Thermomechanical Loading Paths Research Articles

Thermo-mechanical behavior of reconstituted deep-water sediments

Understanding the thermo-mechanical behavior of deep-water sediments is essential for the safe design of high-temperature oil/gas pipelines. In this study, a series of temperature-controlled triaxial tests was conducted to investigate the thermo-mechanical behavior of reconstituted deep-water sediments sampled from the South China Sea. The experimental results revealed the thermo-mechanical behavior of sediments was closely related to their thermo-mechanical loading paths and sodium chloride (NaCl) concentrations. The increasing rate of excess pore water pressure decreases with an increase in temperature increment, effective confining pressure, and overconsolidation ratio, regardless of NaCl concentration. For normally consolidated specimens, the undrained shear strength generally decreases as temperature increases. The undrained shear strength of specimens was lower under undrained heating and higher under drained heating than that at 5 °C, respectively. Factors such as thermal softening, thermal consolidation, and thermal-induced excess pore water pressure significantly impacted the undrained shear strength of sediments under isothermal, drained, and undrained heating conditions. Additionally, the undrained shear strength decreases with increasing NaCl concentration. The results highlighted that the critical state line is unique under varying loading paths and NaCl concentrations. Furthermore, the effect of changes in void ratio induced by NaCl solution on the shear strength of sediments was more pronounced than that of the intergranular stress.

On the Nature of Post‐Constrained Recovery Residual Stress of NiTi Shape Memory Alloys

In this article, the nature of the post‐constrained recovery residual stress (PCRRS) observed in nickel titanium (NiTi) shape memory alloys (SMAs) subjected to constrained recovery and returned to a low‐temperature state while remaining constrained is investigated. After performing the thermomechanical cycling to produce the PCRRS state, four experiments are performed with different deflection profiles applied from the PCRRS state, and the changes in the residual stress is observed. All tests produce a gradual decrease in stress after every load cycle, similar to cyclic softening. However, repetition of the process used to initially generate PCRRS restores the initial magnitude of the PCRRS, indicating that the decrease in residual stress is a stable, repeatable, and reversible phenomenon, and not true material degradation. To better understand the nature of PCRRS, an analysis is performed comparing the modulus relating stress and strain at different points along the thermomechanical loading path. In this analysis, it is shown that NiTi has a combination of twinned and detwinned martensite in the PCRRS state. Understanding the nature of PCRRS, properties and its stability have the potential for advanced engineering applications such as self‐healing and fatigue‐resistant materials by generating stresses without continuous actuation over a long period of time.

Thermally-activated hardening recovery in viscoplastic materials with kinematic hardening at high temperatures

In this work, a new constitutive model is proposed to describe the thermally-activated hardening recovery mechanism in metallic materials. This model takes up the concept of hardening recovery variable, which is extended to the case of kinematic hardening within a thermo-viscoplastic formulation including high temperature dependencies for both elastic and viscoplastic properties. The model is identified for AISI 316L austenitic stainless steel using experimental data from uni-axial tests conducted over a wide range of temperature (from room temperature to 1273 K) and at two different strain rates (2.5×10−4 and 2.5×10−3 s−1). Validation is further achieved with rather good agreements by comparing the simulated responses with additional experimental data where the material is subjected to complex thermomechanical loading paths while other examples are presented to provide a better insight of the model and to illustrate its predictive capabilities.

Rock salt creep: a cross-check test to cover the full relevant range of deviatoric stresses

The time-dependent response of rock salt has been mainly investigated using confined creep tests covering a differential stress range between 5 and 20 MPa. In recent years, efforts have been made to investigate the range 0.1–4.5 MPa, using dead-end drifts in underground mines to take advantage of the very stable ambient conditions (temperature, relative humidity). Up to now, the combination of experimental data in the two ranges is difficult because of the use of different salt facies, sample preparation methods, test temperatures and experimental conditions (e.g., confined vs. unconfined tests, scale of measurements). In this work, we conduct two long-term creep tests on two natural salt samples from the same origin and prepared using the same protocol. The thermo-mechanical loading path is the same for the two tests, with only a small difference in the lateral load. One test is performed in a remote drift in a salt mine and the other test is performed in a climatic chamber in the laboratory. The comparison of the results is consistent, allowing to investigate a large range of deviatoric stresses by combining results in the two facilities. The final goal of this approach is to reduce stress extrapolation by investigating the whole deviatoric range that is relevant for underground operations. Next steps include investigating in more detail the effect of intergranular fluids, testing different temperatures and performing confined tests in the mine.

