Temperature-dependent Elastic Modulus Research Articles

Combined thermal and particle shape effects on powder spreading in additive manufacturing via discrete element simulations

The thermal and mechanical behaviors of powders are crucial for additive manufacturing. In powder bed fusion, capturing temperature profiles and packing structures before melting is challenging due to diverse heat transfer pathways and powder properties. This study tackles this challenge with a discrete element model simulating non-spherical particles with thermal properties during powder spreading. Thermal conduction and radiation are integrated into a multisphere particle formulation to model heat transfer among irregular-shaped powders with temperature-dependent elastic properties. The model is utilized to simulate the spreading of pre-heated PA12 powder over a hot substrate representing the part under manufacturing. Variances in temperature profiles are observed in the spreading cases based on particle shapes, spreading speed, and temperature-dependent elastic modulus. Particle temperature beneath the spreading blade is influenced by the kinematics of the particle heap and temperature-dependent properties.

Nonlinear vibration characteristics of thermo-viscoelastic coupling of moving PET films with temperature-dependent elastic modulus

In order to improve the transport stability of roll-to-roll produced polyethylene terephthalate films (PET films) in high temperature environments, this paper investigates the nonlinear vibrational properties of moving PET films under a uniform temperature field by considering the temperature dependence of the elastic modulus. Firstly, constant tensile tests were conducted to test the elastic modulus values of PET films at different hot air temperatures, and the Wachtman model was improved to establish a temperature-dependent elastic modulus model for PET films. Secondly, based on the Kelvin-Voigt model, the nonlinear vibrational equilibrium differential equations of the system were established by applying the Bubnov-Galerkin method of discretization according to D’Alembert’s principle. Finally, numerical simulations based on the 4th-order Runge-Kutta method were carried out to analyze the effects of films width, external excitation frequency, external excitation amplitude, transfer velocity, ambient temperature, damping coefficient and viscoelasticity coefficient on the nonlinear vibration of the system. This provides a theoretical basis for the commissioning of stabilized transfer parameters for roll-to-roll production of PET films.

Theory-guided materials design of multiphase alloys with superior stiffness at finite temperatures

Aiming at designing Mg alloys with a significantly increased stiffness at elevated temperatures, we propose a high-precision multi-scale methodology to compute temperature-dependent elastic modulus of homogeneous multiphase alloys. The proposed method combines (i) first-principles calculations of temperature- and solid solubility-dependent elastic properties in individual phases with (ii) a two-level multiphase homogenization at the continuum level and (iii) a phenomenological thermodynamic modeling by the CALPHAD approach. According to the post-average approximation during the calculation, the stresses and strains of individual phases in the alloy are superimposed before undergoing the average approximation. This is different from the traditional method which consider forces as acting axially assumptions of isostrain and isostress model and followed by numerical averaging. We applied the proposed method in light-weight Mg-alloys, in particular, a three-phase alloy with the composition Mg0.878Al0.083Si0.039, and verified it through experimental measurements. The present work identifies that MgxAlySi1-x-y with 0 ≤ x ≤ 0.87 and 0 ≤ y ≤ 0.87-x are candidate compositions with Young's modulus exceeding 60 GPa at 623 K.

Temperature-dependent elastic shear modulus of a saturated lateritic clay

The thermo-mechanical behaviour of saturated clays and sands has been studied by many researchers, considering that it is useful in many geotechnical problems, such as the analysis of energy foundations and the effects of climate change on earth structures. Despite the fact that temperature is known to affect the yielding and volume change behaviour of soils, the effects of temperature on the elastic shear modulus (G0) of soils are rarely studied. In this study, a temperaturecontrolled oedometer equipped with bender elements was developed. It was used to investigate the effects of temperature on G0 of a compacted lateritic clay at saturated conditions. The G0 was measured at 5 and 40°C during loading and unloading in the stress range of 30 to 400 kPa. Four tests were conducted in which two different initial densities (95% and 85% of maximum dry density (MDD) were considered. The results will be interpreted and discussed with reference to the elastoplastic modelling of thermo-mechanical soil behaviour.

