A critical review on hole expansion ratio

Journal Pre-proof

A critical review on hole expansion ratio Surajit Kumar Paul PII: DOI: Reference:

S2589-1529(19)30362-X https://doi.org/10.1016/j.mtla.2019.100566 MTLA 100566

To appear in:

Materialia

Received date: Accepted date:

7 October 2019 13 December 2019

Please cite this article as: Surajit Kumar Paul , A critical review on hole expansion ratio, Materialia (2019), doi: https://doi.org/10.1016/j.mtla.2019.100566

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd on behalf of Acta Materialia Inc.

A critical review on hole expansion ratio Surajit Kumar Paul Department of Mechanical Engineering, Indian Institute of Technology Patna, Bihta, Bihar 801106, India * [email protected], [email protected]

Abstract Materials resistance to edge fracture in intricate shape forming is commonly quantified by hole expansion ratio (HER). Hole expansion test is normally used to evaluate HER. To date, the governing factors of HER have not well understood regardless of its importance for automotive part manufacturing with advanced high-strength steels. The present paper comprehensively discussed the recent progress on HER, including fundamental deformation aspects, the effect of punch geometries, correlation with tensile properties, and the influence of microstructure. This reviewed work explains why HER is currently an essential topic of engineering research.

Keywords: hole expansion ratio, uniaxial tensile test, punch geometry, edge defect, microstructure

1. Introduction A flange on a sheet metal component can be formed by deforming the sheet free edge with a bending operation. Flanges are incorporated in the design to provide rigidity of panels or fasten the parts together. The edge of a flange can be stretch, shrink, or remain undeformed depending upon the shape of the component. In stretch flanging, stretching of the material takes place tangentially to the free edge, and simultaneous shrinking occurs along the perpendicular direction to the free edge. Classic examples of stretch flanges in the automobile industry include cut‐ outs in automotive inner panels, corners of the window panel and hub‐ hole of wheel discs, etc. The failure by necking and cracking take place during stretch flanging operation when the circumferential strain is large enough. The limiting criteria below which sheet material should

not fail during stretch flanging operation can express as a hole expansion ratio (HER) [1-5]. HER can define as (1) Where df and d0 are the final and initial diameter of the central hole. HER can be quantified from the hole expansion test. The schematic diagram of a hole expansion test is illustrated in Figure 1 (according to the ISO 16630 standard), where a conical punch with a cone angle of 60o has expanded a central hole of 10 mm diameter. The dimension of the hole expansion test specimen is usually 100 mm x 100 mm (Figure 2). Other punch shapes like flat bottom and hemispherical shapes (non-standard tests) are also used by researchers [1-5]. Recently, advanced high strength steels (AHSS) are increasingly adopted by automobile companies to improve fuel efficiency and to reduce emission without sacrificing passenger’s safety [1-2]. However, cracking during stretch flanging operation of AHSS is the major restriction in their use [1-2]. Figure 3 shows visible cracks in the formed automotive components after the cold forming of AHSS steel. Such edge cracking is unacceptable in modern production and should be appropriately addressed during the design phase, although such problems do not arise for mild steels [6-7]. Classical forming limit diagram (FLD) is unable to predict such type of edge cracking during stretch flanging [1]. To address such edge cracking, HER is successfully used as a failure criterion and has become one of the essential formability parameters for sheet metal forming operation. Through extensive research works on HER or stretch flangeability was started after 2010, though literature can be found on this topic even in 1948. Taylor [8] derived the elastic-plastic numerical solution for the expansion of a pin-hole in a thin sheet by radial pressure. Taylor assumed that material was isotropic and non-work-hardening type. Yoahida [9] studied various flanging operations extensively, including shrink flanging, stretch flanging, and bending. He has considered isotropic and work-hardening type material in this numerical investigation, and also reported experimental findings like a rupture in the flange. Wang and Wenner [10] numerically modeled hole expansion problem by using plane stress plasticity theory incorporating anisotropy and nonlinear strain hardening. Wang and Wenner [10] and Wang et al. [11] reported that localization during hole expansion depends upon the coefficient of normal anisotropy (r) and strain hardening exponent (n) of the material. Yamada et al. [12] reported that the stress state and

deformation in the edge of the hole are uniaxial tension. They also have suggested that hole expansion may be affected by strain hardening, normal anisotropy and strain rate sensitivity (m) of the material. Karima et al. [13] studied the hole expansion with a flat bottomed punch and reported that hole edge deforms in a uniaxial tensile manner and punch profile deforms in a biaxial tensile way. Matsuzu et al. [14] reported that the material’s microstructure could alter the shape of the burr generated during the punching process, damage/crack in punched hole edge, and finally, the hole expansion property. Afterward, extensive research work has been conducted on different aspects of HER on various materials, and which has been reviewed in detail sectionwise in this present article.

2. Fundamentals of HER The stress state at the central hole edge of the hole expansion test sample is roughly uniaxial tensile [1-3]. Almost all researchers have reported this fact from the beginning. Paul et al. [15] and Paul [16] conducted a finite element simulation of hole expansion test on EDD and DP steel sheets respectively. The distribution of hoop strain at the time of failure is illustrated in figure 4(a) and the progression of strain paths is described in figure 4(b). Almost pure uniaxial tensile deformation path (ε1=-2ε2) is followed at the central hole edge during hole expansion test. Figure 4(c) shows the alteration of in-plane maximum principal strain along the increasing distance from the central hole edge. Maximum principal strain (i.e., hoop strain) is evident at the central hole edge and it gradually decreases with increasing distance from the central hole edge. The hoop strain is almost zero, where the sheet specimen is held by upper and lower dies. Therefore, one significant difference between uniaxial tensile and hole expansion tests is the deformation gradient. Deformation is homogeneous at least in macro-scale for uniaxial tensile tests before necking, while a clear deformation gradient is noticed for hole expansion test. The schematic illustration of HER in the classic fracture and forming limit diagram is shown in Figure 5 (a). In forming limit diagram, the path of uniaxial tensile deformation depends upon the coefficient of normal anisotropy (r) and can be described by equation 2. (2)

