for test specimens with a range of crack geometries, material strain hardening behaviors, and loading conditions. The J-A parameters were implemented as fracture criteria and used to predict the test results. For comparison, other fracture criteria were used to predict the same test results. Major findings include: The A constraint parameter A varies with specimen type and applied load thus accurate determination is crucial in predicting the failure load, and the A parameter is asymptotic as the failure load is approached, making an accurate determination difficult (i.e., small differences in the A parameter can cause large variations in failure load) for materials exhibiting elastic-plastic behavior. The failure predictions from J-A methodology were more accurate than the traditionally used KC and J methods, and have comparable scatter to that observed when using the crack-tip opening angle (CTOA) method. However, the J-A methodology requires considerable effort (expertise level and labor) to implement and to evaluate the A parameter for different specimen types and materials, or to apply this methodology to part-through crack (e.g., 3D problems) structural applications.
Hamm, Kenneth R., Jr.↗
Tidal disruption of solid bodies
The problem of stress, strain, and breakup in solid satellites and stray bodies subject to tidal perturbations is presently addressed in view of three novel considerations. After presenting a new analytic solution for the stress tensor in a homogeneous and compressible elastic sphere, where the inclusion of compressibility alters stresses by several percent, realistic failure criteria are noted to demonstrate the general failure of such ductile bodies as iron meteoroids by plastic shear, while brittle ice bodies fail by either tensile or shear fracture. A reexamination of crack propagation after initial failure allows the diverse breakup criteria to be reconciled.
Dobrovolskis, Anthony R.↗
On the thermoelastic analysis of solar cell arrays and related material properties
Accurate prediction of failure of solar cell arrays requires accuracy in the computation of thermally induced stresses. This was accomplished by using the finite element technique. Improved procedures for stress calculation were introduced together with failure criteria capable of describing a wide range of ductile and brittle material behavior. The stress distribution and associated failure mechanisms in the N-interconnect junction of two solar cell designs were then studied. In such stress and failure analysis, it is essential to know the thermomechanical properties of the materials involved. Measurements were made of properties of materials suitable for the design of lightweight arrays: microsheet-0211 glass material for the solar cell filter, and Kapton-H, Kapton F, Teflon, Tedlar, and Mica Ply PG-402 for lightweight substrates. The temperature-dependence of the thermal coefficient of expansion for these materials was determined together with other properties such as the elastic moduli, Poisson's ratio, and the stress-strain behavior up to failure.
Salama, M. A.↗
Fracture Analysis of Semi-Elliptical Surface Cracks in Ductile Materials
Accurate life assessment of structural components may require advanced life prediction criteria and methodologies. Structural components often exhibit several different types of defects, among the most prevalent being surface cracks. A semi-elliptical surface crack subjected to monotonic loading will exhibit stable crack growth until the crack has reached a critical size, at which the crack loses stability and fracture ensues (Newman, 2000). The shape and geometry of the flaw are among the most influential factors. When considering simpler crack configurations, such as a through-the-thickness crack, a three-dimensional (3D) geometry may be modeled under the approximation of two-dimensional (2D) plane stress or plane strain. The more complex surface crack is typically modeled numerically with the Finite Element Method (FEM). A semi-elliptical surface crack is illustrated in Figure 1-1.
Daniewicz, S. R.↗
Strain accommodation beneath structures on Mars
A recent review of tectonic features on Mars shows that most of their subsurface structures can be confidently extended only a few kilometers deep (exceptions are rifts, in which bounding normal faults penetrate the entire brittle lithosphere, with ductile flow at deeper levels). Nevertheless, a variety of estimates of elastic lithosphere thickness and application of accepted failure criteria under likely conditions on Mars suggest a brittle lithosphere that is many tens of kilometers thick. This raises the question of how the strain (extension or shortening) accommodated by grabens and wrinkle ridges within the upper few kilometers is being accommodated at deeper levels in the lithosphere. Herein, the nonrift tectonic features present on Mars are briefly reviewed, along with their likely subsurface structures, and some inferences and implications are presented for behavior of the deeper lithosphere.
Golombek, M. P.↗
Three-Dimensional Stress Fields and Slip Systems for Single Crystal Superalloy Notched Specimens
Single crystal superalloys have become increasingly popular for turbine blade and vane applications due to their high strength, and creep and fatigue resistance at elevated temperatures. The crystallographic orientation of a single crystal material greatly affects its material properties, including elastic modulus, shear modulus, and ductility. These directional properties, along with the type of loading and temperature, dictate an anisotropic response in the yield strength, creep resistance, creep rupture ductility, fatigue resistance, etc. A significant amount of research has been conducted to determine the material properties in the <001> orientation, yet the material properties deviating from the <001> orientation have not been assessed for all cases. Based on the desired application and design criteria, a crystal orientation is selected to yield the maximum properties. Currently, single crystal manufacturing is able to control the primary crystallographic orientation within 15 of the target orientation, which is an acceptable deviation to meet both performance and cost guidelines; the secondary orientation is rarely specified. A common experiment is the standard load-controlled tensile test, in which specimens with different orientations can be loaded to observe the material response. The deformation behavior of single-crystal materials under tension and compression is known to be a function of not only material orientation, but also of varying microdeformation (i.e. dislocation) mechanisms. The underlying dislocation motion causes deformation via slip, and affects the activation of specific slip systems based on load and orientation. The slip can be analyzed by observing the visible traces left on the surface of the specimen from the slip activity within the single crystal material. The goal of this thesis was to predict the slip systems activated in three-dimensional stress fields of a notched tensile specimen, as a function of crystal orientation, using finite element analysis without addressing microstructural deformation mechanisms that govern their activation. Out of three orientations tested, the specimen with a [110] load orientation and a [001] growth direction had the lowest maximum resolved shear stress; this specimen orientation appears to be the best design candidate for a tensile application.
