Analytical and finite element analysis of the concrete stress intensity factor with carbon fibers

Adaptive Gaussian process regression as an alternative to FEM for prediction of stress intensity factor to assess fatigue degradation in offshore pipeline

This paper deals with the analysis of the thermal stress intensity factor for interfacial crack beneath a coating-layer subjected to uniform change of temperature by using the finite element method. In the present method, the stress values at the crack tip calculated by FEM are used under the same mesh pattern and the stress intensity factors are evaluated from the ratio of stress values at the crack-tip-node between a given and a reference problems. This method is based on the fact that the singular stress field near the interface crack tip is controlled by the stress values at the crack tip calculated by FEM. In this calculation, for the center interface crack in the finite rectangular bonded plate, it is found that the dimensionless stress intensity factors for various material combinations are the same when the Dundurs' parameter is the constant. The dimensionless factors of interface crack beneath the coating layer are analyzed for any material combinations and the effect of material combinations and the crack size on the dimensionless stress intensity factors are considered.

A plate containing a central crack and subjected to biaxial stresses has been studied by a finite element method using ANSYS. The stress intensity factor was calculated using displacement extrapolation method and Dugdal model. From the results, it was found that the stress intensity factors increased with the increasing load ratio. There was good agreement between experimental and theoretical results.

The aim of the present work is to provide a parametric analysis of stress intensity factor (SIF) in different functionally graded material (FGM) plates using the extended finite element method (XFEM). Exponential, power laws and sigmoid functions have been used for the material gradation of FGM plates. The relations of SIF have been presented with crack length and FGM material properties such as material modulus ratio, FGM layer thickness and power-law index. The present work reveals that the FGM material properties considerably affect the SIF values. Out of four FGM material models considered in this study, the sigmoid FGM model shows the least value of SIF.

The collapse of overhanging rock is a common geological hazard in mountainous areas. The stability of overhanging rock is usually determined by the growth of a crack along a main structural plane. On the basis of linear fracture mechanics combined with the stress concentration coefficient, an analytical method to determine the stress intensity factor (SIF) of overhanging rock is developed to evaluate its stability. Experiments on pre-cracked sandstone were carried out to simulate failure of overhanging rock and verify the analytical solution to fracturing and failure of overhanging rocks. Additionally, numerical solutions using the finite element method are derived to compare with the experimental results. The J-integral and displacement extrapolation methods are used to determine stress changes at the crack tip in the overhanging rocks, and the results confirm that the analytical solutions are consistent with the results of the numerical solutions, including the displacement extrapolation used to analyze the SIF of the overhanging rock. The ratio of fracture toughness to effective SIF at the crack tip can be considered useful when examining the stability of overhanging rock.

This paper deals with the analysis of the thermal stress intensity factor for interfacial crack in dissimilar materials subjected to uniform change of temperature by using the finite element method. In the present method, the stress values at the crack tip calculated by FEM are used under the same mesh pattern and the stress intensity factors are evaluated from the ratio of stress values at the crack-tip-node between a given and a reference problems. This method is based on the fact that the singular stress field near the interface crack tip is controlled by the stress values at the crack tip calculated by FEM. As the reference problems, a single interface crack in an infinite bi-material plate subjected to tension and shear is selected in this study. The accuracy of the present analysis is verified by the comparing the present results with the results obtained by difference mesh sizes and other researches. The calculation shows that the present method has the sufficient accuracy in the interface crack problems under thermal stress.

The variation of stress intensity factors along the crack front of a crack penetrating through the thickness of a plate is analysed by the finite-element method on the basis of concept of the superposition of analytic and finite-element solutions, which has been successfully employed for two-dimensional and axi-symmetric three-dimensional crack problems.In three-dimensional problems, difficulties exist in finding analytic solutions of the governing differential equations, which have the singularity for cracks. In the present paper the authors propose a method of constructing appropriate series of analytic solution which does not satisfy the governing equation but can easily approximate the variation of stress intensity factors.As a numerical example the stress intensity factor of a compact tension specimen is calculated. It is shown that the stress intensity factor takes the maximum on the middle-surface, which is 7-15% higher than the two-dimensional value.

