Generalized Stress–Strain Curves for IBII Tests on Isotropic and Orthotropic Materials
Tóm tắt
This article presents a particular use of the Virtual Fields Method to exploit the results of Image-Based Inertial Impact (IBII) tests. This test consists on an edge-on impact of a free-standing thin flat rectangular coupon. The specimen response is recorded using an ultra-high speed camera filming the deformation of a grid pattern printed at its surface. From these images, displacement fields are derived, from which strain and acceleration can be obtained. The Virtual Fields Method makes use of the acceleration fields to derive stress information. Until now, a very simple ‘stress-gauge’ approach was used that could only provide relevant stress-strain information if the test was predominantly uniaxial. The alternative was to use the full inverse approach with the Virtual Fields Method but this would not allow the same degree of data understanding as the ‘stress-gauge’ approach. This article proposes an extension to this ‘stress-gauge’ approach for fully multiaxial tests. The equations are first derived and then validated using simulated and experimental IBII test data on isotropic and orthotropic materials.
Tài liệu tham khảo
Kendall MJ, Siviour CR (2014) Experimentally simulating high-rate behaviour: rate and temperature effects in polycarbonate and PMMA. Philos Trans Royal Soc A. https://doi.org/10.1098/rsta.2013.0202
Field JE, Walley SM, Proud WG, Goldrein HT, Siviour CR (2004) Review of experimental techniques for high rate deformation and shock studies. Int J Impact Eng 30(7):725–775
Etoh TG, Mutoh H (2005) An image sensor of 1 Mfps with photon counting sensitivity. Proc SPIE 5580:301–307
Tochigi Y, Hanzawa K, Kato Y, Kuroda R, Mutoh H, Hirose R, Tominaga H, Takubo K, Kondo Y, Sugawa S (2013) A global-shutter CMOS image sensor with readout speed of 1-tpixel/s burst and 780-mpixel/s continuous. IEEE J Solid-State Circuits 48(1):329–338
Specialized imaging Kirana camera. http://specialised-imaging.com/products/video-cameras/kirana. Accessed 3 May 2019
Shimadzu HPV-X camera. https://www.ssi.shimadzu.com/products/high-speed-video-camera/hyper-vision-hpv-x2.html. Accessed 3 May 2019
Sutton MA, Orteu JJ, Schreier HW (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer, New-York
Grédiac M, Sur F, Blaysat B (2016) The grid method for in-plane displacement and strain measurement: a review and analysis. Strain 52(3):205–243
Pierron F, Zhu H, Siviour C (2014) Beyond Hopkinson’s bar. Philos Trans Royal Soc A 372(2023):20130195
Aloui S, Othman R, Poitou A, Guégan P, El-Borgi S (2008) Non-parametric identification of the non-homogeneous stress in high strain-rate uni-axial experiments. Mech Res Commun 35(6):392–397
Moulart R, Pierron F, Hallett SR, Wisnom MR (2009) Full-field strain measurements at high rate on notched composites tested with a tensile Hopkinson bar. Exp Mech 3:1663–1668
Moulart R, Pierron F, Hallett SR, Wisnom MR (2011) Full-field strain measurement and identification of composites moduli at high strain rate with the virtual fields method. Exp Mech 51(4):509–536
Pierron F, Forquin P (2012) Ultra high speed full-field deformation measurements on concrete spalling specimens and stiffness identification with the Virtual Fields Method. Strain 28(5):388–405
Yoon S-H, Giannakopoulos I, Siviour CR (2015) Application of the virtual fields method to the uniaxial behavior of rubbers at medium strain rates. Int J Solids Struct 69–70:553–568
Yoon S-H, Winters M, Siviour CR (2016) High strain-rate tensile characterization of EPDM rubber using non-equilibrium loading and the Virtual Fields Method. Exp Mech 56(1):25–35
Yoon S-H, Siviour CR (2017) Application of the Virtual Fields Method to rubbers under medium strain rate deformation using both acceleration and traction force data. J Dyn Behav Mater 3(1):12–22
Yoon S-H, Siviour CR (2018) Application of the virtual felds method to a relaxation behaviour of rubbers. J Mech Phys Solids 116:416–431
Dreuilhe S, Davis F, Siviour CR, Pierron F (2017) Image-based inertial impact tests on an aluminum alloy. Conf Proc Soc Exp Mech Ser 3:219–223
Fletcher L, Van Blitterswyk J, Pierron F (2019) A novel image-based inertial impact (IBII) test for the transverse properties of composites at high strain rates. J Dyn Behav Mater 5(1):65–92
Fletcher L, Pierron F (2018) An image-based inertial impact (IBII) test for tungsten carbide cermets. J Dyn Behav Mater 4(4):481–504
Van Blitterswyk J, Fletcher L, Pierron F (2018) Image-based inertial impact test for composite interlaminar tensile properties. J Dyn Behav Mater 4:543–572
Dreuilhe S, Pierron F (2016) Extension of the non-linear virtual fields method to inertial heterogeneous high strain rate tests. Conf Proc Soc Exp Mech Ser 4:83–87
Seghir R, Pierron F (2018) A novel image-based ultrasonic test to map material mechanical properties at high strain-rates. Exp Mech 58(2):183–206
Koohbor B, Kidane A, Lu W-Y (2016) Effect of specimen size, compressibility and inertia on the response of rigid polymer foams subjected to high velocity direct impact loading. Int J Impact Eng 98:62–74
Forquin P, Lukić B (2018) On the processing of spalling experiments. Part I: Identification of the dynamic tensile strength of concrete. J Dyn Behav Mater 4(1):34–55
Piro JL, Grédiac M (2004) Producing and transferring low-spatial-frequency grids for measuring displacement fields with moiré and grid methods. Exp Tech 28(4):23–26
Zhu H, Pierron F (2016) Exploration of Saint-Venant’s principle in inertial high strain rate testing of materials. Exp Mech 56(1):3–23
Fletcher L, Van-Blitterswyk J, Pierron F (2018) Combined shear/tension testing of fibre composites at high strain rates using an image-based inertial impact test. In: proceedings of EPJ Web of Conferences, vol. 183
Harding J, Welsh LM (1983) A tensile testing technique for fibre-reinforced composites at impact rates of strain. J Mater Sci 18(6):1810–1826
Seghir R, Pierron F, Fletcher L (2018) Image-based stress field reconstruction. In: proceedings of BSSM annual conference, 29–31 August 2018, Southampton, UK