单向拉伸条件下补片参数对复合材料胶接修复结构的影响

建立含中心半穿透圆孔的损伤金属板修补结构的三维有限元模型,以应力集中系数(Stress Concentration Factor,SCF)和挠度w作为复合材料胶接修复效果的指标,分析单向拉伸条件下,正方形补片的长度、厚度和铺层方式对修复效果的影响。结果表明:补片长度取孔直径的3.5倍、厚度取孔深度的0.6~0.8倍、铺层方式取0°/90°铺层时,复合材料单面修复含损伤裂纹板的效果较好。根据分析结果制备了实验件,进行了单向静拉伸实验,修补实验件的破坏强度比未修补实验件提高了10.1%。     

基于全试验设计方法的含裂纹铝合金板复合材料修补参数优化

建立含穿透裂纹铝合金板复合材料单面胶接修补板条的三维有限元模型,基于位移外推法对裂纹尖端的应力强度因子(SIF)进行求解。使用全试验设计的方法对不同修补参数下修补板条的单向拉伸试验进行仿真模拟,利用二次方程描述并研究了补片长度、补片厚度及胶层弹性模量共同作用时对SIF的影响,确定了以SIF为评价指标时对修补效果影响最大的修补参数,优化了修补设计,并应用优化修补参数进行单向静拉伸试验。结果表明,当三类修补参数共同作用时,补片长度对修补效果影响最大;使用优化修补参数单面修补试验件的破坏强度比未修补板的提高了12.1%,恢复到完好板的90.5%。     

A new method of crack-tip opening displacement determined based on maximum crack opening displacement

In this paper a new method is presented to determine the crack-tip opening displacement (CTOD) for the center cracked plate with uniaxial uniform tension load. The maximum crack opening displacement (MCOD) is adopted to estimate CTOD. Based on the series of calculation results by elastic–plastic finite element simulation, an explicit function expression for the CTOD versus MCOD is determined, which enables to consider the influence effects of crack geometries, plate sizes, applied loads, plane state and material properties. Hence, the presented method of CTOD determined by MCOD is suitable to any center crack finite plate of any material under uniaxial tension.     

FRONT DEVELOPMENT OF A LONG FATIGUE CRACK DURING ITS GROWTH

Abstract— A 3-D elastic-plastic finite element analysis has been developed to simulate the deformation development along the front of a long mode I single edge crack in plates subjected to either monotonic or cyclic loading. Idealisations having both equal and unequal layers through the thickness of the plate were involved. Plane stress and plane strain 2-D finite element analyses were also performed and compared with the present 3-D solutions. The development of the monotonic and cyclic crack tip plastically deformed zones and opening displacements were traced and correlated to accommodate the effect of the plate thickness and the profile of the crack front. A previously developed crack tip deformation parameter was invoked to predict the effect of the specimen thickness on mode I fatigue crack growth and the associated change of crack front profile. Comparison of such a prediction and the experimental findings of the present work reflected the capability of that parameter in modelling fatigue crack growth through the plate thickness.     

Influence of isotropic strain hardening on plane strain dynamic growth in elastic-plastic materials

In this paper, dynamic crack growth in an elastic-plastic material is analysed under mode I, plane strain, small-scale yielding conditions using a finite element procedure. The material is assumed to obey J₂ incremental theory of plasticity with isotropic strain hardening which is of the power-law type under uniaxial tension. The influence of material inertia and strain hardening on the stress and deformation fields near the crack tip is investigated. The results demonstrate that strain hardening tends to oppose the role of inertia in decreasing plastic strains and stresses near the crack tip. The length scale near the crack tip over which inertia effects are dominant also diminishes with increase in strain hardening. A ductile crack growth criterion based on the attainment of a critical crack tip opening displacement is used to obtain the dependence of the theoretical dynamic fracture toughness on crack speed. It is found that the resistance offered by the elastic-plastic material to high speed crack propagation may be considerably reduced when it possesses some strain hardening.     

