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The energy release rates associated with a main crack propagating into a surrounding damage zone, and a damage zone translation relative to the main crack, as well as an energy of interaction between the two are analyzed. The displacement and stress fields for the crack-damage interaction problem are reconstructed employing a semi-empirical stress analysis and experimental evaluation of the average craze density in the crazed zone.
The surface stress is a key diagnostic in wall bounded turbulent flows. Large fluctuations in the stress are believed to be associated with intermittent 'bursting' events during which a large proportion of the turbulence production takes place. If this is so, then a detailed investigation of the structure of the surface stress and its spatial relationship to events within the flow could have wide application in drag reduction and other aspects of flow control. The initial phase of this project, therefore, concentrated on the surface stress field. The first objective is to carry out a statistical analysis of the instantaneous surface stress in a simulated turbulent channel flow, including comparison with multipoint experimental data from a zero pressure gradient turbulent boundary layer. The second objective is to apply a simple pattern recognition procedure to educe the characteristic spatial structure of various flow diagnostics. The final objective is to extend the pattern recognition analysis to examine the whole three dimensional structure of the flow.
Experiments were performed on center-notched specimens of unidirectional AS4/3501-6 graphite-epoxy subjected to varied far-field loading conditions. Specimens tested include on-axis and off-axis tensile coupons and Iosipescu shear specimens, allowing the study of normal, shear, and combined far-field loading conditions. From the tests, the direction of initial crack extension and the far-field stresses at crack initiation and fracture are obtained. The normal stress ratio theory is subsequently applied within a macroscopic-level homogeneous anisotropic stress solution to predict the direction of crack extension, critical stresses, and other crack growth behavior for the experiments. Comparison between experimental results and theoretical predictions indicates that application of the normal stress ratio theory within a macroscopic-level stress analysis has significant potential as an approach to modeling composite crack growth.
Dimensional tolerances for high-speed-machined aluminum products continue to tighten due to the demand for automated assembly of complex monolithic parts in aerospace and other industries. Understanding the contribution of inherent residual stress in wrought Al 7050-T7451 plate, common in aircraft manufacture, to distortion of high-aspect-ratio machined parts is critical but remains problematic due to the alloy's low residual stress magnitude over large geometries. Prior investigations into residual stress effects on machined part distortion suffer inadequate characterizations of the wrought material stress field, either because of low fidelity due to “slitting” methods, confounding effects in machined-layer removal methods, or small sample size when using neutron diffraction (ND). In this work, inherent residual stress is measured via ND at 860 locations in a 90.5 mm thick Al 7050-T7451 plate having dimensions 399 mm in the rolling direction and 335 mm in the transverse direction. Unlike prior studies, the ND residual stress is reconstructed using an iterative algorithm to ensure fully compatible, equilibrated 3D field prior to examining its effect on distortion. Further, the findings from simulations and experiments show that inherent residual stress alone could distort a high-aspect-ratio part beyond aerospace industry requirements, that slitting measurements may not sufficiently characterize residual stress for predicted distortion, and that parts machined from different plate thickness locations could exhibit reversed distortion patterns. Thus, research into distortion prediction that considers machining should carefully characterize and reconstruct inherent residual stress so that the coupled machining effects are accurately modeled.
This paper investigates the effect of hotspot (HS) stress endurance of two of the latest designs of monocrystalline modules: a half-cell glass/backsheet (G/B) module and a full-cell glass/glass (G/G) module. These modules have already been pre-stressed in extended thermal cycling with 600 cycles per the IEC 61215 standard to represent field-stressed modules. This study differs from the other conventional studies wherein only fresh modules are subjected to hotspot endurance stress. The G/G module reached a maximum temperature of approximately 200 °C at a cell shading of 25 %, 55 °C higher than the maximum hotspot temperature of 145 °C in the G/B module. A significant burn mark, without glass shattering, was observed in the hotspot-stressed cell of the G/G module due to the current mismatch induced by partial shading. Most of the cells in the G/G module appear to be severely damaged (severe dark areas), as observed in the electroluminescence (EL) image, while the dark regions were rarely present in the G/B module. The EL image also illustrates multiple cell cracks that resist current flow and eventually contribute to the full-cell module degradation. About 8.3 % degradation in maximum power was observed for the G/G module and 1.3 % for the G/B module after the sequential stress tests. The lower degradation in the G/B module can potentially be attributed to its design, which comprises of two parallel strings, each having 72-half-cells and benefits from lower heat dissipation. Furthermore, this indicates that the half-cell design could potentially minimize the hotspot degradation and failures in crystalline-silicon modules.
