Fracture Forming Limit Curve Research Articles

Stress and strain based fracture forming limit curves for advanced high strength steel sheet

In this work, strain based fracture forming limit curve (FFLC) of advanced high strength (AHS) steel grade 980 was determined by means of experimental Nakajima stretch-forming test and tensile tests of samples under shear deformation. During the tests, a digital image correlation (DIC) technique was applied to capture the developed strain histories of deformed samples up to failure. The gathered fracture strains from different stress states were used to construct the FFLC. Subsequently, the FFLC in the strain space was transformed to a principal stress space by using plasticity theories. As a result, the fracture forming limit stress curve (FFLSC) of examined steel was obtained. Furthermore, fracture locus (FL) as a relationship between stress triaxialities and critical plastic strains was determined. Hereby, two anisotropic yield functions, namely, the Hill’48 and Yld89 model were taken into account and their effects on the calculated curves were investigated. To verify the applicability of the obtained limit curves, rectangular cup drawing test and forming tests of so-called Diabolo and mini-tunnel samples were performed. Obviously, the FFLSCs and FLs more accurately described the failure occurrences of 980 steel sheets than the FFLCs. In addition, it was found that the drawing depths predicted by the FLs and the Yld89 yield criterion slightly better agreed with the experimental results than those from the FFLSCs and the Hill’48 model, respectively.

Investigation Study on Determination of Fracture Strain and Fracture Forming Limit Curve Using Different Experimental and Numerical Methods

Forming Limit Curve (FLC) is a well-known tool for the evaluation of failure in sheet metal process. However, its experimental determination and evaluation are rather complex. From theoretical point of view, FLC describes initiation of the instability not fracture. During the last years Digital Image Correlation (DIC) techniques have been developed extensively. Throughout this paper, all the measurements were done using DIC and as it is reported in the literature, different approaches to capture necking and fracture phenomena using Cross Section Method (CSM), Time dependent Method (TDM) and Thinning Method (TM) were investigated. Each aforementioned method has some advantages and disadvantages. Moreover, a cruciform specimen was used in order to cover whole FLC in the range between uniaxial to equi-biaxial tension and as an alternative for Nakajima test. Based on above-mentioned uncertainty about the fracture strain, some advanced numerical failure models can describe necking and fracture phenomena accurately with consideration of anisotropic effects. It is noticeable that in this paper, dog-bone, notch and circular disk specimens are used to calibrate Johnson-Cook (J-C) fracture model. The results are discussed for mild steel DC01.

Modeling of the ductile fracture during the sheet forming of aluminum alloy considering non-associated constitutive characteristic

This research was aimed to predict the ductile fracture for aluminum alloy 5083-O sheet using a phenomenological Modified Mohr-Coulomb fracture (MMC) criterion. The plasticity anisotropy of sheet was described by a non-associated constitutive relationship whose yield function and plastic potential function were represented by two different Hill’48 functions. The parameters of Hill’48 functions were calibrated on the basis of yield stresses and Lankford r-values, respectively. The loading paths of critical points for six specimens were utilized to calibrate the parameters of MMC fracture model. The determined non-associated constitutive relationship and MMC fracture model were validated to be able to predict the tension-dominated fracture mode of a modified compact-tension (MCT) specimen as well as shear-dominated fracture of a simple shear specimen. Besides, the fracture forming limit curve expressed by major strain and minor strain was derived directly from the MMC fracture model and its advantages were evaluated by comparing it with the conventional forming limit curve.

A New Method to Calculate Threshold Values of Ductile Fracture Criteria for Advanced High-Strength Sheet Blanking

A new approach is presented in this paper to calculate the critical threshold value of fracture initiation. It is based on the experimental data for forming limit curves and fracture forming limit curves. The deformation path for finally a fractured material point is assumed as two-stage proportional loading: biaxial loading from the beginning to the onset of incipient necking, followed plane strain deformation within the incipient neck until the final fracture. The fracture threshold value is determined by analytical integration and validated by numerical simulation. Four phenomenological models for ductile fracture are selected in this study, i.e., Brozzo, McClintock, Rice-Tracey, and Oyane models. The threshold value for each model is obtained through best-fitting of experimental data. The results are compared with each other and test data. These fracture criteria are implemented in ABAQUS/EXPLICIT through user subroutine VUMAT to simulate the blanking process of advanced high-strength steels. The simulated fracture surfaces are examined to determine the initiation of ductile fracture during the process, and compared with experimental results for DP780 sheet steel blanking. The comparisons between FE simulated results coupled with different fracture models and experimental one show good agreements on punching edge quality. The study demonstrates that the proposed approach to calculate threshold values of fracture models is efficient and reliable. The results also suggest that the McClintock and Oyane fracture models are more accurate than the Rice-Tracey or Brozzo models in predicting load-stroke curves. However, the predicted blanking edge quality does not have appreciable differences.

Strategies and limits in multi-stage single-point incremental forming

Multi-stage single-point incremental forming (SPIF) is a state-of-the-art manufacturing process that allows small-quantity production of complex sheet metal parts with vertical walls. This paper is focused on the application of multi-stage SPIF with the objective of producing cylindrical cups with vertical walls. The strategy consists of forming a conical cup with a taper angle in the first stage, followed by three subsequent stages that progressively move the conical shape towards the desired cylindrical geometry. The investigation includes material characterization, determination of forming-limit curves and fracture forming-limit curves (FFLCs), numerical simulation, and experimentation, namely the evaluation of strain paths and fracture strains in actual multi-stage parts. Assessment of numerical simulation with experimentation shows good agreement between computed and measured strain and strain paths. The results also reveal that the sequence of multi-stage forming has a large effect on the location of strain points in the principal strain space. Strain paths are linear in the first stage and highly non-linear in the subsequent forming stages. The overall results show that the experimentally determined FFLCs can successfully be employed to establish the forming limits of multi-stage SPIF.

Revisiting single-point incremental forming and formability/failure diagrams by means of finite elements and experimentation

In a previously published work, the current authors presented an analytical framework, built upon the combined utilization of membrane analysis and ductile damage mechanics, that is capable of modelling the fundamentals of single-point incremental forming (SPIF) of metallic sheets. The analytical framework accounts for the influence of major process parameters and their mutual interaction to be studied both qualitatively and quantitatively. It enables the conclusion to be drawn that the probable mode of material failure in SPIF is consistent with stretching, rather than shearing being the governing mode of deformation. The study of the morphology of the cracks combined with the experimentally observed suppression of neck formation enabled the authors to conclude that traditional forming limit curves are inapplicable for describing failure. Instead, fracture forming limit curves should be employed to evaluate the overall formability of the process.The aim of this paper is twofold: (a) to compare the mechanics of deformation of SPIF, namely the distribution of stresses and strains derived from the analytical framework with numerical estimates provided by finite element modelling; and (b) to compare the forming limits determined by the analytical framework with experimental values. It is shown that agreement between analytical, finite element, and experimental results is good, implying that the previously proposed analytical framework can be utilized to explain the mechanics of deformation and the forming limits of SPIF.