Materials Processing
Research on the Application of Ductile Fracture Criterion in Fracture Prediction during Sheet Metal Deep Drawing
2022 Volume 63 Issue 8 Pages 1179-1187
Details
2022 Volume 63 Issue 8 Pages 1179-1187
In order to obtain the fracture strain of notched samples, the digital image correlation (DIC) technology is employed in this paper. The values of fracture-related state variables such as stress triaxiality and Lode parameter are obtained through mathematical transformation. The fracture parameters of Lou-Huh ductile fracture criterion (DFC) are calibrated by surface fitting with least square method, and the fracture curve is drawn and applied to the fracture prediction during deep drawing. The reliability of DFC is verified considering fracture stroke and location through tests. The results show that the fracture curve can predict the initiation and location of fracture successfully. Fractures are all predicted in advance under multiple blank holder force (BHF) conditions. Comparison results of finite element (FE) simulation and experiment show that the maximum error of fracture stroke is 12.9% and the fracture locations are generally consistent. The prediction of DFC is partial to safety.
Sheet forming is a complex process with geometrical, material and boundary non-linearities, making it difficult to predict the time and location of fracture accurately. It is also difficult to explore the generation and propagation of fracture from a theoretical point of view. However, it is of great practical significance to predict the fracture of metal materials in the optimization of product and process design.1) With the rapid development of FE simulation technology, judging the deformation behavior of metal materials through FE simulation to provide theoretical support for process research has become one of the effective ways to be widely used. Nevertheless, the prerequisite for obtaining accurate and reliable simulation results is to adopt a criterion model that can accurately describe the deformation behavior of metal materials and the calculation of accurate parameters.
From the microscopic point of view, the fracture of metal materials is a process of pore nucleation, growth and aggregation.2) DFC is based on the micro-fracture characteristics, and considers the influence of micro-defects on the macro-mechanical properties of the metal material during deformation process. So far, a number of scholars have proposed various DFC from different perspectives and introducing different state variables. The Cockcroft criterion, Rice criterion, Oh criterion and OY criterion mentioned in Refs. 3)–6) are the most classical and widely used in recent years. Subsequently, the applicability of various criteria and process validation are investigated by many scholars. Tanaka et al.7) applied FE simulation to four punching arrangements to evaluate the OY and C-L ductile fracture criteria during punching processes, found the different ductile fracture criteria influenced the change of cut surface morphology. Ma et al.8) implanted nine DFCs in ABAQUS to simulate the damage evolution of TA2 pipe during spinning. Experiment results showed that the C-L criterion had a higher forming accuracy for simulating titanium tubing. Asl et al.9) used six DFCs to simulate the flexible rolling forming of channel steel, and explored the influence of process parameters on the fracture phenomenon. It was found that the criterion proposed by Argon was more accurate in predicting fracture. Li et al.10) employed five classic DFCs to simulate the hot stamping of B1500HS steel, and found that the simulation results based on the Oyane and Brozzo criteria were close to the test. In addition, the fracture threshold calculated by regression analysis fitting and correction had better reliability and practicality.
In 2012, Lou et al.11) proposed a new DFC (Lou-Huh) for simulating the nucleation and growth of cavities in sheet metal during plastic deformation. In this new criterion, the cavity nucleation process was described by an equivalent plastic strain correlation function and the cavity growth process was characterised by a stress triaxiality correlation function. In the following year, the DFC was transformed from principal stress space (σ1, σ2, σ3) to (η, L, $\bar{\varepsilon }_{f}$) space, and the effects of stress triaxiality and Lode parameter on the equivalent plastic strain were investigated. It was verified through experiments that it was more suitable than the classical Mohr Coulomb criterion for plastic deformation with large stress triaxiality span.12) Yang et al.13) calculated damage thresholds through integral and analytical expressions for the state variables of DFC obtained from 10 designed notched specimens of AA7075-T6 aluminium alloy sheets by tensile tests, and gave a clear explanation of how to select notched specimens in the solution of fracture parameters through error analysis. Chen et al.14) designed 10 notch tensile tests representing different stress states for solving the fracture parameters of high-strength aluminum alloy sheet by integral equation group method, analytical equation group method and curve fitting method respectively, drew the forming limit diagram by using Lou-Huh DFC. The error evaluation of various calculation methods was made in combination with the bulging test. In order to evaluate the prediction accuracy of Lou-Huh DFC, Dong et al.15) plotted the forming limit curve of AA7075-T6 aluminum alloy according to M-K model and Lou-Huh DFC respectively, and it was verified that the prediction accuracy of Lou-Huh DFC after parameter optimization was higher than that of M-K model through hemispherical rigid die bulging test and error analysis.
