Stress intensity factors for circumferential through‐wall cracks in thin‐walled cylindrical shells subjected to tension and torsion

In order to assess the structural integrity of tubular members or pipes containing circumferential through‐wall cracks, their stress intensity factor solutions are required. While stress intensity factors for tension and bending are available, few solutions exist for the case of torsion, even though these components may also be subjected to torque. In this paper, the finite element method is used to compute the stress intensity factors for this geometry under tension and torsion. Shell elements are employed to compute the results for thin shells by the means of the displacement extrapolation technique. The computed results indicate that the available analytical solution for torsional loading, which is based on shallow shell theory, is nonconservative for long cracks in thin shells. Shallow shell theory is in general not applicable to long cracks, and the present work is therefore able to provide solutions for a wider range of crack lengths than what is currently available.     

A method to predict failure pressures of steam generator tubes with multiple through-wall cracks

This paper proposes a simple numerical method to predict burst pressures of steam generator tubes with multiple through-wall cracks, based on the stress-modified fracture strain damage model with stress reduction technique. For validation, simulated results using the proposed method are compared with 31 published experimental data of Alloy 600 plates and tubes with single or two through-wall cracks, showing that predicted loads are within 10% of experimentally-measured ones for all cases considered. Furthermore, a parametric study is performed to investigate the interaction effect of two through-wall cracks in Alloy 600 steam generator tubes under internal pressure.     

Analysis of dynamic characteristics of through‐wall cracks between 2 boreholes in the directed fracture controlled blasting

Through‐wall cracks between 2 boreholes in the directed fracture controlled blasting have been always concerned by researchers. Dynamic characteristics of through‐wall cracks between 2 boreholes and lateral crack propagation of boreholes in the double‐borehole slot mode and the synchronous blasting of boreholes were examined using the explosive loading digital dynamic caustics experiment system. And the effects of borehole loading mode and borehole clearance on through‐wall cracks between boreholes were examined using distinct lattice spring model numerical analysis, based on the experiment model. Findings show that the tips of through‐wall cracks between boreholes did not meet directly but staggered, continuously propagated after meeting, and moved closer to the existing anisotropic crack direction. The velocity and acceleration of crack propagation fluctuated. K_I rapidly decreased from the maximum value, then gradually increased after a repeated volatility, and began to decrease after it reached the second peak. During the process of crack propagation, K_II was basically smaller than K_I. The dynamic energy release rate rapidly decreased from the maximum value, reached the second peak after the volatility, and gradually decreased again. The borehole loading mode and borehole clearance had significant effects on through‐wall cracks between boreholes.     

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.     

Ductile fracture simulation of 304 stainless steel pipes with two circumferential surface cracks

In this paper, ductile fracture behaviours of 304 stainless steel pipes with two circumferential surface cracks under pure bending are simulated using finite element damage analyses. Simulations are based on the stress‐modified fracture strain model with the concept that the critical accumulated damage for progressive cracking is assumed to be dependent on an element size. The proposed method can predict not only maximum loads but also complex ductile fracture patterns observed in experiments.     

A new approach to plate theory based on through‐thickness homogenization

A new approach to linear plate theory for layered structures is introduced. The new theory distances itself from the classical strategy where through the thickness displacement functions are assumed a priori. Instead, the homogenization is based on a single assumption that the plate response is a superposition of fundamental states. An equivalent single‐layer (ESL) formulation is presented, which, for the first time, allows accurate three‐dimensional stress and strain fields to be recovered through a postprocessing strategy that is consistent with the theory's assumptions. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

A high‐order generalized FEM for through‐the‐thickness branched cracks

This paper presents high‐order implementations of a generalized finite element method for through‐the‐thickness three‐dimensional branched cracks. This approach can accurately represent discontinuities such as triple joints in polycrystalline materials and branched cracks, independently of the background finite element mesh. Representative problems are investigated to illustrate the accuracy of the method in combination with various discretizations and refinement strategies. The combination of local refinement at crack fronts and high‐order continuous and discontinuous enrichments proves to be an excellent combination which can deliver convergence rates close to that of problems with smooth solutions. Copyright © 2007 John Wiley & Sons, Ltd.     