Influence of crack closure on the stress intensity factor in bending plates — A classical plate solution

Based on the classical plate theory in conjunction with the assumption of line contact at the compressive edge of a crack face, closed form solutions were presented for a through-the-thickness central crack in an infinite plate subjected to all around bending. The complete solutions were obtained by superposing the membrane components due to the contact forces at the crack face to the non-closure bending components. The distribution of the contact forces was found uniform by considering the contact condition which prevents mutual penetration of the crack faces at the compressive edges. The results showed that the closure of the crack faces tends to reduce the crack opening displacement at the tension side and, consequently, reduce the stress intensity factor. The finite element method was also used to investigate the present problem. The modified crack closure method in combination with the finite element method was used to find the stress intensity factors. Close agreement between the finite element and the analytical solutions was observed.     

Interaction effect of two arbitrarily oriented cracks — Part I

The elastosatic problem solved in this paper is of an isotropic homogeneous infinite plate, with two arbitrarily oriented cracks of different lengths, subjected to uniform uniaxial tension at infinity. The problem is formulated in the complex plane using the Kolossoff-Muskhelishvili stress functions and further the Schwarz's alternating method is used to solve the problem of the doubly connected region. The mode I and mode II stress intensity factors at all the four crack tips for various crack length ratios, crack angles and crack spacings are found, and are in good agreement with those obtained by other research workers. The fracture angles at the four crack tips are evaluated using the strain energy density theory and maximum tangential stress theory. The minimum strain energy density factor is also found at all the tips.     

Modified crack closure integral using six-noded isoparametric quadrilateral singular elements

Six-noded, isoparametric serendipity type quadrilateral regular/singular elements are used for the estimation of stress intensity factors (SIF) in linear elastic fracture mechanics (LEFM) problems involving cracks in two-dimensional structural components. The square root singularity is achieved in the six-noded elements by moving the in-side nodes to the quarter point position. The modified crack closure integral (MCCI) method is adopted which could generate accurate estimates of SIF for a relatively coarse mesh. The equations for strain energy release rate and SIF are derived for mixed mode situations using six-noded quadrilateral elements at the crack tip. The model is validated by numerical studies for a centre crack in a finite plate under uniaxial tension, a single edge notched specimen under uniaxial tension, an inclined crack in a finite rectangular plate and cracks emanating from a pin-loaded lug (or lug attachment). The results compare very well with reference solutions available in the literature.     

Mode II stress intensity factors for central slant cracks with frictional surfaces in uniaxially compressed plates

The effect of crack surface friction on mode II stress intensity factor (SIF) of a central slant crack in a plate uniformly loaded in uniaxial compression is quantified. A previously developed two-dimensional finite element analysis was utilised after its modification to accommodate the friction between the crack surfaces. The plane strain state was assumed. A new numerical technique was devised to avoid the iteration procedures, which had to be employed due to the existence of frictional forces.

The crack inclination angle varied between zero and 75° measured from the horizontal direction. The coefficient of friction of the crack surfaces changed from zero to 1. In case of relatively sliding crack surfaces, mode II SIF existed. As is well known, the resulting mode II SIF decreased with increasing the coefficient of friction of the crack surfaces. Further, mode II SIF increased with increasing crack line inclination angle and then decreased after reaching a maximum value. The angle corresponding to that maximum SIF increased as the coefficient of friction of the crack surfaces increased.     

Crack-tip constraint and j-controllings stable growth of crack in plane stress case

The finite element analyses are performed to model quasi-static crack growth under mode I plane stress in a compact tension specimen and a centre-cracked plain. It is found that the triaxial constraint and stress-field defined by HRR solution in crack-tip regions for a stationary crack have been better met by those presented in the propagating crack-tip for two different thin specimens, namely, J-dominance is continuously valid. The J-resistance curves measured experimentally from the two specimen geometries coincide with each other and agree well with those calculated by FEM simulations.     