Multiaxial thermo-mechanical fatigue life prediction based on notch local stress-strain estimation considering temperature change

The modified incremental multiaxial Neuber rule by considering the temperature change was firstly proposed, which combined with the Chaboche viscoplastic constitutive model to approximately compute the notch local stress and strain under multiaxial thermo-mechanical loading. Based on the proposed method, a life prediction method that can take into account fatigue, oxidation, and creep damage was developed, which can quickly predict notch fatigue failure lifetime under variable amplitude multiaxial thermo-mechanical loading. The proposed method was verified by the coupled thermal-structural nonlinear FEA and the experimental life results for the tenon joint structure specimens under eight thermo-mechanical loading paths. The comparison of computed and analyzed stress-strain history showed that a good agreement can be obtained. Comparing with experimental life data, all predicted lives fall in a 2-factor scatter band.

Deep learning based phase transformation model for the prediction of microstructure and mechanical properties of hot-stamped parts

Hot stamping of boron steel is an effective way for weight reduction of automobiles parts, but suffers from the loss of mechanical properties due to incomplete martensitic transformation. Different from general heat treatment, phase transformation in hot stamping relates to both thermal loading path and deformation history. Unfortunately, the existing models have difficulty in capturing the history-dependent phase transformation behavior of boron steel under hot stamping conditions. In the present work, the gated recurrent unit (GRU) are combined with fully connected neural network (FCNN) to capture the coupling effect of both nonlinear strain history and thermal loading path on phase transformation. A unified deep-learning based phase transformation (DLPT) model is developed to integrate both diffusive and diffusionless transformation to cover all feasible thermo-mechanical loading path in hot stamping process. A hybrid driven thermo-mechanical-metallurgical (TMM) framework is developed by integrating the DLPT model into general TMM framework, which providing a novel approach for two-scale simulation of hot stamping process. A comprehensive database of phase transformation is constructed for model training based on well-designed thermo-mechanical loading experiments to cover hot stamping conditions, and the optimal topology of neural network in DLPT model is obtained by training on this database. The accuracy and reliability of DLPT model is systematically demonstrated by dieless hot V-bending and hot stamping of T-shaped parts besides CCT and DCCT tests. The net effect of local plastic strain on subsequent phase transformation is clarified with accuracy by dieless V-bending with the removal of disturbing factors. Non-uniform distribution in hardness of the final hot stamped parts can be predicted with the DLPT model successfully, which is better in accuracy than in case of working with the conventional model.

A temperature dependent constitutive model for functional fatigue in shape memory alloys

Functional fatigue is a vital aspect when considering the design of components made with shape memory alloys, since it can affect their short- and long-term behavior. With this in mind, a constitutive model considering the functional fatigue in shape memory alloys is developed. The functional fatigue is based on the residual strain, residual stress, residual martensite and a defect volume fraction, which are assumed to all evolve in a similar manner. The evolution is prescribed based on a saturation differential equation which is exponentially dependent on temperature. The residual martensite and defect volume fraction are defined to influence the development of hardening through a hardening energy term and the reduction in dissipation with an appropriate limit function. The model is validated by simulating several experiments of cyclic isothermal and isobaric tests. A fit and prediction is also offered for a set of complex thermomechanical loading paths. The results demonstrate the strong applicability of the model to capture the degradation of the transformation response associated with cyclic loads, even when different temperatures and loads are applied. Moreover, the results point out areas of improvement, such as the use of a logarithmic evolution for the saturation of the internal variables.

