In the very high-cycle fatigue regime there is a well-known lack of data for the assessment of welded joints. This lack of data has led to Codes and Standards with a wide range of recommendations. Most of these recommendations are justified by experience and lack a well-documented technical basis. The difficulty in testing at very high cycles is that the tests currently take too long to be practical and are often suspended between 106 and 107 cycles. However, in piping vibration applications the system may undergo more than 108 cycles per year. Since much of the experimental data in this very high-cycle regime is run-out or “censored” data, we explore approaches to extract the information contained in such data and infer the behaviour of the Master S-N curve in the very high-cycle regime. This paper presents an approach to account for censored data to provide a basis for extending the Master S-N curve to the very high-cycle fatigue regime for welded joints.

The fitness-for-service procedures for local thin areas in pipelines trade complexity for conservatism, with more complex procedures being less conservative. In this paper, we outline a procedure for automating the advanced Level 3 assessment procedure outlined in API 579-1/ASME FFS-1 for local thin areas. The outlined procedure is bundled into a web-enabled, industrial trade tool where the minimum data requirements are the same as those for a Level 2 assessment. The procedure can be applied to an entire in-line inspection scan of UT thickness readings and, after calculation, can identify hotspots of local damage. By reducing the inputs to those of a Level 2 assessment procedure, the Level 3 procedure presents as an attractive alternative to the current Level 2 approaches.

Rate-dependent fracture processes can be investigated by means of cohesive zone models (CZMs). For instance, one approach enhances existing CZMs with phenomenological expressions used to represent the fracture energy, cohesive strength, and/or maximum crack opening as a function of the crack opening rate. Another approach assumes a vis-coelastic CZM in front of the crack tip. Although computationally less expensive, the former approach misses most of the physics driving the rate-dependent fracture process. The latter approach better represents the physics driving the rate-dependent fracture process, yet it is computationally more expensive. This work presents a methodology for studying mixed-mode rate-dependent fracture that is both efficient and approximates the viscoelastic material behavior in front of the crack tip. In this mixed-mode approach, we approximate the viscoelastic behavior in front of the crack tip using two rate-dependent springs. One spring acts in the normal direction to the crack plane, while the other acts in the tangential direction. In order to mimic a viscoelastic CZM, we assume that the stiffness of each spring is a function of the crack opening rate and enforce that their tractions are continuous with respect to changes in the crack opening rates. To account for damage, we scale the tractions from the rate-dependent springs using two damage parameters extracted from the Park-Paulino-Roesler (PPR) cohesive fracture model. The rate-dependent model is implemented as a user defined element (UEL) subroutine in Abaqus. While attaining a high level of accuracy, the present approach allows for significant savings in computational cost when compared with a CZM based on fractional viscoelastic theory. (C) 2017 Elsevier Ltd. All rights reserved.

The 3rd Edition of API 579-1/ASME FFS-1 2016 Fitness-For-Service includes a new Part 14 dedicated to fatigue assessment. An important section in this part covers the fatigue assessment of welded joints. In this paper, an overview of the fatigue methods for welded joints is provided and extensions are recommended. First, an overview is given of the classical fatigue method used in the ASME B&PV Code based on smooth bar fatigue curves in conjunction with a fatigue strength reduction factor. In addition, the mesh insensitive structural stress method is outlined using an equivalent stress parameter based on fracture mechanics considerations in conjunction with a master S-N curve based on the analysis of over 2000 high and low cycle S-N test data. The resulting master S-N curve approach is applicable to high cycle fatigue and low cycle fatigue if a Neuber correction is introduced. In this paper, a new structural strain method is presented to extend the early structural stress based master S-N curve method to the low cycle fatigue regime in which plastic deformations can be significant while an elastic core is present. With this new method, some of the inconsistencies of the pseudo-elastic structural stress procedure can be eliminated, such as its use of Neuber’s rule in approximating structural strain beyond yield. The earlier mesh-insensitive structural stress based master S-N curve method can now be viewed as an application of the structural strain method in the high cycle regime, in which structural strains are linearly related to traction-based structural stresses according to Hooke’s law. Thus, both low cycle and high cycle fatigue behavior can now be treated in a unified manner. In the low-cycle regime, the structural strain method characterizes fatigue damage directly in terms of structural strains that satisfy a linear through-thickness deformation gradient assumption, material nonlinear behavior, and equilibrium conditions. A PVRC Joint Industry Project is currently sponsoring work on the structural strain method that will lead to its incorporation in the next edition of API 579-1/ASME FFS-1.