Stochastic critical stress intensity factor response of single edge notched laminated composite plate using displacement correlation method

Abstract

The second-order statistics of critical stress intensity factor (SIF) of single edge notched fiber reinforced composite plates with random system properties and subjected to uniaxial tensile loadings is investigated. This paper is an extension of reference (Lal and Kapania, 2013) by the present authors by considering more number of input random system parameters for higher accuracy. A C⁰ finite element method based on a higher-order shear deformation plate theory using displacement correlation method via isoparametric quarter point element is proposed for basic formulation. A stochastic finite element method using first-order perturbation technique and Monte Carlo simulation (MCS) is employed to examine the mean, coefficient of variance, and probability density faction of critical first mode SIF. The effect of different fiber orientations, crack length, plate thickness, a number of layers, and the lamination schemes with random system properties on the statistics of SIF of single edge crack laminated composite plate is evaluated. The tensile failure load is predicted using Hashin’s failure criteria. The present approach is validated with results available in literature and by employing independent MCS.     

Influence of crack closure on the stress intensity factor for plates subjected to bending—A 3-D finite element analysis

Plates with central through cracks subjected to bending is analysed taking into account the closure of the crack faces on the compression side. A three-dimensional finite element method employing three-dimensional degenerate solid element is used for the analysis. The crack faces have been modelled such that they come in contact over an area on the compression side and interfere with each other. The influence of the crack closure on the variation of the stress intensity factor across the plate thickness is obtained for finite and infinite plate geometries.     

A new method of plastic zone size determined based on maximum crack opening displacement

This paper presents a new method to determine the crack-tip plastic zone size (R_y) in the center cracked plate in tension. The maximum crack opening displacement (MCOD) is used to estimate R_y in this method. Based on the series of calculation results by finite element analysis, the explicit expression for the crack-tip plastic zone size versus MCOD is fitted by least square method. The expression enables to eliminate the influences of the yield stress of material, crack geometry, plate sizes and transverse stress. Therefore, the presented method of R_y determined by MCOD is suitable to any center crack finite plate of any material under uniaxial or biaxial tension.     

Analytical and Numerical Solution of the Stress Field and the Dynamic Stress Intensity Factors in a Cracked Plate under Sinusoidal Loading

A cracked plate subjected to a sinusoidal loading perpendicular to its plane is considered, and the analytical solution of the dynamic vibration behavior of a plate, which allowed the determination of the stress field near the crack tip, is developed. A mixed mode of loading near the crack tip has been established and described with dynamic stress intensity factors K _I (z,t) and K _II (z,t) associated with modes I and II crack openings, respectively. To validate the analytical results, a finite element analysis (FEA) of a 1 × 1 m square plate with a thickness of 1 cm, having a middle crack of 10 cm in length, is made. The results have shown significant agreement between analytical and FEA findings.     

Cohesive modeling of dynamic fracture in functionally graded materials

The dynamic fracture of functionally graded materials (FGMs) is modeled using an explicit cohesive volumetric finite element scheme that incorporates spatially varying constitutive and failure properties. The cohesive element response is described by a rate-independent bilinear cohesive failure model between the cohesive traction acting along the cohesive zone and the associated crack opening displacement. A detailed convergence analysis is conducted to quantify the effect of the material gradient on the ability of the numerical scheme to capture elastodynamic wave propagation. To validate the numerical scheme, we simulate dynamic fracture experiments performed on model FGM compact tension specimens made of a polyester resin with varying amounts of plasticizer. The cohesive finite element scheme is then used in a parametric study of mode I dynamic failure of a Ti/TiB FGM, with special emphasis on the effect of the material gradient on the initiation, propagation and arrest of the crack.     

Application of a dynamic numerical solution to high speed fracture experiments—I. analysis of experimental geometries

The application of a dynamic, generation mode, finite element program to the analysis of experimental geometries is reported. Particular attention is given to the DCB specimen, which is widely used in high speed fracture studies despite strong inertia effects, which are described. Finite strip and infinite plate results are also considered. Here, idealised cases are discussed, while in Part II the application of the analysis to experimental measurements, to derive propagating crack fracture resistance data, is reported.     