Two uniaxial tensile deformation paths are shown in Figure 5 (a). For higher r-value, the deformation path shifts towards the left side. The red color forming limit curve denotes the initiation of localized necking. Therefore for high r-value, localized necking commences much latter, i.e., higher axial strain. Experimental forming limit curve and HER for DP 600 (data are collated from Pathak et al. [1]) are plotted in Figure 5 (b). HER with reamed and punched hole edge are included in this plot. HER with a punched hole edge is located under the forming limit curve. However, HER with a reamed hole edge is positioned above the forming limit curve. This indicates that forming limit curve unable to explain the HER. Depending upon hole edge condition, HER can be placed above or below the forming limit curve. Researchers unanimously accepted that the uniaxial tensile stress state exists at the central hole edge during hole expansion test. However, researchers [1, 15-20] also reported that uniaxial tensile tests or tensile properties (like ultimate tensile stress, yield stress, total elongation, uniform elongation, etc.) are not enough to predict HER. Therefore, it will be exciting to find out the difference between the uniaxial tensile test and hole expansion test. The differences may direct us to improve the understanding of HER. The differences can be stated as follows: (i) In a uniaxial tensile test, the deformation is uniform along the width of the sample before necking, while a prominent deformation gradient presents for hole expansion test sample (Figure 4(c)). The maximum hoop strain is detected at the edge of the central hole and zero at the location where upper and lower dies to hold the sample. (ii) In a uniaxial tensile test, crack is visible in the necked zone only while multiple cracks may be evident at the full central hole edge at any location in a hole expansion test. (iii) Two free edges are present along its width for the uniaxial tensile test sample, whereas one free edge (i.e., central hole edge) is present in a hole expansion test sample. Another side of the central hole edge is held between upper and lower dies, and zero deformation is detected in that area. (iv) The sheet sample bends twice, one about the punch radius and second time around die radius during the hole expansion test. Those differences may create a discrepancy in the localization and failure of two different test samples. Paul [21] reported that necking in uniaxial tensile and hole expansion tests are different. In a uniaxial tensile test, usually diffuse necking followed by localized necking is detected. However, the diffuse necking is absent/delayed in the hole expansion test with a smooth hole edge [21]. This difference in necking can be schematically represented in Figure 7.

Wang et al. [10] and Wang et al. [11] reported that localized necking takes place by considering uniaxial stress state according to equation 3.

(3) Where ε1 is hoop/circumferential stain, n is the strain hardening exponent, r is the coefficient of normal anisotropy, and εpre is the amount of pre-strain. According to equation 3, HER should increase with strain hardening exponent and coefficient of normal anisotropy. But Chen et al. [22], Paul [16], and Yoon et al. [18] reported that those two parameters are not sufficient to predict HER for various materials. By carefully reviewing the published literature on steel, it can be summarized that the HER depends upon punch geometry, edge preparation, mechanical property and microstructure of the material (Figure 6). Details of each factor have discussed in detail in the next section. Martínez-Donaire et al. [23] have conducted hole-flanging tests by single-stage single point incremental forming over AA7075-O sheet of 1.6 mm thickness. They have obtained very high stretch flangeability as stable plastic deformation can be obtained up to sheet fracture during a single point incremental forming. In this process, local necking is suppressed, and failure takes place at fracture strains, i.e., at fracture limit curve (Figure 5(a)). Therefore, the highest stretch flangeability for a particular material can be obtained from a single point incremental forming.

3. Effect of punch geometry on HER According to the ISO 16630 [24] standard, the hole expansion test is conducted with a conical punch and cone angle of 60o. However, researchers have conducted hole expansion tests with other punch geometries like hemispherical and flat-bottom punches [1-5]. Hole expansion tests with hemispherical and flat-bottom punches are not standardized methods; however, researchers used in their investigation. Konieczny and Henderson [25] have noticed highest HER for conical punch, intermediate HER for hemispherical punch, and lowest HER for flat-bottom punch. Stanton et al. [4] also reported that conical punch usually produces superior HER than the flatbottom punch for aluminum alloys with various edge conditions. Similar findings are also reported by Pathak et al. [1] for dual-phase and complex phase steels, Madrid et al. [26] for dualphase 980 and 1180 steel sheets. Neuhauser et al. [27] explained that failure gets delayed due to

bending in the stretch bend test. Pathak et al. [1] also reported an important finding that the HER with a flat-bottom punch is insensitive to hole edge condition. Paul [28] did extensive finite element simulation with different punch geometries to find out the explanation for such a response. Geometries of flat-bottom, hemispherical, and conical punches are portrayed in Figure 8(a). Paul [28] reported that the failure is initiated at the central hole edge for conical punch, while failure is initiated slightly away from the central hole edge (not at the edge, but inside) for hemispherical and flat-bottom punches. Pathak et al. [1] and Suzuki et al. [29] also have reported same experimental observation for flat-bottom punch, while Yoon et al. [30], Paul et al. [15, 16] and others [2-5] have reported identical experimental finding for conical punch. Therefore, the location of failure initiation and HER values alter with punch geometry. The reason behind this behavior can be explained in Figure 8(b). Experimental forming limit data of DP 600 steel is collected from Pathak et al. [1]. The strain paths at the failure locations are plotted in a diagram of major strain (ε1) versus minor strain (ε2). The strain path is purely uniaxial tensile for conical punch, purely plane strain tensile for flat-bottom punch, and complex for hemispherical punch (initially tensile, followed by biaxial tensile and lastly plane strain tensile). Paul [28] pointed out that variation in the deformation path for different punch geometries is the prime cause of such difference in HER value. He also reported that as the failure location is slightly away from the central hole edge for flat-bottom and hemispherical punches, so hole edge condition has little effect on HER for those punch geometries. Finite element simulation data is collected from Paul [28], and experimental data are collected from Pathak et al. [1] for Figure 9. Just before the initiation of necking, the strain ratio (ratio of in-plane minimum and maximum principal strains) is plotted against distance (along the width and moving away from the hole edge) for various punch geometries. As von Misses yield function is used in this study, the strain ratio = 0.5 indicates uniaxial tension, the strain ratio = 0 specifies plane strain tension, and strain ratio = 1.0 indicates equi-biaxial tension. Regardless of any punch geometry, uniaxial tensile deformation takes place at the edge of the hole (Figure 9(a)). However, the deformation mode sharply alters with punch geometries. For flat-bottom and hemispherical punches, the plane strain deformation state reached slightly away from the hole edge. As the necking limit reaches early in case of plane strain condition, necking and failure happen in that location (slightly away from the hole edge) for flat-bottom and hemispherical punches. For that reason, Paul [28] pointed out that the failure condition in the hole expansion

