Weakening affinity of SUS304 asperities to die surface with TiN coating for preventing delayed cracks in deep-drawn cups

SUS304 stainless steel surface asperities have a strong affinity to tool steel surfaces. Therefore, the flow of material in the flange portion during the deep drawing process is retarded due to adhesive wear, leading to increase in amount of wall thicknening along the cup edge and rising risk for delayed cracks. In this paper, TiN coating is applied to the drawing die surface to weaken the affinity. Under elevated blank holding forces (BHF), the experimental results showed that the crack-free BHF range for the TiN coated and the uncoated dies are 5–10 and 12 kN, respectively. The crack-free BHF magnitude is successfully lowered and the range is enlarged with the coated die. The weakened affinity is evidenced by the low estimated coefficient of friction (COF) obtained from the finite element (FE) simulation. In contrast, the estimated COF of the uncoated die is high even at low BHF due to adhesive wear. Therefore, delayed cracks are observed under BHF range of 7–11 kN. At BHF 12 kN, the amount of wear fragments formed in the boundary layer increases as a result of the continuous polishing of the SUS304 asperities by the uncoated die surface asperities. The COF is sharpyly decreased due to the smooth relative movement of contacting surfaces facilitated by the fragments. Therefore, the cracks are prevented. However, the fragments tend to penetrate into the SUS304 surface under excessive BHF of 13 kN and above resulting in the formation of the cracks again. To eliminate the cracks, drawn cups must achieve threshold values of less than 32.5% wall thickening and more than 33.3 mm cup height in the valley points.


Introduction
SUS304 stainlss steel is a difficult-to-process material due to its strong affinity to tool steel surface. 1 The most common type of stainless steels produced in the world is SUS304 grade. Products such as cookware products, medical equipments and auto parts are made of SUS304. Due to the thermodynamic properties of the metastable austenite phase at room temperature, it tends to transform into a martensitic phase, that is, strain-induced a#-martensite during deformation processes such as deep drawing, leading to increase in hardness. 2 The formation of the delayed cracks is attributed to the coexistent of the internal hydrogen content of material, residual stresses, strain-induced a#martensitic transformation and the chemical composition of the material. 3 The presence of a#-martensite is a necessary prerequisite for delayed cracking to occur in austenitic stainless steels with typical internal hydrogen concentrations (\ 5 ppm). 4 Delayed cracking is a mechanism where a subcritical crack produces timedelayed cracking which there is even no external stress applied to the formed components. 5 Therefore, longitudinal cracks occurs unexpectedly along sidewall of successfully formed SUS304 cups after an incubation period of a few minutes, hours, days or even weeks.
The cracking susceptibility of SUS304 increases with rising a#-martensite content. 6 The variation in a#-martensitic contents under elevated blank holding forces aided by SiO 2 nanolubrication resulting in the formation of crack-free or cracked SUS304 deep drawn cups had been reported. 7 The magnitude of tensile residual stresses is increased with rising amount of straininduced a#-martensitic. 8 The tangential tensile residual stresses that attribute the cracks are considered the most vital. 9 The residual stresses can become very large, that is, up to the yielding stress value in the deep drawing process and cause the appearance of delayed cracks. 10 High concentrations of tensile residual hoop stresses in the valley points along the drawn cup edge after the unloading are obtained in the simulation. 7 Raising the drawing ratio also increases the risk and the severity level of the cracks. 5 The internal hydrogen content of metastable austenitic stainless steel could be reduced by 1-3 wt ppm through heat treatments at 400°C for reduction in risk of delayed cracking. 4 Delayed cracking had been prevented with a deepdrawn temperature of 80°C due to the suppression of the martensitic transformation. 11 In addition, the transformation is also suppressed by the adiabatic heating at high forming rates. Annealing is also effective in removing the residual stresses. However, despite the economic disadvantage, it is also very difficult to maintain the close tolerances and fine surface quality aspects of the products. Cup ironing processes cause a drastic change in the residual stresses resulting in a favourable distribution for preventing the cracks. 