| \begin{align} &\left(\frac{2}{\sqrt{3 + L^{2}}} \right)^{C_{1}}\left(\frac{\langle 1 + 3\eta \rangle}{2} \right)^{C_{2}}\bar{\varepsilon}_{f} = C_{3}\\ & \langle 1 + 3\eta \rangle = \begin{cases} 0 & \textit{when $1 + 3\eta < 0$}\\ 1 + 3\eta & \textit{when $1 + 3\eta \geq 0$} \end{cases} \end{align} | (1) |
In the application of DFC, it is crucial to obtain accurate fracture parameters. In the process of tensile test, fracture-related state variables such as stress triaxiality and Lode parameter can not be obtained directly. Therefore, the industry consensus is reached by combining test and FE reverse calculation. Its reliability has been confirmed by process validation, which has been widely used.16,17) In recent years, the development of image recognition and intelligent algorithm technology provides new solutions for the acquisition of material mechanics test data.18) Yang et al.19) proposed a new method for the calibration of DFC utilizing the DIC technique. The image recognition algorithm was adopted to derive the strain field directly and equivalent plastic strain, stress triaxiality and Lode parameter were calculated after mathematical transformation. Lou-Huh DFC was applied as the theoretical basis for the construction of the forming limit diagram of AA7075-T6 sheet, which provided new ideas for the solution of the criterion parameters and evaluation of material properties.
In this paper, the fracture behaviour of 08Al sheet is investigated by a combination of tensile tests and theoretical analysis. Nine notched tensile specimens with different stress states are designed, the complete process from the beginning of deformation to fracture of the sheet is observed by DIC online measurement technique. Critical fracture state variables are calculated, the relationship between ductile fracture strain and stress triaxiality, Lode parameter are obtained, and the fracture curve is plotted using the Lou-Huh fracture criterion and applied to the FE simulation of box-shaped parts deep drawing.
The material used in this paper is 1 mm thick 08Al cold rolled steel sheet with the chemical composition shown in Table 1. 08Al is a kind of high-quality carbon structural steel, which is widely used in the stamping process of parts. A dog-bone specimen as shown in Fig. 1(b) was designed to test the mechanical properties of the material. The samples were cut from the direction of 0°, 45° and 90° with the rolling direction by EDM to test the anisotropy. In order to reduce the influence of cutting on the material properties, slow cutting speed was adopted. A 100 kN universal material testing machine and DIC were employed to conduct the uniaxial tensile tests at a strain rate of 0.004 s−1. The tensile testing machine is equipped with force and displacement sensors to record test data. In order to ensure the reliability of the data, 3 sets of repeated tests were performed for each directional specimen, and the data with good repeatability was selected as the real data of the material.
The tensile test of dog-bone specimen (a) Experimental equipment (b) Shape and size of specimen (mm) (c) True stress-strain curves at 0°, 45° and 90°.
