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Abstract Pipelines subjected to thermal or mechanical loads may fail due to plastic strain accumulation which leads to ratcheting. In this research, cyclic plastic behavior and shakedown limit are investigated experimentally and numerically for a defected pressurized pipe under cyclic bending moment. In the numerical model, the combined isotropic/kinematic hardening model based on the Chaboche model is adopted to represent the cyclic plastic flow of the material. The hardening parameters are determined experimentally and used in the finite element (FE) model. A four-point bending test rig is manufactured to test a pressurized API 5L steel pipe under cyclic bending. An elliptical defect is created by machining to depict corrosion pits in pipes. The plastic strains are measured experimentally and the results are used to tune the parameters of the FE model. The shakedown limit of the defected pipe is determined numerically by tracking the critical points behavior and the results are verified experimentally. Furthermore, the plastic work dissipated energy (PWD) is estimated within the defective structure to study the behavior of the pipe. By running this compatible model, it is found that the yield and the shakedown limits are lowered by mean values of 55% and 25% respectively due to the presence of metal loss defect occupying almost half of the pipe thickness.

Pipelines subjected to thermal or mechanical loads may fail due to plastic strain accumulation which leads to ratcheting. In this research, cyclic plastic behavior and shakedown limit are investigated experimentally and numerically for a defected pressurized pipe under cyclic bending moment. In the numerical model, the combined isotropic/kinematic hardening model based on the Chaboche model is adopted to represent the cyclic plastic flow of the material. The hardening parameters are determined experimentally and used in the finite element (FE) model. A four-point bending test rig is manufactured to test a pressurized API 5L steel pipe under cyclic bending. An elliptical defect is created by machining to depict corrosion pits in pipes. The plastic strains are measured experimentally and the results are used to tune the parameters of the FE model. The shakedown limit of the defected pipe is determined numerically by tracking the critical points behavior and the results are verified experimentally. Furthermore, the plastic work dissipated energy (PWD) is estimated within the defective structure to study the behavior of the pipe. By running this compatible model, it is found that the yield and the shakedown limits are lowered by mean values of 55% and 25% respectively due to the presence of metal loss defect occupying almost half of the pipe thickness. [ABSTRACT FROM AUTHOR]

Low-amplitude repetitive drained loading may hinder the long-term performance of engineered and natural systems. This study examines the volumetric and shear response of a uniform quarzitic sand subjected to repetitive drained simple shear loading under constant vertical stress while tracking the evolution of the secant stiffness and the small-strain shear modulus. We explore the effects of initial density, initial shear stress and cyclic shear stress amplitude to identify criteria that can be used to anticipate asymptotic volumetric and shear states. We analyze experimental results in reference to the sand response under monotonic simple shear loading. All specimens evolved toward some asymptotic terminal void ratio eT when subjected to simple shear cycles. Contractive specimens exhibited unceasing shear strain accumulation and ratcheting when the normalized shear stress exceeded τ*=(τo+Δτ)/τult>0.85 ; on the other hand, dense-dilative specimens exhibited ratcheting only when the normalized shear stress exceeded τ*=(τo+Δτ)/τult>1.25. The small-strain Gmax and the secant Gpp shear moduli increased during repetitive shear cycles to reflect early fabric changes followed by abrasion/fretting among enduring contacts. Results obtained in this study allow us to propose simple guidelines to predict the asymptotic shear and volumetric response of uniform sands subjected to repetitive simple shear loading for first-order engineering analyses. [ABSTRACT FROM AUTHOR]

This paper presents the interaction system within the mechanical soil processing process, consisting of two large elements, the metal of the tool and the soil. Due to the two main forces acting on the chisel knives—friction and impact with the sandy soil—the wear of these chisel knives was determined. To determine the wear, a stand was used which allowed testing chisel-type knives in laboratory conditions by changing their functional parameters: working depth, angle of the knives to work the soil, working speed, humidity and granulation of the test environment. The present paper presents an application of the Archard-type wear law to the contact between a chisel-type knife and sandy soil (wet and dry sand). The theoretical model regarding the Archard wear coefficient considered three forms of surface damage (shake down, ratcheting and micro-cutting). The sand was considered spherical and rigid and the surface of the knife was flat. The experimental model considered real steel knives with different surface hardness and operation under controlled conditions of sand granulation, humidity, attack angle, depth of penetration and speed of sliding. The theoretical and experimental results highlight the wear behavior of chisel knives (Archard coefficient) in wet and dry sand. [ABSTRACT FROM AUTHOR]

Abstract Mechanical engineering structures and structural components are often subjected to cyclic thermomechanical loading which stresses their material beyond its elastic limits well inside the inelastic regime. Depending on the level of loading inelastic strains may lead either to failure, due to low cycle fatigue or ratcheting, or to safety, through elastic shakedown. Thus, it is important to estimate the asymptotic stress state of such structures. This state may be determined by cumbersome incremental time-stepping calculations. Direct methods, alternatively, have big computational advantages as they focus on the characteristics of these states and try to establish them, in a direct way, right from the beginning of the calculations. Among the very few such general-purpose direct methods, a powerful direct method which has been called RSDM has appeared in the literature. The method may directly predict any asymptotic state when the exact time history of the loading is known. The advantage of the method is due to the fact that it addresses the physics of the asymptotic cycle and exploits the cyclic nature of its expected residual stress distribution. Based on RSDM a method for the shakedown analysis of structures, called RSDM-S has also been developed. Despite most direct methods for shakedown, RSDM-S does not need an optimization algorithm for its implementation. Both RSDM and RSDM-S may be implemented in any Finite Element Code. A thorough review of both these methods, together with examples of implementation are presented herein.

