Plate Of Finite Thickness Research Articles

Investigation of plasticity–induced fatigue crack closure

Plasticity-induced crack closure and constraint effects due to finite plate thickness are both fundamental aspects in the mechanics of fatigue cracks. Moreover, plasticity-induced crack closure provides an effective first-order correction to the crack driving force, as used in the correlation and prediction of fatigue crack growth. The approach developed in this study utilises the distributed dislocation technique to model fatigue cracks growing under constant amplitude loading infinite thickness plates. Numerical results are obtained through the application of Gauss-Chebyshev quadrature and are presented for the crack opening stress ratio. An excellent agreement is observed with previous three-dimensional finite element studies.

The effect of biaxial load on stress and strain concentrations in a finite thickness elastic plate containing a circular hole

AbstractThe elastic stress and strain fields of a finite thickness plate containing a circular hole subjected to a biaxial load are systematically investigated using the finite element method. It is found that the stress and strain concentration factors of the finite thickness plate are different even if the plate is in elasticity state. The maximum stress and strain concentration factors do not always occur on the mid plane of the plate. The maximum stress and strain concentration factors of the notch root increase from their plane stress value to their peak values, then decrease gradually with increasing thickness and tend to constant values related to the load biaxiality ratio, respectively. The stress and strain concentration factors at the notch root of free surface are the monotonic descent functions of thickness. Their values decrease rapidly and tend to lower the limit values related to the load biaxiality ratio with increasing plate thickness. The differences of stress and strain concentration factors between maximum and surface value increase rapidly and tend to constant values related to the load biaxiality ratio with increasing plate thickness. The smaller the load biaxiality ratio, the larger these differences. Copyright © 2007 John Wiley & Sons, Ltd.

Application of the distributed dislocation technique for calculating cyclic crack tip plasticity effects

ABSTRACTThis paper describes a method for modelling cyclic crack tip plasticity effects based on the distributed dislocation technique (DDT). A strip‐yield model is utilised to allow for the determination of the crack opening displacement, size of the plastic zones and in the case of a fatigue crack, the wake of plasticity. The DDT can be easily implemented for a wide range of cracked geometries with reliable control over the accuracy and convergence. Thickness effects can also be incorporated through a recently obtained solution for an edge dislocation in an infinite plate of finite thickness. Results for finite length cracks that have had limited growth, such that there is no plastic wake, are presented for a range of applied loads and R‐ratios. Further results are provided for a steady‐state fatigue crack in a plate of finite thickness. The present results are compared with analytical solutions and they show an excellent agreement.

The concentration of stress and strain in finite thickness elastic plate containing a circular hole

The elastic stress and strain fields of finite thickness large plate containing a hole are systematically investigated using 3D finite element method. It is found that the stress and strain concentration factors of the finite thickness plate are different even if the plate is in elasticity state except at notch root of plate surface. The maximum stress and strain do not always occur on the mid plane of plate. They occur on the mid plane only in thin plate. The maximum stress and strain concentration factors are not on mid plane and the locations of maximum stress and strain concentration factors are different in thick plate. The maximum stress and strain concentration factors of notch root increase from their plane stress value to their peak values, then decrease gradually with increasing thickness and tend to each constant related to Poisson’s ratio of plate, respectively. The stress and strain concentration factors at notch root of plate surface are the same and are the monotonic descent functions of thickness. Their values decrease rapidly and tend to each constant related to Poisson’s ratio with plate thickness increasing. The difference between maximum and surface value of stress concentration factor is a monotonic ascent function of thickness. The thicker the plate is or the larger the Poisson’s ratio is, the larger the difference is. The corresponding difference of strain concentration factor is similar to the one of stress concentration factor. But the difference magnitude of stress concentration factor is larger than that of strain concentration factor in same plate.

Three-Dimensional Elastic Stress Fields of Finite Thickness Plates with Elliptical Hole

Based on detailed three-dimensional finite element analyses, elastic stress and strain field of ellipse major axis end in plates with different thickness and ellipse configurations subjected to uniaxial tension have been investigated. The plate thickness and ellipse configuration have obvious effects on the stress concentration factor, which is higher in finite thickness plates than in plane stress and plane strain cases. The out-of-plane stress constraint factor tends the maximum on the mid-plane and approaches to zero on the free plane. Stress concentration factors distribute ununiformly through the plate thickness, the value and location of maximum stress concentration factor depend on the plate thickness and the ellipse configurations. Both stress concentration factor in the middle plane and the maximum stress concentration factor are greater than that under plane stress or plane strain states, so it is unsafe to suppose a tensioned plate with finite thickness as one undergone plane stress or plane strain. For the sharper notch, the influence of three-dimensional stress state on the SCF must be considered.

