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The effect of microstructure on the formability of stainless steel sheets is a major concern for sheet metalworking engineers. For austenitic steels, the presence of deformation martensite (\({\alpha}^{^{\prime))\)-martensite) in the microstructure leads to significant hardening and a decrease in formability. In this study, we aimed to evaluate the formability of AISI 316 steels with different martensitic strengths by experimental and artificial intelligence methods. In the first step, AISI 316 steel with an initial thickness of 2 mm was annealed and cold rolled to various thicknesses. Subsequently, the relative strain martensite area was measured by metallographic testing. The formability of the rolled sheets was determined using a hemisphere burst test to obtain a strain limit diagram (FLD). The data obtained as a result of the experiments is further used to train and test the artificial neuro-fuzzy interference system (ANFIS). After ANFIS training, the dominant strains predicted by the neural network were compared to a new set of experimental results. The results show that cold rolling has a negative effect on the formability of this type of stainless steel, but the strength of the sheet is greatly improved. In addition, ANFIS shows satisfactory results compared to experimental measurements.
The ability to form sheet metal, although the subject of scientific articles for decades, remains an interesting area of research in metallurgy. New technical tools and computational models make it easier to find potential factors affecting formability. Most importantly, the importance of microstructure for shape limit has been revealed in recent years using the Crystal Plasticity Finite Element Method (CPFEM). On the other hand, the availability of scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) helps researchers observe the microstructural activity of crystal structures during deformation. Understanding the influence of different phases in metals, grain size and orientation, and microscopic defects at the grain level is critical to predicting formability.
Determining formability is in itself a complex process, as formability has been shown to be highly dependent on paths 1, 2, 3. Therefore, the conventional notions of ultimate forming strain are unreliable under disproportionate loading conditions. On the other hand, most load paths in industrial applications are classified as non-proportional loading. In this regard, traditional hemispherical and experimental Marciniak-Kuchinsky (MK) methods4,5,6 should be used with caution. In recent years, another concept, the Fracture Limit Diagram (FFLD), has attracted the attention of many formability engineers. In this concept, a damage model is used to predict sheet formability. In this regard, path independence is initially included in the analysis and the results are in good agreement with the unscaled experimental results7,8,9. Formability of a sheet metal depends on several parameters and the processing history of the sheet, as well as on the microstructure and phase of the metal10,11,12,13,14,15.
Size dependence is a problem when considering the microscopic features of metals. It has been shown that, in small deformation spaces, the dependence of vibrational and buckling properties strongly depends on the length scale of the material16,17,18,19,20,21,22,23,24,25,26,27,28,29,30. The effect of grain size on formability has long been recognized in the industry. Yamaguchi and Mellor [31] studied the effect of grain size and thickness on the tensile properties of metal sheets using theoretical analysis. Using the Marciniac model, they report that under biaxial tensile loading, a decrease in the ratio of thickness to grain size leads to a decrease in the tensile properties of the sheet. Experimental results by Wilson et al. 32 confirmed that reducing the thickness to the average grain diameter (t/d) resulted in a decrease in the biaxial extensibility of metal sheets of three different thicknesses. They concluded that at t/d values of less than 20, noticeable deformation inhomogeneity and necking are mainly affected by individual grains in the thickness of the sheet. Ulvan and Koursaris33 studied the effect of grain size on the overall machinability of 304 and 316 austenitic stainless steels. They report that the formability of these metals is not affected by grain size, but small changes in tensile properties can be seen. It is the increase in grain size that leads to a decrease in the strength characteristics of these steels. The influence of the dislocation density on the flow stress of nickel metals shows that the dislocation density determines the flow stress of the metal, regardless of the grain size34. Grain interaction and initial orientation also have a great influence on the evolution of aluminum texture, which was investigated by Becker and Panchanadiswaran using experiments and modeling of crystal plasticity35. Numerical results in their analysis are in good agreement with experiments, although some simulation results deviate from experiments due to limitations of the applied boundary conditions. By studying crystal plasticity patterns and experimentally detecting, rolled aluminum sheets show different formability36. The results showed that although the stress-strain curves of the different sheets were almost the same, there were significant differences in their formability based on the initial values. Amelirad and Assempour used experiments and CPFEM to obtain the stress-strain curves for austenitic stainless steel sheets37. Their simulations showed that the increase in grain size shifts upward in the FLD, forming a limiting curve. In addition, the same authors investigated the effect of grain orientation and morphology on the formation of voids 38 .
