Accumulation Of Irreversible Strains Research Articles

Feasibility of using superelastic shape memory alloy in plastic hinge regions of steel bridge columns for seismic applications

AbstractThis paper contributes to the further development of seismic resilient infrastructure by introducing a novel prototype bridge which integrates tubular steel piers with superelastic shape memory alloy (SMA). The proposed bridge pier is composed of a circular steel tube which is bonded to a superelastic SMA tube in regions of high stress. The pier is distinguished by its ability to minimize residual drifts following inelastic deformations induced by cyclic loading. Three‐dimensional continuum finite element (FE) models are utilized to examine its lateral behavior. Experimental data is used to demonstrate the effectiveness of the continuum FE procedure in replicating the cyclic response and capturing both global and localized behaviors. A novel composite material model is proposed to represent the degradation of strength and accumulation of irreversible strains in the cyclic response of superelastic SMAs. An iterative procedure for the calibration of this material is presented. Investigations, employing the calibrated FE procedure, focus on the quasi‐static cyclic response of steel piers with superelastic SMA in the plastic hinge zone, aiming to identify the optimal length of the SMA tube for achieving a self‐centering response with reduced residual deformation. The study is then further expanded to examine the seismic response of a bridge structure incorporating such piers. Development of the FE model for the prototype bridge includes the modelling of the piers using continuum elements, while the superstructure, bearing units, abutment walls, and backfill material are modelled using discrete elements. Nonlinear time history analyses are undertaken to investigate the effects of column wall thickness and materials used in the plastic hinge zones of the piers. Dynamic FE study results indicate that bridges employing such piers are capable of returning to their original position, provided the SMA tube is of adequate length.

Fatigue characteristics of deep excavation-disturbed Jinping marble

Deep rocks encountered in underground engineering are frequently in complex in situ environments and experience both excavation disturbance during construction and cyclic loading throughout the long-term operation. Understanding the fatigue behavior of excavation-disturbed rocks in complex stress environments is critical for assessing the long-term stability of deep rock structures. Hence, an experimental method has been developed to capture the fatigue damage process of rocks while considering the in situ environment and excavation disturbance. Using this method, a series of triaxial fatigue damage experiments were conducted on Jinping deep marble samples from various in situ environments of 100 m, 1000 m, 1800 m, and 2400 m to better understand the variation in fatigue characteristics at different depths. With increasing depth, the samples experienced more cycles and greater fatigue deformation before failure. Further insights were gained into the fatigue damage behavior in terms of stiffness degradation, energy dissipation and irreversible strain accumulation. A decrease in the elastic modulus and an increase in the dissipated energy and irreversible strain exhibit an evolution pattern of initial→stabilization→acceleration, reflecting the nonlinear fatigue process that occurs inside marble. With increasing depth, marble samples have longer fatigue lives but exhibit more significant stiffness loss, energy dissipation and irrecoverable deformation accumulation; thus, evaluating the instability of deep rock structures solely using fatigue life alone is inadequate. Moreover, the previously reported inverted S-shaped evolution of fatigue damage was observed, and it was found that an increase in depth leads to an earlier onset of the accelerated fatigue damage stage with greater dominance of fatigue failure. Based on the nonlinear strain, loading cycle variable and fatigue life, a highly accurate nonlinear fatigue model was developed to describe the complete inverted S-shaped evolution pattern of fatigue damage, which demonstrated excellent practical implications for the theoretical characterization of anisotropic fatigue damage in disturbed Jinping marble.

Experimental study on the freezing-thawing behavior of compacted earth

Most of compacted earthen constructions are located at temporary and seasonal frozen areas, consequently exposed to repeated freezing-thawing (F-T) environment induced by significant temperature fluctuations. The F-T cycles can cause severe damage to the compacted earthen materials and reduce the structure’s durability. In this paper, a series F-T tests were performed in order to study the damage mechanism of the compacted earthen materials subjected to F-T cycles. The experiments were carried out under two confining pressures (σc= 0 kPa and 50 kPa) and three freezing temperatures (TF=−5℃, −8℃ and −13℃), with a thawing temperature of TT= 9℃. Evolution of elastic moduli and accumulation of irreversible strain at the end of each F-T processes were analyzed through cyclic loading–unloading tests under undrained condition. Results indicate that each F-T cycle could be characterized by main six stages, whose physical meaning has been explained through a thermodynamic approach. With increasing number of F-T cycles, a growth of the Young’s modulus was observed when the material was in a frozen state, and the opposite was found for the thawed state. This may be explained by an increase in macro-porosity as F-T cycles progress, which would be in line with the accumulation of residual deformation and the increase of freezing and thawing temperatures. The applied confining pressure was eventually found to provide a positive resistance against permanent deformation. This discovery can provide experimental support to the safety design of earthen wall situated in cold regions.

