Multi-Scale Investigation On Fracture Behavior Of Zirconium And Its Alloys In Complex Conditions

Zirconium and its alloys have excellent physical and chemical properties,such as corrosion resistance,radiation resistance,small thermal neutron capture cross section and so on.Zirconium alloys have become the fuel cladding and core structural materials widely used in reactors currently in service and under construction around the world.Furthermore,zirconium alloys have the advantages of low density,higher hydrogen storage density,lower hydrogen absorption expansion and lower linear expansion coefficient.Therefore,zirconium alloys are also very suitable as structural materials in special fields such as military industry,aerospace,metallurgy and chemical engineering.The dynamic and static mechanical behavior of zirconium and its alloys under complex and extreme conditions has always been concerned by nuclear industry,materials and mechanics.In recent years,there have been a large number of studies on the failure of zirconium and its alloys under complex service conditions,which mainly focus on the following two cases.(ⅰ)Delayed hydride crack(DHC)behavior.zircon shell will absorb hydrogen from the corrosion of cooling medium when it is in service in the core of nuclear reactor,and then gradually become brittle and cracked.Zirconium alloy cladding,when used in the core of a nuclear reactor,absorb hydrogen generated by corrosion in cooling media.After that,the cladding gradually embrittles and then cracks.DHC is the repeated cycle of zirconium alloy hydriding-embrittlement-cracking,which eventually leads to fracture.It seriously affects the operational safety of nuclear reactions.(ⅱ)Dynamic failure behavior at high strain rates.In addition to their excellent nuclear properties,zirconium and its alloys are widely used in modern military and industrial fields.In these applications,zirconium and its alloys will be subjected to extreme environments with high stress and high strain rate loads,such as adiabatic shear under blasting impact,explosive welding,high speed cutting and combustion explosion effect.Under such complicated service conditions,the microstructure of zirconium and zirconium alloy often shows a very complicated failure process which is completely different from that under normal conditions.Based on the above background,the main research contents and corresponding conclusions of this paper are as follows.(1)Void nucleation,growth and coalescence failure behavior of HCP-Zr under extreme conditions.Molecular dynamics(MD)method was used to simulate the mechanism of void nucleation,growth and coalescence in HCP-Zr under high temperature and high strain rate.The effect of temperature and strain rate on the nucleation threshold of void is discussed.The complex symbiotic and competitive relationships between void and dislocation,void and phase transition are deeply analyzed.The parameters of void nucleus and growth(NAG)model are solved and optimized.The main conclusions are as follows:①Voids grow preferentially along the[0110]orientation instead of the[0001]orientation under a high volumetric strain rate in HCP-Zr.②It is found that there is a complex symbiotic competition relationship between voids and dislocations.In the nucleation stage,dislocations form around the voids and promote each other.When the void enters the exponential growth period,it always grows towards the direction of dislocation density,resulting in the rapid decrease of dislocation density.③The influence of competition between void and phase transition on the nucleation threshold of void is revealed.When the void nucleation lags behind the phase transformation,there are two peaks in the stress time curve.The first peak is caused by the phase transformation,and the second peak is caused by the void nucleation.When the void nucleation occurs before or at the same time with the phase transformation,there is only one peak in the stress curve,which is the threshold of void nucleation.④The parameter set of NAG model was solved and optimized,and the void volume fraction obtained by the optimized NAG model was highly consistent with the calculated results of MD.It provides effective void nucleation threshold and growth threshold for the failure behavior of HCP-Zr at high strain rate.(2)Multi-scale calculation of diffusion behavior of hydrogen in zirconium under multi-field coupling.The DHC behavior depends on the diffusion of hydrogen.In this paper,the diffusion process of hydrogen under multi field coupling is calculated at micro and macro scale.At the micro scale,the MSD curve of hydrogen in HCP-Zr was simulated by molecular dynamics(MD).At the micro scale,the MSD curve of hydrogen in HCP-Zr was simulated by molecular dynamics(MD).The diffusion coefficient of hydrogen was calculated according to Einstein relation,and the diffusion coefficient was fitted by Arrhenius equation.Based on Fick’s first law and the diffusion coefficient obtained from MD,the numerical model of hydrogen diffusion in zirconium alloy under the non-uniform stress field,hydrogen concentration field and temperature field was established by using the sequential coupling of multiple fields.Based on Fick’s first law and the diffusion coefficient obtained from MD,a numerical model of hydrogen diffusion in zirconium alloy under the non-uniform stress field,hydrogen concentration field and temperature field was established by using the sequential coupling of multiple fields.The main conclusions are as follows:① MD was used to calculate the MSD-time curves at 300K,350K and 400k.According to the Einstein relation,the diffusion coefficients of hydrogen in HCP-Zr at corresponding temperatures were calculated.The diffusion coefficient of hydrogen was fitted according to Arrhenius equation,and the law of hydrogen diffusion coefficient with temperature was obtained,which was in good agreement with the experimental data.