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There are a number of different approaches for calculating creep-fatigue (CF) damage for design, such as the French nuclear code RCC-MRx, the American ASME III NH and the British R5 assessment code. To acquire estimates for the CF damage, that are not overly conservative, both the cyclic material softening/hardening and the potential changes in relaxation behavior have to be considered. The data presented here and models are an initial glimpse of the ongoing European FP7 project MATISSE effort to model the softening and relaxation behavior of Grade 91 steel under CF loading. The resulting models are used for calculating the relaxed stress at arbitrary location in the material cyclic softening curve. The initial test results show that softening of the material is not always detrimental. The initial model development and the pre-assessment of the MATISSE data show that the relaxed stress can be robustly predicted with hold time, strain range and the cyclic life fraction as the main input parameters. The paper aims to discuss these issues.

Engineering models have been developed for predicting cyclic softening and relaxation for Gr. 91 steel at 550 and 600°C.

A simple engineering model can adequately predict the low cycle fatigue (LCF) and CF softening rates of Gr. 91 steel. Also a simple relaxation model was successfully defined for predicting relaxed stress of both virgin and cyclically softened material.

The data are not yet complete and the models will be updated when the complete set of data in the MATISSE project is available.

The models described can be used for predicting P91 material softening in an arbitrary location (n/N_f0) of the LCF and CF cyclic life. Also the relaxed stress in the softened material can be estimated.

The models are simple in nature but are able to estimate both material softening and relaxation in arbitrary location of the softening curve. This is the first time the Wilshire methodology has been applied on cyclic relaxation data.

The localized strain softening behaviour of concrete has been modelled by two approaches: (i) the stiffness degrading model based on the total stress‐strain constitutive relationship, and (ii) the tangent softening model based on the incremental stress‐strain relationship. The models are implemented using a new softening initiation criterion proposed for application in multi‐dimensional finite element analysis. Parametric analyses on plain concrete beams, tested experimentally by other researchers, have been carried out to investigate the required numerical efforts, the mesh objectivity, and the energy dissipation characteristics of the structures. The stiffness degrading model is very stable even when applied with relatively coarse finite element meshes. However, the computational demand of this model is relatively high. The combination of a total stress‐strain constitutive relationship to compute the element responses, and an incremental relationship to formulate the stiffness matrix, appears to be computationally efficient and stable, provided that adequately refined finite element mesh is used to model the structure.

This paper presents a comparison of various models for strain‐softening due to damage such as cracking or void growth, as proposed recently in the literature. Continuum‐based models expressed in terms of softening stress—strain relations, and fracture‐type models expressed in terms of softening stress—displacement relations are distinguished. From one‐dimensional wave propagation calculations, it is shown that strain‐localization into regions of finite size cannot be achieved. The previously well‐documented spurious convergence is obtained with continuum models, while stress—displacement relations cannot model well smeared‐crack situations. Continuum models may, however, be used in general if a localization limiter is implemented. Gradient‐type localization limiters appear to be rather complicated; they require solving higher‐order differential equations of equilibrium with additional bourdary conditions. Non‐local localization limiters, especially the non‐local continuum with local strain, in which only the energy dissipating variables are non‐local, is found to be very effective, and also seems to be physically realistic. This formulation can correctly model the transition between homogeneous damage states and situations in which damage localizes into small regions that can be viewed as cracks. The size effect observed in the experimental and numerical response of specimens in tension or compression is shown to be a consequence of this progressive transition from continuum‐type to fracture‐type formulations.

The dispersive behaviour of waves in softening problems is analysed. Attention is focused on the influence of the numerical scheme on the dispersion characteristics in the process of localization of deformation. Distinction has been made between softening models defined in a standard plasticity framework and in a gradient‐dependent plasticity theory. Waves in a standard softening plasticity continuum do not disperse but due to spatial discretization dispersion is introduced which results in a mesh size dependent length scale effect. On the other hand, wave propagation in a gradient‐dependent softening plasticity continuum is dispersive. By carrying out the dispersion analysis on the discretized system the influence of numerical dispersion on material dispersion can be quantified which enables us to determine the accuracy for the solution of the localization zone. For a modelling with and without the inclusion of strain gradients accuracy considerations with respect to mass discretization, finite element size, time integration scheme and time step have been carried out.

The aim of this study was to understand the stick-slip properties of single and multiple yarn pull-out in dry and treated polyester satin woven fabric in boundary regions.

Polyester satin pattern woven fabric was used to conduct the pull-out tests in order to examining the kinetic region of the force-displacement curve. Data generated from this research help the authors to obtain stick-slip force and accumulative retraction force.