Inspection of ratcheting models for pathological error sensitivity and overparametrization

Accurate analysis of plastic strain accumulation under stress-controlled cyclic loading is vital for numerous engineering applications. Typically, models of plastic ratcheting are calibrated against available experimental data. Since actual experiments are not exactly accurate, one should check the identification protocols for pathological dependencies on experimental errors. In this paper, a step-by-step algorithm is presented to estimate the sensitivities of identified material parameters. As a part of the sensitivity analysis method, a new mechanics-based metric in the space of material parameters is proposed especially for ratcheting-related applications. The sensitivity of material parameters to experimental errors is estimated, based on this metric. Moreover, a relation between pathological error sensitivity and overparametrization is established. This relation gives rise to a new criterion of overparametrization. The advantages of the new overparametrization criterion are exposed and its plausibility is checked by alternative criteria, like the consideration of correlation matrices and validation of identified parameters on “unseen” data. For demonstration purposes, the accumulation of irreversible strain in the titanium alloy VT6 (Russian analog of Ti-6Al-4V) is analysed. Three types of phenomenological models of plastic ratcheting are considered. They are the Armstrong-Frederick model as well as the first and the second Ohno-Wang models. Based on real data, a new rule of isotropic hardening is proposed for greater accuracy of simulation. The ability of the sensitivity analysis to determine reliable and unreliable parameters is demonstrated.

Modelling of a production process of irreversible strains in a material of a thick-walled cylindrical tube under the influence of inner pressure

This article considers the processes of the accumulation of irreversible strains in an elastoviscoplastic material of a thick-walled cylindrical tube in the framework of small strains. The material is deformed under the action of uniform inner pressure changing with time. Irreversible strains accumulate in the material by means of two different mechanisms, namely creep and plastic flow. Initially, whereas stresses increase in the deformed body due to mechanical influence, irreversible strains are produced as creep strains because of the viscous material properties. When the stress state reaches a loading surface, the production mechanism of irreversible strains becomes plastic. When unloading, this sequence in the production mechanisms is opposite, i.e. the fast plastic mechanism is replaced by the slow viscous one. The continuity in the growth of irreversible strains is provided by the corresponding setting of creep and plastic potentials. The possibility of the use of these potentials in the form of piecewise linear functions is investigated. It makes possible to use the developed mathematical formalism of the ideal plasticity theory. The creep and plastic flow processes under increasing and constant inner pressures are considered. The unloading process and repeated plastic flow under decreasing inner pressure, the stress relaxation after the full removal of a loading force are investigated. The reversible and irreversible strains, stresses and displacements in the medium are calculated. The laws of the motion of elastoplastic boundaries in the cylindrical layer are determined.

On the mechanisms of production of large irreversible strains in materials with elastic, viscous and plastic properties

A thermodynamically and geometrically consistent mathematical model of large strains of materials with elastic, viscous and plastic properties is proposed. The viscous properties of a material are considered to provide a creep process and, therefore, the slow growth of irreversible strains during unloading and the stage preceding plastic flow. Under the fast growth of irreversible strains under the conditions of plastic flow, the viscous properties emerge as a mechanism that resists to this flow. Thus, the accumulation of irreversible strains initially occurs in the creep process, then under the plastic flow condition and finally because of material creep (during unloading). The change in the mechanism of irreversible strain growth occurs on elastoplastic boundaries moving in the deformed material. This change is only possible under the conditions of the continuity of irreversible strains and their rates. This continuity requires the coordination in the definitions of irreversible strain rates in the dependence on stresses, i.e. in laws of creep and plasticity. The change in the production mechanisms of irreversible strains means a different setting of the sources in differential equations of change (transfer equations) for these strains. Thus, irreversible strains are not divided into creep and plastic ones. The hypothesis of the independence of thermodynamic potentials (internal energy, free energy) from irreversible strains is applied with the aim of most visibility of the model relations. Under the condition of the acceptance of this hypothesis, an analogue of the Murnaghan formula is obtained, i.e. the stresses are completely determined by the level and distribution of the reversible strains as in the classical elastoplasticity theory. The main statements of the proposed model are illustrated by a boundary value problem solved in the framework of the model. This problem is about the deformation of an elastoviscoplastic material placed in the gap between two rigid cylindrical surfaces under the rotation of one of them and the material slipping in the neighbourhood of the internal surface.

