A Perspective on Strain Hardening Behavior of Materials Considering Mobile Dislocation Density and Activation Volume
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Over the years, empirical equations, such as Hollomon, Ludwik, and Ludwigson, have been used to describe strain hardening behavior of materials for engineering purposes.[1] Subsequently, phenomenological models were developed based on the idea that flow stress at a given strain rate and temperature depends upon a parameter that describes the current structure of [2,3] postulated that the material. Mecking and Kocks forest dislocation density qf can be used as structure parameter and developed the one-parameter model. A significant number of changes in one parameter model have been made since then to accommodate the effects of different microstructural variables (grain size, precipitates, twins, etc.) on strain hardening behavior.[4–6] Another approach, viz. composite model, which considers heterogeneity in dislocation density distribution between cell walls and cell interiors was also developed.[7,8] The flow stress in composite model is the
SUMEET MISHRA, VIKRANT KUMAR BEURA, AMIT SINGH, and MANASIJ YADAVA are with the Department of Materials Science and Engineering, Indian Institute of Technology Kanpur, Kalyanpur, Kanpur 208016, India. Contact e-mail: [email protected] Manuscript submitted February 9, 2019. Article published online June 12, 2019 3472—VOLUME 50A, AUGUST 2019
weighted sum of stresses in these two regions. In recent years, a number of changes have also been made in the composite model to take into account the effect of strain gradient (geometrically necessary dislocations) and long-range internal stress on strain hardening behavior.[9,10] Apart from these landmark models, other approaches that make use of additional parameters such as subgrain size and misorientation between subgrains have also been used to describe strain hardening behavior, although with limited success.[11,12] However, the above-mentioned models do not consider the rate- or temperature-dependent part of the flow stress, viz. effective stress. It is well known that effective stress can be determined from Orowan equation which in turn implies that mobile dislocation density should be taken into account for an accurate description of flow curves.[13] Kubin and Estrin[14] were the first ones to consider the possibility of taking into account mobile dislocation density as the second structure parameter in combination with forest dislocation density. Another parameter which enters into the expression of effective stress is activation volume (Eq. [4]). Activation volume is a fundamental entity and depends upon the type of obstacles present in the microstructure. In the current study, we present the interplay between mobile dislocation density and activation volume and its subsequent effect on strain hardening. In order to carry out the current study, we have selected two age-hardenable Al alloys, viz. AA 2195 (Al-Cu-Li) and AA 6061 (Al-Mg-Si). Age-hardenable Al alloys are ideal to undertake the current study as drastically different strain hardening behaviors are reported in the presence of obstacles such as solutes and precipitates.[6] The a
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