Phenomenology of the creep process of a precipitation-hardenable AlMgSi alloy wires for overhead power lines. Experimental tests. Simulation

The article presents the results of the experimental test on the creep process of AlMgSi alloy wires (series 6xxx) under the conditions of variable stress. A theoretical analysis of equivalency rheological results of stress and temperature changes by means of Bayley-Norton function, which describes well the low-temperature aluminum alloys creep, was carried out. Therefore, the described issue became one-dimensional. On the basis of experimental tests, it has been proved that negative gradients of stress and temperature may generate three types of rheological behaviour, such as: Temporary decrease of creep speed (type 1), Temporary stop of creep deformation (‘dead’ time)—type 2 and reverse after creep (type 3). The applicable nature of tests is placed in overhead power lines, which undergo cyclical stress- and time-dependent operation. Such a nature of conductor operation creates favourable conditions to decrease creep intensity, whereas its history and value and speed of stress and temperature lowering decide whether conductor rheological activity loss will take place. The actual material parameter controlling the conductor rheological behaviour is stress and temperature rheological equivalent. The article contains exemplary results of current-carrying capacity changes of AlMgSi alloy conductor on a given temperature range, and the calculations include actual creep characteristic and cumulated rheological inactivity caused by negative gradients of stress and temperature.     

Time-dependent mechanical behavior of lime-mortar masonry

An extensive experimental program has been set up to characterize the time-dependent deformation behavior of masonry, subjected to the creep failure mode. Different types of short-term creep tests were performed on small masonry specimens, which were constructed with air-hardening lime mortar. To assess the influence of the carbonation process on creep behavior, several specimens were subjected to accelerated carbonation. The time-dependent deformations are modeled using a viscoelastic, rheological model which includes damage effects. The applicability of the model is validated by comparing theoretical and experimental results and extending the time frame to long-term predictions. Good agreement was found between experimental and simulated time-dependent deformations. The accuracy of the proposed model is estimated by including the scatter on the most important material parameters in the analysis.     

Behavior of AISI 316L Steel Subjected to Uniaxial State of Stress at Elevated Temperatures

This paper presents an experimental investigation on an AISI 316L stainless steel regarding mechanical properties and short uniaxial creep tests at elevated temperatures. The short time creep tests were carried out under different but constant stresses. The obtained data of ultimate tensile strength, yield strength, creep curves and effects of elevated temperatures on mechanical properties were presented. For a selected rheological model,material parameters were obtained. As a justification, such rheological model is implemented in the finite element procedure for an uniaxially stressed specimen in selected environmental conditions.     

The effect of rolling direction on the creep process of Al–Cu bimetallic sheet

The study of the mechanical properties of aluminium–copper (Al–Cu) metal layered composite, formed by joining aluminium and copper sheets in the process of rolling have been presented in this paper. The influence of the rolling direction on the basic strength parameters and rheological properties of the composite was analysed. All tests were carried out on flat specimens cut from a sheet in the direction compatible with the rolling direction (RD) and transverse direction (TD). Preliminary tests of monotonic uniaxial tension at a temperature of 293 K were carried out and the basic mechanical properties of Al–Cu bimetal were determined. The hardening process of the material was described by the three-parameter Swift’s equation. The essential creep tests were carried out at a temperature of 523 K in the range of stress 88.5–137.9 MPa. The relation between minimum creep rate and applied stress for the specimens cut from the RD and TD directions were determined. The relationships between the time to fracture, stress, and rupture elongation, obtained from the creep tests, were determined as well. Variations of the steady creep rate with time to fracture by using the Monkman–Grant’s model and its modifications were analysed. It was found that the rolling process strongly affected the short-time monotonic deformation at 293 K and the creep process at 523 K temperature.     

Estimating the creep behavior of polycarbonate with changes in temperature and aging time

Thermoplastic resins are typically used without any kind of physical aging treatment. For such materials, creep behavior and physical aging, which depend on time and temperature, occur simultaneously. The effects of these processes are evident after quenching and are recorded in the material as a thermal history. This history strongly influences mechanical properties and creep behavior in particular. Thus, a more thorough understanding of the physical aging process is desirable. We examined the creep deformation of polycarbonate (PC) to reveal the effects of physical aging on creep behavior. The effects were dependent on both time and temperature. The relationship between physical aging and creep behavior exemplified superposition principles with regard to time and both pre-test aging time and pre-test aging temperature. The superposition principles allowed the calculation of creep deformations at a given temperature; the calculated results were corroborated by experimental data.     

