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Discrete models for boundary value problems analysis in first strain-gradient elasticity theory, using extended finite element method
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.
An X-ray technique for the measurement of internal residual strain gradients near the continuous reinforcements of metal matrix composites has been investigated. The technique utilizes high intensity white X-ray radiation from a synchrotron radiation source to obtain energy spectra from small (0.001 cu mm) volumes deep within composite samples. The viability of the technique was tested using a model system with 800 micron Al203 fibers and a commercial purity titanium matrix. Good agreement was observed between the measured residual radial and hoop strain gradients and those estimated from a simple elastic concentric cylinders model. The technique was then used to assess the strains near (SCS-6) silicon carbide fibers in a Ti-14Al-21Nb matrix after consolidation processing. Reasonable agreement between measured and calculated strains was seen provided the probe volume was located 50 microns or more from the fiber/matrix interface.
The explicit transient dynamics technology in use today for simulating the impact and subsequent transient dynamic response of a structure has its origins in the 'hydrocodes' dating back to the late 1940's. The growth in capability in explicit transient dynamics technology parallels the growth in speed and size of digital computers. Computer software for simulating the explicit transient dynamic response of a structure is characterized by algorithms that use a large number of small steps. In explicit transient dynamics software there is a significant emphasis on speed and simplicity. The finite element technology used to generate the spatial discretization of a structure is based on a compromise between completeness of the representation for the physical processes modelled and speed in execution. That is, since it is expected in every calculation that the deformation will be finite and the material will be strained beyond the elastic range, the geometry and the associated gradient operators must be reconstructed, as well as complex stress-strain models evaluated at every time step. As a result, finite elements derived for explicit transient dynamics software use the simplest and barest constructions possible for computational efficiency while retaining an essential representation of the physical behavior. The best example of this technology is the four-node bending quadrilateral derived by Belytschko, Lin and Tsay. Today, the speed, memory capacity and availability of computer hardware allows a number of the previously used algorithms to be 'improved.' That is, it is possible with today's computing hardware to modify many of the standard algorithms to improve their representation of the physical process at the expense of added complexity and computational effort. The purpose is to review a number of these algorithms and identify the improvements possible. In many instances, both the older, faster version of the algorithm and the improved and somewhat slower version of the algorithm are found implemented together in software. Specifically, the following seven algorithmic items are examined: the invariant time derivatives of stress used in material models expressed in rate form; incremental objectivity and strain used in the numerical integration of the material models; the use of one-point element integration versus mean quadrature; shell elements used to represent the behavior of thin structural components; beam elements based on stress-resultant plasticity versus cross-section integration; the fidelity of elastic-plastic material models in their representation of ductile metals; and the use of Courant subcycling to reduce computational effort.
Recent results from sensitivity analysis for strain energy with anisotropic elasticity are applied to thickness and orientational design of laminated membranes. Primarily, the first order gradients of the total elastic energy are used in an optimality criteria based method. This traditional method is shown to give slow convergence with respect to design parameters, although the convergence of strain energy is very good. To get a deeper insight into this rather general characteristic, second order derivatives are included and it is shown how they can be obtained by first order sensitivity analysis. Examples of only thickness design, only orientational design, and combined thickness--orientational design are presented.
An analogy between inelastic strains caused by temperature and those caused by creep is presented in terms of isotropic elasticity. It is shown how the theoretical aspects can be blended with existing finite-element computer programs to exact a piecewise linear solution. The creep effect is determined by using the thermal stress computational approach, if appropriate alterations are made to the thermal expansion of the individual elements. The overall transient solution is achieved by consecutive piecewise linear iterations. The total residue caused by creep is obtained by accumulating creep residues for each iteration and then resubmitting the total residues for each element as an equivalent input. A typical creep law is tested for incremental time convergence. The results indicate that the approach is practical, with a valid indication of the extent of creep after approximately 20 hr of incremental time. The general analogy between body forces and inelastic strain gradients is discussed with respect to how an inelastic problem can be worked as an elastic problem.
Hot section components of aircraft gas turbine engines are subjected to severe thermal structural loading conditions, especially during the start up and take off portions of the engine cycle. The most severe and damaging stresses and strains are those induced by the steep thermal gradients induced during the start up transient. These transient stresses and strains are also the most difficult to predict, in part because of the temperature gradients and distributions are not well known or readily predictable, and also because the cyclic elastic viscoplastic behavior of the materials at these extremes of temperature and strain are not well known or readily predictable. A broad spectrum of structures related technology programs is underway to address these deficiencies. One element of the structures program is developing improved time varying thermal mechanical load models for the entire engine mission cycle from start up to shutdown. Another major part of the program is the development of new and improved nonlinear 3-D finite elements and associated structural analysis programs, including the development of temporal elements with time dependent properties to account for creep effects in the materials and components.
Hot-section components of aircraft gas turbine engines are subjected to severe thermal structural loading conditions, especially during the startup and takeoff portions of the engine cycle. The most severe and damaging stresses and strains are those induced by the steep thermal gradients induced during the startup transient. These transient stresses and strains are also the most difficult to predict, in part because the temperature gradients and distributions are not well known or readily predictable and, in part, because the cyclic elastic-viscoplastic behavior of the materials at these extremes of temperature and strain are not well known or readily predictable. A broad spectrum of structures related technology programs is underway to address these deficiencies at the basic as well as the applied level. The three key program elements in the HOST structural analysis program are computations, constitutive modeling, and experiments for each research activity. Also shown are tables summarizing each of the activities.
