Fracture Toughness Analysis of Automotive-Grade Dual-Phase Steel Using Essential Work of Fracture (EWF) Method

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Article Fracture Toughness Analysis of Automotive-Grade Dual-Phase Steel Using Essential Work of Fracture (EWF) Method

Sunil Kumar M R 1,* , Eva Schmidova 1 , Pavel Konopík 2, Daniel Melzer 2, Fatih Bozkurt 3 and Neelakantha V Londe 4

1 Faculty of Transport Engineering, University of Pardubice, 53210 Pardubice, Czech Republic; [email protected] 2 Mechanical Testing and Thermophysical Measurement, COMTES FHT a.s., 33441 Dobˇrany, Czech Republic; [email protected] (P.K.); [email protected] (D.M.) 3 Vocational School of Transportation, Eskisehir Technical University, 26140 Eskisehir, Turkey; [email protected] 4 Department of Mechanical Engineering, Mangalore Institute of Technology & Engineering, Moodabidre 574225, India; [email protected] * Correspondence: [email protected]; Tel.: +420-777-95-5826

Received: 2 July 2020; Accepted: 27 July 2020; Published: 29 July 2020

Abstract: Fracture toughness determination of dual-phase DP450 steel using the essential work of fracture (EWF) methodology is the major focus of this research work. The EWF method is used for the determination of fracture toughness of thin sheets in a plane stress dominant condition. The EWF method is discussed in detail with the help of DP450 steel experimental results. Double edge notched tension (DENT) specimens with fatigue pre-crack and without fatigue crack (notched) have been e used for testing. Specific essential work of fracture (we), crack tip opening displacement (δc) and crack tip opening angle (ψe) parameters were used for the comparative analysis. High-intensity laser beam cutting technology was used for the preparation of notches. Fracture toughness values of fatigue pre-cracked and notched samples were compared. The effect of notch tip radius and fatigue crack on the fracture toughness values were analysed. Digital image correlation (DIC) technology was used for the identification of local strain distribution and validation of the methodology. Fractured surfaces were examined by a scanning electron microscope (SEM) to analyse the fracture morphology and stress state.

Keywords: essential work of fracture (EWF); double edge notch tension (DENT); DP450; fracture toughness

1. Introduction The automotive industry is under constant pressure to increase the eﬃciency of vehicles, reduce emissions and get better crashworthiness. Various public norms, as well as competition, are the driving forces. Weight reduction is achieved by using new generation advanced high strength steels (AHSS) [1]. These steels have high strength compared to conventional steels. Steels used for the manufacturing of white-in-body doors and hood are required to have high strength, as well as better formability, weldability, corrosion resistance and fracture toughness. Dual-phase (DP) steel is one of the new generation steels with a high ultimate strength to yield strength ratio. Dual-phase steel primarily contains ferrite structure and islands of martensite, achieved through heat treatment and the addition of alloying elements. Martensite content increases the strength of the steel, meanwhile, the ferrite

