Temperature Dependent Material Behavior Research Articles

The Impact of Various Heating Rates on Real-Time Degree of Hybrid Fire Simulation

Global fire performance of structures in fire is proven to be more advantageous in many cases of engineering practice than the prescriptive fire resistance based on isolated structural member testing. Hybrid fire simulation (HFS) is a novel well-suited method trending in recent years for analysis of global performance of structures in fire. In the principles of this method, the part of a structure which has unknown behavior or is uncertain to be numerically modeled (subjected to fire) would be physically tested, while the rest of the structure is numerically simulated. HFS method enables capturing the beneficial interaction mechanisms evolving between fire-exposed structural members and the adjacent cooler substructure. Due to the continuous temperature increase in a fire test and the existing thermal inertia as well as the rate- and temperature-dependent material behavior of structures exposed to fire, a real-time performance in hybrid fire simulation counts as a necessity. This challenge is more critical for hybrid fire simulations with higher applied heating rates relevant to structural fire engineering. Within scope of this paper, (a) a robust and rigorous approach for real-time HFS is presented; (b) a series of proof-of-concept studies of different hybrid fire simulations with various applied heating rates are carried out for a thermomechanical benchmark problem; (c) the important results of four representative hybrid fire simulations with relevant heating rates to structural fire engineering are discussed; (d) the importance of an appropriate calculation method for stiffness update of the fire-exposed structural member over HFS procedure is highlighted, and e) the precision and accuracy of the applied HFS approach with respect to interface error and real-time degree are evidenced.

Simulation-Based Investigations of the Load-Bearing Behavior of Concrete Hollow Sphere Slabs Exposed to Fire

This paper concerns the investigations of the flexural capacity of concrete slabs with integrated concrete hollow spheres that are subjected to fire and their mass saving potential compared to solid slabs. (1) Background: The overuse of concrete in construction contributes considerably to global CO2 emissions; therefore, the potential for mass reduction in structural components must be fully exploited. However, the design regulations for weight-minimized components, particularly slabs with internal voids, are often not explicitly covered by standards, such as the fire design standard relevant to this paper. (2) Methods: Based on the design guidelines for statically determinate structures in Eurocode 2-2 and DIN 4102-4, a solid slab and a concrete slab with concrete hollow spheres are designed and evaluated with regard to their weight and flexural capacity when subjected to fire. The temperature profiles within the slab cross-section exposed to fire are simulated using ABAQUS finite element software, considering the physically nonlinear, temperature-dependent material behavior of concrete and steel. Using these results, the strain distribution corresponding to the maximum flexural moment is iteratively determined at the weakest cross-section, which exhibits the largest void. (3) Results: All components show sufficient flexural capacity for the target fire duration of 90 min. (4) Conclusion: In the context of this study, the design guidelines according to Eurocode 2-2 and DIN 4102-4 are proven to be fully applicable also for concrete hollow sphere slabs.

Determination of the linear viscoelastic material behaviour of interlayers with semi-crystalline structures shown by the example of a semi-crystalline ionomer

The temperature dependent linear viscoelastic material behaviour of the most commonly used interlayer PVB is typically determined by means of Dynamic-Mechanical-Thermal-Analysis (DMTA). By horizontally shifting the isothermal modulus curves, a mastercurve is created at a certain reference temperature, which can then be mathematically approximated with a Prony series. A time–temperature superposition principle can be derived from the shift factors. In contrast to PVB, EVA and ionomer (or ionoplastic) interlayers have semi-crystalline structures that melt when the melting temperature is reached and form again when the sample is cooled below the crystallization temperature. The exact structure and number of crystallites depend e.g. on the cooling rate and the physical age (or thermal prehistory) of the sample. These factors must be taken into account in the experimental determination of the material parameters with DMTA. Using the example of SentryGlas®, this article shows that the stiffness of semi-crystalline interlayers is affected by the crystallinity. Mastercurves from DMTA with different temperature programs are created. The degrees of crystallization for the different temperature programs are determined with Differential Scanning Calorimetry (DSC). A time–temperature superposition principle, which applies to the purely amorphous material, and a time-crystallinity superposition principle are derived, which enable the determination of the material parameters for different temperatures and degrees of crystallization.

