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.     

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.     

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.     

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.     

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.     

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.     

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.     

Through‐wall welding residual stress profiles for dissimilar metal nozzle butt welds in pressurized water reactors

This paper provides approximate expressions for through‐wall welding residual stresses in dissimilar metal nozzle butt welds of pressurized water reactors. An idealized shape of nozzle is proposed, based on which systematic elastic–plastic thermo‐mechanical finite element analyses are conducted by varying the thickness and radius of the nozzle and the length of the safe‐end. Based on the results, a through‐wall welding residual stress profile for dissimilar metal nozzle butt welds is proposed by modifying the existing welding residual stress profile for austenitic pipe butt welds in the R6 procedure.     

A method to estimate plastic loads for elbows with non‐uniform thicknesses

This paper provides a method to estimate plastic loads [defined by the twice‐elastic‐slope (TES)] for elbows with non‐uniform thicknesses under in‐plane bending and under internal pressure, based on systematic FE limit analyses using elastic‐perfectly plastic materials. The intrados thickness is assumed to be up to 30% thicker than the straight pipe thickness, whereas the extrados thickness up to 30% thinner. The FE plastic loads are compared with estimated ones using closed‐form approximations for elbows with uniform thicknesses, to provide guidance on the choice of a representative thickness to predict plastic loads for elbows with non‐uniform thicknesses. Results suggest that the use of the straight pipe thickness gives overall satisfactory predictions. Estimated plastic loads are conservative, and differ from FE results by less than 10% for all cases considered. Despite its simplicity, results look very promising, and thus the use of the straight pipe thickness can be recommended to estimate plastic loads for elbows with non‐uniform thicknesses in practice.     

Effects of CFRP bond locations on the Mode I stress intensity factor of centre‐cracked tensile steel plates

The fatigue life of cracked steel members can be greatly extended by externally attached carbon fibre reinforced plastics (CFRP), which reduces the stress intensity factors (SIFs) at the crack tip. Access to cracks is sometimes limited and the CFRP has to be attached away from the cracks. There is a lack of knowledge on SIFs for such strengthening scheme. This paper presents the effects of CFRP bond locations on the Mode I SIF of centre‐cracked tensile (CCT) steel plate. The Mode I SIF at the crack tip is calculated using the finite element (FE) models. A correction factor is introduced as a function of CFRP bond location and crack length. The FE results are compared and agree well with experimental tests conducted by the authors. By combining with another two factors (one considering CFRP mechanical properties and the other considering CFRP bond width) derived previously by the authors, SIF formulae are proposed for CFRP reinforced CCT steel plates.     

A non‐local continuum damage approach to model dynamic crack branching

Dynamic crack‐branching instabilities in a brittle material are studied numerically by using a non‐local damage model. PMMA is taken as our model brittle material. The simulated crack patterns, crack velocities, and dissipated energies compare favorably with experimental data gathered from the literature, as long as the critical strain for damage initiation as well as the parameters for a rate‐dependent damage law are carefully selected. Nonetheless, the transition from a straight crack propagation to the emergence of crack branches is very sensitive to the damage initiation threshold. The transition regime is thus a particularly interesting challenge for numerical approaches. We advocate using the present numerical study as a benchmark to test the robustness of alternative non‐local numerical approaches. Copyright © 2014 John Wiley & Sons, Ltd.     

Three‐dimensional numerical modelling by XFEM of spring‐layer imperfect curved interfaces with applications to linearly elastic composite materials

The spring‐layer interface model is widely used in describing some imperfect interfaces frequently involved in materials and structures. Typically, it is appropriate for modelling a thin soft interphase layer between two relatively stiff bulk media. According to the spring‐layer interface model, the displacement vector suffers a jump across an interface whereas the traction vector is continuous across the same interface and is, in the linear case, proportional to the displacement vector jump. In the present work, an efficient three‐dimensional numerical approach based on the extended finite element method is first proposed to model linear spring‐layer curved imperfect interfaces and then applied to predict the effective elastic moduli of composites in which such imperfect interfaces intervene. In particular, a rigorous derivation of the linear spring‐layer interface model is provided to clarify its domain of validity. The accuracy and convergence rate of the elaborated numerical approach are assessed via benchmark tests for which exact analytical solutions are available. The computated effective elastic moduli of composites are compared with the relevant analytical lower and upper bounds. Copyright © 2011 John Wiley & Sons, Ltd.     