There are few methods capable of capturing the full spectrum of pervasive fracture behavior in three-dimensions. Throughout pervasive fracture simulations, many cracks initiate, propagate, branch and coalesce simultaneously. Because of the cohesive element method framework, this behavior can be captured in a regularized manner. However, since the cohesive element method is only able to propagate cracks along element facets, a poorly designed discretization of the problem domain may introduce artifacts into the simulated results. To reduce the influence of the discretization, geometrically and constitutively unstructured means can be used. In this paper, we present and investigate the use of three-dimensional nodal perturbation to introduce geometric randomness into a finite element mesh. We also discuss the use of statistical methods for introducing randomness in heterogeneous constitutive relations. The geometrically unstructured method of nodal perturbation is then combined with a random heterogeneous constitutive relation in three numerical examples. The examples are chosen in order to represent some of the significant influencing factors on pervasive fracture and fragmentation; including surface features, loading conditions, and material gradation. Finally, some concluding remarks and potential extensions are discussed.

Neuber’s rule is commonly applied in fatigue analysis to estimate the plasticity of purely elastic FEA results. In certain cases, this is more efficient than running elastic-plastic models. However, the applicability of Neuber’s rule is not well understood for complex models and may not always be appropriate. In this paper, the applicability of Neuber’s rule is investigated. The background of Neuber’s rule is discussed, theoretical limitations are derived, and algorithmic outlines of the procedures are presented. Neuber’s plasticity correction procedure is applied to both the Ramberg-Osgood elastic-plastic constitutive relation and the advanced Chaboche isotropic/kinematic nonlinear hardening relation. Throughout the manuscript, the aspects of each model are discussed from an educational perspective, highlighting each step of the implementation in sufficient detail for independent reproduction and verification. This level of detail is often absent from similar publications and, it is hoped, may lead to the wider dissemination of Neuber’s rule for plasticity correction. The final component of the paper presents a multiaxial correction of the Chaboche hardening model. To the best of the authors’ knowledge, this is the first published application of Neuber’s rule to the multiaxial plasticity correction of the Chaboche combined isotropic/kinematic hardening model. Examples are used to illustrate the behavior of the method and to present some of the commonly overlooked components when assessing the applicability of Neuber’s method.

As early as the 1950's, practitioners observed progressive distortion in thin-walled pressure vessels subjected to a constant axial stress and a cyclic thermal stress. In the late 1960's, Bree [1] developed a theory and corresponding diagram plotting the primary membrane stress versus the cyclic thermal stress which delineates the various zones of plastic behavior. The zones include elastic cycling, plastic cycling, elastic cycling after initial plasticity, and ratcheting leading to incremental growth. This paper revisits the original Bree problem and investigates many of the recent advancements made to alleviate several of the simplifying assumptions Bree made in developing the diagram, to bring it in line with more modern operating conditions. In particular, a novel modification to the Bree diagram to account for the ratio of the yield stress at the operating extremums is proposed. This paper also reviews some advancements made to incorporate creep into the problem and discusses the operating conditions wherein creep effects may be significant. The outcomes of this paper will help expand the applicability of the Bree diagram, broadening its scope to encompass operating conditions more representative of modern applications.