Thermo-metallurgical-mechanical modeling of FG titanium-matrix composites in powder bed fusion

The build-up of residual stress plays a crucial role in the formation quality of as-built parts fabricated by powder bed fusion (PBF). However, the comprehensive understanding of residual stress and distortion fields in PBF-printed functionally graded titanium matrix composites (FGTMCs) has not been achieved. Furthermore, the effect of metallurgical transformation on thermo-mechanical behavior of these materials during the PBF remains unclear. In this paper, considering the phase transition effect due to thermal evolution in the PBF process, a thermo-metallurgical-mechanical coupled model of printed FGTMCs is developed. The equivalent temperature-dependent elastic modulus and heat conductivity of FGTMCs are calculated based on the homogenization method. The differential quadrature method is first employed to efficiently predict the temperature, residual stress, and distortion distributions of PBF-printed FGTMCs. The accuracy of the proposed model is verified by a comparison with predictions in the literature. Furthermore, the effect of crucial process and geometrical parameters on the thermo-mechanical behaviors of FGTMCs is analyzed. The results indicate that the residual stress and vertical distortion of FGTMCs increase as the laser penetration, energy densities, and power index increase, while decreasing significantly with the increased ceramic content, preheating temperature, and layer thickness. These results provide valuable insights for guiding the process optimization of additively manufactured FGTMCs.

Study on Temperature-Dependent Uniaxial Tensile Tests and Constitutive Relationship of Modified Polyurethane Concrete.

Modified polyurethane concrete (MPUC) is a new material for steel deck pavements. In service, the pavement is often cracked due to excessive tensile stress caused by temperature changes. In order to study the tensile properties of MPUC in the diurnal temperature range of steel decks, uniaxial tensile tests of MPUC were carried out at five temperatures. Three kinds of specimens and a novel fixture were designed and fabricated to compare the results of four different tensile test methods. The deformation of the specimen was collected synchronously by two methods: pasting strain gauge and digital image correlation (DIC) technique. Based on the experiment, the tensile mechanical properties, failure modes, and constitutive relations of MPUC were studied under the effect of temperature. The research results show that the novel fixture can avoid stress concentration. By observing the fracture surface of the specimens, the bonding performance is great between the binder and the aggregate at different temperatures. The tensile strength and elastic modulus of MPUC decrease with increasing temperatures, while the fracture strain, and fracture energy increase with increasing temperatures. The formulas of temperature-dependent tensile strength, fracture strain, and elastic modulus of MPUC were established, and the constitutive relationship of MPUC is further constructed in the rising stage under uniaxial tension. The calculation results show good agreement with experimental ones.

Performance based design of bonded whitetopping overlays

This paper proposes a new performance based design method for bonded concrete overlays of existing asphalt pavements. Important input parameters such as the residual bearing capacity of the hot mix asphalt (HMA) layer and its thickness, the temperature-dependent interface bonding properties between the existing HMA and the new concrete layer, the climatic conditions and the traffic loads are being characterised. The implementation of temperature-dependent elastic modulus of the HMA and interface bonding properties in the design model allows for a more realistic determination of the overlay thickness and the design life. Further, a design catalogue was derived based on the results from a number of pavement structure analysis with varying parameters. For a given expected number of heavy goods vehicles (HGV) passes, the thickness of the existing HMA and its residual bearing capacity it is possible to determine the required concrete overlay thickness.

Thermally activated viscoelasticity of cement paste: Minute-long creep tests and micromechanical link to molecular properties

The stiffness of cementitious materials decreases with increasing temperature. Herein, macroscopic samples of mature cement pastes are subjected at 20, 30, and 45 °C, respectively, to three-minutes-long creep compression experiments. The test evaluation is based on the linear theory of viscoelasticity and Boltzmann’s superposition principle. This yields macroscopic elastic and creep moduli as a function of temperature. A state-of-the-art multiscale model for creep homogenization of cement paste is extended to account for temperature-dependent elastic and creep moduli of the hydrate gel. This extension is based on results from published molecular simulations. Temperature-independent stiffness is assumed for cement clinker. Upscaling to the macroscale of cement paste yields elastic and creep moduli which agree well with the aforementioned experimental results. The Arrhenius-type activation energy of the creep modulus is found to be independent of scale, composition, and maturity, because of ineffective stress redistributions from creeping to non-creeping constituents.

Grain size effect on the temperature-dependence of elastic modulus of nanocrystalline NiTi

The effect of grain size on temperature-dependent elastic modulus (TDEM) of polycrystalline NiTi over a temperature span of 200 °C was investigated by dynamic thermomechanical analysis (DMA). It is found that the TDEM rapidly reduced with grain size down to nanoscale. In-situ neutron diffraction and molecular dynamics (MD) simulation reveal that the volume fraction and thermal stability of austenite phase at low temperature gradually increased with the reduction of grain size due to the mechanical constraint of grain boundary, which results in the two-phase coexistence during cooling. The compensation of the intrinsic opposite TDEM of austenite and martensite leads to the overall reduced TDEM in nanocrystalline NiTi. This study strongly implies that the TDEM of shape memory alloy can be tailored by grain size.