Gradient‐Enhancement of a Rock Model Applied to Numerical Simulations of Tunnel Advance

AbstractRock is classified as a frictional cohesive material characterized by nonlinear stress‐strain relations including softening leading to structural failure. To describe the mechanical behavior of rock comprising the accumulation of irreversible strains, strain hardening, and the degradation of stiffness and strength, an isotropic damage plasticity model for intact rock and rock mass was proposed in [1]. In the context of numerical simulations of tunneling, considering strain softening of rock allows to predict the formation of shear bands emanating from the tunnel surface due to the excavation process, which is crucial for engineers to forecast potentially dangerous situations related to failure. To ensure objective results in the softening regime upon mesh refinement, in the aforementioned rock model the concept of the crack band approach by Bažant and Oh was adopted. As a remedy of known deficiencies related to this regularization approach, the rock model is extended by the over‐nonlocal implicit gradient‐enhancement proposed in [2]. Accordingly, a nonlocal field of the damage‐driving variable, implicitly defined as the solution of a Helmholtz‐like partial differential equation, is introduced yielding a fully coupled system of second‐order PDEs. In the present contribution, the over‐nonlocal gradient enhancement of the rock model is presented and applied together with a linear‐elastic material model for shotcrete to finite element simulations of a deep tunnel constructed by the New Austrian Tunneling Method. Based on this real example, objectivity of the results with respect to the finite element discretization is discussed.

Postpeak Deformability Parameters of Localized and Nonlocalized Damage Zones of Rocks under Cyclic Loading

Previous studies on the effects of cyclic loading on the strength and deformability behavior of rocks under uniaxial conditions, i.e., strength damage together with the degradation of rocks’ mechanical properties, have solely taken into account the postpeak stress strain regime. Nevertheless, rock may experience cyclic loading history in the postpeak regime as well. In this study, the effects of cyclic loading on the deformational characteristics of both the nonlocalized damage zone (NLDZ) and the localized damage zone (LDZ) of rock in the postpeak regime are investigated. A series of postpeak damage-controlled tests were carried out on three different rock types, including sandstone, limestone, and granite specimens. Three-dimensional digital image correlation was implemented to measure the strain development in the surface of the specimens. Strain localization was found to be more significant in the lateral direction and less occurrent in the axial direction. In addition, it was observed that the material located in the NLDZ experiences much less damage in contrast to material located in the LDZ. Both large irreversible strain accumulation and Young’s modulus degradation were found to take place progressively in the LDZ, initially occurring at a lower rate and then faster as the number of loading-unloading cycles increased. In this regard, the extent of irreversible deformation and stiffness degradation in the LDZ is considered to be a major contributor to the global loss of strength of the entire specimen.

Static and dynamic nonlinear response of masonry walls

A nonlocal damage-plastic model is proposed to investigate the mechanical response of masonry elements, under static and dynamic actions. The adopted constitutive relationship is able to capture degrading mechanisms due to propagation of microcracks and accumulation of irreversible strains. Moreover, the stiffness recovery, due to re-closure of tensile cracks when material undergoes compression strains, is taken into account to properly simulate the masonry cyclic response. The proposed relationship is implemented in a 2Dplane stress finite element and a predictor–corrector procedure is developed to solve the nonlinear evolution problem of damage and plastic variables.The model validation is carried out by comparing numerical and experimental results on masonry panels under cyclic quasi-static conditions. Then, to analyze the effect of the evolution of degrading mechanisms on masonry dynamic response, the frequency response curves of a slender wall are evaluated by highlighting the influence of the proposed masonry constitutive relationship with respect to other widely studied models characterized by nonlinear invariant restoring forces.