It was found that stick-slip force and accumulative retraction force depend on the number of pulled ends in the fabric, fabric sample dimensions and softening treatments. Stick-slip forces of polyester satin fabric in the multiple yarn pull-out test were higher than those of the single yarn pull-out test. Stick-slip force in single and multiple yarn pull-out tests in the dry polyester satin fabric was generally higher than those of the softening treated polyester satin fabric. In addition, the warp directional single and multiple yarn stick-slip and accumulative retraction forces in the dry and softening treated polyester fabrics were generally higher than those in the weft direction in the fabric edges due to fabric density. On the other hand, the amount of stick-slip force was related to the number of interlacement points in the fabric, whereas the amount of accumulative retraction force was related to fabric structural response.

The mechanism of stick-slip and accumulative retraction force of dry-treated polyester satin pattern woven fabrics were explained. This research could be valuable for development of multifunctional fabrics in technical textiles and ballistic.

Due to its inexpensive production costs, low stress concentration and maintenance-friendliness, the adhesive bonded pipe joint is frequently utilized for pipe connection. However, further theoretical analysis is needed to understand the debonding failure mechanism of such bonded pipe joints under axial tension.

In this study, based on the bi-linear cohesive zone model, the integrated closed-form solutions were derived by considering the axial stiffness ratio and failure stage to determine the relative interfacial slip, interfacial shear stress and relationship of tension–displacement in the bonded pipe joint.

Additionally, solutions for the critical bonded length and the ultimate load capacity were put forth. Besides, the numerical study was conducted to verify the theoretical solutions regarding the load–displacement relationship. The interfacial shear stress distribution at different failure stages was presented to understand the interfacial shear stress transmission and debonding process. The effect of bonded length on the ultimate load and ductility of pipe joints was also discussed.

The findings in this study can give a reference for the design of bonded pipe joints in their actual engineering applications.

Plane strain constitutive behaviour of von Mises and isotropic Hoffman materials is examined using single element tests. Two kinds of tests are conducted – (a) prescribed displacement tests; and (b) tests with a mixture of displacements and boundary tractions prescribed. While (a) are used to understand the manner of stress traversal on the yield surface in principal stress space, (b) are employed to study the load displacement response and the possibility of ensuing localization. Associated plasticity is assumed throughout. The tests are conducted using perfect and strain softening plasticity. It is found that for the von Mises criterion limited exact solutions can be evolved even under softening (or hardening) conditions. For isotropic Hoffman materials the nature of the stress traversal, load deflection response and the satisfaction of the localization conditions are strongly influenced by the ratio and difference of uniaxial yield strengths, in tension and compression, as well as by the softening parameters.

A new approach is proposed toward accurately matching any given realistic hardening and softening data from uniaxial tensile test up to failure and moreover, toward bypassing usual tedious implicit trial-and-error iterative procedures in identifying numerous unknown parameters.

Finite strain response features of metals with realistic hardening-to-softening transition effects up to eventual failure are studied for the first time based on the self-consistent elastoplastic J₂-flow model with the logarithmic stress rate. As contrasted with usual approximate and incomplete treatments merely considering certain particular types of hardening effects such as power type hardening, here a novel and explicit approach is proposed to obtain a complete form of the plastic-work-dependent yield strength over the whole hardening and softening range.

A new multi-axial evolution equation for both hardening and softening effects is established in an explicit form. Complete results for the purpose of model validation and prediction are presented for the finite strain responses of monotonic uniaxial stretching up to failure.

New finite strain elastoplastic equations are established with a new history-dependent variable equivalently in place of the usual plastic work. With these equations, a unified and accurate simulation of both gardening and softening effects up to failure is achieved for the first time in an explicit sense without involving usual tedious implicit trial-and-error iterative procedures.

The behaviour of cracked finite elements is investigated. It is shown that spurious kinematic modes may emerge when softening type constitutive laws are employed. These modes are not always suppressed by surrounding elements. This is exemplified for a double‐notched concrete beam and for a Crack‐Line‐Wedge‐Loaded Double‐Cantilever‐Beam (CLWL—DCB). The latter example has been analysed for a large variety of finite elements and integration schemes. To investigate the phenomenon in greater depth an eigenvalue analysis has been carried out for some commonly used finite elements.

As the normality concept for frictional dilatant material has a serious drawback, the key feature in this numerical study is that the material here is characterized by elastic-viscoplastic constitutive relation with plastic non-normality effect for two different hardness functions. The paper aims to discuss this issue.

Quasi-static, mode I plane strain crack tip fields have been investigated for a plastically compressible isotropic hardening–softening–hardening material under small-scale yielding conditions. Finite deformation, finite element calculations are carried out in front of the crack with a blunt notch. For comparison purpose a few results of a hardening material are also provided.

The present numerical calculations show that crack tip deformation and the field quantities near the tip significantly depend on the combination of plastic compressibility and slope of the hardness function. Furthermore, the consideration of plastic non-normality flow rule makes the crack tip deformation as well as the field quantities significantly different as compared to those results when the constitutive equation exhibits plastic normality.

To the best of the authors’ knowledge, analyses, related to the constitutive relation exhibiting plastic non-normality in the context of plastic compressibility and softening (or softening hardening) on the near tip fields, are not explored in the literature.