A new void coalescence mechanism during incremental sheet forming: Ductile fracture modeling and experimental validation
Graphical abstract
Introduction
Incremental sheet forming shows promising advantages in the flexible deformation of sheet metal without relying on conventional press and tooling system. The method of ISF process exerts cyclic and localized deformation incrementally to the edge-restrained sheet metal by a forming tool with semi-spherical end, as shown in Fig. 1. The sheet metal part with complex geometry can be obtained after the tool moves along the designed three-dimensional path. ISF was verified to significantly improve the formability and forming limit of sheet metal compared with stamping or tensile process by Jeswiet et al.(2005), but the root reason for the improved formability has not been fundamentally revealed yet. Therefore, the deformation mechanism and ductile fracture behavior of ISF process have attracted lots of instructive researches.
Jeswiet and Young (2005) considered that the bending effect, through-thickness stress and shearing are the primarily mechanisms in ISF process. Emmens and Boogaard (2008) proposed that bending effect, shearing stress and cyclic loading maintain the dominant effect on affecting the fracture behavior of ISF process. After investigation of deformation mechanisms, Jackson and Allwood (2009) indicated that the circumferential and meridianal stretching and through-thickness shearing are the dominated mechanisms. Malhotra et al.(2012) found that the shearing inhibits damage accumulation while bending has the effect of expediting the process. To reveal the inhibition of necking during ISF, Seong et al.(2014) proposed stress-based criterion for forming limit prediction of ISF after considering the gradient of through-thickness stress. Silva et al.(2016) established an analytical model of fracture strain based on the consideration of ductile damage and void behavior during ISF process. Liu et al.(2020) developed a ultra high-strength steel with intensive and controlled cracks at grain boundaries normal to thickness direction. Crack under plane strain state is transformed into parallel and stratified cracks through the thickness direction, which significantly improves the formability of sheet metal. This method offers a feasible way to obtain superior plasticity by controlling the direction of void coalescence or crack propagation.
The Gurson-Tvergaard-Needleman (GTN) void-based criterion is a widely-used model of predicting the ductile fracture for porous materials. Gurson (1977) developed a continuous damage model through the representative volume element analysis to describe the void growth and its effect on the ductile fracture at maximum principle stress components. To consider the effect of void mechanism on damage accumulation, Tvergaard (1981) and Tvergaard and Needleman (1984) extended the Gurson model, and established the classic GTN model. Assuming that material failures when the porosity reaches a critical value, the Gurson model is not only used to consider the void evolution of ductile materials in macro level, but also to predict ductile fracture behavior. However, GTN model is not applicable to the prediction of shear-dominated ductile fracture.
To consider the void shearing mechanism, Xue (2008) introduced a separate variable of shear damage and extended the GTN model, which can be described by the third stress invariant. Nielsen and Tvergaard (2010) proposed an extension to better describe the damage contribution under low triaxiality shearing condition, and extended the application of GTN model in high or low stress triaxiality. Malcher et al.(2014) developed a shear mechanism term under low stress triaxiality described by the Lode parameter, stress triaxiality and equivalent plastic strain, and introduced a shear-dominated formulation to describe fracture behavior. Jiang et al.(2016) and Zhou et al.(2014) modified the widely-used GTN model by introducing shear and volumetric damage parameters into flow potential and yield function.
Li et al.(2015) applied the shear-modified GTN model to analyze the failure behavior of ISF, and found that the maximum value of porosity is much larger than the critical value obtained by tension tests. Guzmán et al.(2018) deployed the shear- extended GTN model for the prediction of fracture strain in ISF, and found that the original GTN model significantly underestimates the fracture strain in ISF. An improvement of prediction failure results was obtained by physically delaying the onset of coalescence. It can be concluded that original GTN models are not applicable to the accurate prediction of ductile fracture behavior during ISF process, which needs to be further extended based on the deformation mechanism of ISF.
In the present work, a micro-scale investigation of oriented void coalescence and its effect on ductile fracture behavior during ISF process is conducted. The evolution and micro-mechanism of closely-packed void clusters by this new coalescence is investigated and an extended ductile fracture model with the consideration of void clusters is developed. First, the void evolution, especially the void coalescence and closely-packed void clusters, during ISF under the influence of through-thickness stress is observed and studied. The significant improvement of sheet formability during ISF process is considered to be attributed to the formation of void clusters along meridianal direction rather than thickness direction, which may stably exist in the sheet metal even after void coalescence. Besides, independent parameters describing geometric characteristics of closely-packed void clusters are introduced into Thompson coalescence model of GTN, and the extended GTN model is established to predict ductile fracture during ISF. Finally, the established ductile fracture model is validated with high accuracy and wide applicability through a series of experiments for AA2024 and AA6061 materials. The influence of void coalescence approach on ductile fracture, and the influences of different deformation modes, material properties and deformation parameters on forming limit are all considered in this extended model. Therefore, this study provides an in-depth understanding for the mechanism of oriented-coalescence based ductile fracture, and reveals the fundamental mechanism of improved formability of sheet metal formed by ISF process.
Section snippets
Experimental methodology
The uniaxial tension experiments are conducted to determine the related GTN parameters of selected materials, and ISF experiments are also carried out to investigate the void evolution and ductile fracture behavior. The sheet materials used in this work are AA2024 and AA6061, and the comparison of forming limit between tension and ISF process is conducted to investigate the ductile fracture behavior. Fig. 2 shows the designed dimensions of parts for uniaxial tension and ISF experiments. As
GTN model
A continuous damage model for isotropic materials was proposed by Gurson (1977), which takes hydrostatic stress into account to capture the growth of void in damage accumulation process. Based on the consideration of the voids behavior, this model was extended by Tvergaard and Needleman (1984) to solve the problem of elastic-plastic damage. The classical plastic damage of GTN is expressed by Gurson potential Ф as shown in Eq. (1).
The Mises stress is
Parameter calibration
At first, seven related parameters (f0, fN, fc, ff, εN, sN, kw) in GTN model need to be calibrated for the validation of the developed model. By embedding subroutine VUMAT into ABAQUS, the simulation of extended GTN model can be validated through the comparison of experimental values. Four solid elements through the thickness in a implicit model and Mises yield criterion are deployed for AA2024 and AA6061 with sheet thickness as 1 mm. Uniaxial tension tests of AA2024 and AA6061 are simulated by
Conclusions
In the present work, a new void coalescence mechanism for ISF is investigated and the effect of void cluster on the ductile fracture is identified and revealed. An extended ductile fracture model is developed to consider the effect of oriented void cluster during ISF. The following conclusions are drawn.
- 1)
A new void coalescence mechanism which the voids coalesce closely along meridianal direction rather than thickness direction and grow steadily is figured out. The improved formability in sheet
CRediT authorship contribution statement
Zhidong Chang: Conceptualization, Methodolog y, Formal analysis, Investigation, Writing - original draft, Visualization, Resources, Validation, Software, Data curation. Jun Chen: Writing - review & editing, Supervision, Project administration, Funding acquisition.
Declaration of Competing Interest
The authors report no declarations of interest.
Acknowledgement
The authors are grateful for the financial supports from National Natural Science Foundation of China through grant #U1737210 and the Program of Shanghai Excellent Academic Research Leadership through grant #19XD1401900.
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