ON ACCOUNT OF VISCOUS PROPERTIES OF MATERIALS IN THE THEORY OF LARGE ELASTOPLASTIC STRAINS

A geometrically and thermodynamically consistent mathematical model of large strains of materials with elastic, viscous and plastic properties is proposed. It is believed that at the stage of a strain, which precedes the plastic flow and during unloading, the viscous material properties provide the creep process and thus a slow growth of irreversible strains. While rapid growth of irreversible strains under plastic flow conditions, viscous properties act as a mechanism that retards the flow. The accumulation of irreversible strains, therefore, occurs successively: initially, in the creep process, then under plastic flow and, finally, again due to creep of the material (during unloading). On the elastoplastic boundaries advancing along the deformable material, there is a change in the growth mechanism of irreversible strains from creep to plasticity and vice versa. Such a change is possible only under conditions of continuity of irreversible strains and their change rates, which imposes the requirement of consistency in the definitions of irreversible stress distribution rates, i.e., the laws of creep and plasticity. Changing the production mechanisms of irreversible strains means various setting up of the source in the differential equation of the change (transfer) of these strains, hence irreversible strains are not divided into plastic strains and creep strains. To maximize the visibility of the model’s correlations, the hypothesis on the independence of thermodynamic potentials (internal energy, free energy) on irreversible strains is accepted. As a consequence of the hypothesis, an analog of the Murnaghan formula is obtained, the classical position of the elastoplasticity is that the stresses in the material are completely determined by the level and distribution of reversible strains. The main provisions of the proposed model are illustrated by the solution in its framework of the boundary value problem of the elastoviscoplastic material motion in a pipe due to a varying pressure drop.

Influence of Structural Stiffness on Ratcheting Convection Cells of Granular Soil under Cyclic Lateral Loading

In granular soils, long-term cyclically loaded structures can lead to an accumulation of irreversible strain by forming closed convective cells in the upper layer of the bedding. The size of the convective cell, its formation and grain migration inside this closed volume have been studied with reference to different stiffness of the embedded structure and different maximum force amplitudes applied at the head of the structure.This relation was experimentally investigated by applying a cyclic lateral force to a scaled flexible vertical element embedded in a dry granular soil. The model was monitored with a camera in order to derive the displacement field by means of the PIV technique. Furthermore, the ratcheting convective cell was also simulated with DEM with the aim of extracting some micromechanical information. The main results regarded the different development, shape and size of the convection cell and the surface settlements.

Effect of loading frequency and stress level on low cycle fatigue behavior of plain concrete in direct tension

Due to the difficulties of direct tensile testing on concrete, only limited and often conflicting data are available. In this paper, to investigate the effect of loading frequency on the low cycle fatigue behavior of plain concrete in direct tension, several series of cyclic tension tests at different frequencies and stress levels were carried out. Especially the behavior before the initiation of macroscopic fatigue cracks in concrete, such as irreversible strain accumulation and damage evolution with the number of fatigue cycles through experiments. Test results show that the fatigue life increases with the increasing of the applied loading frequency, while decreases with the increasing of stress level. The stiffness degradation shows a typical three-stage process with the number of fatigue cycles. A new damage model considering the effect of the applied loading frequency and stress level is proposed based on the stiffness degradation and the secondary strain rate during low-cycle fatigue tests. Also, a fatigue model is proposed herein to characterize the deformation and damage behavior of concrete under cyclic tension. The calculated fatigue lives of concrete are compared with experimental data and show good fitting results.

Effect of dynamic stress state perturbation on irreversible strain accumulation at interfaces in block-structured media

The paper studies how the stress state of the interface between structural elements in a block-structured medium affects its deformation response to dynamic loading. It is shown that the normalized shear stress and mean stress are the major factors that determine the deformation response of the interface. We propose to describe the dependence of the value of induced irreversible displacement at the interface on the normalized shear stress using a logistic function. The central point of this function is the point of transition from the quasi-elastic to quasi-plastic stage of the interface shear deformation. The obtained empirical dependences are important for understanding the mechanism of irreversible strain accumulation in fault zone fragments and, particularly, for the development of an earlier proposed approach to estimate the characteristic level of active shear stresses in separate tectonic fault regions.

