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At least 91 records · Page 5

On the existence and stability conditions for mixed-hybrid finite element solutions based on Reissner's variational principle

The extensions of Reissner's two-field (stress and displacement) principle to the cases wherein the displacement field is discontinuous and/or the stress field results in unreciprocated tractions, at a finite number of surfaces ('interelement boundaries') in a domain (as, for instance, when the domain is discretized into finite elements), is considered. The conditions for the existence, uniqueness, and stability of mixed-hybrid finite element solutions based on such discontinuous fields, are summarized. The reduction of these global conditions to local ('element') level, and the attendant conditions on the ranks of element matrices, are discussed. Two examples of stable, invariant, least-order elements - a four-node square planar element and an eight-node cubic element - are discussed in detail.

Karlovitz, L. A.↗

Development of a Fatigue Crack Growth Coupon for Highly Plastic Stress Conditions

This paper presents an analytical approach used to develop a novel fatigue crack growth coupon for a highly plastic 3-D stress field condition. The flight hardware investigated in this paper is a large separation bolt that fractures using pyrotechnics at the appointed time during the flight sequence. The separation bolt has a deep notch that produces a severe stress concentration and a large plastic zone when highly loaded. For this geometry, linear-elastic fracture mechanics (LEFM) techniques are not valid due to the large nonlinear stress field. Unfortunately, industry codes that are generally available for fracture mechanics analysis and fatigue crack growth (e.g. NASGRO (11) are limited to LEFM and are available for only a limited number of geometries. The results of LEFM based codes are questionable when used on geometries with significant plasticity. Therefore elastic-plastic fracture mechanics (EPFM) techniques using the finite element method (FEM) were used to analyze the bolt and test coupons. scale flight hardware is very costly in t e r n of assets, laboratory resources, and schedule. Therefore to alleviate some of these problems, a series of novel test coupons were developed to simulate the elastic-plastic stress field present in the bolt.

Allen, Phillip A.↗

Finite element modeling of stress in the Nazca plate - Driving forces and plate boundary earthquakes

The state of stress within the Nazca plate due to plate driving forces and large plate boundary earthquakes has been analyzed by applying a finite element method using the wave front solution technique to models of the intraplate stress field in a single plate using a refined grid. Although only static elastic models have been explicitly calculated, certain limiting cases of an elastic plate over a viscous asthenosphere were also treated. A state of nearly east-west compression inferred from the source mechanism of thrust earthquakes in the interior of the plate requires ridge pushing forces. The net pulling force on the oceanic plate by the subducted slab has a maximum value comparable to pushing forces. The estimated horizontal deviatoric stress in intraplate regions, based on potential forces associated with the ridge, is on the order of a few hundred bars. The intraplate stress field in the region of the 1960 earthquake may change by a few tens of bars at most once the asthenosphere has relaxed, with changes on the order of one bar occurring at greater distances into the plate. The changes in the intraplate stress field are probably not noticeable unless the lithosphere is near failure.

Richardson, R. M.↗

Structural Analysis of Helios Filament-Wound Tanks Subjected to Internal Pressure and Cooling

A finite-element stress analysis is performed on Helios filament-wound hydrogen tanks to examine the stress field and effect of end dome geometry on the stress field. Each tank is composed of a central circular cylindrical section with either geodesic or hemispherical end domes, which have metallic polar bosses. The tanks are subjected to combined and separate internal pressure and temperature loading conditions, and the stress contributions of each loading component are examined. The tank-wall-polar-boss interfacial meridional tensile stress in the hemispherical dome is found to be approximately 27 percent lower than that in the geodesic dome. The effects of both material anisotropy and the aluminum lining on the intensities of tensile meridional stress at the tank-wall-polar-boss bonding interface are examined.

