Abstract
In this work, a novel method is presented to track site-specific microstructure evolution in metallic materials deformed biaxially along proportional and complex strain paths. A miniaturized bulge test setup featuring a removable sample holder was designed to enable incremental measurements to be performed in a scanning electron microscope, by probing the same position on the sample at different deformation levels, with electron backscatter diffraction (EBSD), electron channeling contrast imaging (ECCI) and other imaging modes. Validation experiments were performed at room temperature on samples prepared from commercial sheet metal (dual-phase steel) and foils (stainless steel). Local strain measurements with the digital image correlation technique confirmed that proportional strain paths with a strain ratio up to 5 can be investigated using elliptical dies in the bulge test holder. It is also shown how complex strain paths can be obtained using a combination of overlapping elliptical dies. Incremental EBSD and ECCI were conducted in configurations relevant for the multi-scale investigation of localized plasticity and damage mechanisms in dual-phase steel. Quantitative information regarding microstructure evolution (phase fractions, orientation fields, dislocation structures, etc.) and regarding local strain distributions could be successfully obtained. This type of data sheds light on underlying deformation mechanisms and provides opportunities to calibrate crystal plasticity models.
Similar content being viewed by others
Notes
Cruciform geometry enforces fracture to take place in the thinned center region of the sample, overriding local microstructural effects. The Marciniak test, on the other hand, creates a homogeneous multi-axially strained region where the fracture point is dictated by the microstructure.
References
Tasan CC, Hoefnagels JPM, ten Horn CHLJ, Geers MGD (2009) Experimental analysis of strain path dependent ductile damage mechanics and forming limits. Mech Mater 41:1264–1276. https://doi.org/10.1016/j.mechmat.2009.08.003
Hoefnagels JPM, Tasan CC, Maresca F, Peters FJ, Kouznetsova VG (2015) Retardation of plastic instability via damage-enabled microstrain delocalization. J Mater Sci 50:6882–6897. https://doi.org/10.1007/s10853-015-9164-0
Horstemeyer MF, Lathrop J, Gokhale AM, Dighe M (2000) Modeling stress state dependent damage evolution in a cast Al-Si-Mg aluminum alloy. Theor Appl Fract Mech 33:31–47. https://doi.org/10.1016/S0167-8442(99)00049-X
Bonora N, Gentile D, Pirondi A, Newaz G (2005) Ductile damage evolution under triaxial state of stress: Theory and experiments. Int J Plast 21:981–1007. https://doi.org/10.1016/j.ijplas.2004.06.003
Xue L (2007) Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading. Int J Solids Struct 44:5163–5181. https://doi.org/10.1016/j.ijsolstr.2006.12.026
Gardey B, Bouvier S, Richard V, Bacroix B (2005) Texture and dislocation structures observation in a dual-phase steel under strain-path changes at large deformation. Mater Sci Eng A 400–401:136–141. https://doi.org/10.1016/j.msea.2005.01.066
Volkov IA, Korotkikh YG, Tarasov IS (2009) Modeling complex plastic deformation and fracture of metals under disproportionate loading. J Appl Mech Tech Phys 50:891–900
Lapovok R, Hodgson D (2009) A damage accumulation model for complex strain paths: Prediction of ductile failure in metals. J Mech Phys Solids 57:1851–1864. https://doi.org/10.1016/j.jmps.2009.07.008
Dietrich L, Socha G (2012) Accumulation of damage in A336 GR5 structural steel subject to complex stress loading. Strain. 48:279–285. https://doi.org/10.1111/j.1475-1305.2011.00821.x