Nonlocal thermodynamical vibrations in a rotating magneto-thermoelastic medium based on modified Ohm's law with temperature-dependent properties

PurposeThe purpose of this paper is to study the transient thermoelastic interactions in a nonlocal rotating magneto-thermoelastic medium with temperature-dependent properties. Three-phase-lag (TPL) model of generalized thermoelasticity is employed to study the problem. An initial magnetic field with constant intensity acts parallel to the bounding plane. Therefore, Maxwell's theory of electrodynamics has been effectively introduced and the expression for Lorentz's force is obtained with the help of modified Ohm's law.Design/methodology/approachThe normal mode technique has been adopted to solve the resulting non-dimensional coupled field equations to obtain the expressions of physical field variables.FindingsFor uniformly distributed thermal load, normal displacement, temperature distribution and stress components are calculated numerically with the help of MATLAB software for a copper material and the results are illustrated graphically. Some particular cases of interest are also deduced from the present study.Originality/valueInfluences of nonlocal parameter, rotation, temperature-dependent properties, magnetic field and time are carefully analyzed for mechanically stress free boundary and uniformly distributed thermal load. The present work is useful and valuable for analysis of problem involving thermal shock, nonlocal parameter, temperature-dependent elastic and thermal moduli.

Exceptional strength-ductility combination of additively manufactured high-entropy alloy matrix composites reinforced with TiC nanoparticles at room and cryogenic temperatures

The cryogenic mechanical properties and deformation behaviour of additively manufactured (AM) medium/high-entropy alloys (MEA/HEA) and their composites are seldom studied. This work fills this gap by systematically studying the mechanical properties, deformation behaviour and strengthening mechanism of the additively manufactured CoCrFeMnNi high-entropy alloy (HEA) and 2 wt% TiC/CoCrFeMnNi composite (HEC) at room (293 K) and cryogenic (93 K) temperatures. The TiC nanoparticles promote the densification behaviour, and they are uniformly distributed around and in interior of the cellular substructures of the HEC sample. The tensile tests reveal that the strength and ductility can be simultaneously increased in both HEA and HEC samples when the temperature decreases from 293 K to 93 K. The TiC nanoparticles significantly promote a remarkable combination of strength and ductility in the HEC at both 293 K and 93 K, and the cryogenic tensile strength of HEC (1506 ± 6.6 MPa) is the highest value reported for AM-fabricated MEA/HEAs. For the HEA sample, the significant increase in strength and ductility is attributed to an additional hardening contribution induced by multiple twin systems at 93 K, which results in a steady and even increased strain hardening rate. When the temperature decreases from 293 K to 93 K, a remarkable yield strength increment (344.4 MP) is found in the HEC sample, which is significantly higher than that of HEA (229.0 MPa). The difference in the increase in yield strength between HEA and HEC sample is ascribed to the difference in dislocation strengthening and Orowan strengthening, which are related to the temperature-dependent thermal expansion coefficient and elastic modulus, respectively. However, the HEC sample has a smaller ductility increase (10.3%) than the HEA sample (26.4%), since no additional hardening mechanism is generated during the cryogenic deformation in the HEC sample. This research provides a new route to design materials with a good combination of strength and ductility for cryogenic applications.

Prediction of buckling failure load of 304 stainless-steel column at elevated temperatures using lead–antimony alloys

A novel prediction model for the buckling failure load of 304 stainless steel under compression was developed using lead–antimony (Pb–Sb) alloys. The temperature-dependent modulus of elasticity of 304 stainless steel was characterized by changing the Sb concentration of the Pb–Sb alloys from 0 to 15 wt%. Slender Pb–Sb plate columns with a rectangular cross section were fabricated by casting. Buckling tests were performed with Pb–Sb alloys under compression at room temperature and compared with numerical simulations that considered the nonlinearity of the specimen, such as initial bending. Based on the buckling failure load and the modulus of elasticity measurements, the linear relationship between the normalized buckling failure loads and the normalized modulus of elasticity was obtained for both Pb-Sb alloy and 304 stainless steel. The relationship between these two correlations makes it possible to predict the buckling failure load of 304 stainless steel at elevated temperatures up to 1200 °C.