Ko, William L↗

Global Failure Modes in Composite Structures

Composite materials provide well-known advantages for space and aeronautical applications in terms of strength and rigidity to weight ratios and other mechanical properties. As a consequence, their use has experienced a constant increase in the past decades and it is anticipated that this trend will be maintained in the near future. At the same time, being these materials relatively new compared to metals, and having failure characteristics completely different from them, their damage growth and their failure mechanisms are not as well understood in a predictive sense. For example, while in metals fracture produces "clean" cracks with their well defined analytically stress fields at the crack tip, composite fracture is a more complex phenomenon. Instead of a crack, we confront a "damage zone" that may include fiber breakage, fiber microbuckling, fiber pullout, matrix cracking, delamination, debonding or any combination of all these different mechanisms. These phenomena are prevalent in any failure process through an aircraft structure, whether one addresses a global failure such as the ripping of a fuselage or wing section, or whether one is concerned with the failure initiation near a thickness change at stringers or other reinforcement. Thus the topic that has been under consideration has wide application in any real structure and is considered an essential contribution to the predictive failure analysis capability for aircraft containing composite components. The heterogeneity and the anisotropy of composites are not only advantageous but essential characteristics, yet these same features provide complex stress fields, especially in the presence of geometrical discontinuities such as notches, holes or cutouts or structural elements such as stiffeners, stringers, etc. To properly address the interaction between a damage/crack front and a hole with a stringer it is imperative that the stress and deformation fields of the former be (sufficiently well) characterized. The question of "scaling" is an essential concern in any structural materials investigation. For example, experiments in the past have shown that the "strength" of a composite depends on hole size. As a consequence the validity of traditional fracture mechanics concepts applied to composite materials failure must be questioned. The size of the fibers, the dimensions of the laminae, etc. together with the fact that, because of the layered anisotropy, the stress field is no longer two-dimensional, prevent the otherwise obviously confident use of "similarity concepts". Therefore, the question needs to be raised of whether in composites "size matters or not", i.e., whether the results obtained in a laboratory using small coupons are truly representative of the situation involving a full scale component.

Knauss, W. G.↗

Fatigue response of perforated titanium for application in laminar flow control

The room temperature tensile and fatigue response of non-perforated and perforated titanium for laminar flow control application was investigated both experimentally and analytically. Results showed that multiple perforations did not affect the tensile response, but did reduce the fatigue life. A two dimensional finite element stress analysis was used to determine that the stress fields from adjacent perforations did not influence one another. The stress fields around the holes did not overlap one another, allowing the materials to be modeled as a plate with a center hole. Fatigue life was predicted using an equivalent MW flow size approach to relate the experimental results to microstructural features of the titanium. Predictions using flaw sizes ranging from 1 to 15 microns correlated within a factor of 2 with the experimental results by using a flow stress of 260 MPa. By using two different flow stresses in the crack closure model and correcting for plasticity, the experimental results were bounded by the predictions for high applied stresses. Further analysis of the complex geometry of the perforations and the local material chemistry is needed to further understand the fatigue behavior of the perforated titanium.

Johnson, W. Steven↗

An evaluation of the Iosipescu specimen for composite materials shear property measurement

A detailed evaluation of the suitability of the Iosipescu specimen tested in the modified Wyoming fixture is presented. A linear finite element model of the specimen is used to assess the uniformity of the shear stress field in the vicinity of the notch, and demonstrate the effect of the nonuniform stress field upon strain gage measurements used for the determination of composite shear moduli. Based upon test results from graphite-epoxy laminates, the proximity of the load introduction point to the test section and the material orthotropy greatly influence the individual gage readings, however, shear modulus determination is not significantly affected by the lack of pure shear. Correction factors are needed to allow for the nonuniformity of the strain field and the use of the average shear stress in the shear modulus evaluation. The correction factors are determined for the region occupied by the strain gage rosette. A comparison of the strain gage readings from one surface of a specimen with corresponding data from moire interferometry on the opposite face documented an extreme sensitivity of some fiber orientations to eccentric loading which induced twisting and spurious shear stress-strain curves. The discovery of specimen twisting explains the apparently inconsistent shear property data found in the literature. Recommendations for improving the reliability and accuracy of the shear modulus values are made, and the implications for shear strength measurement discussed.

