Temperature Dependent Constitutive Model Research Articles

A data-driven rate and temperature dependent constitutive model of the compression response of a syntactic foam

Polymeric syntactic foams are used in aerospace and marine applications requiring low density and low moisture absorption together with high specific strength and stiffness. Their mechanical response is highly sensitive to temperature and strain rate and such sensitivity must be modelled accurately. In this study, the uniaxial compressive response of a polymeric syntactic foam is measured at strain rates in the range [10−3, 2.5·103] /s and temperatures varying between −25°C and 100°C. The resulting dataset is used to train a neural network to predict the compressive response of the foam at arbitrary strain rates and temperatures. It is found that the surrogate model is highly effective in predicting the material response at temperature and rates not included in its training set. Finally, a stochastic version of the data-driven model to allow predictions of the variability in the stress versus strain response is proposed.

Cryogenic damage mechanisms of CFRP laminates based on in-situ X-ray computed tomography characterization

Carbon fiber reinforced polymer (CFRP) composites possess excellent properties suitable for use in spacecraft liquid fuel tanks. However, the cryogenic reliability of composites remains challenging owing to the variation in mechanical responses under cryogenic environments. So far, most previous studies have focused on the cryogenic properties of composites, and little has been devoted to the cryogenic damage behaviors of laminates. Herein, the cryogenic damage evolution of CFRP laminates was investigated by micro-computed tomography (μCT) characterization and micromechanical analysis for the first time. To this end, in-situ μCT tensile tests for quasi-isotropic CFRP laminates were conducted at temperatures of 293 K, 193 K, and 93 K, and the observed cryogenic damage characteristics were analyzed. A micromechanical computational model was then developed, and the temperature-dependent constitutive model of epoxy resin was utilized to investigate the cryogenic damage evolution process of laminates. The effects of matrix property variation and thermal stresses on the cryogenic damage of laminates were examined, and the cryogenic fracture toughness for transverse cracking was deduced. The characterization results revealed a significantly increased damage volume fraction of laminates from 0.65% to 1.56% at cryogenic temperatures, mainly originating from the increased delamination (from 0.08% to 0.54%) and 90° ply transverse cracks (from 0.48% to 0.87%). The numerical analyses indicated the cryogenic brittle transition of the matrix as the primary factor responsible for the delamination, while the transverse cracks were influenced by matrix properties and thermal stresses. This study provides critical insight into the cryogenic damage behavior of CFRP laminates, essential for cryogenic applications of composites.

Data provenance - from experimental data to trustworthy simulation models and standards

FAIR (findable, accessible, interoperable and reusable) data usage is one of the main principals that many of the research and funding organizations include in their strategic plans, which means that following the main principals of FAIR data is required in many research projects. The definition of data being FAIR is very general. When implementing that for a specific application or project or even setting a standardized procedure within a working group, a company or a research community, many challenges arise. In this contribution, an overview about our experience with different methods and tools is outlined.We begin with a motivation on potential use cases for the application of FAIR data with increasing complexity starting from a reproducible research paper over collaborative projects with multiple participants such as Round-Robin tests up to data-based models within standardization codes, applications in machine learning or parameter estimation of physics-based simulation models.In a second part, different options for structuring the data (including metadata schema) are discussed. The first one is the openBIS system, which is an open-source lab notebook and PostgreSQL based data management system. A second option is a semantic representation using RDF based on ontologies for the domain of interest.In a third section, requirements for workflow tools to automate data processing are discussed and their integration into reproducible data analysis is presented with an outlook on required information to be stored as metadata in the database.Finally, the presented procedures are exemplarily demonstrated for the calibration of a temperature dependent constitutive model for additively manufactured mortar. A metadata schema for a rheological measurement setup is derived and implemented in an openBIS database. After a short review of a potential numerical model predicting the structural build-up behavior, the automatic workflow to use the stored data for model parameter estimation is demonstrated.