Kang J, Ososkov Y, Embury JD, Wilkinson DS (2007) Digital image correlation studies for microscopic strain distribution and damage in dual phase steels. Scr Mater 56:999–1002. https://doi.org/10.1016/j.scriptamat.2007.01.031
Tasan CC, Diehl M, Yan D, Zambaldi C, Shanthraj P, Roters F, Raabe D (2014) Integrated experimental–simulation analysis of stress and strain partitioning in multiphase alloys. Acta Mater 81:386–400. https://doi.org/10.1016/j.actamat.2014.07.071
Wang QG (2003) Microstructural effects on the tensile and fracture behavior of aluminum casting alloys A356/357. Metall Mater Trans A Phys Metall Mater Sci 34:2887–2899. https://doi.org/10.1007/s11661-003-0189-7
Bieler TR, Eisenlohr P, Roters F, Kumar D, Mason DE, Crimp MA, Raabe D (2009) The role of heterogeneous deformation on damage nucleation at grain boundaries in single phase metals. Int J Plast 25:1655–1683. https://doi.org/10.1016/j.ijplas.2008.09.002
Pineau A (2006) Development of the local approach to fracture over the past 25 years: Theory and applications. Int J Fract 138:139–166. https://doi.org/10.1007/s10704-006-0035-1
Li H, Fu MW, Lu J, Yang H (2011) Ductile fracture: Experiments and computations. Int J Plast 27:147–180. https://doi.org/10.1016/j.ijplas.2010.04.001
Wu W, Wang YW, Makrygiannis P, Zhu F, Thomas GA, Hector LG, Hu X, Sun X, Ren Y (2018) Deformation mode and strain path dependence of martensite phase transformation in a medium manganese TRIP steel. Mater Sci Eng A 711:611–623. https://doi.org/10.1016/j.msea.2017.11.008
Oh ST, Park KK, Han HN, Park SH, Oh KH (2009) Transformation Behavior of Retained Austenite in Hydroformed TRIP Steel. Mater Sci Forum 408–412:1341–1346. https://doi.org/10.4028/www.scientific.net/msf.408-412.1341
Iwamoto T, Tsuta T, Tomita Y (1998) Investigation on deformation mode dependence of strain-induced martensitic transformation in trip steels and modelling of transformation kinetics. Int J Mech Sci 40:173–182. https://doi.org/10.1016/S0020-7403(97)00047-7
Schwartz AJ, Kumar M, Adams BL, Field DP (2009) Electron Backscatter Diffraction in Materials Science, 2nd edn. Springer US, Boston, MA. https://doi.org/10.1007/978-0-387-88136-2
Zaefferer S, Elhami NN (2014) Theory and application of electron channelling contrast imaging under controlled diffraction conditions. Acta Mater 75:20–50. https://doi.org/10.1016/j.actamat.2014.04.018
Ram F, Li Z, Zaefferer S, Hafez Haghighat SM, Zhu Z, Raabe D, Reed RC (2016) On the origin of creep dislocations in a Ni-base, single-crystal superalloy: An ECCI, EBSD, and dislocation dynamics-based study. Acta Mater 109:151–161. https://doi.org/10.1016/j.actamat.2016.02.038
Kamaya M, Wilkinson AJ, Titchmarsh JM (2005) Measurement of plastic strain of polycrystalline material by electron backscatter diffraction. Nucl Eng Des 235:713–725. https://doi.org/10.1016/j.nucengdes.2004.11.006
Pantleon W (2008) Resolving the geometrically necessary dislocation content by conventional electron backscattering diffraction. Scr Mater 58:994–997. https://doi.org/10.1016/j.scriptamat.2008.01.050
Wilkinson AJ, Meaden G, Dingley DJ (2006) High-resolution elastic strain measurement from electron backscatter diffraction patterns: New levels of sensitivity. Ultramicroscopy. 106:307–313. https://doi.org/10.1016/j.ultramic.2005.10.001
Maurice C, Driver JH, Fortunier R (2012) On solving the orientation gradient dependency of high angular resolution EBSD. Ultramicroscopy. 113:171–181. https://doi.org/10.1016/j.ultramic.2011.10.013
Plancher E, Petit J, Maurice C, Favier V, Saintoyant L, Loisnard D, Rupin N, Marijon JB, Ulrich O, Bornert M, Micha JS, Robach O, Castelnau O (2016) On the Accuracy of Elastic Strain Field Measurements by Laue Microdiffraction and High-Resolution EBSD: a Cross-Validation Experiment. Exp Mech 56:483–492. https://doi.org/10.1007/s11340-015-0114-1
