Plate Of Finite Thickness Research Articles

Stress intensity analyses on tension of a finite thickness plate with two coplanar semi-elliptical surface cracks

This paper analyzes the interactions of two coplanar semi-elliptical surface cracks located, respectively, at the front and back surfaces in a finite thickness plate under uniform tension. Few numerical solutions appear to be available in the literature so far for this kind of interaction. The analyzed ratios of crack depth to crack length ( b 1/ a 2, b 2/ a 2) are 0.25, 0.5 and 1.0; the minimum relative distances between two cracks ( s 2/ b min) range from 0.5 to 2.0. In total, 18 crack configurations are analyzed. The mode I stress intensity factors along the crack front and the interacting coefficient of two cracks are presented. The numerical analyses are carried out by the hybrid boundary element method.

Stress intensity factors and weight functions for a corner crack in a finite thickness plate

Weight functions for the two surface points of a quarter-elliptical corner crack in a finite thickness plate of infinite width are derived from a general weight function and two reference stress intensity factors. The weight functions have been validated for several linear and non-linear crack face stress fields against finite element data. The weight functions appear to be particularly suitable for fatigue and fracture analysis of quarter-elliptical cracks in complex stress fields.

Crack branching in float glass subjected to biaxial loading

Failure of float glass plates in biaxial loading, occurs by well defined crack branching. As part of a study of the effect of handling damage on the strength of annealed glass, extensive observations have been made of crack branching in 4 mm thickness plates with strengths between 40 and 270 MPa, and more limited observations in plates of other thicknesses. Testing was carried out on discs loaded by hydraulic pressure against a circular anvil. For the 4 mm thick 280 mm diameter glass samples a 254 mm diameter anvil was used. Crack length at branching 2c b is related to the applied fracture stress σ b: σ b − σ 0 = A b/✓c b, where the branching constant, A b, is close to published mirror constants for uniaxial loading. The intercept σ 0 is larger than the residual surface stress in the sample, of which it is often considered to be a measure. The results have been analysed using the stress intensity factors for circular and elliptical cracks in a finite thickness plate and found to give good agreement with experiment for the variation of branch length with failure stress.

Flow around the afterbody of a plate in a longitudinal gas stream with transverse injection from the lateral surface

The flow around the afterbody of a plate of finite thickness in a supersonic gas stream is investigated on the basis of a numerical solution of the time-dependent Navier-Stokes equations for a compressible viscous heat-conducting gas. The change in the flow pattern with the onset of transverse slot injection from the body surface in the vicinity of the base section is studied. For constant supersonic injection, both steady and unsteady flow regimes could be obtained depending on the values of certain relevant parameters.

A finite element solution for elliptical cracks using the ICCI method

In one of our recent publications, a formula for the computation of the strain energy release rate from 3-D singularity finite elements was derived based on the Irwin's Crack Closure Integral (ICCI) method. In this paper, the stress intensity factors of embedded elliptical and semi-elliptical surface cracks in a finite thickness plate subjected to tension are calculated using this formula. Comparisons between the numerical results obtained using the formula and those from the literature showed that the proposed technique yields accurate stress intensity factors.

Experimental measurements of STW properties on quartzplates of finite thickness

Surface transverse waves (STW) propagating on quartz plates of finite thickness have been studied theoretically and experimentally. Multiple frequency stopbands are predicted and measured for plate thicknesses close to a few acoustic wavelengths. Temperature sensitivities are measured. Three temperature-compensated modes are found on AT-cut plates.

Crack front curvature effect on stress intensity factor of through and part-through thickness cracks

The character of the local stresses and displacements are determined for a through crack with finite radius of curvature in a finite thickness plate. Numerical results obtained from the boundary element method show that the solutions are sufficiently accurate for ϱ/ a ≤ 0.03 and 0.03 ≤ ϱ/ a ≤ 0.1, where ϱ and a represent, respectively, the crack front radius of curvature and crack dimension such that a is the width of a through thickness crack and the depth of a part-through crack. For ϱ/ a ≤ 0.1, the asymptotic singular stress field dominates such that the Mode I stress intensity factor K 1 can be evaluated. As the crack border radius of curvature is increased for ϱ/ a ≥ 0.1, the non-singular terms become significant such that K I would no longer dominate. Other failure criteria would have to be invoked to address fracture initiation.

Interactions of coplanar surface semi-elliptical cracks and embedded elliptical cracks in finite thickness plates under uniform tension

This paper analyzes the interactions of coplanar surface semi-elliptical cracks and embedded elliptical cracks in a finite thickness plate under uniform tension, for which no numerical solutions appear to be available in the literature. The ratios of crack depth to crack length ( b 1 a 1 and b 2 a 2 ) are 0·25 and 1·0; the relative distances between two cracks ( s 1 b min and s 2 b min ) range from 0·5 to 2·0. Two kinds of interactions, interaction 1 for which neither the long principal axes nor the short principal axes of two cracks are collinear and interaction 2 for which the short principal axes of two cracks are collinear within a total of 48 crack configurations, are studied. The mode I stress intensity factors along the crack front and the interacting coefficient of two cracks are presented. The numerical results show that interaction 2 has a stronger interacting effect from interaction 1. The numerical analyses are carried out by the hybrid boundary elements method.