Experimental determination and numerical simulation of temperature dependent material and damage behaviour of additively manufactured polyamide 12

Temperature dependent material and damage behaviour of additively manufactured polyamide 12 was analysed. Two different types of tests were carried out. Very slow isothermal and non-isothermal tensile tests at various temperature levels. The results served as basis for the determination of the parameters of the numerical simulation. In a previous study, it was observed that the viscoplastic material model of Chaboche and the damage model of Gurson-Tvergaard-Needleman are very well suited to the material and damage behaviour at room temperature. This work presents that the material model of Chaboche and the damage model of Gurson-Tvergaard-Needleman can be used for isothermal tensile tests at various temperature levels to simulate material and damage behaviour of selectively laser-sintered polyamide 12, with the requirement that the parameters are adjusted for each temperature level. Furthermore, the temperature dependence of the GTN parameters and a sensitivity analysis is presented. Finally, by extending the Chaboche model with the Johnson-Cook approach and coupling it with the Gurson-Tvergaard-Needleman damage model, the material and damage behaviour can be applied under non-isothermal test conditions.

Modelling concrete slabs subjected to fires using nonlinear layered shell elements and concrete damage-plasticity material

Floor slabs are crucial in the global load bearing mechanism during fire by providing critical alternate load-paths including tensile membrane action. It is desirable, but expensive and difficult, to predict their behaviour accurately with minimal calibration of model parameters. Two new developments are added to OpenSEES for this purpose. First, a thermo-mechanical nonlinear shell element extended for modelling large deflection of slabs in fire along with a multi-layered section to account for temperature-dependent material behaviour including plasticity and thermal expansion. The shell model is ported to include fire induced thermal action definitions induced by real fire exposure, which is critical in accurate simulation of deflections and stress states. Second, a plane-stress formulation of the concrete damage-plasticity material at elevated temperature is introduced to effectively model concrete response and damage in fire. These state-of-the-art developments provide a new, powerful, and open-source tool for researchers and engineers to investigate structural-fire problems at different scales with satisfying accuracy. The code is verifiedusing benchmark solutions and validated by modelling flat reinforced concrete slabs tested at ambient temperature and in fire,followed by simulating the large-scale Cardington Corner fire test. The results of these exercises agree well with analytical and experimental data and show that the new developments are well conceived and implemented.

Thermo‐mechanical modeling of the temperature dependent forming behavior of thermoplastic prepregs

AbstractNumerical optimization of the manufacturing process of hybrid lightweight structures consisting of fiber‐reinforced plastics is of great importance. This article introduces an industry‐oriented modeling approach for the thermoforming process of thermoplastic prepregs. A laminate model combined with established elastic‐plastic constitutive laws is used for the numerical treatment of the temperature dependent material behavior of the composite. The mechanical properties of the Polyamide 66 (PA66) matrix are acquired from a data sheet provided by the manufacturer. Experiments including tensile, shear, and bending tests are performed to characterize the effective deformation behavior of the prepreg in the full temperature range. Appropriate model parameters are determined to represent the temperature dependent deformation behavior of the composite according to the experimental observations. The parameterized material model for the prepreg is eventually applied in the simulation of thermoforming processes to show the influence of process and material parameters on the forming behavior of thermoplastic prepregs.

Dynamic evolution of nonuniform temperature-stress distributions in continuously eroding thermal barrier coatings

Erosion is the risk main factor for thermal barrier coating systems (TBCs). The resulting inhomogeneities introduce nonuniform temperature distributions, which affect temperature-dependent material behavior (e.g., growth of thermally grown oxide (TGO) and creep), complicating the stress states at the interfaces between the top coat (TC), TGO and the bond coat (BC). In this work, a finite element TBCs model considering dynamic erosion pit growth and TGO growth is built to evaluate the effects of the nonuniform erosion. The simulation results show that the growth of the erosion pit creates a high-temperature zone in TBCs, leading to the formation of oblique temperature gradients. Large temperature variations accelerate TGO growth and increase the thermal stress in TBCs, causing higher stress levels in the TC and BC layer during both the hot dwelling and cooling stages. Meanwhile, the gradually-growing erosion pit makes crack initiation and propagation more likely at interface zones located at both sides of the pit. Cracks occur in the maximum interfacial stress zones at the interface, which are off-peak during the hot dwelling stage and in-peak during the cooling stage. This work provides a relatively complete evaluation of erosion-induced effects, which is instructive for the design and operation of TBCs.