Notch ductile failure with significant strain‐hardening: The modified equivalent material concept

The equivalent material concept (EMC) assumes that the ductile material has a valid K‐based fracture toughness (K_Ic or K_c). For ductile materials with significant strain‐hardening, no valid K_Ic or K_c is determined by the standard experiments and, hence, EMC seems null. The modified EMC (MEMC) is proposed in this study by which a virtual K_c value is defined and computed for the ductile material with significant strain‐hardening. In this way, Mode I and mixed Mode I/II fracture behaviors of U‐notched aluminum alloy 5083 are assessed in the view points of experiments and theories. Several U‐notched rectangular samples are used for performing the experiments and obtaining the failure loads. Then, the MEMC is coupled with the maximum tangential stress and mean stress criteria and utilized to predict the failure loads theoretically. Finally, it is shown that both the MEMC‐stress‐based criteria can provide very good predictions of the test data.     

Engineering C*‐integral and COD estimates for nonidealized circumferential through‐wall cracked pipes at elevated temperature

In this study, creep fracture mechanics parameters, C^*‐integral and crack opening displacement (COD) rate, are estimated for a nonidealized circumferential through‐wall crack (TWC) in pipes. The GE/EPRI and enhanced reference stress (ERS) methods are employed. As for creep condition, the Norton and RCC‐MRx creep models are considered for secondary and primary‐secondary creep strain, respectively. The bending moment, axial tension, and internal pressure are applied to a pipe with a nonidealized circumferential TWC, as individual loads. Three‐dimensional elastic‐creep finite element (FE) analyses are performed, and the predictions from the GE/EPRI and ERS methods are compared with FE results. For the Norton creep model, both methods show good agreement with the FE results. For the RCC‐MRx creep model, only the ERS method can be used, and it provides accurate predictions comparing with FE results. Based on the comparison results, the use of the present engineering C^*‐integral and COD estimation methods for nonidealized circumferential TWC is validated.     

Computation of the stress intensity factors of sharp notched plates by the fractal‐like finite element method

The fractal‐like finite element method (FFEM) is an accurate and efficient method to compute the stress intensity factors (SIFs) of different crack configurations. In the FFEM, the cracked/notched body is divided into singular and regular regions; both regions are modelled using conventional finite elements. A self‐similar fractal mesh of an ‘infinite’ number of conventional finite elements is used to model the singular region. The corresponding large number of local variables in the singular region around the crack tip is transformed to a small set of global co‐ordinates after performing a global transformation by using global interpolation functions. In this paper, we extend this method to analyse the singularity problems of sharp notched plates. The exact stress and displacement fields of a plate with a notch of general angle are derived for plane‐stress/strain conditions. These exact analytical solutions which are eigenfunction expansion series are used to perform the global transformation and to determine the SIFs. The use of the global interpolation functions reduces the computational cost significantly and neither post‐processing technique to extract SIFs nor special singular elements to model the singular region are needed. The numerical examples demonstrate the accuracy and efficiency of the FFEM for sharp notched problems. Copyright © 2008 John Wiley & Sons, Ltd.     

Phase‐field modeling of ductile fracture at finite strains: A robust variational‐based numerical implementation of a gradient‐extended theory by micromorphic regularization

