A Mike, I'm really impressed with your research and consideration of beam mechanics - good work. However, on with the discussion.
"But by increasing the yield point of the steel the frame can take more displacement without plastic bending."
Remember, only the CH steel case has a higher yield; the low carbon steel part is unchanged.
"And since spring rates go up with some power(d squared or d to the power of 1.5 etc...) of displacement and a higher yield point receiver can take more displacement it's spring rate is higher right before plastic failure that a "soft" frame.
No, spring rate is a force per displacement number. A "hard" spring will have more spring force than an equal soft spring, but only after the "soft" spring has yielded and the "hard" spring has not and continues to deflect without yielding. The two will have essentially the same spring rate if of equal dimensions. Spring rate must not be confused with spring force; spring force is spring rate times deflection.
In the case of the action/frame, it does, indeed, act like a beam with a strain gradient across it. However, the bulk of the stress will still be carried by the far more massive "soft" core. The case will add only "steel" strength to resist bending. The fact that the case is "hard" will add nothing extra until after the core has yielded. In a yielded frame, the "soft" core will resist returning to original dimensions and the "hard" case will attempt to force the "soft" core back. The "hard" case will be able to return the "soft" core part way back. It would take a very thick case to return it most of the way. As the yielded action moves toward original dimension, the yielded core would increase its resistance (spring force) and the spring force from the case would decrease. Once yielded, the case will not be able to overcome the core and return the action all the way to original dimensions.
Questions? Comments? Opposing views?
DDA
