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AbstractÐStress±strain responses of single and polycrystals of Had®eld steel were modeled using a viscoplastic self-consistent approach. A unique hardening formulation was proposed in the constitutive model incorporating length scales associated with spacing between twin lamellae and grain boundaries. TEM observations lend further support to the length scales incorporated into the constitutive model. Many of the experimental ®ndings were made on " 111 and " 144 crystal orientations deformed in tension, displaying ®ne twin lamellae at small strains in addition to slip in intra-twin regions. A natural outcome of the model was the small deformation activity inside the twinned regions and higher deformations between the twins. The model utilized dislocation density as a state variable and predicted the stress±strain responses and texture evolution in single crystals accurately over a broad range of strains. The responses of polycrystals with three grain sizes (100, 300, and 1000 mm) were also captured closely with the model in addition to the twin volume fraction evolution with increasing deformation. Based on the simulations, it was possible to explain unequivocally the upward curvature in stress±strain curves in the single crystals and in coarse grained polycrystals of Had®eld steel. Overall, the combined experimental and modeling e orts provide a reliable tool to characterize slip±twin interaction in low stacking fault energy f

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We studied the role of nitrogen content on the stress-strain response of Hadfield steel (HS) single crystals under compressive loading. Two different nitrogen concentrations were examined for each orientation (0.05 wt pct and 1.06 wt pct) with drastic increase in critical resolved shear stresses (CRSSs) and strain-hardening coefficients compared to HS without nitrogen. The stress-strain response was strongly dependent on both the crystallographic orientation and the nitrogen concentration. Transmission electron microscopy (TEM) results revealed that, for the HS with 1.06 wt pct nitrogen, the hardening is influenced by the coexisting deformation twins and precipitates, which both act as strong obstacles against dislocation motion. A visco-plastic self-consistent (VPSC) model was modified to account for precipitation and twinning length scales in HS with 1.06 wt pct nitrogen for selected crystallographic orientations. Incoherent precipitates in the hardening formulation were treated as factors affecting the mean free path of dislocations. The model also accounts for plastic relaxation of precipitates with increasing strain and accurately predicts the stress-strain response.