Archie F, Li X, Zaefferer S (2017) Micro-damage initiation in ferrite-martensite DP microstructures: A statistical characterization of crystallographic and chemical parameters. Mater Sci Eng A 701:302–313. https://doi.org/10.1016/j.msea.2017.06.094
Caër C, Pesci R (2017) Local behavior of an AISI 304 stainless steel submitted to in situ biaxial loading in SEM. Mater Sci Eng A 690:44–51. https://doi.org/10.1016/j.msea.2017.02.087
M.A. Sutton, J.-J. Orteu, H.W. Schreier, Image Correlation for Shape, Motion and Deformation Measurements, 2009. doi:https://doi.org/10.1017/CBO9781107415324.004
Sutton MA, Li N, Joy DC, Reynolds AP, Li X (2007) Scanning electron microscopy for quantitative small and large deformation measurements Part I: SEM imaging at magnifications from 200 to 10,000. Exp Mech 47:775–787. https://doi.org/10.1007/s11340-007-9042-z
Allais L, Bornert M, Bretheau T, Caldemaison D (1994) Experimental characterization of the local strain field in a heterogeneous elastoplastic material. Acta Metall Mater 42:3865–3880
Yan D, Tasan CC, Raabe D (2015) High resolution in situ mapping of microstrain and microstructure evolution reveals damage resistance criteria in dual phase steels. Acta Mater 96:399–409. https://doi.org/10.1016/j.actamat.2015.05.038
Fullwood D, Vaudin M, Daniels C, Ruggles T, Wright SI (2015) Validation of kinematically simulated pattern HR-EBSD for measuring absolute strains and lattice tetragonality. Mater Charact 107:270–277. https://doi.org/10.1016/j.matchar.2015.07.017
Vermeij T, De Graef M, Hoefnagels J (2019) Demonstrating the potential of accurate absolute cross-grain stress and orientation correlation using electron backscatter diffraction. Scr Mater 162:266–271. https://doi.org/10.1016/j.scriptamat.2018.11.030
Plancher E, Favier V, Maurice C, Bosso E, Rupin N, Stodolna J, Loisnard D, Marijon JB, Petit J, Micha JS, Robach O, Castelnau O (2017) Direct measurement of local constitutive relations, at the micrometre scale, in bulk metallic alloys. J Appl Crystallogr 50:1–9. https://doi.org/10.1107/S1600576717006185
Tatschl A, Kolednik O (2003) On the experimental characterization of crystal plasticity in polycrystals. Mater Sci Eng A 342:152–168. https://doi.org/10.1016/S0921-5093(02)00278-2
Tasan CC, Diehl M, Yan D, Zambaldi C, Shanthraj P, Roters F, Raabe D (2014) Integrated experimental-simulation analysis of stress and strain partitioning in multiphase alloys. Acta Mater 81:386–400. https://doi.org/10.1016/j.actamat.2014.07.071
Torres EA, Ramírez AJ (2011) In situ scanning electron microscopy. Sci Technol Weld Join 16:68–78. https://doi.org/10.1179/136217110X12785889550028
Ghadbeigi H, Pinna C, Celotto S (2013) Failure mechanisms in DP600 steel: Initiation, evolution and fracture. Mater Sci Eng A 588:420–431. https://doi.org/10.1016/j.msea.2013.09.048
Alaie A, Ziaei Rad S, Kadkhodapour J, Jafari M, Asadi Asadabad M, Schmauder S (2015) Effect of microstructure pattern on the strain localization in DP600 steels analyzed using combined in-situ experimental test and numerical simulation. Mater Sci Eng A 638:251–261. https://doi.org/10.1016/j.msea.2015.04.071
Tasan CC, Hoefnagels JPM, Geers MGD (2010) Microstructural banding effects clarified through micrographic digital image correlation. Scr Mater 62:835–838. https://doi.org/10.1016/j.scriptamat.2010.02.014
Tasan CC, Hoefnagels JPM, Dekkers ECA, Geers MGD (2012) Multi-Axial Deformation Setup for Microscopic Testing of Sheet Metal to Fracture. Exp Mech 52:669–678. https://doi.org/10.1007/s11340-011-9532-x
