Development of the Maximum Rate of Dissipation Criterion to Analyze the Deformation Mechanisms in Semi-Solid State

Document Type : Research Paper

Authors

Faculty of Materials Science and Engineering, K. N. Toosi University of Technology, Tehran 19991-43344, Iran

Abstract

This study presents a new perspective on semi-solid rheology by applying the maximum dissipation rate criterion and stability analysis. Using this approach, we developed a criterion that identifies the conditions under which different deformation mechanisms dominate. A key finding is the critical role of rate-sensitivity in shaping both the mode and intensity of deformation. Specifically, we identify a threshold rate-sensitivity value of m = 0.21. Below this threshold, deformation is governed by granular processes such as grain rearrangement, jamming, and dilatancy. Above it, conversely, solid grains undergo plastic deformation instead. The analysis also establishes a strong correlation between dilatancy and rate-sensitivity. In the granular regime, higher rate dependency, resulting from increased solid fraction and stronger grain interconnections, promotes greater dilatancy and increased tendency for shear localization. At the critical threshold, localization emerges as bonds between grain agglomerates break, triggering Reynold’s dilatancy. Collectively, these findings highlight that semi-solid materials exhibit granular-like behavior, wherein grain and agglomerate rearrangement, coupled with dilatancy, drive the transition toward shear banding following the failure of inter-particle bonds. These insights provide a clearer framework for understanding and predicting the complex behavior of semi-solid materials under load.