A coke drum experiences operating conditions that are severe and unrelenting, and their lifespans reflect this. In this paper, a coupled thermal-mechanical model of an operating coke drum is presented. The impacts of important operating parameters, such as the cycle time and quench rate, on an ideal operating cycle and a cycle that produces hotspots are discussed. The model is constructed in three stages: (i) the through-wall temperature distribution is probabilistically determined using a Bayesian inverse approach that calculates the heat flux profile on the inside of the drum wall from a temperature reading on the outside of the wall; (ii) a thermal-mechanical finite element analysis of the drum wall is conducted using the heat flux profile as a spatially and temporally varying boundary condition — to obtain the stress and strain behavior at a critical location (weld seam) on the drum; and (iii) hotspots are introduced in the vicinity of the weld through a novel approach, and their impact on the plastic behavior of the drum wall is examined. The influence of the operating conditions on the behavior of the coke drum is to be incorporated into a financial analysis of the entire coke drum’s life cycle — in a companion paper — to determine an optimal operating strategy.

The third edition of API 579-1/ASME FFS-1 Fitness-For-Service includes a new Part 14 covering fatigue assessment procedures for in-service components. This new part provides methods for estimating the time to crack initiation using strain life approaches, which are important for low-cycle fatigue, and is written as a multi-tiered approach covering screening, current design code methods, and advanced methods that take into account the latest in technology. Cycle counting methods for both welded joint and smooth-bar fatigue methods are included for uniaxial and multiaxial loading histories. In addition, the multiaxial incremental plasticity correction procedure presented in the new Level 3 Assessment represents a significant update to the plasticity correction used previously. Part 14 of API 579-1/ASME FFS-1 is a procedural document that is written for accurate and practical implementation. WRC Bulletin 550 is the basis for Part 14 and provides the background and supporting documentation for its development. This paper summarizes the work that went into developing Part 14, and WRC 550, and provides a specific example of its implementation for a practical problem of interest using software developed by The Equity Engineering Group, Inc. In-depth comparisons, key findings, and limitations of the presented methods are included.

Although the Park-Paulino-Roesler (PPR) potential-based cohesive zone fracture model was not derived based on a thermodynamics consistency principle, we investigate the thermodynamic consistency of the PPR model under conditions of loading, unloading and reloading. First, we present a general anisotropic Helmholtz free energy function. Then, we reformulate the PPR model into the anisotropic Helmholtz form, and investigate its consistency and the various unloading/reloading relations which have been proposed for use with the model. By recasting the PPR model into the Helmholtz form, we illustrate that the PPR cohesive potential, while not designed with thermodynamic consistency in mind, is thermodynamically consistent under the pure loading conditions for which it was designed (as expected). We also demonstrate that the unloading/reloading relations, which are commonly used with the PPR model, are not thermodynamically consistent; however, through our investigation, we develop a new coupled unloading/reloading relation, which maintains the thermodynamic consistency of the PPR cohesive model. The considerations addressed in this paper are aimed at achieving a better understanding of the PPR model and other models of similar nature. (C) 2016 Elsevier Ltd. All rights reserved.

A new concrete fracture geometry is presented, which can quantify multiple fracture properties from a single specimen test. The disk-shaped compact tension (DCT) geometry allows specimens to be fabricated from laboratory cylinders or field cores. The DCT fracture test characterizes the concrete's critical stress intensity factor, K-IC, critical crack-tip opening displacement, CTODc, and initial fracture energy, G(f), as well as the specimen-dependent total fracture energy, G(F). The DCT-based fracture properties have the same experimental variation as the single-edge notched beam test. The experimentally derived fracture parameters were implemented into a cohesive zone model, which enabled estimation of concrete tensile strength from field-extracted cores.