The virtual extensometer function in DIC system was utilised to calculate the true stress-strain curves and anisotropic coefficient of the material. The tensile testing machine and DIC system were synchronous operation. The data of load and displacement were achieved by monitoring the elongation of the specimen at the standard distance length (initial length L0 = 50 mm) in real time by the DIC camera and extracting the tensile machine load data at corresponding time. According to eq. (2) and eq. (3), the true stress-strain curves can be obtained using above data, as shown in Fig. 1(c).
| \begin{equation} \sigma = F \cdot L/\mathrm{A}_{0} \cdot \mathrm{L}_{0} \end{equation} | (2) |
| \begin{equation} \varepsilon = \ln (1 + \Delta L/\mathrm{L}_{0}) \end{equation} | (3) |
| \begin{equation} \sigma = E\varepsilon_{e} \end{equation} | (4) |
| \begin{equation} \sigma = K(\varepsilon_{P} + \varepsilon_{0})^{n} \end{equation} | (5) |
By calculating and fitting the above equations, the basic mechanical property parameters of 08Al sheet are shown in Table 2.
In DIC post-processing software, virtual elongation gauges were established in the length and width directions of the dog-bone specimen to monitor the elongation of the standard distance length and the shortening of the width of the transverse centre line before necking, the plastic strain ratio r for the different orientations were calculated by eq. (6), and the values of anisotropic parameters were calculated according to the equations of the Hill48 anisotropic yield criterion in Table 3.
| \begin{equation} r = \frac{\varepsilon_{b}}{\varepsilon_{t}} = \frac{\varepsilon_{b}}{- \varepsilon_{l} - \varepsilon_{b}} \end{equation} | (6) |
In the process of solving for the ductile fracture parameters, multiple sets of specimen data with different stress states are required to be solved in conjunction. In order to obtain mechanical property parameters of sheet over a wide range of stress triaxiality, it is common to design notched specimens of different shapes and sizes for unidirectional tensile testing in the industry.20–22) In this paper, 9 types of notched specimens were designed as shown in Fig. 2, involving triangular specimens (TRI1, TRI2), shear specimens (SHE1, SHE2, SHE3) and circular arc specimens (ARC1, ARC2, ARC3, ARC4), whose detailed dimensions and numbers are shown in Fig. 2.
Notched specimens.
A 100 kN universal tensile testing machine was employed to perform the tensile test on each specimen. In order to obtain a similar deformation rate, the tensile speed of circular arc and triangular specimen was 12 mm/min, the tensile speed of shear specimen was 5 mm/min. The whole process from deformation to fracture was detected in real time by DIC system. Before the test, the samples cut by EDM were cleaned with alcohol, and then sprayed with white and black paint after natural air drying to obtain the speckle required by DIC. In order to obtain a stable and good quality of scattered spots, it was essential to spray the black paint after 20 minutes of spraying the white paint. In order to prevent the paint from being uncured for a short time or for too long to cause the paint to become brittle and easy to fall off, the paint must be sprayed at a uniform speed to ensure that the speckle thickness and density were consistent.
According to eq. (1), fracture criterion is a function of three state variables, including fracture strain, stress triaxiality and Lode parameter, which are difficult to acquire directly using traditional test methods. In this paper, DIC is used to obtain the full field strain of specimens from the beginning of deformation to fracture. Stress triaxiality and Lode parameter are calculated from the stress field, so it is necessary to solve the stress field from strain field according to the relevant theory of plastic mechanics. Based on the mathematical transformation idea provided by Ref. 19), the fracture related state variables of each notch specimen are obtained.