Interactions of two coplanar elliptical cracks embedded in finite thickness plates under uniform tension

This paper includes the analysis of the interactions of two coplanar elliptical cracks, with equal or different crack sizes, embedded in finite thickness plates under uniform tension. The ratios of crack depth to crack length ( b 1 a 1 , and b 2 a 2 ) are 0.25 and 1.0; the relative distances between two cracks ( s 1 b min and s 2 b min ) range from 0.5 to 2.0. Two kinds of interactions, interactions 1 and 2, with a total of 42 crack configurations, are studied and the stress intensity factors along the crack front are presented. The numerical results show that interaction 2 has a stronger interaction than interaction 1. The numerical analyses are carried out by the hybrid boundary element method.

Stress intensity factors for semi-elliptical surface cracks in plates and cylindrical pressure vessels using the hybrid boundary element method

At first, a hybrid boundary element method used for three-dimensional linear elastic fracture analysis is established on the basis of the first and the second kind of boundary integral equations. Then the concerned basic theories and numerical approaches including the discretization of boundary integral equations, the divisions of different boundary elements, and the procedures for the calculations of singular and hypersingular integrals are presented in detail. Finally, the stress intensity factors of surface cracks in finite thickness plates and cylindrical pressure vessels are computed by the proposed method. The numerical results show that the hybrid boundary element method has very high accuracy for the analysis of surface crack.

Local weight functions for semi-elliptical surface cracks in finite thickness plates

Weight functions for any local point, 0 < Φ < π/2 along a semi-elliptical surface crack in finite thickness plates were derived from an assumed approximate general weight function and two reference stress intensity factors. The resulting weight functions were verified using available finite element results for two nonlinear stress fields and good agreement was achieved. When used together with weight functions for Φ = 0 and Φ = π/2 the weight functions are suitable for the calculation of stress intensity factors anywhere along the crack front for semi-elliptical surface cracks in complex stress fields with aspect ratios in the range 0 ≤ a c ≤ 1 and relative depths 0 ≤ a t ≤ 0.8 .

Geoid data and thermal structure of the oceanic lithosphere

A long‐standing question is whether old oceanic lithosphere continues cooling as the boundary layer of a halfspace or approaches thermal equilibrium, as modeled by a finite thickness plate. Although the latter is the most direct inference from seafloor depths and heat flow, other explanations have been proposed. We investigate this issue using published results for the derivative of the oceanic geoid with age estimated from geoid offsets across fracture zones. Such data have not been used extensively in analyses of the thermal evolution of the lithosphere, primarily because they are inconsistent with two commonly used thermal models: a halfspace or a 125‐km‐thick plate. Recent studies, however, find that depth and heat flow data are better fit by a thinner (95 km) plate model. We thus compile published geoid slope results, and find that these data, though scattered, can discriminate between the models. Geoid slope changes with age, rather than being constant as predicted for a cooling halfspace. This variation is greater than predicted for a thick plate and is better fit by a thin plate. Geoid data should thus be useful for improving thermal models of the lithosphere.

Marine geodynamics: Depth‐age revisited

More than 20 years have passed since the subsidence of the seafloor away from midocean ridges was explained by the cooling of the lithosphere (Figure 1), a thermal boundary layer at the Earth's surface [Turcotte and Oxburgh, 1967], Although the general concept has proven quite sound and found much practical application, the details of the model have never been completely agreed upon. For example, if no process limits the growth of the thermal boundary layer, the seafloor should continue to deepen as the square root of lithospheric age. In contrast, the observations indicate that little deepening occurs for lithosphere aged greater than about 100 Ma (Ma = million years before present). Early on this fact was explained by supposing that there was a limit to the depth of cooling of the boundary layer, such that the lithosphere cools as a plate of finite thickness rather than as a semi‐infinite half space [McKenzie, 1967]. According to the plate model, the depth of old lithosphere approaches a maximum as the geothermal gradient in the plate reaches thermal equilibrium. However, this theoretical model merely provided a better fit to the observations without addressing the fundamental question of what process might limit the growth of the Earth's uppermost thermal boundary layer.

Stress intensity factors for low aspect ratio semi-elliptical surface cracks in finite-thickness plates subjected to nonuniform stresses

Three-dimensional finite element analyses have been conducted to calculate the stress intensity factors for low aspect ratio semi-elliptic cracks. The stress intensity factors are presented for the deepest and surface points on semi-elliptic cracks with low aspect ratios of 0.05 and 0.1, and a/ t values of 0.2, 0.4, 0.6 and 0.8. Uniform, linear, parabolic or cubic stress distributions were applied to the crack face. The results for uniform and linear stress distributions were combined with corresponding results for higher aspect ratio surface cracks and edge cracks to derive the weight function over the entire range of 0 ⩽ a/ c ⩽ 1 and 0 ⩽ a/ t ⩽ 0.8. The weight function is then verified against finite element data for the parabolic or cubic stress distributions. Differences were less than 3% for the surface point and 5% for the deepest point.