Metals 2020, 10, 1019; doi:10.3390/met10081019 www.mdpi.com/journal/metals Metals 2020, 10, 1019 2 of 12 content gives ductility to the steel [2,3]. Dual-phase steel is better suitable for stamping applications due to its high ultimate strength to yield strength ratio [4,5]. During the stamping of automotive components, materials with low fracture toughness often develop new edge cracks or pre-existing minute cracks, formed during shear cutting, piercing and trimming of sheets, which may grow. Material fracture toughness of has a direct influence on edge cracking resistance [6] and crashworthiness in passive safety. The forming limit diagram (FLD) is an excellent choice to identify necking during stamping applications. However, FLD does not emphasise fracture toughness or edge cracking resistance. The determination of fracture toughness is vital for material selection in stamping applications. The international ASTM E399 [7] (linear elastic plane strain fracture toughness) standard uses plane strain dominant condition to keep plastic deformation low and constant. The fracture toughness value obtained from this method is independent of thickness. Due to its minimum thickness restriction (1 W/B 4 range for various specimens) and plastic size restriction, this standard is not feasible ≤ ≤ for thin samples. The ASTM E1820 [8] standard measurement of fracture toughness (J-integral and CTOD) is ideal for elastic–plastic material. The minimum thickness constraint is less restrictive than E399; although, automotive thin steel sheets do not fulfil the thickness requirement. ASTM E561 [9] (K–R curve) could be used for thin sheets, as it does not have any thickness restriction. However, the results are thickness sensitive. The results from the above standard have no single critical value, unlike KIc or Jc. Fracture resistance is dependent on the stress field in front of the crack tip. Thicker sections of the same material may exhibit less resistance to the crack growth, one of the main reasons of which is the plane strain dominant condition [10]. To find out the fracture toughness of thin sheets in their original sheet thickness, the essential work of fracture (EWF) method is used. Double edge notch tension (DENT) specimens are used in the experiments. Broberg first explained the concept of different energy zones near the crack tip [11]. Broberg divided the crack tip into two regions, namely the fracture process zone (FPZ) and outer plastic zone. Energy consumed in the FPZ is spent to create two new surfaces. FPZ is independent of crack tip stresses or loading condition. The outer plastic zone depends on the stress state, crack length, loading and geometry. The essential work of the fracture concept was first proposed by Cotterell and Reddel in 1976 [12]. Cotterell and Reddel used the Broberg concept of energy consumed in the independent autonomous end region (FPZ) as material property for the sheet thickness. In Linear elastic fracture mechanics, the plastic region around the crack tip is assumed to be very small. In ductile materials, the plastic region is large and dependent on various loading parameters. The autonomous end region in ductile materials can be characterised by necking. Marchal and Delannay performed EWF experiments on zinc sheets under varying conditions like deformation rate, thickness, grain size and rolling direction [13]. Marchal and Delannay observed better linearity in specific essential work of fracture for different ligament lengths but expressed their concern on the hypothesis of EWF about zone separation (FPZ and outer plastic zone). Chandra et al. [14] have worked on the essential work of fracture method for interstitial free steel and determined specific essential work of fracture, crack tip opening displacement (CTOD) and crack tip opening angle (CTOA). The ESIS protocols [15,16] conducted in round-robin experiments on polymers give enhancing knowledge about dimensions and parameters affecting the EWF results. Golling et al. [17] have conducted experiments using the EWF method at a higher loading rates on different AHSS and found the specific essential work of fracture increases with an increase in the loading rate. Frómeta et al. [18] conducted experiments to relate the essential work of fracture and crash resistance of automotive steels. Materials with higher fracture toughness values obtained from the EWF test showed better crash resistance. Several researchers simulated the EWF test in FEM analysis to find the influence of various parameters on fracture toughness [19–21]. Some researchers have even attempted to compare the specific essential work of fracture we with critical Jc integral [22]. Rink et al. [23] calculated and compared Jc and we for different polymers using the Begley–Landes method and EWF method, Metals 2020, 10, 1019 3 of 12

respectively. we is obtained from fracturing the entire ligament and represents both initiation and crack propagation resistance. While the Jc value is highly dependent on a small crack extension resistance. In the EWF method, energy absorbed by the specimen to completely fracture it is the work of fracture. The area under the load–displacement curve is equivalent to work of fracture (W f ). The total work of fracture is divided into two energies (Equation (1)), essential energy and non-essential energy, respectively. W f = We + Wp (1)

Essential work of fracture (We) is the energy consumed by the fracture process zone; it is a factor of the area along the crack path. The non-essential work of fracture (Wp) is the energy consumed by the plastic deformation; it is a function of the volume of the plastic zone.

2 W f = weLt + wpL tβ (2)

In Equation (2), we is the speciﬁc essential work of fracture, wp is the speciﬁc non-essential work of fracture, L is the ligament length, t is the thickness of the sheet and β is the plastic zone shape factor, π which is 4 for the circular shape. If the whole Equation (2) is divided by the area of the ligament, then,

W f w = = w + w Lβ (3) f Lt e p

In Equation (3), wf is the specific work of fracture energy; it is a linear function of the ligament length with slope wpβ. The value of we can be calculated by testing samples of different ligament lengths. In the plot of wf versus ligament length, the value of we is the ordinate at zero ligament length. Theoretical background and related experiments regarding EWF methodology can be found in the literature [24–27]. The energy spent in FPZ, we, can further be divided into final separation energy and necking energy, but it is beyond the scope of this paper. The primary focus of the EWF test is to find the specific essential work of fracture (we). Cotterell e proposed parameters, such as crack tip opening displacement (δc or CTOD) and crack tip opening angle (ψe or CTOA), based on the elongation data during EWF test [27]. The CTOD and CTOA obtained from the EWF test, compared to the standard test, have little constraints and are purely dependent on FPZ. The total elongation of the sample in terms of CTOD and CTOA is written in Equation (4).