A finite element simulation model of convective heat-assisted single-point incremental forming of thermoplastics

The objective of this research is to simulate the effects of temperature on the stress, strain, and forming forces in the single-point incremental forming process of polymers through the development of a FEA model. Currently available SPIF simulation models are limited to room temperature and are not suited to processes that use localized heating to increase formability. The model developed in this research consists of three key components: (a) simulated temperature spot using a distribution of convective heat transfer coefficients (HTC) values, (b) temperature-dependent material behavior using the Three Network model (TNM), and (c) and the integration of thermal and mechanical behavior of the SPIF process. The forming of a polycarbonate cone with a constant wall angle of 45 degrees is simulated using the model under two conditions: (i) room temperature SPIF and (ii) CHASPIF using an external hot air source of 250 °F (121.11 °C). The accuracy of the predicted deformation and temperatures varies in the different zones. Inside the formed wall, the temperature distribution is predicted within ± 5 °C for CHASPIF, and deformation within 0.766 mm for CHASPIF and 0.786 mm for SPIF compared to experimental results. Future research will be focused on improving the accuracy of the model and evaluating process limits for more complex shapes. The simulation model is ultimately intended to be used for model-based manufacturing.

A computationally rigorous approach to hybrid fire testing

Real fire incidents have shown that the structural systems of high-rise buildings perform much better during a fire attack than what classical structural fire analysis predicts. The reason behind this phenomenon is the empirically established fact that beneficial interaction mechanisms evolve between the fire-exposed and the fire-unexposed parts of structural systems. However, there is no computational method available to reliably quantify such interaction mechanisms for design purposes. Pure numerical methods are too uncertain, because they cannot be validated, and isolated structural member testing does not allow considering the interaction. Hybrid fire testing, however, can precisely fill this fundamental methodological gap when set up as an extended finite-element analysis technique. Here, we provide the first computationally rigorous method for hybrid fire testing. We have validated the novel method with several proof-of-concept tests covering the entire temperature-range relevant for structural fire engineering. In contrast to other approaches, only our method can deal, so far, at the same time suitably, accurately and robustly with the experimental and computational challenges of temperature-dependent material behavior. We therefore place hybrid fire testing on a sound scientific basis enabling existing fire test facilities to do more realistic (hybrid) assessments of the fire performance of structural systems.

Prediction of the behaviour of copper alloy components under complex loadings by electro-thermomechanical coupled simulations

ABSTRACT Electronic devices must be served with electric power for different reasons. A robust and reliable electric connectivity is often realised by electric connectors. For its leading properties, precipitation hardened copper alloys are widely used for designing connectors with high level mechanical or conductance properties. However, copper alloys show a characteristic stress relaxation under mechanical or thermal loads. Finite element analysis is a standard method to design and optimise components with respect to reliability and performance. Hence, a material model considering the characteristic of the mechanical properties and allowing for the simulation of time and temperature dependent elasto-viscoplastic material behavior was developed at the Fraunhofer IWM. The parameters of the model were determined using tensile and relaxation test data of a C19010 alloy. The material model is applied to electro-thermomechanical coupled finite element simulations of connectors with different load histories. The goal of the simulations is the analysis of the impact of stress relaxation on the mechanical properties of systems over time. From the numerical results with the new model it is shown, how stress relaxation influences the connector clamping forces or contact pressure, respectively, in dependence with time or temperature. The simulation results documents that stress relaxation has to be taken into account in finite element simulations during the designing process of electrical devices. This paper is part of a Thematic Issue on Copper and its Alloys.