Nonlinear fully coupled thermoelastic transient analysis of axial functionally graded composite panel

In this article, the two-way coupled thermoelastic behavior of axially graded composite plate and doubly-curved (cylindrical, spherical, hyperbolic, and elliptical) panels is examined under conductive-convective boundary and uniformly distributed loading conditions. Here, the material properties of the axial functionally graded panel are computed by employing the power-law-based Voigt’s scheme. The material and geometric nonlinearities are incorporated using the cubic-polynomial-based temperature-dependent constitutive model and higher-order kinematics-based Green-Lagrange strain, respectively. The temperature profile is obtained through thermally nonlinear theory associated with high temperature, which is used to extract the energy equations obtained from the first law of thermodynamics and deformation-dependent entropy relation. The weak forms of motion and heat-transfer equations are derived using Galerkin’s method and further combined into the two-way coupled field equation through 2D-finite element approximation via Lagrangian elements. The transient responses are computed via the Newmark and the Crank-Nicolson schemes, whereas the nonlinear iterations are executed through Picard’s iteration technique. The performance of the fully coupled model for an axially graded (metal/ceramic) structure is verified with analytical, numerical, and experimental results and tested through a variety of numerical illustrations under various sets of conditions.

A temperature dependent constitutive model for hybrid fibre reinforced concrete

The use of fibre reinforced concrete (FRC) in engineering constructions has attracted increasing attention due to its excellent performance, including its improved strength, toughness, impact resistance and fire resistance. In recent years, hybrid fibres have been used in FRC to obtain better performance. To provide a reliable predicting tool and promote the application of hybrid fibre reinforced concrete (HFRC), a constitutive model is developed in this study to mimic the behaviour of HFRC under fire condition. The governing equations of damage function and strength envelope are modified in the new model. To calibrate the relationship between the mechanical properties of HFRC and temperature, a series of empirical equations are proposed. The effects of various influencing factors are considered, including fibre type, fibre shape, fibre dosage, water-binder ratio, moisture content and chemical composition. The effectiveness and accuracy of the proposed model is validated by comparing the simulation results with the test data from literature.

Temperature-Dependent modelling of tension, in-Plane shear, and bending behaviour in non-isothermal thermo-Stamping process simulation of unidirectional UHMWPE fibre reinforced thermoplastic TPU composites

This study proposes a macroscopic finite element modelling and simulation approach considering the temperature dependency of both in-plane membrane and out-of-plane bending behaviours. This approach enables the investigation of the effect of the deformation mechanisms on the quality of the formed thermoplastic composite parts during the thermo-forming process. The temperature-dependent constitutive model of the in-plane tensional behaviour is considered linear, whereas the in-plane shear stiffness is modelled based on the nonlinear hypoelastic constitutive equation. The out-of-plane bending behaviour is considered by decoupling the membrane and bending method. A numerical simulation strategy is developed by implementing the ABAQUS software via a VUMAT subroutine. Moreover, a modified method is introduced for the qualitative and quantitative assessment of the wrinkling intensity generated in the forming process. The validated strategy is used to investigate the influences of the various temperature conditions of the forming process and the underlying mechanisms to optimise the thermo-stamping process.

Temperature-dependent constitutive modeling of a magnesium alloy ZEK100 sheet using crystal plasticity models combined with in situ high-energy X-ray diffraction experiment

A multiscale crystal plasticity model accounting for temperature-dependent mechanical behaviors without introducing a larger number of unknown parameters was developed. The model was implemented in elastic-plastic self-consistent (EPSC) and crystal plasticity finite element (CPFE) frameworks for grain-scale simulations. A computationally efficient EPSC model was first employed to estimate the critical resolved shear stress and hardening parameters of the slip and twin systems available in a hexagonal close-packed magnesium alloy, ZEK100. The constitutive parameters were thereafter refined using the CPFE. The crystal plasticity frameworks incorporated with the temperature-dependent constitutive model were used to predict stress–strain curves in macroscale and lattice strains in microscale at different testing temperatures up to 200 °C. In particular, the predictions by the crystal plasticity models were compared with the measured lattice strain data at the elevated temperatures by in situ high-energy X-ray diffraction, for the first time. The comparison in the multiscale improved the fidelity of the developed temperature-dependent constitutive model and validated the assumption with regard to the temperature dependency of available slip and twin systems in the magnesium alloy. Finally, this work provides a time-efficient and precise modeling scheme for magnesium alloys at elevated temperatures.