ψe u = δe + L (4) f c 2 In the plot of total elongation versus ligament length, the ordinate at zero ligament length is e equal to the crack tip opening displacement (δc or CTOD). The slope of the curve is equal to the ψe half-subtended angle by two surfaces ( 2 ) in FPZ. Faccoli et al. [28] and Kamat et al. [29] conducted experiments to relate the critical J-integral Jc with notch tip radius ρ. The value of critical Jc integral increases with an increase in notch tip radius. The value of Jc integral will become insensitive to the notch tip radius below the critical value ρc. The determination of ρc is quite challenging and depends on various factors. There is no established standard to relate notch tip radius and fracture toughness. To determine the effect of notch tip radius on specific essential work of fracture, a notch tip radius of 55 µm was selected and the results are compared with fatigue cracked samples. Generally, ASTM standards suggest EDM technology for notch preparation. In this work, high intensity laser technology is used for notch preparations to ensure the lowest possible radius without significantly affecting the material properties. To verify the state of plane stress during the loading, the maximum stress in the ligament should be independent of ligament length. This criterion can be analysed using Hill’s theory [30] of ideal elastic–plastic materials. The maximum stress along the ligament should be in the range of 1.15σY > σ > 0.9σY [15]. Due to excessive strain hardening, the stresses are far higher. The yield Metals 2020, 10, 1019 4 of 12 strength cannot be used as a limiting criterion here. The yield strength is replaced by the ultimate strength to verify the plane stress state in the ligament length [14].

2. Material and Experimental Details

2.1.Metals Material 2020,, 10,, xx FORFOR PEERPEER REVIEWREVIEW 4 of 12 The dual-phase DP450 steel used in this research work comprises a maximum chemical The dual-phase DP450 steel used in this research work comprises a maximum chemical composition in percent by weight, exclusive of iron, of 0.083% carbon, 1.72% manganese, 0.026% composition in percent by weight, exclusive of iron, of 0.083% carbon, 1.72% manganese, 0.026% silicon, 0.209% chromium, 0.163% titanium, 0.056% aluminium, 0.021% phosphorus and 0.014% copper. silicon, 0.209% chromium, 0.163% titanium, 0.056% aluminium, 0.021% phosphorus and 0.014% Thecopper. microstructure The microstructu of DP450re of isDP450 shown is shown in Figure in 1Figure. DP450 1. DP450 steel has steel yield has strength yield strength ( σy) of (휎 290) of MPa, 290 copper. The microstructure of DP450 is shown in Figure 1. DP450 steel has yield strength (휎푦 ) of 290 ultimateMPa, ultimate strength strength (σu) of ( 480.60휎 ) of MPa,480.60 elongation MPa, elongation at fracture at fracture (A50%) of (A 30.36%,50%) of elongation 30.36%, elongation at ultimate at MPa, ultimate strength (휎푢 ) of 480.60 MPa, elongation at fracture (A50%) of 30.36%, elongation at stress (Ag%) of 18.81%g and strain hardening exponent (n) of 0.18. The standard engineering stress–strain ultimate stress (Ag%) of 18.81% and strain hardening exponent (n) of 0.18. The standard engineering curve for DP450 steel is shown in Figure2. The large dark grains in Figure1 are ferrite and shiny stress–strain curve for DP450 steel is shown in Figure 2. The large dark grains in Figure 1 are ferrite small islands of martensite are located close to the grain boundaries. The strength of DP450 steel is and shiny small islands of martensite are located close to the grain boundaries. The strength of DP450 on the lower band compared to other dual-phase steels. The martensitic volume fraction is relatively steel is on the lower band compared to other dual-phase steels. The martensitic volume fraction is low compared to other dual-phase steels [2]. Low carbon content in the material is attributed to the relatively low compared to other dual-phase steels [2].. Low Low carbon carbon content content in in the the material material is is presence of large ferrite volume fraction. The 1.72% manganese count helps in stabilising the premature attributed to the presence of large ferrite volume fraction. The 1.72% manganese count helps in formation of martensite and strengthens the ferrite [31]. stabilising the premature formation of martensite and strengthens the ferrite [31].