test with hemispherical and flat-bottom punches is closely similar to the forming experiment (Nakajima test) with a plane strain condition. Therefore, Paul [28] concluded that hole expansion tests with conical punch only could provide the true stretch-flangeability of sheet metals.

4. Effect of hole preparation on HER Researchers reported from hole expansion test with a conical punch that the hole preparation technique has a vital role in the HER [1, 31-33]. Hance et al. [34] reported that different hole preparation methods like punching, milling, wire-EDM cutting, laser cutting, etc. can introduce various levels of damage at the hole edge. Kadarno et al. [35] reported that maximum damage happens in the hole preparation by a punching process because the material is essentially forced to undergo catastrophic failure through shear. Figure 10 shows a schematic diagram of a punched edge, i.e., shears affected zone (SAZ). It has distinct three zones, they are (i) shear drop or burnish region, (ii) sheared surface, and (iii) fractured surface. A burr is normally visible at the bottom of the fractured surface. The presence of voids and crack especially near the sheared and fractured surfaces, are reported by various research groups [19, 36-37]. Edge of a punched dualphase steel sheet with YS of 395MPa and UTS of 769 MPa is collected from Levy et al. [33]. Dual-phase steel has soft ferrite and hard martensite phases. In the shear drop zone, rotation and elongation of both ferrite grains and martensite islands are observed. By calculating the aspect ratio before and after shear, the extent of severe deformation during the shearing process can be recognized. Due to high plastic deformation in the ferrite phase, strain hardening and exhaustion of ductility also take place in the shear affected zone. Levy et al. [33] even have observed elongation of the hard martensite islands. They reported that the shear affected zone exists within 3-20 microns from the shear face. Researchers [25, 38] reported that the shear affected zone is depended upon the clearance during the punching process. The clearance can be stated as (4) where dd and dp are die and punch diameters, dp is usually 10 mm, and t is the thickness of the test piece (all in millimeters) [24]. Shear drop (i.e., rollover) and shear surface (i.e., burnishing zone) are depended on clearance [25, 38]. The size of the fractured region and burr height are controlled by the tensile strength of the sheet [25, 38]. Levy and Van Tyne [36] reported that shearing is a high strain rate deformation process, and strain path is close to pure shear. They also reported that the high deformed region present behind the sheared edge up to 200 microns.

Lee et al.[39] reported that ideal pure shear deformation does not occur during the shearing process, rather stress and strain gradients are present in the SAZ. Dalloz et al.[40] have noticed voids up to 200 microns from the shear face for DP steel. Inside the shear affected zone, clear evidence of void is detected (Figure 11). The presence of voids and cracks near the shear edge for different materials have reported many researchers [19, 36-37, 41-42]. Therefore, the preexistence of defects (voids and cracks) near the hole edge severely influences the HER with a punched hole. As a consequence, Casellas et al. [17], Yoon et al. [18, 19], and Paul [20] have used fracture based concepts to correlate HER. A detailed discussion regarding this will be done in the next section. In all hole preparation methods like punching, milling, wire-EDM cutting, laser cutting, etc., damage zone near hole edge is expected. The severity and size of the damage zone finally control HER. Branagan et al. [43] did a hole expansion test with different hole conditions on three 3rd generation AHSS. Experimental data for Figure 12 is collected from Branagan et al. [43]. They reported that HER values are the lowest for all three alloys in the case of punched holes, while HER values are the highest for EDM cut and milled holes. The sheared edge is not symmetric from top and bottom, and a burr is located at the bottom surface (Figure 10). Paul [16] and Paul et al. [15] reported that maximum hoop strain accumulates at the outer (i.e., top) edge of the center hole of hole expansion test sample. Voids (i.e., defects) are located at the burr and fracture surface, while no voids are visible at the shear drop region. Therefore, maximum damage takes place during punching at the bottom or inner edge of the hole expansion test sample. As a consequence, burr up position shows lower HER, while burr down position shows little better HER [1.] Karelova et al. [37] reported from their optical microscopy investigation that the level of plastic deformation near the hole edge decreasing in the order of punched surface, drilled and wire cut surface. They have also noticed circumferential cracks on the edge of the drilled hole. Paul [44] has conducted hole expansion test on DP steel with two different hole edge preparation methods. The uniform elongation of DP steel is around 17.5%, the HER with a punched hole edge is 30%, while the HER with an EDM cut hole edge is 110%. The hole edge after the hole expansion test is shown in Figure 13. After the hole expansion test, one through-thickness crack and a large number of small cracks are visible for punched hole edge sample, while only two through-thickness cracks are evident for EDM cut hole edge sample. Paul [21] reported from the

experiment with digital image correlation and finite element simulation that delay/suppression of diffuse necking consequences higher HER for a sample with EDM cut hole. During the hole expansion test, the central hole edge is exposed to maximum deformation, i.e., hoop strain. Different hole preparation methods result in different central hole edge conditions. HER highly depends upon the central hole edge condition, so HER depends upon the hole preparation method [21, 37, 43]. Moreover, the work hardening of the SAZ during mechanical shearing should be small enough to confirm sufficient remaining deformation capacity for edge forming. After initial hole preparation, any secondary operation to improve central hole edge condition may result in improvement in HER [1]. For example, the polishing of punched hole edge results in an enhancement in HER [1].