Novel thermomechanical characterization for shrinkage evolution of unidirectional semi-crystalline thermoplastic prepregs (PPS/CF) in melt, rubbery and glassy states

Shrinkages, distortions and high residual stresses in the thermoplastic composite parts are induced due to high processing temperature, anisotropy, and fiber–matrix shrinkage mismatch. In this paper the shrinkages have been investigated experimentally and modeled by thermo-mechanical constitutive equations for PolyPhenylene Sulfide (PPS) and the unidirectional Carbon Fiber (PPS/CF) composite prepreg. The thermal shrinkage and the crystallization shrinkage were retrieved from Thermal Mechanical Analysis and compared to a Pressure specific volume Temperature diagram. To describe the crystallization shrinkage in the cooling process accurately, the crystallization kinetics of PPS was evaluated using Differential Scanning Calorimetry. The temperature-dependent elastic modulus was measured by a shear rheometer to formulate a new constitutive model. The mathematical model for shrinkage was validated by a press consolidated [0]12 laminate and unbalanced laminates in four lay-ups. The thermo-mechanical model results presented here provide significant rules for the thermomechanical and shrinkage predictions for the industrial applications of thermoplastic composite.

A methodology for predicting processing induced thermal residual stress in thermoplastic composite at the microscale

A computational finite element (FE) model of thermal residual stress was developed for carbon fiber/thermoplastic composites at the microscale and implemented via user material subroutine (UMAT) in ABAQUS. This model accounts for cooling-rate effects on crystallinity and stress-free temperature, temperature-dependent elastic modulus, temperature-dependent coefficient of thermal expansion (CTE) of the matrix, and the temperature-independent transversely isotropic properties of the carbon fiber. Results are generated for a model composite, consisting of a single carbon fiber embedded in a polypropylene thin film. Single filaments are pre-tensioned in the polymer melt to induce different levels of residual axial strain as well as maintain straight fibers during cool-down. Three different preload conditions (1g, 4g, and 8g) were experimentally fabricated and modeled. The residual strain along the length of the fiber is quantified and validated including the shear lag region that develops at the free edge of the sample. Experimentally measured residual strain shows a good correlation with the FE predictions for the applied fiber preloading conditions.

A thermo-viscoplasticity model for metals over wide temperature ranges- application to case hardening steel

In this contribution, a model for the thermomechanically coupled behaviour of case hardening steel is introduced with application to 16MnCr5 (1.7131). The model is based on a decomposition of the free energy into a thermo-elastic and a plastic part. Associated viscoplasticity, in terms of a temperature-depenent Perzyna-type power law, in combination with an isotropic von Mises yield function takes respect for strain-rate dependency of the yield stress. The model covers additional temperature-related effects, like temperature-dependent elastic moduli, coefficient of thermal expansion, heat capacity, heat conductivity, yield stress and cold work hardening. The formulation fulfils the second law of thermodynamics in the form of the Clausius–Duhem inequality by exploiting the Coleman–Noll procedure. The introduced model parameters are fitted against experimental data. An implementation into a fully coupled finite element model is provided and representative numerical examples are presented showing aspects of the localisation and regularisation behaviour of the proposed model.

A multi-material topology optimization with temperature-dependent thermoelastic properties

This is a study on the development of a novel multi-material topology optimization scheme considering temperature-dependent thermoelastic properties for engineering structure design. Two cases, a three-point-bending beam under a uniform temperature field and a cantilever beam under a non-uniform temperature field, are investigated for the effects of thermoelastic properties on topology optimization. The proposed optimization scheme is compared with two existing topology optimization approaches: conventional topology optimization and thermoelastic topology optimization. The results show that the temperature-dependent elastic modulus dominantly influences the design optimization outcomes, in terms of material distribution, structural shape and compliance, while the temperature-dependent thermal expansion coefficient has a much more crucial impact on determining the material distribution and structural geometry than on compliance. Taken together, the findings demonstrate that the developed topology optimization scheme can be used to design thermally sensitive multi-materials in industrial applications, e.g. aerospace structures under high temperature and polymers in additive manufacturing.