A fast numerical method of introducing the strengthening effect of residual stress and strain to tensile behavior of metal matrix composites

Thermal residual stress and strain (TRSS) in particle reinforced metal matrix composites (PRMMCs) are believed to cause strengthening effects,according to previous studies.Here,the representative volume element (RVE) based computational homogenization technique was used to study the tensile deformation of PRMMCs with different particle aspect ratios (AR).The influence of TRSS was assessed quantitatively via comparing simulations with or without the cooling process.It was found that the strengthening effect of TRSS was affected by the particle AR.With the average strengthening effect of TRSS,a fast method of introducing the strengthening effect of TRSS to the tensile behavior of PRMMCs was developed.The new method has reduced the computational cost by a factor 2.The effect of TRSS on continuous fiber-reinforced metal matrix composite was found to have a softening-effect during the entire tensile deformation process because of the pre-yield effect caused by the cooling process.     

A finite‐volume particle‐in‐cell method for the numerical treatment of Maxwell‐Lorentz equations on boundary‐fitted meshes

A new conceptual framework solving numerically the time‐dependent Maxwell–Lorentz equations on a non‐rectangular quadrilateral mesh in two space dimensions is presented. Beyond a short review of the applied particle treatment based on the particle‐in‐cell method, a finite‐volume scheme for the numerical approximation of the Maxwell equations is introduced using non‐rectangular quadrilateral grid arrangements. The coupling of a high‐resolution FV Maxwell solver with the PIC method is a new approach in the context of self‐consistent charged particle simulation in electromagnetic fields. Furthermore, first simulation results of the time‐dependent behaviour of an externally applied‐B ion diode developed at the Forschungszentrum in Karlsruhe are presented. Copyright © 1999 John Wiley & Sons, Ltd.     

A numerical method for evaluation of J‐integral in plates made of functionally graded materials with sharp and blunt V‐notches

The main purpose of the paper is to propose a numerical method for evaluation of J‐integral in plates made of functionally graded materials (FGM) with sharp and blunt V‐notches under Mode I loading. The material properties have been assumed to be varied exponentially along the specimen width (notch direction). Using the proposed method, the effect of material gradient on the J‐integral for two cases of sharp and blunt V‐notches has been studied. The results have shown that in FGMs with sharp V‐notches, the J‐integral is not proportional to . So, the parameter J_L is path dependent. It has been observed that the material gradient has larger effect on the J‐integral in sharp V‐notch compared with that in blunt V‐notch.     

On the use of an anti‐symmetric four‐point bend specimen for mode II fracture experiments

The edge‐cracked beam specimen subjected to anti‐symmetric four‐point bend (ASFPB) loading has been conventionally used in the past for investigating the pure mode II fracture experiments in many engineering materials. However, it is shown through finite element analysis that the ASFPB specimen sometimes fails to produce pure mode II conditions. For anti‐symmetric loads applied close to the crack line, there are considerable effects from K_I and T‐stress in the ASFPB specimen. Pure mode II is provided only when the applied loads are sufficiently far from the crack plane.     

On stability and reflection‐transmission analysis of the bipenalty method in contact‐impact problems: A one‐dimensional,homogeneous case study

The stability and reflection‐transmission properties of the bipenalty method are studied in application to explicit finite element analysis of one‐dimensional contact‐impact problems. It is known that the standard penalty method, where an additional stiffness term corresponding to contact boundary conditions is applied, attacks the stability limit of finite element model. Generally, the critical time step size rapidly decreases with increasing penalty stiffness. Recent comprehensive studies have shown that the so‐called bipenalty technique, using mass penalty together with standard stiffness penalty, preserves the critical time step size associated to contact‐free bodies. In this paper, the influence of the penalty ratio (ratio of stiffness and mass penalty parameters) on stability and reflection‐transmission properties in one‐dimensional contact‐impact problems using the same material and mesh size for both domains is studied. The paper closes with numerical examples, which demonstrate the stability and reflection‐transmission behavior of the bipenalty method in one‐dimensional contact‐impact and wave propagation problems of homogeneous materials.