A unified description of mechanical and actuation fatigue crack growth in shape memory alloys

The damage tolerance approaches to fatigue rely on fracture mechanics concepts to explicitly account for the fatigue crack growth process. These approaches typically adopt the Paris equation, which relates the crack growth per cycle to the range of variation of the stress intensity factor, ΔK, during cyclic loading by means of experimentally calibrated parameters. Conditions on the validity of a single parameter description of the near crack tip stress and strain fields restrict the applicability of ΔK to fatigue crack growth resistance in Shape Memory Alloys (SMAs) under general thermomechanical loading paths. These conditions are substantially relaxed for the cyclic ΔJ–integral approach, which can achieve similitude over a wider range of loading conditions and geometric configurations. Thus, ΔJ qualifies as a potential unified descriptor of thermomechanical fatigue crack growth resistance in SMAs, an assertion, which is tested in this work for data from both purely mechanical and actuation fatigue crack growth experiments of a high temperature SMA, Ni50.3Ti29.7Hf20. In the latter, compact tension specimens are subjected to thermal cycling under constant load between an upper and a lower cycle temperature that allows for the stable phase to alternate in each cycle. It is shown here that a Paris-type power-law crack growth expression based on the ΔJ-integral can fit fatigue crack growth rate data from both types of experiments with a single set of parameters. This new analysis method for both actuation and mechanical fatigue crack growth rates provides a unified description for fatigue crack growth in SMAs and can allow estimating actuation fatigue crack growth rates, laborious and challenging to measure, from easier to detect mechanical fatigue crack growth rates.

The influence of hysteresis loop in a NiTi shape memory oscillator behavior

This work consists of an experimental and a numerical investigation on how heat treated Ti-50.7% at Ni springs can affect the dynamical behavior of a single degree of freedom (1DOF) oscillator. Initially, the springs are solution annealed at 300°C, 400°C and 500°C over 30, 60, 90, and 120 min. After, the springs are characterized, through quasi-static loadings following a cyclic thermomechanical loading path until the inelastic strains saturate and the behavior of the springs stabilizes. The results demonstrate that springs aged at 400°C and 500°C present a larger hysteresis loop area when compared with those aged at 300°C. Then, the springs aged at 500°C are used in an experimental apparatus that represents a 1DOF system—the SMA spring represents the element of stiffness—and are analyzed in an up and down sweep frequency at two different temperatures. It is observed that the maximum amplitudes strongly depends on the temperatures and on the frequency test. It is also noticeable that the springs with higher hysteresis loop area results in lower maximum amplitudes. Finally, the 1DOF system is numerically modeled, in which a constitutive model is used to describe the SMA spring behavior. When the numerical and experimental results are compared, it is observable a difference, suggesting that the hysteresis loop may present a very different and counter intuitive behavior when subjected to dynamic loads.

Texture Evolution during Isothermal, Isostrain and Isobaric Loading of Polycrystalline Shape Memory NiTi.

In situ neutron diffraction was used to provide insight into martensite variant microstructures during isothermal, isobaric, and isostrain loading in shape memory NiTi. Results show variant microstructures were equivalent for the corresponding strain and more importantly, the reversibility and equivalency was immediately evident in variant microstructures that were first formed isobarically but then reoriented to a near random self-accommodated microstructure following isothermal deformation. Variant microstructures formed isothermally were not significantly affected by a subsequent thermal cycle under constant strain. In all loading cases considered, the resulting variant microstructure correlated with strain and did not correlate with stress. Based on the ability to select a variant microstructure for a given strain despite thermomechanical loading history, the results demonstrated here can be obtained by following any sequence of thermomechanical loading paths over multiple cycles. Thus for training shape memory alloys (repeating thermomechanical cycling to obtain the desired variant microstructure), optimal paths can be selected so as to minimize the number of training cycles required thereby increasing the overall stability and fatigue life of these alloys in actuator or medical applications.

ACMEG-TVP: A thermoviscoplastic constitutive model for geomaterials

In this paper, a thermoviscoplastic constitutive model for geomaterials is presented. The model is formulated based on two aspects: (i) the nonstationary flow surface theory, which is used to describe the viscous behaviour of geomaterials, and (ii) the thermoplasticity concept, which is adopted to introduce the effect of temperature on geomaterials. In the model, the yield surface evolves with the viscoplastic strain, viscoplastic strain rate and temperature. Thus, it allows the description of combined effects of strain rate and temperature on the mechanical behaviour of geomaterials. The model has been used to simulate various tests involving different thermomechanical loading paths, including non-isothermal constant rate of strain tests, cyclic heating and cooling tests, creep tests with temperature changes and stress relaxation tests. The simulation results agree well with measurements, demonstrating the capacity of the proposed model to reproduce the various thermoviscoplastic behaviour of geomaterials.