In the process of sheet metal deep drawing, the thickness stress is very small and can be ignored. Therefore, it is assumed that the stress state of the plate is a plane stress state and the anisotropy is planar isotropy and normal anisotropy. In the principal axis coordinate system, while the anisotropic principal axis coincides with the stress principal axis, eq. (7) and eq. (8) can be derived according to Hill48 anisotropic yield criteria:
| \begin{equation} \bar{\sigma} = \sqrt{\frac{3(1 + \bar{r})}{2(2 + \bar{r})}} \sqrt{\sigma_{1}^{2} - \frac{2\bar{r}}{1 + \bar{r}}\sigma_{1}\sigma_{2} + \sigma_{2}^{2}} \end{equation} | (7) |
| \begin{equation} \bar{\varepsilon} = \sqrt{\frac{2(1 + \bar{r})(2 + \bar{r})}{3(1 + 2\bar{r})}} \sqrt{\varepsilon_{1}^{2} + \frac{2\bar{r}}{1 + \bar{r}}\varepsilon_{1}\varepsilon_{2} + \varepsilon_{2}^{2}} \end{equation} | (8) |
Set stress ratio as α = σ2/σ1, set strain ratio as β = ε2/ε1, under simple loading conditions, it can be obtained from the incremental theory:
| \begin{equation} \alpha = \frac{(1 + \bar{r})\beta + \bar{r}}{1 + (1 + \beta)\bar{r}} \end{equation} | (9) |
The transformation from strain field to stress field can be completed through eq. (9). According to the definition, stress triaxiality and Lode parameter can be expressed by stress ratio (eq. (10) and eq. (11)). Combining eqs. (9)–(11), stress triaxiality and Lode parameter can be expressed by strain field.
| \begin{equation} \eta = \frac{\sigma_{m}}{\bar{\sigma}} = \frac{1 + \alpha}{3\sqrt{\alpha^{2} - \alpha + 1}} \end{equation} | (10) |
| \begin{equation} L = \frac{2\sigma_{2} - \sigma_{1} - \sigma_{3}}{\sigma_{1} - \sigma_{3}} = 2\alpha - 1 \end{equation} | (11) |
The acquisition frequency of tensile testing machine is 50 Hz and that of DIC system is 5 Hz. The data at the same time of the two systems are calculated according to the frequency ratio. In post-processing software, the areas of strain concentration in the sheet are searched in strain cloud, and the moment before the crack starts to appear is regarded as the fracture initiation time. Points on both sides of the crack are taken as fracture points and the values of the first and second principal strain are extracted to calculate the instantaneous strain ratio, which is used to obtain stress triaxiality and Lode parameter at each moment through eqs. (9)–(11). The maximum equivalent plastic strain is considered as the fracture strain.
Through the post-processing of DIC data and the mathematical transformation described above, the trend of the stress triaxiality and Lode parameter with equivalent plastic strain of each notched specimen is obtained, as shown in Fig. 3.
Evolution of stress triaxiality and Lode parameter with plastic deformation: (a) TRI1; (b) TRI2; (c) SHE1; (d) SHE2; (e) SHE3; (f) ARC1; (g) ARC2; (h) ARC3; (i) ARC4.
The parameter calibration of DFC requires the determination of stress triaxiality and Lode parameter. In the process of plastic deformation of metal materials, stress triaxiality and Lode parameter are unstable and change continuously with deformation process. Therefore, how to determine a reliable stress triaxiality and Lode parameter becomes the key to solving the fracture parameters. Many researchers choose to use averaging processing. According to eq. (12) and eq. (13), stress triaxiality and Lode parameter that evolved with the deformation process are averaged, the changed parameters are expressed as average values. This method is proved to be effective by experiments and has been used widely in the industry.23–25)
| \begin{equation} \eta_{\textit{avg}} = \frac{1}{\bar{\varepsilon}_{f}}\int_{0}^{\bar{\varepsilon}_{f}}\eta (\varepsilon_{p}) \mathrm{d}\varepsilon_{p} \end{equation} | (12) |
| \begin{equation} L_{\textit{avg}} = \frac{1}{\bar{\varepsilon}_{f}}\int_{0}^{\bar{\varepsilon}_{f}}L(\varepsilon_{p}) \mathrm{d}\varepsilon_{p} \end{equation} | (13) |
The evolution of stress triaxiality and Lode parameter with plastic deformation in Fig. 4 are averaged according to eq. (12) and eq. (13) to obtain the mean values of the state variables related to DFC of each notch sample, as shown in Table 4.
