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 theory
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Plastic strain and energy density data for cracked plates compared with elastic theory, establishing ductile fracture theory
A study was performed to examine the applicability of path-independent (P-I) integrals to crack growth problems in hot section components of gas turbine aircraft engines. Alloy 718 was used and the experimental parameters included combined temperature and strain cycling, thermal gradients, elastic-plastic strain levels, and mean strains. A literature review was conducted of proposed P-I integrals, and those capable of analyzing hot section component problems were selected and programmed into the postprocessor of a finite element code. Detailed elastic-plastic finite element analyses were conducted to simulate crack growth and crack closure of the test specimen, and to evaluate the P-I integrals. It was shown that the selected P-I integrals are very effective for predicting crack growth for isothermal conditions.
Elastic wave propagation in two dimensions using theory of characteristics
The capability of a computer program which can be part of a larger computer program for a fully automated multiaxial testing facility is described. The program was designed to process test data from tubular or flat specimens made from isotropic or anistropic materials, including high modulus fiber composites. Data from a large number of strain gages and combinations of applied loads can be used. Options are provided for single element, 90-degree, rectangular or Delta rosettes, or any combinations of these types of strain gages. Options are provided for strain gage transverse sensitivities. The program outputs include: structural axes strains and stresses, initial and strain-dependent elastic constants, shift of principal strain direction with load, and local curvatures from back-to-back strain gages, and either Calcomp or microfilm plots. The computer program is described with respect to its flow chart, input/output, embedding or linking with other programs.
The capability of a computer program which can be part of a larger computer program for a fully automated multiaxial testing facility is described. This computer program is designed to process test data from tubular or flat specimens made from isotropic or anisotropic materials including high modulus fiber composites. The program can receive data from a large number of strain gages and combinations of applied loads. Options are provided for single element, 90-degree, rectangular or Delta rosettes, or any combinations of these types of strain gages. Options are provided for strain gage transverse sensitivities. The program outputs include: structural axes strains and stresses, initial and strain dependent elastic constants, shift of principal strain direction with load, and local curvatures from back-to-back strain gages, and either calcomp or microfilm plots. The computer program is described with respect to its flow chart, input/output, embedment or linking with other programs and its possible utility in a fully automated testing system.
Three supplementary X-ray techniques new to semiconductor applications are discussed. These are the Computer Aided Rocking Curve Analyzer, the Divergent Beam Method and a new method based on enhanced X-ray flourescence. The first method is used for quantitative mapping of an elastic or plastic strain field while the other two methods are used only to measure elastic strains. The divergent beam method is used for measuring the full strain tensor while the microfluorescence method is useful for monitoring strain uniformity. These methods are discussed in detail and examples of their application is presented. Among these are determination of the full strain ellipsoid in state-of-the-art liquid phase epitaxy deposited III-V epitaxial films; mapping of the plastic strain concentrations in tensile deformed Si; and quantitative determination of damage in V3Si due to ion implantation.
Digital computer program for analyzing elastic and plastic deformations and creep strains in solid and hollow cylindrical bodies
Recent experimental fatigue crack growth studies have concluded an apparent anomalous behavior of short cracks. To investigate the reasons for this unexpected behavior, the present paper focuses on identifying the crack length circumstances under which the requirements for a single parameter (K(sub I) or delta K(sub I) if cyclic loading is considered) characterization are violated. Furthermore, an additional quantity, the T stress, as introduced by Rice, and the related biaxiality ratio, B, are calculated for several crack lengths and two configurations, the single-edge-cracked and the centrally-cracked specimen. It is postulated that a two-parameter characterization by K and T (or B) is needed for the adequate description of the stress and strain field around a short crack. To further verify the validity of this postulate, the influence of the third term of the Williams series on the stress, strain and displacement fields around the crack tip and in particular on the B parameter is also examined. It is found that the biaxiality ratio would be more negative if the third term effects are included in both geometries. The study is conducted using the finite element method with linearly elastic material and isoparametric elements and axial (mode I) loading. Moreover, it is clearly shown that it is not proper to postulate the crack size limits for 'short crack' behavior as a normalized ratio with the specimen width, a/w; it should instead be stated as an absolute, or normalized with respect to a small characteristic dimension such as the grain size. Finally, implications regarding the prediction of cyclic (fatigue) growth of short cracks are discussed.