②The diffusion process of hydrogen under the non-uniform stress field,hydrogen concentration field and temperature field is simulated by using the sequential coupling of multiple fields.It is found that hydrogen will continuously accumulate towards the crack tip under the induction of hydrostatic stress gradient.And the concentration of hydrogen at the crack tip increases linearly with time,which is consistent with the existing reports.Under the same conditions as experiment,the calculated hydrogen concentration at the crack tip is in good agreement with the experimental results.③The phase transition rate of solid solution hydrogen to hydride at low temperature was calculated.The lower the temperature,the smaller the diffusion coefficient of hydrogen,the longer the time of hydrogen accumulation.Therefore,the rate of hydride precipitation decreases with decreasing temperature.④A set of hydrogen diffusion calculation method from the bottom atomic scale to the macro model is established,which can provide prediction and estimation for the time-consuming low-temperature diffusion experiment.(3)The critical condition of delay hydride cracking(DHC)was established.The DHC process of zirconium alloy containing hydrides was calculated by numerical method,and the variation range of normal stress at crack tip was determined.By introducing adjustable parameters c to characterize the relationship between peak stress and boundary stress in the plastic zone,the plastic boundary condition was solved and the critical condition of DHC was obtained.The main conclusions are as follows:①A method for calculating the critical stress intensity factor K1H of DHC is developed.The normal stress at the crack tip is obtained by numerical calculation in accordance with the HRR solution.In order to solve the boundary conditions of the plastic zone,the adjustable parameter c was innovatively introduced to characterize the relationship between the peak stress and the boundary stress in the plastic zone.Then the K1H was obtained,which was consistent with the existing experiments.②The relationship between the critical hydride length and K1H of Zr-2.5Nb pressure tube is predicted by the improved DHC model.The obtained lC-K1 fitting curve is in good agreement with the existing experimental results.③The fracture behavior of two-phase materials containing Zr-2.5Nb and hydride was simulated by XFEM.The fracture process can be divided into four stages:(ⅰ)Elastic-plastic deformation stage;(ⅱ)Slow crack initiation stage in the zirconium matrix in front of the initial crack tip(r≤rM);(ⅲ)Rapid crack propagation stage in the hydride;(ⅳ)Smooth crack propagation stage in the zirconium alloy after the crack passes through the hydride.(4)A cross-scale discrete fracture method was developed to simulate the discrete fracture behavior of hydride in zirconium alloys.The equivalent fracture criterion of FE2 model was established,the modeling method of two-scale finite element was improved,and a cross-scale discrete fracture calculation method suitable for heterogeneous materials was developed.The fracture behavior of discrete hydride at the crack tip was simulated by this method,and the effect of hydride morphology on the critical condition of DHC and the direction of hydride precipitation on the propagation direction of DHC were found.The main conclusions are as follows:①The potential energy loss term is introduced into the equilibrium equation.According to the Direct FE2 theory and the characteristics of the fracture process zone,the macroscopic strain energy and the potential energy of the crack surface are transformed into microscopic quantities for characterization,and the equivalent fracture criterion in the FE2 model is established.A multi-scale discrete fracture calculation method for heterogeneous materials is developed,which is compatible with the commercial finite element software ABAQUS.This method provides a new perspective and method for solving the discrete fracture problem of heterogeneous materials.②The discrete fracture processes of single macro element and CT specimens,including homogeneous and heterogeneous materials,are simulated by the multi-scale method.The calculated F-δCurve is consistent with the experimental data,which verifies the validity of the discrete fracture model and the equivalent energy release rate in RVE.③The effect of hydride morphology and precipitation direction on the DHC behavior is studied by using the multi-scale discrete fracture method.(ⅰ)The increase of hydrogen concentration,the continuity coefficient of hydride increases,which leads to the decrease of fracture parameters.(ⅱ)The resistance of zirconium alloy to hydrogen-induced cracking is influenced by the hydride habit plane｛1017}.When the habit plane is parallel to the loading direction,the resistance to cracking is the strongest,while when the two are perpendicular,the resistance to cracking is the weakest.(ⅲ)Macro crack is formed by the coalescence of discrete cracks of brittle hydride,which leads to the direction of macro cracks always along the habit plane｛1017} of hydride texture.