Stress concentration factor (SCF) for a circular shaft with fillet subjected to torque load \(T\), diameters \(D\) and \(d\), fillet radius \(r\).
\(K_t\) is calculated so that the max. shear stress can be calculated as \( \tau = K_t (16 T) / (\pi d^3) \).
In this site, \(K_t\) is calculated by a response surface that has been adjusted to 32 data points spanning the domain \(D/d=[1.05,1.5]\), \(r/d=[0.025,0.3]\), as shown below.
The 32 data points have been calculated automatically by 96+ Abaqus simulations using a parameterized (Python) script. The number of simulations is 3X the number of data points because computing \(K_t\) for each pair \([D/d,r/d]\) requires 3+ simulations to achive a solution with less than 1% error, by invoking automatic adaptive mesh refinement for each data point within the script.
Red dots are data points. A few may be hidden right below the blue surface.
You can learn how to produce similar simulations here [link to be provided].
Here is a plot of \(K_t\) vs. \(r/d\).