This paper presents the interaction system within the mechanical soil processing process, consisting of two large elements, the metal of the tool and the soil. Due to the two main forces acting on the chisel knives—friction and impact with the sandy soil—the wear of these chisel knives was determined. To determine the wear, a stand was used which allowed testing chisel-type knives in laboratory conditions by changing their functional parameters: working depth, angle of the knives to work the soil, working speed, humidity and granulation of the test environment. The present paper presents an application of the Archard-type wear law to the contact between a chisel-type knife and sandy soil (wet and dry sand). The theoretical model regarding the Archard wear coefficient considered three forms of surface damage (shake down, ratcheting and micro-cutting). The sand was considered spherical and rigid and the surface of the knife was flat. The experimental model considered real steel knives with different surface hardness and operation under controlled conditions of sand granulation, humidity, attack angle, depth of penetration and speed of sliding. The theoretical and experimental results highlight the wear behavior of chisel knives (Archard coefficient) in wet and dry sand.

A semianalytical model is introduced to assess rolling contact fatigue problems in railway applications. The constitutive law is based on the nonlinear kinematic and isotropic hardening model of Chaboche–Lemaitre, which allows the cyclic elastoplastic strain under the contact surface to be evaluated. The much higher computational effectiveness in comparison with finite element (FE) analyses is quantified. The Dang Van multiaxial fatigue criterion is implemented to evaluate the rolling contact fatigue in the subsurface elastic region where cracking is relatively rare but more dangerous than surface cracks. The influence of the presence of sulfides in the wheel matrix in decreasing fatigue strength is also assessed by means of Murakami's approach. The model is used to compare conditions under small‐scale twin‐disk experiments to full‐scale wheel/rail contact conditions. It is found that, for the same Hertzian pressure, the small‐scale contact is more conservative in that it causes a deeper plasticized layer as compared with the elliptical full‐scale contact. In the investigated cases, crack initiation is also not expected according to Dang Van criterion in neither of the studied contact conditions. Highlights: A semianalytical model is developed to study the rail–wheel contact problem.Full‐scale rail–wheel contact and small‐scale twin‐disk contact problems are compared.The line contact problem experiences a deeper plasticized layer.The subsurface crack initiation is assessed using the Dang Van fatigue criterion. [ABSTRACT FROM AUTHOR]

Mechanical engineering structures and structural components are often subjected to cyclic thermomechanical loading which stresses their material beyond its elastic limits well inside the inelastic regime. Depending on the level of loading inelastic strains may lead either to failure, due to low cycle fatigue or ratcheting, or to safety, through elastic shakedown. Thus, it is important to estimate the asymptotic stress state of such structures. This state may be determined by cumbersome incremental time-stepping calculations. Direct methods, alternatively, have big computational advantages as they focus on the characteristics of these states and try to establish them, in a direct way, right from the beginning of the calculations. Among the very few such general-purpose direct methods, a powerful direct method which has been called RSDM has appeared in the literature. The method may directly predict any asymptotic state when the exact time history of the loading is known. The advantage of the method is due to the fact that it addresses the physics of the asymptotic cycle and exploits the cyclic nature of its expected residual stress distribution. Based on RSDM a method for the shakedown analysis of structures, called RSDM-S has also been developed. Despite most direct methods for shakedown, RSDM-S does not need an optimization algorithm for its implementation. Both RSDM and RSDM-S may be implemented in any Finite Element Code. A thorough review of both these methods, together with examples of implementation are presented herein. [ABSTRACT FROM AUTHOR]

