Time Dependent Mechanical Behavior And Constitutive Model Of Polyethylene Pipe Material

Polymer pipelines are widely used in oil,natural gas,water supply and drainage applications.More than 90% of medium and low pressure urban gas pipelines in China are polyethylene(PE)pipes.PE is a typical viscoelastic material.Due to the time-dependent characteristics of its mechanical properties,the delayed failure of PE pressure pipes often occurs after a long service time.Therefore,it is of great significance and engineering value to study the time-dependent mechanical behavior and corresponding constitutive models of the PE pipe materials.This work,supported by the National Natural Science Foundation Project,focuses on the time-dependent mechanical behavior and the constitutive model of PE100 pipe material.For this purpose,the effects of strain rate,temperature,load level and load history on the time-dependent mechanical behavior of PE100 pipe material are analyzed and the linear and/or nonlinear viscoelastic constitutive models of the material are discussed through constant strain rate uniaxial tensile tests,stress relaxation tests,creep tests,temperature and frequency sweep DMA measurements and cyclic tensile tests.The main research contents and conclusions are listed as follows:(1)The room temperature uniaxial tensile stress-strain behavior of the PE100 pipe material under various strain rates is analyzed.Based on the Kondner hyperbolic constitutive model,a modified rate dependent hyperbolic constitutive model is proposed and.Two specific forms,power-law and logarithm law,of the modified hyperbolic constitutive model are developed by considering the strain rate dependences of the initial elastic modulus and the yield stress.Both models can accurately describe the uniaxial tensile stress-strain behavior of the PE100 pipe material prior to yielding at different strain rates.The predictions of the models are in good agreement with the experimental results.The power-law rate dependent hyperbolic constitutive model can reasonably predict the stress-strain response at very low strain rate.Based on the linear correlation between the initial elastic modulus and the yield stress,a simplified rate dependent hyperbolic constitutive model is further proposed by using the focus point method.(2)Based on the modified Boltzmann superposition principle and considering the nonlinearity caused by viscoplastic deformation of the material,a nonlinear relaxation type constitutive model is developed by introducing a strain dependent viscoplastic factor into the viscoelastic kernel function.The viscoelastic kernel function is determined by the stress relaxation tests,and the viscoplastic factor is expressed by power series.The proposed nonlinear model can accurately describe the tensile and post yielding behavior of the PE100 pipe material at different temperatures and strain rates.(3)The room temperature creep tests of the PE100 pipe material under different stresses are carried out.When the stress does not exceed 5.4MPa,the creep compliance of the material is independent to the applied stress level,showing a linear viscoelastic behavior.When the stress is higher than 5.4MPa,the material behaviors in a nonlinear viscoelastic mode.Within the framework of the single integral nonlinear viscoelasticity,the creep behavior is analyzed by the Findley model and the Struik model.The results show that Findley model is a reduced case of the Schapery model,and the Schapery model is a generalized form of the modified Boltzmann superposition principle.Both the Findley model and the Struik model can describe the creep behavior of the PE100 pipe material,and the Findley model can more accurately simulate the nonlinear creep behavior under high stress than Struik model does.(4)Based on the time temperature superposition principle,the generalized Kelvin model and the Boltzmann superposition principle,a method for characterizating the temperature-and rate-dependent initial elastic modulus is proposed from the DMA test data of a single specimen.The temperature-frequency sweep DMA test is carried out on a single PE100 pipe material specimen.The dynamic compliance master curve of the material is constructed through the time-temperature superposition principle.The material meets the thermal rheological simplicity,and the temperature shift factor conforms to the WLF equation.The generalized Kelvin model in the form of Prony series and the Park-Schapery collocation method are used to convert the frequency-domain viscoelastic functions to the time-domain ones.The tensile stress-strain behavior under various strain rates and temperatures can be simulated by Boltzmann superposition principle with the relaxation function converted from DMA dada,and then the variation of the initial elastic modulus with temperature and strain rate can be simulated.The simulation results are in good agreement with the experiments.(5)The stress controlled uniaxial cyclic tensile tests of the PE100 pipe material under different loading conditions are carried out.The effects of the stress ratio,the maximum stress and the loading history of cyclic load on the ratcheting behavior of the material are studied,and the temperature dependence of the ratcheting behavior is also discussed.The results show that under a given maximum stress,the ratchet strain increases with the increase of the stress ratio.At the beginning of stress cycle loading,the ratchet strain increases rapidly,then its increse speed decreases gradually with the increase of cycle times;Under the same cyclic stress,the ratchet strain of the material increases with the increase of temperature.Compared with room temperature,the growth speed of the ratchet strain at high temperature increases significantly;In the multi-step cyclic tensile process with monotonic increase of stress ratio,the ratchet strain increases with the increase of stress ratio,but if the stress ratio increases first and then decreases in the multi-step cyclic loading process,the cyclic load with higher stress ratio in the early stage will inhibit the ratchet effect under lower stress ratio and lead to the decrease of ratchet strain.