Modeling of coupled phase transformation and reorientation in shape memory alloys under non-proportional thermomechanical loading

In the present study, a new 3D thermodynamic coupled model is proposed for SMAs. The behavior of SMA structures is described through several strain mechanisms, each associated with its proper internal variables. This model is built to capture the particular behavior of SMAs when subjected to complex loading, namely non-proportional thermomechanical loading. To achieve this task, a new approach to describe the martensitic reorientation mechanism has been introduced in conjuction with a new method to account for forward and reverse transformation. Thermomechanical coupling, related to dissipation and latent heat is fully implemented. The validity of the model is demonstrated by comparing experimental results of complex thermomechanical loading paths of SMA structures with numerical simulations.

A three-dimensional description of shape memory alloy thermomechanical behavior including plasticity

This paper introduces a novel three-dimensional constitutive model that describes the thermomechanical behavior of shape memory alloys (SMAs). The model is developed within the framework of continuum mechanics and the standard generalized materials. Four macrocospic phases are considered associated with austenite and three variants of martensite. Phase transformations can be induced by temperature, volumetric and deviatoric strains. The description of plasticity is also of concern assuming kinematic and isotropic hardening. Numerical simulations are carried out showing that the proposed model is able to capture the general thermomechanical behavior of SMAs for uniaxial and multiaxial tests, even in situations with complex thermomechanical loading paths.

A two‐surface thermomechanical model for saturated clays

SummaryThis paper presents an advanced thermomechanical model – TEAM in the framework of two‐surface plasticity for saturated clays, with emphasis put on some important thermomechanical features of natural clays evidenced experimentally such as the limited thermomechanical elastic zone, the smooth transition from elastic to plastic behavior. Two plastic mechanisms are introduced in the model: one is to reproduce the thermoplasticity involving thermal expansion and contraction observed at high over‐consolidation ratios and the second one describes the temperature effect on the yield behavior. The model adopts additional yield surfaces, namely inner yield surfaces that are associated with the two proposed plastic mechanisms to account for the plastic behavior inside the existing conventional thermomechanical yield surface namely yield surfaces. The general expressions of the yield surfaces and plastic potentials in p′–q–T space are introduced. A progressive plastic hardening mechanism associated with the inner yield surface is defined, enabling the plastic modulus to vary smoothly during thermomechanical loadings inside the yield surfaces. Several tests on natural Boom clay along different thermomechanical loading paths have been simulated by TEAM, and results show its relevance in describing the thermomechanical behavior of saturated clays. Copyright © 2015 John Wiley & Sons, Ltd.

Deformation behavior of woven glass/epoxy composite substrate under thermo-mechanical loading

Abstract The deformation behaviors of woven glass/epoxy composite substrate under four thermo-mechanical loading paths, i.e. rectangular and triangular paths in clockwise and anticlockwise directions within a temperature range of 25–250 °C were investigated. Temperature scanning tests were conducted to identify the viscoelastic property of the material. The glass transition temperature of the composite substrate was 138 °C, above which significant reduction of storage modulus was observed. The deformation behavior of the composite substrate was temperature and history dependent, and change of deformation rate resulted from state transition was noticeable. The residual deformation of specimen following the anticlockwise rectangular loading path was the largest in contrast with the lowest in clockwise rectangular path. The residual deformations in two triangular paths were close after each cycle.

Temperature and stress state influence on void evolution in a high-strength dual-phase steel

The formability of dual-phase steels strongly depends on void nucleation and growth resulting from strain heterogeneities at the microscale between soft ferrite and hard martensitic phases. These mechanisms are dependent on the thermomechanical loading paths undergone by the alloy during the forming process. This work provides new experimental results concerning void evolution in high-strength dual-phase steel at different temperatures. Traditional and notched tensile samples were used with a geometry that provides stress triaxiality values similar to those attained in bending processes. Mechanical tests were performed for temperatures in the range of 293 to 723K, and the quantification of voids (i.e., size and number) was performed for different levels of equivalent plastic strain, temperature and stress triaxiality. The results show that the mechanical properties of the dual-phase steels are maintained up to a temperature of 573K. For higher temperatures, a degradation of plastic flow properties occurs in relation to the decrease of the martensite phase ratio and the softening of the ferritic phase; triaxiality also has less influence on the mechanical properties at warm test conditions. These results were discussed in terms of diffusional processes and local evolution of the microstructure with TEM observations. This work could be used to optimise the bending forming conditions of these alloys in industrial processes.