Rheological model incorporating gap element

Viscoelastic materials undergo creep due to elasticity and viscosity, two intrinsic material characteristics, and a representative rheological model can be constructed for creep behavior analysis. Based on the viscoelasticity theory, this model simulates creep by formalizing elastic and viscous deformations in spring and dash-pot elements, respectively. However, most materials have internal gaps caused by the generation process, changes in the internal or external stress, etc. In this paper, a rheological model is proposed in which a gap is introduced; hence, the phenomenological behaviors are formalized using spring, dash-pot, and gap elements. The gap element has strain, but no material property. The opening or closing of the gap according to time history influences the structural changes in the model. Owing to the gap element, the energy due to external forces is dissipated before the gap is closed. After the gap is closed, it is converted and stored as internal strain energy in the spring element, which causes creep recovery. The proposed rheological model has two types, which depend on the element combination. Further, a generalized model is obtained by constructing n models on the basis of the element material properties. To validate the proposed rheological model for various stress conditions, the results predicted by three creep models (the proposed model, Burgers model, and the step-by-step method) are compared with the previously experimental results of concrete specimens because there is a large difference between the evaluations of internally stored strain energy by the creep prediction models. Analysis of a stepwise loading case and an unloading case reveal the following characteristics and mechanism of the model. When additional stress is applied, the principle of superposition is not applied to the proposed model. Instead, the model predicts creep by considering the linearity and structural change of each element. In addition, the proposed model simulates creep recovery and permanent strain more precisely compared to other creep models, which occur due to stress removal, by considering the structural change caused by the gap.     

Modelling of creep in continuous RC beams under high levels of sustained loading

A nonlinear theoretical model is developed in this paper for the long-term analysis of continuous reinforced concrete beams. The model accounts for creep, cracking, nonlinear behaviour in compression, shrinkage, aging, yielding of the reinforcement. The constitutive relations follow the modified principle of superposition, which are presented in the form of nonlinear rheological generalized Maxwell models with strain and time dependent springs and dashpots that account for material nonlinearity and aging of the concrete. The governing equations are presented in an incremental form, and are solved through a step-by-step algorithm in time along with the numerical shooting method for the solution along the beam. An iterative procedure is implemented at each time step for the determination of the rigidities and the creep strains. The capabilities of the model are demonstrated through numerical examples. The results show that creep and shrinkage have various influences on the structural response, and they may decrease the load carrying capacity and the factor of safety of continuous reinforced concrete beams with time.     

Time-dependent creep stress redistribution analysis of thick-walled functionally graded spheres

Time-dependent creep stress redistribution analysis of thick-walled spheres made of functionally graded material (FGM) subjected to an internal pressure and a uniform temperature field is performed using the method of successive elastic solution. The material creep and mechanical properties through the radial graded direction are assumed to obey a simple power-law variation. Total strains are assumed to be the sum of elastic, thermal and creep strains. Creep strains are time, temperature and stress dependent. Using the equations of equilibrium, compatibility and stress–strain relations a differential equation, containing creep strains, for radial stress are obtained. Ignoring creep strains, a closed-form solution for initial thermoelastic stresses at zero time is presented. It has been found that the material in-homogeneity parameterβ has a substantial effect on thermoelastic stresses. From thermoelastic analysis the material identified by β=2 in which a more uniform shear stress distribution occurs throughout the thickness of the FGM sphere is selected for time-dependent stress redistribution analysis. Using the Prandtl–Reuss relations and Norton’s creep constitutive model, history of stresses and strains are obtained. It has been found that radial stress redistributions are not significant, however, major redistributions occur for circumferential and effective stresses. It has also been concluded that stresses and strains are changing with time at a decreasing rate so that there is a saturation condition beyond which not much change occurs. Indeed after 50 years the solution approaches the steady-state condition.     

Ein neues Zeitstandgerät für Kriechversuche bei wechselnden Belastungen und Temperaturen

A New Instrument for Measuring Creep under Alternating Loading and Temperature Conditions. It is an established fact that plastics are particularly subject to creep, i. e. deformation over a period of time under load. Under practical conditions unchanged load and constant temperature are seldom realized. The deformations associated with changing mechanical loads cannot generally be derived from the results of ordinary creep tests. In order to be able to study creep behaviour of plastics under intermittent load conditions (i. e. a sequence of loading and unloading), a special instrument has been developed at the Austrian Plastics Institute. The period of time as well as the ratio of loading and unloading phase can be programmed within wide ranges. Creep tests at varying temperatures can also be carried out with this instrument. Under intermittent load very significant differentiation of deformation and fracturing behaviour depending on the polymeric structure has been observed. Comparison of results of ordinary creep with those under intermittent loading at constant temperature shows, that in the case of amorphous thermoplastics destruction by stress crazing and fracture is markedly accelerated. On the other hand semicrystalline thermoplastics have excellent resistance against intermittent load.     