Ductile fracture surface in ($\bar{\varepsilon }_{f}$, η, L).
According to Lou-Huh DFC equation in eq. (1), there are three unknown fracture parameters C1, C2 and C3 to be determined. Therefore, fracture parameters can be calibrated by combining only three sets of equations with known fracture strain $\bar{\varepsilon }_{f}$, stress triaxiality ηavg and Lode parameter Lavg. In this paper, in order to avoid solution errors due to the small number of specimens, 9 sets of notched specimens are designed to obtain the mechanical parameters of the sheet metal in a wide range of stress triaxiality to solve for fracture parameters, and this is of great significance to improve the precision. To facilitate the solution of fracture parameters, transforming eq. (1) into eq. (14), it is obvious that the fracture strain $\bar{\varepsilon }_{f}$ is a function of the stress triaxiality ηavg and Lode parameter Lavg, noted as $\bar{\varepsilon }_{f} = f(\eta_{\textit{avg}},L_{\textit{avg}})$, and fracture parameters C1, C2 and C3 are the coefficients to be determined for the function. The least square method is used to solve the fracture parameters, and the fitting principle is shown in eq. (15). When the value of eq. (15) is the smallest, C1, C2 and C3 are determined. By fitting the data in Table 4 to the analysis, the fracture parameters C1, C2 and C3 are calculated to be 9.085, 0.2641 and 1.297 respectively, with a fitted variance R2 of 0.8524. The ductile fracture surface in three-dimensional ($\bar{\varepsilon }_{f}$, η, L) space is shown in Fig. 4.
| \begin{equation} \bar{\varepsilon}_{f} = C_{3}\left(\frac{\sqrt{3 + L_{\textit{avg}}^{2}}}{2} \right)^{C_{1}}\left(\frac{2}{1 + 3\eta_{\textit{avg}}} \right)^{C_{2}} \end{equation} | (14) |
| \begin{equation} \sum_{i = 1}^{N}r_{i}^{2} = \sum_{i = 1}^{N}[f(\eta_{\textit{avg}},L_{\textit{avg}};C_{1},C_{2},C_{3}) - \bar{\varepsilon}_{fi}]^{2} = \min \end{equation} | (15) |
As can be seen from Fig. 4, when Lode parameter is constant, the fracture strain of 08Al sheet decreases with the increase of stress triaxiality. The reason is that the increase of stress triaxiality promotes the diffusion of micro pores and reduces the plasticity of the material. When the stress triaxiality is constant, the fracture strain of 08Al sheets tends to decrease as the Lode parameter approaches 0. When the value of Lode parameter is −1, the fracture strain reaches the maximum value. This may be due to the fact that the elongation and torsional mechanisms of the holes are enhanced with the value of τmax/σeq increases, thereby reducing the fracture strain of the material.26)
3.3 Drawing of fracture curveThe purpose of calibrating the parameters of the DFC is to guide practice and serve production through theoretical calculations and FE simulation, as well as to select the applicable judgement criterion for different processes and materials. There is a special interface for simulating material damage and fracture on FE simulation platform ABAQUS, but the software needs the relationship curve between fracture strain and stress triaxiality, so it is necessary to convert the three-dimensional ductile fracture surface in ($\bar{\varepsilon }_{f}$, η, L) space in Fig. 5 into a two-dimensional curve ($\bar{\varepsilon }_{f}$, η). According to eq. (10) and eq. (11), stress triaxiality and Lode parameter both can be expressed by strain ratio α, so it is theoretically feasible to convert three-dimensional fracture surface into two-dimensional fracture curve. In the plane stress condition, the stress triaxiality from −1/3 to 2/3 cover a variety of stress states from unidirectional compression to equi-biaxial tension, which covers the possible stress triaxiality spatial range in sheet drawing. Reference 27) derived a relationship between the stress triaxiality and the Lode parameter in the range (−1/3 2/3) and brought into Lou-Huh DFC to express the fracture strain in terms of a single variable stress triaxiality η (eq. (16)). Based on the fracture parameters C1, C2, and C3 calculated in the previous section, the Lou-Huh ductile fracture curve in ($\bar{\varepsilon }_{f}$, η) space shown in Fig. 5 is obtained by two-dimensional transformation of the fracture surface in different stress triaxiality intervals by eq. (16).
