Pre-strain Effect on Bendability in Three-point Bending Test
This study investigates the influence of pre-strain on the bendability of sheet metals, specifically focusing on a three-point bending test using the Gurson-Tvergaard-Needleman model. The research delves into the deformation behavior and fracture properties, particularly in AA5754 aluminum alloys, shedding light on how pre-strain impacts tensile and bending characteristics. The constitutive model utilized in the analysis provides insights into void volume fractions, stress tensors, and material behavior under bending conditions.
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Study of Pre-strain Effect on Bendability in Three-point Bending Test Presented by: Mehdi Shahzamanian Co-authors: Amir Partovi Dr. Peidong Wu Department of Mechanical Engineering McMaster University August 27th, 2020
[1]. Introduction: Bending is an important deformation mode in many applications and it is important property in a range of applications and extensively used in the auto industry [1]. Three-point bending test Gurson-Tvergaard-Needleman (GTN) model with considering growth and coalescence is used in [2, 3] to investigate the ductile fracture in bending test for sheet metals. In [4], the influence of pre-strain on the tensile and bending properties of AA5754 aluminum alloys is studied and it is found that fracture occurs early in both tests. [1] D.J. Lloyd, M. Gallerneault, and R.B. Wagstaff, The deformation of clad aluminum sheet produced by direct chill casting. Metallurgical and Materials Transactions A, 2010. 41(8): p. 2093 2103. [2] Soyarslan, C., et al., A combined experimental numerical investigation of ductile fracture in bending of a class of ferritic martensitic steel, International Journal of Solids and Structures. 2012. 49(13): p. 1608-1626. [3] Cha, W.-g., N. J. M. Kim, and M. International, Quantification of micro-cracks on the bending surface of roll formed products using the GTN model, Metals and Materials International. 2014. 20(5): p. 841-850. [4] Sarkar, S.J., Kutty, T.R.G., Conlon, K.T., Wilkinson, D.S., Embury, J.D., Lloyd, D.J.: Tensile and bending properties of AA5754 aluminum alloys. Materials Science Engineering: A 316(1-2), 52-59 (2001). 1/8
[2]. Constitutive model; Gurson-Tvergaard-Needleman (GTN) model: Gurson-Tvergaard-Needleman (GTN) model [5-7]: ? ?, ?,? =??2 3?2?? 2 ? ?2+ 2? ?1??? 1.0 + ?2? 2= 0 2 ?, ??+?? ?? ?? ?? ??? ? ?? ??? ? ?? ?? 2???? 1 ?? ? = 1 ? ???:? ??? + ? = 2 ? ?? ??? ? > ?? ???? ????? ???? ?????????? ?: void volume fraction ?: Macroscopic Cauchy stress tensor ?: Matrix stress ??: Hydrostatic pressure ?1 and ?2: Calibrated parameters ??: Critical void volume fraction ??: Void volume fraction at failure 1 ?1 ?? Void nucleation volume fraction ??: Plastic strain standard deviation for void nucleating ?: Mean equivalent plastic strain ?? = ? ? ?1 ?2 ?? ?? ?? ?? ??? ?? Matrix material 0.0033 0.3 10 1.5 1.0 0.04 0.3 0.1 0.15 0.25 [5] Tvergaard, V. and A. J. A. m. Needleman, Analysis of the cup-cone fracture in a round tensile bar. Acta Metallurgica, 1984. 32(1): p. 157-169. [6] Tvergaard, V. J. I. J. o. f., Influence of voids on shear band instabilities under plane strain conditions, International Journal of Fracture. 1981. 17(4): p. 389-407. [7] Tvergaard, V. J. I. J. o. f., On localization in ductile materials containing spherical voids, International Journal of Fracture. 1982. 18(4): p. 237-252. 2/8
[3]. Problem formulation: Schematic of three-point bending ?? ?? ?? ?? ?? Sheet geometry plane strain parameters (mm) thickness 20 2.5 10 0.25 0.2 13 3/8
[4]. Results: plane strain quadrilateral element CPE4R in ABAQUS/Explicit Middle section of specimen FE configuration of three-point bending test in ABAQUS 1200 1000 Force (N) 800 600 100x150 elements 400 60x110 elements 200 0 0 1 2 3 4 Punch stroke (mm) Mesh sensitivity effect on force-displacement curve 4/8
[4]. Results; effect of pre-strain on force-displacement curve: 1200 1000 800 Force (N) 0% prestrain 5% prestrain 10% prestrain 15% prestrain 600 400 200 0 0 1 2 3 4 Punch stroke (mm) Maximum force decreases with increase of pre-strain value. Fracture initiation happens early with increase of pre-strain value. 5/8
[4]. Results; effect of pre-strain on void volume fraction: 0.3 0.25 Void volume fraction 0.2 0% prestrain 5% prestrain 10% prestrain 15% prestrain 0.15 0.1 0.05 0 0 1 2 3 4 Punch stroke (mm) The initial void volume fraction in bending test increases with increase of pre-strain value. Although the initial void volume fraction in the bending test is not significant, this small value has a significant effect on fracture strain. 6/8
[4]. Results; effect of pre-strain on void volume fraction: 0.14 ?? ???? ?= ln ?? 0.13 Bending fracture strain 0.12 0.11 0.1 0.09 0.08 0.07 0.06 0 5 10 15 20 Pre-strain percentage (%) As mentioned earlier, the initial void volume fraction in the bending test is not significant, but this small value has a significant effect on fracture strain. Fracture strain decreases with increase of pre-strain value. 7/8
[5]. Conclusion: The GTN model is able to simulate the three-point bending test and analyze the pre- strain value on bendability in a good agreement with experiment. The initial void volume fraction in bending test increases with increase of pre-strain value. Pre-strain is found to reduce maximum force in the bending test and cause early fracturing. The fracture strain decreases with increase of pre-strain value. 8/8