This paper presents an integrated theoretical and computational investigation into the macroscopic behavior of composite materials containing multi-phase reinforcing particles with simultaneous nonlinear debonding along the microconstituent interfaces. The interfacial debonding is characterized by the nonlinear Park–Paulino–Roesler potential-based cohesive zone model. The extended Mori–Tanaka method is employed as the basis for the theoretical model, which enables micromechanical formulations for composite materials with high particle volume fractions. The computational analysis is performed using a three-dimensional finite element-based cohesive zone model with intrinsic cohesive elements. To place the generality and robustness of the proposed technique in perspective, we consider several examples of composite materials with single or double separation along the interfaces of coated particles. The effects of many microstructural parameters, such as the geometry of the microstructure, the location of debonding, the material properties of the coating layer (i.e. homogenous and functionally graded coatings), and the fracture parameters, are comprehensively investigated by both theoretical and numerical approaches. We verify that both theoretical and numerical results agree well with one another in estimating the macroscopic constitutive relationship of corresponding composite materials. The strong dependence of the overall response of composite materials on their microstructure is well recognized for all hardening, snap-back, and softening stages.

There are four primary factors which influence the macroscopic constitutive response of particle reinforced composites: component properties, component concentrations, interphases, and interfacial debonding. Interphases are often a byproduct of surface treatments applied to the particles to control agglomeration. Alternatively, in polymer based materials such as carbon-black reinforced rubber, an interphase or “bound rubber” phase often occurs at the particle–matrix interface. This interphasial region has been known to exist for many decades, but is often omitted in computational investigations of such composites. In this paper, we present an investigation into the influence of interphases on the large deformation response of particle reinforced composites. In addition, since particles tend to debond from the matrix at large deformations, we investigate the influence of interfacial debonding on the macroscopic constitutive response. The investigation considers two different microstructures; both a simplified single particle model, and a more complex polydisperse representative unit cell. Cohesive elements, which follow the Park–Paulino–Roesler traction–separation relation, are inserted between each particle and its corresponding interphase to account for debonding. To account for friction, we present a new, coupled cohesive–friction model and detail its formulation and implementation. For each microstructure, we discuss the influence of the interphase thickness and stiffness on the global constitutive response in both uniaxial tension and simple shear. To validate the computational framework, comparisons are made with experimental results available in the literature.

Experimental evidence has by now established that (i) the hydrodynamic effect and (ii) the presence of stiff interphases (commonly referred to as bound rubber) "bonding" the underlying elastomer to the fillers are the dominant microscopic mechanisms typically responsible for the enhanced macroscopic stiffness of filled elastomers. Yet, because of the technical difficulties of dealing with these fine-scale effects within the realm of finite deformations, the theoretical reproduction of the macroscopic mechanical response of filled elastomers has remained an open problem.The object of this paper is to put forward a microscopic field theory with the capability to describe, explain, and predict the macroscopic response of filled elastomers under arbitrarily large nonlinear elastic deformations directly in terms of: (i) the nonlinear elastic properties of the elastomeric matrix, (ii) the concentration of filler particles, and (iii) the thickness and stiffness of the surrounding interphases. Attention is restricted to the prominent case of isotropic incompressible elastomers filled with a random and isotropic distribution of comparatively rigid fillers. The central idea of the theory rests on the construction of a homogenization solution for the fundamental problem of a Gaussian elastomer filled with a dilute concentration of rigid spherical particles bonded through Gaussian interphases of constant thickness, and on the extension of this solution to nonGaussian elastomers filled with finite concentrations of particles and interphases by means of a combination of iterative and variational techniques.For demonstration purposes, the theory is compared with full 3D finite-element simulations of the large-deformation response of Gaussian and non-Gaussian elastomers reinforced by isotropic distributions of rigid spherical particles bonded through interphases of various finite sizes and stiffnesses, as well as with experimental data available from the literature. Good agreement is found in all of these comparisons. The implications of this agreement are discussed. (C) 2015 Elsevier Ltd. All rights reserved.