10 The variation in amount of wall thickening along the cup edge and the change in cup heights under elevated BHF for the formation of cracked or crack-free cups aided by SiO 2 nanolubrication using an uncoated die had been reported. 12 However, the magnitude and the range of the crack-free BHF are too high and too narrow. SiO 2 nanolubrication had been successfully applied in the deep drawing processes for increase in seizure resistance and in ironing limit. 13,14 A multi-point forming process as a preforming step before conducting the incremental sheet forming processing had been introduced to improve the material flow and the thickness distribution of the sheet parts, resulting in formed parts having a more uniform thickness distribution. 15 Although the reduction in risk for delayed cracks is possible with the incremental sheet metal forming process, the productivity is low. Due to the excellent adhesion to substrates, resistance to elevated temperatures, hard surfaces (2400 Hv) to reduce abrasive wear and a low coefficient of friction, TiN coating has been widely used for cutting tool and dies coating. 16 In sheet metal forming of metallics products, the forming limits such as the limiting drawing ratios, bending limits, etc., are often determined from the localized thinning zones resulting from stretching. The formability of the austenitic stainless steel is markedly enhanced by martensitic transformations during straining. The enhancement is the largest on the biaxial side of the Forming Limit Diagram (FLD) because of the highest martensite fraction in the balanced biaxial strain state. 17 The application of TiN coated tools could significantly reduce the forming loads in deep drawing due to the better lubricating effect. 18,19 Die coating could slightly increase the limiting drawing ratio of the aluminium cups by 4.59%. 19 The drawability is limited by the maximum thinning ratio of the metal in the failure zone. On the other hand, Abe et al. determined the drawability of ultra-high strength steel sheets based on formation of seizures along the outer side wall surfaces of drawn cups under elevated ironing ratios. 20 They concluded that TiN-coated dies lubricated with anti-rust oil only are not suitable for the deep drawing of the cups. TiCN-based cermet die having fine lubricant pockets by polishing a shot-peened surface is effective in preventing the seizure in the ironing of stainless steel drawn cups. 21 The excellent tribology performances of TiN coated tools such as improved wear resistant, high hardness, extended service life, etc., through some tribo-tests such as dry-sliding pin-on-disk, 22 block-ondisc, 23 bending under tension, 24 strip reduction tests, 24 etc., had been reported. The tribological behaviours of uncoated cold work steels in ball-on-disc sliding experiments against austenitic stainless-steel balls had been reported. 1 The adhesion of austenitic slider material to the cold work steels dominates the wear behaviour, ploughing the austenitic slider and protecting the discs from wear. The friction behaviours of the uncoated steels are determined by its carbide content. High carbide content of the steels increases the resistance against ploughing and reduces the adhesive component of the friction coefficient. All tribo-tests above are used to emulate industrial processes (such as deep drawing and ironing) conditions in the laboratory. However, discussions on the effect of the improved tribology performance of TiN coating on increasing the limiting strain of stainless-steel sheets are very limited. The effect of die coating on preventing the formation of delayed cracks in deep drawn SUS304 cups by reducing the amount of wall thickening along the cup edge are yet to be reported.
In this study, the effect of using a finely polished uncoated die and a TiN coated die separately on the formation of delayed cracks in the deep drawing process of SUS304 cylindrical cups under the same experimental and lubrication conditions is investigated. The time taken for the first appearance of the cracks, the total number of cracks, drawing load profiles, cup heights, wall thickness and residual stress distributions are recorded. A 3D FE simulation of the process is performed to estimate the variation in COF under the elevated BHF.

Experimental and simulation conditions
The chemical and mechanical properties of the SUS 304 blanks are shown in Tables 1 and 2, respectively. It is an austenitic steel possessing of a minimum of 18 wt% chromium and 8 wt % nickel or named as 18-8 type stainless steel.