Featured Application: The presented method allows applying the limit analysis of structures and reformulates the method in terms of displacements and permanent strain. In this perspective, it results that the method is stated directly considering the strain rather than the stress. Hence when one calculates the limit load factor, i.e., collapse load limit or shakedown load limit, one obtains the Melan residual strain immediately. The main disadvantage of limit analysis of structure is the uncertainty about the dissipated energy. As a consequence, the limit analysis does not occupy, within the structural analysis practice, the position it deserves. The proposed method, which can be extended to the general Finite Element Method, allows us to calculate the dissipation and to evaluate the permanent displacement compatible with it. It is, in our opinion, a useful tool to assess the structural safety in the masonry building, seismic analysis of frames to support push over and step-by-step approaches. The analogous application concerns the mechanical forecast of structural integrity under severe loads when plastic deformation is expected to occur, and one wants to allow the structure to dissipate extra-energy to prevent hazards. Safety assessment of structures can be obtained employing limit design to overcome uncertainties concerning actual response due to inelastic constitutive behavior and more generally to non-linear structural response and loads' random variability. The limit analysis is used for evaluating the safety of the structures, starting directly from load level without any knowledge of the load history. In the paper, the lower bound calculation is proposed where a new strain-based approach is used that allowed describing the residual stress and displacement in terms of permanent strain. The strategy uses the permanent strain as effective parameters of the procedure so that it is possible to assess the ductility requirements for the complete load program developed till collapse or shakedown. The procedure is compared to experimental results obtained on aluminum beams in shakedown. [ABSTRACT FROM AUTHOR]

The present paper proposes a kinematic hardening model with a memory surface to more accurately reproduce cyclic hardening and the behaviour of saturated granular soils subjected to cyclic loads. The new cyclic hardening law offers improved accuracy in predicting soil ratcheting in drained conditions and failures due to liquefaction in undrained conditions. Simulating these two aspects has been challenging due to issues such as significant loss of accuracy and numerical instability, particularly under extended (or a large number of) cyclic loads. To deal with the challenge, in addition to the novel theoretical framework, we also developed a robust sub-stepping algorithm based on an explicit stress integration scheme with automatic error control. The proposed model is compared with several existing models and its performance is evaluated by conducting sensitivity analyses and performing validations against a wide range of laboratory test results. [ABSTRACT FROM AUTHOR]

Safety assessment of structures can be obtained employing limit design to overcome uncertainties concerning actual response due to inelastic constitutive behavior and more generally to non-linear structural response and loads’ random variability. The limit analysis is used for evaluating the safety of the structures, starting directly from load level without any knowledge of the load history. In the paper, the lower bound calculation is proposed where a new strain-based approach is used that allowed describing the residual stress and displacement in terms of permanent strain. The strategy uses the permanent strain as effective parameters of the procedure so that it is possible to assess the ductility requirements for the complete load program developed till collapse or shakedown. The procedure is compared to experimental results obtained on aluminum beams in shakedown.

In case of cyclic loading, strain may accumulate due to a ratcheting mechanism until the state of shakedown is possibly achieved. Design Codes frequently require strain limits to be satisfied at the end of the specified lifetime of the structure. In addition, the strain range is required for performing fatigue analyses in case of plastic shakedown. However, little guidance is usually provided by Design Codes on how the accumulated strains and strain ranges are to be calculated, and some of the guidelines implemented in Design Codes are not well founded and may therefore be misleading. This is, for example, true for the ASME B&PV Code, Section III. Of course, strains and strain ranges can be determined by means of incremental elastic-plastic analyses, which require to go step-by-step through many cycles of a given load histogram until the state of shakedown is reached. This is rather costly in terms of engineering time and numerical effort. As an alternative, simplified methods can be adopted, e.g. the Simplified Theory of Plastic Zones (STPZ) as used in the present paper. Being a direct method, effects from load history are disregarded. The theory is described shortly and illustrated by some examples. It is shown that the Simplified Theory of Plastic Zones is well suited to provide reasonable estimates of strains accumulated in the state of elastic and plastic shakedown at the cost of few linear elastic analyses. [ABSTRACT FROM AUTHOR]

The present research revisits rare experiments which determined elastic shakedown (SD) limit pressures of full scale radial and oblique nozzles partially penetrating spherical vessels. The experiments were conducted at Berkeley Nuclear Laboratories in England [1]. The SD limit pressures were determined via conducting consecutive series of internal pressure cycles and observing cyclic strain variation recorded by strain gauges cemented at predetermined various critical locations within the junctions' vicinities. The Nonlinear Superposition Method (NSM), formulated for computing elastic SD limit loads based on Melan's lower bound SD theorem, is successfully validated against recorded experimental outcomes for both nozzle configurations. Furthermore, full elastic-plastic cyclic loading finite element simulations were executed and illustrated very good correlation to the NSM results. [ABSTRACT FROM AUTHOR]