Numerical solution of cracked thin plates subjected to bending, twisting and shear loads

A semi-analytical method namely fractal finite element method is presented for the determination of mode I and mode II moment intensity factors for thin plate with crack using Kirchhoff's theory. Using the concept of fractal geometry, infinite many of finite elements is generated virtually around the crack border. Based on the analytical global displacement function, numerous degrees of freedom (DOF) are transformed to a small set of generalised coordinates in an expeditious way. The stress intensity factors can be obtained directly from the generalized coordinates. No post-processing and special finite elements are required to develop for extracting the stress intensity factors. Examples of cracked plate subjected to bending, twisting and shear loads are given to illustrate the accuracy and efficiency of the present method. The influence of finite boundaries on the calculation of the moment intensity factors is studied in details. Very accuracy results when compare with the theoretical and numerical counterparts are found.     

Elastodynamic analysis of crack by finite element method using singular element

The finite element method using a singular element near the crack tip is extended to the elastodynamic problems of cracks where the displacement function of the singular element is taken from the solution of a propagating crack. The dynamic stress intensity factor for cracks of mode III or mode I deformations in a finite plate is determined.The results of computation for stationary cracks or propagating cracks under dynamic loadings are compared with the analytical solutions of other authors. It is shown that the present method satisfactorily describes the time variation of the stress intensity factor in dynamic crack problems.

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Résumé La méthode des éléments finis utilisant un élément singulier au voisinage de l'extrémité d'une fissure a été étendue aux problèmes élastodynamiques des fissures tels qu'ils se posent lorsque la fonction de déplacement d'un élément singulier est prise à partir de la solution d'une fissure en cours de propagation. Le facteur d'intensité des contraintes dynamiques correspondant à des fissures de mode III ou des déformations de mode I dans une plaque finie a été déterminé. Les résultats des calculs correspondant à des fissures stationnaires ou des fissures en cours de propagation sous des charges dynamiques sont comparées aux solutions analytiques obtenues par d'autres auteurs. On montre que la méthode présentée décrit de façon satisfaisante la variation en fonction du temps du facteur d'intensité des contraintes dans les problèmes de fissuration dynamique.

     

Determination of dynamic fracture toughness for PMMA

A dynamic FEM (finite element method) and a strain gage method are applied to analyze the dynamic fracture toughness and SIF (stress intensity factor) for PMMA (polymethyl methacrylate). The analyses are carried out for plates with an edge crack subjected to one-point bending in a plane of the plate. A simple procedure that the present author has proposed is applied to the problem of using a triangular element of assumed constant strain on finite element analysis. The numerical simulation by FEM provides values for the applied forces as measured with the strain gages. Also, a crack initiation time is measured with the strain gage mounted around the crack tip. The dynamic fracture toughness is determined by adapting the crack initiation time to the simulation curve of the dynamic SIF calculated by the FEM. In this study, the usefulness of the method to determine the dynamic fracture toughness is investigated by comparing predictions with the experimental results for dynamic stresses and SIFs.     

A method for testing interlaminar dynamic fracture toughness of polymeric composites

Static and dynamic Mode I delamination fracture in two polymeric fiber composites was studied using a WIF test method. The dynamic test was conducted on a Split Hopkinson Pressure Bar apparatus. Crack speeds up to 1000 m/s were achieved. Dynamic fracture and crack propagation were modeled by the finite element method. Dynamic initiation fracture toughness of S2/8552 and IM7/977-3 composites were obtained. The dynamic fracture toughness of IM7/977-3 associated with the high speed propagating crack was extracted from the finite element simulation based on the measured data. It was found that the dynamic fracture toughness of the delamination crack propagating at a speed up to 1000 m/s approximately equals the static fracture toughness.