The experimental setup of the deep drawing test is shown in Figure 1. A 25 t motorized hydraulic press compresses a circular blank into a fully drawn cylindrical cup at a constant speed of 1.1 mm/s. The drawing die is positioned right below the blank holder. Six Commercial JSM coil springs (Model CB 40 3 40) having a spring constant of 0.785 kN/mm are inserted into the corresponding circular holes machined inside the upper plate. Compressing the upper plate generates the BHF acting on the blank. Two locking nuts are used to prevent the return of the coil spring and to maintin a constant BHF value during the drawing test. A punch holder is placed at the top of the blank holder to ensure that the central alignment of the punch during the process. A 30 t load cell is placed on top of the drawing punch through a support plate. Then, the press compresses the load cell and the press plate, resulting in the movement of the punch into the die. The distance travel of the punch is recorded by a laser distance meter pointing vertically to the press plate. Since the punch and the press plate are moving together during the compression, the punch travel distance is measured. A data logger with a sampling rate of 10 Hz is used.
The detailed experimental conditions are labelled in the 3D quarter model of deep drawing tool as illustrated in Figure 2(a). The diameter of the punch is f34 mm and the inner diameter of the die is f37.4 mm. Laser-cut circular SUS304 blanks measuring 72.0 mm in diameter with an initial measured sheet thickness of 1.18 mm are used in the experiment. The central alignment of the blank on top of the drawing die is adjusted with a digital calliper. All cups are drawn at its limiting drawing ratio of 2.12. Cutting edges around the circumferences of all blanks are all finely polished with sandpapers to remove the hard oxide layers. The commercial lubricant is applied to the blank holder-blank and the die-blank interfaces, including the die corner. However, the interface of punch bottom-blank, including the punch corner is kept dry. The punch and die corner radii are set at the same value of 5 mm. A punch holder is used to maintain the central alignment of the punch in relative to the die during the drawing test. Each condition is repeated twice to prevent result scattering. An additional test is performed if the first two results are conflicting. The photos of the TiN coated and uncoated drawing dies are shown in Figure 2(b) and (c). Both dies have the same dimensions with different surface conditions. The uncoated die is made of SKD-11 tool steel. Before each drawing test, both the uncoated die and the blank holder are polished with an orbital sander polisher machine at rotational speed of 4000 rpm using sandpapers of Grade 800 followed by Grade 1000. Finally, a solution of diamond paste with particle size ranging from 2 to 4 mm in a compatible diamond lubricant is used in the final stage of the polishing process. However, no polishing is applied to the TiN coated die surface at the beginning of each test. Only the blank holder is polished with the same method as mentioned above. TiN coating is applied to The residual stresses along the sidewall of deepdrawn cups are estimated using a ring slitting method that bases on the concept of residual stress relaxation. Deep drawn cups are sectioned with Electrical Discharge Machining (EDM) into rings. The slit rings obtained for cup heights of 30%, 60%, 80% and 100% from the bottom of the deep-drawn cup. The rings are then slit in the longitudinal direction with EDM to obtain an opening gap. The ring-opening distance, the inner diameter of the ring before slitting and the sidewall thickness of the ring are measured and recorded. The residual stresses, s are then computed using the following formula 25 : Where, E = modulus of elasticity (200 GPa) t = ring wall thickness D 0 = inner ring diameter before slitting d = ring-opening gap s = EDM wire diameter (0.2 mm) The simulation of the deformation process is performed using a commercial ABAQUS/Standard software. The simulation conditions are summarized in Table 3. These values are characterized using specimen no. JIS 13B as specified in JIS Z 2201:1998 standard. The tensile tests are conducted following the JIS Z 2241:2011 standard.
