Square grid deformation in wedge indentation: a new mathematical approach
Tóm tắt
The square grid deformation approach is generally employed to forming processes solved with the aid of slip-line field in which a ductile body is supposed to be made with arrays of square grids of finite sizes before the deformation process. After the application of the load, as the deformation occurs, square grids are deformed. The square grid deformation has three utilities—(1) visualization of actual deformation process, (2) prediction of trajectory at any point and (3) computation of strain. The theory of square grid deformation mathematics was originally developed by Hill considering the linear formation of the lip. The present work develops a new mathematical approach for deformation of square grids considering a parabolic lip formation when a rigid wedge is gradually indented to a ductile block of semi-infinite size.
Tài liệu tham khảo
Hill R, Lee EH, Tupper SJ (1947) The theory of wedge indentation in ductile materials. Proc R Soc A 188:273–279
Grunzweig J, Longman IM, Petch NJ (1954) Calculation and measurement of wedge-indentation. J Mech Phys Solids 2:81–86
Johnson W, Mathab FU, Haddow JB (1964) The indentation of a semi-infinite block by a wedge of comparable hardness—I: theoretical. Int J Mech Sci 6:329–336
Mulhern TO (1959) The deformation of metals by Vickers-type pyramidal indenter. J Mech Phys Solids 7:85–96
Schmalinga B, Hartmaier A (2012) Determination of plastic material properties by analysis of residual imprint geometry of indentation. J Mater Res 27(16):2167–2177
Moharrami N, Bull SJ (2014) A comparison of nanoindentation pile-up in bulk materials and thin films. Thin Solid Films 572:189–199
Chen J, Shen Y, Liu W, Beake B, Shi S, Wang Z, Zhang Y, Guo X (2016) Effects of loading rate on development of pile-up during indentation creep of polycrystalline copper. Mater Sci Eng A 656:216–221
Biswas AK, Das S, Das B, Das S (2015) A slip line field solution for micro-indentation of a rigid conical wedge by numerical technique. Int J Innov Res Sci Eng Technol 4:90–94
Biswas AK, Das S, Das S (2017) Micro-indentation of a conical rigid wedge by numerical slip-line field theory: a hybrid approach. Indian Sci Cruiser 31(3):36–42. https://doi.org/10.24906/isc/2017/v31/i3/155592
Biswas AK, Das S, Das S (2018) Estimating conical indentation load by numerical slip-line field technique. J Struct Eng 45(1):118–124
Biswas AK, Das S, Das S (2019) Comparisons extends of plastic zones for micro-indentation of a rigid wedge to a semi-infinite block by finite element analysis and numerical slip-line field techniques. Indian Sci Cruiser 33(6):48–52
Shimmin EW (1982) A theoretical and experimental investigation of deformation in plane strain rolling and drawing through circular dies. PhD Thesis, Faculty of Engineering, University of New South Wales
Busquet M, Torrance A (2000) A numerical slipline field for the sliding cylinder problem. Wear 24:86–98
Rousseau T, Song Y, Wang W, Rastogi S, Voyiadjis GZ, Kysar JW (2020) Order in polycrystalline plasticity deformation fields: short-range intermittency and long-range consistency. Int J Plast. https://doi.org/10.1016/j.ijplas.2020.102674