• PDF / 1,063,839 Bytes
• 10 Pages / 630 x 792 pts Page_size
• 63 Downloads / 280 Views

DOWNLOAD

REPORT

---

I.

INTRODUCTION

IN zirconium and

its alloys, hydrogen can precipitate as small, misfitting platelets or needles of zirconium hydride, t~i The presence of these hydrides can influence the long-term integrity of the material by making it susceptible to a slow crack initiation and propagation mechanism known as delayed hydride cracking (DHC) t2J and by decreasing the material's overall ductility (if hydrides are present in sufficient quantity). To quantify these cracking phenomena, it is necessary to know the local stresses and strain induced by the misfitting precipitate as well as the total accommodation energy of the solid containing them. The stresses and strains in and around a misfitting hydride precipitate are important in determining its tendency to fracture under applied stresses. In addition, the total accommodation energy of formation of the hydride has an effect on the terminal solid solubility (TSS) of hydrogen in the solid. In the DHC model, this influence on the TSS has a significant effect on the diffusion flux of hydrogen to the crack tip and, hence, on DHC initiation and velocity. Within linear elasticity, values for the total accommodation energy and the stresses and strains in and around the precipitate can be obtained from the elegant theory of inclusions and inhomogeneities developed by Eshelby. p,4j The Eshelby I3,4~ approach provides general analytical solutions for the total elastic (accommodation) energy and for the stresses and strains inside and just outside an ellipsoidal inhomogeneity, inclusion, or inhomogeneous inclusion. By approximating the shapes of

BRIAN W. LEITCH, Research Engineer, and M A N F R E D P. PULS, Manager, are with the Materials and Mechanics Branch, AECL Research, Whiteshell Laboratories, Pinawa, MB, Canada, ROE IL0. Manuscript submitted May 20, 1991. METALLURGICAL TRANSACTIONS A

precipitates in real materials to appropriately chosen ellipsoidal inclusions, the Eshelby theory is thus capable of providing solutions for a wide variety of precipitates. Specific solutions have been given by many workers such as, for instance, Barnett et al. ES] and Shibata and Ono./61 The solutions provided by the Eshelby approach are limited to linear elasticity. This is a good approximation for actual precipitates provided that they are very small or have only a small misfit; moreover, for all precipitates, it gives an idea of the maximum energy or the stresses and strains that are involved. However, hydride precipitates have large misfits (stress-free volume expansion of - 1 7 pct) and grow to large sizes (in t h e / z m range). Such large misfit strains produce sizable stresses that can be expected to result in plastic deformation of the matrix surrounding the hydride (by punching out dislocation loops). Using transmission electron microscopy, such loops have, in fact, been experimentally observed in the material surrounding zirconium hydrides.~TM The previous discussion shows that a more realistic solution requires an elastic-plastic treatment. Lee et al.[9] have provided an anal