The quarter FE model of the deep drawing process is shown in Figure 3. All tools are modelled as discrete rigid and meshed with four-node tetrahedral elements. The blank has an initial wall thickness of 1.18 mm and is divided into deformable 3D shell elements (four-node doubly thin curved shell, reduced integration and hourglass control) with five integration points across its thickness. Since the solid elements have locking problem during bending, shell elements are used to model the thin sheet in this study as it consumes less disk space for the results and the post-processing of the shells is faster. The average mesh size of the blank is 1.2 mm. The blank is defined as an elastic-plastic  A ring-shaped insert measuring a wall thickness of 1.16 or 0.02 mm less than the blank thickness is added between the holder and the die outside the circumference of the blank to prevent the direct contact between the two rigid tools after the flange being pulled out from the holding region. A lifter is placed right below the blank and in contact with the bottom surface. Both the punch and lifter are displaced by 41.0 and 41.1 mm, respectively, during the drawing process. With the additional 0.1 mm of displacement, the reaction force of the lifter would not increase the peak drawing load of the punch. The total drawing load profile is obtained by subtracting the punch loads from the lifter loads in opposite direction along the displacement. Lifter is used in the simulation only for establishing a more stable contact between the tools and the blank surfaces. A homogenous coulomb friction is assumed for all contact surfaces between the tools and the blank. A penalty friction of 0.5 is assumed for dry contact interfaces of punch/blank and lifter/blank. The penalty friction for the lubricated interfaces, that is, blank-holder/blank and die/blank are estimated by matching the simulated peak loads with the experimental ones for both the coated and uncoated dies. The COF is increased at 0.01 increment for the matching until the necking occur as shown in Figure 3(c). The COF limit of the successful drawn cup are determined. Advanced methods for predicting forming defects such as local thinning in the deep drawing process had been reported. 26 A new dimensionless method for estimating the deep drawing force had also been reported. 27 The only dimensionless parameter that can significantly change the drawing force is the coefficient of friction.
In the deep drawing process, the most severe friction takes place in the flange area. As the blank holder pressure, P b increases, the frictional stress, t also increases based on Coulomb's law t = mP b . Kim et al. estimated the COF of the lubricated holder-blank interface through the FE-based inverse analysis by matching the simulated and the experimental peak values of the load-stroke curves. 28 We use the same method to estimate the COF of the same interface in this study.

Experimental results
The drawn cups formed with the finely polished uncoated die at elevated BHF are presented in Figure 4. The lowest BHF limit for a successful drawn cup is determined at 7 kN as wrinkle is observed in the cup formed at BHF 6 kN. Tearing is observed around the cup bottom due to the stretching by the punch corner during the drawing process under an excessive BHF 16 kN. Therefore, the BHF range for the successful drawn cups is from 7 to 15 kN. Within this range, delayed cracks are observed in all cups except the one for BHF 12 kN. Most of the delayed cracks are observed around the valley points of the cups due to the large amount of wall thickening resulting from the short height. All drawn cups have four ears consisting of four peak and four valley points.
The number of cracks and the time taken for its first appearance in the cups formed with the uncoated die are summarized in Table 4 and presented in Figure 5. The time is recorded immediately after completing the test until the formations of all cracks are complete. It clearly shows that the duration for the first crack increases with increasing BHF. The formation of the cracks is gradually suppressed with increase in BHF. However, the suppression becomes weak when excessive BHFs are applied, that is, from 14 kN and above. A crack-free cup is obtained at BHF 12 kN. The highest number of cracks is obtained at BHF 13 kN, followed by 8 kN and others. The longest duration for the first crack is obtained at BHF 13 kN. The duration sharply decreases for BHF greater than 13 kN.
The drawn cups formed with the TiN coated die at elevated BHF is shown in Figure 6. Wrinkle and tearing around cup bottoms are observed at BHF 4 and 11 kN, respectively. Therefore, the BHF range for successful drawn cups is 5-10 kN. In comparison to the uncoated die, the successful BHF range is reduced from 7-15 to 5-10 kN. The width of the successful BHF range is only 2/3 of the one obtained with the uncoated die. However, the lower BHF limit for the wrinkle-free cups is reduced from 7 to 5 kN. Delayed cracks are not observed in the entire BHF range for successful drawn cups formed with the coated die. Lower and wider BHF ranges are preferred in the industries as it is difficult to maintain a precise, constant and high BHF value with coil springs or die cushion during the process.