Stress intensity factors due to surface crack propagation were analyzed by using the influence function method and inherent strain analysis of the residual stress fields caused by welding. The initial residual stress in a plate welded-butt joint was calculated by using inherent strain analysis, and the redistribution of residual stress and the stress intensity factor due to crack propagation were analyzed as changes in the structure's shape. Stress intensity factor was also calculated by using an influence function database. The stress intensity factor in the residual stress fields due to crack propagation obtained by using inherent strain analysis completely agreed with that obtained by using the influence function method. The results of the crack propagation analysis were compared with the experimental results of a fatigue test. It was validated that both the inherent strain analysis and the influence function method were efficient for analyzing stress intensity factors in residual stress fields caused by welding.

The fatigue life of an externally cracked modern tank gun barrel is controlled by the prevailing combined stress intensity factor (SIF) <em>K</em>_<em>IN</em>, which consists of two components:<em>K</em>_<em>IP</em>-the SIF caused by internal pressure; <em>K</em>_<em>IA</em>-the positive SIF due to the tensile residual stresses induced by autofrettage. <em>K_IA</em> values for a single external radial semi-elliptical crack originating at the outer surface of an autofrettaged gun barrel were calculated for a large number of crack configurations by Perl and Saley. In order to assess the combined effect of overstraining and the pressurizing of the barrel during firing, values of <em>K</em>_<em>IP</em>, the SIF caused by internal pressure, and those of <em>K</em>_<em>IN</em>, the combined SIF, are evaluated. The 3D analysis is performed using the finite element method (FEM) employing singular elements along the crack front. The novel realistic overstrain residual stress fields, incorporating the Bauschinger effect, for the three types of autofrettage, Swage, Hydraulic and Hill's, previously developed, are applied to the barrel. The RSFs are simulated in the finit element (FE) analysis using equivalent temperature fields. Values of <em>K</em>_<em>IP</em> and <em>K</em>_<em>IN</em> are evaluated for a typical barrel of radii ratio <em>R</em>_<em>0</em>/<em>R</em>_<em>i</em>=2, crack depths (<em>a/t</em>=0.005-0.1), crack ellipticities (<em>a/c</em>=0.2-1.0), and five levels of the three types of autofrettage, (<em>ε</em>=40%, 60%, 70%, 80%, and 100%). A detailed analysis of the effect of the above parameters on the prevailing SIF is conducted. All three types of autofrettage are found to have a detrimental effect on the barrel's fatigue life. However, the magnitude of life reduction is autofrettage-type dependent. In the case of external cracking, Hydraulic autofrettage is found to be somewhat superior to Swage autofrettage, and Hill's autofrettage is found to be non-realistic. Finally, the results accentuate the importance of the three dimensional analysis and the incorporation of the Bauschinger effect.

Delamination at ply drops in composites with thickness tapering has been a concern in applications of carbon fibers. This study explored the resistance to delamination under fatigue loading of carbon and glass fiber prepreg laminates with the same resin system, containing various ply drop geometries, and using thicker plies typical of wind turbine blades. Applied stress and strain levels to produce significant delamination at ply drops have been determined, and the experimental results correlated through finite element and analytical models. Carbon fiber laminates with ply drops, while performing adequately under static loads, delaminated in fatigue at low maximum strain levels except for the thinnest ply drops. The lower elastic modulus of the glass fiber laminates resulted in much higher strains to produce delamination for equivalent ply drop geometries. The results indicate that ply drops for carbon fibers should be much thinner than those commonly used for glass fibers in wind turbine blades.