Elastic stability and the onset of plastic flow in accelerated solid plates

For accelerated incompressible, ideal elastoplastic plates of finite thickness with a preformed sinusoidal perturbation at the interface, we investigate the stability behavior encompassing neutral and most-unstable modes, stable oscillatory modes, and the onset of plastic flow. We show that the largest perturbation wavelength that can maximize the growth rate corresponds to a finite thickness plate. For elastically stable configurations, stress gradients that arise as a result of the interfacial disturbance can lead to the formation of counter-rotating particle displacement trajectories that tessellate the extent of the plate. By computing the spatiotemporal evolution of the stress tensor, we are able to construct the boundaries that demarcate the transition from elastically stable oscillatory modes to the onset of plastic flow based on the von Mises yield criterion. Earlier estimates of these boundaries for thick plates differ qualitatively and quantitatively from the present results, in which the common simplifying assumptions of thin-plate theory were not invoked. We show that multimodal solutions are necessary to accurately represent the actual oscillatory behavior of the stress tensor, which in general is not time periodic, that thin-plate bimodal solutions are unable to capture.

The distributed dislocation technique for calculating plasticity-induced crack closure in plates of finite thickness

An analytical method for calculating plasticity-induced fatigue crack closure in plates of finite thickness is presented. The developed method utilizes the distributed dislocation technique (DDT) and Gauss-Chebyshev quadrature. Crack tip plasticity is incorporated by adopting a Dugdale type strip yield model. The finite plate thickness effects are taken into account by using a recently obtained three-dimensional solution for an edge dislocation in an infinite plate. Numerical results for the ratio of the size of the crack tip plasticity zones are presented for the cases of uniform thickness wake and linearly increasing wake for a range of plate thickness to crack length ratios and applied load ratios. The results show a very good agreement with previous analytical solutions in the limiting cases of very thick and very thin plates. Further results for the opening stress to maximum stress ratio are also provided and are compared with known three-dimensional finite element (FE) solutions. A good agreement is observed. The developed method is shown to be an effective and very powerful tool in modeling the crack closure phenomenon.

Stress intensity factors for three-dimensional cracks in functionally graded materials using enriched finite elements

A three-dimensional enriched finite-element methodology is presented to compute stress intensity factors for three-dimensional cracks contained in functionally graded materials (FGMs). A general-purpose 3D finite-element based fracture analysis program, FRAC3D, is enhanced to include this capability. First, using available solutions from the literature, comparisons have been made in terms of stresses under different loading conditions, such as uniform tensile, bending and thermal loads. Mesh refinement studies are also performed. The fracture solutions are obtained for edge cracks in an FGM strip and surface cracks in a finite-thickness FGM plate and compared with existing solutions in the literature. Further analyses are performed to study the behavior of stress intensity factor near the free surface where crack front terminates. It is shown that three-dimensional enriched finite elements provide accurate and efficient fracture solutions for three-dimensional cracks contained in functionally graded materials.

Fracture in plates of finite thickness

Application of the plane theory of elasticity to planar crack or angular corner geometries leads to the concept of stress singularity and stress intensity factor, which are the cornerstone of contemporary fracture mechanics. However, the stress state near an actual crack tip or corner vertex is always three-dimensional, and the meaning of the results obtained within the plane theory of elasticity and their relation to the actual 3D problems is still not fully understood. In particular, it is not clear whether the same stress field as found from the well-known 2D solutions of the theory of elasticity do describe the corresponding stress components in a plate made of a sufficiently brittle material and subjected to in-plane loading, and what effect the plate thickness has. In the present study we adopt, so called, first order plate theory to attempt to answer these questions. New features of the elastic solutions obtained within this theory are discussed and compared with 2D analytical results and experimental studies as well as with 3D numerical simulations.

Analyses of stress components for a circular crowned roller compressed between two flat plates

Stiffness models of a roller compressed between two plates, based on contact mechanics with either a finite plate thickness condition or a half-space plate, can describe the deformation curve very well. By using the prescribed deformed curve, stress component analyses is an important research topic for engineering purposes. Therefore, the main purpose of this paper is to determine stress components when a circular crowned roller is compressed between two plates. A deformed curve on a plate surface and the stiffness of the model are evaluated. Thereafter, normal contact pressure on the plate surface is calculated with the help of the calculated deformation curve and the accuracy of the computation is validated by comparing it with finite-element results. Finally, stress components in the plate are obtained in terms of contact theories, and parametric studies were conducted to learn about the variation of stress components inside the plate. The results reveal that the stress concentration effect becomes large near the edge when the stress is close to the surface of the plate. Moreover, the direction of shear stress is changed at half the contact line distance from the centre of contact and the stress components decrease with increasing depth of the plate. The parametric studies also indicate that the stress components increase with increasing applied displacements.