| \begin{equation} \begin{cases} \bar{\varepsilon}_{f} = \dfrac{C_{3}}{2^{C_{1}}[(1 + 3\eta)/2]^{C_{2}}} \times \left[\left(\dfrac{27\eta^{2} + \sqrt{108\eta^{2} - 243\eta^{4}}}{4 - 9\eta^{2} + \sqrt{108\eta^{2} - 243\eta^{4}}} \right)^{2}{} + 3 \right]^{C_{1}/2} & \text{$- \dfrac{1}{3} < \eta < 0$}\\ \bar{\varepsilon}_{f} = \dfrac{C_{3}}{2^{C_{1}}[(1 + 3\eta)/2]^{C_{2}}} \times \left[\left(\dfrac{27\eta^{2} - \sqrt{108\eta^{2} - 243\eta^{4}}}{4 - 9\eta^{2} - \sqrt{108\eta^{2} - 243\eta^{4}}} \right)^{2} {}+ 3 \right]^{C_{1}/2} & \text{$0 \leq \eta < \dfrac{1}{3}$}\\ \bar{\varepsilon}_{f} = C_{3} & \text{$\eta = \dfrac{1}{3}$}\\ \bar{\varepsilon}_{f} = \dfrac{C_{3}}{[(1 + 3\eta)/2]^{C_{2}}} \times \dfrac{1}{\left\{2\Big/\sqrt{\big[(3 - \sqrt{108\eta^{2} - 243\eta^{4}})/(9\eta^{2} - 1)\big]^{2} + 3} \right\}^{C_{1}}} & \text{$\dfrac{1}{3} < \eta < \dfrac{2}{3}$}\\ \bar{\varepsilon}_{f} = \dfrac{C_{3}}{(3/2)^{C_{2}}} & \text{$\eta = \dfrac{2}{3}$} \end{cases} \end{equation} | (16) |
($\bar{\varepsilon }_{f}$, η) fracture curve.
In order to verify the applicability and reliability of the DFC calibrated in this paper, a drawing experiment of box-shaped parts was carried out. 08Al cold rolled sheet with thickness of 1 mm was used for the test on a 500 T hydraulic press in the laboratory. The drawing speed was 30 mm/min and lubricated with oil-based drawing lubricating oil. The test equipment and die are shown in Fig. 6. BHF was controlled by three groups of A71 butterfly springs. The butterfly spring was calibrated for spring stiffness through compression test, and deformed at 75% of the maximum compression to prevent damage to the spring. The exact BHF was obtained by accurately measuring the spring compression. The detailed dimensions of die and sheet are shown in Fig. 7. The sheet was cut by wire cutting and polished to prevent the die straining.
Test equipment and die: (a) Test equipment; (b) Schematic diagram of die.
Size specifications of die and sheet (mm): (a) Die; (b) Sheet.
In this paper, ABAQUS Standard/Explicit FE simulation software was employed to simulate the drawing process of box-shaped parts. The material model was the same as that used for the deep drawing experiment. Hill48 anisotropic yield criterion was adopted in the simulation, and the anisotropic coefficients and true stress-strain curve have been calculated in the above section. In FE simulation, the dies were set as discrete rigid and the plate was meshed with solid element. The shape and dimensions of the simulation model were consistent with those of the process test in Fig. 7. The simulation model is shown in Fig. 8.
Simulation model.