The corner point singularity of surface cracks by finite element method (FEM) has become a numerical concern decades ago. The literature showed that the stress intensity factors (SIFs) at the corner points were often excluded. Further, most SIFs were reported for larger ratios of the crack depth over cylinder diameter. This paper presents the SIFs (Modes I, II and III) of a semi-elliptical surface crack at a solid round bar under torsion. The tetrahedral and hexahedral elements were used in the finite element modelling. The effects of the loading mode and the crack aspect ratio on the corner point singularity were discussed. The tetrahedral meshing was generally observed to be more suitable for modelling relatively small surface cracks, particularly in respect to the corner point singularity. For all loading modes, the SIFs away from the corner points of using the tetrahedral meshing were found to have fairly good agreement with those by dual boundary element method (DBEM).

The Extended Finite Element Method is a numerical solution based on the Finite Element Method (FEM) XFEM has really become a very important generalization of classical finite element techniques, by establishing a mesh independent generalization of classical finite elements to reduce the mesh-dependent shortcomings of the solution. The application of XFEM in crack simulation should improve the modeling of the crack tip environment and also apply to generalized advanced global failure criteria, which is specifically designed to deal with problems in the engineering field Such as the fracture behaviour model. The purpose of this paper is to identify the application of the Extended Finite Element Method to a technical problem, namely fracture behaviour model. The media used is pure boneless concrete modelled with COMSOL Multiphysics 5.6 software by combining stress ratio, lateral strain due to axial loading, concrete density, and crack growth rate. The crack growth process provides initial prolonged growth along with the increase in crack size. In the end, the growth is faster. The reason for this accelerated growth is the stress intensity factor at the crack tip. As the crack grows, the stress intensity factor increases, leading to faster growth. The crack grows until it reaches a critical value, and fracture occurs. The test results obtained the cause of failure: the critical stress intensity is exceeded. See a comparison of crack size and stress cycle as the crack size increases. This accelerated growth is because the growth rate depends on the stress intensity factor at the crack tip, and the stress intensity factor depends on the crack size. As the crack grows, the stress intensity factor increases, leading to faster growth. The crack grows to a critical size, and failure occurs. The results show a relatively strong relationship between increasing crack size and increasing crack growth rate.

Electrical conductivity and mechanical properties of melt-spun ternary composites comprising PMMA, carbon fibers and carbon black

Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier–Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack subjected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.

The influence of the Bauschinger effect (BE) on the three dimensional, Mode I, combined stress intensity factor (SIF) distributions for arrays of longitudinal coplanar, surface cracks emanating from the bore of a fully or partially autofrettaged thick-walled cylinder is investigated. The combined SIFs, KIN, that depend on pressure effects and the “realistic”—Bauschinger effect dependent Autofrettage (BEDA), or, that depend on pressure effects and the “ideal”—Bauschinger effect independent autofrettage (BEIA), are obtained and compared for crack depth to wall thickness, a∕t=0.01–0.25; crack ellipticity, a∕c=0.5–1.5; crack spacing ratio, 2c∕d=0.25–0.75; and autofrettage level, e=30%, 60%, and 100%. The 3D analysis is performed via the finite element method and the submodeling technique, employing singular elements along the crack front. Both autofrettage residual stress fields, BEDA and BEIA, are simulated using an equivalent temperature field. The combined SIF, KIN, is found to vary along the crack front with the maximum determined by the crack ellipticity, crack depth, and crack spacing ratio. For a partially autofrettaged cylinder, the influence of the BE on the combined SIF, KIN, is substantially reduced as the level of overstrain becomes smaller. For some cases, when comparing like crack distributions, the KIN values obtained from the BEDA model are found to be as much as 100% higher than the KIN values that are computed using the BEIA model. A pressurized thick-walled cylinder with BEDA can be most critical when small cracks are farther apart. As crack depth increases, or when the spacing between cracks is smaller, the SIFs increase. Though the differences in the BEDA SIF, KIA, between e=100% and 60% are small (7–15%, in most cases), the increased level of autofrettage produces a 23–30% decrease in the combined SIF values, KIN. In certain cases, the BEIA model implies an infinite fatigue life, whereas the BEDA model for the same parameters implies a finite life. Therefore, it is important to perform a full 3D analysis to determine the real life cycle of the pressurized cylinder for materials that exhibit the BE.