5. Effect of mechanical properties on HER In section 2, from finite element simulation results clearly, reveal that the stress state at the central hole edge during hole expansion test is uniaxial tensile. As a result, many researchers try to correlate HER (samples with punched central hole edge) with various tensile properties like yield stress (YS) [2, 16], ultimate tensile stress (UTS) [2, 16, 45], YS/UTS [46], total elongation (TEL) [16, 47], post uniform elongation (PUEL) [16, 30, 47-49], reduction of area (ROA) [1], strain hardening exponent (n) [48], strain rate sensitivity (m) [22, 30, 48], coefficient of normal anisotropy (r) [16, 22, 48] etc. Apart from those, many researchers try to correlate HER (samples with punched central hole edge) with fracture parameters like fracture toughness (K1C, J1C) [17, 19], notch mouth opening displacement (NMOD) [20], etc. as pre-existing defects present at the punched hole edge before starting hole expansion test. In the uniaxial tensile test, initiation of necking is the primary step of failure. Therefore, parameters influence necking likely to have a strong correlation with HER. Wang et al. [10, 11] reported that strain hardening exponent (n) and the coefficient of normal anisotropy (r) (Equation 3) control HER. Chen et al. [22] re-examined Equation 3 from experimental results and reported that the coefficient of normal anisotropy (r) and strain rate sensitivity (m) has a prominent correlation with HER. Yoon et al. [30] also have reported a strong correlation between HER and strain rate sensitivity (m). Sadagopan et al. [2] confirmed that HER has a wonderful relationship with UTS and coefficient of normal anisotropy (r). They also noticed that HER had no correlation with thickness. Pathak et al. [1] have presented a positive correlation between HER

and reduction of area (ROA) for commercial DP and complex phase steels. Jin et al.[50] determined HER on IA QP, DP and TRIP steels with different thicknesses and noticed that HER variations between different edge preparations are minimum for materials with low strain hardening exponents. They explained that lesser strain hardening exponent results in minor hardness enhancement at the hole edge during edge preparation. Paul [16] has collected HER and different tensile properties from literature and has derived a correlation between HER and tensile properties. Figure 14 shows that HER has a positive correlation with YS, UTS, r, TEL, and PUEL. Sheared edge central hole is used in the hole expansion test for all HER data reported in Figure 14. All steel sheets are commercially available sheets; no further processing (e.g., heat treatment) is done before the hole expansion test. Paul [16] proposed that post uniform elongation is a crucial parameter for HER. He also noticed that HER had no correlation with YS/UTS, strain hardening exponent (n), and uniform elongation (UEL). Finally, Paul [16] has proposed a non-linear correlation between HER and tensile properties of steel. The non-linear correlation can be described as (5) where HER is the hole expansion ratio in %, et is the total elongation in %, r is the coefficient of normal anisotropy, and σUTS is the ultimate tensile stress. From the above discussion, it can be summarized that the coefficient of normal anisotropy (r) and strain rate sensitivity (m) have an immense role in necking resistance and, consequently, HER. Similarly, as diffuse necking is absent/delayed in HER with a conical punch, so PUEL has an excellent correlation with HER. Figure 15 summarizes the critical tensile properties affecting HER. Usually, dimples and micro-cracks are present at the punched hole edge. During the hole expansion test, stress concentration at defects and defect growth resistance will control macro crack initiation and, finally, HER. For that reason, Casellas et al. [17] and Yoon et al. [19] have correlated HER (samples with punched central hole edge) with the fracture toughness of the commercially available steel sheets, and Paul [20] has also related HER (samples with punched central hole edge)

with notch mouth opening displacement (NMOD) of the commercially

available steel sheets. Figure 16 (a) shows a positive correlation between HER and fracture toughness, while Figure 16 (b) illustrates a linear relationship between HER and NMOD. Mechanical properties determined from destructive testing are closely related to resistance to failure, i.e., necking and fracture resistance. HER determined from the punched hole normally

controlled by the material’s resistance to local necking or resistance to the growth of existing defects [17-20]. Therefore, HER and mechanical properties of the metal are linked, but one to one correlations are not viable because of the alteration of deformation form and complexity. Generally, HER improves with the enhancement of the post uniform elongation, strain rate sensitivity, and fracture toughness (i.e., MNOD) of the metal [16, 17, 19, 20, 22, 30]. 6. Effect of microstructure on HER Microstructural characteristics such as volume fraction and morphology of the hard phase, strength difference between soft and hard phases, the volume fraction of retained austenite, etc. have an immense influence on HER. Figure 17 illustrates schematically the main microstructural factors that can affect HER. Researchers reported that HER of dual-phase steel depends upon volume fraction of martensite [26], the difference in hardness between ferrite and martensite [5153] i.e., the carbon content in martensite [51-54], and morphology of martensite [60]. Larger the strength or hardness difference between ferrite and martensite results in higher strain localization on the ferrite phase by hard martensite islands and finally inferior HER [51-53]. Taylor et al. [53] did the nano-indentation measurement in ferrite and martensite phases individually and observed that punched-hole HER improves with reducing the ratio of hardness in martensite and ferrite phases. Terrazas et al. [52] did hole expansion testing on commercially available DP steels sample with a punched central hole and reported that fine and evenly distribution of martensite colonies provide more impediments for crack propagation, and as a result, HER is improved. Terrazas et al. [52] have determined martensite colonies per unit area for various dual-phase steels. Figure 18 shows that HER has an excellent correlation with martensite colonies per unit area. For Figure 18, experimental data are collected from Terrazas et al. [52]. Kim et al. [54] and Miura et al. [55] noticed that plastic deformation takes place in interconnected martensite, and failure gets delayed by reducing deformation localization in ferrite, and finally, HER improves. Madrid et al. [26] observed that HER decreases with increasing martensite volume fraction, and martensite morphology influence HER more at a high volume fraction of martensite. However, they also stated that maximum HER could be possible for around 50% volume fraction of martensite or fully martensitic alloy [49, 51-52, 54]. Sudo et al.[56] have observed a reduction of HER with the increase in martensite island size from 2 to 4 microns, and little or no effect in HER after further increment of martensite island size to 12 microns.