The present paper aims to perform an experimental and theoretical study regarding the inelastic deformation progressive accumulation observed in a polyvinylidene fluoride (PVDF) specimen machined from flexible pipe internal pressure sheaths under cyclic load-unload tensile tests and in monotonic tensile tests. Experiments show that the elastic mechanical behaviour is not rate-dependent because the Young's modulus does not suffer a considerable variation with change in the strain rate. However, the strain hardening induced by the plastic deformation is strongly rate-dependent. Hence, the mechanical behaviour of this polymer is not elasto-plastic or viscoelastic, but elasto-viscoplastic. Also, the kinematic hardening strongly increases with growth of accumulated inelastic strain, making it much more significant than the isotropic hardening. This paper proposes an elasto-viscoplastic mechanical model capable of describing the cyclic and monotonic inelastic behaviour for an arbitrary loading history. The kinenatic hardening observed for this PVDF makes it possible to identify experimentally all material parameters that arise in the model by performing load-unload tests using flat specimens, eliminating buckling problems and the need to control eventual misalignment in the universal test machine grips. Good agreement was noted when comparing the theoretical results with experiments. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Progressive deformation (ratcheting) can occur as a response to variable loads as soon as the elastic limit is exceeded. If this is the case, strains and displacements accumulate in the event of cyclic loading in each load cycle. Widely known as triggers for ratcheting and already being considered in some design codes are configurations, in which a structure is subjected to at least two different types of load, namely a constant load (the primary load) and a superimposed cyclic load. In this paper, another mechanism that generates ratcheting is introduced. It can be attributed solely to the effect of a single load. In the simplest case, this can be explained by the successive activation of (an infinite number of) plastic hinges if a load of constant magnitude is moved in space. The increments of strains and displacements can decrease or increase from cycle to cycle, when the material is hardening, or if elastic foundation is present, or if the equilibrium condition is formulated for the deformed system (second-order theory) or if 'large' rotations are taken into account (third-order theory). [ABSTRACT FROM AUTHOR]

Cyclic uniaxial stress-controlled ratcheting behaviors of 35CrMo structural steel were investigated at 500 °C. The effects of stressing rates and stress amplitudes were discussed in detail. Results present that the accumulated ratcheting strain increases with the increment of stress amplitude, while decreases with the reduction of stress rate at elevated temperature. Moreover, the ratcheting evolution curves with increasing number of cycles are similar to traditional static creep curves, and can be mainly divided into three stages. Especially, the ratcheting strain rate during the steady stage can be easily obtained to estimate the ratcheting or shakedown behavior. Furthermore, the steady ratcheting strain rate significantly decreases with increasing the stressing rate when the stressing rate is relatively slow. However, when the applied stressing rate is greater than a critical value, such as ≥ 2·5 MPa s−1for = 200 MPa and ≥ 25 MPa s−1forσmax = 500 MPa, the effect of stressing rate has little effect on the cyclic ratcheting strain rate. [ABSTRACT FROM PUBLISHER]

The present paper is concerned with the experimental and theoretical investigation of the progressive accumulation of inelastic deformation observed in cyclic tension tests performed on a particular polyamide. The elastic properties are not strongly affected by the strain rate, but the strain hardening induced by the plastic deformation is rate-dependent. Thus, the material behaviour is elasto-viscoplastic rather than viscoelastic or elasto-plastic. For the polymer studied in this paper, the kinematic hardening is much more significant than the isotropic hardening, and a negative plastic strain rate may occur even with a positive stress. The kinematic hardening is strongly dependent, not only on the accumulated plastic strain, but also on the loading rate. An elasto-viscoplastic mechanical model able to describe the cyclic inelastic behaviour for an arbitrary loading history is proposed. All parameters that arise in the theory are identified experimentally. The preliminary theoretical results concerning the modelling of cyclic load-unload tests are in good agreement with the experiments. [ABSTRACT FROM AUTHOR]

Cyclic uniaxial stress-controlled ratcheting behaviors of 35CrMo structural steel were investigated at 500 °C. The effects of stressing rates and stress amplitudes were discussed in detail. Results present that the accumulated ratcheting strain increases with the increment of stress amplitude, while decreases with the reduction of stress rate at elevated temperature. Moreover, the ratcheting evolution curves with increasing number of cycles are similar to traditional static creep curves, and can be mainly divided into three stages. Especially, the ratcheting strain rate during the steady stage can be easily obtained to estimate the ratcheting or shakedown behavior. Furthermore, the steady ratcheting strain rate significantly decreases with increasing the stressing rate when the stressing rate is relatively slow. However, when the applied stressing rate is greater than a critical value, such as σ≥ 2.5 MPa/s for σ= 200 MPa and σ≥ 25 MPa/s for σmax = 500 MPa, the effect of stressing rate has little effect on the cyclic ratcheting strain rate. [ABSTRACT FROM AUTHOR]

The integrity assessment of structures subjected to cyclic loading must be verified with regard to cyclic type damage including time-independent fatigue and progressive deformation or ratcheting. Cyclic damage is verified simulating the material elastic-plastic loop and looking at the accumulated net plastic strain during each cycle at all points of the structure subjected to the complete time history of loadings. This work deals with the development of a numerical model producing the Chaboche hardening parameters starting from stress-strain data produced by testing of materials. Then, the total plastic strain can be simulated using the Chaboche inelastic constitutive model requested for finite element analyses. This is particularly demanding for pressure vessels, pressurised piping, boilers, and mechanical components of nuclear installations made of stainless steels. A design optimisation by iterative analyses is developed to approach the stress-strain test data with the Chaboche model. The parameters treated as design variables are the Chaboche parameters and the objective function to be minimised is a combination of the deviations from test data. The optimiser calls a macroinstruction simulating cyclic loading of a sample for different material temperatures. The numerical model can be used to produce hardening parameters of materials for inelastic finite element verifications of structures with complex joints like elbows subjected to a combination of steady sustained and cyclic loads. [ABSTRACT FROM AUTHOR]

