A Viscoelastic Analysis of the Creep Behaviour of a Chopped Strand Mat E-Glass Fibre Reinforced Vinylester Resin

The viscoelastic response of a chopped strand mat E-glass fibre reinforced vinylester resin has been studied over a wide range of applied stress levels. At low applied stress levels, the material exhibited a linear viscoelastic response well represented by Schapery's power law model with constant C and n terms. At higher stresses nonlinear behaviour was observed which apparently is caused by the multiplicity of complex local phenomena associated with and preceding damage development (plastic deformation of the matrix, interfacial slippage, fiber-matrix debonding). The limits of linear viscoelastic behaviour and of damage initiation – about 0.48% strain or 42 MPa – coincide for this material. However, for successful modelisation of uniaxial creep strain in the nonlinear range a modified power law is proposed which uses stress-dependent creep parameters C and n.     

A model based creep equation for 9Cr–1Mo–0·2V (P91 type) steel

Abstract

The isothermal constant stress creep tests data for a 9Cr–1Mo–0·2V (P91 type) steel were submitted for a phenomenological analysis in order to obtain the relevant creep equation for such steel. Namely, the minimum creep strain rate of P91 type steel cannot be described by the simple Arrhenius type power law constitutive model. The incorporation of the threshold stress concept in the analysis of creep data leads to a modified power law, which satisfactorily describes the creep behaviour of the examined P91 steel. However, the threshold stress is not a good material parameter, as it often varies with temperature and/or applied stress. This adds uncertainty to the extrapolation of the creep rates into ranges where experimental data are not available. Besides the fact that the physical foundation for a threshold stress is questionable from a scientific point of view, this is a serious practical limitation of the modified power law creep equation. The second creep equation proposed in the present paper is the improved stress dependent energy barrier model. The improvement of the standard model is based on two assumptions: first, on the hypothesis that the application of a stress also affects the energy barrier to be overcome when a local region transitions from the initial to the final state, and second, by applying a simple power function of stress instead of a hyperbolic sin function in the model based equation. The obtained value of stress exponent, n=5·5, is too high for entirely climb controlled creep. The apparent activation energy of approximately 510 to 545 kJ mol^?1, which is considerably higher than the activation energy for lattice diffusion, is the stress dependent activation energy of the slowest, dominant rate controlling process of the supposed multiple creep mechanisms.     

混凝土结构非线性徐变计算方法研究

为准确分析既有病害条件下的混凝土结构长期变形及受力行为, 该文进行了混凝土材料非线性徐变计算方法研究。以非线性弹性徐变本构理论为基础, 利用Hongnestad模型推导出材料软化系数, 提出一种新的非线性徐变本构模型, 采用初应变法进行显式迭代, 实现混凝土材料非线性徐变分析。以混凝土徐变及开裂的线性耦合假定为基础, 模拟长期持载过程中裂缝的扩展。采用ADINA用户子程序二次开发实现了相关算法, 并通过混凝土非线性徐变经典试验的对比分析, 验证了计算方法的可靠性。     

Computer simulation of impression creep by the finite element method

The steady state impressing velocity of the punch during an impression creep test is calculated by the finite element method based on a single power law constitutive equation for the deformation of each and every element. The calculated impressing velocities and their stress dependence agree very well with the experimental values on succinonitrile crystals using empirical power laws obtained from unidirectional creep tests.     

Analysis of non-localized creep induced strains and stresses in notches

A method for the estimation of time-dependent strains and stresses induced in notches has been developed. The aim of the method is to generate a solution for the creep strain and stress at the notch root based on the linear-elastic stress state, the constitutive law, and the material creep model. The proposed solution is an extension of Neuber’s total strain energy density rule for the case of time-independent deformation. The method was derived for both localized and non-localized creep in a notched body. Predictions were compared with finite element data and good agreement was obtained for various geometrical and material configurations in plane stress conditions.     

Analysis of Garofalo equation parameters for an ultrahigh carbon steel

Isothermal stress–strain curves data from torsion tests conducted at high temperature (950–1200 °C) and strain rates (2–26 s⁻¹) were analyzed in an ultrahigh carbon steel (UHCS) containing 1.3%C. The sine hyperbolic Garofalo equation was selected as an adequate constitutive equation for the entire range of the forming variables considered. The Garofalo parameters were assumed strain dependent allowing the prediction of stress–strain curves under transient and steady-state conditions. The average relative errors obtained were below 3% in stress. In addition, the creep deformation mechanisms in the UHCS were analyzed from the Garofalo equation parameters. For this aim, the stress exponent of the Garofalo equation was, for the first time, related to that of the power law equation. The results show that the controlled deformation mechanism at steady state is lattice diffusion-controlled slip creep.     

