Plane stress finite element prediction of mixed-mode rubber fracture and experimental verification

This study demonstrates through experimental validation, that one can predict critical loads of arbitrarily shaped cracked rubber specimens of the mixed-mode type (mode I and II) using a plane stress finite element method and utilizing material constants that characterize the mechanical and fracture properties of SBR (Styrene Butadiene Rubber) material determined from experimental tests on a mode I specimen. Conversely, the finite element method can be used to extract useful critical tearing energy information from complicated, arbitrarily shaped cracked rubber specimens. The predicted critical loads or critical tearing energies for crack growth initiation and final fracture, as well as the crack growth initiation direction are compared to the experimental data with good agreement.     

Quantification of the yield strength-to-elastic modulus ratio effect on TES plastic loads from finite element limit analyses of elbows

This paper quantifies the effect of the yield strength-to-elastic modulus ratio on twice-elastic-slope plastic loads for 90-degree elbows under in-plane and out-of-plane bending. Based on extensive and systematic finite element limit analyses using elastic-perfectly plastic materials, simple regression equations between the yield strength-to-elastic modulus ratio and twice-elastic-slope plastic loads for elbows under in-plane closing, in-plane opening and out-of-plane bending are proposed, and validated against published experimental data. Applicability of the proposed equations to circumferential cracked elbows under in-plane bending is also investigated.     

Fracture assessment of damaged square hollow section (SHS) K-joint using BS7910:2005

A pre-cracked square hollow section K-joint was tested under static loads up to failure. It is found that the load-displacement curves are in good agreement with the finite element results. Ductile tearing was observed to initiate from the crack front parallel to the chord side wall where fracture toughness is smaller. Using plastic collapse load obtained via twice elastic compliance technique and fracture toughness obtained from crack tip opening displacement, the two fracture parameters K_r and L_r are plotted on the standard failure assessment diagram. It shows a conservative assessment for the cracked K-joint subjected to brace end axial loads.     

Ductile tearing analyses of cracked TP304 pipes using the multiaxial fracture strain energy model and the Gurson–Tvergaard–Needleman model

Ductile crack growth behaviours of TP304 pipes containing different circumferential defects were investigated in the study. Finite element (FE) damage analysis of the ductile fracture was carried out based on an uncoupled multiaxial fracture strain energy (MFSE) model with only two model parameters, which can be calibrated by data from tensile tests and fracture toughness tests. For the purpose of comparison, the Gurson–Tvergaard–Needleman (GTN) model was also employed in the FE damage analysis. It is observed that the MFSE model can reproduce the ductile tearing experiments as excellently as the GTN model does. Despite its simplicity, the MFSE model can reasonably predict the magnitudes of the crack initiation load and maximum load, the load‐line displacement, the crack mouth opening displacement, the crack extension and the crack profiles in the full‐scale cracked pipe tests.     

Ductile tearing simulation of Battelle pipe test using simplified stress‐modified fracture strain concept

In this paper, numerical ductile tearing simulation results are compared with six circumferential through‐wall and surface cracked pipes made of two materials (SA‐333 Gr. 6 and A106 Gr. B carbon steels), performed at Battelle. For simulation, a model using a simplified fracture strain model is employed, by analysing tensile data of the material. By comparing experimental J‐R data with FE simulation results, the damage model dependent on the element size is determined based on the ductility exhaustion concept. The model is used to simulate ductile tearing behaviour of six circumferential through‐wall and surface cracked pipes. In all cases, simulated results agree well with experimental load, crack length and crack mouth opening displacement versus load line displacement data.     

Elastic–plastic J and COD estimation schemes for 90° elbow with throughwall circumferential crack at intrados under in-plane opening moment

Leak-before-break (LBB) assessment of primary heat transport piping of nuclear reactors involves detailed fracture assessment of pipes and elbows with postulated throughwall cracks. Fracture assessment requires the calculation of elastic–plastic J-integral and crack opening displacement (COD)¹ for these piping components. Analytical estimation schemes to evaluate elastic–plastic J-integral and COD simplify the calculations. These types of estimation schemes are available for pipes with various crack configurations subjected to different types of loading. However, such schemes for elbow (or pipe bend), which is one of the important components for LBB analyses, is very meager. Recently, elastic–plastic J and COD estimation scheme has been developed for throughwall circumferentially cracked elbow subjected to closing bending moment. However, it is well known that the elbow deformation characteristics are distinctly different for closing and opening bending modes because the ovalisation patterns of elbow cross section are different under these two modes. Development of elastic–plastic J and COD estimation scheme for an elbow with throughwall circumferential crack at intrados subjected to opening bending moment forms the objective of the present paper. Experimental validation of proposed J-estimation scheme has been provided by comparing the crack initiation, unstable ductile tearing loads and crack extension at instability with the test data. The COD estimation scheme has been validated by comparing the COD of test data with the predictions of the proposed scheme.     

Ductile failure analysis and crack behavior of X65 buried pipes using extended finite element method

This paper aims to study the ductile fracture mechanism of API X65 buried pipes including crack initiation and propagation using the extended finite element method (XFEM). First, the crack evolution histories of X65 specimens with initial crack-like flaws during tensile and three-point bending tests are illustrated, and the numerical results are compared with experimental data. In addition, effects of different crack configurations, damage initiation and evolution criteria are investigated. Second, the burst processes of straight pipes with initial gouge flaws are presented, and the FE results are compared with assessment in related standards and experiments. Finally, the crack onset and growth of buried pipes due to deflection arising from landslide movements are predicted, and the numerical results are compared with previous study. Particularly, the internal pressure, wall thickness, and soil properties on crack behavior and limit load-bearing ability are investigated. This paper provides a fundamental support for the integrity assessment and safety evaluation of buried pipes.     

THE FRACTURE BEHAVIOUR OF AN AXIAL CRACK IN A PRESSURISED PIPE

Abstract— The multiple specimen technique was developed to measure the crack growth fracture resistance of a through axial crack in a pressurised pipe and the results compared with data measured from test specimens. The comparison indicates that there is no significant difference between pipe and specimen behaviour. The results are also compared with elastic-plastic three-dimensional finite element analyses of the pipe and the R6 failure assessment curve. Reasonably good agreement was found between the experimental results and finite element analyses. The experimental results all lie outside the material specific failure assessment curve of the R6 structural integrity assessment procedure.     

Limit pressures of 90° elbows with circumferential surface cracks

This paper provides approximate limit pressure solutions for circumferential cracked elbows, resulting from small strain finite element limit analyses using elastic-perfectly plastic materials. Circumferential through-wall and constant-depth surface cracks of which the circumferential lengths are limited to 50% of the circumference are considered. Two locations along the longitudinal direction are considered; one in the centre of the elbow, and the other in the junction between the elbow and the attached straight pipe. Along the circumference, either extrados or intrados cracks are considered. It is found that limit pressures of circumferential cracked elbows are not affected by the presence of the circumferential surface crack, unless it is sufficiently deep and long. Moreover, normalized limit pressures with respect to un-cracked limit pressures decrease almost linearly with increasing the relative crack depth and length. Based on finite element results, approximate closed-form solutions for limit pressures are proposed.     

Plastic collapse moment equations of throughwall axially cracked elbows subjected to in-plane bending moment

A throughwall axial crack may develop in an elbow or pipe bend due to service related degradation mechanism. It is very important to know the plastic collapse moment (PCM) of an elbow in the presence of a throughwall axial crack. The existing PCM equations of throughwall axially cracked (TAC) elbows are based on very few test data points of Griffiths without detailed analyses and also the range of applicability of their proposed equations are limited. Further, they do not differentiate between closing and opening modes of bending although deformation characteristics under these two modes are completely different. Therefore, the present study has been undertaken to investigate through 3D elastic-plastic finite element analysis. A total of 84 elbows with various sizes of axial cracks (a/D_m = 0-1), different wall thickness (R/t = 5-20), different elbow bend radii (R_b/R = 2, 3) and two different bending modes, namely closing and opening have been considered in the analysis. Elastic-perfectly plastic stress-strain response of material has been assumed. Both geometric and material non-linearity are considered in the analysis. Crack closing is observed in most of the cases. To capture the crack closure effect, contact analysis has been performed. Plastic collapse moments have been evaluated from moment-end rotation curves by twice-elastic slope method. From these results, closed-form equations are proposed to evaluate plastic collapse moments of elbows under closing and opening mode of bending moment. The predictions of these proposed equations are compared with the test data available in the literature. Matching between predictions and experimental results is found to be satisfactory.     

Fracture Analysis of a Special Cracked Lap Shear (CLS) Specimen with Utilization of Virtual Crack Closure Technique (VCCT) by Finite Element Methods

Some of the most important characteristics due to a fracture investigation of a special specimen are taken into account. Debonding considerations for a composite/steel cracked lap shear (CLS) specimen by utilization of finite element methods (FEM) as well as a virtual crack closure technique (VCCT) approach have been investigated. Strain energy release rate, delamination load case and direct cycle fatigue analysis have taken into consideration in this study, and the corresponding simulations have been done by ABAQUS/Standard. Linear elastic fracture criteria are used for validation of numerical results from the simulation. For comparison of three different categories of analysis, some special characteristics such as effective energy release rate ratio, bond state, time at bond failure and opening behind crack tip at bond failure have been illustrated. In this work, a detailed analysis of a special CLS specimen debonding by using VCCT and FEM is presented and varied results for validation of this kind of combination are obtained and have been discussed.     

Calculation of stress intensity factors based on mode I crack opening integral parameters

We present stress intensity factor assessment using nodal displacements of the crack surfaces determined by the finite element method for cracked bodies. The equation is solved by expanding the crack opening displacement in the Chebyshev function, where crack front asymptotic behavior corresponds to the regulations of the linear elastic fracture mechanics. Results of the stress intensity factor calculations are obtained for test problems with analytical solution. Crack opening displacements are defined with the help of the 3D SPACE software package designed to model mixed variational formulation of the finite element method for displacements and strains of the thermoelastic boundary value problems. Translated from Problemy Prochnosti, No. 6, pp. 122–127, November–December, 2008.     

Elastic stress intensity factors and crack opening displacements for circumferential through-walled cracked elbows

This paper provides tabulated solutions of elastic stress intensity factors and crack opening displacements for circumferential through-wall cracked elbows under internal pressure and under in-plane bending, based on extensive three-dimensional elastic finite element analyses covering a wide range of crack lengths and elbow/pipe geometries. The effect of crack length and elbow/pipe geometry on the results is discussed, with particular emphasis on the crack closure behaviour under in-plane bending.     

THE FRACTURE BEHAVIOUR OF A CENTRE CRACKED TENSILE SPECIMEN

Abstract— This paper reviews the stress intensity factor, limit load, compliance and J-integral functions for a centre cracked tensile (CCT) specimen available in the literature. Compliance and J-integral functions are derived from the optimum stress intensity factor and limit load solutions. The functions are compared with the results obtained from two-dimensional finite element analyses of the specimen.
The finite element results have confirmed the accuracy of the compliance and limit load functions available in the literature and suggest that the unloading compliance technique, based on crack mouth opening displacement, could be developed for a CCT specimen. Non-linear finite element analyses have shown that J can be estimated from the measured load versus load-point displacement behaviour providing a/W ≥ 0.5     

A wide range weight function for a single edge cracked geometry with clamped ends

A single edge cracked geometry with clamped ends is well suited for fracture toughness and fatigue crack growth testing of composites and thin materials. Stress intensity factors may be determined by the weight function method. A weight function for the single edge cracked geometry with clamped ends is developed and verified in this paper. It is based on analytical forms for the reference stress intensity factor and crack mouth opening displacement. The analytical forms are shown to be valid, by comparison with finite element results, over a wide range of crack depths and plate aspect ratios. Use of the analytical form enables the weight function to be calculated for any plate aspect ratio without the need for preliminary finite element analysis. Stress intensity factors and crack mouth opening displacements, predicted using this weight function, correlated well with finite element results for non-uniform crack surface stress distributions. This revised version was published online in August 2006 with corrections to the Cover Date.     

A new expression for crack opening stress determined based on maximum crack opening displacement under tension–compression cyclic loading

The maximum crack opening displacement is introduced to investigate the effect of compressive loads on crack opening stress in tension–compression loading cycles. Based on elastic–plastic finite element analysis of centre cracked finite plate and accounting for the effects of crack geometry size, Young's modulus, yield stress and strain hardening, the explicit expression of crack opening stress versus maximum crack opening displacement is presented. This model considers the effect of compressive loads on crack opening stress and avoids adopting fracture parameters around crack tip. Besides, it could be applied in a wide range of materials and load conditions. Further studies show that experimental results of da/dN ? ΔK curves with negative stress ratios could be condensed to a single curve using this crack opening stress model.     

Elastic-plastic fracture mechanics assessment for steam generator tubes with through-wall cracks

The present work provides an elastic‐plastic fracture mechanics (EPFM) assessment scheme for a steam generator tube with a through‐wall crack under internal pressure. Noting that the geometry and material are rather uniform for steam generator tubes, and furthermore the only loading to be considered is internal pressure, an engineering EPFM analysis method is proposed to assess through‐wall cracks in steam generator tubes. Important outcomes of the present work are closed‐form approximations for J and crack opening displacement (COD). Sufficient confidence in the proposed J and COD estimates is gained from good agreements with the finite element results over a wide range of the crack length and pressure magnitude. Another important element of the EPFM assessment is to determine relevant J‐resistance curve for steam generator tubes. To improve the accuracy of predicting tube failure, the present paper also proposes a new method to determine fracture toughness using an actual tubular specimen instead of using a standard specimen, from which J‐resistance curves of steam generator tubes are obtained. Using the proposed J and toughness estimates, maximum pressures of steam generator tubes with through‐wall crack are estimated based on EPFM analysis, which is compared with experimental results and predicted ones based on limit load approach.     

A finite element ductile failure simulation method using stress-modified fracture strain model

This paper proposes a new method to simulate ductile failure using finite element analysis based on the stress-modified fracture strain model. A procedure is given to determine the stress-modified fracture strain as a function of the stress triaxiality from smooth and notched bar tensile tests with FE analyses. For validation, simulated results using the proposed method are compared with experimental data for cracked bar (tensile and bend) tests, extracted from API X65 pipes, and for full-scale burst test of gouged pipes, showing overall good agreements. Advantages in the use of the proposed method for practical structural integrity assessment are discussed.