Shakedown and ratcheting behaviors of pipes under thermo-mechanical loading have an important role in their design. In this study, Plastic, Elastic shakedown and ratcheting limit of the pipelines with different types of defects were analyzed. The pipelines were subjected to the constant internal pressure and the cyclic thermal gradient. Different dimensions of these defects were also studied. Nonlinear kinematic hardening model of Armstrong–Frederick coupled with continuum damage mechanics was used and material properties were considered temperature-dependent. The unified Lemaitre’s model was used in continuum damage mechanics. Interaction diagrams (Bree's diagram) of the defective pipelines were obtained and parametric studies involving different types and dimensions of part-through slot in the defective pipeline were investigated. Continuum Damage Mechanics was used to predict life time of some defected pipelines. [ABSTRACT FROM AUTHOR]

The ratchet and shakedown boundaries are derived analytically for a thin cylinder composed of elastic-perfectly plastic Tresca material subject to constant internal pressure with capped ends, plus an additional constant axial load, F , and a cycling secondary global bending load. The analytic solution is in good agreement with solutions found using the linear matching method. When F is tensile, ratcheting can occur for sufficiently large cyclic bending loads in which the pipe gets longer and thinner but its diameter remains the same. When F is compressive, ratcheting can occur in which the pipe diameter increases and the pipe gets shorter, but its wall thickness remains the same. When subject to internal pressure and cyclic bending alone ( F = 0), no ratcheting is possible, even for arbitrarily large bending loads, despite the presence of the axial pressure load. The reason is that the case with a primary axial membrane stress exactly equal to half the primary hoop membrane stress is equipoised between tensile and compressive axial ratcheting, and hence does not ratchet at all. This remarkable result appears to have escaped previous attention. [ABSTRACT FROM AUTHOR]

The current research utilizes a direct non-cyclic technique to generate elastic shakedown domains for thinned-wall 90° elbows. The elbows are subjected to simultaneous steady internal pressures and cyclic in-plane and out-of-plane bending moments. Wall thinning is located at the intrados, extrados, and crown once at a time. Effects of thinning depth and thinning location under both cyclic in-plane and out-of-plane bending modes are investigated. Generated shakedown boundaries are compared to those corresponding to sound elbows. Elbows subjected to out-of-plane bending moments revealed relatively higher shakedown domains compared to corresponding elbows subjected to in-plane bending. It is generally noticed that thinning at the intrados or crown has more severe effect on reducing elbows shakedown domains as compared to thinning at the extrados for both in-plane and out-of-plane bending modes. [ABSTRACT FROM AUTHOR]

The behavior of elastic-plastic structures under cyclic loading can be determined by incremental elastic-plastic analyses where a given load histogram is analysed cycle-by-cycle until shakedown is achieved. Many cycles may be required for this, if a ratchet mechanism is causing plastic strains to accumulate in each cycle until either elastic or plastic shakedown is achieved. The complexity of the elastic-plastic response of a structure is further increased if geometric effects are present. It may be very costly to get the accumulated strains and strain ranges in the state of shakedown by incremental analyses so that simplified or direct methods have been developed as an alternative. The Simplified Theory of Plastic Zones (STPZ) has proven itself for estimating the required quantities in the state of elastic and plastic shakedown within the framework of the 1st order theory, i.e., if the equilibrium conditions are satisfied for the undeformed structure. It is shown in this paper, how the STPZ can be expanded to capture 2nd order effects introduced by the equilibrium of the deformed structure. Some examples are used to demonstrate its applicability and the quality of the results, but also its limitations with respect to determining the accumulated strains and elastic-plastic strain ranges. • Stress stiffening may increase the elastic-plastic strain range. • The Simplified Theory of Plastic Zones (STPZ) is suited to capture stress stiffening. • The STPZ may be used to estimate cyclic accumulated strains and strain ranges. [ABSTRACT FROM AUTHOR]