Multiphysical time-dependent creep response of FGMEE hollow cylinder in thermal and humid environment

In this paper, we investigate the history of radial displacement, stresses, electric potential, and magnetic potential of a functionally graded magneto-electro-elastic (FGMEE) hollow cylinder subjected to an axisymmetric hygro-thermo-magneto-electro-mechanical loading for the plane strain condition. The material properties are taken as a power-law function of radius. Using stress-displacement relations, equations of equilibrium, electrostatic and magnetostatic equations, we find a differential equation including creep strains. Initially, eliminating creep strains, we obtain an analytical solution for the primitive stresses and electric and magnetic potential. In the next step, considering creep strains, we find the creep stress rates by applying the Norton law and Prandtl–Reuss equations for steady-state hygrothermal boundary condition. Finally, using an iterative method, we find the time-dependent creep stresses, radial displacement, and magnetic and potential field redistributions at any time. In numerical section, are comprehensively investigate the effects of grading index, hygrothermal environmental conditions, rotating speed, and temperature- and moisture-dependency of elastic constant of FGMEE.

     

Nonlinear creep damage constitutive model for soft rocks

In some existing nonlinear creep damage models, it may be less rigorous to directly introduce a damage variable into the creep equation when the damage variable of the viscous component is a function of time or strain. In this paper, we adopt the Kachanov creep damage rate and introduce a damage variable into a rheological differential constitutive equation to derive an analytical integral solution for the creep damage equation of the Bingham model. We also propose a new nonlinear viscous component which reflects nonlinear properties related to the axial stress of soft rock in the steady-state creep stage. Furthermore, we build an improved Nishihara model by using this new component in series with the correctional Nishihara damage model that describes the accelerating creep, and deduce the rheological constitutive relation of the improved model. Based on superposition principle, we obtain the damage creep equation for conditions of both uniaxial and triaxial compression stress, and study the method for determining the model parameters. Finally, this paper presents the laboratory test results performed on mica-quartz schist in parallel with, or vertical to the schistosity direction, and applies the improved Nishihara model to the parameter identification of mica-quartz schist. Using a comparative analysis with test data, results show that the improved model has a superior ability to reflect the creep properties of soft rock in the decelerating creep stage, the steady-state creep stage, and particularly within the accelerating creep stage, in comparison with the traditional Nishihara model.     

Mechanics of creep resistance in nanocrystalline solids

Summary In a nanocrystalline solid a significant portion of atoms resides in the grain boundary and the nearby outer grain. This combined region, known as the grain-boundary affected zone (GBAZ), is plastically softer than the grain interior, and it are the combined contributions of the grain interior and GBAZ that give rise to the overall response. In this spirit a two-phase composite model is developed to study the high-temperature creep resistance of nanocrystalline materials. Here the rate equation of each phase is represented by a power law and the Arrhenius function, but that of the grain interior is further taken to scale with the Hall–Petch relation whereas that of the GBAZ remains independent of grain size. This unified constitutive equation in turn leads to the concept of secant viscosity. Then a homogenization theory is developed by means of a transition from linear viscoelasticity to nonlinear viscoplasticity with the Maxwell viscosity constantly replaced by the secant viscosity. Subsequently a field-fluctuation method is called upon to determine the effective stress of both phases. The developed theory is applied to model the creep behavior of nanocrystalline Cu, NiP alloy, and Ni at various levels of stress, temperature, and grain size, with results that reflect good agreement with available experiments. We then applied the theory to examine the nature of creep resistance as the grain size decreases in the nanometer range in some detail, and it was discovered that creep resistance in the Hall–Petch like plot undergoes a transition from a positive slope to leveled off, and then to a negative slope. The leveled-off value in effect represents the maximum creep resistance that a material can attain, and it is found that this occurs at a critical grain size, d _crit, that exists in the nanometer range. Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday     

Analytical investigation of crack tip fields in viscoplastic materials

A macroscopic stationary crack in viscoplastic materials is considered under mode I creep loading conditions. Typical representations of constitutive laws with internal variables. (back stress) which can be derived from a scalar potential function are used to model the inelastic material behaviour. It is shown that, in the limit of high stresses, the constitutive equation adopt the form of Norton's law thus leading to a singular field of the HRR-type at the crack tip, if the material functions for the constitutive equations are represented by power laws. The amplitude of the crack tip field can be evaluated using a crack tip integral. It reduces to the well-known C ^* expression at the crack tip and includes additonal domain integrals which ensure the independence of the choice of the integration contour and the area enclosed around the crack tip in regions where primary creep and linear eleastic effects cannot be neglected. The paper concentrates on results characterising the crack tip fields which can be derived analytically. Numerical aspects focused upon the right modelling of the crack tip zone, the range of validity of the crack tip field and the calculation of the crack tip parameter and the creep zones will be discussed in a subsequent paper.     

