The superposition of strengthening contributions in engineering alloys

In engineering alloys strengthened by a combination of solid solution, precipitation and work hardening, plasticity is controlled by the interaction between dislocations and different sets of obstacles on the glide plane. How to add the strengthening contributions of these obstacles to predict yield stresses and work hardening is an important question. To answer this question, a 2D areal glide model based on the method of Nogaret and Rodney that simulates the glide of a single dislocation through an array of randomly distributed point obstacles was used. The effect of one, two and three sets of obstacles was studied with their strengths varying from weak (Φc=180°) to strong (Φc=0°). The results of these simulations were used for the first time to develop a mathematical expression for the exponent of the addition law τq=τ1q+τ2q. An extension of this addition law to three sets of obstacles was also derived. These new laws were then applied to predict the work hardening response of an Al-Mg-Sc alloy.