The comparison of forming load profiles between cups formed with (a) TiN coated die and (b) Uncoated die is shown in Figure 7. Since the two dies have the same dimensions, typical bell-shape drawing load profiles are obtained for both dies. The increase in drawing load with increasing BHF is very minimal in both cases. Peak drawing loads range from 105 to 115 kN are obtained around 60% of the total punch travel distance for both dies.
The comparison of the experimental and the simulated peak drawing loads between the TiN coated and the uncoated dies under elevated BHF is shown in Figure 8. Overall, the experimental peak loads for the coated die are lower than that of the uncoated die within the same BHF range due to the excellent tribological performance of the coating. For the coated die, the experimental peak loads increased linearly with the elevated BHF as shown in Figure 8(a). This trend agreed well with the Coulomb's law of friction. The COF in the simulation is controlled to match the simulated peak loads with the increasing trend of the experimental data. However, necking is observed around the bottom corner of the cup at BHF 10 kN in the simulation for COF 0.28, resulting in a prediction error of 6.3%. Therefore, a constant COF 0.27 is set for the  Tearing at bottom entire BHF range while maintaining a bias error of 6.9-7.8 kN or 6.3-7.3% between the experimental and the simulated values. In fact, COF 0.3 for SUS304/TiN interface had been reported from a micro-scale abrasion test. 29 The contact boundary condition of the coated die remains unchanged due to the low affinity of the coating layer to the blank surface despite the elevated BHF. Therefore, a constant COF is estimated for the coated die.
In contrast, the change in experimental peak loads for the uncoated die is very minimal, that is, maintained at approximately 113 kN level under elevated BHF due to the change in contact boundary conditions. The decrease in estimated COF from 0.30 to 0.23 under the elevated BHF for the uncoated die is illustrated in Figure 8(b). For BHF 10 kN and above, COF limits ranging from 0.23 to 0.27 are set in the simulation to prevent the necking of the cups. For BHF less than 10 kN, the COF is increased to maintain the same bias error of 7.7-8.9 kN or 6.8-7.8%. The bias error for   BHF 10 kN and above is 7.5-9.9 kN or 6.6-8.8%. Overall, COF decreased with rising BHF under the same lubrication condition. The same downward trend in COF under elevated BHF for cups formed with an uncoated die using SiO 2 nanolubrication had been reported. 12 High drawing load level is recorded for BHF less than 12 kN. This is mainly due to the strong affinity of SUS304 asperities to the uncoated die surface asperities. Cold welds tend to form between both surface asperities under the elevated BHF. The continuous forming and breaking of the cold welds have produced some wear fragments that facilitate the sliding motion of the tool over the blank, resulting in decreasing COF trend. At BHF 12 kN, a sharp decrease in COF from 0.27 to 0.25 is predicted. With the increasing amount of wear fragments, the flow of materials in both radial and hoop directions in the flange portion of the cup is facilitated. This has resulted in increase in tensile radial strain and decrease in compressive hoop strain in the flange portion that are favourable for eliminating the cracks due to less amount of deformation-induced martensite. This is evidenced by the sharp increase in cup height and the less % wall thickening in the high-risk cracking zones, that is, the valley points for BHF 12 kN in the experiment (see Figure 12), resulting in the formation of the crack-free cup. For BHF 13 kN and above, the cup heights and the amount of wall thickening in the valley points returned to normal level due to the excessive number of cold welds and the penetration of the wear fragments into the blank surface asperities under the extreme holding pressure. Friction is determined by the contributions of asperity deformation, adhesion and ploughing by hard asperities and wear debris. 30 Therefore, the favourable conditions could not be maintained resulting in the formation of the cracked cups again.