Case study and numerical modelling of heat transfer in a snow-covered building roof

We explored the heat transfer in a snow-covered building roof by setting a prototype field measurement in Harbin during the winter of 2018. Several sets of data were measured, including the meteorological elements and snow properties. Hence, a temperature-dependent constitutive model for a heterogeneous medium, the deposited snow on the roof, was accordingly proposed. To validate this, this model was adopted in a new proposed 3-D finite element modelling (FEM), in ANSYS software, to quantitatively analyze the heat transfer process. All heat transfer patterns, including roof heat-loss conduction, surrounding turbulent exchange, and net radiation, as well as the involved phase-changes in snow metamorphism, were considered. Using the birth and death element technique, the snowmelt and subsequent ice-layer formation can also be visually reproduced. The feasibility of the FEM was validated by comparing both the snow metamorphic features and the hourly temperature gradient in the snow between the FEM and the prototype measurement. In future work, the influence of water vapor transport in snow and the range of time-scales should be increased in further studies.

Temperature Dependence of Rubber Hyper-Elasticity Based on Different Constitutive Models and Their Prediction Ability.

Based on the electronic universal testing machine with a temperature chamber, this paper investigated the temperature and filler effects on the hyper-elastic behavior of reinforced rubbers and revealed the regulation of the stress and strain of the natural rubber and filled rubber with temperature. The experimental results showed that the hyper-elastic behavior of the filled rubber was temperature-dependent in a wide range. Comparing the adaptability of different models to the stress–strain variation with temperature, the Yeoh model was proven to reasonably characterize the experimental data at different temperatures. Based on the Yeoh model, an explicit temperature-dependent constitutive model was developed to describe the stress–strain response of the filled rubber in a relatively large temperature range. The prediction data of this proposed constitutive model fit well with the test data of the mechanical experiments, indicating that the model is suitable to characterize the large deformation behavior of filled rubbers at different temperatures to a certain degree. The proposed model can be used to obtain the material parameters and has been successfully applied to finite element analysis (FEA), suggesting a high application value. Notably, the model has a simple form and can be conveniently applied in related performance tests of actual production or finite element analysis.

Fractional modeling of temperature-dependent mechanical behaviors for glassy polymers

The mechanical behaviors of glassy polymers, including viscoelastic, softening, and re-hardening stages, exhibit high temperature-sensitivity, which makes it a challenge to construct temperature-dependent constitutive models. To address the issue, a temperature-dependent variable-order fractional constitutive model is proposed to describe such multistage polymeric mechanical behaviors, where the criteria for elastic modulus and relaxation time with respect to temperature are established. The viscoelastic stage at different temperatures can be described by a constant initial order followed by a linearly varying one, which is found to be temperature-insensitive. A power-law order is structured subsequently to describe both the strain-softening and re-hardening stages, while that in the re-hardening stage are more temperature sensitive. The physical interpretations of fractional orders are revealed on the basis of molecular chains mechanisms. Applications of the proposed model in different kinds of glassy polymers further validate the effectiveness and predictability.

A temperature-dependent material model for numerical simulation of steel fibre reinforced concrete

Steel fibre reinforced concrete (SFRC) has been increasingly used in super high-rise buildings, nuclear facilities and infrastructures in recent years. Fire is one of the inevitable threats to these structures during their service life, therefore it is of great significance to study the behaviour of SFRC at elevated temperatures. In this study, a new temperature-dependent constitutive model is proposed to describe the mechanical behaviour of SFRC at elevated temperatures. In the present model, the plastic damageof SFRC is considered using the sum of accumulated shear damage and compaction damage, and a temperature-dependent coefficient is introduced to evaluate the plastic strain at fracture. To predict the mechanical properties of SFRC at elevated temperatures, a set of equations are proposed based on the collected experimental data. Particularly, three indexes, i.e. water to binder ratio, moisture content and alumina content, are introduced to calibrate the normalised compressive strength of SFRC. Besides, the effects of fibre dosage and fibre shape are taken into account. The proposed model is used to predict the mechanical behaviour of SFRC subjected to elevated temperatures and is demonstrated to be effective.