Printed Circuit Heat Exchangers (PCHEs) is a kind of compact plate heat exchanger with a lot of fine channels in a solid block, called PCHE core. It can withstand high temperature and high pressure. And beyond that, it has many advantages, such as high heat exchange efficiency, low pressure drop, high compactness, good corrosion resistance, long service life and many other advantages. However, PCHEs will endure complex mechanical and thermal loads in service. Meanwhile, shakedown and ratcheting assessment, especially how to determine shakedown and ratcheting boundary for PCHEs in an efficient and accurate way, is still an intractable problem so far. This article makes deep research and analysis to shakedown and ratcheting boundary for PCHEs subjected to complex cyclic load combinations as well as the effect of channel shape and size effects based on the linear matching method (LMM). The influences of load parameters, e.g. temperature difference and pressure difference between hot and cold channels, and geometric parameters, e.g. channel radii, channel shapes, arrangement of channels, and transition radius of the local corner of the semicircular channel, were all discussed in detail. Based on these different types of influence parameters, two-dimensional shakedown and ratcheting boundaries for different kinds of PCHEs models under complex mechanical-thermal load combinations are presented in this paper. It is demonstrated that pressure differences between the hot and cold channel have significant effect, but different channel radii are not so significant. Core size and channel shape are observed to influence the shakedown and ratcheting responses significantly, however, the corner radius shows more significant effect on the shakedown boundary than the ratcheting limit boundary. The PCHE core arrangement, i.e. total number and position, is also found to influence the shakedown and ratcheting responses significantly, especially for the constant pressure loading case. Based on a series of LMM analysis results, it can be concluded that accumulative incremental plastic strain will occur at the region between the cold and the hot channel when the combination of mechanical and thermal loads exceeds the ratcheting limit, which should be under strict control. The results from current parametric studies can be an effective reference for design and optimization of the diffusion bonded PCHE channels in high temperature nuclear applications. • A new shakedown and ratcheting limit assessment for PCHEs under multiple cyclic mechanical and thermal loads. • The Linear Matching Method provides an efficient and accurate tool. • Complex cyclic thermal and mechanical load combinations considered. • Detailed parametric studies for design and optimization of the diffusion bonded PCHE channels. • Comprehensive discussions to reveal fundamental mechanisms of shakedown and ratcheting. [ABSTRACT FROM AUTHOR]

In this study, the elastoplastic analysis of thin-walled tubes under cyclic bending and internal pressure is presented. A simple method is presented and verified. In order to predict ratcheting or shakedown behavior in the cyclic loading, von-Mises yield criterion as the yield surface and Chaboche’s nonlinear kinematic hardening model are used. The stress–strain variation is obtained with the help of return mapping algorithm. The present solution is in good agreement with experimental results. Shakedown or ratcheting behavior of the tube under various combinations of applied constant internal pressure and cyclic curvature is considered, Bree’s interaction diagram is obtained and the boundary between shakedown and ratcheting zone is determined. [ABSTRACT FROM PUBLISHER]

Corroded pipes for oil transportation can eventually undergo ratcheting after several years of operation. Evaluation of the defects caused by corrosion in these pipes is important when deciding either to repair the line or to continue its operation. Under normal operational conditions, these pipes are subjected to constant internal pressure and cyclic loading due to bending and/or tension. Under such loading conditions, regions in the pipes with a reduction in thickness due to corrosion could experience a phenomenon known as ratcheting. The objective of this paper is to study the effect of a loss in thickness due to the corrosion through combined numerical models and experiments. Three constitutive models capable of representing the ratcheting phenomenon were selected and assessed. Experimental tests were developed to verify the eventual occurrence of ratcheting in corroded pipes under typical operational load conditions. In parallel small-scale cyclic tests were performed to obtain the material parameters necessary to calibrate the constitutive models that were adopted to simulate the phenomenon. The results reveal the existence of loading combinations that cause ratcheting in the defect region, but for the intact pipe, would result in elastic behavior. Numerical and experimental results were compared and showed that a good prediction of the plastic strain along the cycles can only be achieved with the model that requires a more complex calibration, but the shakedown/ratcheting occurrence can be accurately predicted with a model calibrated solely with uniaxial tests. [ABSTRACT FROM AUTHOR]

Cyclic loading may cause elastic-plastic strains to accumulate if a ratcheting mechanism is present. After a number of cycles, strain accumulation may cease so that a state of either elastic or plastic shakedown is reached. Determination of strains and other quantities in the state of shakedown (post-shakedown quantities) by means of incremental analyses is costly. Direct methods such as the Simplified Theory of Plastic Zones (STPZ) aim at providing estimates of the post-shakedown quantities, bypassing cycle-by-cycle analyses. If geometric effects such as stress stiffening play a role, determination of accumulated strains even becomes more complicated. The STPZ has been further developed in order to account for the combination of plasticity and stress stiffening with respect to elastic shakedown. The theory is described and illustrated using examples such as a pipe bend subjected to cyclic in-plane bending. The implications of cyclic as opposed to constant stress stiffness are discussed. The effect of stress stiffening on ratcheting interaction diagrams (RID), separating regions of elastic and plastic shakedown in the space of loading parameters, is discussed. • Stress stiffening may affect strain accumulation in state of elastic shakedown. • Stress stiffening may be accounted for by the Simplified Theory of Plastic Zones. • The STPZ is suited to estimate cyclic accumulated strain at elastic shakedown. [ABSTRACT FROM AUTHOR]