Magnan, Shannon M.↗
Coatings for high-temperature bearings and seals
Criteria are discussed for predicting the probable lubricating ability of candidate solid materials from a consideration of their basic chemical and physical properties. The properties considered to be important in the model are thermochemical potential, adhesion, low hardness, plasticity, yield strength in shear, and brittle-to-ductile transition characteristics. A review of the selection and tribological testing of materials, which were selected for use in self-lubricating composite coatings by employing this model, is given. Two series of plasma-sprayed coatings with good tribological properties over a wide temperature spectrum are described. The PS 100 series of coatings contain oxidatively stable solid lubricants in a nichrome matrix. The PS 200 series contains the same solid lubricants in a very wear resistant metal-bonded chromium carbide matrix. Examples are given of applications of these coatings in high speed shaft seals, sliding contact bearings, and Stirling engine cylinder liners.
Sliney, Harold E.↗
Wear of seal materials used in aircraft propulsion systems
A review of various types of seal locations in a gas turbine engine and the significance of wear for each type are presented. Material selection guidelines and the PV (contact pressure times sliding velocity) criteria for seal materials are discussed, and examples of wear mechanisms in positive contact seals are given. It is suggested that improved wear, erosion, and oxidation resistant materials will be required for improved seal durability; finally, a correlation is proposed between wear characteristics and a factor that includes material strength, ductility, specific heat and hot-working temperature to attain low porosity metallic gas path seal materials.
Bill, R. C.↗
Dynamic fracture mechanics
Dynamic fracture and crack propagation concepts for ductile materials are reviewed. The equations for calculating dynamic stress integrity and the dynamic energy release rate in order to study dynamic crack propagation are provided. The stress intensity factor versus crack velocity relation is investigated. The uses of optical experimental techniques and finite element methods for fracture analyses are described. The fracture criteria for a rapidly propagating crack under mixed mode conditions are discussed; crack extension and fracture criteria under combined tension and shear loading are based on maximum circumferential stress or energy criteria such as strain energy density. The development and use of a Dugdale model and finite element models to represent crack and fracture dynamics are examined.
Kobayashi, A. S.↗
Effects of thermally induced porosity on an as-HIP powder metallurgy superalloy
The effect of thermally induced porosity on the mechanical properties of an as-hot-isostatically pressed and heat-treated pressing made from low carbon Astroloy is examined. Tensile, stress-rupture, creep, and low cycle fatigue tests were performed and the results were compared with industrial acceptance criteria. It is shown that the porous pressing has a porosity gradient from the rim to the bore with the bore having 1-1/2% greater porosity. Mechanical properties of the test ring below acceptance level are tensile reduction in area at room temperature and 538 C and time for 0.1% creep at 704 C. It is also found that the strength, ductility, and rupture life of the rim are slightly inferior to those of the rim of the sound pressings, while those of the bore are generally below the acceptable level. At strain ranges typical of commercial aircraft engines, the low cycle fatigue life of the rim of the porous pressings is slightly lower than that of the sound pressings.
Dreshfield, R. L.↗
Strain Rate Dependent Deformation and Strength Modeling of a Polymer Matrix Composite Utilizing a Micromechanics Approach
Potential gas turbine applications will expose polymer matrix composites to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under extreme conditions. Specifically, analytical methods designed for these applications must have the capability of properly capturing the strain rate sensitivities and nonlinearities that are present in the material response. The Ramaswamy-Stouffer constitutive equations, originally developed to analyze the viscoplastic deformation of metals, have been modified to simulate the nonlinear deformation response of ductile, crystalline polymers. The constitutive model is characterized and correlated for two representative ductile polymers. Fiberite 977-2 and PEEK, and the computed results correlate well with experimental values. The polymer constitutive equations are implemented in a mechanics of materials based composite micromechanics model to predict the nonlinear, rate dependent deformation response of a composite ply. Uniform stress and uniform strain assumptions are applied to compute the effective stresses of a composite unit cell from the applied strains. The micromechanics equations are successfully verified for two polymer matrix composites. IM7/977-2 and AS4/PEEK. The ultimate strength of a composite ply is predicted with the Hashin failure criteria that were implemented in the composite micromechanics model. The failure stresses of the two composite material systems are accurately predicted for a variety of fiber orientations and strain rates. The composite deformation model is implemented in LS-DYNA, a commercially available transient dynamic explicit finite element code. The matrix constitutive equations are converted into an incremental form, and the model is implemented into LS-DYNA through the use of a user defined material subroutine. The deformation response of a bulk polymer and a polymer matrix composite are predicted by finite element analyses. The results compare reasonably well to experimental values, with some discrepancies. The discrepancies are at least partially caused by the method used to integrate the rate equations in the polymer constitutive model.
Goldberg, Robert K.↗