The phenomenology was studied of the processes of vortex formation and transport in the near wake, at a Reynolds number sufficiently high to insure a fully turbulent wake, but low enough to insure a laminar separation. The apparatus developed for measuring this flow consisted of X-array hot wire probes mounted on the ends of a pair of whirling arms. A computer controlled data acquisition system was slaved to the position of the rotating arm and managed, monitored, edited, and recorded the vast profusion of data which is continuously poured out by the device. Results are presented which show the instantaneous velocity, intermittency, vorticity, and stress fields as a function of phase for the first six diameters of the near wake. The stresses in the near wake emerge as a concatenation of peaks and valleys, some the result of strong induced motions in the outer flow which cause free stream fluid to move rapidly inward toward the center of the wake, others the result of the random motions of the background turbulence.
Crack propagation in a rotating inner raceway of a high-speed roller bearing is analyzed using the boundary integral method. The model consists of an edge plate under plane strain condition upon which varying Hertzian stress fields are superimposed. A multidomain boundary integral equation using quadratic elements was written to determine the stress intensity factors KI and KII at the crack tip for various roller positions. The multidomain formulation allows the two faces of the crack to be modeled in two different subregions, making it possible to analyze crack closure when the roller is positioned on or close to the crack line. KI and KII stress intensity factors along any direction were computed. These calculations permit determination of crack growth direction along which the average KI times the alternating KI is maximum.
The energy release rates associated with the main crack advancing into its surrounding damage zone, and the damage zone translation relative to the main crack, as well as the energy of interaction between the crack and the damage zone are analyzed. The displacement and stress fields for this crack-damage interaction problem are reconstructed by employing a semi-empirical stress analysis which involves experimental evaluation of the average microcrack density in the damage zone.
An effective approach in the finite element analysis of the stress field at the traction free boundary of a solid continuum was studied. Conventional displacement and assumed stress finite elements were used in the determination of stress concentrations around circular and elliptical holes. Specialized hybrid elements were then developed to improve the satisfaction of prescribed traction boundary conditions. Results of the stress analysis indicated that finite elements which exactly satisfy the free stress boundary conditions are the most accurate and efficient in such problems. A general approach for hybrid finite elements which incorporate traction free boundaries of arbitrary geometry was formulated.
This primer is intended to remove the blackbox perception of fracture mechanics computer software by structural engineers. The fundamental concepts of linear elastic fracture mechanics are presented with emphasis on the practical application of fracture mechanics to real problems. Numerous rules of thumb are provided. Recommended texts for additional reading, and a discussion of the significance of fracture mechanics in structural design are given. Griffith's criterion for crack extension, Irwin's elastic stress field near the crack tip, and the influence of small-scale plasticity are discussed. Common stress intensities factor solutions and methods for determining them are included. Fracture toughness and subcritical crack growth are discussed. The application of fracture mechanics to damage tolerance and fracture control is discussed. Several example problems and a practice set of problems are given.
Stress field concentrations produced by cylindrical inclusions in composite materials
Advanced vehicle technology and juncture stress fields peculiar to multicellular pressure vessels
A multi-scale computational model for determining plastic behavior in two-phased CMSX-4 Ni-based superalloys is developed on a finite element analysis (FEA) framework employing crystal plasticity constitutive model that can capture the microstructural scale stress field. The generalized method of cells (GMC) micromechanics model is used for homogenizing the local field quantities. At first, GMC as stand-alone is validated by analyzing a repeating unit cell (RUC) as a two-phased sample with 72.9% volume fraction of gamma'-precipitate in the gamma-matrix phase and comparing the results with those predicted by finite element analysis (FEA) models incorporating the same crystal plasticity constitutive model. The global stress-strain behavior and the local field quantity distributions predicted by GMC demonstrated good agreement with FEA. High computational saving, at the expense of some accuracy in the components of local tensor field quantities, was obtained with GMC. Finally, the capability of the developed multi-scale model linking FEA and GMC to solve real life sized structures is demonstrated by analyzing an engine disc component and determining the microstructural scale details of the field quantities.
Cracks in the skin of aircraft fuselages or other shell structures can be subjected to very complex stress states, resulting in mixed-mode fracture conditions. For example, a crack running along a stringer in a pressurized fuselage will be subject to the usual in-plane tension stresses (Mode-I) along with out-of-plane tearing stresses (Mode-III like). Crack growth and initiation in this case is correlated not only with the tensile or Mode-I stress intensity factor, K(sub I), but depends on a combination of parameters and on the history of crack growth. The stresses at the tip of a crack in a plate or shell are typically described in terms of either the small deflection Kirchhoff plate theory. However, real applications involve large deflections. We show, using the von-Karman theory, that the crack tip stress field derived on the basis of the small deflection theory is still valid for large deflections. We then give examples demonstrating the exact calculation of energy release rates and stress intensity factors for cracked plates loaded to large deflections. The crack tip fields calculated using the plate theories are an approximation to the actual three dimensional fields. Using three dimensional finite element analyses we have explored the relationship between the three dimensional elasticity theory and two dimensional plate theory results. The results show that for out-of-plane shear loading the three dimensional and Kirchhoff theory results coincide at distance greater than h/2 from the crack tip, where h/2 is the plate thickness. Inside this region, the distribution of stresses through the thickness can be very different from the plate theory predictions. We have also explored how the energy release rate varies as a function of crack length to plate thickness using the different theories. This is important in the implementation of fracture prediction methods using finite element analysis. Our experiments show that under certain conditions, during fatigue crack growth, the presence of out-of-plane shear loads induces a great deal of contact and friction on the crack surfaces, dramatically reducing crack growth rate. A series of experiments and a proposed computational approach for accounting for the friction is discussed.