Highlights: [•] We examine a three dimensional elastic rolling contact with Coulomb friction. [•] Slight oscillatory rolling leads to frictional shakedown or ratcheting. [•] We derive the analytical shakedown limits and the shakedown displacement. [•] Shakedown leads to a significant reduction of the tangential load capacity. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to obtain the dependency of the ratcheting, reversed plasticity, or shakedown behavior of spherical vessels made of some anisotropic materials to the stress category of imposed cyclic loading. The Hill anisotropic yield criterion with the kinematic hardening theories of plasticity based on the Prager and Armstrong–Frederick models are used to predict the yield of the vessel and obtain the plastic strains. An iterative numerical method is used to simulate the cyclic loading behavior of the structure. The effect of mean and amplitude of the mechanical and thermal loads on cyclic behavior and ratcheting rate of the vessel is investigated respectively. The ratcheting rate for the vessels made of transversely isotropic material is evaluated for the various ratios of anisotropy. [Copyright &y& Elsevier]

Abstract: Deformation of homogeneous elastic-perfectly plastic (EPP) and elastic-linear kinematic hardening plastic (ELKP) half-spaces due to repeated adhesive sliding contact is examined with a two-dimensional finite element model. Interfacial adhesion is modeled by nonlinear springs with a force-distance constitutive relation derived from the Lennard–Jones potential. Deformation behavior is interpreted in terms of dimensionless parameters, such as the Maugis parameter, interaction distance (interfacial gap), and plasticity parameter. Numerical results provide insight into the stress–strain response and the evolution of subsurface plasticity. The effects of the interaction distance, plasticity parameter, interfacial adhesion, and Maugis parameter on the friction and normal forces and the accumulation of plastic strain are analyzed in terms of the number of sliding cycles. Deformation maps providing information about the steady-state mode of deformation are presented for both EPP and ELKP material behaviors. Results of this study illustrate the importance of elastic–plastic material behavior and interfacial adhesion in contact deformation due to repeated surface sliding. [Copyright &y& Elsevier]

Abstract: The present paper is concerned with the experimental investigation of the progressive accumulation of deformation observed in cyclic tension tests performed on an epoxy polymer. The strain rate dependency is almost negligible and the material behaviour is elastic-plastic rather than elastic-viscoplastic or viscoelastic. Under cyclic loading and unloading, this polymer exhibits hysteresis (a phase lag), which leads to dissipation of mechanical energy and to the accumulation of cyclic plastic deformation. It is verified experimentally that this phenomenon is essentially due to kinematic hardening. Preliminary ideas for an elastic-plastic phenomenological model able to describe the plastic cyclic behaviour of this epoxy polymer are also presented. [Copyright &y& Elsevier]

Abstract: Shakedown and ratcheting behaviour is derived for uniaxial primary membrane and thermal bending stresses both cycling strictly in-phase. The complete analytic solution for perfect plasticity is presented, including the shakedown/ratcheting diagram and the ratchet strains or cyclic plastic strains where relevant. This cyclic loading is shown to be considerably more benign than that of the original Bree problem in which the primary membrane stress does not cycle. [Copyright &y& Elsevier]

Abstract: From the practical point of view, the classical elastic shakedown methods are not very useful for design, since in most components the stresses can safely exceed the elastic limit locally. This paper generalizes the static shakedown theorem (Melan’s theorem) to allow the analysis of plastic shakedown. Since the method is derived from a lower bound formulation in shakedown, it is very useful for the design purposes (safe). The ratchet boundary is analytically determined using the proposed method for several examples with uniform stress distributions. The numerical implementation of the method along with several examples is discussed in an accompanying paper. [Copyright &y& Elsevier]

Abstract: Determining the boundary between the shakedown and ratcheting domains (ratchet boundary) for a component using cyclic elastic-plastic analysis is computationally very expensive since it requires a solution over several loading cycles to be repeated several times. A non-cyclic method to identify the ratchet boundary directly without the need for cyclic analysis was recently proposed. The numerical implementation of the non-cyclic method offers the promise to be an attractive alternative to cyclic elastic-plastic analysis since it is simple, and requires considerably less computational effort and computer storage space. Another attractive feature is that the method provides a go/no go criterion for the ratchet boundary, whereas the results of a cyclic elastic-plastic analysis are often difficult to interpret near the ratchet boundary. To explore the performance of the method further, it is applied to a number of configurations that include two-dimensional and three-dimensional effects. [Copyright &y& Elsevier]

Abstract: This paper extends the Bree’s cylinder behaviors, which is subjected to the constant internal pressure and cyclic temperature gradient loadings, with considering continuum damage mechanics coupled with nonlinear kinematic hardening model. The Bree’s biaxial stress model is modified using the unified damage and the Armstrong–Frederick nonlinear kinematic hardening models. With the help of the return mapping algorithm, the incremental plastic strain in axial and tangential directions is obtained. Continuum damage mechanics approach can be used to extend the Bree’s diagram to the damaging structures and reduce the plastic shakedown domain. Kinematic hardening behavior was considered in the material model which shifts the ratcheting zone. The role of the material constants in the Bree’s diagram is also discussed. [Copyright &y& Elsevier]

