Cyclic behavior

The last step, detailed in Chapter 5 , deals with cyclic pseudoelasticity of polycrystalline SMAs by generalizing the second-step model. This model captures several fundamental characteristics related to cyclic behavior of SMAs, i.e., large accumulated residual strain, degeneration of superelasticity and hysteresis loop, rate dependence, and evolution of phase transformation from abrupt to smooth transition. The formulation of the model is based on the decomposition of finite Hencky strain into elastic, transformation, residual and thermal components. A thermodynamically consistent framework is established in compliance with the reduced form of energy balance and the Clausius-Duhem form of entropy inequality, while a Helmholtz free energy function including elastic, thermal, interaction and constraint parts is constructed. Constitutive equations, i.e., thermoelasticity, evolution of martensite volume fraction, flow rule of residual strain, martensite reorientation and heat production are then derived from them. The 3D model is reduced to a 1D version and the heat transfer condition of the cyclic tensile experiment on NiTi wire is simplified. Model parameters are calibrated from the experimental data. Finally, numerical simulations of the cyclic experiments at different strain rates are carried out to validate the model. The model is able to capture the rate dependence, the temperature variation, the abrupt to smooth transition, and the evolutions of the dissipated energy, the reversible transformation strain, the residual strain, the transformation stresses and the transformation hardening modulus during cyclic deformations. Finite element simulation of a torsion spring shows the potential of the proposed model for fatigue analysis of SMA structures.

It is widely held that the construction industry is competitive and costs are driven by the costs of inputs, such as material and labor costs. Once we ascertain whether statistically relevant construction cost indices may be created using FW Dodge bid data, we can then examine whether the construction industry behaves as a supply elastic commodity, or whether it exhibits cyclic behavior related to the level of building activity. Classical real estate economics states that changes in real estate values redound to the land value component of property value, as construction supply is presumed to be elastic while land supply is fixed. This is known as the "residual theory of land value.” Yet casual empirical evidence suggests that construction costs are higher when where real estate values are higher. In this research we hope to ascertain whether construction supply is price elastic and changes based on the level of building activity.

bounding surface. In addition, the kinematic hardening models are still not widely used to describe the cyclic behavior of natural stiff clays, such as Boom Clay. In this study, a kinematic hardening model for modeling the cyclic behavior of natural stiff clays is developed. Basically, the developed model has a structure similar to that of bubble models. However, instead of defining an interpolation function for the plastic hardening modulus, a unified kinematic hardening law associated with the kinematic yield surface is defined, enabling the plastic modulus to vary smoothly along a plastic loading process. With a translation rule incorporated, this hardening law ensures that the two yield surfaces do not intersect but tend to coincide at the current stress point. Thereby, the constitutive equations can be simply obtained based on the consistency condition of the kinematic yield surface which is equivalent to the classic yield surface. Hence, in the numerical implementation, all the features of the stress integration schemes for classic elastoplastic models can be applied. This allows the model to be employed easily in the analysis of geotechnical problems. Furthermore, different model parameters for describing hardening rate in the loading/unloading/reloading processes are introduced enabling the cyclic loading behavior of natural stiff clays to be described in a flexible fashion. Also, a non-associated flow rule is adopted in order to properly describe the dilatancy behavior. The simulation of a series of tests on natural Boom Clay along different loading paths including the complex oedometric path show the relevance of the model proposed.

d’Albi-Carmaux, Route de Teillet, 81013 Albi cedex 9, France Abstract In this paper, a non unified elasto-viscoplastic behavior model based on internal state variables, is investigated in order to describe the thermo-mechanical stress-strain fa- tigue response of 55NiCrMoV7 tempered martensitic steels (AISI L6). This model considers a quadratic yield criterion to define the elasticity domain. It allows the de- termination of two inelastic strain mechanisms resulting from two stress states which can be related to the typical continuous cyclic softening of the tempered martensitic steels. This cyclic softening is reproduced through an isotropic component (drag stress). A memory effect is also introduced to take into account the influence of the plastic strain range on the amount of the cyclic softening. The kinematic component (back stress) of the model allows the description of complex load conditions to which tool steels are subjected. Strain recovery (Baushinger effect), time recovery terms (cyclic behavior including tensile dwell times) and ratcheting effects are considered. The numerical implementation is addressed and two integration methods (explicit and implicit) of the constitutive equations are presented. Moreover, the identifica- tion methodology of the model parameters from only two sets of experimental data is presented; the coefficients of the kinematic and isotropic parts are determined successively. The main difficulty consists in reaching a good description both of the cyclic behavior for different strain rates and the ratcheting effect. Last, a validation stage of the three dimensional model is investigated from low cycle fatigue tests performed on different notched specimens.