Van Petegem S, Guitton A, Dupraz M, Bollhalder A, Sofinowski K, Upadhyay MV, Van Swygenhoven H (2017) A Miniaturized Biaxial Deformation Rig for in Situ Mechanical Testing. Exp Mech 57:569–580. https://doi.org/10.1007/s11340-016-0244-0
Gorji MB, Mohr D (2017) Micro-tension and micro-shear experiments to characterize stress-state dependent ductile fracture. Acta Mater 131:65–76. https://doi.org/10.1016/j.actamat.2017.03.034
M. Kubo, H. Yoshida, A. Uenishi, S. Suzuki, Y. Nakazawa, Development of Biaxial Tensile Test System for In-situ Scanning Electron Microscope and Electron Backscatter Diffraction Analysis, 56 (2016) 669–677
ISO 16808, ISO 16808:2014 Metallic materials - sheet and strip - determination of biaxial stress-strain curve by means of bulge test with optical measuring systems, 2014
Mulder J, Vegter H, Aretz H, Keller S, Van Den Boogaard AH (2015) Accurate determination of flow curves using the bulge test with optical measuring systems. J Mater Process Technol 226:169–187. https://doi.org/10.1016/j.jmatprotec.2015.06.034
Reis LC, Prates PA, Oliveira MC, Santos AD, Fernandes JV (2017) Anisotropy and plastic flow in the circular bulge test. Int J Mech Sci 128–129:70–93. https://doi.org/10.1016/j.ijmecsci.2017.04.007
Min J, Stoughton TB, Carsley JE, Carlson BE, Lin J, Gao X (2017) Accurate characterization of biaxial stress-strain response of sheet metal from bulge testing. Int J Plast 94:192–213. https://doi.org/10.1016/j.ijplas.2016.02.005
Chen K, Scales M, Kyriakides S, Corona E (2015) Effects of anisotropy on material hardening and burst in the bulge test. Int J Solids Struct 82:70–84. https://doi.org/10.1016/j.ijsolstr.2015.12.012
Suttner S, Merklein M (2016) Experimental and numerical investigation of a strain rate controlled hydraulic bulge test of sheet metal. J Mater Process Technol 235:121–133. https://doi.org/10.1016/j.jmatprotec.2016.04.022
Livescu V, Bingert JF, Liu C, Lovato ML, Patterson BM (2015) Biaxial deformation in high purity aluminum. Mater Sci Eng A 648:330–339. https://doi.org/10.1016/j.msea.2015.09.086
Neggers J, Hoefnagels JPM, Hild F, Roux S, Geers MGD (2014) Direct Stress-Strain Measurements from Bulged Membranes Using Topography Image Correlation. Exp Mech 54:717–727. https://doi.org/10.1007/s11340-013-9832-4
O. Paul, J. Gaspar, M. Engineering, Thin-Film Characterization Using the Bulge Test, in: Reliab. MEMS, Wiley-VCH Verlag GmbH & Co. KGaA, 2008: pp. 67–121. doi:https://doi.org/10.1002/9783527622139.ch3
Tonge TK, Atlan LS, Voo LM, Nguyen TD (2013) Full-field bulge test for planar anisotropic tissues: Part I-Experimental methods applied to human skin tissue. Acta Biomater 9:5913–5925. https://doi.org/10.1016/j.actbio.2012.11.035
Jayyosi C, Bruyère-Garnier K, Coret M (2017) Geometry of an inflated membrane in elliptic bulge tests: Evaluation of an ellipsoidal shape approximation by stereoscopic digital image correlation measurements. Med Eng Phys 48:150–157. https://doi.org/10.1016/j.medengphy.2017.06.020
Rees DWA (1995) Plastic flow in the elliptical bulge test. Int J Mech Sci 37:373–389. https://doi.org/10.1016/0020-7403(94)00071-Q
Rees DWA (1996) Sheet orientation and forming limits under diffuse necking. Appl Math Model 20:624–635. https://doi.org/10.1016/0307-904X(96)00010-8
Ragab AR, Habib OE (1984) Determination of the Equivalent Stress. Mater Sci Eng 64:5–14
Williams BW, Boyle KP (2016) Characterization of anisotropic yield surfaces for titanium sheet using hydrostatic bulging with elliptical dies. Int J Mech Sci 114:315–329. https://doi.org/10.1016/j.ijmecsci.2016.05.022
Atkinson M (1994) Hydraulic bulging of near-isotropic sheet metal through an elliptical aperture. Int J Mech Sci 36:247–255. https://doi.org/10.1016/0020-7403(94)90073-6