Constitutive-damage modeling and computational implementation for simulation of elasto-viscoplastic-damage behavior of polymeric foams over a wide range of strain rates and temperatures

The material behavior and damage of polymeric foams (e.g., polyurethane foam and polystyrene foam) are extremely complex under compression, depending on strain rates and temperatures. In the present study, the elasto-viscoplastic-damage behavior of polymeric foams over a wide range of strain rates and temperature is evaluated and predicted using the modified Gurson-Tvergaard-Needleman-Lemaitre (GTNL) model and the modified Khan-Huang-Liang (KHL) model. A modified GTNL model is introduced to describe phenomena of decreasing void volume fraction and elastic modulus for polymeric foams under uniaxial compression. The modified KHL model is proposed to evaluate the nonlinear strain rate- and temperature-dependent material behavior of polymeric foams. The full derivation of the implicit integration algorithm of the proposed modified GTNL-KHL model is introduced, and a user-defined material (UMAT) subroutine for commercial finite element analysis code (i.e., ABAQUS) is established. Using the UMAT, the damage characteristics (e.g., void volume fraction and elastic modulus changes) and the nonlinear material behavior (e.g., linear elastic, softening/plateau and densification) of polymeric foams under uniaxial compression with various strain rates and temperatures are successfully simulated.

Fire-Resistance of Eccentrically Loaded Rectangular Concrete-Filled Steel Tubular Slender Columns Incorporating Interaction of Local and Global Buckling

A mathematical model using the fiber approach is presented in this paper for quantifying the strength and fire-resistance of eccentrically loaded slender concrete-filled steel tubular (CFST) columns with rectangular sections incorporating the interaction of local and global buckling. The model utilizes the thermal simulator to ascertain the temperature distribution in cross-sections, and the nonlinear global buckling analysis to predict the interaction responses of local and global buckling of loaded CFST slender columns to fire effects. The initial geometric imperfection, air gap between the concrete and steel tube, tensile concrete strength, deformations caused by preloads, and temperature-dependent material behavior are included in the formulation. The computational theory, modeling procedure and numerical solution algorithms are described. The computational model is verified by existing experimental and numerical results. The structural responses and fire-resistance of CFST columns of rectangular sections exposed to fire are investigated. The mathematical model proposed is demonstrated to be an efficient computer simulator for the fire-performance of slender CFST columns loaded eccentrically.

Engineering design of laminated safety glass considering the shear coupling: a review

The use of glass and, in particular, laminated glass (LG) in the building industry is a continuously rising trend. Thus, in order ensure a safe fracture and a post-breakage load bearing capacity but still be economical, the consideration of the shear transfer by the polymeric interlayer between the glass panes is gaining importance in the structural design. This also relates to future European harmonised product and design standards in glass construction. In addition to simple models using particular shear modulus values for certain load situations and temperatures, linear viscoelastic material models for the interlayer can be applied for more complex design situations. We present the basics of mechanical modelling of the time- and temperature dependent material behaviour of polymers used in LG. The procedure for the experimental determination of the material parameters is explained for the most common product polyvinyl butyral. For practical application in glass design, different standards (national and international) and other building regulations are compared. The analysis of the compliant composite shows that already low shear modulus values lead to a significant reduction in glass stresses. Finally, a comparative example shows the design of laminated glass considering the shear transfer with different methods.

A finite-strain thermomechanical model for severe superplastic deformation of Ti-6Al-4V at elevated temperature

This paper presents a new finite-strain and thermomechanically-coupled constitutive model for severe superplastic deformation of Ti-6Al-4V at elevated temperature. The kinematic hypothesis of this model is a multiplicative decomposition of the deformation gradient into elastic, superplastic and thermal components, allowing the model to simultaneously take into account the large superplastic flowing deformation, the evident thermal expansion and the local temperature evolution. The model begins with the establishment of a thermodynamically consistent framework, including the Helmholtz free energy function, the entropy inequality and the heat production, from which constitutive equations are derived. The strain rate and temperature dependent material behavior is formulated by using a bilinear interpolation scheme and an exponential function. The ABAQUS/Explicit user-defined material subroutine VUMAT is employed to realize the numerical implementation of the model. The model is validated against the experimental data obtained in tensile tests on Ti-6Al-4V specimens. Finite element simulation of the superplastic gas-blow forming of Ti-6Al-4V sheet well demonstrates the model capabilities of accurately describing large superplastic deformation of Ti-6Al-4V at elevated temperature.