Morton, J.↗

Ethiopian Tertiary dike swarms

Mapping of the Ethiopian rift and Afar margins revealed the existence of Tertiary dike swarms. The structural relations of these swarms and the fed lava pile to monoclinal warping of the margins partly reflect a style of continental margin tectonics found in other parts of the world. In Ethiopia, however, conjugate dike trends appear to be unusually strongly developed. Relation of dikes to subsequent margin faulting is ambiguous, and there are instances where the two phenomena are spatially separate and of differing trends. There is no evidence for lateral migration with time of dike injection toward the rift zone. No separate impingement of Red Sea, Gulf of Aden, and African rift system stress fields on the Ethiopian region can be demonstrated from the Tertiary dike swarms. Rather, a single, regional paleostress field existed, suggestive of a focus beneath the central Ethiopian plateau. This stress field was dominated by tension: there is no cogent evidence for shearing along the rift margins. A gentle compression along the rift floor is indicated. A peculiar sympathy of dike hade directions at given localities is evident.

Mohr, P. A.↗

Separating the Influence of Environment from Stress Relaxation Effects on Dwell Fatigue Crack Growth in a Nickel-Base Disk Alloy

Both environmental embrittlement and crack tip visco-plastic stress relaxation play a significant role in determining the dwell fatigue crack growth (DFCG) resistance of nickel-based disk superalloys. In the current study performed on the Low Solvus High Refractory (LSHR) disk alloy, the influence of these two mechanisms were separated so that the effects of each could be quantified and modeled. Seven different microstructural variations of LSHR were produced by controlling the cooling rate and the subsequent aging and thermal exposure heat treatments. Through cyclic fatigue crack growth testing performed both in air and vacuum, it was established that four out of the seven LSHR heat treatments evaluated, possessed similar intrinsic environmental resistance to cyclic crack growth. For these four heat treatments, it was further shown that the large differences in dwell crack growth behavior which still persisted, were related to their measured stress relaxation behavior. The apparent differences in their dwell crack growth resistance were attributed to the inability of the standard linear elastic fracture mechanics (LEFM) stress intensity parameter to account for visco-plastic behavior. Crack tip stress relaxation controls the magnitude of the remaining local tensile stresses which are directly related to the measured dwell crack growth rates. It was hypothesized that the environmentally weakened grain boundary crack tip regions fail during the dwells when their strength is exceeded by the remaining local crack tip tensile stresses. It was shown that the classical creep crack growth mechanisms such as grain boundary sliding did not contribute to crack growth, but the local visco-plastic behavior still plays a very significant role by determining the crack tip tensile stress field which controls the dwell crack growth behavior. To account for the influence of the visco-plastic behavior on the crack tip stress field, an empirical modification to the LEFM stress intensity parameter, Kmax, was developed by incorporating into the formulation the remaining stress level concept as measured by simple stress relaxation tests. The newly proposed parameter, Ksrf, did an excellent job in correlating the dwell crack growth rates for the four heat treatments which were shown to have similar intrinsic environmental cyclic fatigue crack growth resistance.

Dwell crack growth↗

Separating the Influence of Environment from Stress Relaxation Effects on Dwell Fatigue Crack Growth

Seven different microstructural variations of LSHR were produced by controlling the cooling rate and the subsequent aging and thermal exposure heat treatments. Through cyclic fatigue crack growth testing performed both in air and vacuum, it was established that four out of the seven LSHR heat treatments evaluated, possessed similar intrinsic environmental resistance to cyclic crack growth. For these four heat treatments, it was further shown that the large differences in dwell crack growth behavior which still persisted, were related to their measured stress relaxation behavior. The apparent differences in their dwell crack growth resistance were attributed to the inability of the standard linear elastic fracture mechanics (LEFM) stress intensity parameter to account for visco-plastic behavior. Crack tip stress relaxation controls the magnitude of the remaining local tensile stresses which are directly related to the measured dwell crack growth rates. It was hypothesized that the environmentally weakened grain boundary crack tip regions fail during the dwells when their strength is exceeded by the remaining local crack tip tensile stresses. It was shown that the classical creep crack growth mechanisms such as grain boundary sliding did not contribute to crack growth, but the local visco-plastic behavior still plays a very significant role by determining the crack tip tensile stress field which controls the dwell crack growth behavior. To account for the influence of the visco-plastic behavior on the crack tip stress field, an empirical modification to the LEFM stress intensity parameter, Kmax, was developed by incorporating into the formulation the remaining stress level concept as measured by simple stress relaxation tests. The newly proposed parameter, Ksrf, did an excellent job in correlating the dwell crack growth rates for the four heat treatments which were shown to have similar intrinsic environmental cyclic fatigue crack growth resistance.