Abstract: A modular helium-cooled divertor design HEMJ (helium-cooled modular divertor concept with multiple-jet cooling) for the “post-ITER” demonstration (DEMO) fusion reactor has been developed at the Forschungszentrum Karlsruhe. The design goal is to withstand a surface heat flux of at least 10MW/m2 at an acceptable pumping power. A conical design of a brazed joint between two structural components of the HEMJ finger module which are made of different materials has been investigated. This new transition piece design should withstand at least 1000 temperature load cycles between operating and room temperatures. Due to the large mismatch of the thermal expansion coefficients (TECs) of the different materials used, high thermal stresses caused by the thermocyclic loads could lead to the plasticization of both materials in the joint region. To demonstrate the feasibility of this transition piece design, a systematic investigation is required, which includes a numerical simulation, the choice of the brazing material, a study of the brazing technology, and thermocyclic tests of the finger mock-up. This paper shall present a method of numerical investigation as the first step of investigation. Plastic stress calculations are performed using the commercial software ANSYS® taking into account thermocyclic as well as internal pressure loads. The calculation results, in particular the plastic behavior of the brazed joint, will be discussed. [Copyright &y& Elsevier]

Abstract: A two-dimensional model has been developed for thermal stresses, elastic strains, creep strains, and creep energy density at the interfaces of short and long trilayer assemblies under both plane stress and plane strain conditions. Both linear (viscous) and non-linear creep constitutive behavior under static and cyclic thermal loading can be modeled for all layers. Interfacial stresses and strains are approximated using a combination of exact elasticity solutions and elementary strength of materials theories. Partial differential equations are linearized through a simple finite difference discretization procedure. The approach is mathematically straightforward and can be extended to include plastic behavior and problems involving external loads and a variety of geometries. The model can provide input data for thermal fatigue life prediction in solder or adhesive joints. For a typical solder joint, it is demonstrated that the predicted cyclic stress–strain hysteresis shows shakedown and a rapid stabilization of the creep energy dissipation per cycle in agreement with the predictions of finite element analysis. [Copyright &y& Elsevier]

Fatigue life of heavily loaded rolling bearings is strongly dependent on elastic-plastic material properties. For bearing steels these elastic-plastic properties can be accurately obtained by performing monotonic or half-compressive tests. A three-dimensional strain deformation analysis based on the incremental theory of plasticity and the use of Prandtl-Reuss relations in conjunction with the von Mises yield criterion was developed in order to evaluate the permanent deformation in dry contacts loaded above the elastic limit in case of normal loading. The Ramberg-Osgood stress-strain relation for two martensitically hardened variants of SAE 52100 bearing steel considered the nonlinear kinematic and/or isotropic material behavior. Parameters describing the influence of retained austenite are modeled by using a nonlinear isotropic law. Pressure distribution and contact surface displacements during incremental loading are evaluated by using a conjugate gradient method and the internal stress field is derived by using the superposition principle. Further, a fast analysis of smooth surfaces in elastic-plastic static and rolling contact is developed based on analytical relations for the internal stress field. Cyclic evaluation of plastic strains and residual stresses is carried out until shakedown. In order to verify the theoretical model, rolling contact tests under high normal load were performed. Residual stresses and residual profiles measurements show excellent agreement between numerical and measured cyclic values. [ABSTRACT FROM AUTHOR]

Compacted unbounded granular materials are extensively used as sub-layer in pavement design. Most pavement design guides assume that they are responsible for the degradation and deformation of the roads and railways that they support. Biaxial tests are usually employed to investigate the elasto-plastic response of these materials to cyclic loading. A particularly interesting question is whether a limit load exists, below which the excitations shake down, in the sense that the material does not accumulate further deformations. We have carried out a detailed study of the elasto-plastic behavior of a simple model of unbound granular matter submitted to cyclic loading. The dissipated energy throughout the simulation has been used for the characterization of the different regimes of responses. [ABSTRACT FROM AUTHOR]

Abstract: Part 1 gives the basis for the use of cyclic reference stresses for high temperature design and assessment. The methodology relies on elastic–plastic calculations for limit loads, ratcheting and shakedown. In this paper we use a commercial non-linear finite element code for these calculations. Two fairly complex and realistic geometries with cyclic loads are analysed, namely a pipe elbow and a traveling thermal shock in a pressurized pipe. The special case of start-up shut-down cycles is also discussed. Creep and rupture predictions may be made from the results. When reference stresses can be economically calculated, their use for high temperature design has the following advantages.[•] Accuracy. Limit loads, shakedown and ratcheting limits are based on detailed analysis, and do not rely on rules or judgement. [•] Efficiency. Use of shakedown and ratcheting reference stresses to predict rupture and creep strain, respectively, allowing details of time and temperature to be dealt with as material data, not affecting the analysis. [•] Factors of safety. For both low and high temperature problems, factors of safety can be determined or applied, based on the real failure boundaries. [•] Conservatism. The rupture and strain calculations reflect the limit of rapid cycle behaviour. Cycles with relaxation will be associated with longer lives. [Copyright &y& Elsevier]