Rayleigh–Lamb waves in a microstretch elastic plate cladded with liquid layers

Propagation of Rayleigh–Lamb waves in an infinite plate of finite thickness and composed of microstretch elastic material is considered. The top and bottom of the plate are cladded with finite layers of a homogeneous and inviscid liquid (non-micropolar and non-microstretch). There exist two sets of boundary conditions at solid/liquid interface and the choice on these sets of boundary conditions is arbitrary. Frequency equations are derived for symmetric and antisymmetric modes of propagation for Rayleigh–Lamb waves propagation. It is found that the frequency equations for both the modes of propagation are dispersive in nature and the presence of microstretch has negligible effect on the dispersion curves. However, the attenuation coefficient is found to be influenced by the presence of microstretch in the plate with free boundaries. Considerable effect of the liquid layers is noticed on the dispersion curves. Numerical computations are performed for a specific model to compute the phase velocity and attenuation coefficient for different values of wavenumber, for both symmetric and antisymmetric vibrations. Results of some earlier workers have been deduced as special cases.

Analysis of Anti-Plane Shear Crack in Finite Thickness Plate

The anti-plane shear crack in a finite thickness plate is analyzed by the continuously distributed dislocations model and the stress intensity factors are calculated. The results are compared with those in an infinite thickness plate. It is found that the larger the ratio of the crack length to the plate thickness is, the larger the stress intensity factor is and that the Mode II component accompanies with the Mode III component, which does never appear in an infinite thickness plate. The Mode II stress intensity factor appears strongly near the plate surfaces and vanishes at the center of the plate in the thickness direction. This indicates the crack surface inclines steeply near the plate surfaces and does not incline at the center.

2725 面外せん断荷重を受ける有限厚さの板におけるき裂の解析(G04-3 機械材料・材料加工(3),G04 機械材料・材料加工)

An anti-plane shear crack in a plate with finite thickness and with finite width is analyzed by the continuously distributed dislocations model. The elastic stress field of a screw dislocation in a finite thickness plate is obtained in the form of Bessel's series and that in a finite width plate is obtained by the method of image dislocations. Using the continuous dislocations model with the stress field of screw dislocations, the Mode III stress intensity factors are calculated. And the relationship between the stress intensity factors, the width of a plate to the crack length and the crack length to the thickness is shown.

Free-surface wave interaction with a thick flexible dock or very large floating platform

In this paper the recently developed semi-analytic method to solve the free-surface wave interaction with a thin elastic plate is extended to the case of a plate of finite thickness. The method used is based on the reformulation of the differential–integral equation for this problem. The thickness of the plate is chosen such that the elastic behavior of the plate can be described by means of thin-plate theory, while the water pressure at the plate is applied at finite depth. The water depth is finite.

Transverse shear and pressurization effects in the bending of plates with reinforced cracks

The authors develop an eigth-order model for bending of transversally isotropic plates and use integral transforms and a collocation method to form a line-spring model for a cracked plate. The eigth-order model allows satisfaction of the three standard plate bending boundary conditions; the normal moment, twisting moment, and transverse shear force, and an additional shear stress resultant that allows analysis of transverse normal stresses near the crack tip. The line-spring model is used to develop geometry correction factors for bending of finite-thickness plates, accounting for transverse shear deformation and pressurization of the plate near the crack tip. The line-spring model is then applied to the problem of a plate with a reinforced crack, and the results are used to validate an interpolation solution based on an energy method. While not explicitly analysed, the models are applicable to many problems, including bending of bonded repairs, fracture and fatigue of composite and layered materials, surface cracks, crack tip plasticity and crack closure or crack face interaction.

