Macroscopic elastic stress and strain produced by irradiation

Abstract

Using the notion of eigenstrain produced by the defects formed in a material exposed to high energy neutron irradiation, we develop a method for computing macroscopic elastic stress and strain arising in components of a fusion power plant during operation. In a microstructurally isotropic material, the primary cause of macroscopic elastic stress and strain fields is the spatial variation of neutron exposure. We show that under traction-free boundary conditions, the volume-average elastic stress always vanishes, signifying the formation of a spatially heterogeneous stress state, combining compressive and tensile elastic deformations at different locations in the same component, and resulting solely from the spatial variation of radiation exposure. Several case studies pertinent to the design of a fusion power plant are analysed analytically and numerically, showing that a spatially varying distribution of defects produces significant elastic stresses in ion-irradiated thin films, pressurised cylindrical tubes and breeding blanket modules.

Volume of a dislocation network

“…This quantity represents a tensorial measure of the volume change to first order [13], with the relaxation volume Ω given by the trace…”

“…Using ( 4) and ( 12), the field of displacements generated by a continuous distribution of defects can now be expressed as a volume integral [13,40]…”

“…Similarly, there is no need to use the symmetrised form (14) in the right-hand side of the equation. As a slight digression, we note that the equation for the dipole tensor density of dislocations, required for evaluating the field of displacements (13), can be represented in a differential form, compatible with the treatment of elastic fields of curved line dislocations [45]. To derive the differential form of (18), we use the Burgers formula for the displacement field of a dislocation…”

“…A material exposed to neutron or ion irradiation changes its volume [1][2][3][4] and, in some cases, its anisotropic spatial dimensions [5]. If the exposure of the material to a flux of energetic particles is low and the defects produced by irradiation can be treated as a dilute gas of localised centres of lattice distortion [6], the degree of volumetric expansion or contraction [1,[7][8][9] can be estimated from the relaxation volumes of individual defects [10][11][12][13]. These volumes can now be accurately computed using ab initio methods [14][15][16][17][18].…”

“…To relate the complexity of dislocation structures and dislocation networks to the macroscopic dimensional changes that they produce, and enable including dislocations in the finite-element model formalism for the numerical treatment of dimensional changes and radiation swelling of nuclear fusion reactor components [10,13], we propose a method for computing relaxation volume tensors and relaxation volumes of arbitrary dislocation configurations, and show how to evaluate the degree of volumetric expansion in a material containing an interconnected network of line dislocations.…”