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A New Ductile Fracture Criterion for the Formability Prediction of Steel Sheets and Its Application to Finite Element Analysis (강판의 성형성 예측을 위한 새로운 연성 파괴 조건 및 유한 요소 해석에의 응용)
Sheet metal forming, one of the most important metal working operations, concerns with the shaping of thin metal sheets (normally less than 6 mm or ¼ in.) by applying force to punches and drawing sheets into dies. There processes are accomplished basically by stretching, bending, deep drawing, embossing, bulging, flanging, rolling, and spinning. There are three important issues in sheet metal forming processes: failure, wrinkling and excessive springback. Failure is the focus of this study. Two failure mechanisms are dominant for metals forming: necking and ductile fracture. Necking failure occurs in tension of conventional carbon steels while ductile fracture is observed for advanced high strength steel sheets not only in tension but also in compression and pure shear such as upsetting tests.
Necking is widely accepted as the main failure model from the uniaxial tension to the balanced biaxial tension for sheet metals. Failure due to necking is normally expressed by forming limit diagrams (FLDs). In the last decades, many experiments are carried out to construct FLDs of sheet metal alloys such as steel, aluminum and magnesium. Many theoretical models are proposed to predict FLDs such as the Hill’s localized necking model, the Swift’s diffuse necking model, the popular Marciniak and Kuczynski model (M-K model), the vertex theory and the modified maximum force criterion (MMFC). The analytical models above are mainly applied to predict formability of sheet metals based on necking or thickness reduction. Consequently, failure cannot be estimated by these models in low or negative stress triaxiality where there is no or negligible thickness reduction.
Metals and alloys usually fail as ductile fracture induced by nucleation, growth and coalescence of microscopic voids. Therefore, ductile fracture occurs in a wide stress state from compressive upsetting to the balanced biaxial tension.
A ductile fracture criterion is proposed to model fracture behavior of sheet metals for nucleation, growth and shear coalescence of voids during plastic deformation. In the new ductile fracture criterion, void nucleation is described as a function of the equivalent plastic strain, void growth is a function of the stress triaxiality and void coalescence is controlled by the normalized maximal shear stress. The new ductile fracture criterion is applied to construct a fracture forming limit diagram (FFLD) of a dual phase steel sheets of DP780 (1.0t). The FFLD is approximated using both the reverse engineering method and circle grid analysis (CGA) since DP780 fails with negligible thickness reduction from the analysis of the fracture surface. Predicted FFLDs are compared to experimental results to validate the performance of the new criterion in the intermediate stress triaxiality between 1/3 and 2/3. The new criterion is also applied to construct the fracture locus of Al 2024-T351 to validate the performance of the new criterion in the low and negative stress triaxiality. The fracture locus constructed by the new criterion are close to the experimental data points for all these two materials in a wide stress range from the uniaxial compression to the balanced biaxial tension. The new ductile fracture criterion is recommended to be utilized in finite element analysis to predict the onset of ductile fracture of sheet metals.
The new micro-mechanism-motivated ductile fracture criterion is extended to a general three-dimensional stress space with dependence on the stress triaxiality and the Lode parameter. The effect of the stress triaxiality and the Lode parameter on the equivalent plastic strain to fracture is investigated in the space of (),,Lηε. For the purpose of comparison, the Mohr-Coulomb criterion is also transformed into the space of (),,Lηε using the technique of the Mohr’s circles. Both criteria are applied to construct fracture loci of Al 2024-T351. Fracture loci constructed are compared to experimental data points to validate the performance of two criteria. The comparison demonstrates that fracture loci constructed by two criteria are close to experimental results except for two data points in the high stress triaxiality. The big difference between two criteria is that a cut-off value for the stress triaxiality is extremely small for the Mohr-Coulomb criterion while the new ductile fracture criterion endows a constant cut-off value of –1/3 which is reasonable for ductile materials. Due to this limitation of the Mohr-Coulomb criterion, the new criterion is more suitable to model ductile fracture in metal forming processes.
The new ductile fracture criterion is applied to predict the onset of ductile fracture for nine specimens with special designed shapes which cover a wide range of stress states from shear to plane strain tension for the validation of the new ductile fracture criterion. The new ductile fracture criterion is first calibrated by the equivalent plastic strain to fracture measured by the hybrid experimental-numerical method from three type specimens of DP980 sheet: specimens with a central hole, plane strain tensile specimens and in-plane shear specimens. The calibrated criterion is utilized to construct the fracture locus of DP980. The constructed fracture locus is then employed into ABAQUS/Explicit to predict the onset of fracture for these three specimens. Another three notched specimens are further designed for the validation of the new criterion from uniaxial tension to plane strain tension by comparison of experimental results to those numerically predicted by the new criterion. Moreover, three types of shear tensile specimens are utilized to validate predictability of the new ductile fracture criterion between shear and uniaxial tension. The validation suggests that the new ductile fracture criterion can accurately predict the onset of fracture for these specimens. High accuracy reveals that the new criterion can correctly describe ductile fracture behaviors of metals in a wide stress state from shear to the plane strain tension. In addition, fractographic analysis of fracture surfaces demonstrates that coalescence of voids is caused by shear linking-up of voids, which is assumed by the new ductile fracture criterion.
The cut-off value for the stress triaxiality is investigated experimentally and abstractively. The investigation presents that the cut-off value is dependent on materials and the Lode parameter. The changeable cut-off value with dependence on the Lode parameter is coupled by slightly modification of the original ductile fracture criterion. The Lode dependence of the cut-off value, however, is not easily determined experimentally or analytically. Thus, a suggestion is proposed for the Lode dependence of the cut-off value. By proper modeling of the Lode dependence of the cut-off value, the modified criterion is observed to have great flexiblity to describe a reasonable cut-off value for materials with different ductility.