Takahashi et al.[57] and Sudo et al.[58] illustrated that HER of ferrite-bainite steel is better than ferrite-martensite steel. Sudo et al.[56] also explained that with the increase of volume fraction hard phase from 2.5% to 20 %, results in a drastic reduction of HER for ferrite-martensite steels and moderate reduction of HER for ferrite-bainite steel. They explain these experimental facts by a proposal that voids initiate at bainite in higher strains than martensite. Sudo et al.[56] noticed that voids initiate at approximately 20% strain by cracking of martensite islands and by decohesion at ferrite–martensite interfaces for ferrite-martensite steels, while voids initiate at around 25% strain by the only decohesion at ferrite and hard-phase interfaces for steels with ferrite, bainite and martensite microstructures. De Cooman et al. [59] and Chen [60] recommended that the lower HER of TWIP steels is related to low strain rate sensitivity. Xu [61] studied hole expansion response of high-Mn twinninginduced plasticity (TWIP) steel and observed that crack is initiated by decohesion between the matrix and MnS particle elongated along the rolling direction. There is limited literature available on the TRIP effect and HER. Sugimoto et al. [62] and De Moor et al. [63] stated that early retained austenite to martensite that transforms during deformation is detrimental to HER [50, 64]. Kim et al. [47] informed that low stability and a high fraction of retained austenite induced consequences exceedingly low HER in the punched specimen for 0.22C-3.79Mn-1.48Si-0.98Cr quenched and partitioned steel. This low HER is due to the transformation of retained austenite during hole preparation by punching. Kim et al. [65] observed that increasing volume fraction of retained austenite regardless of the prior austenite grain size consequences deterioration of HER; however, the tensile elongation improves. Larger prior austenite grain size can lessen this degradation of the HER. Kim et al. [65] proposed that increasing the prior austenite grain size could be an opportunity to improve the balance between HER and tensile elongation. Karelova et al. [31] reported that complex phase (CP) steel shows better HER than DP steels. The hard phase is in CP steel comprises of a mixture of bainite, and tempered martensite, while, martensite is the hard phase in DP steel. They have experimentally explained the high HER in CP steel by the relatively less strength difference between hard and soft phases in CP steel in comparison with DP steels. Kaijalainen et al. [66] reported that secondary particles like TiN inclusions and cementite act as void nucleation locations. The precipitation strengthening with small homogeneously distributed

coherent precipitates within the grain can result in improvement in strength with the reduction in void nucleation sites i.e. without or little scarifies of ductility. They also concluded that higher HER can be obtained in equiaxed single-phase ferritic microstructure. Kamibayashi et al. [67] described that precipitation-hardened steel with added Ti displays a healthier strength–ductility– HER balance than steel with Nb added. They had stated that the poorer strength–ductility–HER combination of Nb added steel was primarily caused by the formation of MnS and large textural colonies. Figure 19 summarizes the important microstructural aspects which control the HER of high strength steel. It is expected that grain size, texture [68], chemical composition [67], type of precipitate [67, 61], size and distribution of precipitate [66], volume fraction [26, 49, 51-52, 56] and morphology [60] of different phases, distribution of phases [52], strength difference among phases [31, 5153], phase transformation during deformation [47, 50, 62-65], mechanism of deformation i.e., dislocation glide or twining, etc. [59-60] have an effect on HER. For example, proper introduction of texture improves the coefficient of normal anisotropy (r) [68], i.e., improves in resistance of thinning and necking as well, and as a result, the HER may improve. Alteration in chemical composition or different heat treatment may result in a change in grain size &/ texture &/ precipitate &/ phase &/ mechanism of deformation, and which definitely alter the post uniform elongation and strain rate sensitivity of the metal, and as a result HER may change. An extensive microstructural investigation is still required to establish all possible correlations with HER. Few microstructural studies are already done in the recent past [49-67] to build few relationships between HER and microstructural features of AHSS, but much more experimentation is essential in the future to reveal the complete fact. In general, microstructural features which improve the post uniform elongation, strain rate sensitivity and fracture toughness (i.e., MNOD) of the metal should increase the HER actively.

7. Conclusions After a comprehensive evaluation of the past experimental and simulation work on HER for several decades, a review is presented focusing on the effect of punch geometry, fundamentals of deformation and damage, the impact of edge preparation method, the influence of various uniaxial tensile properties, and finally the effect of microstructure. This comprehensive

summarize information clarifies why HER is at present a topic of engineering research. The following conclusions can be prepared based on the present review work: 

Stress state at the central hole edge is uniaxial tensile during hole expansion test. However, hole expansion and uniaxial tensile tests are different in subsequent points like the existence of deformation gradient, presence of one free edge, and multiple crack initiation sites.



Diffuse necking followed by localized necking takes place typically in uniaxial tensile tests, while diffuse necking suppressed/delayed and only localized necking occurs in hole expansion test. Suppression/delay of diffuse necking consequences higher HER for EDM cut hole than the total elongation of the material during a uniaxial tensile test.



HER depends upon the punch geometry. HER value increases in the ascending order as conical, hemispherical, and flat-bottom punches. Crack (failure) is initiated at the hole edge for conical punch, while a little bit away from the hole edge for hemispherical and flatbottom punches. The deformation mode at the failure location is pure uniaxial tensile deformation for conical punch, pure plane strain tensile deformation for flat-bottom punch, and uniaxial –biaxial-plane strain tensile deformation for hemispherical punch.



Hole edge condition has an influence on HER with conical punches, while no or little influence for hemispherical and flat-bottom punches.



HER has a prominent definite correlation with the coefficient of normal anisotropy, strain rate sensitivity, post uniform elongation and fracture toughness i.e., NMOD. Apart from those, HER systematically varies with the yield stress, ultimate tensile stress, total elongation, reduction of area, etc.