Long-rod penetration into targets of finite thickness at normal impact

In this paper, a theory for one-dimensional penetration of long-rods into targets of finite thickness (plates) is developed. The target is defined as a “finite” mass that resides within the bulk of the target so that an equation of motion for the target mass can be constructed. This, together with an equation of motion for the penetrator and erosion equations for the two masses, provides a penetration solution for the finite-thickness target problem. The axial extent of the target mass is simply the thickness of the plate. Results provide expected penetration rates into plate targets, as well as unpenetrated target thickness (plug or spall) and residual penetator length, mass, and velocity. Good agreement was found between the theory, hydrocode results and experimental data. Also, the formulation becomes hydrodynamic penetration in appropriate limits and therefore encompasses jet penetration of these targets as well.

NUMERICAL PREDICTION OF FATIGUE CRACK GROWTH OF A SURFACE DEFECT

AbstractFatigue crack growth is modelled by an improved step‐by‐step finite element technique for a shallow and long surface crack in a finite thickness plate under different combinations of tension and bending loads. The predicted crack shape development is presented for growth through the plate thickness and the shape compared with the widely assumed semi‐elliptical profile. The predictions of the present simulation technique for the aspect ratio and the number of crack growth cycles are compared with those obtained both by Newman and Raju's method, and experimental results for aspect ratio changes taken from the literature.

Mantle convection models of continental collision and breakup incorporating finite thickness plates

A two-dimensional numerical model has been developed to study mantle convection during continental collision and breakup. The model incorporates rigidly moving continental and oceanic plates with distinct thermal and mechanical properties, and finite thickness. We systematically investigate the influences of continental width, diffusivity, thickness and internal heating on continental collision and breakup. In addition, we consider the influence of different degrees of internal heating in the mantle. For each case considered we model a pair of identical continents being carried towards a site of plate convergence by underlying counter-rotating mantle convection cells. The continents collide at the mid-plane of the model to form a motionless, rigid, conducting supercontinent whereas oceanic plate material continues to recycle through the mantle. We find that changes in the mechanical boundary conditions at the upper surface are important factors in initiating flow reversals below the supercontinent. More generally, our findings, based on 144 models, are that the following factors favour the initiation of flow reversals below the supercontinent: wider continents, lower thermal diffusivity of continental plates, thicker plates and continental crustal heating. Furthermore, lower percentages of internal heating in the mantle are necessary to sustain and promote the subcontinental flow reversals in our models.

Analysis of embedded elliptical cracks in cylindrical pressure vessels

This paper presents a comprehensive range of results of Mode I stress intensity factors for the embedded elliptical cracks in cylindrical pressure vessels. The hybrid boundary element method developed by the author is used to calculate the stress intensity factors. For practical uses an approximate method is proposed which is used to estimate the stress intensity factors of embedded elliptical cracks in cylindrical pressure vessels from the results of embedded cracks in finite thickness plates.

EFFECT OF THICK HORIZONTAL PARTIAL PARTITION ATTACHED TO ONE OF THE ACTIVE WALLS OF A DIFFERENTIALLY HEATED SQUARE CAVITY

The effect of a partial horizontal partition plate of finite thickness, attached to the heated vertical wall of a differentially heated square cavity, has been studied numerically using the finite element method. The partition thickness is varied from 0.5% of the height of the cavity to 10%. The partition is considered to be located at the middle of the hot wall of a width equivalent to 20% of the cavity width. It is observed that as the partition thickness is reduced, heat transfer across the cavity decreases at first, until a critical thickness of the partition plate is reached. Beyond this value, heat transfer increases as the thickness of the partition is further reduced. Streamline maps are found to be notably sensitive to the partition thickness. The effect of conductivity of the partition material on heat transfer is also studied. Except for material with poor thermal properties, conductivity of the partition is observed to have a negligible effect on heat transfer.

Surface action of a heat pulse in a tangential flow

The three-dimensional unsteady problem of the action of a localized radiation pulse on an aluminum plate of finite thickness in a tangential airflow is solved on the basis of the Euler equations in the gas phase and the heat conduction equation in the solid. The process is accompanied by the intense evaporation of plate material and the subsequent (after the action of the radiation pulse ceases) intense condensation of aluminum vapor and condensate particles on the surface. The problem is solved on the assumption that the surface is not screened by its disintegration products and the processes associated with the self-radiation of the gas are disregarded. Heat pulses of intensityq=106−107 W/cm2 and durationti≈10−4 sec are investigated. Various regimes are calculated and the effect of the governing parameters on the impulse transmitted to the surface and ablation of the target material is established. A nontraditional approach, based on the idea of statistical modeling of the motion of an inviscid non-heat-conducting gas at the kinetic level, is used for solving the gas dynamic problem. The application of the approach in question to the solution of problems of this class is justified.