Cracks In Finite Thickness Plate Research Articles

Stress Intensity Factors for Embedded, Surface, and Corner Cracks in Finite-Thickness Plates Subjected to Tensile Loading.

The aim of this study is to obtain the stress intensity factor (SIF) along the crack front of elliptical cracks located in finite-thickness plates subjected to imposed displacement or applied tensile load, for different crack geometries (relative depths and aspect ratios) and crack configurations (embedded, surface, and corner). The SIF was calculated from the J-integral, obtained by the finite element method. The results show how the SIF grows with the increase in the relative crack depth and with the decrease in the aspect ratio, with the corner crack being the most dangerous configuration and the embedded crack the most favorable configuration. By increasing the plate length, the SIF rises when the plate is under imposed displacement and decreases when the plate is subjected to applied tensile load, both cases tending towards the same SIF curve.

2D weight functions of stress intensity factors for high aspect ratio semi-elliptical surface cracks in finite thickness plate

This paper presents the application of the weight function method for calculating the stress intensity factors for high aspect ratio semi-elliptical surface cracks in finite thickness plate subjected to arbitrary two-dimensional stress fields. Based on the formulation initially proposed by Wang and Glinka (2009), an extended 2D weight function for surface cracks with aspect ratio 1.0 ≤ a/c ≤ 8.0 is developed. The unknown coefficients in the formulation can be determined from reference stress intensity factors which are obtained by finite element analysis with the J-integral method. The effectiveness of the proposed weight functions have been verified by comparing the stress intensity factors available in the literatures and those obtained from FEM for several linear and nonlinear two-dimensional stress distributions, indicating a good accuracy. The present results complement the application range of 2D weight functions for low-aspect-ratio cracks, 0.0 < a/c ≤ 1.0, developed by the previous researchers.

Aspect Ratio Evolution in Embedded, Surface, and Corner Cracks in Finite-Thickness Plates under Tensile Fatigue Loading

This article deals with the computational modelling of the fatigue crack aspect ratio evolution in embedded, surface, and corner cracks located in finite-thickness plates under tensile fatigue. The approach is based on the Paris law for fatigue propagation and an expression for the stress intensity factor (SIF) provided by Newman and Raju. Numerical results indicate that the crack path develops in such a manner that all flaws tend to reach similar aspect ratios, i.e., a preferential crack path does exist along which there is a one-to-one relationship between the aspect ratio and the relative crack depth (a sort of master curve in the matter of fatigue crack path evolution). Such a reference curve corresponds to that of a very superficial initial flaw with almost circular shape. The convergence (quicker or slower approach between fatigue crack paths starting from different initial defects) is higher for surface flaws than for corner cracks, and quicker for the latter than for embedded discontinuities. Corner defects increase their size faster than surface cracks, and the latter do the same quicker than the embedded ones.

Analysis of semi-elliptical surface cracks in the interface of bimaterial plates under tension and bending

A semi-elliptical surface crack widely exists in the multilayered electronic devices, fibre reinforced laminated composites and solder joints. To ensure the safety of these structural components, three-dimensional interface fracture mechanics analysis is required. In this study, three-dimensional finite element analyses have been conducted to calculate the fracture mechanics parameters, including the stress intensity factors (SIFs), the strain energy release rate G and two phase angles ψ and φ for semi-elliptical interface surface cracks in finite thickness plates. A wide range of crack aspect ratios and relative depths are considered. The SIF computations are presented along the front of a three-dimensional bimaterial interface cracks with a/t values of 0.2, 0.4, 0.6 or 0.8 and a/c values of 0.2, 0.4, 0.6 or 1.0. In particular, far-field loads i.e., remote tension and bending, and various combinations of bimaterials are investigated. These fracture mechanics parameters’ solutions are suitable for fracture and fatigue life prediction for semi-elliptical bi-material interface surface cracks in engineering components.

