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The interfacial hydrostatic stress of the working electrode, not its surface-normal stress, is a more general and widely applicable stress descriptor to use for the mechanics-modified equilibrium potential Δ U .
The purpose of this study was to examine the applicability of linear-elastic fracture mechanics to graphite under multiaxial stress conditions. The specimens were thick-walled graphite cylinders with flat heads which were internally pressurized. Two series of specimens were used. The first series had complete circumferential notches machined diagonally into the head-cylinder juncture region, while the second series was unnotched. The methods of linear-elastic fracture mechanics and a finite-element analysis were used to predict pressures to cause fracture for both notched and unnotched specimens.
Investigation of the basic requirements for modeling slender member shadowing effects on thermally induced deformation continues. The theoretical formulation is complete and computer programming is underway. The basic requirements for thermal finite elements to model heat transfer in orbiting structures were also studied. The need for planar isothermal elements to model large space structures' antenna meshes was established. Finite Element approaches for modeling space structure cable and membrane components with thermal effects is underway. Three levels of structural modeling and analysis were identified: (1) a linear-elastic small deflection analysis that does not permit cable slackening; (2) a linear-elastic analysis that includes stress stiffening (the ANSYS program), but not large deflections; and (3) full nonlinear large deflection analysis with stress stiffening. Methods of determining cable initial tensions are currently being evaluated.
This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.
We modify the traditional linear-elastic field of an edge dislocation. The modifications stem from symmetry and energy requirements imposed in terms of embedded (deformed) coordinates. These requirements are satisfied if a line force is added to the dislocation field. The modification to the stress field is expressed by coefficients that are a function only of Poisson’s ratio. Qualitatively, the field of the dislocation is increased in the glide direction and decreased in the climb direction. There are small changes to the field of a screw dislocation that do not entail the addition of a line force. Effects of nonlinearity, anisotropic elasticity, and image forces are briefly considered.
Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.
Discussion of some of the precaution needs the development of fracture-mechanics based test methods for studying stress corrosion cracking involves. Following a review of pertinent analytical fracture mechanics considerations and of basic test methods, the implications for test corrosion cracking studies of the time-to-failure determining kinetics of crack growth and life are examined. It is shown that the basic assumption of the linear-elastic fracture mechanics analyses must be clearly recognized and satisfied in experimentation and that the effects of incubation and nonsteady-state crack growth must also be properly taken into account in determining the crack growth kinetics, if valid data are to be obtained from fracture-mechanics based test methods.
A two-parameter fracture criterion was derived which relates the linear-elastic stress-intensity factor at failure, the elastic nominal failure stress, and two material parameters. The fracture criterion was used previously to analyze fracture data for surface- and through-cracked sheet and plate specimens under tensile loading. The fracture criterion was applied to center-crack tension, compact, and notch-band fracture specimens made of steel, titanium, or aluminum alloy materials tested at room temperature. The fracture data included a wide range of crack lengths, specimen widths, and thicknesses. The materials analyzed had a wide range of tensile properties. Failure stresses calculated using the criterion agreed well (plus or minus 10 percent) with experimental failure stresses. The criterion was also found to correlate fracture data from different specimen types (such as center-crack tension and compact specimens), within plus or minus 10 percent for the same material, thickness, and test temperature.
The J sub I relation, introduced by Rice (1968), expresses the work done on a quasiplanar specimen of specified width (or depth) for a fixed uniform crack length when the displacement of the load is increased from zero to some given value. The relation remains the same if the work done and its logarithmic derivative are calculated in terms of the component of the displacement that is 'due to the crack' rather than the total displacement. J sub I is studied as a function of displacement for a precracked, three-point-loaded bend specimen and also in the extremes of linear-elastic, and rigid/perfectly plastic behavior.
A two-parameter fracture criterion has been derived which relates the linear-elastic stress-intensity factor at failure, the elastic nominal failure stress, and two material parameters. The fracture criterion was applied to center-crack tension, compact, and notch-bend fracture specimens made of steel, titanium, or aluminum alloy materials tested at room temperature. The fracture data included a wide range of crack lengths, specimen widths, and thicknesses. The materials analyzed had a wide range of tensile properties. Failure stresses calculated using the criterion agreed well (plus or minus 10 percent) with experimental failure stresses. The criterion was also found to correlate fracture data from different specimen types (such as center-crack tension and compact specimens), within plus or minus 10 percent for the same material, thickness, and test temperature.