Constitutive analysis of shale: a coupled damage plasticity approach

Shales have become increasingly important because they play key roles in modern energy and environmental geomechanics applications, such as nuclear waste storage, non-conventional oil and gas operations and CO2 geological storage. Shale behaves in a quasi-brittle manner, often exhibiting linear elasticity before reaching its peak stress. Furthermore, softening of the material leads to a residual state in which pure plastic flow is observed under constant values of deviatoric stress. Degradation of the elastic moduli and the accumulation of irreversible strains are believed to be primarily caused by the debonding and decohesion mechanisms in the structure, as well as the growth of microcracks. To capture these features, a constitutive model that couples elastic, plastic and damage theories is developed. The isotropic damage model is based on the Weibull probabilistic theory and describes the failure of brittle materials. This model is coupled with a modified version of the Lade–Duncan criterion to account for non-linear dependency of shear resistance with a mean stress typical of geomaterials. The two surfaces of damage and plasticity and the rate equations for the internal variables are postulated and thermodynamic consistency is subsequently investigated. The coupled plastic-damage constitutive model is integrated with an implicit stress return algorithm for the plastic part, while the damage part can be integrated implicitly. Numerical back-calculations of experimental results from two quasi-brittle shales demonstrate the ability of the model to reproduce the primary features of their mechanical behavior.

Nonlocal damage propagation in the dynamics of masonry elements

In this work, a nonlocal damage-plasticity model for dynamic finite element analyses of cohesive structural elements is presented. The proposed cohesive model is able to reproduce the main relevant behaviors of quasi-brittle materials despite being quite simple, i.e. governed by only a few parameters which can be determined by standard laboratory tests. In particular, the model is able to reproduce the mechanisms of cohesive materials under static or dynamic loads: degradation of the mechanical properties (damage) and accumulation of irreversible strains (plasticity). Moreover, the model also simulates the cyclic macroscopic behavior of quasi-brittle materials, taking into account the loss and recovery of stiffness due to crack closure and reopening. The latter effect represents a particularly important characteristic in the case of dynamic loads. The proposed formulation is implemented as a constitutive model for two-dimensional plane stress four-node quadrilateral elements. The second order equations of motion are solved adopting the implicit Newmark time integration scheme. The proposed model is validated and its dynamic performance is numerically demonstrated through the analysis of a large-scale structural element.

Pressure dependence on the remanent magnetization of Fe-Ni alloys and Ni metal

We measured the acquisition of magnetic remanence of iron-nickel alloys (${\mathrm{Fe}}_{64}{\mathrm{Ni}}_{36}$, ${\mathrm{Fe}}_{58}{\mathrm{Ni}}_{42}$, and ${\mathrm{Fe}}_{50}{\mathrm{Ni}}_{50}$) and pure Ni under pressures up to 23 GPa at room temperature. Magnetization decreases markedly for ${\mathrm{Fe}}_{64}{\mathrm{Ni}}_{36}$ between 5 and 7 GPa yet remains ferromagnetic until at least 16 GPa. Magnetization rises by a factor of 2--3 for the other compositions during compression to the highest applied pressures. Immediately upon decompression, magnetic remanence increases for all Fe-Ni alloys while magnetic coercivity remains fairly constant at relatively low values (5--20 mT). The amount of magnetization gained upon complete decompression correlates with the maximum pressure experienced by the sample. Martensitic effects best explain the increase in remanence rather than grain-size reduction, as the creation of single domain sized grains would raise the coercivity. The magnetic remanence of low Ni Invar alloys increases faster with pressure than for other body-centered-cubic compositions due to the higher magnetostriction of the low Ni Invar metals. Thermal demagnetization spectra of ${\mathrm{Fe}}_{64}{\mathrm{Ni}}_{36}$ measured after pressure release broaden as a function of peak pressure, with a systematic decrease in Curie temperature. Irreversible strain accumulation from the martensitic transition likely explains the broadening of the Curie temperature spectra, consistent with our x-ray diffraction analyses.