Lightweight, flexible, large-aperture mirrors of a type being developed for use in outer space have unimorph structures that enable precise adjustment of their surface figures. A mirror of this type includes a reflective membrane layer bonded with an electrostrictive grafted elastomer (G-elastomer) layer, plus electrodes suitably positioned with respect to these layers. By virtue of the electrostrictive effect, an electric field applied to the G-elastomer membrane induces a strain along the membrane and thus causes a deflection of the mirror surface. Utilizing this effect, the mirror surface figure can be adjusted locally by individually addressing pairs of electrodes. G-elastomers, which were developed at NASA Langley Research Center, were chosen for this development in preference to other electroactive polymers partly because they offer superior electromechanical performance. Whereas other electroactive polymers offer, variously, large strains with low moduli of elasticity or small strains with high moduli of elasticity, G-elastomers offer both large strains (as large as 4 percent) and high moduli of elasticity (about 580 MPa). In addition, G-elastomer layers can be made by standard melt pressing or room-temperature solution casting.
Small deformations for stress-strain relationship of axisymmetric nonlinear elastic plate with reinforced hole
Successive approximation procedure for solving elastic-plastic problem for torsion of solid prismatic bar made of strain hardening material
Contact problem for elastic foundations subjected to bending strains
The solution of small strain elastic-plastic stress analysis problems by the p-version of the finite element method is discussed. The formulation is based on the deformation theory of plasticity and the displacement method. Practical realization of controlling discretization errors for elastic-plastic problems is the main focus. Numerical examples which include comparisons between the deformation and incremental theories of plasticity under tight control of discretization errors are presented.
The strain formulation in elasticity and the compatibility condition in structural mechanics have neither been understood nor have they been utilized. This shortcoming prevented the formulation of a direct method to calculate stress. We have researched and understood the compatibility condition for linear problems in elasticity and in finite element analysis. This has lead to the completion of the method of force with stress (or stress resultant) as the primary unknown. The method in elasticity is referred to as the completed Beltrami-Michell formulation (CBMF), and it is the integrated force method (IFM) in structures. The dual integrated force method (IFMD) with displacement as the primary unknown has been formulated. IFM and IFMD produce identical responses. The variational derivation of the CBMF yielded the new boundary compatibility conditions. The CBMF can be used to solve stress, displacement, and mixed boundary value problems. The IFM in structures produced high-fidelity response even with a modest finite element model. The IFM has influenced structural design considerably. A fully utilized design method for strength and stiffness limitation has been developed. The singularity condition in optimization has been identified. The CBMF and IFM tensorial approaches are robust formulations because of simultaneous emphasis on the equilibrium equation and the compatibility condition.
An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is ideally suited to isotropically hardening Prandtl-Reuss materials. Further, the formulation is given in a manner which allows any conventional finite element program, for 'small strain' elastic-plastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. The paper closes with a unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures. Further, a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain, and the inadequacies of some of these are commented upon.
Strain redistribution corrections were developed for a simplified inelastic analysis procedure to economically calculate material cyclic response at the critical location of a structure for life prediction proposes. The method was based on the assumption that the plastic region in the structure is local and the total strain history required for input can be defined from elastic finite-element analyses. Cyclic stress-strain behavior was represented by a bilinear kinematic hardening model. The simplified procedure predicts stress-strain response with reasonable accuracy for thermally cycled problems but needs improvement for mechanically load-cycled problems. Neuber-type corrections were derived and incorporated in the simplified procedure to account for local total strain redistribution under cyclic mechanical loading. The corrected simplified method was used on a mechanically load-cycled benchmark notched-plate problem. The predicted material response agrees well with the nonlinear finite-element solutions for the problem. The simplified analysis computer program was 0.3% of the central processor unit time required for a nonlinear finite-element analysis.
An elastic large displacement thick-shell mixed finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at the element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses is included in the mixed variational functional. The nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the nonlinear elastic equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to computationally simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.
An elastic large displacement thick-shell hybrid finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at he element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses in included in the mixed variational functional. Nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to numerically simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.