(a) (b) Figure 1. Microstructure of DP450 steel: (a) Optical microscope image; (b) Scanning electron Figure 1. 1. MicrostructureMicrostructure of of DP450 steel: ( (aa)) Optical microscope image; (b) Scanning Scanning electron electron microscope image.image.

Figure 2. Engineering stress–strain curve of DP450 steel with specimen scheme (mm). Figure 2. Engineering stress–strain curve of DP450 steel with specimen scheme (mm)..

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2.2. Specimen The double-edge notched tension (DENT) specimen was chosen for the experiments. Transverse stress in the ligament between notches is tensile; hence, no anti-buckling plates were required. Figure3a shows the simple schematic representation of the DENT specimen used in the experiments. The specimen has a general dimension of 45 mm width, 150 mm height and 0.6 mm thickness with a Metals30 mm 2020 gripping, 10, x FOR section PEER REVIEW on either side. Ligament lengths were chosen in the range between 5t < L 5< ofW 12/3 (t is the thickness of the specimen; W is the width of the specimen). The lower limit of the ligament (t is the thickness of the specimen; W is the width of the specimen). The lower limit of the ligament length is to avoid the quasi-plain strain condition, and the higher limit of the ligament is to avoid length is to avoid the quasi-plain strain condition, and the higher limit of the ligament is to avoid the the formation of two separate plastic zones [12]. Nine samples were prepared to have a ligament formation of two separate plastic zones [12]. Nine samples were prepared to have a ligament length length from ﬁve to thirteen millimetres. Specimens were prepared using high-intensity laser cutting. from five to thirteen millimetres. Specimens were prepared using high-intensity laser cutting. The The notch tip radius is 55 µm and it is shown in Figure3b. Fatigue cracks are created in the samples notch tip radius is 55 µm and it is shown in Figure 3b. Fatigue cracks are created in the samples using using cycling loading in a fatigue machine. The ASTM E399 [7] recommends that the maximum cycling loading in a fatigue machine. The ASTM E399 [7] recommends that the maximum stress stress intensity factor during fatigue pre-crack shall not exceed 80% for crack initiation and 60% for intensity factor during fatigue pre-crack shall not exceed 80% for crack initiation and 60% for the the terminal stage of the critical stress intensity factor. Since KIc is not an appropriate limit for thin terminal stage of the critical stress intensity factor. Since KIc is not an appropriate limit for thin ductile ductile sheet material, a more conservative parameter yield stress was used as a critical parameter. sheet material, a more conservative parameter yield stress was used as a critical parameter. The The maximum stress in the ligament was kept below 80% of the yield stress. Thereby, the maximum maximum stress in the ligament was kept below 80% of the yield stress. Thereby, the maximum load load during fatigue crack initiation was kept well below the critical stress intensity factor to avoid low during fatigue crack initiation was kept well below the critical stress intensity factor to avoid low cycle fatigue. The direction of loading was changed for every few thousand cycles to get equal crack cycle fatigue. The direction of loading was changed for every few thousand cycles to get equal crack growth on either side of the notch. The length of the fatigue crack was about 1 mm on either side. growth on either side of the notch. The length of the fatigue crack was about 1 mm on either side.

(a) (b)

FigureFigure 3. DoubleDouble edge edge notched notched tension tension (DENT) (DENT specimen:) specimen: (a) Schematic (a) Schematic representation representation of the specimen of the specimen(mm); (b) (mm) Notch; ( tipb) Notch geometries tip geometries of the specimen of the spe (digitalcimen microscope). (digital microscope).