Gradient-elastic tensor of ions in sodium chloride and sodium bromide crystals determined from effects of static elastic strain on nuclear magnetic resonance
Lee (1969) has proposed a theory based on the decomposition of the total deformation gradient to an elastic and plastic part, and from it has concluded that the additive decomposition of the strain rates holds only approximately. Lubarda and Lee (1981) have declared that Lee's 'exact finite-deformation kinematics shows the almost universal assumption that the total velocity strain or rate of deformation is the sum of elastic and plastic rates to be in error'. Hence questions are raised regarding the validity of essentially all finite deformation elasto-plasticity theories. The present investigation is concerned with these questions. It is shown that the additive decomposition of the strain rates follows from all common finite elasto-plasticity concepts. Lee's theory is examined, and it is shown that this theory also leads to an additive strain rate decomposition, and therefore, his conclusion stems from misinterpretation. It is found that the elastic and the plastic strain rates considered by Lee do not correspond to the same configuration. They are, therefore, not compatible measures.
A comprehensive experimental analysis of deformations of the surface of a metal-matrix specimen is reported. The specimen is a 6-ply 0 + or - 45 sub s boron-aluminum tensile coupon with a central slot. Moire interferometry is used for high-sensitivity whole-field measurements of in-plane displacements. Normal and shear strains are calculated from displacement gradients. Displacement fields are analyzed at various load levels from 15% to 95% of the failure load. Deformations of the boron fibers could be distinguished from those of the matrix. Highly localized plastic slip zones occur tangent to the ends of the slot. Shear strains and concurrent transverse compressive strains in the slip zones reach approximately 10% and 1%, respectively. Upon unloading, elastic recovery in surrounding regions causes a reverse plastic shear strain in the slip zone of about 4%. Longitudinal normal strains on the unslotted ligament peak at the slot boundary at about 1% strain. The strain concentration factor at the end of the slot decreases with load level and the advance of plasticity.
Though butt-welds are among the most preferred joining methods in aerostructures because of their sealing and assembly integrity and general elastic performance; their inelastic mechanics are generally the least understood. This study investigated experimental strain distributions across a thick aluminum U-grooved weld and identified two weld process considerations for improving the multipass weld strength. The extreme thermal expansion and contraction gradient of the fusion heat input across the tab thickness between the grooves produce severe peaking, which induces bending moment under uniaxial loading. The filler strain hardening decreased with increasing filler pass sequence. These combined effects reduce the weld strength, and a depeaking index model was developed to select filler pass thicknesses, pass numbers, and sequences to improve the welding process results over the current normal weld schedule.
The present paper describes a transient translating elastoplastic thermomechanical finite element model to study two-dimensional frictional rolling contact. Frictional two-dimensional contact is simulated by repeatedly translating a nonuniform thermomechanical distribution across the surface of an elastoplastic half space. The half space is represented by a two-dimensional finite element mesh with appropriate boundaries. Calculations are for an elastic-perfectly plastic material and the selected thermophysical properties are assumed to be temperature independent. The paper presents temperature variations, stress and plastic strain distributions and deformations. Residual tensile stresses are observed. The magnitude and depth of these stresses depends on (1) the temperature gradients and (2) the magnitudes of the normal and tangential tractions.
Results are presented of elastic, elastic-plastic, and elastic-plastic-creep analyses of a test-rig component of an actively cooled cowl lip. A cowl lip is part of the leading edge of an engine inlet of proposed hypersonic aircraft and is subject to severe thermal loadings and gradients during flight. Values of stresses calculated by elastic analysis are well above the yield strength of the cowl lip material. Such values are highly unrealistic, and thus elastic stress analyses are inappropriate. The inelastic (elastic-plastic and elastic-plastic-creep) analyses produce more reasonable and acceptable stress and strain distributions in the component. Finally, using the results from these analyses, predictions are made for the cyclic crack initiation life of a cowl lip. A comparison of predicted cyclic lives shows the cyclic life prediction from the elastic-plastic-creep analysis to be the lowest and, hence, most realistic.
Results are presented of elastic, elastic-plastic and elastic-plastic-creep analyses of a test-rig component of an actively cooled cowl lip. A cowl lip is part of the leading edge of an engine inlet of proposed hypersonic aircraft and is subject to severe thermal loadings and gradients during flight. Values of stresses calculated by elastic analysis are well above the yield strength of the cowl lip material. Such values are highly unrealistic, and thus elastic stress analyses are inappropriate. The inelastic (elastic-plastic and elastic-plastic-creep) analyses produce more reasonable and acceptable stress and strain distributions in the component. Finally, using the results from these analyses, predictions are made for the cyclic crack initiation life of a cowl lip. A comparison of predicted cyclic lives shows the cyclic life prediction from the elastic-plastic-creep analysis to be the lowest and, hence, most realistic.
The very high sensitivity of moire interferometry has permitted the present edge effect experiments to be conducted at a low average stress and strain level, assuring linear and elastic behavior in the composite material samples tested. Sensitivity corresponding to 2450 line/mm moire was achieved with a 0.408 micron/fringe. Simultaneous observations of the specimen face and edge displacement fields showed good fringe definition despite the 1-mm thickness of the specimens and the high gradients, and it is noted that the use of a carrier pattern and optical filtering was effective in even these conditions. Edge effects and dramatic displacement gradients were confirmed in angle-ply composite laminates.
A system of plate equations for the thickness-shear and flexural vibrations superposed on large initial deflection due to bending is derived; in the stress-strain relations, the terms associated with the fourth-order elastic stiffness coefficients are retained. An explicit formula for the change in the fundamental cut-off thickness shear frequency is obtained, and the effects of the terms associated with the fourth-order constants appear to be significant for large gradients of the rotation angles.
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.