In this work an intermediate model is used, which reduces to the free quenching stress model at low holding pressures and to the pressure-induced stress model at higher holding pressures.
This means that shrinkage started directly after the injection stage, and the ultimate stress distribution is expected to be dominated by the free quenching stress contribution.
An expression for the free quenching stress distribution valid for larger times is given by Struik (5), p.
Struik (5) proposed a simple analytical model for predicting free quenching stresses, thus coupling restricted thermal shrinkage with stress formation.
Hence also Eqs 21 through 25 are expected to be different and the true free quenching stresses and strains should be calculated from Eqs 16 through 19.
In order to obtain the quenching stresses, we need to obtain the material parameters corresponding to the quenching state, and tests were conducted within 20 minutes after the 7050 aluminum alloy specimens were quenched.
For further study of the quenching stresses in the forging, FEM result of x-, y-, z-component residual stresses and Mises stresses in path L1 and L2 are shown in Fig.
Results were found out and it is stated that residual stresses are combination of quenching stresses and thermal stresses.
Rapid cooling of molten coat material happens, which results in generation of quenching stresses. It can be formulated as below 
For best relief of quenching stresses
, use the highest tempering temperature which will give the desired hardness.