environmental damage↗

The mode 3 crack problem in bonded materials with a nonhomogeneous interfacial zone

The mode 3 crack problem for two bonded homogeneous half planes was considered. The interfacial zone was modelled by a nonhomogeneous strip in such a way that the shear modulus is a continuous function throughout the composite medium and has discontinuous derivatives along the boundaries of the interfacial zone. The problem was formulated for cracks perpendicular to the nominal interface and was solved for various crack locations in and around the interfacial region. The asymptotic stress field near the tip of a crack terminating at an interface was examined and it was shown that, unlike the corresponding stress field in piecewise homogeneous materials, in this case the stresses have the standard square root singularity and their angular variation was identical to that of a crack in a homogeneous medium. With application to the subcritical crack growth process in mind, the results given include mostly the stress intensity factors for some typical crack geometries and various material combinations.

Erdogan, Fazil↗

The mode III crack problem in bonded materials with a nonhomogeneous interfacial zone

The mode 3 crack problem for two bonded homogeneous half planes was considered. The interfacial zone was modelled by a nonhomogeneous strip in such a way that the shear modulus is a continuous function throughout the composite medium and has discontinuous derivatives along the boundaries of the interfacial zone. The problem was formulated for cracks perpendicular to the nominal interface and was solved for various crack locations in and around the interfacial region. The asymptotic stress field near the tip of a crack terminating at an interface was examined and it was shown that, unlike the corresponding stress field in piecewise homogeneous materials, in this case the stresses have the standard square root singularity and their angular variation was identical to that of a crack in a homogeneous medium. With application to the subcritical crack growth process in mind, the results given include mostly the stress intensity factors for some typical crack geometries and various material combinations.

Erdogan, F.↗

Thermoelastic stress - How important as a cause of earthquakes in young oceanic lithosphere?

Thermoelastic or thermal stress is a potentially important contributor to the state of stress in the oceanic lithosphere. The present paper provides several simple models for the state of thermoelastic stress in a young oceanic lithosphere, taking into account a comparison of the predictions of these models with the characteristics of near-ridge earthquakes. Attention is given to the characteristics of near-ridge earthquakes, sources of stress in an oceanic lithosphere, previous models of thermal stress, the calculation of thermal stress, and thermal stress models. A test is conducted of the hypothesis that thermoelastic stress is a significant component of the stress field in a young oceanic lithosphere. The considered models support the hypothesis that thermoelastic stress is a significant component of the stress field in a young oceanic lithosphere.

Bratt, S. R.↗

Ultrasonic measurement of stress in 2219-T87 aluminum plate

The basic relationship of ultrasonic signal velocity to directional subsurface stress is reviewed. Inappropriateness of dependency on a single correlative value of constant for a three dimensional stress field in metallic materials is discussed. Implementation of conventional ultrasonic nondestructive testing capabilities integrated to provide a composite technique for the measurement of orthogonal stress components is described, and the procedures for performing the preparatory calibration and subsequent stress field measurements are presented. In conclusion, the prime effect of stress on ultrasonic signal velocity occurs only in the direction of material excitation or particle motion.

Clotfelter, W. N.↗

Wavy and Cycloidal Lineament Formation on Europa from Combined Diurnal and Nonsynchronous Stresses

In a companion abstract, we show that fractures propagated into combined diurnal and nonsynchronous rotation (NSR) stress fields can be cycloidal, "wavy," or arcuate in planform as the relative proportion of NSR stress in increased. These transitions occur as NSR stress accumulates over approx. 0 to 10 deg of ice shell rotation, for average fracture propagation speeds of approx. 1 to 3 m/s. Here we consider the NSR speed parameter space for these morphological transitions, and explore the effects on cycloids of adding NSR to diurnal stress. Fitting individual Europan lineaments can constrain the combined NSR plus diurnal stress field at the time of formation.