Development of the temperature-dependent constitutive model of glass fiber reinforced polypropylene composites

ABSTRACT Plain-woven glass fiber-reinforced polypropylene (PW-GFRPP), as the typical advanced CoFRTP, has been rapidly emerged in aerospace, civil and automobile fields, thanks to its low cost and excellent performances. The fiber yarns of PW-GFRPP will undergo large rotations and shear deformations with immersions of molten polypropylene resin during the hot mold pressing process. The shear deformations of fiber yarns not only directly affect the formability quality of the preformed structures but also make an impact on the mechanical performances of cured products. Thus, the scope of this study is to construct the temperature-dependent material constitutive model of PW-GFRPP and investigate the influences of temperature and blank holding force (BHF) on the formability of PW-GFRPP prepregs. Differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) tests were first implemented to determine the melting and degradation temperatures of polypropylene. Next, the bias-extension tests for PW-GFRPP prepregs were carried out accounting for three temperature values (190°C, 220°C and 250°C). Then the temperature-dependent constitutive model was developed and validated. Finally, the validated constitutive model was used to explore the influences of temperature and blank holding force on the formability of PW-GFRPP composites on a double dome benchmark.

Dynamic tensile mechanisms and constitutive relationship in CrFeNi medium entropy alloys at room and cryogenic temperatures

Harsh service conditions in aerospace, defense and military, and other fields are calling for materials with excellent mechanical properties to undergo extreme deformation (such as elevated and cryogenic temperatures and high strain rates) without sustaining damage while retaining high strength. Outstanding mechanical properties of high or medium entropy alloys (MEAs) render them potential candidates. In this paper, as the temperature decreases, a breakthrough of the strength-ductility tradeoff is achieved in a CrFeNi MEA with partially recrystallized face-centered cubic phases, together with body-centered cubic (BCC) precipitates. At a strain rate of $3000\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, the yield strength (YS) is increased from 920 MPa at 298 K to 1320 MPa at 77 K, while the uniform elongation (UE) increases by 28.5%. This phenomenon also occurs at quasistatic tension. Under low-temperature loading, nanotwins are popularly activated due to the decreased stacking fault energy with decreasing temperatures. A positive strain-rate dependent YS arises owing to the contributions from the short-range dislocation obstacles, BCC phases, and refined grains. High-density dislocations and BCC phases result in the degeneration of UE, especially with the increase of strain rates. Strain-rate- and temperature-dependent constitutive models were successfully established to predict the deformation behaviors of CrFeNi MEAs under such a wide range of strain rates at room and cryogenic temperatures.

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.

Temperature effects and temperature-dependent constitutive model of magnetorheological fluids

Temperature effects and temperature-dependent constitutive model of magnetorheological fluids

A novel phenomenological constitutive model for Ti-6Al-4V at high temperature conditions and quasi-static strain rates

Phenomenological constitutive modeling of Ti-6Al-4V at temperatures between 923 and 1023 K under 0.0005–0.05 s−1 quasi-static rates is studied based on a phenomenological approach. For this purpose, the Johnson–Cook constitutive model is revisited. At low temperature conditions under moderate to high strain rates, the material’s stress–strain curves are the most similar to power-law function. Contrary to this, at high temperature conditions under low to moderate strain rates, the saturation-type function well describes the stress–strain curves. On the other hand, it is illustrated that the Johnson–Cook constitutive model is feeble to predict the material’s behavior correctly. Accordingly, in this study, a viscoplastic temperature-dependent constitutive model is developed. The strain rate hardening as well as thermal softening of the developed model is the same as the Johnson–Cook model. But a temperature-dependent strain hardening function is proposed in which both the saturation-type and power-law hardening behaviors of the material are implemented. In comparison with the Johnson–Cook model, the new constitutive model’s fidelity in capturing the titanium behavior is depicted. At last, by considering an Arrhenius-type phenomenological constitutive model, it is noted that the developed constitutive model has the best correctness in predicting the Ti-6Al-4V stress–strain behavior at high temperature conditions under quasi-static rates.

