The elastic bend radius can be calculated by the formula :
SBa/ (D/2) =E/R
R/D=E/2SBa
Where
R= The elastic bending radius
E= Young modulus of the material
D= the outside diameter of the pipe
SBa= the maximum allowable stress for bending.
Some references will give also this formula (which is more conservative)
R/D=3E/2SBa
The most important thing about the above two formulas is to calculate how much is the allowable bending stress, which can be done by calculating the max. allowable longitudinal stresses , and then deducting from that the internal pressure related stresses, the thermal expansion stresses,,, etc.