Gleeson, Damhnait↗

Orientation, relative age, and extent of the Tharsis Plateau ridge system

The orientations of the Tharsis Plateau ridge system on Mars and the symmetry of the inferred compressive stress field, the relative ages of the compressional events that generated the ridges, and the extent of Tharsis-related compressional deformation are investigated. Models for the origin of stresses in the Tharsis region are studied in relation to the formation of the ridges. The data indicate either that the Tharsis ridge system did not form in response to a single regional compressional event with a single stress center or that the majority of the ridge system did form in a single event but with locally controlled deflections in the generally radially oriented stress field. Superposition relationships and relative ages suggest that the compressional stresses that produced the ridges occurred after the emplacement of the ridged plains volcanic units but did not extend beyond the time of emplacement of the Syria Planum Formation units or the basal units of the Tharsis Montes Formation.

Watters, T. R.↗

Interlaminar stress analysis of dropped-ply laminated plates and shells by a mixed method

A mixed method of approximation based on Reissner's variational principle is developed for the linear analysis of interlaminar stresses in laminated composites, with special interest in laminates that contain terminated internal plies (dropped-ply laminates). Two models are derived, one for problems of generalized plane deformation and the other for the axisymmetric response of shells of revolution. A layerwise approach is taken in which the stress field is assumed with an explicit dependence on the thickness coordinate in each layer. The dependence of the stress field on the thickness coordinate is determined such that the three-dimensional equilibrium equations are satisfied by the approximation. The solution domain is reduced to one dimension by integration through the thickness. Continuity of tractions and displacements between layers is imposed. The governing two-point boundary value problem is composed of a system of both differential and algebraic equations (DAE's) and their associated boundary conditions. Careful evaluation of the system of DAE's was required to arrive at a form that allowed application of a one-step finite difference approximation. A two-stage Gauss implicit Runge-Kutta finite difference scheme was used for the solution because of its relatively high degree of accuracy. Patch tests of the two models revealed problems with solution accuracy for the axisymmetric model of a cylindrical shell loaded by internal pressure. Parametric studies of dropped-ply laminate characteristics and their influence on the interlaminar stresses were performed using the generalized plane deformation model. Eccentricity of the middle surface of the laminate through the ply drop-off was found to have a minimal effect on the interlaminar stresses under longitudinal compression, transverse tension, and in-plane shear. A second study found the stiffness change across the ply termination to have a much greater influence on the interlaminar stresses.

Harrison, Peter N.↗

Molecular-dynamics Simulation-based Cohesive Zone Representation of Intergranular Fracture Processes in Aluminum

A traction-displacement relationship that may be embedded into a cohesive zone model for microscale problems of intergranular fracture is extracted from atomistic molecular-dynamics simulations. A molecular-dynamics model for crack propagation under steady-state conditions is developed to analyze intergranular fracture along a flat 99 [1 1 0] symmetric tilt grain boundary in aluminum. Under hydrostatic tensile load, the simulation reveals asymmetric crack propagation in the two opposite directions along the grain boundary. In one direction, the crack propagates in a brittle manner by cleavage with very little or no dislocation emission, and in the other direction, the propagation is ductile through the mechanism of deformation twinning. This behavior is consistent with the Rice criterion for cleavage vs. dislocation blunting transition at the crack tip. The preference for twinning to dislocation slip is in agreement with the predictions of the Tadmor and Hai criterion. A comparison with finite element calculations shows that while the stress field around the brittle crack tip follows the expected elastic solution for the given boundary conditions of the model, the stress field around the twinning crack tip has a strong plastic contribution. Through the definition of a Cohesive-Zone-Volume-Element an atomistic analog to a continuum cohesive zone model element - the results from the molecular-dynamics simulation are recast to obtain an average continuum traction-displacement relationship to represent cohesive zone interaction along a characteristic length of the grain boundary interface for the cases of ductile and brittle decohesion. Keywords: Crack-tip plasticity; Cohesive zone model; Grain boundary decohesion; Intergranular fracture; Molecular-dynamics simulation

Yamakov, Vesselin I.↗