New stress intensity factor solutions for an elliptical crack in a plate

Crack assessment in engineering structures relies first on accurate evaluation of the stress intensity factors. In recent years, a large work was conducted in France by the Atomic Energy Commission to develop influence coefficients for surface cracks in pipes. However, the problem of embedded cracks in plates (and pipes), which is also of practical importance, has not received so much attention. Presently, solutions for elliptical cracks are available either in infinite solid with a polynomial distribution of normal loading or in plate, but restricted to constant or linearly varying tension. This paper presents the work conducted at EDF R&D to obtain influence coefficients for plates containing an elliptical crack with a wide range of the parameters: relative size (2 a/ t ratio), shape ( a/ c ratio) and free surface proximity ( a/ d ratio, where d is the distance from the center of the ellipse to the closest free surface). These coefficients were developed through extensive 3D finite element calculations: 200 geometrical configurations were modeled, each containing from 18,000 to 26,000 nodes. The limiting case of the tunnel crack ( a/ c = 0) was also analyzed with 2D finite element calculation (50 geometrical configurations). The accuracy of the results was checked by comparison with analytical solutions for infinite solids and, when possible, with solutions for finite-thickness plates (generally loaded in constant tension). These solutions have been introduced in the RSE-M Code that provides rules and requirements for in-service inspection of French PWR components.

Solutions of T-stresses for quarter-elliptical corner cracks in finite thickness plates subject to tension and bending

The non-singular terms in the series expansion of the elastic crack-tip stress fields, commonly referred to as the T-stresses, play an important role in fracture and fatigue problems where a single fracture mechanics parameter such as stress intensity factor K or the J-integral cannot completely characterize the crack tip stress states. In addition to K in elastic analysis, or the J-integral in elastic–plastic analysis, T-stresses provide an effective two-parameter characterization of the constraint levels in the vicinity of a crack. A quarter-elliptical corner crack in a finite thickness plate is a representative model for many cracks in engineering components, such as corner cracks found in weld toes, rivet holes or the nozzle areas of pressure vessels. In this paper, three-dimensional finite element analyses are conducted to calculate the T-stresses for a quarter-elliptical corner crack in a finite thickness plate with a wide range of crack aspect ratios and relative depths. Both remote tension and bending loads are considered. For engineering applications, empirical equations for T-stresses at two points near the free surfaces are also presented. When combined with the solutions for stress intensity factor K or J, these T-stresses solutions are suitable for constraint-based fracture and fatigue analysis for quarter-elliptical corner cracks in engineering components.

Three-dimensional stress concentrations at elliptic holes in elastic isotropic plates subjected to tensile stress

The through-thickness variations of stress concentration factors along the wall of elliptic holes in finite thickness plates of isotropic materials subjected to remote tensile stress have been systematically analyzed using the finite element method. The three-dimensional stress concentration factor K t is found to be a function of the thickness to root radius ratio B/ ρ and the aspect ratio t (short to long axial length) of the elliptic hole under tensile loading. It is found that the maximum stress concentration factor through the thickness, ( K t ) max, is 24–123% higher than the value on the free surface ( K t ) surf when t changes from 1 to 0.01, and the ratio of the surface value ( K t ) surf to the corresponding planar solution ( K t ) p− σ at the root is only 0.82–0.48 when t ranges from 1 to 0.01 if B/ ρ is large enough. When B/ ρ is smaller than 1, both of the ratios will approach 1. Simple and efficient empirical formulae for the relationships between the three values were obtained by fitting the numerical results with good engineering accuracy for large range of B/ ρ (from 1 to 100,000) and t (from 0.01 to 1). Combining with the plentiful known two-dimensional stress concentration factors in handbooks, the proposed formulae can be used to solve the maximum three-dimensional stress concentration factors of holes, notches and be useful for strength and fatigue designs of engineering structures with similar defects.

Mixed mode stress intensity factors for deflected and inclined corner cracks in finite-thickness plates

Mixed mode stress intensity factor solutions are presented for deflected and inclined corner cracks in finite-thickness plates under uniform tensile remote loading. Three-dimensional enriched finite elements, which contain analytically known crack tip displacement and strain fields, are employed in the analyses. The stress intensity factor solutions are generated for quarter-circular corner cracks with various deflection and inclination angles ranging from 0° to 75°. The effect of plate thickness on the mixed mode fracture solution is also investigated. In the analyses presented, crack length/plate thickness ( a/ t) ratio ranges from 0.2 to 0.8. It is shown that decreasing the plate thickness results in magnification of mixed mode stress intensity factors along the crack front. Crack propagation angles are also determined along the deflected and inclined corner crack fronts based on the computed mixed-mode stress intensity factor distributions. The solutions presented can be used to assess fail/safe conditions and fatigue crack growth for the three-dimensional cracks studied.

Mathematical Modeling for One New Method of Breaking Ice Cover

The spatial problem of determining the stress-strain state of an ice plate of finite thickness broken by a patented method is solved using the theory of small elastoplastic strains and a proven numerical method.