It is difficult to predict the forming limit of sheet metal drawing through theoretical calculation, especially for non-axisymmetric components such as rectangular parts. Therefore, it is of great significance to carry out FE simulation for process design and blank planning. Under the conditions of 50 kN, 60 kN, 70 kN, and 80 kN BHF, drawing process of box-shaped parts were simulated using the fracture curve constructed in this paper based on Lou-Huh DFC. Fracture was considered to have occurred when grid cracks were found and elements disappeared. Assume that the drawing depth at the breaking time of experiment is Hi, the drawing depth at the breaking time of FE simulation is hi, and the error is si = |Hi − hi|/Hi. The results of FE simulation and experiment were compared as shown in Fig. 9.
Results comparison of experiment and FE simulation: (a) Q = 50 kN; (b) Q = 60 kN; (c) Q = 70 kN; (d) Q = 80 kN.
As shown in Fig. 9, in the test, there is no fracture at a drawing depth of 65 mm under the condition of 50 kN BHF, the strokes at the moment of fracture gradually decrease as BHF increasing under the conditions of 60 kN, 70 kN and 80 kN, and the values are 53.6 mm, 48.2 mm and 46.2 mm respectively. This is due to the fact that as BHF increasing, the resistance to flow of sheet in the flange area increases, which leads to an increase in forming force and fracture occurrence. In the FE simulation implanted fracture curve, fracture occurs at 57.8 mm when BHF is 50 kN. It is a conservative prediction compared to the test with an error of 11.1%. Under the conditions of 60 kN, 70 kN, and 80 kN BHF, the strokes at the time of fracture gradually decrease with the increase of BHF, the values are 46.7 mm, 43.5 mm and 41.9 mm respectively. The trend is consistent with the test results. The fracture strokes of FE simulations under 60 kN, 70 kN and 80 kN BHF are all smaller than the test results, which indicates the safety of the predictions utilizing fracture criterion calculated in this paper, with errors of 12.9%, 9.8% and 9.3% respectively.
5.2 Comparative analysis of fracture locationsDuring sheet forming process, fracture often first appears at regions of stress concentration. Therefore, stress concentration should be avoided in the die design and the maximum stress should be avoided at main area in the structure design. As shown in Fig. 9, fracture position is at the side wall when BHF is 50 kN in FE simulation, while there is no fracture at the same location in the experiment, so there is a deviation between FE simulation and experiment. In FE simulation, when BHF is 60 kN, 70 kN and 80 kN respectively, the earliest fracture position is at the fillet at the bottom of boxes, which is consistent with experiment results. It indicates that the stress concentration at the fillet of the punch is the most serious during the sheet forming process under this die size.
In addition, an attempt is made in the simulation to increase the size of the die fillet to reduce stress concentration under the same conditions of other process parameters. As can be seen in Fig. 10, when r1 (Fig. 7(a)) increases to 15 mm, fracture strokes and locations both change under the conditions of 60 kN, 70 kN, and 80 kN BHF, the values of punch strokes are 59.4 mm, 47.0 mm and 44.2 mm respectively when fracture occurs. The punch fillet increases from 10 mm to 15 mm, the maximum fracture stroke increases by 27.2%. At the same time fracture locations change, which transfer from box bottom fillet to side wall. This indicates that increasing the fillet radius can reduce stress concentration and delay fracture. In deep drawing process, straight wall of the box-shaped part thins under the action of tensile stress and the load-bearing capacity is reduced, resulting in the transfer of fracture locations to straight wall. FE simulation results show that the implementation of fracture criteria in FE simulation has certain guiding significance for predicting the sheet forming performance and optimizing the size of die structure.
Simulation results of punch fillet r1 = 15 mm: (a) Q = 50 kN; (b) Q = 60 kN; (c) Q = 70 kN.
The authors would like to thank the staff of Forging and Packaging laboratory (Yanshan University) for their great help and suggestions in the experiment.