In addition to grain morphology and orientation in austenitic stainless steels, the state of twins and secondary phases is also important. Twinning is the main mechanism for hardening and increasing elongation in TWIP 39 steel. Hwang40 reported that the formability of the TWIP steels was poor despite sufficient tensile response. However, the effect of deformation twinning on the formability of austenitic steel sheets has not been sufficiently studied. Mishra et al. 41 studied austenitic stainless steels to observe twinning under various tensile strain paths. They found that twins could originate from decay sources of both annealed twins and the new generation of twins. It has been observed that the largest twins form under biaxial tension. In addition, it was noted that the transformation of austenite into \({\alpha}^{^{\prime}}\)-martensite depends on the strain path. Hong et al. 42 investigated the effect of strain-induced twinning and martensite on hydrogen embrittlement over a range of temperatures in selective laser melting of 316L austenitic steel. It was observed that, depending on the temperature, hydrogen could cause failure or improve the formability of 316L steel. Shen et al. 43 experimentally measured the volume of deformation martensite under tensile loading at various loading rates. It was found that an increase in tensile strain increases the volume fraction of the martensite fraction.
AI methods are used in science and technology because of their versatility in modeling complex problems without resorting to the physical and mathematical foundations of the problem44,45,46,47,48,49,50,51,52 The number of AI methods is increasing. Moradi et al. 44 used machine learning techniques to optimize chemical conditions to produce finer nanosilica particles. Other chemical properties also influence the properties of nanoscale materials, which has been investigated in many research articles53. Ce et al. 45 used ANFIS to predict the formability of plain carbon steel sheet metal under various rolling conditions. Due to cold rolling, the dislocation density in mild steel has increased significantly. Plain carbon steels differ from austenitic stainless steels in their hardening and restorative mechanisms. In simple carbon steel, phase transformations do not occur in the metal microstructure. In addition to the metal phase, the ductility, fracture, machinability, etc. of metals are also affected by several other microstructural features that occur during various types of heat treatment, cold working, and aging54,55,56,57,58,59,60. , 61, 62. Recently, Chen et al. 63 studied the effect of cold rolling on the formability of 304L steel. They took into account phenomenological observations only in experimental tests in order to train the neural network to predict formability. In fact, in the case of austenitic stainless steels, several factors combine to reduce the tensile properties of the sheet. Lu et al.64 used ANFIS to observe the effect of various parameters on the hole expansion process.
As briefly discussed in the review above, the effect of microstructure on the shape limit diagram has received little attention in the literature. On the other hand, many microstructural features must be taken into account. Therefore, it is almost impossible to include all microstructural factors in analytical methods. In this sense, the use of artificial intelligence can be beneficial. In this regard, this study investigates the effect of one aspect of microstructural factors, namely the presence of stress-induced martensite, on the formability of stainless steel sheets. This study differs from other AI studies with regard to formability in that the focus is on microstructural features rather than just experimental FLD curves. We sought to evaluate the formability of 316 steel with various martensite contents using experimental and artificial intelligence methods. In the first step, 316 steel with an initial thickness of 2 mm was annealed and cold rolled to various thicknesses. Then, using metallographic control, the relative area of martensite was measured. The formability of the rolled sheets was determined using a hemisphere burst test to obtain a strain limit diagram (FLD). The data received from him was later used to train and test the artificial neuro-fuzzy interference system (ANFIS). After ANFIS training, the neural network predictions are compared to a new set of experimental results.
The 316 austenitic stainless steel metal sheet used in the present study has a chemical composition as shown in Table 1 and an initial thickness of 1.5 mm. Annealing at 1050°C for 1 hour followed by water quenching to relieve residual stresses in the sheet and obtain a uniform microstructure.
The microstructure of austenitic steels can be revealed using several etchants. One of the best etchants is 60% nitric acid in distilled water, etched at 1 VDC for 120 s38. However, this etchant only shows grain boundaries and cannot identify double grain boundaries, as shown in Fig. 1a. Another etchant is glycerol acetate, in which twin boundaries can be well visualized, but grain boundaries are not, as shown in Fig. 1b. In addition, after the transformation of the metastable austenitic phase into the \({\alpha }^{^{\prime}}\)-martensite phase can be detected using the glycerol acetate etchant, which is of interest in the current study.
Microstructure of metal plate 316 after annealing, shown by various etchants, (a) 200x, 60% \({\mathrm{HNO}}_{3}\) in distilled water at 1.5 V for 120 s, and (b) 200x, glyceryl acetate.