This paper presents a robust fatigue behavior and lifetime methodology developed during the last years on tempered martensitic steels. It is based on constitutive behavior laws to evaluate the stress- strain response of the material combined with a continuum damage model to assess the number of cycles to failure. This approach was successfully applied on martensitic hot work tool steels for uniaxial, isothermal and non isothermal conditions. It allows to take into account a great number of test conditions (different strain rates, strain amplitudes, temperature levels). The lifetime model can be connected to two different behavior laws able to take into account, on the one hand, the micro- structure evolution induced by time-temperature ageing and on the other hand, very complex loading paths (dwell times, plastic shakedown or ratchetting effects) by the introduction of two inelastic mechanisms related to microstructural evolutions responsible to the cyclic softening. Both models have required a deep knowledge of microstructural evolution during tempering and fatigue as well as stress strain responses under iso-thermal and thermo-mechanical fatigue loading paths. The complete methodology has been validated on isothermal and thermomechanical fatigue tests [3,5] and on structural specimens [1,31]. For that purpose, important numerical developments were also performed in order to implement these approaches in a finite element code [1,18].

Saberian, M., Li, J., & Cameron, D. (2019) Effect of crushed glass on behavior of crushed recycled pavement materials together with crumb rubber for making a clean green base and subbase. Journal of Materials in Civil Engineering , 31 (7), 1-7. Saberian, M., Mehrinejad Khotbehsara, M., Jahandari, S., Vali, R., & Li, J. (2018) Experimental and phenomenological study of the effects of adding shredded tire chips on geotechnical properties of peat.

Comprehension and quantification of quasi-brittle materials behavior requires complex experiments when focusing on cyclic or multi-axial loadings. As an alternative, virtual testing, which can be computed using lattice discrete el- ements models (LDEM), is particularly interesting. LDEM already provide a physical description of the quasi-brittle materials behavior, but further attention has to be paid to numerical integration. LDEM are explicitly inte- grated, such integration has been proven in the literature to be accurate when cracking is involved, by means of efficient schemes such as the “Saw-tooth” algorithm. In order to extend the range of application of LDEM to more complex loading paths, such as compressive or cyclic loadings, involving con- tact and friction mechanisms, qualitativeness as well as quantitativeness of explicit integration has to be assessed anew. We hereby propose an implicit quasi-static integration scheme for LDEM based on specific non-linearities encountered in quasi-brittle materials, namely contact and fracture, to cir- cumvent expected stability and accuracy issues. Efficiency of both schemes is investigated by means of simulations of a uniaxial cyclic test and a com-

Figure 1: 300 grain polycrystals for the FE simulations, along with the inverse pole figures of the crystallographic orientations used in the VEs Computational requirements The implicit finite element code (Z–set package, 2013) is used to solve the problem. The global equilibrium is solved using a Newton-Raphson algorithm. Integration of constitutive equations at the Gauss points is performed using the second order Runge-Kutta method with automatic time stepping (Besson et al., 2009). For a crystal plasticity simulation, loading one job of the present size requires 31.5 gigabytes RAM. The MPI parallel computing algorithm implemented in Zebulon is used with 4 processors for each job. Each job requires around 24 hours to complete one cycle and to run one hundred cycles, it required 100 days each. More than 320 simulations are being post-processed for this paper, while the actual number of calculated test cases is at least fifty times more than this. Given the number of degrees of freedom of each mesh and the cyclic nature of the problem, data of more than 20 TBytes were generated.

