The elastic interaction between solute atoms and stress field at the tip of cracks and notches

As for a mechanical interaction between a general stress singularity and an-environmental factor (e.g. hydrogen) which has influence on delayed failure characteristics of materials, it has not hitherto been analysed, although it is an important problem. In the present article an analytical basis is given for the problem of elastic interaction between solute atom as an environmental factor accelerating delayed failure and stress field around a crack and further a general V-shaped notch.The result of analysis shows that the number of solute atoms which accumulate to crack tip due to elastic interaction is proportional to a parameter. $\text{ρ}{}_0\text{(}\text{DKt}\text{kT}\text{)}{}^{\mathrm{<mtext>4</mtext><mtext>5</mtext>}}$ where K is stress intensity factor,ρ₀ initial uniform density of the solute atom, D diffusion constant, t time, k Boltzman's constant and T absolute temperature. It is further shown that the abovementioned parameter is generalized to $\text{ρ}{}_0\text{(}\text{Dkt}\text{kT}\text{)}{}^{\mathrm{<mtext>2</mtext><mtext>(2+q)</mtext>}}$ for the number of what accumulate to the apex of a general V-shaped notch due to elastic interaction where k is a factor representing a stress singularity of the notch apex and q is a constant related to apex angle a.The above analysis indicates that it is possible to describe development of delayed failure in terms of a parametre of fracture mechanics K, when viewed from a standpoint inclusive of diffusion and mechanical processes, since it is shown that the rate of concentration to crack tip of solute atoms as an environmental factor is uniquely determined by a factor $\text{ρ}{}_0\text{(}\text{DK}\text{kT}\text{)}{}^{\mathrm{<mtext>4</mtext><mtext>5</mtext>}}$.