This work provides a robust variational‐based numerical implementation of a phase field model of ductile fracture in elastic–plastic solids undergoing large strains. This covers a computationally efficient micromorphic regularization of the coupled gradient plasticity‐damage formulation. The phase field approach regularizes sharp crack surfaces within a pure continuum setting by a specific gradient damage modeling with geometric features rooted in fracture mechanics. It has proven immensely successful with regard to the analysis of complex crack topologies without the need for fracture‐specific computational structures such as finite element design of crack discontinuities or intricate crack‐tracking algorithms. The proposed gradient‐extended plasticity‐damage formulation includes two independent length scales that regularize both the plastic response as well as the crack discontinuities. This ensures that the damage zones of ductile fracture are inside of plastic zones or vice versa and guarantees on the computational side a mesh objectivity in post‐critical ranges. The proposed setting is rooted in a canonical variational principle. The coupling of gradient plasticity to gradient damage is realized by a constitutive work density function that includes the stored elastic energy and the dissipated work due to plasticity and fracture. The latter represents a coupled resistance to plasticity and damage, depending on the gradient‐extended internal variables that enter plastic yield functions and fracture threshold functions. With this viewpoint on the generalized internal variables at hand, the thermodynamic formulation is outlined for gradient‐extended dissipative solids with generalized internal variables that are passive in nature. It is specified for a conceptual model of von Mises‐type elasto‐plasticity at finite strains coupled with fracture. The canonical theory proposed is shown to be governed by a rate‐type minimization principle, which fully determines the coupled multi‐field evolution problem. This is exploited on the numerical side by a fully symmetric monolithic finite element implementation. An important aspect of this work is the regularization towards a micromorphic gradient plasticity‐damage setting by taking into account additional internal variable fields linked to the original ones by penalty terms. This enhances the robustness of the finite element implementation, in particular, on the side of gradient plasticity. The performance of the formulation is demonstrated by means of some representative examples. Copyright © 2016 John Wiley & Sons, Ltd.     

Minimizing dynamic effects while using dynamic codes to simulate binder‐set processes

When using a dynamic code to simulate a quasi‐static job, the dynamic effect is a very serious problem, such as in the binder set simulation in stamping process design. Dynamic effects generally consist of two different acting types, oscillation due to the kinetic energy of the blank and additional deformation thanks to the inertial action. For the binder set simulation, the inertial effect is more apt to change the simulation result due to less‐constrained forming of the blank. Light effect varies the magnitude of blank deformation. Seriousness shall result in the deformation type change of the forming blank, which could make simulating results useless for real‐world application. To aim at the dynamic problems, especially in the inertial effect, several useful and practical ways have been proposed in this paper. Some parameters that we can use to minimize dynamic effects during a simulation effectively include: the velocity type of the travelling part, damping, defining the travelling part and imposing additional loads on the forming blank. Finally, four associated simulation cases have been discussed to show how these enhancing methods can be applied in real stamping production. Copyright © 2003 John Wiley & Sons, Ltd.     

Damage mechanics models of ductile crack growth in welded specimens

Two-dimensional, plane strain, finite element analyses of strength-mismatched welded joints have been performed using the modified boundary layer formulation. The welds were idealized as two-material joints with the material interface running parallel to the crack, which was embedded in the weld material. The Rousselier ductile damage model was employed within the weld material to simulate crack extension due to the growth and coalescence of microvoids. By analysing models with different levels of material mismatching, weld dimensions and applied T -stress levels, it was possible to analyse the effects of crack tip constraint due to both material mismatching and specimen geometry on the fracture resistance of the weld material.
The results show that material strength overmatching (where the weld material is stronger than the base material) reduces the level of constraint ahead of the crack, which can increase the resistance to fracture of the weld material. Conversely, material strength undermatching increases crack tip constraint, reducing the fracture resistance of the joint. By employing estimates for the crack tip constraint levels, Q _M , based on the applied load, level of material mismatching and weld region thickness, it has been possible to 'order' the J– resistance curves of overmatched joints by generating a family of J–Q _M loci which describe the effects of constraint on the fracture resistance of the weld material. However, it is shown that the Q _M-stress parameter is not capable of describing the effect of material strength undermatching on the fracture resistance of a joint, which can be much lower than that obtained from a high-constraint homogeneous specimen of weld material.     

A numerical approach to the analysis of failure modes in anisotropic plates

This study is motivated by the attempt to characterize failure modes of silicon chips commonly used in electronic industries. Previous experimental investigations provided the failure probability of dies made of a single-crystal and produced a large variety of crack patterns, but were not able to elucidate the link between defect distributions and crack initiation and propagation. To get some insight in the fracture activation and propagation mechanisms, we resort to finite element analyses and adopt an explicit methodology for crack tracking, based on the self-adaptive insertion of cohesive elements into a coherent mesh of solid elements. Finite kinematics material models with anisotropic features for both bulk and cohesive surfaces are employed to describe the behavior of single-crystal silicon plates undergoing a particular bending test up to failure. The cohesive model adopted in the calculation is fully anisotropic and newly formulated to accomplish the present study. Numerical simulations considering different material properties were able to ascertain the effects of particular flaws on failure modes of brittle silicon plates.     