A nonlinear constitutive relationship for asphalt binders

A nonlinear constitutive relationship was developed for asphalt binders. Two binders, one polymer modified and one unmodified, were tested in shear using creep and recovery loading. Five different stress levels and four loading times were considered, to capture the response of the binders in the linear and nonlinear viscoelastic range. The creep response of the binders was successfully modeled with a nonlinear power law function. The modified superposition principle was unable to predict the recovery phase of the testing data. A nonlinear constitutive relationship composed of a nonlinear viscous part plus a linear viscoelastic part was developed. The constitutive relationships successfully predicted the binders’ response in creep and recovery. The predictions of the constitutive relationships matched accurately the response of the binders subjected to the Multiple Stress Creep and Recovery loading pattern.     

Estimation of power-law creep parameters from bend test data

Power-law creep parameters of brittle ceramic materials are commonly deduced from load-point displacement data generated by four-point bend experiments, under the assumption that tensile and compressive behaviours obey the same constitutive law. However, because of microcracking and cavitation, it is now well recognized that this premise may not always be valid. The present paper presents an analysis which takes the differences into account. Governing equations are first derived for the location of the neutral axis of a beam under bending which does not in general pass through the centroid of the cross-section, and for the creep response in terms of both curvature rate and load-point displacement rate as functions of the applied moment and power-law creep parameters. Numerical solutions are obtained for any given set of material constants over a wide range of applied moments. It is shown from the plots of creep response against applied moment on a logarithmic scale that even linear curves over a narrow range of applied moment do not necessarily imply identical stress exponents, and that non-linear curves concave upward signify a profound difference in stress exponent between tension and compression. An example is given of applying the present analysis to a set of load-point displacement data on glass-alumina beam specimens crept at 1100° C. The results show that the conventional method over/underestimates the creep rates in compression/tension by two orders of magnitude, indicating a need for using the more accurate analysis presented here. Several recommendations are offered to improve the estimation of power-law creep parameters from bend test data.     

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.     

Combined plasticity and creep analysis in 2D by means of the boundary element method

This work presents a formulation to make a combined analysis of plasticity and creep in two-dimensional (2D) using the Boundary Element Method. This new approach is developed to combine the constitutive equation for time hardening creep and the constitutive equation for plasticity, the latter based on the Von Misses criterion and the Prandtl–Reuss flow. The implementation of creep strain in the formulation is achieved through domain integrals. The creep phenomenon takes place in the domain which is discretized into quadratic quadrilateral continuous and discontinuous cells. The creep analysis is applied to metals with a power law creep for the secondary creep stage. The results, obtained with reference to three models, show a good agreement when compared to those published in the literature. This finding shows that the Boundary Element Method is a suitable tool to deal with combined nonlinear problems.     

Origins of tertiary creep in microalloyed 25Cr–35Ni centrifugally cast alloy tubes

Abstract

Constant stress tensile creep tests have been undertaken in air on as cast 25Cr35Ni austenitic steel at temperatures of 880, 900 and 950°C. The creep curves were found to consist of a relatively short primary stage, a minimum strain rate and an extended tertiary stage. There was no convincing evidence of a period of steady-state creep but the minimum creep rate was found to be highly dependent on applied stress through a power law with a stress exponent of ～10. The early occurrence of tertiary creep, after strains of only ～0·01, was shown not to be caused by a loss of section associated with necking, internal void development nor with the formation of surface cracks. It is concluded that the most likely cause of the early onset of tertiary creep in this alloy is the coarsening of strengthening precipitates.     

Creep and recovery of nonlinear viscoelastic materials of the differential type

In this work, the creep and recovery properties of rubberlike viscoelastic materials in simple shear are studied by two special constitutive equations for isotropic, nonlinear incompressible viscoelastic material of the differential type. The creep and recovery processes are of significant importance to both the mechanics analysis and engineering applications. The constitutive equations introduced in this work generalize the Voigt-Kelvin solid and the 3-parameter model of classical linear viscoelasticity. They describe the uncoupled non-Newtonian viscous and nonlinear elastic response of an isotropic, incompressible material. The creep and recovery processes are treated for simple shear deformation superimposed on a longitudinal static stretch. Closed form solutions are provided and both processes are described effectively by the exponential function.