Here we report on an atomic-scale study of trap generation in the initial/intermediate stages of time-dependent dielectric breakdown (TDDB) in high-field stressed (100) Si/SiO2 MOSFETs using two powerful analytical techniques: electrically detected magnetic resonance (EDMR) and near-zero-field magnetoresistance (NZFMR). We find the dominant EDMR-sensitive traps generated throughout the majority of the TDDB process to be silicon dangling bonds at the (100) Si/SiO2 interface (Pb0 and Pb1 centers) for both the spin-dependent recombination (SDR) and trap-assisted tunneling (SDTAT) processes. We find this generation to be linked to both changes in the calculated interface state densities as well as changes in the NZFMR spectra for recombination events at the interface, indicating a redistribution of mobile magnetic nuclei which we conclude could only be due to the redistribution of hydrogen at the interface. Additionally, we observe the generation of traps known as E’ centers in EDMR measurements at lower experimental temperatures via SDR measurements at the interface. Our work strongly suggests the involvement of a rate-limiting step in the tunneling process between the silicon dangling bonds generated at the interface and the ones generated throughout the oxide.
Here, in this work, an elasto-viscoplastic fast-Fourier-transform (EVP-FFT) model with a dislocation-density (DD) based hardening law is employed to study the growth of a {10$\bar{1}$2} tensile twin that is blocked by basal-precipitates in precipitate-hardened AZ91 magnesium alloy. It is frequently reported that twin growth is hindered in precipitate-hardened Mg alloys; however, thick twin domains are often observed experimentally in these material systems. Detailed numerical investigation of deformation twinning starting from an early propagation stage, before twin growth, reveals that the stress fields that result from two sequentially propagated twins co-impinging on a precipitate relaxes the twin back stress locally and promotes twin growth at the twin-precipitate junction. Based on these findings, a two-step growth mechanism is proposed for twins arrested by precipitates. In the first step, the interaction of a twin tip with a precipitate develops a stress concentration on the other side of the precipitate, prompting the formation of a second twin. Subsequently, the back stresses associated with the first twin are relaxed by the formation of the second twin, allowing the first twin to grow at the twin-precipitate junction and eventually engulf the precipitate. This mechanism suggests that twin growth can be achieved locally with minimal additional external forces, explaining how relatively large twin domains can develop even in the presence of arrays of precipitates.
The present paper provides a qualitative discussion of the evolution of contact traction fields beneath rigid shallow foundations resting on granular materials. A phenomenological similarity is recognized in the measured contact traction fields of rigid footings and at the bases of sandpiles. This observation leads to the hypothesis that the stress distributions are brought about by the same physical phenomena, namely the development of arching effects through force chains and mobilized intergranular friction. A set of semi-empirical equations are suggested for the normal and tangential components of this contact traction based on past experimental measurements and phenomenological assumptions of frictional behaviors at the foundation system scale. These equations are then applied to the prescribed boundary conditions for the analysis of the settlement, resistance, and stress fields in supporting granular materials beneath the footing. A parametric sensitivity study is performed on the proposed modelling method, highlighting solutions to the boundary-value problems in an isotropic, homogeneous elastic half-space.
Numerical models of the strike-slip earthquake cycle, assuming a viscoelastic asthenosphere coupling model, are examined. The time-dependent simulations incorporate a stress-driven fault, which leads to tectonic stress fields and earthquake recurrence histories that are mutually consistent. Single-fault simulations with constant far-field plate motion lead to a nearly periodic earthquake cycle and a distinctive spatial distribution of crustal shear stress. The predicted stress distribution includes a local minimum in stress at depths less than typical seismogenic depths. The width of this stress 'trough' depends on the magnitude of crustal stress relative to asthenospheric drag stresses. The models further predict a local near-fault stress maximum at greater depths, sustained by the cyclic transfer of strain from the elastic crust to the ductile asthenosphere. Models incorporating both low-stress and high-stress fault strength assumptions are examined, under Newtonian and non-Newtonian rheology assumptions. Model results suggest a preference for low-stress (a shear stress level of about 10 MPa) fault models, in agreement with previous estimates based on heat flow measurements and other stress indicators.