Effective acquisition of elastoplastic and creep parameters of lead-free solder alloy from high-temperature micro-indentation eliminating the size effect

Effective acquisition of the related mechanical properties of lead-free solder alloys through micro-indentation tests is of great significance in the research on electronic interconnection design and reliability for the multi-functionalization and high integration of electronic products. The temperature-dependent elastoplastic and creep parameters of Sn–3.0Ag–0.5Cu (SAC) solder are systematically investigated by micro-indentation with plural indenters and the “rapid loading-holding-rapid unloading” test mode. Based on the depth dependence of indentation hardness from mechanism-based strain gradient plasticity and the stress independence of creep compliance for linear viscous assumption, the complete indentation load-depth curves eliminating the indentation size effect of SAC solder under different temperature and two pyramidal indenters with different equivalent semi-cone angles are reconstructed. Combining with the temperature-dependent elastic modulus measurements from cylindrical indentation, corrected load-depth curves for pyramidal indentation, and the concept of representative stress and representative plastic strain, the elastoplastic parameters eliminating the indentation size effect under different temperature are uniquely determined through numerical simulation and inversion analysis, as well as the corresponding creep parameters. The temperature dependence of elastoplastic and creep parameters of SAC solder is analyzed, and related deformation mechanism is discussed. Results of forward and inverse analyses indicate the effectiveness of proposed characterization method.

Multi-level micromechanical analysis of elastic properties of ultra-high performance concrete at high temperatures: Effects of imperfect interface and inclusion size

Ultra-high performance concrete (UHPC), as a typical multi-phase composite material, is vulnerable to mechanical degradation and explosive spalling at high temperatures. In this work, the temperature-dependent elastic modulus of UHPC is estimated through the step-by-step homogenization from gel matrix level to ultra-high performance fiber-reinforced concrete level. Totally three forms of C-S-H gels are considered to determine the elastic properties of the initial matrix, and the phase transformation and volume fractions of individual phases at high temperatures are calculated based on the hydration and dehydration kinetics models. Moreover, the effects of imperfect interface and inclusion size are taken into account by introducing the spring-layer interface model and log-normal size distribution function to the homogenization scheme. The predicted elastic moduli are validated by analytical and experimental results, showing that accurate predictions can be obtained at up to 800°C. Interestingly, the imperfect interface matters when high-modulus inclusions are embedded in the low-modulus matrix, and the effect of imperfect interface on effective elastic modulus varies a lot at different microscopic levels. The findings highlight the synergistic effects of imperfect interface and inclusion size on the elastic properties, which is helpful to the mechanical design of UHPC at high temperatures.

Free vibration of rotating pretwisted FG-GRC sandwich conical shells in thermal environment using HSDT

The free vibration behavior of rotating pretwisted sandwich conical shell panels with functionally graded graphene-reinforced composite (FG-GRC) face sheets and homogenous core is investigated in uniform thermal environment using finite element method in conjunction with a higher-order shear deformation theory (HSDT). The volume fraction distribution of the graphene in the face sheets is considered to be uniform or layer-wise functionally graded across its thickness. The temperature-dependent effective elastic moduli of the FG-GRC face sheets are computed employing the refined Halpin-Tsai model, while the effective Poison’s ratio, density, and thermal expansion coefficients are obtained using the mixture-rule. The effects of non-linearity arising out of the initial stresses due to thermal and centrifugal loads are incorporated via geometric stiffness based on Green-Lagrange’s strains. The governing equations for sandwich conical shell panels are derived using Lagrange’s equation of motion at moderate rotational speeds. The influence of graphene distribution patterns on the fundamental frequencies of FG-GRC sandwich conical shells under different thermal conditions is studied with emphasis on triggering parameters like pretwist angle, cone length-to-thickness ratio, core-to-face sheets thickness ratio, and dimensionless rotational speed.

Mean-field homogenization of thermoelastic material properties of a long fiber-reinforced thermoset and experimental investigation

Fiber-reinforced polymers contribute significantly to weight-reducing components for various industrial applications. A discontinuous glass fiber-reinforced thermoset resin is considered which is produced by the sheet molding compound (SMC) process. Related to the production process, the samples considered in this work exhibit an anisotropic fiber orientation distribution which highly affects the thermomechanical properties. The thermoviscoelastic material behavior of three selected samples is characterized by means of dynamic mechanical analysis. These tests show the temperature-dependent elastic modulus and the glass transition of the composite. Measurements of the thermal expansion of the SMC composite provide data on the coefficient of thermal expansion (CTE). These experimental investigations provide data for the thermoelastic material modeling. Aiming at the prediction of the effective thermal and mechanical properties, a Hashin–Shtrikman-based homogenization method is presented. Based on an eigenstrain formulation, the effective Young’s modulus and CTE are computed in two steps. Moreover, the mean-field method is given in dependence of a variable reference stiffness allowing to tailor the approach to the material system. The influence of this variable reference stiffness on the effective quantities as well as the predicted behavior is analyzed with respect to the experiments. The presented numerical results are in good agreement with the experimental data.