Increasing martensite volume fraction, rising strength difference between hard and soft phases, increasing the volume fraction of retained austenite, and growing hard phase size have a detrimental effect on HER. Ferrite-bainite steel shows better HER performance than ferrite-martensite steel.



Single-phase steel shows better HER than multiphase steel for the same strength level. Equiaxed single-phase ferritic microstructure shows superior HER. Minimization of void nucleating sites, i.e. non-coherent secondary precipitates i.e. TiN precipitate and cementite can results enhancement in HER. On the contrary, precipitation strengthening with small homogeneously distributed coherent precipitates can act as an instrument to optimize strength and HER.

8. Open areas for future research There are a number of significant and inspiring challenges coming up in the near future to understand the HER for advanced materials and safe industrial production of engineering components by sheet metal forming operation despite that intensive research work carried out on HER to date. This state of the art demonstrates that efforts should be made explicitly in order to have:  Effect of pre-straining/forming on HER.  Effect of deformation rate and temperature on HER  More experimentation and modeling on the physics of deformation and damage during HER experiment will be required to understand the HER and develop a material with high HER.  For multiphase materials, how the applied stress/strain is partitioned among phases and contribution of phases in HER performance.  Improvement of hole edge condition by some secondary process and its effect on HER.

References [1]

Pathak N, Butcher C, Worswick M. Assessment of the Critical Parameters Influencing the Edge Stretchability of Advanced High-Strength Steel Sheet. J. Mater. Eng. Perform. 2016; 25:4919–4932.

[2]

Sadagopan S, Urban D. Formability Characterization of a New Generation of High Strength Steels. DOE Report No.0012.

[3]

Larour P, Freudenthaler J, Grunsteidl A, Wang K. Evaluation of Alternative Stretch Flangeability Testing Methods to ISO 16630 Standard. IDDRG Conf Proc. 2014; pp. 188-193.

[4]

Stanton M, Bhattacharya R, Dargue I, Aylmore R, Williams G. Hole Expansion of Aluminum Alloys for the Automotive Industry. AIP Conf Proc , 2011;1488-1493.

[5]

Iizuka E, Urabe M, Yamasaki Y, Hiramoto J. Effect of Strain Gradient on Stretch Flange Deformation Limit of Steel Sheets. IDDRG Conf Proc 2017;1-6.

[6]

Wu X, Bahmanpour H, K. Schmid. Characterization of mechanically sheared edges of dual phase steels. J. Mat. Proc. Technol 2012; 212: 1209–24.

[7]

Luo M, Wierzbicki T. numerical failure analysis of stretch-bending test on dual-phase steel sheets using a phenomenological fracture model. Int. J. Solids Struct 2010;47:3084– 102.

[8]

Taylor GI. The formation and enlargement of a circular hole in a thin plastic sheet. Q J Mech appl Math 1948;1:103-124.

[9]

K. Yoshida, Inst. Phys. Chem. Res., 53 (1959), p. 126

[10]

Wang N M, Wenner M L. An analytical and experimental study of stretch flanging. Int. J Mech Sci 1974; 16:135–143.

[11]

Wang CT, Kinzel G, Altan T. Failure and wrinkling criteria and mathematical modeling of shrink and stretch flanging operations in sheet-metal forming. J Mater Process Tech 1995; 53:759–780.

[12]

Yamada, Koide. Analysis of the bore-expanding test by the incremental theory of plasticity. Int J Mech Sci 1968;10:1–14.

[13]

Karima M, Chandrasekaran N, Tse W. Process signature in metal stamping: Basic concepts. J Mater Shaping Technology 1989;7:169–183.

[14]

Matsuzu N, Itami A, Koyama K. Stretch-Flange Formability of High-Strength Steel. SAE Technical Paper 1991; 910513.

[15]

Paul SK, Mukherjee M, Kundu S, Chandra S. Prediction of Hole Expansion Ratio for automotive grade steels. Comput Mater Sci 2014; 89:189-197.

[16]

Paul SK. Non-linear correlation between uniaxial tensile properties and shear-edge hole expansion ratio. J Mater Eng Perform 2014; 23:3610-3619.

[17]

Casellas D, Lara A, Frómeta D, Gutiérrez D, Molas S, Pérez L, Rehrl J, Suppan C. Fracture Toughness to Understand Stretch- Flangeability and Edge Cracking Resistance in AHSS. Metall and Mat Trans A 2017; 48:86-94.

[18]

Yoon JI, Jung J, Kim JG, Sohn SS, Lee S, Kim HS. Key factors of stretch-flangeability of sheet materials. J Mater Sci 2017; 52:808–7823.

[19]

Yoon JI, Jung J, Joo S-H, Song TJ, Chin K-G, Seo MH, Kim S-J, Lee S, Kim HS. Correlation between fracture toughness and stretch-flangeability of advanced high strength steels. Mater Lett 2016; 180:322–326.

[20]

Paul SK. Correlation between hole expansion ratio (HER) and notch tensile test. Manuf Lett 2019; doi.org/10.1016/j.mfglet.2019.02.003.

[21]

Paul SK. Fundamental aspect of stretch-flangeability of sheet metals. Proc Inst Mech Eng B 2018. doi.org/10.1177/0954405418815370.

[22]

Chen L, Kim JK, Kim SK, Kim GS, Chin KG, Cooman BCDe. Stretch-Flangeability of High Mn TWIP steel. Steel Res Int. 2010; 81(7):552-568.

[23]

Martínez-Donaire AJ, Borrego M, Morales-Palma D, Centeno G, Vallellano C. Analysis of the influence of stress triaxiality on formability of hole-flanging by single-stage SPIF. Int J Mech Sci 2019;151:76–84.

[24]

ISO, Metallic Materials - Method of Hole Expanding Test, http://www.iso.org (2009). (accessed May 17, 2016)

[25]

Konieczny A, Henderson T. On Formability Limitations in Stamping Involving Sheared Edge Stretching. SAE Int Tech Pap 2007;20-29.2007-01-01-0340.