Surface cracks in finite thickness plates under thermal and displacement-controlled loads – Part 1: Stress intensity factors

In this study, surface cracks in finite-thickness plates subjected to thermal or displacement-controlled loads are considered. These loads produce a uniform or bending stress state, i.e., a linear distribution over the thickness, in the corresponding uncracked structure. Stress intensity factors are calculated using enriched crack tip finite elements and compared with those of the respective mechanical loads. It is shown that the stress intensity factors along the crack front for plates under thermal or displacement-controlled loads are lower than those of cracks under mechanical loads and that this difference increases with increasing crack size due to the increasing compliance of the structure.

Surface cracks in finite thickness plates under thermal and displacement-controlled loads – Part 2: Crack propagation

Surface cracks in finite-thickness plates subjected to thermal or displacement-controlled loads are considered with a focus on crack propagation. Detailed crack propagation analyses are performed and the effect of loading type on crack propagation patterns and lives are systematically investigated. The results show that although there are some slight differences between the crack propagation patterns and lives for the uniform stress and displacement loading, there exist increasingly higher differences for the bending stress and displacement loads during crack growth. It is shown that propagation lives are higher in the case of displacement/thermal loading compared to those of mechanical/stress loads.

English

Shielding interaction effects of two parallel edge cracks in finite thickness plates subjected to remote tension load is analyzed using a developed finite element analysis program. In the present study, the crack interaction limit is evaluated based on the fitness of service (FFS) code, and focus is given to the weak crack interaction region as the crack interval exceeds the length of cracks (b > a). Crack interaction factors are evaluated based on stress intensity factors (SIFs) for Mode I SIFs using a displacement extrapolation technique. Parametric studies involved a wide range of crack-to-width (0.05 ≤ a/W ≤ 0.5) and crack interval ratios (b/a > 1). For validation, crack interaction factors are compared with single edge crack SIFs as a state of zero interaction. Within the considered range of parameters, the proposed numerical evaluation used to predict the crack interaction factor reduces the error of existing analytical solution from 1.92% to 0.97% at higher a/W. In reference to FFS codes, the small discrepancy in the prediction of the crack interaction factor validates the reliability of the numerical model to predict crack interaction limits under shielding interaction effects. In conclusion, the numerical model gave a successful prediction in estimating the crack interaction limit, which can be used as a reference for the shielding orientation of other cracks.

Weight functions for the determination of stress intensity factor and T‐stress for semi‐elliptical cracks in finite thickness plate

ABSTRACTThis paper presents the application of weight function method for the calculation of stress intensity factors (K) and T‐stress for surface semi‐elliptical crack in finite thickness plates subjected to arbitrary two‐dimensional stress fields. New general mathematical forms of point load weight functions for K and T have been formulated by taking advantage of the knowledge of a few specific weight functions for two‐dimensional planar cracks available in the literature and certain properties of weight function in general. The existence of the generalised forms of the weight functions simplifies the determination of specific weight functions for specific crack configurations. The determination of a specific weight function is reduced to the determination of the parameters of the generalised weight function expression. These unknown parameters can be determined from reference stress intensity factor and T‐stress solutions. This method is used to derive the weight functions for both K and T for semi‐elliptical surface cracks in finite thickness plates, covering a wide range of crack aspect ratio (a/c) and relative depth (a/t) at any point along the crack front. The derived weight functions are then validated against stress intensity factor and T‐stress solutions for several linear and nonlinear two‐dimensional stress distributions. These derived weight functions are particularly useful for the development of two‐parameter fracture and fatigue models for surface cracks subjected to fluctuating nonlinear stress fields, such as these resulting from surface treatment (shot peening), stress concentration or welding (residual stress).

Investigation on &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;11&lt;/sub&gt;-Stress for Semi-Elliptical Surface Cracks in Finite Thickness Plates under Remote Tension

In the present work, three-dimensional finite element analyses have been conducted to calculate the-stress for semi-elliptical surface cracks in finite thickness plates under remote tension. The-stress solutions are presented along the crack front for cracks with values of 0.2, 0.4, 0.6 or 0.8 and values of 0.2, 0.4, 0.6 or 1.0. The current-stress solutions are suitable to be used as the constraint parameter for the fracture analysis.

Point Load Weight Functions for Semi-Elliptical Cracks in Finite Thickness Plate

Abstract This paper presents the application of the weight function method for the calculation of stress intensity factors for surface semi-elliptical cracks in finite thickness plates subjected to arbitrary two-dimensional stress fields. A new general mathematical form of point load weight function has been formulated by taking advantage of the knowledge of a few specific weight functions for two-dimensional planar cracks available in the literature and certain properties of the weight function in general. The existence of the generalized form of the weight function simplifies the determination of a specific weight function for specific crack configurations. The determination of a specific weight function is reduced to the determination of the parameters of the generalized weight function expression. These unknown parameters can be determined from reference stress intensity factor solutions. This method is used to derive the weight functions for semi-elliptical surface cracks in finite thickness plates. The derived weight functions are then validated against stress intensity factor solutions for several linear and non-linear two-dimensional stress distributions. The derived weight functions are particularly useful for the fatigue crack growth analysis of planar surface cracks subjected to fluctuating nonlinear stress fields resulting from surface treatment (shot peening), stress concentration, or welding (residual stress)

Stress intensity factor equations for mixed-mode surface and corner cracks in finite-thickness plates subjected to tension loads

Normalized mixed-mode stress intensity factor equations are presented for deflected and inclined circular surface and corner cracks in finite-thickness plates under uniform remote tensile loading. The equations are obtained by performing non-linear regression analyses on the data from previous numerical solutions based on three-dimensional enriched finite elements. In the equations, the effects of deflection/inclination angles and plate thickness on mixed-mode stress intensity factors are included. The comparisons of normalized stress intensity factors from the equations with those of the finite element analyses show good agreement. Thus, it is concluded that, as a reasonable approximation, the presented equations can be used to assess stress intensity factors and fracture conditions of mixed-mode circular surface and corner cracks in finite-thickness plates.

Investigation on Mixed Mode Stress Intensity Factors for Inclined Surface Crack in Finite-Thickness Plates and Parameters Influence

In this paper, mixed mode stress intensity factor (SIF) solutions are computed for inclined surface cracks in finite-thickness plates. The S-version finite element method (S-FEM), which is an adaptive method and multi-scale computing method, are employed in the analyses. When S-FEM is applied to solve the fracture problem, local mesh model including cracks can be built independently from the global mesh model for modeling overall structure. The local model is superposed on the g- lobal one. Therefore, it is easy to introduce cracks in an existing mesh model. The influences of inc- lination angles, crack shape and plate thickness on the mixed mode fracture solution were investiga- ted. The solutions presented can be used to assess fail/safe conditions and fatigue crack growth for the three-dimensional cracks studied.

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.

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.

Weight functions forT-stress for semi-elliptical surface cracks in finite-thickness plates

This paper presents the application of the weight function method for the calculation of elastic T-stress for semi-elliptical surface cracks. First, the weight function method for the calculation of T-stress previously developed for two-dimensional crack problems was extended for the T-stress calculation for three-dimensional crack problems. Then, the T-stress weight functions for the deepest point (corresponding to the parametric angle ϕ = 90°) and for any general point (5° ≤ ϕ &lt; 90°) along the crack front of semi-elliptical surface cracks in finite-thickness plates for wide ranges of crack aspect ratios a/c and relative depths a/t were derived. The resulting weight functions were validated using available finite element results for non-linear stress fields and remote tension and bending cases, and very good agreement was achieved. The weight functions are suitable for the calculation of the T-stress under complex loading conditions for any general point (5° ≤ ϕ ≤ 90°) of surface cracks with wide ranges of aspect ratios, 0 ≤ a/c ≤ 1, and relative depths, 0 ≤ a/t ≤ 0.8.

Analysis of interacting semi-elliptical surface cracks in finite thickness plates under remote bending load

Interaction effects of two coplanar self-same shallow and deep semi-elliptical surface cracks in finite thickness plates subjected to remote tension have been previously investigated by Sethuraman et al. Using the finite element based force method. In the present study, the effect of remote bending load on interacting semi-elliptical surface cracks in a finite thickness plate is analyzed. Stress intensity factors are evaluated along the entire crack front using a modified force method based on the three-dimensional finite element solution. The line spring model has also been used to evaluate stress intensity factors at the deepest point of a crack using shell finite element analysis. Parametric studies involving a wide ranges of geometric dimensions and crack configurations viz. crack shape aspect ratio (0.2≤ a/ c≤1.0), crack depth ratio (0.2≤ a/ t≤0.9), relative crack location (0.2≤2 c/ d≤0.9) and normalized location on the crack front (0≤2 ϕ/π≤2) are carried out for numerical estimation of crack interaction factors. Due to the crack interaction, the stress intensity factor distribution is observed to be asymmetric along the crack front. The interaction is also observed to cease when the distance between two cracks is more than five times the crack width (i.e. 2 c/ d less than 0.2) irrespective of crack shape aspect ratio. Finally, an empirical relation is proposed for the evaluation of crack interaction crack interaction factors for the range of parameters considered. For the ranges considered, the proposed empirical relation predicts the crack interaction factors at the inner and outer surface points of the crack within ±4% of the three-dimensional finite element solutions.

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

Using three-dimensional enriched finite elements, mixed mode stress intensity factor solutions are presented for deflected and inclined surface cracks in finite-thickness plates under uniform tensile remote loading. It is demonstrated that the enriched finite element technique provides fracture solutions for these types of problems in a very direct and convenient manner without a need for post-processing the finite element solution. Mixed mode stress intensity factor solutions are generated for semi-circular surface 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. Based on the computed mixed mode stress intensity factors, crack propagation angles along the deflected and inclined crack fronts are also determined.

Elastic T-stress solutions for semi-elliptical surface cracks in finite thickness plates subject to non-uniform stress distributions

This paper deals with the T-stress calculation for surface cracks in plates. Three-dimensional finite element analyses have been conducted to calculate the elastic T-stress for semi-elliptical surface cracks in finite thickness plates. The T-stress solutions are presented along the crack front for cracks with a/ t values of 0.2, 0.4, 0.6 or 0.8 and a/ c values of 0.2, 0.4, 0.6 or 1.0. Four stress distributions: uniform, linear, parabolic and cubic were applied to the crack face. The superposition method for the calculation of T-stress for three-dimensional cracks is presented. Using the obtained solutions for the four polynomial stress distributions, the application of the superposition method to calculate the T-stress for other stress distributions is demonstrated. These current T-stress solutions together with the corresponding K or J values for surface cracks are suitable for the analysis of constraint effects for surface cracked components under non-uniform stress distributions.

Elastic T-stress solutions for semi-elliptical surface cracks in finite thickness plates

Three-dimensional finite element analyses have been conducted to calculate the elastic T-stress for semi-elliptical surface cracks in finite thickness plates. Far-field tension and bending loads were considered. The analysis procedures and results were verified using both exact solutions and approximate solutions. The T-stress solutions are presented along the crack front for cracks with a/ t values of 0.2, 0.4, 0.6 or 0.8 and a/ c values of 0.2, 0.4, 0.6 or 1.0. Based on the present finite element calculations for T-stress, empirical equations for the T-stress at three locations: the deepest, the surface and the middle points of the crack front under tension or bending are presented. The numerical results are approximated by empirical formulae fitted with an accuracy of 1% or better. They are valid for 0.2⩽ a/ c⩽1 and 0⩽ a/ t⩽0.8. These T-stress results together with the corresponding K or J values for surface cracks are suitable for the analysis of constraint effects for surface cracked components.

Stress intensity factors and weight functions for deep semi‐elliptical surface cracks in finite‐thickness plates

ABSTRACT Three‐dimensional finite element analyses have been conducted to calculate the stress intensity factors for deep semi‐elliptical cracks in flat plates. The stress intensity factors are presented for the deepest and surface points on semi‐elliptic cracks with a/t‐values of 0.9 and 0.95 and aspect ratios (a/c) from 0.05 to 2. 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 surface cracks with a/t= 0.6 and 0.8 to derive weight functions over the range 0.05 ≤ a/c ≤ 2.0 and 0.6 ≤ a/t ≤ 0.95. The weight functions were then verified against finite element data for parabolic or cubic stress distributions. Excellent agreements are achieved for both the deepest and surface points. The present results complement stress intensity factors and weight functions for surface cracks in finite thickness plate developed previously.