Abstract of: Investigations on the Thermorheologically Complex Material Behaviour of the Laminated Safety Glass Interlayer Ethylene-Vinyl-Acetate

Laminated safety glass has become an indispensable component in building construction, automotive and solar industry. It consists of at least two glass panes, that are laminated together with a polymeric interlayer. Mechanically speaking, the polymeric interlayer enables a shear transfer between the two glass panes. Here, the difficulty lies in the understanding of the real shear transmission. On the one hand, polymeric interlayers show a time dependent material behaviour, which can be described with a ‘Prony-series’ in the linear viscoelastic area. On the other hand, polymeric interlayers show a temperature dependent material behaviour. Hence, a Prony-series is only valid for one specific temperature. However, since relaxation is based on molecular movements and rearrangement processes, which can be thermally activated, an increase in temperature leads to an acceleration of the relaxation process. The time-temperature correlation can be taken into account by means of a ‘Time-Temperature-Superposition-Principle’ (TTSP). The relaxation curve of a thermorheologically simple material shifts solely horizontal along the time axis due to temperature changes, while its shape remains constant. Mathematically, this means, that all relaxation times of the Prony-series are multiplied by the same shift factor aT. Recent research of the authors shows, that some polymeric interlayers don’t follow a simple TTSP. The experimental identification through ‘Dynamical-Mechanical-Thermal-Analysis’ as well as ‘Differential Scanning Caliometry’ and numerical incorporation of this thermorheologically complex material behaviour into state-of-the-art Finite-Element-Software will be investigated on the example of ‘Ethylene-vinyl acetate’ in the following paper.

Investigations on the thermorheologically complex material behaviour of the laminated safety glass interlayer ethylene-vinyl-acetate

Laminated safety glass has become an indispensable component in building construction, automotive and solar industry. It consists of at least two glass panes, that are laminated together with a polymeric interlayer. Mechanically speaking, the polymeric interlayer enables a shear transfer between the two glass panes. Here, the difficulty lies in the understanding of the real shear transmission. On the one hand, polymeric interlayers show a time dependent material behaviour, which can be described with a ‘Prony-series’ in the linear viscoelastic area. On the other hand, polymeric interlayers show a temperature dependent material behaviour. Hence, a Prony-series is only valid for one specific temperature. However, since relaxation is based on molecular movements and rearrangement processes, which can be thermally activated, an increase in temperature leads to an acceleration of the relaxation process. The time-temperature correlation can be taken into account by means of a ‘Time-Temperature-Superposition-Principle’ (TTSP). The relaxation curve of a thermorheologically simple material shifts solely horizontal along the time axis due to temperature changes, while its shape remains constant. Mathematically, this means, that all relaxation times of the Prony-series are multiplied by the same shift factor aT. Recent research of the authors shows, that some polymeric interlayers don’t follow a simple TTSP. The experimental identification through ‘Dynamical-Mechanical-Thermal-Analysis’ as well as ‘Differential Scanning Caliometry’ and numerical incorporation of this thermorheologically complex material behaviour into state-of-the-art Finite-Element-Software will be investigated on the example of ‘Ethylene-vinyl acetate’ in the following paper.

Characterization and modeling of poly(methyl methacrylate) and thermoplastic polyurethane for the application in laminated setups

Transparent polymeric laminates are increasingly used for the substitution of conventional glass and laminated safety glass respectively and thus require reliable and efficient prediction and modeling techniques, in particular for numerical simulations. In the present work, the components of a polymeric laminate consisting of poly(methyl methacrylate) (PMMA) plies combined with a thermoplastic polyurethane (TPU) interlayer were subjected to experimental and numerical investigation. Uniaxial tensile tests and dynamic mechanical thermal analysis (DMTA) were used to determine the strain-rate and temperature dependent material behavior. Adiabatic heating of the interlayer was observed using infrared (IR) surveillance. Based on the experimental basis, viscoelastic material models were applied for both materials. The corresponding parameter identification was performed in two ways. One was based on the DMTA master curve, the other on uniaxial tensile test data. The material models were able to capture the temperature and time dependent behavior of both materials adequately and enable their usage in a laminated structure.

