A continuous threshold model for the visco-elasto-plastic behavior of PET based multi-layer polymeric films

The envelopes of the super-pressure balloons fabricated by the French space agency (CNES) are made of a multi-layer polymeric film that shows substantial viscoelastic and viscoplastic behavior, both depending nonlinearly on stress. A model is presented that takes into account stress depending viscoelastic and viscoplastic strain response functions observed in uniaxial creep experiments. For easy numerical implementation, the strain response functions are represented by a Prony series, whose coefficients form a continuous spectrum on the logarithmic retardation time scale. The observed response functions are generated by an exponential power law distribution of the Prony coefficients with exponent 3. The distribution is fully characterized by three stress dependent parameters: its center, width, and an intensity factor, corresponding to the maximum coefficient. Creep and recovery experiments show that both viscoelastic and viscoplastic strain are highly stress dependent over a limited stress range and are approximately linear at low stresses and around the maximum stress reached during flight. A continuous threshold function is proposed that approximates well the observed stress dependence of the intensities. It is assumed that the other viscoelastic (viscoplastic) parameters change around the same threshold as the viscoelastic (viscoplastic) intensity and are approximately constant elsewhere. The model reproduces very well the strain response observed in creep and recovery experiments with different creep stresses.     

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.     

Nonlinear Viscoelastic,Viscoplastic Characterization of Unidirectional GF/EP Composite

Viscoplastic strains of unidirectional continuous fiber composite (HEXCEL GF/EPprepreg system) are studied experimentally and theoretically. Creep and strainrecovery tests are used. Schapery's nonlinear viscoelastic viscoplasticconstitutive equations are used and generalized to describe inelastic behavior ofunidirectional composite under isothermal creep and strain recovery conditions. Themethodology to quantify the viscoplastic strains with respect to applied stress isproposed. Viscoplastic strains of composite are described by plastic shear strain inmaterial symmetry axis. Assumptions has been used and validated that the functiondescribing the stress and time dependence of viscoplastic strain can be presented asa product of two, time and correspondingly stress dependent, master curves.     

A nonlinear viscoelastic–viscoplastic model for adhesives

We consider the nonlinear viscoelastic–viscoplastic behavior of adhesives. We develop a one-dimensional nonlinear model by combining Schapery’s nonlinear single integral model and Perzyna’s viscoplastic model. The viscoplastic strain was solved iteratively using the von Mises yield criterion and nonlinear kinematic hardening. The combined viscoelastic–viscoplastic model was solved using Newton’s iteration and implemented into a finite element model. The model was calibrated using creep-recovery data from bulk adhesives and verified from the cyclic behavior of the bulk adhesives. The finite element model results agreed with experimental creep and cyclic responses, including recoverable and permanent strain after load removal. Although the contribution of the viscoplastic strain was small, both viscoplastic and viscoelastic components of strain response were required to describe the adhesive creep and cyclic response.

     

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.     

Simulation of creep crack growth in ceramic composites

The elevated temperature response resulting from tensile creep of fiber reinforced ceramic composites was modeled using Monte Carlo simulation. The model consisted of a uniaxially loaded fiber tow aligned with the direction of applied load, and modeled the growth of matrix cracks resulting from creep failure of bridging fibers. A creep strain rate consisting of primary and steady state components was assumed, and each component was modeled by a power law relationship. Power law creep exponents in the range of 2.0–2.5 for a selected SiC/SiC system at stress levels ranging from 60 MPa to 200 MPa were evaluated. Fatigue-like behavior was predicted as a result of tensile creep, and a fatigue exponent of 3.03 ± 0.07 was predicted for nominal stress levels less than 200 GPa. The influence of initial crack length on failure lifetime was also studied, but was found to have little influence on the predicted lifetime. The predicted failure response suggested a stress dependent creep process could be used to model experimental data and evaluate the failure mechanism of reinforced composites.     

钛合金高温短时蠕变与应力松弛的关系研究*

蠕变或应力松弛被认为是钛合金板材热成形降低回弹的主要机理。目前对热校形阶段中的蠕变与应力松弛的区别及联系尚缺乏深入研究。本文主要进行了钛合金高温短时蠕变及应力松弛实验, 利用TEM对实验后的显微组织进行了观察。分别研究了温度、应力及时间对蠕变和应力松弛行为的影响规律, 从蠕变率-时间和蠕变-时间角度建立了蠕变与应力松弛之间的联系。研究表明: 钛合金在低温低应力下蠕变以原子扩散为主, 高温高应力下以位错滑移和攀移为主, 而应力松弛在不同温度时均以位错攀移为主要变形机制, 基于蠕变数据预测的应力松弛行为与实验结果符合较好。     

Creep and stress rupture behaviour of Be/Al composite material Albemet 162

Abstract

Creep and stress rupture tests were conducted on Albemet 162, a Be particulate reinforced Al matrix composite with a 70% volume fraction of reinforcement. A power law relationship was observed between steady state creep rate, stress rupture life, and applied stress. Considerable differences were seen between transverse and longitudinal specimens in terms of creep and rupture behaviour. Fractography of the specimens revealed that particle agglomeration of the Be phase is highly susceptible to creep damage and the primary cause of creep failure, which was observed in specimens of both orientations.     

