Exact solution of diffusion and absorption of hydrogen in uranium followed by fracture of the hydride

The diffusion of hydrogen in uranium and its absorption to form the hydride can be crudely modeled below approximately 2500C by a simple expression which may be numerically integrated. When a certain fraction of the uranium has turned to hydride, the material will tend to fracture. The fracture or ''spall'' front may be modeled as a moving boundary. When this is done in conjunction with the diffusion-absorption model, it is found that the hydrogen and hydride concentrations are simple functions of the normalized distance from the spall front. These distributions may be used to develop an expression for the motion of the spall front and integrated to give an expression for total weight gain. The analytic solution for weight gain rate matches available data below 2500C within a factor of 2