A generalized J-integral for thermal shock analyses of 3D surface cracks in spatially and temperature dependent materials

Thanks to their favorable mechanical properties and modern manufacturing technologies, functionally graded materials (FGM) and structures have gained increasing utilization in engineering. One major applications of functionally graded ceramics, refractories or heat protecting layers is to improve the resistance against thermal shock impact. Here, fracture mechanical methods are needed to evaluate the strength and durability of such structures exposed to transient thermomechanical loading. Despite a lot of theoretical work has been done for two-dimensional crack configurations in thermoelastic FGM, real defects and structural components are of three-dimensional (3D) nature. In most cases the real gradation of the thermoelastic material properties does not obey simple mathematical functions, but shows a complex physical dependency on location due to manufacturing. Moreover, the elastic and thermodynamic properties depend on temperature itself.In this paper, we present the derivation of the 3D J-integral for arbitrary location and temperature dependent anisotropic material behavior. The functionally varying material properties are implemented in the finite element method (FEM) by means of »graded elements«. The J-integral is calculated in post-processing using the equivalent domain integral technique. The method is applied to surface cracks in a functionally graded plate under mechanical and thermal shock loading. Hereby, the real measured variation of all thermal and mechanical properties with porosity and temperature is exploited for a CaAl ceramic. The influence of the material gradation on the fracture parameters J and KI is investigated in various examples in order to find optimal gradation functions. It could be shown that the temperature dependency of thermoelastic material properties has an important effect on the results and must not be neglected.

Coupled thermal-mechanical-contact analysis of hot cracking in laser welded lap joints

Laser welding offers numerous advantages and has been widely adopted in the automotive industry. However, its application in light-weight vehicle manufacturing is still limited due to hot cracking that commonly occurs in Al-Mg-Si alloys. An in-depth understanding of the hot cracking mechanism is of great importance to the optimal design of welding processes. To this end, a 3-D coupled thermomechanical finite element model is developed to investigate the laser welding of lap joints made of 5xxx and 6xxx Al sheets. The temperature-dependent material behavior of aluminum alloys is described by a thermo-elastic-plastic constitutive law, the plastic history variable of which is re-initialized during material recrystallization processes. Moreover, a material state variable representing the irreversible welding process is introduced into the model to properly describe the thermal and mechanical contact behaviors at the interface between two alloy sheets. Using the simulated thermal field, the weld mushy zone susceptible to crack initiation during solidification is identified. Accordingly, critical mechanical state and field variables are analyzed to investigate the potential cracking mechanisms. It is found that the tensile interfacial stress is a key factor for the initiation of hot cracks close to the free edge of the welding specimen. The influence of weld line-to-edge distance on the cracking susceptibility is numerically evaluated and compared with experimental observations. The numerical simulation reveals that increasing the weld line-to-edge distance can reduce the cracking susceptibility, which is consistent with the experimental observation.

Thermomechanical numerical analysis of hot cracking during laser welding of 6XXX aluminum alloys

The finite element method is applied to study the mechanisms inducing hot cracking during laser welding of 6xxx aluminum alloys. The welding process of a single-sheet plate is modeled by adopting a three dimensional fully coupled thermomechanical finite element formulation, where the energy distribution due to a fiber laser heat source and the motion trajectory of the moving laser beam are specified. The temperature dependent material behavior of aluminum alloys is described by a thermo-elastic-plastic constitutive law which assumes isotropic hardening, and the plastic strain history is reinitialized during the melting and solidification process. With this numerical model, the critical mechanical and thermal responses in the welded metal sheet are used to investigate potential hot cracking mechanisms. It is found that the heat flux vector field obtained through simulation is consistent with the grain orientation in the weld bead observed experimentally. The large tensile stress in the semisolid mushy zone near the fusion line is used as an indicator for identification of hot crack initiation, which is shown to be in the direction normal to the welding line. As the crack grows from the fusion line into the weld centerline, due to the high transverse tensile thermal stress developed inside the weld central region, the crack propagation then shifts to the weld line direction. Furthermore, the effects of several manufacturing process parameters on hot cracking susceptibility are investigated. The results reveal that a smaller weld line-to-edge distance would result in a higher tensile stress state near the fusion line in the mushy zone, and thus increase the possibility of crack formation which is consistent with the experimental observations. Preliminary results also suggest that higher laser power or slower welding speed could increase the hot cracking susceptibility.