Abstract
Flow stress relation with dislocation densities due to various types of inter-plane interactions between perfect dislocations in face-centred-cubic crystals is formulated. Compared to the widely used Taylor-type hardening relations, the derived formulae resolve more details from the underlying discrete dislocation dynamics. The shear flow stress is found weaker than the critical resolved shear stress to remobilise a singly locked primary dislocation, because dislocations can dynamically pile up against junctions resulting from dislocation interactions. With the derived formulae, the roles played by dislocations belonging to different slip systems in strain hardening are further clarified.
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