From observations made by many authors, different micromechanical models have been proposed for the prediction of the 316LN stainless steel [3–5]. Despite the fact that these models better describe the deformation process by taking into account some of the physical mechanisms of deformation, they usually require the adjustment of numerous parameters, involving experimental cyclic test in the adjustment process.

Mots clés — Elasto-plasticity, Porous materials, Cyclic loading, Homogenization. 1 Introduction Although significant advances have been made these last years in ductile fracture and monotonic loading conditions, a lot of questions remain open in the domain of cyclic response of materials. In particular, large amount of experimental data [1, 2] has shown a strong dependence of the material cyclic response upon the applied pressure. In this regard, consideration of a porous-matrix material system allows for a physical interpretation of pressure-dependent cyclic responses. More precisely, non linear homogenization models [3, 4] and micromechanical models [5] for elasto-plastic porous materials have been used for the prediction of material softening mainly due to the porosity evolution under monotonic loading conditions. To achieve that, a precise prediction of the evolution of the microstructure is needed (e.g., evolution of volume, shape and orientation of voids). On the other hand, many numerical and analytical results have been obtained concerning the influence of stress triaxiality [6, 7], denoted here as X Σ , and defined as the ratio between the mean stress to the von Mises equivalent or effective deviatoric stress. Recently, the effects of the third stress invariant, through the Lode angle [8, 9] in monotonic loading states have also been investigated. Nevertheless, much less has been studied in the context of cyclic loading conditions [10, 11] with a main emphasis on axisymmetric loading states. Even if in the majority of studies in the bibliography, cyclic response is analyzed using small strain calculations considering macroscopic strain amplitudes in the range of 1% − 5%, local strains can be in excess of 100% due to strong localization of the deformation around impurities or voids as is the present case. For that reason, it is critical that a finite deformation analysis is carried out. In this regard, the scope of this study is to investigate the effect of cyclic loading conditions and finite deformations upon microstructure evolution and material softening/hardening using FEM periodic unit-cell calculations with 3D geometry.

Abstract Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a stochastic model for the evolution of a discrete population structured by a trait taking finitely many values, with density-dependent competition. Traits are vertically inherited unless a mutation occurs, and can also be horizontally transferred by unilateral conjugation with frequency dependent rate. Our goal is to analyze the trade-off between natural evolution to higher birth rates on one side, and transfer which drives the population towards lower birth rates on the other side. Simulations show that evolutionary outcomes include evolutionary suicide or cyclic re-emergence of small populations with well-adapted traits. We focus on a parameter scaling where individual mutations are rare but the global mutation rate tends to infinity. This implies that negligible sub-populations may have a strong contribution to evolution. Our main result quantifies the asymptotic dynamics of subpopulation sizes on a logarithmic scale. We characterize the possible evolutionary outcomes with explicit criteria on the model parameters. An important ingredient for the proofs lies in comparisons of the stochastic population process with linear or logistic birth-death processes with immigration. For the latter processes, we derive several results of independent interest.

The matter comprising the human body is in a constant state of change, part of a cycle of death and new life, of destruction and reconstitution. From geophysics to cellular biology, processes across scales exhibit cyclic behavior, providing a framework toward understanding both the physical and the metaphysical potential of death as a process. This project interrogates the rituals and material of death through the frame of the cycle to propose an architecture of the death process that confronts multiple contemporary issues. There is first the problem, magnified by the COVID-19 crisis, of how to dispose of bodies. Second, is a cultural denial of death, leading to an avoidance of death at all costs and a lack of contemplation for the inherent meaning in this transition. Last, is the banality of the spaces in which death occurs or a passing is marked. The goal of the project is to question how as a society, we might discover a new attitude towards death, bodies, and how to commemorate those who have passed. Through a synthesis of ritual, materials, and cycles in life and in nature, the material of this project: the building, the landscape, and the human users become reinforcing participants in the creation of a new cycle of death and life.