2.3.2.3. EWF EWF Testing Testing TheThe standard standard mechanical mechanical properties properties of the of thematerial material were were determined determined by testing by testing three dog three bone dog- shapedbone-shaped sample sampless according according to ASTM to ASTM E8/E8M E8 [32]/E8M and [32 ]average and average values values were taken were taken(Section (Section 2.1). The 2.1). 1 standardThe standard strain strain rate rateof 0.002 of 0.002 s-1 and s− anda gauge a gauge length length of 50 of 50mm mm were were used. used. An An in in-built-built extensometer extensometer measuremeasuredd accurate accurate displacement displacement during during tensile tensile testing. testing. ToTo determine determine the the specific speciﬁc essential essential work work of of the the fracture fracture using using DENT DENT specimens, specimens, the the specimen specimen wawass pulled pulled in in Zwick Zwick Z030 Z030 universa universall tensile tensile testing testing machine machine (ZwickRoell (ZwickRoell GmbH, GmbH, Ulm Ulm,, Germany) Germany) until until thethe final ﬁnal fracture. fracture. The The d displacementisplacement of of the the specimen specimen during during EWF EWF testing testing wa wass automatically automatically recorded recorded byby the the crosshead crosshead movement. movement. The The crosshead crosshead speed speed of of 1 1mm/min mm/min wa wass used used as as the the standard standard in in all all te tests.sts. TheThe grip grip on on either either end end wa wass limited limited to to a a maximum maximum of of 30 30 mm. mm. To To analyse analyse the the strain strain distribution distribution in in the the ligamentligament and and validate validate the the EWF EWF methodology, methodology, ARAMIS ARAMIS digital digital image image correlation correlation technology technology (DIC) (DIC) (GOM GmbH, Braunschweig, Germany) was used. A stochastic pattern was created on the specimens using white and black synthetic spray paints. A series of images were taken (up to 10 images per second) with the help of two cameras in the DIC system. These images were then automatically computed and post-processed by the ARAMIS software (version 6.3, GOM GmbH, Braunschweig, Germany). The local strain distribution, displacements and necking of the specimen were evaluated using the DIC system [33].

3. Results and Discussions

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3.1. Essential Work of Fracture Figure 4 shows the force versus displacement curve for all ligament lengths ranging from 5 mm to 13 mm. All curves follow an identical curve shape. In addition, from the graph it clear that large plastic deformation happened before and after reaching the maximum force. The maximum stress in the ligament is plotted against ligament length for various samples and is shown in Figure 5. The variation of stress for all ligament lengths is in the earlier-specified range (introduction), which is an empirical indication of similar stress states in all samples. The area under the force–displacement diagram is the work of fracture Wf. The work of fracture is calculated by the direct integration of the curve data. The values of specific essential work of fractureMetals 2020 w,f 10is, plotted 1019 against the ligament length to find the essential work of fracture we (Figure6 of6). 12 The detailed results are tabulated in Table 1. The value of we is 230.45 kJ/m2 for fatigue pre-cracked samples. The value of we is 332.3 kJ/m2 for notched samples. The introduction of fatigue crack into the (GOM GmbH, Braunschweig, Germany) was used. A stochastic pattern was created on the specimens sample reduced the specific essential work of fracture by about 30%. The specific essential work of using white and black synthetic spray paints. A series of images were taken (up to 10 images per fracture results are highly dependent on the presence of fatigue crack, and a we value calculated second) with the help of two cameras in the DIC system. These images were then automatically without fatigue crack would overestimate the results. The value of we is dependent on the thickness computed and post-processed by the ARAMIS software (version 6.3, GOM GmbH, Braunschweig, of the specimen and generally increases linearly with thickness [34]. The value of wf for a shorter Germany). The local strain distribution, displacements and necking of the specimen were evaluated ligament length is slightly offset of the regression line because of the increased ratio of transitional using the DIC system [33]. distance to uniform necking length. The chosen lower ligament length will have a considerable effect on3. w Resultse result. and The Discussions experimental results show that the fracture toughness values are still sensitive to the notch tip radius. The critical notch tip radius 휌푐 is much lower than 55 µm. The R-values indicate good3.1. Essential linearity Work of the of Fractureresults for all kinds of samples and notched samples showed better linearity. The valueFigure of4 wshowspβ is higher the force for versusfatigue displacement pre-cracked curvesamples for compared all ligament to lengthsnotched ranging samples. from 5 mm to 13 mm.Extrapolating All curves followthe plot an of identical displacement curve shape.at the final In addition, fracture from versus the ligament graph it clear length that gives large CTOD plastic anddeformation CTOA (Figure happened 7). CTOD before for andthe fatigue after reaching pre-cracked the maximum specimen is force. 0.4088 The mm, maximum and the same stress for in the the notchedligament sample is plotted is 0.6891 against mm. ligament The presence length for of variousfatigue samplescracks in and the issamples shown indecreased Figure5. the The CTOD variation by aboutof stress 40%. for However, all ligament in lengths the case is in of the CTOA, earlier-speciﬁed the difference range between (introduction), the fatigue which pre is-cracked an empirical and notchedindication sample of similar is not stress significant. states in all samples.