Strain accumulation in bituminous binders under repeated creep-recovery loading predicted from small-amplitude oscillatory shear (SAOS) experiments

The creep-recovery (CR) test starts out with a period of shearing at constant stress (creep) and is followed by a period of zero-shear stress where some of the accumulated shear strain gets reversed. Linear viscoelasticity (LVE) allows one to predict the strain response to repeated creep-recovery (RCR) loading from measured small-amplitude oscillatory shear (SAOS) data. Only the relaxation and retardation time spectra of a material need to be known and these can be determined from SAOS data. In an application of the Boltzmann superposition principle (BSP), the strain response to RCR loading can be obtained as a linear superposition of the strain response to many single creep-recovery tests. SAOS and RCR data were collected for several unmodified and modified bituminous binders, and the measured and predicted RCR responses were compared. Generally good agreement was found between the measured and predicted strain accumulation under RCR loading. However, in the case of modified binders, the strain accumulation was slightly overestimated (≤20% relative error) due to the insufficient SAOS information at long relaxation times. Our analysis also demonstrates that the evolution in the strain response under RCR loading, caused by incomplete recovery, can be reasonably well predicted by the presented methodology. It was also shown that the outlined modeling framework can be used, as a first approximation, to estimate the rutting resistance of bituminous binders by predicting the values of the Multiple Stress Creep Recovery (MSCR) test parameters.     

Werkstoffanstrengung bei zeitabhängiger Spannung-Verformung-Beziehung

Equivalent Stress and Strain for Time dependent Materials Behaviour This paper deals with the generalized plastomechanics and the flow behavior of materials whose volume does mot remain constant during plastic deformation. The usual assumption of plastic incompressibility is treated as a special case. The relations deduced are formally applied to creep of polymers with nonlinear stress-strain behaviour. The concept of equivalent stress and strain is examined for this group of plastics and compared with experimental results under combined stress. A modified superposition principle and a power function of time are employed to describe creep in the nonlinear range under abrupt changes in state of combined stress. The usual assumption of linear viscoelastic analogy of Hookes law is treated as a special case.     

Crack propagation during steady state creep

A model is proposed tor the steady propagation of a creep crack under steady state creep conditions. Creep is envisaged to take place everywhere in the solid, though higher creep rates at the crick tip lead to a local concentration of the creep strain. A critical local strain criterion is used to describe the condition for crack advance. Local damage is envisaged to accumulate at the crack tip as a result of, or in parallel with the creep strain. The model correctly predicts a dependence of crack propagation rate with the nett section stress varied to the power m, where m is the exponent of stress in the creep equation, for large values of m. An approximate dependence of propagation rate on the elastic stress intensity factor is also shown. Tnese predictions are in accord with experimental work.     

瓦楞纸箱蠕变模型的研究

对A型单瓦楞空纸箱进行蠕变试验,并分析常见的蠕变模型的特征,从而确定描述瓦楞纸箱蠕变行为的合理蠕变模型,并运用数据处理软件SAS进行非线性回归,确定模型中的各个参数.     

Beschreibung des Zeitdehnverhaltens warmfester Stähle Teil 2: Kriechgleichungen für die Stahlsorten 10 CrMo 9 10 und X 20(22) CrMoV 12 1

Creep Behaviour of Heat Resistant Steels Part II: Creep Equations for Steels 2.25 Cr-1 Mo and 12 Cr-1 Mo-0.3 V Creep data scatter bands of steels 2.25 Cr-1 Mo and 12 Cr-1 Mo-0.3 V were evaluated with the aid of model functions based on time temperature parameters. From the times to reach given strain values, mean isostrain curves in the stress time diagramme were calculated and therefrom, mean creep curves were derived. On this basis, creep equations were established, which include primary-, secondary- and tertiary-creep and are valid in the main range of application of each steel. Further, mean stress strain curves from hot tensile tests were used to describe the initial plastic strain in the creep equations. The values calculated with the established creep equations agreed relatively well with the correspondent original scatter band values from the creep tests.     

