A thermodynamically complete multi-phase equation of state(EOS)applicable to both dense and porous metals at wide ranges of temperature and pressure is constructed.A standard three-term decomposition of the Helmholtz ...A thermodynamically complete multi-phase equation of state(EOS)applicable to both dense and porous metals at wide ranges of temperature and pressure is constructed.A standard three-term decomposition of the Helmholtz free energy as a function of specific volume and temperature is presented,where the cold component models both compression and expansion states,the thermal ion component introduces the Debye approximation and melting entropy,and the thermal electron component employs the Thomas-Fermi-Kirzhnits(TFK)model.The porosity of materials is considered by introducing the dynamic porosity coefficientαand the constitutive P-αrelation,connecting the thermodynamic properties between dense and porous systems,allowing for an accurate description of the volume decrease caused by void collapse while maintaining the quasi-static thermodynamic properties of porous systems identical to the dense ones.These models enable the EOS applicable and robust at wide ranges of temperature,pressure and porosity.A systematic evaluation of the new EOS is conducted with aluminum(Al)as an example.300 K isotherm,shock Hugoniot,as well as melting curves of both dense and porous Al are calculated,which shows great agreements with experimental data and validates the effectiveness of the models and the accuracy of parameterizations.Notably,it is for the first time Hugoniot P-σcurves up to 10~6 GPa and shock melting behaviors of porous Al are derived from analytical EOS models,which predict much lower compression limit and shock melting temperatures than those of dense Al.展开更多
采用van der Waals等效单组分流体模型和Ross硬球微扰理论软球修正模型,计算了爆轰气相产物的状态方程;用石墨相、金刚石相、类石墨液相和类金刚石液相4种相态描述凝聚成分,由Gibbs自由能最小确定了不同状态下的凝聚产物相态。对爆轰产...采用van der Waals等效单组分流体模型和Ross硬球微扰理论软球修正模型,计算了爆轰气相产物的状态方程;用石墨相、金刚石相、类石墨液相和类金刚石液相4种相态描述凝聚成分,由Gibbs自由能最小确定了不同状态下的凝聚产物相态。对爆轰产物混合系统采用自由能最小原理,通过化学平衡方程组求解了炸药爆轰产物系统的平衡组分。使用该理论计算了高含碳炸药PBX9502 Chapman-Jouguet(CJ)点的爆轰参数,计算值与实验值符合很好;同时计算了3条等温线,并与Sesame库比较,发现温度超过1000℃时,计算值与Sesame库的计算结果比较接近。在计算的5 802K等温线上发现了一个拐点,分析发现是由于在此处游离态的碳发生了相变。展开更多
Hydride precipitation in zirconium cladding materials can damage their integrity and durability.Service temperature and material defects have a significant effect on the dynamic growth of hydrides.In this study,we hav...Hydride precipitation in zirconium cladding materials can damage their integrity and durability.Service temperature and material defects have a significant effect on the dynamic growth of hydrides.In this study,we have developed a phasefield model based on the assumption of elastic behaviour within a specific temperature range(613 K-653 K).This model allows us to study the influence of temperature and interfacial effects on the morphology,stress,and average growth rate of zirconium hydride.The results suggest that changes in temperature and interfacial energy influence the length-to-thickness ratio and average growth rate of the hydride morphology.The ultimate determinant of hydride orientation is the loss of interfacial coherency,primarily induced by interfacial dislocation defects and quantifiable by the mismatch degree q.An escalation in interfacial coherency loss leads to a transition of hydride growth from horizontal to vertical,accompanied by the onset of redirection behaviour.Interestingly,redirection occurs at a critical mismatch level,denoted as qc,and remains unaffected by variations in temperature and interfacial energy.However,this redirection leads to an increase in the maximum stress,which may influence the direction of hydride crack propagation.This research highlights the importance of interfacial coherency and provides valuable insights into the morphology and growth kinetics of hydrides in zirconium alloys.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12205023,U2230401,12374056,U23A20537,11904027)。
文摘A thermodynamically complete multi-phase equation of state(EOS)applicable to both dense and porous metals at wide ranges of temperature and pressure is constructed.A standard three-term decomposition of the Helmholtz free energy as a function of specific volume and temperature is presented,where the cold component models both compression and expansion states,the thermal ion component introduces the Debye approximation and melting entropy,and the thermal electron component employs the Thomas-Fermi-Kirzhnits(TFK)model.The porosity of materials is considered by introducing the dynamic porosity coefficientαand the constitutive P-αrelation,connecting the thermodynamic properties between dense and porous systems,allowing for an accurate description of the volume decrease caused by void collapse while maintaining the quasi-static thermodynamic properties of porous systems identical to the dense ones.These models enable the EOS applicable and robust at wide ranges of temperature,pressure and porosity.A systematic evaluation of the new EOS is conducted with aluminum(Al)as an example.300 K isotherm,shock Hugoniot,as well as melting curves of both dense and porous Al are calculated,which shows great agreements with experimental data and validates the effectiveness of the models and the accuracy of parameterizations.Notably,it is for the first time Hugoniot P-σcurves up to 10~6 GPa and shock melting behaviors of porous Al are derived from analytical EOS models,which predict much lower compression limit and shock melting temperatures than those of dense Al.
文摘采用van der Waals等效单组分流体模型和Ross硬球微扰理论软球修正模型,计算了爆轰气相产物的状态方程;用石墨相、金刚石相、类石墨液相和类金刚石液相4种相态描述凝聚成分,由Gibbs自由能最小确定了不同状态下的凝聚产物相态。对爆轰产物混合系统采用自由能最小原理,通过化学平衡方程组求解了炸药爆轰产物系统的平衡组分。使用该理论计算了高含碳炸药PBX9502 Chapman-Jouguet(CJ)点的爆轰参数,计算值与实验值符合很好;同时计算了3条等温线,并与Sesame库比较,发现温度超过1000℃时,计算值与Sesame库的计算结果比较接近。在计算的5 802K等温线上发现了一个拐点,分析发现是由于在此处游离态的碳发生了相变。
基金Project supported by the National Natural Science Foundation of China (Grant Nos.U2230401,U1930401,and 12004048)the National Key Research and Development Program of China (Grant No.2021YFB3501503)+1 种基金the Science Challenge Project (Grant No.TZ2018002)the Foundation of LCP。
文摘Hydride precipitation in zirconium cladding materials can damage their integrity and durability.Service temperature and material defects have a significant effect on the dynamic growth of hydrides.In this study,we have developed a phasefield model based on the assumption of elastic behaviour within a specific temperature range(613 K-653 K).This model allows us to study the influence of temperature and interfacial effects on the morphology,stress,and average growth rate of zirconium hydride.The results suggest that changes in temperature and interfacial energy influence the length-to-thickness ratio and average growth rate of the hydride morphology.The ultimate determinant of hydride orientation is the loss of interfacial coherency,primarily induced by interfacial dislocation defects and quantifiable by the mismatch degree q.An escalation in interfacial coherency loss leads to a transition of hydride growth from horizontal to vertical,accompanied by the onset of redirection behaviour.Interestingly,redirection occurs at a critical mismatch level,denoted as qc,and remains unaffected by variations in temperature and interfacial energy.However,this redirection leads to an increase in the maximum stress,which may influence the direction of hydride crack propagation.This research highlights the importance of interfacial coherency and provides valuable insights into the morphology and growth kinetics of hydrides in zirconium alloys.
