Hall petch relationship hardness

hall petch relationship hardness

Keywords: Grain refinement, Hall-Petch relation, steel, strength, toughness, brittle mechanical properties of steel, including yield strength and hardness, the. The transition from the Hall–Petch relationship to the coherent polycrystal mechanism was shown to be a gradual process. The hardness in the. and statically annealed specimens were used to determine the variation in microhardness with grain size, and results confirm that the Hall-Petch relationship.

The nanocrystalline materials have been considered as a three-component composite consisting of grains, grain boundaries and triple junctions, where three-grain boundaries meet [ 30 ], or a four-component composite consisting of crystallite grain interiorgrain boundaries, triple lines and quadruple nodes [ 31 ]. For the sake of simplicity, the nanocrystalline materials could be approximated as a composite with two phases only—grain interior and grain boundary [ 32—35 ], since all plastic deformation was observed to be accommodated in the grain boundary and no intra-grain deformation occurred [ 2223 ].

The results of MD simulations provide a basis for identifying the role of the grain interior and grain boundary during plastic deformation, and a potential for predicting the strength of nanocrystalline materials via composite models or the rule of mixtures [ 303133 ].

hall petch relationship hardness

It was also shown that the results of the finite element calculations are almost the same as those obtained using the rule of mixtures [ 31 ].

Based on the above consideration a coherent polycrystal model was proposed in which the nanocrystalline materials were regarded as a coherent precipitate strengthened two-phase alloy [ 6 ].

Grain boundary strengthening

Similarly, Dao et al [ 37 ] observed that nano-twinned Cu after tensile testing showed dislocation pile-ups along twin boundaries TBs and curved TBs; a region within a few nanometers of a TB was often heavily influenced by the dislocations along the TBs. Each of the TBs may be treated as a special grain boundary, where the plastic deformation in copper with nanoscale twins is concentrated in the vicinity of the TBs. High resolution TEM imaging directly confirmed the presence of partial dislocation dissociation, dislocation pile-up and TB bending.

The grain boundaries or twin boundaries in the above models were basically considered as a continuous matrix and the grains were embedded in the grain boundary matrix. These recent observations and models basically support the two-phase coherent polycrystal model [ 6 ]. Therefore, the coherent polycrystal model [ 6 ] involving the dependence of strength on grain sizes in the nanoscale range will be considered in this study.

Experimental observations have also revealed that intragranular dislocation sources like the Frank—Read source cease to operate in nanocrystalline materials and result in high strength and reduced plasticity in these materials. The traditional dislocation theories may no longer be applicable to the deformation behavior of nanocrystalline materials. Consistent with the recent experimental observations or models mentioned above, atomistic simulations also suggested that dislocations nucleated at grain boundaries GBs carry out plastic deformation in the nanocrystalline regime; once nucleated, these dislocations travel across the grains and are eventually absorbed in the opposite grain boundary [ 38—40 ].

In a very recent investigation on the plastic deformation recovery in nanocrystalline aluminum and gold films, it was reported that the enhancement of recovery rate could be due to the reduction in pinning sites caused by redistributions of grain boundary impurities during annealing [ 41 ]. This suggests that not only the average grain size but also the inherent variation or distribution of the grain size should be taken into consideration [ 41 ].

Modeling the dependence of strength on grain sizes in nanocrystalline materials

This investigation was, therefore, aimed at describing the dependence of strength or hardness of nanocrystalline materials on the grain size, based on the Hall—Petch relationship and coherent polycrystal model via further integrating a log-normal distribution of grain sizes. Modeling In the coherent polycrystal model [ 6 ], the grain phase was assumed to be a perfect crystallite while the grain boundary phase contained potential defects e.

The strengthening effect of the grain boundary matrix by the coherent precipitates, i. Since there is a large volume of experimental data available as hardness values, it is convenient to convert the strength values to hardness values using the method given in [ 42 ], Then the equivalent equation for the grain size dependence of the hardness in the coherent polycrystal model may be expressed as, where H, Hgbo and Kco are the corresponding terms to those specified in equation 2.

That is, H and Hgbo are the hardness of the nanocrystalline material and the grain boundary, respectively, and Kco is a material parameter that reflects the measure of the hardening effect of grain cores on the grain boundary matrix. It follows that the larger the atomic diameter, the larger the effective grain boundary thickness. As suggested by Rajagopalan et al [ 41 ], the inherent variations in grain sizes in nanocrystalline materials should be taken into account in exploring their plastic deformation.

hall petch relationship hardness

We consider the grain size distribution which follows a log-normal function. Hall wrote three papers which appeared in volume 64 of the Proceedings of the Physical Society. In his third paper, Hall [7] showed that the length of slip bands or crack lengths correspond to grain sizes and thus a relationship could be established between the two.

hall petch relationship hardness

Hall concentrated on the yielding properties of mild steels. Based on his experimental work carried out in —, N. Petch of the University of LeedsEngland published a paper in independent from Hall's. Petch's paper [8] concentrated more on brittle fracture.

By measuring the variation in cleavage strength with respect to ferritic grain size at very low temperatures, Petch found a relationship exact to that of Hall's.

Modeling the dependence of strength on grain sizes in nanocrystalline materials

Thus this important relationship is named after both Hall and Petch. Reverse or inverse Hall—Petch relation[ edit ] The Hall—Petch relation predicts that as the grain size decreases the yield strength increases. The Hall—Petch relation was experimentally found to be an effective model for materials with grain sizes ranging from 1 millimeter to 1 micrometer. Consequently, it was believed that if average grain size could be decreased even further to the nanometer length scale the yield strength would increase as well.

A number of different mechanisms have been proposed for this relation. As suggested by Carlton et al. Once grain sizes drop below the equilibrium distance between dislocations, though, this relationship should no longer be valid.

hall petch relationship hardness