We present a method to reduce mesh bias in dynamic fracture simulations using the finite element method with adaptive insertion of extrinsic cohesive zone elements along element boundaries. The geometry of the domain discretization is important in this setting because cracks are only allowed to propagate along element facets and can potentially bias the crack paths. To reduce mesh bias, we consider unstructured polygonal finite elements in this work. The meshes are generated with centroidal Voronoi tessellations to ensure element quality. However, the possible crack directions at each node are limited, making this discretization a poor candidate for dynamic fracture simulation. To overcome this problem, and significantly improve crack patterns, we propose adaptive element splitting, whereby the number of potential crack directions is increased at each crack tip. Thus, the crack is allowed to propagate through the polygonal element. Geometric studies illustrate the benefits of polygonal element discretizations employed with element splitting over other structured and unstructured discretizations for crack propagation applications. Numerical examples are performed and demonstrate good agreement with previous experimental and numerical results in the literature. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we present the implementation of a small library of three-dimensional cohesive elements. The elements are formatted as user-defined elements, for compatibility with the commercial finite element software ABAQUS. The PPR, potential-based traction-separation relation is chosen to describe the element's constitutive model. The intrinsic cohesive formulation is outlined due to its compatibility with the standard, implicit finite element framework present in ABAQUS. The implementation of the cohesive elements is described, along with instructions on how to incorporate the elements into a finite element mesh. Specific areas of the user-defined elements, in which the user may wish to modify the code to meet specific research needs, are highlighted. Numerical examples are provided which display the capabilities of the elements in both small deformation and finite deformation regimes. A sample element source code is provided in an appendix, and the source codes of the elements are supplied through the website of the research group of the authors. (C) 2014 Elsevier Ltd. All rights reserved.

This paper presents a scheme for adaptive mesh refinement on unstructured polygonal meshes to better capture crack patterns in dynamic cohesive fracture simulations. A randomly seeded polygonal mesh leads to an isotropic discretization of the problem domain, which does not bias crack patterns, but restricts the number of paths that a crack may travel at each node. An adaptive refinement scheme is proposed and investigated through a detailed set of geometric studies. The refinement scheme is selectively chosen to optimize the number of paths that a crack may travel, while still maintaining a conforming domain discretization. The details of the refinement scheme are outlined, along with the criterion used to determine the region of refinement and the method of interpolating nodal attributes. Extrinsic cohesive elements are inserted when and where necessary, and follow the constitutive response of the Park–Paulino–Roesler cohesive model. The influence of bulk and cohesive material heterogeneity is investigated through the use of a statistical distribution of material properties. The adaptive mesh modifications are handled through a compact topological data structure. Numerical examples highlight the features of adaptive refinement in capturing physical fracture patterns while addressing computational cost. Thus, the present approach is a step towards obtaining accurate dynamic fracture patterns and fields with polygonal elements.

The estimation of concrete fracture properties is essential for an accurate cracking prediction of concrete pavement systems. The single-edge notched beam test has been used to characterize fracture parameters of concrete materials in the laboratory, but obtaining a field specimen with this geometry is not always practical. Currently, a standard exists, ASTM D7313, for the measurement of fracture energy in asphalt concrete using the disk-shaped compact tension (DCT) test. The benefit of this specimen geometry for both concrete and asphalt is that it can easily be fabricated in the laboratory or cored from the field. The total fracture energy (GF) of the material is estimated by using the concept of the work-of-fracture. Additional properties, such as the initial fracture energy (Gf) and the critical crack tip opening displacement (CTODC), can be extracted from the same test through employing compliance measurements and the concept of an equivalent elastic crack model. In this pilot study, the DCT specimen is adopted for concrete materials with small changes to the hole and notch geometry and loading rate of the specimen relative to ASTM D7313. The initial DCT experimental results for concrete containing virgin limestone aggregate and recycled concrete aggregate have been consistent and repeatable. A finite element model (FEM) of the specimen was developed to check the published KIC equation for this geometry and to derive the CTODC correction factor. A cohesive zone model was also successfully implemented to simulate the DCT specimen, which verified the validity of the calculated fracture properties from the DCT experiments.