Modeling of Nonlinear Mechanical Behavior for 3D Needled C/C-SiC Composites Under Tensile Load

This paper established a macroscopic constitutive model to describe the nonlinear stress–strain behavior of 3D needled C/C-SiC composites under tensile load. Extensive on- and off-axis tensile tests were performed to investigate the macroscopic mechanical behavior and damage characteristics of the composites. The nonlinear mechanical behavior of the material was mainly induced by matrix tensile cracking and fiber/matrix debonding. Permanent deformations and secant modulus degradation were observed in cyclic loading-unloading tests. The nonlinear stress–strain relationship of the material could be described macroscopically by plasticity deformation and stiffness degradation. In the proposed model, we employed a plasticity theory with associated plastic flow rule to describe the evolution of plastic strains. A novel damage variable was also introduced to characterize the stiffness degradation of the material. The damage evolution law was derived from the statistical distribution of material strength. Parameters of the proposed model can be determined from off-axis tensile tests. Stress–strain curves predicted by this model showed reasonable agreement with experimental results.     

A temperature dependent creep damage model for polycrystalline ice

We present a continuum damage model for the temperature dependent creep response of polycrystalline ice under a multiaxial state of stress, suited for ice in polar regions. The proposed model is based on a thermo-viscoelastic constitutive law for ice creep and a local orthotropic damage accumulation law for tension, compression and shear loadings. Orthotropic damage is represented by a symmetric second-order damage tensor and its effect on creep is incorporated through the effective stress concept. The unknown model parameters are first calibrated using published experimental data from constant uniaxial stress tests and then predictions are made for constant strain rate and multiaxial loadings. The predicted results are in good agreement with both experimental and numerical results in the literature illustrating the viability of the proposed model. The model is mainly intended for studying the failure mechanisms of polar ice at low deformation rates with depth varying temperature profiles.     

Characterization and modeling of stain-rate-dependent behavior of polymeric foams

A polymeric foam was characterized under quasi-static and dynamic loading and a constitutive model was proposed to describe its nonlinear behavior at varying strain rates. Four characteristic properties were identified in the compressive stress–strain curves: (1) yield stress, (2) peak or “critical” stress corresponding to collapse initiation of the cells, (3) plateau stress following the initial collapse of the cells, and (4) strain hardening stress at the end of the plateau region and before the onset of densification. All of the above characteristic stresses vary linearly with the logarithm of strain rate. A strain-based nonlinear constitutive model was proposed. A unified (master) constitutive model with built-in strain rate dependence was formulated and was shown to be in very good agreement with experimental results. The master stress–strain response was modeled in two parts, a power law and one consisting of two exponential terms.     

Creep and strain recovery in hot-pressed silicon nitride

It is observed that creep response in hot-pressed silicon is characterized by two parallel phenomena; one accounts for a persistent non-recoverable plastic deformation and the other for a transient viscoelastic recoverable deformation. The persistent creep component is time-dependent, and apparently follows parabolic time kinetics. It is further observed that creep is characterized by a power law stress exponent of about 4 and an activation energy of 848 kJ mol^–1. The viscoelastic recoverable component of strain is found to be independent of the total plastic strain in the material. The recovery rate at any given time is directly proportional to the preceding creep stress and therefore can be considered linear viscoelastic. The creep compliance of the viscoelastic transient is temperature-dependent with an activation energy of about 722 kJ mol^–1. It is further observed that the viscoelastic recovery is characterized by a spectrum of retardation times and can be modelled by a series of Kelvin analogue models. Finally, the viscoelastic recovery and the viscoelastic component of subsequent creep appear to be inversely related and apparently obey Boltzman superposition. A model is developed for the creep and recovery behaviour of hot-pressed silicon nitride consistent with all experimental observations and based in relative grain motion accommodated by the fluid grain-boundary glass liquid flow, cavitation and wedge opening.     

Stress dependence on stress relaxation creep rate during tensile holding under creep-fatigue interaction in 1Cr-Mo-V steel

A quantitative analysis of the stress dependence on stress relaxation creep rate during hold time under creep-fatigue interaction conditions has been conducted for 1Cr-Mo-V steel. It was shown that the transient behavior of the Norton power law relation is observed in the early stage of stress relaxation in which the instantaneous stress is relaxed drastically, which occurs due to the initial loading condition. But after the initial transient response in a 5 hour tensile hold time, the relations between strain rate and instantaneous stress represented the same creep behavior, which is independent of the initial strain level. The value of stress exponent after transition was 17 which is the same as that of the typical monotonic creep suggested from several studies for 1Cr-Mo-V steel. Considering the value of the activation energy for the saturated relaxation stage, it is suggested that the creep rate is related to instantaneous stress and temperature by the Arrhenius type power law.