Modeling of materials with fading memory using neural networks

A neural network‐based concept for the solution of a fractional differential equation is presented in this paper. Fractional differential equations are used to model the behavior of rheological materials that exhibit special load (stress) history characteristics (e.g. fading memory). The new concept focuses on rheological materials that exhibit Newtonian‐like displacement behavior when undergoing (time varying) creep loads. For this purpose, a partial recurrent artificial neural network is developed. The network supersedes the storage of the entire load (stress) history in contrast to the exact solution of the fractional differential equation, where access to all previous load (stress) increments is required to determine the new displacement (strain) increment. The network is trained using data obtained from six different creep simulations. These creep simulations have been conducted by means of the exact solution of the fractional differential equation, which is also included in the paper. Furthermore, the network architecture as well as a complete set of network parameters is given. A validation of the network has been carried out and its outcome is discussed in the paper. To illustrate the particular way the network works, all relevant algorithms (e.g. scaling of the input data, data processing, transformation of the output signal, etc.) are provided to the reader in this paper. Copyright © 2008 John Wiley & Sons, Ltd.     

Elastic–plastic void expansion in near-self-similar shapes

For void growth in an elastic–plastic strain hardening material the preferred shape of the void is calculated, dependent on the macroscopic stress state. Axisymmetric cell model analyses are carried out with a very small initial void size relative to the cell dimensions. Large deformations of the material around the void are modeled until the void volume is four orders of magnitude larger than the initial volume. An iterative procedure is used until the final void shape and the initial void shape are identical. Even when this convergence has been obtained, the void shape does not stay constant during the growth. Thus, the shapes found give only approximately self-similar growth. The results are compared with self-similar shapes determined previously for nonlinear viscous solids, subject to power law creep. For the time independent elastic–plastic material considered here the effect of the strain hardening level and of the initial yield strain are studied.     

Parametric study of the creep failure of double lap adhesively bonded joints

In this paper the influence of adhesive thickness and adhesive fillet on the creep deformation and creep life time of the adhesively bonded double lap joint have been studied experimentally. Also finite element modeling was used to simulate creep behavior of bonded joints and the results are compared with those obtained from experimental tests. The adhesive used in this research was Araldite 2015 which is an epoxy based adhesive. Research procedure is carried out in two major stages. Firstly, uniaxial creep tests were conducted in 63 °C to obtain the creep characteristics and constitutive equation parameters of the adhesive at 63 °C. An empirical based rheological model based on Maxwell and Zener’s model is proposed to simulate the creep behavior of the adhesive and it is used to predict the creep behavior of the bonded joint using finite element method. Numerical results show good agreement with experimental data. It was observed that applying fillet increases creep life and decreases joint creep deformation, however increasing adhesive thickness has slight effect on the creep life time of the joint.     

Characterizing and modeling the non-linear viscoelastic tensile deformation of a glass fiber reinforced polypropylene

On the basis of comprehensive experimental investigations on a long glass fiber reinforced polypropylene (PP-LGF) a novel rheological material model is developed. It features a decomposition of the stress into a time independent quasi-static and a time and strain dependent viscous contribution. Furthermore it allows for plastic deformations starting from the very beginning of straining and is thereby able to reproduce the absence of a purely linear elastic domain going along with the nonexistence of a defined yield point, characteristic for many fiber reinforced thermoplastic polymers. In order to approach the true quasi-static material behavior, various tensile tests were carried out. The viscous material behavior was deduced from a series of stress relaxation experiments and is described by Eyring’s equation with strain dependent viscosity parameters.     

Generalized viscoelastic model for creep analysis coupled with plastic deformation

A creep analysis capability, using a generalized viscoelastic model, is introduced to process the creep behaviour coupled with elastoplastic deformation. The formulation is based on the step-by-step time integration of the Kelvin-Maxwell rheological model with non-constant parameters. The concept of a rheological model is extended to the multiaxial stresses by the Prandtl-Reuss stress-strain relationship, from which the tangential stiffness matrix is formed for Newton's iteration. If the plastic deformation is coupled with creep, the algorithm will seek a solution in two distinct steps. Various choices of empirical creep laws are available and small variations in temperature are allowed as implemented in the general purpose finite element analysis program.     