The annealed sheets were cut into sheets 11 cm wide and 1 m long for rolling. The cold rolling plant has two symmetrical rolls with a diameter of 140 mm. The cold rolling process causes the transformation of austenite to deformation martensite in 316 stainless steel. Looking for the ratio of the martensite phase to the austenite phase after cold rolling through different thicknesses. On fig. 2 shows a sample of the microstructure of sheet metal. On fig. 2a shows a metallographic image of a rolled sample, as viewed from a direction perpendicular to the sheet. On fig. 2b using ImageJ65 software, the martensitic part is highlighted in black. Using the tools of this open source software, the area of the martensite fraction can be measured. Table 2 shows the detailed fractions of the martensitic and austenitic phases after rolling to various reductions in thickness.
Microstructure of a 316 L sheet after rolling to a 50% reduction in thickness, viewed perpendicular to the plane of the sheet, magnified 200 times, glycerol acetate.
The values presented in Table 2 were obtained by averaging the measured martensite fractions over three photographs taken at different locations on the same metallographic specimen. In addition, in fig. 3 shows quadratic fitting curves to better understand the effect of cold rolling on martensite. It can be seen that there is an almost linear correlation between the proportion of martensite and thickness reduction in the cold rolled condition. However, a quadratic relationship can better represent this relationship.
Variation in the proportion of martensite as a function of thickness reduction during cold rolling of an initially annealed 316 steel sheet.
The shaping limit was evaluated according to the usual procedure using hemisphere burst tests37,38,45,66. In total, six samples were fabricated by laser cutting with the dimensions shown in Fig. 4a as a set of experimental samples. For each state of the martensite fraction, three sets of test specimens were prepared and tested. On fig. 4b shows cut, polished, and marked samples.
Nakazima molding limits sample size and cutting board. (a) Dimensions, (b) Cut and marked specimens.
The test for hemispherical punching was carried out using a hydraulic press with a travel speed of 2 mm/s. The contact surfaces of the punch and sheet are well lubricated to minimize the effect of friction on forming limits. Continue testing until a significant narrowing or break is observed in the specimen. On fig. 5 shows the destroyed sample in the device and the sample after testing.
The shaping limit was determined using a hemispherical burst test, (a) test rig, (b) sample plate at break in the test rig, (c) the same sample after testing.
The neuro-fuzzy system developed by Jang67 is a suitable tool for leaf formation limit curve prediction. This type of artificial neural network includes the influence of parameters with vague descriptions. This means that they can get any real value in their fields. Values of this type are further classified according to their value. Each category has its own rules. For example, a temperature value can be any real number, and depending on its value, temperatures can be classified as cold, medium, warm, and hot. In this regard, for example, the rule for low temperatures is the rule “wear a jacket”, and the rule for warm temperatures is “enough T-shirt”. In fuzzy logic itself, the output is evaluated for accuracy and reliability. The combination of neural network systems with fuzzy logic ensures that ANFIS will provide reliable results.
Figure 6 provided by Jang67 shows a simple neural fuzzy network. As shown, the network takes two inputs, in our study the input is the proportion of martensite in the microstructure and the value of minor strain. At the first level of analysis, input values are fuzzified using fuzzy rules and membership functions (FC):
For \(i=1, 2\), since the input is assumed to have two categories of description. The MF can take on any triangular, trapezoidal, Gaussian, or any other shape.
Based on the categories \({A}_{i}\) and \({B}_{i}\) and their MF values at level 2, some rules are adopted, as shown in Figure 7. In this layer, the effects of the various inputs are somehow combined. Here, the following rules are used to combine the influence of the martensite fraction and minor strain values:
The output \({w}_{i}\) of this layer is called the ignition intensity. These ignition intensities are normalized in layer 3 according to the following relationship:
In layer 4, the Takagi and Sugeno rules67,68 are included in the calculation to take into account the influence of the initial values of the input parameters. This layer has the following relationships:
The resulting \({f}_{i}\) is affected by the normalized values in the layers, which gives the final result, the main warp values:
where \(NR\) represents the number of rules. The role of the neural network here is to use its internal optimization algorithm to correct unknown network parameters. The unknown parameters are the resulting parameters \(\left\{{p}_{i}, {q}_{i}, {r}_{i}\right\}\), and the parameters related to the MF are considered generalized wind chimes shape function:
The shape limit diagrams depend on many parameters, from the chemical composition to the deformation history of the sheet metal. Some parameters are easy to evaluate, including tensile test parameters, while others require more complex procedures such as metallography or residual stress determination. In most cases, it is advisable to carry out a strain limit test for each batch of sheet. However, sometimes other test results can be used to approximate the shaping limit. For example, several studies have used tensile test results to determine sheet formability69,70,71,72. Other studies included more parameters in their analysis, such as grain thickness and size31,73,74,75,76,77. However, it is not computationally advantageous to include all allowed parameters. Thus, the use of ANFIS models may be a reasonable approach to address these issues45,63.