Abu-Farha F, Verma R, Hector LG (2012) High temperature composite forming limit diagrams of four magnesium AZ31B sheets obtained by pneumatic stretching. J Mater Process Technol 212:1414–1429. https://doi.org/10.1016/j.jmatprotec.2012.01.008
Zhu T, Sutton MA, Li N, Orteu JJ, Cornille N, Li X, Reynolds AP (2011) Quantitative Stereovision in a Scanning Electron Microscope. Exp Mech 51:97–109. https://doi.org/10.1007/s11340-010-9378-7
Kammers AD, Daly S (2013) Digital Image Correlation under Scanning Electron Microscopy: Methodology and Validation. Exp Mech 53:1743–1761. https://doi.org/10.1007/s11340-013-9782-x
Liao J, Sousa JA, Lopes AB, Xue X, Barlat F, Pereira AB (2017) Mechanical, microstructural behaviour and modelling of dual phase steels under complex deformation paths. Int J Plast 93:269–290. https://doi.org/10.1016/j.ijplas.2016.03.010
D. Banabic, H.-J. Bunge, K. Pöhlandt, A. E. Tekkaya, Formability of Metallic Materials, 2000. doi:10.1007/978-3-662-04013-3
Nolze G (2007) Image distortions in SEM and their influences on EBSD measurements. Ultramicroscopy. 107:172–183. https://doi.org/10.1016/j.ultramic.2006.07.003
Britton TB, Maurice C, Fortunier R, Driver JH, Day AP, Meaden G, Dingley DJ, Mingard K, Wilkinson AJ (2010) Factors affecting the accuracy of high resolution electron backscatter diffraction when using simulated patterns. Ultramicroscopy. 110:1443–1453. https://doi.org/10.1016/j.ultramic.2010.08.001
Maurice C, Dzieciol K, Fortunier R (2011) A method for accurate localisation of EBSD pattern centres. Ultramicroscopy. 111:140–148. https://doi.org/10.1016/j.ultramic.2010.10.007
Abu-Farha F, Hu X, Sun X, Ren Y, Hector LG, Thomas G, Brown TW (2018) In Situ Local Measurement of Austenite Mechanical Stability and Transformation Behavior in Third-Generation Advanced High-Strength Steels. Metall Mater Trans A Phys Metall Mater Sci 49:2583–2596. https://doi.org/10.1007/s11661-018-4660-x
Park T, Hector LG, Hu X, Abu-Farha F, Fellinger MR, Kim H, Esmaeilpour R, Pourboghrat F (2019) Crystal Plasticity Modeling of 3rd Generation Multi-phase AHSS with Martensitic Transformation. Int J Plast. https://doi.org/10.1016/j.ijplas.2019.03.010
SHI Q, Roux S, Latourte F, Hild F, Loisnard D, Brynaert N (2018) On the use of SEM correlative tools for in situ mechanical tests. Ultramicroscopy. 184:71–87. https://doi.org/10.1016/j.ultramic.2017.08.005
Acknowledgements
We gratefully acknowledge Michael J. Tarkanian, James Hunter, David Bono, Qilong Cheng and Jiyun Kang for their input in the design of the bulge test setup. Valuable help provided by Ashley Brown Raynal is gratefully acknowledged. The authors thank Pr. Tomasz Wierzbicki and Pr. Ian Hunter for their kindly support. Dr. Guilhem Martin is acknowledged for his assistance in the finalization of this manuscript. This work made use of the shared experimental facilities supported in part by the MRSEC program of the National Science Foundation under award number DMR – 1419807.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix 1: Development of a Thinning Process for DP Steel
Appendix 1: Development of a Thinning Process for DP Steel
DP600 and DP800 steel used in this study were non-commercial grades provided by Tata Steel (IJmuiden, the Netherlands) in the shape of 1.3 mm-thick sheets. The following thinning method was developed to prepare thin samples from the thick commercial sheets. The goal was to obtain EBSD-polished samples with a homogeneous thickness (typically 100 μm ±5 μm) to perform well-controlled bulge tests. The composition and overall properties of these two steels are provided in Table 2 for reference.