An affine formulation for the self-consistent modeling of elasto-viscoplastic heterogeneous materials based on the translated field method

The modeling of heterogeneous materials with an elasto-viscoplastic behavior is generally complex because of the differential nature of the local constitutive law. Indeed, the resolution of the heterogeneous problem involves space–time couplings which are generally difficult to estimate. In the present paper, a new homogenization model based on an affine linearization of the viscoplastic flow rule is proposed. First, the heterogeneous problem is written in the form of an integral equation. The purely thermoelastic and purely viscoplastic heterogeneous problems are solved independently using the self-consistent approximation. Using translated field techniques, the solutions of the above problems are combined to obtain the final self-consistent formulation. Then, some applications concerning two-phase fiber-reinforced composites and polycrystalline materials are presented. When compared to the reference solutions obtained from a FFT spectral method, a good description of the overall response of heterogeneous materials is obtained with the proposed model even when the viscoplastic flow rule is highly non-linear. Thanks to this approach, which is entirely formulated in the real-time space, the present model can be used for studying the response of heterogeneous materials submitted to complex thermo-mechanical loading paths with a good numerical efficiency.

Modeling and Simulation of SMA Medical Devices Undergoing complex Thermo-mechanical Loadings

There are SMA medical applications which undergo complex thermo-mechanical loading paths to meet specific and accurate requirements. In this work, a 3D model and its implementation techniques are presented. This model is currently deployed to design and model SMA medical devices subjected to multi-axial loading in both isothermal and dynamic regimes. Some of these devices are introduced and studied as examples to show the efficiency of the proposed platform.

A unified viscoplastic constitutive model with damage for multi-axial creep–fatigue loading

A unified viscoplastic constitutive model with damage is presented to describe creep–fatigue deformation behavior. The primary improvement on the existing models is to introduce creep and fatigue damage variables into the constitutive equations of adapted complexity. The material model, which is developed from the thermodynamic framework, combines nonlinear isotropic and kinematic hardening variables, and is implemented using a user-defined subroutine. A standard specimen and a hollow cylinder are used to carry out uniaxial and multi-axial creep–fatigue tests to validate the material model. Good agreement is obtained between the simulation and the measurement under various thermo-mechanical loading paths.

Thermo-mechanical Response and Damping Behavior of Shape Memory Alloy–MAX Phase Composites

NiTi/Ti3SiC2 interpenetrating composites that combine two unique material systems—a shape memory alloy (SMA) and a MAX phase—demonstrating two different pseudoelastic mechanisms, were processed using spark plasma sintering. The goal of mixing these two material systems was to enhance the damping behavior and thermo-mechanical response of the composite by combining two pseudoelastic mechanisms, i.e., reversible stress-induced martensitic transformation in SMA and reversible incipient kink band formation in MAX phase. Equal volume fractions of equiatomic NiTi and Ti3SiC2 were used. Microstructural characterization was conducted using scanning electron microscopy to study the distribution of NiTi, Ti3SiC2, and remnant porosity in the composite. Thermo-mechanical testing in the form of thermal cycles under constant stress levels was performed in order to characterize shape memory behavior and thereby introducing residual stresses in the composites. Evolution of two-way shape memory effect was studied and related to the presence of residual stresses in the composites. Damping behavior, implying the energy dissipation per loading–unloading cycle under increasing compressive stresses, of pure NiTi, pure Ti3SiC2, as-sintered, and thermo-mechanically cycled (TC) NiTi/Ti3SiC2 composites, was investigated and compared to the literature data. In this study, the highest energy dissipation was observed for the TC composite followed by the as-sintered (AS) composite, pure NiTi, and pure Ti3SiC2 when compared at the same applied stress levels. Both the AS and TC composites showed higher damping up to 200 MPa stress than any of the metal—MAX phase composites reported in the literature to date. The ability to enhance the performance of the composite by controlling the thermo-mechanical loading paths was further discussed.