In this paper, the influence of the martensite content on the shaping limit diagram of a 316 austenitic steel sheet was investigated. In this regard, a data set was prepared using experimental tests. The developed system has two input variables: the proportion of martensite measured in metallographic tests and the range of small engineering strains. The result is a major engineering deformation of the forming limit curve. There are three types of martensitic fractions: fine, medium and high fractions. Low means that the proportion of martensite is less than 10%. Under moderate conditions, the proportion of martensite ranges from 10% to 20%. High values of martensite are considered to be fractions of more than 20%. In addition, secondary strain has three distinct categories between -5% and 5% near the vertical axis, which are used to determine FLD0. Positive and negative ranges are the other two categories.
The results of the hemispherical test are shown in FIG. The figure shows 6 shaping diagrams of limits, 5 of which are the FLD of individual rolled sheets. Given a safety point and its upper limit curve forming a limit curve (FLC). The last figure compares all FLCs. As can be seen from the last figure, an increase in the proportion of martensite in 316 austenitic steel reduces the formability of the sheet metal. On the other hand, increasing the proportion of martensite gradually turns the FLC into a symmetrical curve about the vertical axis. In the last two graphs, the right side of the curve is slightly higher than the left, which means that the formability in biaxial tension is higher than in uniaxial tension. In addition, both minor and major engineering strains before necking decrease with increasing proportion of martensite.
316 forming a limit curve. Influence of the proportion of martensite on the formability of austenitic steel sheets. (safety point SF, formation limit curve FLC, martensite M).
The neural network was trained on 60 sets of experimental results with martensite fractions of 7.8, 18.3 and 28.7%. A data set of 15.4% martensite was reserved for the verification process and 25.6% for the testing process. The error after 150 epochs is about 1.5%. On fig. 9 shows the correlation between the actual output (\({\epsilon }_{1}\), basic engineering workload) provided for training and testing. As you can see, the trained NFS predicts \({\epsilon} _{1}\) satisfactorily for sheet metal parts.
(a) Correlation between predicted and actual values after the training process, (b) Error between predicted and actual values for the main engineering loads on the FLC during training and verification.
At some point during training, the ANFIS network is inevitably recycled. To determine this, a parallel check is performed, called a “check”. If the validation error value deviates from the training value, the network starts to retrain. As shown in Figure 9b, before epoch 150, the difference between the learning and validation curves is small, and they follow roughly the same curve. At this point, the validation process error starts to deviate from the learning curve, which is a sign of ANFIS overfitting. Thus, the ANFIS network for round 150 is preserved with an error of 1.5%. Then the FLC prediction for ANFIS is introduced. On fig. 10 shows the predicted and actual curves for the selected samples used in the training and verification process. Since the data from these curves was used to train the network, it is not surprising to observe very close predictions.
Actual experimental FLC and ANFIS predictive curves under various martensite content conditions. These curves are used in the training process.
The ANFIS model does not know what happened to the last sample. Therefore, we tested our trained ANFIS for FLC by submitting samples with a martensite fraction of 25.6%. On fig. 11 shows the ANFIS FLC prediction as well as the experimental FLC. The maximum error between the predicted value and the experimental value is 6.2%, which is higher than the predicted value during training and validation. However, this error is a tolerable error compared to other studies that predict FLC theoretically37.
In industry, the parameters that affect formability are described in the form of a tongue. For example, “coarse grain reduces formability” or “increased cold working reduces FLC”. Input to the ANFIS network in the first stage is classified into linguistic categories such as low, medium and high. There are different rules for different categories on the network. Therefore, in industry, this type of network can be very useful in terms of including several factors in their linguistic description and analysis. In this work, we tried to take into account one of the main features of the microstructure of austenitic stainless steels in order to use the possibilities of ANFIS. The amount of stress-induced martensite of 316 is a direct consequence of the cold working of these inserts. Through experimentation and ANFIS analysis, it has been found that increasing the proportion of martensite in this type of austenitic stainless steel leads to a significant decrease in the FLC of plate 316, so that increasing the proportion of martensite from 7.8% to 28.7% reduces the FLD0 from 0.35. up to 0.1 respectively. On the other hand, the trained and validated ANFIS network can predict FLC using 80% of the available experimental data with a maximum error of 6.5%, which is an acceptable margin of error compared to other theoretical procedures and phenomenological relationships.
The datasets used and/or analyzed in the current study are available from the respective authors upon reasonable request.
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Post time: Jun-08-2023