A two-dimensional, linear-elastic, finite element analysis of selected graphite/polyimide rail shear test specimens was made to determine the mechanical loading and the effect of heating the specimen to a uniform temperature. The presence of specimen free edges and their influence on the accuracy of the rail shear test is discussed. Parameters include the length-to-width ratio of the specimen and the ply layup for symmetric, balanced laminates. Results presented include shear and normal stress distributions and the deflection behavior of various specimens caused by the mechanical loading and elevated temperature.
DESAP 2 synthesizes linear-elastic structures under static loads. Objective is to find element sizes (cross-sectional areas, plate thicknesses, and the like) that minimize total structural weight without changing layout of structure. Weight is minimized for given layout subject to prescribed contstraints.
Fatigue crack growth patterns and lives for surface cracks, surface cracks at holes, and corner cracks at holes in three dimensional bodies were predicted using linear-elastic fracture mechanics concepts that were modified to account for crack-closure behavior. The predictions were made by using stress intensity factor equations for these crack configurations and the fatigue crack-growth (delta K against rate) relationship for the material of interest. The crack configurations were subjected to constant-amplitude fatigue loading under either remote tension or bending loads. The predicted crack growth patterns and crack growth lives for aluminum alloys agreed well with test data from the literature.
Elastic and plastic deformations calculated under variety of loading conditions. Prediction of fatigue-crack-growth lives made with FatigueCrack-Growth Structural Analysis (FASTRAN) computer program. As cyclic loads are applied to initial crack configuration, FASTRAN predicts crack length and other parameters until complete break occurs. Loads are tensile or compressive and of variable or constant amplitude. FASTRAN incorporates linear-elastic fracture mechanics with modifications of load-interaction effects caused by crack closure. FASTRAN considered research tool, because of lengthy calculation times. FASTRAN written in FORTRAN IV for batch execution.
Fatigue crack growth patterns and lives for surface cracks, surface cracks at holes, and corner cracks at holes in three dimensional bodies were predicted using linear-elastic fracture mechanics concepts that were modified to account for crack-closure behavior. The predictions were made by using stress intensity factor equations for these crack configurations and the fatigue crack-growth (delta K against rate) relationship for the material of interest. The crack configurations were subjected to constant-amplitude fatigue loading under either remote tension or bending loads. The predicted crack growth patterns and crack growth lives for aluminum alloys agreed well with test data from the literature.
The objective of the Elevated Temperature Crack Growth Program is to evaluate proposed nonlinear fracture mechanics methods for application to hot section components of aircraft gas turbine engines. Progress during the past year included linear-elastic fracture mechanics data reduction on nonlinear crack growth rate data on Alloy 718. The bulk of the analytical work centered on thermal gradient problems and proposed fracture mechanics parameters. Good correlation of thermal gradient experimental displacement data and finite element prediction was obtained.
An algorithm is developed to construct the compliance matrix for a cracked solid in the integral-equation formulation of two-dimensional linear-elastic fracture mechanics. The integral equation is reduced to a system of algebraic equations for unknown values of the dislocation-density function at discrete points on the interval from -1 to 1, using the numerical procedure described by Gerasoulis (1982). Sample numerical results are presented, and it is suggested that the algorithm is especially useful in cases where iterative solutions are required; e.g., models of fiber-reinforced concrete, rocks, or ceramics where microcracking, fiber bridging, and other nonlinear effects are treated as nonlinear springs along the crack surfaces (Ballarini et al., 1984).
The dynamic behavior of a spinning linear-elastic paraboloid subject to nonaxisymmetric deformation is investigated analytically, applying the Rayleigh-Ritz procedure described by Utku et al. (1983). Energy-density, strain-displacement, and velocity-displacement expressions are generated; expressions for the generalized strain and position vector are derived; and the discretized dynamic equations are obtained. Numerical results obtained with a computer-program implementation of the method are presented in extensive tables and graphs. The effects of spin rate and bending rigidity and results for the special case of a spinning disk are included.