[26]

Madrid M, Van Tyne CJ, Sadagopan S, Pavlina E, Hu J et al. Effects of Testing Method on Stretch-Flangeability of Dual-Phase 980/1180 Steel Grades. JOM 2018;70: 918-923.

[27]

Neuhauser FM, Terrazas OR, Manopulo N, Hora P, Van Tyne CJ. Stretch Bending – The Plane Within the Sheet Where Strains Reach the Forming Limit Curve. IOP Conf Series Mater Sci Eng 2016; 159:1-8.

[28]

Paul SK. Effect of punch geometry on hole expansion ratio. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 2019. doi: 10.1177/0954405419863222.

[29]

Suzuki T, Okamura K, Capilla G, Hamasaki H, Yoshida F. Effect of anisotropic evolution on circular and oval hole expansion behavior of high-strength steel sheets. Int J Mech Sci 2018; 146:556–570.

[30]

Yoon JI, Jung J, Lee HH, Kim GS, Kim HS. Factors governing hole expansion ratio of steel sheets with smooth sheared edge. Met Mater Int 2016; 22:1009–1014.

[31]

Karelova A, Krempaszky C, Werner E, Tsipouridis P, Hebesberger T, Pichler A, Hole Expansion of Dual-Phase and Complex-Phase AHS Steels – Effect of Edge Conditions. Steel Res Int 2009; 80;71-77.

[32]

Comstock RJ, Scherrer DK, Adamczyk RD. Hole Expansion in a Variety of Sheet Steels, J Mater Eng and Perform 2006;15: 675-683.

[33]

Levy BS, Gibbs M, Van Tyne CJ. Failure during sheared edge stretching of dual-phase steels. Metall Mater Trans A 2013; 44:3635-3648.

[34]

Hance B, Comstock R, Scherrer D. The Influence of Edge Preparation Method on the Hole Expansion Performance of Automotive Sheet Steels. SAE Tech Pap 2013.2013/04/08

[35]

Kadarno P, Mori KI, Abe Y, Abe T. Punching process including thickening of hole edge for improvement of fatigue strength of ultra-high strength steel sheet. Manuf Rev. 2014; 1:4-8.

[36]

Levy BS, Van Tyne CJ. Review of the Shearing Process for Sheet Steels and Its Effect on Sheared-Edge Stretching. J Mater Eng Perform 2012; 21:1205–1213.

[37]

Karelova A, Krempaszky C, Werner E, Tsipouridis P, Hebesberger T, Pichler A. Hole Expansion of Dual-phase and Complex-phase AHS Steels - Effect of Edge Conditions. Steel res Int 2009;80(1):71-77.

[38]

Nakata M, Uematsu K, Koseki S. Shear Deformation Properties of Ultra High Strength Steel Sheet. IDDRG Conf Portugal 2006;527-534.

[39]

Lee SB, Speer JG, Matlock DK, Chin K.G. Proceedings of the 3rd International Conference on Advanced Structural Steels, Korean Institute of Metals and Materials, Seoul, Korea, 2006, pp. 841–49.

[40]

Dalloz A, Besson J, Gourgues-Lorenzon AF, Sturel T, Pineau A. Effect of shear cutting on ductility of a dual phase steel. Eng Fract Mech 2009;76:1411–24.

[41]

Mukherjee M, Tiwari S, Bhattacharya B. Evaluation of factors affecting the edge formability of two hot rolled multiphase steels. Int J Miner Metall Mater 2018;25:199215.

[42]

Wu X, Bahmanpour H, Schmid K. Characterization of mechanically sheared edges of dual phase steels. J Mater Process Tech 2012; 212: 1209-1224.

[43]

Branagan DJ, Frerichs A, Meacham BE, Cheng S, Sergueeva AV. New Mechanisms Governing Local Formability In 3rd Generation AHSS," SAE Tech Pap 2017.2017/03/28

[44]

Paul SK. Effect of deformation gradient in necking/failure during hole expansion test. Manufacturing Letters 2019; 21: 50-55.

[45]

Chen X, Jiang H, Cui Z, Lian C, Lu C. Hole expansion characteristics of ultra high strength steels. Procedia Engineering 2014; 81:718 – 723.

[46]

Fang X, Fan Z, Ralph B, Evans P, Underhill R. The relationships between tensile properties and hole expansion property of C-Mn steels, J Mater Sci 2003;38: 3877 - 3882.

[47]

Kim JH, Seo1 EJ, Kwon MH, Kang S, Cooman BC. De. Effect of quenching temperature on stretch flangeability of a medium Mn steel processed by quenching and partitioning. Mater Scie Eng A 2018;729:276–284.

[48]

Chen L, Kim J, Kim SK, Chin KG and Cooman BC De. On the stretch-flangeability of High Mn TWIP steels. Mater Sci Forum 2010; 654-656: 278-281.

[49]

Lee J, Lee SJ, Cooman BC De. Effect of micro-alloying elements on the stretchflangeability of dual phase steel. Mater Sci Eng A 2012;536 :231– 238.

[50]

Jin X, Want L, Speer JG,. Hole Expansion in Q&P, DP, and TRIP Steel Sheets. Int Symposium of Automotive Steels Conf Proc 2013: 60-67.

[51]

Hasegawa K, Kawamura K, Urabe T, Hosoya Y. Effects of microstructure on stretchflange-formability of 980 MPa grade cold-rolled ultra high strength steel sheets. ISIJ Int 2004; 44:603-609.

[52]

Terrazas O, Findley KO, Van Tyne CJ. Influence of Martensite Morphology on ShearedEdge Formability of Dual-Phase Steels. ISIJ Int 2017; 57: 937.

[53]

Taylor MD, Choi KS, Sun X, Matlock DK. Packard CE, Xu L, Barlat F. Correlations Between Nanoindentation Hardness and Macroscopic Mechanical Properties in DP980 Steels. Mater Sci Eng A, 2014;597:431-439.

[54]

Kim J, Lee MG, Kim D, Matlock DK, Wagoner RH. Hole-Expansion Formability of Dual-Phase Steels Using Representative Volume Element Approach with BoundarySmoothing Technique. Mater Sci Eng A, 2010;527: 7353-7363.