Modelling of localized ductile fracture with volumetric locking-free tetrahedral elements

Finite element analysis of ductile fracture with tetrahedral elements faces two numerical issues: volumetric locking and mesh sensitivity. In this paper, two widely adopted remedies for volumetric locking (F-bar and mixed field) are evaluated, and the superior performance of the mixed field method is demonstrated. Building on the mixed field formulation, a gradient enhancement is further incorporated to resolve the mesh sensitivity. It is shown that a localizing gradient enhancement can avoid a spurious spreading of damage induced by the conventional gradient approach. A locking-free, regularized ductile fracture is first presented via a uniformly tapering plate example. Finally, a shear plate test on ferrite-bainite steel is considered. Numerical results obtained with the proposed approach are shown to capture the rapid strain softening and localized shear fracture phenomenon observed experimentally.     

Analysis of ductile to cleavage transition in part-through cracks using a cell model incorporating statistics

This paper describes an approach to study ductile/cleavage transition in ferritic steels using the methodology of a cell model for ductile tearing incorporating weakest link statistics. The model takes into account the constraint effects and puts no restriction on the extent of plastic deformation or amount of ductile tearing preceding cleavage failure. The parameters associated with the statistical model are calibrated using experimental cleavage fracture toughness data, and the effect of threshold stress on predicted cleavage fracture probability is investigated. The issue of two approaches to compute Weibull stress, the 'history approach' and the 'current approach', is also addressed. The numerical approach is finally applied to surface-cracked thick plates subject to different histories of bending and tension, and a new parameter, ψ, is introduced to predict the location of cleavage initiation.     

Strain ratcheting and stress relaxation around interference‐fitted single‐holed plates under cyclic loading: experimental and numerical investigations

Longitudinal strain ratcheting and stress relaxation in interference‐fitted single‐holed plates were investigated both experimentally and numerically. In the experimental part single‐holed plates made from Al‐alloy 7075‐T6 were force‐fitted with oversized pins to create 1% and 2% nominal interference fit sizes. Then these plates (specimens) were instrumented with dynamic strain gauges in longitudinal direction around the hole to measure the strain during interference fit and strain ratcheting during subsequent cyclic loading. In the numerical part, 2D finite element code has been written to simulate the interference fit process and subsequent cyclic loading to obtain strains and stresses around the force fitted hole. To predict the strain ratcheting, Ohno–Wang kinematic hardening model was applied for simulation of stress/strain path. The strain ratcheting predicted from the finite element code and experimental test results were compared. The results showed that there is a good agreement between the measured and numerically evaluated strains, and the strain ratcheting is bigger for higher cyclic load level, but it is smaller for larger interference size.     

Finite element modelling of cracked inelastic shells with large deflections: two‐dimensional and three‐dimensional approaches

Higher utilization of structural materials leads to a need for accurate numerical tools for reliable predictions of structural response. In some instances, both material and geometrical non‐linearities are allowed for, typically in assessments of structural collapse or residual strength in damaged conditions. The present study addresses the performance of surface‐cracked inelastic shells with out‐of‐plane displacements not negligible compared to shell thickness. This situation leads to non‐linear membrane force effects in the shell. Hence, a cracked part of the shell will be subjected to a non‐proportional history of bending moment and membrane force. An important point in the discretization of the problem is whether a two‐dimensional model describes the structural performance sufficiently, or a three‐dimensional model is required. Herein, the two‐dimensional modelling is performed by means of a Mindlin shell finite element. The cracked parts are accounted for by means of inelastic line spring elements. The three‐dimensional models employ eight‐noded solid elements. These models also account for ductile crack growth due to void coalescence by means of a modified Gurson–Tvergaard constitutive model, hence providing detailed solutions that the two‐dimensional simulations can be tested against. Using this, the accuracy of the two‐dimensional approach is checked thoroughly. The analyses show that the two‐dimensional modelling is sufficient as long as the cracks do not grow. Hence, using fracture initiation as a capacity criterion, shell elements and line springs provide acceptable predictions. If significant ductile tearing occurs before final failure, the line spring ligaments have to be updated due to crack growth.