Plastic temperature-dependent constitutive modeling of pure aluminum diaphragms at large strains by using bulge test

A plastic temperature-dependent constitutive model is developed for 0.05 mm thickness pure aluminum diaphragms at large strains by using bulge test method. Rupture strain of the material is recorded below two percent according to tensile tests. In order to achieve the material behavior at larger strains, an own bulge test apparatus is used to extract equi-biaxial stress–strain curves at different temperatures, i.e. from room to 150 °C. Effective stress–strain behavior is then computed via a transformation scheme using the plastic work definition as well as the room temperature uniaxial stress–strain curve. It is illustrated that the Johnson–Cook constitutive model is not able to capture this stress–strain behavior. Thus, a modified Johnson–Cook model is developed in which the strain hardening is assumed to be temperature-dependent accompanying by a novel thermal softening relation. Using the Least-square method as well as the Ant colony optimization algorithm, the material parameters of the both models are calculated. It is depicted that the new model follows the material behavior more precisely than the Johnson–Cook model. The new model is then numerically implemented into finite element software via a user subroutine. In order to compare the accuracy of both models in capturing the hot bi-axial deformation of pure aluminum, an experiment is performed and numerically simulated.

Elasto-Viscoplastic Material Model of a Directly-Cast Low-Carbon Steel at High Temperatures.

A model-based process control of material production processes demands realistic material models describing the local evolution of the thermal and mechanical state variables, i.e., temperature, stress, strain, or plastic strain, for the relevant microstructure state. In the present work, a material model for the specific microstructure in a continuously cast strand shell, viable for reproducing cyclic viscoplastic effects, was developed for a 0.17 wt.% C steel. Experimental data was generated using directly-cast samples and a well-controllable testing facility to apply representative loading conditions. Displacement- and force-controlled experiments in the temperature range of 700–1100 °C were conducted, with a special focus on the relevant strain rates documented for the straightening operation. A temperature-dependent constitutive material model combining elastic, plastic, and viscoplastic effects was parameterized to fit the whole set of experimentally-determined material response curves. In order to account for the cyclic plastic material response, a combination of isotropic and kinematic hardening was considered. The material model sets a new standard for the material description of a continuously cast strand shell, and it can be applied in elaborate continuous casting simulations.

Temperature-Dependence of Rubber Hyperelasticity Based on the Eight-Chain Model.

Rubber-based materials are widely used in a variety of industrial applications. In these applications, rubber components withstand various loading conditions over a range of temperatures. It is of great significance to study the mechanical behavior of vulcanized rubber at different temperatures, especially in a range of high temperatures. The temperature dependence of the constitutive behavior of filled rubber is important for the performance of the rubber. However, only a few constitutive models have been reported that investigate the stress–temperature relationship. In this paper, based on an analysis of experimental data, the effects of temperature on the hyperelastic behaviors of both natural rubber and filled rubber, with different mass fractions of carbon black, were studied. The regulation of stress and strain of natural rubber and filled rubber with temperature was revealed. In addition, an eight-chain model that can reasonably characterize the experimental data at different temperatures was proved. An explicit temperature-dependent constitutive model was developed based on the Arruda-Boyce model to describe the stress–strain response of filled rubber in a relatively large temperature range. Meanwhile, it was proved that the model can predict the effect of temperature on the hyperelastic behavior of filled rubber. Finally, the improved Arruda-Boyce model was used to obtain the material parameters and was then successfully applied to finite element analysis (FEA), which showed that the model has high application value. In addition, the model had a simple form and could be conveniently applied in related performance test of actual production or finite element analysis.

An enhanced distortional-hardening-based constitutive model for hexagonal close-packed metals: Application to AZ31B magnesium alloy sheets at elevated temperatures

In this study, a new material model for hexagonal close-packed (HCP) metals for predicting their flow responses under monotonic/cyclic loadings at various temperatures is proposed. The temperature-dependent constitutive model is re-formulated using a continuum-based distortional hardening law, which affects the shape of the yield surface depending on the loading direction, and also uses the concept of the dominant deformation modes in magnesium alloys: twin, untwin, and slip-dominate modes, considering the role of the twins in plastic deformation. In terms of the material asymmetry in yield strength, the Cazacu–Barlat–Plunkett (CPB) ’06 yield criterion is extended to include thermal effects. A numerical formulation of the material model has also been developed to allow its implementation into finite element analysis software via a user-defined material subroutine (UMAT). The predicted results of stress–strain response for monotonic and cyclic loadings are excellent agreement with the experimental data. Moreover, the simulated results show the strength differential (SD) effect and unusual flow responses of AZ31B magnesium alloy sheets at room temperature, as well as the variation in the SD effect and anisotropic hardening behavior at elevated temperatures.