The comparison of the average heights and the average changes in wall thickness between the drawn cups formed with the TiN coated and uncoated dies at elevated BHF is shown in Figure 9. Overall, the average cup height formed with the coated die is larger than the uncoated die. Large cup heights formed with low BHF could be obtained by applying TiN coating to the die surface. Most of the peak and valley heights are slightly  increased with rising BHF for both dies. The heights for both the coated and the uncoated dies hit peak values at BHF 8 and 12 kN, respectively. Since the only crack-free cup for the uncoated die is obtained at BHF 12 kN, increase in cup height, particularly in the valley points is favourable for eliminating the delayed crack.
Overall, the wall thickness in the valleys for cups formed with the coated die is smaller than that formed with the uncoated die. Therefore, the crack-free BHF range for the coated die is much larger than the uncoated die. For the uncoated die, the minimum wall thickness and the largest cup height in the valley points are obtained at BHF 12 kN and the cracks are successfully eliminated. The relationship between the average changes in wall thickness and the average heights of the peaks and valleys of the crack-free cups formed with the TiN coated die is illustrated in Figure 10. Overall, the amount of wall thickening decreases with increasing cup height until it reaches a turning point at BHF 8 kN. An opposite trend is recorded for BHF greater than 8 kN. Since crack-free cups are formed within the entire BHF range, the threshold values of % wall thickening and cup height in the valley points for eliminating the cracks are determined at 32.5% and 33.3 mm, respectively. Delayed cracking could be eliminated if the cups have less than 32.5% wall thickening and greater than 33.3 mm cup height in the valley points.
The relationship between the average changes in wall thickness and the average heights of the peaks and valleys of the cups formed with the uncoated die is illustrated in Figure 11. Overall, the relationship has a similar trend with the one for the coated die. The turning point representing the largest height and the smallest % wall thickening is obtained at BHF = 12 kN or 50% higher than one with the coated die. The minimum BHF for obtaining a crack-free cup with the coated die is 140% less than the one with the uncoated die (i.e. reduced from 12 to 5 kN).
The longitudinal distributions of residual hoop stresses passing through the valley points along the outer surfaces of the crack-free cups obtained from the ring-slitting test are shown in Figure 12. Overall, the amount of tensile residual stresses of the cup formed with the uncoated die is larger than the ones formed with the coated die in the middle height of the cups due to its high BHF value. For the coated die, the increase in BHF reduces both the magnitude and the slope of the stress distributions for cup height greater than 80%. High stress magnitudes and steep slopes along the upper cup height increase the risk for delayed cracking. Cups formed with the TiN coated die have more favourable residual stress distribution along its outer surface than the one formed with the coated die.

Conclusions
The followings are the summary of the study: (a) The crack-free BHF ranges for the cups formed with the coated and the uncoated dies are 5-10 and 12 kN, respectively. The width of the range is enlarged six times by means of the TiN coating, resulting in a more robust process. (b) A 140% reduction in minimum BHF for obtaining a crack-free cup with the coated die (i.e. reduce from 12 to 5 kN) if compared to the one with the finely polished uncoated die. (c) The elimination of the cracks is mainly due to the decrease in % wall thickening and increase in cup height, particularly in the valley points along its earring profiles. Threshold values of maximum 32.5% wall thickening and minimum 33.3 mm cup height in the valley points are determined for the crack-free drawn cups. (d) Unlike the uncoated die, the estimated COF of the coated die maintains at a low and constant value under the elevated BHF. This is the evidence of the weakened affinity of SUS304 asperities to the TiN coating in comparison to the uncoated die. The flow of material is enhanced in the flange portion resulting in bigger tensile radial strain and smaller compressive hoop strain. (e) The favourable residual stress distribution for eliminating the delayed cracks can be easily obtained with the TiN coated die at BHF values much lower than that with the coated die.

Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.