In previous work, a quantitative analysis of continuous cyclic thermogravimetry (CTGA) was developed [1] and applied to the high temperature cyclic oxidation of NiAl [1] and [2], NiCoCrAlYTa coated or uncoated MC2 superalloy [3], NiPtAlHf alloy [4] and FeNiCr austenitic steels [5]. This technique allows to follow the Net Mass Change (NMC) but also the Gross Mass Gain, the oxide scale thickness, the oxidation kinetics, the amount of spalling and the mass of consumed metal as a function of cycle number. Then, the cyclic oxidation test becomes an

3 Al bond-coatings (BC) were fabricated by spark plasma sintering (SPS). The former had the highest possible Pt content (Ni-30Pt-25Al in at.%) while the latter had the highest possible Al level (Ni-28Al-17Pt in at.%). Hf was added as a reactive element. TBCs were fabricated on different superalloys (AM1, Rene´ N5 and MCNG) with the aforementioned BCs and with zirconia sta- bilized with yttria top coats made by SPS or electron beam physical vapor depo- sition (EBPVD). The cyclic oxidation resistance of these systems was studied at

interpreted by the positive effect of Hf present in the superalloy. This beneficial effect has already been observed in the cyclic oxidation of aluminide BCs [ 23 ]. The Co level can also explain this better resistance. Indeed, Wu et al. [ 10 , 24 ] recently demonstrated that a higher Co content in the superalloy may be detrimental to Pt diffusion coating performance. As MCNG is a Co-free superalloy, the large endurance of the MCNG-2?Cu system could be attributed to the absence of Co. In addition, it appeared that the N5-2?Cu system lasted as long as the AM1-2?Cu one, around 700 cycles. Knowing that Ti has a detrimental effect on the thermal cycling resistance [ 9 , 25 ] and that Rene´ N5 is a Ti-free superalloy, this result is surprising. However, it should be noted that Rene´ N5 superalloy contained higher Co and Hf contents than AM1. As many Hf-rich oxides formed in this system, the BC might be overdoped in Hf, decreasing its lifetime. Also, as only one sample of N5-base system was cycled, this result needs to be confirmed by testing more samples.

Table 3.3 – Calibrated material parameters for the evolution equation (rolled specimen) 3.5 Concluding remarks A new transformation criterion in terms of stresses and strains suitable for accurately describing the transformation of SMAs has been developed and imple- mented. The mathematical expressions governing the criterion in terms of stresses are studied with respect to convexity and capturing random anisotropy in SMAs transformation. Furthermore, an accurate evolution rule to govern the evolution of transformation strain has been formulated. It is a non-associated evolution rule which captures incompressibility and still the anisotropy in strains. The equations of the criterion and the evolution rule have been calibrated for a copper based textured SMA (Cu-Zn-Al), using the results from simulations of proportional uniaxial and biaxial plane-stress loading states. These simulations were achieved by utilizing the numerical results from a self-consistent micromechanical model on three polycrystal configurations: isotropic, rolled and drawn. Further results of the model have been used to assess and establish the accuracy of the propo- sed anisotropic criterion and the related non-associated evolution rule. A good agreement has been obtained by comparing the micromechanical simulations to results provided by the new formulated macroscopic model that can be easily implemented in FE codes. Accordingly, the effects of asymmetry and anisotropy of SMAs behavior can be accounted for structural design of SMA actuators.

tive subgroup generated by integers which lie in subfields that are cyclic over K. This index is finite, it only depends on the Galois group and the degree of K, and we give an explicit combinatorial formula for it. When generalizing to more general Dedekind do-

Univ Lyon, CNRS, ENS de Lyon, UCBL, LIP UMR 5668, F-69342, LYON Cedex 07, France Abstract We consider a fragment of a cyclic sequent proof system for Kleene algebra, and we see it as a computational device for recognising languages of words. The starting proof system is linear and we show that it captures precisely the regular languages. When adding the standard contraction rule, the expressivity raises significantly: the system captures exactly the class of deterministic logspace languages. We prove this result by introducing as an intermediary model a new notion of multihead finite automata where heads can jump.

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):cyclic Figure S9. The dependence of the intrinsic viscosity on the number of beads. The limiting slopes of linear and cyclic polymers at high N are 0.72 and 0.70, respectively. They are in good agreement with the values of Mansfield and Douglas, 0.71 1 and 0.69 2 , respectively.