The first preparation step (illustrated in Fig. 11(a)) consisted in cutting a 300 μm-thick sample out of the 1.3 mm-thick sheet using a wire EDM machine (Charmilles Robofil 1020SI). To perform a homogeneous cut, the sheet was clamped in a precision tool maker vise on both sides. Then, a disk of diameter 24 mm was cut out with the same process. As schematized in Fig. 11(b), the cutting introduces damaged layers on both surfaces which had to be removed by polishing. These layers bear compressive residual stress and make the polishing step a complex task as samples progressively bend when the damaged layer is removed from one side. A cross section observation of the damaged layer was performed to estimate its depth below 60 μm (cf. Figure 11(c)). As a safe target, 100 μm of mater was removed on both sides, by polishing, to obtain a sample with a microstructure fully representative of the original one.
The following procedure gave the best results for polishing the sample while keeping a homogeneous thickness. First, sacrificial rings were cut out using a waterjet cutter from hardened stainless steel foils (yield strength of 1240 MPa). When the first side of the sample was polished, a 200 μm-thick foil was used whereas a 100 μm-thick one was used for the second side. One sacrificial ring was fixed with super glue on a borosilicate glass stub (McMaster-Carr) fitting in an automated polisher (cf. Figure 11(c)). The surface of the glass stub was extremely flat, within ±1μm (measurement realized with a stylus profilometer DekTakTX from Bruker). To glue the ring, the stub was positioned in a vertical precision vise, the glue was deposited, and then the ring, a foil of Teflon and finally a second glass stub before closing the vise. The Teflon foil keeps the glue from adhering on the second glass stub and can simply be removed by peeling it off. The sample was then glued in the center of the ring with the same procedure. The quality of the gluing was checked by looking at the transparent backside of the stub. Three glass stubs were inserted in an automated polishing machine (to maintain balance and avoid wobbling movements) and they were polished with a 9 μm diamond solution on a hard polishing cloth. The polishing step was stopped when the sacrificial ring (originally thinner than the sample) started to get polished on the whole surface. Conventional polishing steps were then used to reach a 1 μm polishing grade (first side) or a OPS polishing grade (second side). Three baths of acetone were used to unglue and clean the samples.
One difficulty we faced was to monitor the sample thicknesses as the thinning process introduces a slight waviness in their shape. This waviness is likely caused by released residual stress initially present in the rolled thick sheet. The challenge with profilometery techniques was to hold and flatten the sample properly (with glue or a magnet) and still get an absolute measurement of the thickness. In further experiments, one should consider using X-ray tomography to get a 3D visualization of the sample and hence decouple shape waviness from thickness variations. A mechanical profilometer (DekTakTX, Bruker) was used several times to make sure the top surface after gluing was parallel to the glass stub (cf. Figure 11(d)). However, because of the variability in the layer of glue deposited, an estimation of the absolute thickness by this method was hardly reliable. As a consequence, the thicknesses reported in Table 3 have been measured simply with a caliper at four points on the sample. For DP600 samples, polished without using sacrificial polishing rings but with a similar process, the scatter found was in the order of 10 μm. For DP800, the scatter found was in the order of 5 μm. This decreased in scatter is attributed to the stability and corrective mechanism provided by the sacrificial rings. Note that when only the central part of the sample is considered (the tested area), the thickness scatter reported in Table 3 can be considered an upper bound.
Rights and permissions
About this article
Cite this article
Plancher, E., Qu, K., Vonk, N. et al. Tracking Microstructure Evolution in Complex Biaxial Strain Paths: A Bulge Test Methodology for the Scanning Electron Microscope. Exp Mech 60, 35–50 (2020). https://doi.org/10.1007/s11340-019-00538-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11340-019-00538-8