Keywords

References

[1] Atkinson, H. V. (2005). Modelling the semi-solid processing of metallic alloys. Progress in Materials Science, 50(3), 341-412. https://doi.org/10.1016/j.pmatsci.2004.04.003
[2] Wang, W., Guo, E., Phillion, A. B., Eskin, D. G., Wang, T., & Lee, P. D. (2020). Semi-solid compression of nano/ micro-particle reinforced Al-Cu composites: An in-situ synchrotron tomographic study. Materialia, 12, 100817. https://doi.org/10.1016/j.mtla.2020.100817
[3] Li, H., Cao, M., Niu, L., Huang, K., & Zhang, Q. (2021). Establishment of macro-micro constitutive model and deformation mechanism of semi-solid Al6061. Journal of Alloys and Compounds, 854, 157124. https://doi.org/10.1016/j.jallcom.2020.157124
[4] Wang, K., Wang, L., Li, F., Zhang, Z., & Luo, R. (2022). Anisotropic microstructure and thixo-compression deformation behavior of extruded 7075 aluminum alloy in semi-solid state. Materials Science and Engineering: A, 833, 142514. https://doi.org/10.1016/j.msea.2021.142514
[5] Liu, Z., Zhou, R., Xiong, W., He, Z., Liu, T., & Li, Y. (2022). Compressive rheological behavior and microstructure evolution of a semi-solid CuSn10P1 alloy at medium temperature and low strain. Metals 2022, 12(1), 143. https://doi.org/10.3390/met12010143
[6] Boluri Gashti, A. H., Abedi, H. R., & Salehi, M. T. (2023). Microstructure evolution and constitutive modeling of as-cast A356 aluminum alloy in semi-solid deformation regime. Journal of Materials Research and Technology, 24(18), 7720-7731. https://doi.org/10.1016/j.jmrt.2023.05.025
[7] Burgos, G. R., Alexandrou, A. N., & Entov, V. (2001). Thixotropic rheology of semi-solid metal suspensions. Journal of Materials Processing Technology, 110(2), 164-176. https://doi.org/10.1016/S0924-0136(00)00731-7
[8] Modigell, M., & Koke, J. (2001). Rheological modelling on semi-solid metal alloys and simulation of thixocasting processes. Journal of Materials Processing Technology, 111(1-3), 53-58. https://doi.org/10.1016/S0924-0136(01)00496-4
[9] Cézard, P., Favier, V., Bigot, R., Balan, T., & Berveiller, M. (2005). Simulation of semi-solid thixoforging using a micro-macro constitutive equation. Computational Materials Science, 32(3-4), 323-328. https://doi.org/10.1016/j.commatsci.2004.09.036
[10] Favier, V., & Atkinson, H. V. (2011). Micromechanical modelling of the elastic-viscoplastic response of metallic alloys under rapid compression in the semi-solid state. Acta Materialia, 59(3), 1271-1280. https://doi.org/10.1016/j.actamat.2010.10.059
[11] Wang, J., Phillion, A. B., & Lu, G. (2014). Development of a viscoplastic constitutive modeling for thixoforming of AA6061 in semi-solid state. Journal of Alloys and Compounds, 609, 290-295. https://doi.org/10.1016/j.jallcom.2014.04.140
[12] Koeune, R., & Ponthot, J. P. (2014). A one phase thermomechanical model for the numerical simulation of semi-solid material behavior. Application to thixoforming. International Journal of Plasticity, 58, 120-153. https://doi.org/10.1016/j.ijplas.2014.01.004
[13] Gourlay, C. M., Dahle, A. K., Nagira, T., Nakatsuka, N., Nogita, K., Uesugi, K., & Yasuda, H. (2011). Granular deformation mechanisms in semi-solid alloys. Acta Materialia, 59(12), 4933-4943. https://doi.org/10.1016/j.actamat.2011.04.038
[14] Kareh, K. M., Lee, P. D., Atwood, R. C., Connolley, T., & Gourlay, C. M. (2014). Revealing the micromechanisms behind semi-solid metal deformation with time-resolved X-ray tomography. Nature Communications 2014 5:1, 5(1), 4464. https://doi.org/10.1038/ncomms5464
[15] Su, T. C., O’Sullivan, C., Yasuda, H., & Gourlay, C. M. (2020). Rheological transitions in semi-solid alloys: In-situ imaging and LBM-DEM simulations. Acta Materialia, 191, 24-42. https://doi.org/10.1016/j.actamat.2020.03.011
[16] Su, T. C., O’Sullivan, C., Nagira, T., Yasuda, H., & Gourlay, C. M. (2019). Semi-solid deformation of Al-Cu alloys: A quantitative comparison between real-time imaging and coupled LBM-DEM simulations. Acta Materialia, 163(7123), 208-225. https://doi.org/10.1016/j.actamat.2018.10.006
[17] Ansari, M. H. S., & Aghaie Khafri, M. (2017). Predicting flow localization in semi-solid deformation. International Journal of Material Forming 2017 11:2, 11(2), 165-173. https://doi.org/10.1007/s12289-017-1339-6
[18] Sheikh Ansari, M. H., & Aghaie Khafri, M. (2018). Shear localization in semi-solid deformation: A bifurcation theory approach. Mechanics Research Communications, 89, 1-5. https://doi.org/10.1016/j.mechrescom.2018.02.002
[19] Sheikh Ansari, M. H., & Aghaie Khafri, M. (2018). An extension of Rice localization criterion to predict the onset of shear localization in semi-solid materials. International Journal of Material Forming 2018 12:4, 12(4), 703-716. https://doi.org/10.1007/s12289-018-1445-0
[20] Sheikh Ansari, M. H., & Aghaie Khafri, M. (2019). Constitutive modeling of semi-solid deformation for the assessment of dilatant shear bands. Applied Mathematical Modelling, 70, 128-138. https://doi.org/10.1016/j.apm.2019.01.028
[21] Esquivel, E. V., & Murr, L. E. (2005). Grain boundary contributions to deformation and solid-state flow in severe plastic deformation. Materials Science and Engineering: A, 409(1-2), 13-23. https://doi.org/10.1016/j.msea.2005.04.063
[22] Ziegler, H.  (1963). Progress in solid mechanic, (Sneddon, I. N., Hill, R., Ed.), New York, 93-193
[23] Ziegler, H. (1983). An introduction to thermomechanics (1st Ed.). North-Holland Publishing Company
[24] Rajagopal, K. R., & Srinivasa, A. R. (1998). Mechanics of the inelastic behavior of materials-part 1, theoretical underpinnings. International Journal of Plasticity, 14(10-11), 945-967. https://doi.org/10.1016/S0749-6419(98)00037-0
[25] Rajagopal, K. R., & Srinivasa, A. R. (1998). Mechanics of the inelastic behavior of materials. Part II: Inelastic response. International Journal of Plasticity, 14(10-11), 969-995. https://doi.org/10.1016/S0749-6419(98)00041-2
