Modeling of Mesoscale Creep Behaviors and Macroscale Creep Responses of Composite Fuels Under Irradiation Conditions

Abstract

A finite-strain homogenization creep model for composite fuels under irradiation conditions is developed and verified, with the irradiation creep strains of the fuel particles and matrix correlated to the macroscale creep responses, excluding the contributions of volumetric strain induced by the irradiation swelling deformations of fuel particles. A finite element (FE) modeling method for uniaxial tensile creep tests is established with the irradiation effects of nuclear materials taken into account. The proposed models and simulation strategy are numerically implemented to a kind of composite nuclear fuel, and the predicted mesoscale creep behaviors and the macroscale creep responses are investigated. The research results indicate that: (1) the macroscale creep responses and the mesoscale stress and strain fields are all greatly affected by the irradiation swelling of fuel particles, owing to the strengthened mechanical interactions between the fuel particles and the matrix. (2) The effective creep rates for a certain case are approximately two constants before and after the critical fission density, which results from the accelerated fission gas swelling after fuel grain recrystallization, and the effects of macroscale tensile stress will be more enhanced at higher temperatures. (3) The macroscale creep contributions from the fuel particles and matrix depend mainly on the current volume fractions varying with fission density. (4) As a function of the macroscale stress, temperature, initial particle volume fraction and particle fission rate, a multi-variable mathematical model for effective creep rates is fitted out for the considered composite fuels, which matches well with the FE predictions. This study supplies important theoretical models and research methods for the multi-scale creep behaviors of various composite fuels and provides a basis for simulation of the thermal–mechanical behavior in related composite fuel elements and assemblies.

Appendices

Appendix 1

Considering the bi-linear relation between the effective creep strains and irradiation time, the effective creep rate model with a temperature of 523 K and an initial particle volume fraction of 30% is obtained as

$$ \dot{\overline{\varepsilon}}_{{}}^{\text{cr}} = \left\{ {\begin{array}{*{20}c} {2.84562 \times 10^{ - 5} } \,\,\,& ({\text{Fd} \le {\text{Fd}}_{x} }) \\ {4.27086 \times 10^{ - 5} } \,\,\,& ({\text{Fd} > {\text{Fd}}_{x} }) \\ \end{array} } \right. $$

(19)

where $\dot{\overline{\varepsilon }}_{{}}^{{{\text{cr}}}}$ is in 1/d, and other parameters are the same as those in Table 1.

Table 1 Material models for PuO₂ and zircaloy

To verify the effectiveness of Eq. (19) and the homogenization creep model, the verification method in [38] is adopted. A macroscale homogenized-medium model is established in Fig. 7a, and then the virtual multi-axial compression tests are implemented and the macroscale creep results are obtained, which are compared with the creep results of multi-particle composite model, as shown in Fig. 7b. The model parameters of homogenized-medium model are described in Table 2. Similarly, the mechanical constitutive relation for the homogenized media contains the elastic, plastic, irradiation swelling and creep deformations. The effective swelling model used herein is developed in our previous study [28]. It should be noted that two compression tests with different pressure conditions are implemented to better verify the creep results. The boundary conditions are described in Table 2.

Fig. 7

a Homogenized-medium model, b multi-particle composite model and comparisons of the effective creep results from c Test 1 and d Test 2

Table 2 The model parameters of homogenized-medium model and the boundary conditions of the multi-axial compression tests

Figure 7c, d give the creep strains along the z-direction of the two models for Test 1, together with the creep strains along the x-direction for Test 2. It can be seen that the absolute values of the homogenized-medium model for Test 1 are a little higher than those of the multi-particle composite model, and the maximum relative error is ~ 6.67%. As for Test 2, the absolute results of the homogenized-medium model are slightly lower than those of the multi-particle composite model, with the maximum relative error of ~ 8.27%. The relative error is acceptable, which indicates that the macroscale creep model is effective, and can be used for the three-dimensional thermal–mechanical behavior simulations of inert matrix composite fuel elements and assemblies.

Appendix 2

2.1 Effects of Fission Rate

Figure 8a displays the effective creep strains under different fission rates for the designated calculation conditions. It can be seen that the effective creep strains give rise to fission density, but are almost the same at different fission rates. Figure 8b displays the creep contributions of each part for different fission rates. It can be seen that the fission rate has a slight effect on the creep contribution proportions. This is induced by the similar current particle volume fractions under different fission rates. These similar values indicate that the mechanical interactions between the fuel particles and the matrix will be almost the same at certain fission densities. It should be stated that the fission rate has a slight influence on effective creep strain, but will affect the effective creep rate, owing to its description with the irradiation time.

Fig. 8

a The FE results of the effective creep strain under different fission rates and b the contributions of particle creep strains and matrix creep strains under different fission rates