A multi-scale model for coupled heat conduction and deformations of viscoelastic functionally graded materials

An integrated micromechanical-structural framework is presented to analyze coupled heat conduction and deformations of functionally graded materials (FGM) having temperature and stress dependent viscoelastic constituents. A through-thickness continuous variation of the thermal and mechanical properties of the FGM is approximated as an assembly of homogeneous layers. Average thermo-mechanical properties in each homogeneous medium are computed using a simplified micromechanical model for particle reinforced composites. This micromechanical model consists of two isotropic constituents. The mechanical properties of each constituent are time–stress–temperature dependent. The thermal properties (coefficient of thermal expansion and thermal conductivity) of each constituent are allowed to vary with temperature. Sequentially coupled heat transfer and displacement analyses are performed, which allow analyzing stress/strain behaviors of FGM having time and temperature dependent material properties. The thermo-mechanical responses of the homogenized FGM obtained from micromechanical model are compared with experimental data and the results obtained from finite element (FE) analysis of FGMs having microstructural details. The present micromechanical-modeling approach is computationally efficient and shows good agreement with experiments in predicting time-dependent responses of FGMs. Our analysis forecasts a better design for creep resistant materials using particulate FGM composites.     

Computer Simulation of the Indentation Creep Tests on Particle-Reinforced Composites

A systematical simulation has been carried out on the indentation creep test on particle-reinforced composites.The deformation ,failure mechanisms and life are analyzed by three reasonable models.The following five factors have been considered simultaneously:creep property of the particle,creep property of the matrix,the shape of the particle, the volume faction of the particle and the size(relative size to the particle )of the indentation indenter.For all the cases,the power law respecting to the applied stress can be used to model the steady indentation creep depth rate of the indenter,and the detail expressions have been presented.The computer simulation is analyzed by the two-phase model and the three-phase model.Two places of the stress concentration are found in the composites.One is ahead of the indentation indenter, where the high stress state is deduced by the edge of theindenter and will decrease rapidly near to a steady value with the creep time The other one is at the interface,where the high stress state is deduced by the misfit of material properties between the particles and matrix.It has been found that the creep dissipation energy density other than a stress parameter can be used to be the criterion to model the debonding of the interfaces.With the criterion of the critical creep dissipation energy density, a power law to the applied stress with negative exponent can be used to model the failure life deduced by the debonding of interfaces.The influences of the shape of the particles and the matching of creep properties of particle and matrix can be discussed for the failure.With a crack model,the further growthe of interface crack is analyzed, and some important experimental phenomena can be predicted.The failure mechanism which the particle will be punched into matrix has been also discussed.The critical differences between the creep properties of the particles and matrix have been calculated, after a parameter has been defined.In the view of competition of failure mechanisms, the best matching of the creep properties of the two phases and the best shape of the particles are discussed for the composite design.     

The effect of time and temperature on flexural creep and fatigue strength of a silica particle filled epoxy resin

Composite materials that use an epoxy resin as a matrix resins have superior mechanical properties over standard structural materials, but these materials exhibit time and temperature behavior when used for long periods and under high temperatures. This time and temperature behavior has not been fully explained. The purpose of this paper is to further describe this time and temperature behavior, increasing the reliability of this class of composite materials. The time and temperature dependence of flexural strength was examined by creep and fatigue testing. Flexural creep tests were carried out at various temperatures below the glass transition temperature. Flexural fatigue tests were carried out at various stress ratios, temperatures below the glass transition temperature and 2 frequencies. The time-temperature superposition principle held for the flexural creep strength of this material. A method to predict flexural creep strength based on the static strength master curve and the cumulative damage law is proposed. When the fatigue frequency was decreased while temperature and stress ratio are held constant the flexural fatigue strength decreases. The time-temperature superposition principle was also found to hold for the flexural fatigue strength with respect to frequency.     

Temperature effects on creep behavior of continuous fiber GMT composites

The effects of temperature on the tensile creep of continuous random fiber glass mat thermoplastic composite (GMT) have been studied following an accelerated characterization procedure. The objectives of this work are twofold. First, is to obtain a long-term creep model using time–temperature superposition (TTS) that can represent behavior within the linear viscoelastic regime (up to 20 MPa) at room temperature. The second is to develop a non-linear viscoelastic model that accounts for a wide range of stresses and temperatures. Creep and recovery tests were carried out for a stress range between 20 and 60 MPa over a temperature range of room temperature to 90 °C. TTS was applied to obtain a master curve which was curve fitted to a nine-term Prony series. It was found that material generally behaved non-linearly for all stresses and temperature. For stresses up to 50 MPa, the non-linear viscoelastic behavior due to temperature can be reasonably modeled by only the time–temperature shift factors from TTS. At 60 MPa, however, the non-linear parameters have to be modeled as a product of stress and temperature dependent functions. The model predictions are in good agreement with the experimental results at most stress and temperature levels. The creep curves predicted at higher temperatures especially at 60 MPa tend to underestimate at longer times.