[26] Suery, M., & Flemings, M. C. (1982). Effect of strain rate on deformation behavior of semi-solid dendritic alloys. Metallurgical Transactions A 1982, 13(10), 1809-1819. https://doi.org/10.1007/bf02647837
[27] Tzimas, E., & Zavaliangos, A. (1999). Mechanical behavior of alloys with equiaxed microstructure in the semi-solid state at high solid content. Acta Materialia, 47(2), 517-528. https://doi.org/10.1016/S1359-6454(98)00356-5
[28] Nguyen, T. G., Favier, D., & Suery, M. (1994). Theoretical and experimental study of the isothermal mechanical behavior of alloys in the semi-solid state. International Journal of Plasticity, 10(6), 663-693. https://doi.org/10.1016/0749-6419(94)90028-0
[29] Martin, C. L., Brown, S. B., Favier, D., & Suéry, M. (1995). Shear deformation of high solid fraction (> 0.60) semi-solid Sn-Pb under various structures. Materials Science and Engineering: A, 202(1-2), 112-122. https://doi.org/10.1016/0921-5093(95)09797-X
[30] Rudnicki, J. W., & Rice, J. R. (1975). Conditions for the localization of deformation in pressure-sensitive dilatant materials. Journal of the Mechanics and Physics of Solids, 23(6), 371-394. https://doi.org/10.1016/0022-5096(75)90001-0
[31] Hosford, W. F. (1972). A generalized isotropic yield criterion. Journal of Applied Mechanics, 39(2), 607-609. https://doi.org/10.1115/1.3422732
[32] Butcher, C., & Abedini, A. (2017). Shear confusion: Identification of the appropriate equivalent strain in simple shear using the logarithmic strain measure. International Journal of Mechanical Sciences, 134, 273-283. https://doi.org/10.1016/j.ijmecsci.2017.10.005
[33] Ferrante, M., & De Freitas, E. R. (2001). Rheological behavior and deformation characteristics of a commercial and a laboratory-cast Al-4% Cu alloy in the semi-solid state. Acta Materialia, 49(18), 3839-3847. https://doi.org/10.1016/S1359-6454(01)00239-7
[34] Narumi, T., Ohta, K., Ohta, M., Numata, T., Asahi, K., Katsube, R., & Yasuda, H. (2023). Observation of grain motion during semi-solid deformation by using 4D-CT and 3D-XRD. IOP Conference Series: Materials Science and Engineering, 1274(1), 012053. https://doi.org/10.1088/1757-899x/1274/1/012053
[35] Su, T. C., O’sullivan, C., Yasuda, H., & Gourlay, C. M. (2022). Understanding the rheological transitions in semi-solid alloys by a combined in-situ imaging and granular micromechanics modeling approach. Solid State Phenomena, 327, 127-132. https://doi.org/10.4028/www.scientific.net/SSP.327.127
[36] Wu, M., Liu, Y., Wang, T., & Yu, K. (2016). Deformation behavior and characteristics of sintered porous 2024 aluminum alloy compressed in a semi-solid state. Materials Science and Engineering: A, 674, 144-150.  https://doi.org/10.1016/j.msea.2016.07.120
[37] Zhang, C., Zhao, S., Yan, G., & Wang, Y. (2018). Deformation behavior and microstructures of semi-solid A356.2 alloy prepared by radial forging process during high solid fraction compression. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 232(3), 487-498. https://doi.org/10.1177/0954405416646002
[38] Chino, Y., Kobata, M., Iwasaki, H., & Mabuchi, M. (2003). An investigation of compressive deformation behavior for AZ91 Mg alloy containing a small volume of liquid. Acta Materialia, 51(11), 3309-3318. https://doi.org/10.1016/S1359-6454(03)00162-9
[39] Chen, Y., Yuan, Z., Zhan, H., Zhao, Y., Song, X., Wang, G., & Gu, Y. (2017). Unexpected dynamic recrystallization behavior of Ti-7Cu alloy in semi-solid state. Journal of Alloys and Compounds, 712, 468-476. https://doi.org/10.1016/j.jallcom.2017.04.091
[40] Sheikh Ansari, M. H., & Aghaie Khafri, M. (2019). Effect of semi-solid deformation on the restoration mechanisms and texture evolution in AA7075. JOM 2019, 71(12), 4696-4704. https://doi.org/10.1007/s11837-019-03835-8
[41] Jiang, J., Liu, Y., Xiao, G., Wang, Y., & Xiao, X. (2020). Effects of plastic deformation of solid phase on mechanical properties and microstructure of wrought 5A06 aluminum alloy in directly semi-solid thixoforging. Journal of Alloys and Compounds, 831, 154748. https://doi.org/10.1016/j.jallcom.2020.154748
[42] Prasad, Y. V. R. K., & Rao, K. P. (2011). Materials modeling and finite element simulation of isothermal forging of electrolytic copper. Materials & Design, 32(4), 1851-1858. https://doi.org/10.1016/j.matdes.2010.12.018
[43] Gupta, A. K., Krishnamurthy, H. N., Singh, Y., Prasad, K. M., & Singh, S. K. (2013). Development of constitutive models for dynamic strain aging regime in austenitic stainless steel 304. Materials & Design, 45, 616-627. https://doi.org/10.1016/j.matdes.2012.09.041
[44] Alaneme, K. K., Kareem, S. A., & Bodunrin, M. O. (2023). Hyperbolic-sine constitutive model determined hot deformation mechanisms and workability response of Al-Zn/ Cu and Al-Zn/ SiC based composites. Results in Engineering, 19, 101255. https://doi.org/10.1016/J.RINENG.2023.101255
[45] Xu, X., Zhang, P., Fang, J., Wen, L., Yang, Y., Zhao, Y., & Chen, L. (2024). The hot deformation behavior and processing map analysis of a high-nitrogen austenitic stainless steel. Journal of Materials Research and Technology, 33, 1359-1365. https://doi.org/10.1016/j.jmrt.2024.09.162
[46]  Li, X., Hao, Y., Wang, Y., Shi, H., Wang, X., Hu, X., & Yu, J. (2024). Hot deformation and processing map of in-situ graphene reinforced magnesium matrix nanocomposites. Journal of Alloys and Compounds, 1005, 175978. https://doi.org/10.1016/j.jallcom.2024.175978
[47] Xiao, Y., Deng, Y., An, Y., Yuan, L., Zhan, X., & Wang, B. (2024). Strain rate affects the deformation mechanism of a Ti-55511 titanium alloy: Modeling of constitutive model and 3D processing map using machine learning. Materials Today Communications, 40, 109881. https://doi.org/10.1016/j.mtcomm.2024.109881
 
Iranian Journal of Materials Forming
Volume 13, Issue 3
July 2026
Pages 34-51

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