Modeling of smart concrete beams with shape memory alloy actuators

In the present work, a computational strategy for the modeling of reinforced concrete beams with SMA actuators for cracks repair is developed. In particular, for the concrete, an original transition damage–fracture technique is proposed in order to simulate the microcrack arising, their coalescence and, finally, the macrocrack development. Microcracks are modeled adopting a nonlocal damage and plasticity approach, which is able to consider the tensile and compressive damaging, accumulation of irreversible strains and the unilateral phenomenon. Macrocracks are modeled using a cohesive zone interface which accounts for the mode I, mode II and mixed mode of damage, the unilateral contact and the friction effects. The interface models the transition from the continuum damage (simulating the presence of microcracks) to fracture. A uniaxial SMA model able to reproduce both the pseudo-elastic behavior and the shape memory effect is adopted for the reinforcing SMA bars.Finite element simulations are developed in order to reproduce the behavior of smart concrete beams subjected to three-point bending experimental tests available in literature (Kuang and Ou, 2008, Daghia et al., 2011). The construction phases of the beam are simulated and the loading history, consisting in three-point bending tests, are reproduced; in particular, the repairing phase due to pseudo-elastic behavior and shape memory effect is reproduced. Numerical results are compared with experimental data to validate the computational strategy.

Efficiency and work performance of TiNi alloy undergoing B2 ↔ R martensitic transformation

Abstract This study is devoted to the investigation of the ability of Ti48Ni52 alloys for production of effective work during thermal cycling over a narrow temperature range. Effective work output and efficiency were studied in Ti48Ni52 alloy subjected to thermal cycling through the temperature range of the B2 ↔ R martensitic transformation under different stress regimes. The optimal stress regimes for production of effective work output and maximum efficiency were found. The data obtained have shown that under optimal stress conditions (cooling of the sample under a stress of 100 MPa and heating under a stress of 400 MPa), one may develop a device with effective work being equal to 1.5 MJ m−3 and an efficiency of 2.5 %. During repeated thermal cycling under the optimal stress regime the alloy accumulated 8 % irreversible strain per 30 cycles. Starting from the 20th cycle the rate of irreversible strain accumulation was equal to ∼ 0.06 % per cycle.

A nonlocal constitutive model for trabecular bone softening in compression

Using the three-dimensional morphological data provided by computed tomography, finite element (FE) models can be generated and used to compute the stiffness and strength of whole bones. Three-dimensional constitutive laws capturing the main features of bone mechanical behavior can be developed and implemented into FE software to enable simulations on complex bone structures. For this purpose, a constitutive law is proposed, which captures the compressive behavior of trabecular bone as a porous material with accumulation of irreversible strain and loss of stiffness beyond its yield point and softening beyond its ultimate point. To account for these features, a constitutive law based on damage coupled with hardening anisotropic elastoplasticity is formulated using density and fabric-based tensors. To prevent mesh dependence of the solution, a nonlocal averaging technique is adopted. The law has been implemented into a FE software and some simple simulations are first presented to illustrate its behavior. Finally, examples dealing with compression of vertebral bodies clearly show the impact of softening on the localization of the inelastic process.

Elementary Transformation and Deformation Processes and the Cyclic Stability of NiTi and NiTiCu Shape Memory Spring Actuators

The present work addresses functional fatigue of binary NiTi and ternary NiTiCu (with 5, 7.5, and 10 at. pct Cu) shape memory (SM) spring actuators. We study how the alloy composition and processing affect the actuator stability during thermomechanical cycling. Spring lengths and temperatures were monitored and it was found that functional fatigue results in an accumulation of irreversible strain (in austenite and martensite) and in increasing martensite start temperatures. We present phenomenological equations that quantify both phenomena. We show that cyclic actuator stability can be improved by using precycling, subjecting the material to cold work, and adding copper. Adding copper is more attractive than cold work, because it improves cyclic stability without sacrificing the exploitable actuator stroke. Copper reduces the width of the thermal hysteresis and improves geometrical and thermal actuator stability, because it results in a better crystallographic compatibility between the parent and the product phase. There is a good correlation between the width of the thermal hysteresis and the intensity of irrecoverable deformation associated with thermomechanical cycling. We interpret this finding on the basis of a scenario in which dislocations are created during the phase transformations that remain in the microstructure during subsequent cycling. These dislocations facilitate the formation of martensite (increasing martensite start (M S ) temperatures) and account for the accumulation of irreversible strain in martensite and austenite.