[55]

Miura M, Nakaya M, Mukai Y. Cold-rolled, 980 MPa Grade Steel-sheets with Excellent elongation and stretch flangeabilityhttp://www.kobelco.co.jp/english//ktr/pdf/ktr_28/008012.pdf.Accessed 15 2017.

[56]

Sudo M, Kokubo I. Microstructure--Mechanical Property Relationships in Multi-Phase Steel Sheet. Scand J Metall, 1984;13:329-342.

[57]

Takahashi Y, Kawano O, Tanaka Y. Fracture Mechanical Study on Edge Flange-ability of High Tensile-strength Steel Sheets. Proc of MS&T, 2009;1317-1328.2009/10/25.

[58]

Sudo M, Hashimoto SI, Kambe S. Niobium bearing ferrite-bainite high strength hotrolled sheet steel with improved formability. Transactions of ISIJ, 1983; 23: 303-311.

[59]

Cooman BC De, Kim HS, Chen L, Estrin Y, Voswinckel H, Kim SK, Hole expansion performance of TWIP steel, in: D.Y. Yang (Ed.), ICTP 2008, Gyeongju, Korea, 2008;554-555.

[60]

Chen L, Kim JK, Kim SK, Chin KG, Cooman BC De. On the stretch-flangeability of high Mn TWIP steels. Mater. Sci. Forum 2010; 278;654–656.

[61]

Xu L, Barlat F, Lee MG. Hole expansion of twinning-induced plasticity steel. Scripta Materialia 2012; 66:1012–1017.

[62]

Sugimoto K, Sakaguchi J, Iida T, Kashima T. Stretch-flangeability of a High-strength TRIP Type Bainitic Sheet Steel. ISIJ International, 2000; 40: 920–926.

[63]

Moor E De, Lacroix S, Clarke AJ, Penning J, Speer JG. Effect of retained austenite stabilized via quench and partitioning on the strain hardening of martensitic steels,” Metall Mater Transactions A 2008; 39:2586–2595.

[64]

Chen X, Jiang H, Cuit Z, Lian C, Lu C. Hole Expansion Characteristics of Ultra High Strength Steels. ProceEng, 2014; 1:718-723.

[65]

Kim JH, Lee SW, Lee K, Kim JK, Suh DW. Effect of Prior Austenite Grain Size on Hole Expansion Ratio of Quenching and Partitioning Processed Medium-Mn Steel. JOM 2019;1-9.

[66]

Kaijalainen A, Kesti V, Vierelä R, Ylitolva M, Porter D, Kömi J, The effect of microstructure on the sheared edge quality and hole expansion ratio of hot-rolled 700 MPa steel. Journal of Physics: Conf. Series 2017; 896: 012103.

[67]

Kamibayashi K, Tanabe Y, Takemoto Y, Shimizu I, Senuma T. Influence of Ti and Nb on the Strength–Ductility–Hole Expansion Ratio Balance of Hot-rolled Low-carbon High-strength Steel Sheets. ISIJ International 2012; 52 (1): 151–157.

[68]

Suwas S, Ray RK, Crystallographic texture of materials. Springer, London (2014)

Figure 1: Schematic representation of hole expansion test (a) before the test, and (b) after test completion.

Figure 2: Schematic representation of specimen geometry for the hole expansion test

Figure 3: Visible cracks after cold forming AHSS automotive parts [17]

Figure 4: Finite element simulation of hole expansion test: (a) distribution of hoop strain at the time of failure (HER = 107.7%) for EDD steel [16], (b) principal strain histories for EDD steel [16], and (c) variation of in-plane maximum principal strain along the width of the DP steel sample (i.e., moving away from the central hole edge) [44].

Figure 5: (a) Schematic illustration of HER in classic fracture and forming limit diagram, and (b) position of HER with punched and reamed hole on the forming limit diagram. Experimental data of forming limit and HER are collated from Pathak et al. [1].

Figure 6: Key factors affecting HER of steels

Figure 7: Schematic diagram of deformation and necking in (a) uniaxial tensile test: diffuse neck followed by the localized neck, and (b) hole expansion test: no diffuse neck, only localize neck &/ crack propagation.

Figure 8: (a) Various punch geometry for hole expansion test, (b) deformation paths during hole expansion test for different punch geometries, experimental forming limit diagram collected from Pathak et al. [1].

Figure 9: (a) variation of strain ratio (ratio of in-plane minimum and maximum principal strains) along the width of the sample (i.e., distance specified) for different punch. (b) comparison of HER for different punch geometries, experimental data collected from Pathak et al. [1];

Figure 10: Schematic representation of a punched surface: cross-sectional view of edge.

Figure 11: SEM picture of a punched edge of dual phase steel; (a) Full cross-section of shearaffected zone (SAZ) near the shear face; (b) the burnish region, arrows indicate the general flow direction; (c) middle of the fracture region, with the arrows representing voids; and (d) the burr. [33]

Figure 12: Variation in HER with hole preparation method: three 3rd generation AHSS: Alloys A, B, and C. Adapted from experimental work by Branagan et al. [43]

Figure 13: Hole expansion test samples of DP steel after completion of hole expansion test for punched and EDM machined hole [44].

Figure 14: Correlation between HER (%) and tensile properties: (a) yield stress, MPa (b) ultimate tensile stress, MPa (c) coefficient of normal anisotropy (d) total elongation, % (e) post uniform elongation, %. [16]

Figure 15: Important tensile properties affecting HER

Figure 16: Correlation between HER and (a) fracture toughness [19], (b) versus notch mouth opening displacement at peak load (Δδm) for 60o notch angle [21]. Hole expansion test specimens prepared using a punching process, and conical punch is used.

Figure 17: Key microstructural factors affecting HER of multiphase steel

Figure 18: Variation of HER with martensite colonies per unit area. Adapted from experimental work by [52].

Figure 19: Important microstructural aspects controlling HER of high strength steel

Graphical abstarct

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐ The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: