Fracture mechanics analysis of geometrically nonlinear shear deformable plates

This paper presents boundary integral equations for fracture mechanics analysis of geometrically nonlinear shear deformable plates. A radial basis function and dual reciprocity method are utilized to evaluate the derivative terms and the domain integrals that appear in the formulations, respectively. Numerical examples of the clamped and simply supported plates containing a center crack subjected to uniform transversal loadings are presented. Displacement extrapolation technique is used to compute the stress intensity factors (SIFs). Stress intensity factors of mode I for plate bending and membrane problems are presented. The normalized stress intensity factors in membrane significantly increase after few increments of the load while the normalized stress intensity factors in bending decrease. Less displacement and rotational constraints in cracked plates under uniform transversal loadings will raise the stress intensity factors. The bending stress intensity factors of a central crack in clamped square plate were found to be the highest values compared to those for clamped non-square plates.     

Stress intensity factors for cracks in some fracture mechanics test specimens under displacement control

The stress intensity factors for cracks of varying length in some common fracture mechanics test specimens have been calculated when the displacement at the loading pins is held constant. For centre and edge cracked plates with a given crack length the stress intensity factor decreases with the decrearing separation of the loading pins. For a three-point bend specimen of span to width of 8 a plateau is observed in the stress intensity factory over a range 0.3< a/w <0.6. For CKS-type and T-type wedge-open-loaded specimens the stress intensity factor decreases monotonically with increasing crack length for a/w > 0.3. The implications of these results to fracture mechanics testing are discussed.     

Line-spring model for surface cracks in a reissner plate

In this paper the line-spring model developed by Rice and Levy for a surface crack in elastic plates is reconsidered. The problem is formulated by using Reissner's plate bending theory. For the plane strain problem of a strip containing an edge crack and subjected to tension and bending new expressions for stress intensity factors are used which are valid up to a depth-to-thickness ratio of 0.8. The stress intensity factors for a semi-elliptic and a rectangular crack are calculated. Considering the simplicity of the technique and the severity of the underlying assumptions, the results compare rather well with the existing finite element solutions.     

A general weight function approach to compute mode-II stress intensity factors and crack paths for slightly curved or kinked cracks in finite bodies

A simple procedure is proposed that allows computing the stress intensity factors for slightly curved and kinked cracks in finite bodies. Basis of the method is the computation of the stress field around a straight crack under externally applied tractions. Then, this auxiliary crack is replaced by the crack of interest. The stress intensity factors are computed from the stresses caused by the auxiliary crack using the weight function technique. In a practical application of the method, mode-II stress intensity factors are computed for the edge-cracked half-space. From the usual crack path condition, K_II = 0, the paths of propagating cracks under biaxial loading and the critical biaxiality ratio for global directional instability are computed. The results are in very good agreement with finite element computations.     

Crack Growth analysis of plates Loaded by bending and tension using dual boundary element method

This paper presents an extension of the dual boundary element method to analysis of crack growth in plates loaded in combine bending and tension. Five stress intensity factors, two for membrane behaviour and three for shear deformable plate bending are computed using the J-Integral technique. Crack growth processes are simulated with an incremental crack extension analysis based on the maximum principal stress criterion. The method is considered effective since no remeshing is required and the crack extension is modelled by adding new boundary elements to the previous crack boundaries. Several incremental crack growth analysis for different configurations and loadings are presented.     

Arbitrary loading problems of doubly symmetric regions containing a central crack

This paper presents a method of analysis of doubly symmetric plates with a central crack subjected to symmetric concentrated forces at points on the outer boundary. The problem is treated by using complex stress functions appropriate for the traction free crack and by means of a kind of boundary collocation method. The method is also valid for arbitrary loading problems, since the applied loads can be replaced by concentrated forces so far as the crack tip stress intensity factors are concerned.Numerical examples are given for elliptical and rectangular plates and plates of other configurations of practical importance. Results of rectangular plates give informations on experimental estimation of crack tip stress intensity factors in complex structures.     

A theory for the fracture of thin plates subjected to bending and twisting moments

Stress fields near the tip of a through crack in an elastic plate under bending and twisting moments are reviewed assuming both Kirchhoff and Reissner plate theories. The crack tip displacement and rotation fields based on the Reissner theory are calculated here for the first time. These results are used to calculate the J-integral (energy release rate) for both Kirchhoff and Reissner plate theories. Invoking Simmonds and Duva's [16] result that the value of the J-integral based on either theory is the same for thin plates, a universal relationship between the Kirchhoff theory stress intensity factors and the Reissner theory stress intensity factors is obtained for thin plates. Calculation of Kirchhoff theory stress intensity factors from finite elements based on energy release rate is illustrated. A small scale yielding like model of the crack tip fields is discussed, where the Kirchhoff theory fields are considered to be the far field conditions for the Reissner theory fields. It is proposed that, for thin plates, fracture toughness and crack growth rates be correlated with the Kirchhoff theory stress intensity factors.     

Locally refined p-FEM modeling of patch repaired plates

An accurate and practical modeling technique is proposed to analyze cracked metal plates with patch repair. In the single-model approach, a p-convergent high-precision element is developed with three-dimensional elasticity theory. Whereas, in the mixed-model approach, a p-convergent transition element is developed to connect the p-convergent high-precision elements for threedimensional response and p-convergent ESL (equivalent single layer) elements for two-dimensional response. For the developed elements, two- and three-dimensional virtual crack closure techniques based on linear elastic fracture mechanics are modified to estimate the stress intensity factor. Modeling simplicity and calculation efficiency of the mixed-model approach using the p-convergent transition elements is shown for the analysis of patch repaired plates. Some results of present analysis are verified by comparison with published results. Also, performance of analysis using the proposed technique with simplicity and efficacy of modeling is investigated for patch repaired plates with respect to a number of parameters such as thicknesses of patch and adhesive, patch size, single-sided patch vs. double-sided patch.     

The mode I crack problem for layered piezoelectric plates

The plane strain singular stress problem for piezoelectric composite plates having a central crack is considered. For the case of the crack which is normal to and ends at the interface between the piezoelectric plate and the elastic layer, the order of stress singularity around the tip of the crack is obtained. The Fourier transform technique is used to formulate the problem in terms of a singular integral equation. The singular integral equation is solved by using the Gaus–Jacobi integration formula. Numerical calculations are carried out, and the main results presented are the variation of the stress intensity factor as functions of the geometric parameters, the piezoelectric material properties and the electrical boundary conditions of the layered composites.     

Investigating the Effects of Locks on the Fracture Force and Stress Intensity Using Experimental Photoelasticity

Most of the engineering materials are faced with fracture phenomenon that needs to be controlled. There are several methods for controlling crack growth such as hole technique, using locks etc. In order to predict crack growth, stress intensity factor can be conducted as a useful tool. In this paper, the photoelasticity method is conducted as an experimental stress analysis tool in order to calculate the stress intensity factor (SIF). The investigations were conducted to find the effects of holes and locks on the fracture resistance and the SIF. This research is specially focused on the crack stitch as a unique technique to control crack propagation. In this technique, holes of locks are drilled close to each other in rows perpendicular to the crack then keys are inserted into the holes. Three batches including six different edge crack samples of polymethyl methacrylate rectangular plates were used for fracture tests. In the present study, the effects of locks in various geometries were investigated on the SIF. The results were obtained using a polariscope and the tensile load was applied to the specimens on the mode fracture (I) strength; then, the fracture forces were measured. The results showed that the samples with lock and hole have more fracture strength and thus their SIF decreases in comparison with the lock-less or hole-less samples.     

An assumed displacement hybrid finite element model for linear fracture mechanics

This paper deals with a procedure to calculate the elastic stress intensity factors for arbitrary-shaped cracks in plane stress and plane strain problems. An assumed displacement hybrid finite element model is employed wherein the unknowns in the final algebraic system of equations are the nodal displacements and the elastic stress intensity factors. Special elements, which contain proper singular displacement and stress fields, are used in a fixed region near the crack tip; and the interelement displacement compatibility is satisfied through the use of a Lagrangean multiplier technique. Numerical examples presented include: central as well as edge cracks in tension plates and a quarter-circular crack in a tension plate. Excellent correlations were obtained with available solutions in all the cases. A discussion on the convergence of the present solution is also included.     

Photoelastic determination of stress intensity factors in patched cracked plates

In this paper, the influence of patch parameters on stress intensity factors in edge cracked plates is studied by employing transmission photoelasticity. Edge cracked plates made of photo-elastic material are patched on one side only by $\text{E}$ glass-epoxy and carbon-epoxy unidirectional composites. The patch is located on the crack in such a way that the crack tip is not covered. Magnified isochromatic fringes are obtained by using a projection microscope of magnification 50, converted into a polariscope. Irwin's method is used to compute stress intensity factors from photoelastic data. The reduction in stress intensity factors is presented in graphical form as a function of patch parameters, namely stiffness, location and length. An empirical equation connecting reduction in stress intensity factor and these patch parameters is presented.     

Evaluation of C* integral for interacting cracks in plates under tension

A closed form solution for C* integral of two interacting cracks in plates under tension is developed on the basis of reference stress method. Comprehensive finite element (FE) creep analyses are carried out to provide the benchmark of the interaction evaluation of multiple cracks. Results indicate that more pronounced interaction is observed between the C* of double cracks and that of a single crack compared to that denoted by stress intensity factor (SIF). Overall good agreement is achieved between the proposed method for C* of multiple crack interaction and the FE results which provides confidence in practical application.     

A semi-theoretical and experimental approach for the determination of the stress intensity factors

The stress intensity factors for plexiglass plates containing edge cracks and subjected to either pure bending or tension are determined herein. The method of investigation was based on a semi-theoretical and experimental approach, where the stress intensity factors are expressed in terms of the measured diameter of the caustic, the crack length, and the width of the specimen. First, two basic crack arrangements (single and double edge cracks) were studied and then the method was utilized for the investigation of more complicated crack arrangements which are difficult or maybe impossible to be investigated otherwise. In particular, the stress intensity factor for plates having a sharp V-notch of various angles θ, and semi-infinite plates containing equal parallel edge cracks subjected to pure bending and tension respectively, were investigated in order to verify the validity of this method.     

Mode I weight functions for an orthotropic double cantilever beam

Approximate weight functions are proposed and validated numerically for an orthotropic double cantilever beam (DCB) loaded in mode I. They define the stress intensity factor at the crack tip due to a pair of point forces acting on the crack surfaces and have been deduced from the corresponding isotropic result using an orthotropy rescaling technique. The weight functions allow mode I large scale bridging problems in beams and plates to be formulated as integral equations, in terms of stress intensity factors at the crack tip, without the limitations imposed on accuracy by beam theory approximations. The proposed functions are applied to investigate the influence of the orthotropy of the material on the fracture behavior of DCBs in the presence of large scale bridging.     

Elastic T-stress for cracks in test specimens subjected to non-uniform stress distributions

Finite element analyses have been conducted to calculate elastic T-stress solutions for cracked test specimens. The T-stress solutions are presented for single edge cracked plates, double edge crack plates and centre cracked plates. Uniform, linear, parabolic or cubic stress distributions were applied to the crack face. The results for uniform and linear stress distributions were used to derive weight functions for T-stress for the corresponding specimens. The weight functions for T-stress are then verified against several linear and non-linear stress distributions. The derived weight functions are suitable for the T-stress calculation for cracked specimens under any given stress field.     

A METHOD FOR ESTIMATING FATIGUE CRACK PROPAGATION IN PRE-STRAINED AND MEAN STRESSED SPECIMENS

Abstract A method for quantifying the effect of plane stress, plane strain, mean stress and pre-strain on fatigue crack propagation rates in plates of different thicknesses is proposed. Experimental verification was carried out on mild steel plates of 0·2, 0·4, 0·6, 0·8, 1·0, 1·2 and 1·4 mm thick specimens. The conflicting effects of variations in stress intensity factors along the crack front and changes from plane stress to plane strain conditions along the crack front are also discussed.     

Fatigue crack growth in CFRP-strengthened steel plates

In this paper fatigue crack growth in steel plates reinforced by using carbon fiber reinforced (CFRP) strips is investigated from the experimental, numerical and analytical point of view. Single edge notched tension (SENT) specimens were strengthened with different reinforcement configurations and tested at a stress ratio R of 0.4. Different initial damage levels were considered and the experimental results showed that the reinforcement application can effectively reduce the crack growth rate and significantly extend the fatigue life. Numerical models (finite elements) were also developed to evaluate the stress intensity factor (SIF) and the crack opening displacement (COD) profile. Based on the numerical results, an analytical model was proposed to predict the fatigue crack growth rate and the fatigue crack growth curves. The analytical results are validated by comparing the fatigue crack growth curves to the experimental ones.     

Stress intensity factor analysis of an interface crack between dissimilar anisotropic materials under thermal stress using the finite element analysis

New numerical methods were presented for stress intensity factor analyses of two-dimensional interfacial crack between dissimilar anisotropic materials subjected to thermal stress. The virtual crack extension method and the thermal M-integral method for a crack along the interface between two different materials were applied to the thermoelastic interfacial crack in anisotropic bimaterials. The moving least-squares approximation was used to calculate the value of the thermal M-integral. The thermal M-integral in conjunction with the moving least-squares approximation can calculate the stress intensity factors from only nodal displacements obtained by the finite element analysis. The stress intensity factors analyses of double edge cracks in jointed dissimilar isotropic semi-infinite plates subjected to thermal load were demonstrated. Excellent agreement was achieved between the numerical results obtained by the present methods and the exact solution. In addition, the stress intensity factors of double edge cracks in jointed dissimilar anisotropic semi-infinite plates subjected to thermal loads were analyzed. Their results appear reasonable.     

Predicting fatigue crack growth rate in a welded butt joint: The role of effective R ratio in accounting for residual stress effect

A simple and efficient method is presented in this paper for predicting fatigue crack growth rate in welded butt joints. Three well-known empirical crack growth laws are employed using the material constants that were obtained from the base material coupon tests. Based on the superposition rule of the linear elastic fracture mechanics, welding residual stress effect is accounted for by replacing the nominal stress ratio (R) in the empirical laws by the effective stress intensity factor ratio (R_eff). The key part of the analysis process is to calculate the stress intensity factor due to the initial residual stress field and also the stress relaxation and redistribution due to crack growth. The finite element method in conjunction with the modified virtual crack closure technique was used for this analysis. Fatigue crack growth rates were then calculated by the empirical laws and comparisons were made among these predictions as well as against published experimental tests, which were conducted under either constant amplitude load or constant stress intensity factor range. Test samples were M(T) geometry made of aluminium alloy 2024-T351 with a longitudinal weld by the variable polarity plasma arc welding process. Good agreement was achieved.