(a) (b)

MetalsFigureFigure 2020, 104. 4. ,Force xForce–displacement FOR– displacementPEER REVIEW graph graph for for all all ligament ligament lengths lengths for: for: (a (a) )N Notchedotched specimens; specimens; ( (bb)) Fatigue Fatigue 7 of 12 prepre-cracked-cracked specimens specimens..

FigureFigure 5.5.Maximum Maximum stressstress versusversus ligamentligament lengthlength forfor allall DENTDENT specimens.specimens.

The area under the force–displacement diagram is the work of fracture Wf. The work of fracture is calculated by the direct integration of the curve data. The values of specific essential work of fracture wf is plotted against the ligament length to find the essential work of fracture we (Figure6). 2 The detailed results are tabulated in Table1. The value of we is 230.45 kJ/m for fatigue pre-cracked 2 samples. The value of we is 332.3 kJ/m for notched samples. The introduction of fatigue crack into the sample reduced the specific essential work of fracture by about 30%. The specific essential work of fracture results are highly dependent on the presence of fatigue crack, and a we value calculated

Figure 6. Specific work of fracture versus ligament length for notched and fatigue pre-cracked specimens.

(a) (b)

Figure 7. Elongation at fracture versus ligament length for: (a) notched specimens; (b) fatigue pre- cracked specimens.

Table 1. Essential work of fracture experimental results. 풆 풆 흍 풘풔 = 풘풆 + 풘풑푳휷 풖 = 휹 + 푳 풇 풄 ퟐ Type 풆 wpβ 풆 흍 /ퟐ we (kJ/m2) R 휹 (mm) R (kJ/m3) 풄 (흍풆퐢퐧 휽°) 0.1517 Fatigue pre-cracked 230.45 36.99 0.9836 0.4088 0.9883 (17.38°) 0.1192 Notched 332.3 28.59 0.9966 0.6891 0.9956 (13.65°)

3.2. Fractured Surfaces

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without fatigue crack would overestimate the results. The value of we is dependent on the thickness of the specimen and generally increases linearly with thickness [34]. The value of wf for a shorter ligament length is slightly oﬀset of the regression line because of the increased ratio of transitional distance to uniform necking length. The chosen lower ligament length will have a considerable eﬀect on we result. The experimental results show that the fracture toughness values are still sensitive to the µ notch tip radius. The critical notch tip radius ρc is much lower than 55 m. The R-values indicate good linearity of the results for all kinds of samples and notched samples showed better linearity. The value Figure 5. Maximum stress versus ligament length for all DENT specimens. of wpβ is higher for fatigue pre-cracked samples compared to notched samples. Metals 2020, 10, x FOR PEER REVIEW 7 of 12

FigureFigure 6. 6.Speciﬁc Specific work work of fracture of fracture versus versus ligament ligament length for length notched for andnotched fatigue and pre-cracked fatigue specimens.pre-cracked specimens. Figure 5. Maximum stress versus ligament length for all DENT specimens. Table 1. Essential work of fracture experimental results.

e w = w + w L e ψ s e p β uf = δc + 2 L Type e wpβ ψ /2 w (kJ/m2) R δe(mm) R e (kJ/m3) c (ψein θ◦ ) 0.1517 Fatigue pre-cracked 230.45 36.99 0.9836 0.4088 0.9883 (17.38◦) 0.1192 Notched 332.3 28.59 0.9966 0.6891 0.9956 (13.65◦)

Extrapolating the plot of displacement at the final fracture versus ligament length gives CTOD and CTOA (Figure7). CTOD for the fatigue pre-cracked specimen is 0.4088 mm, and the same for the (a) (b) notched sample is 0.6891 mm. The presence of fatigue cracks in the samples decreased the CTOD by aboutFigureFigure 40%. However,6. 7. SpecificElongation in work the at fracture caseof fracture of CTOA,versus versus ligament the ligament difference length length between for: ( fora) nn theotchedotched fatigue specimens; and pre-cracked fatigue (b )pre fatigue- andcracked notchedpre - samplespecimenscracked is not specimens significant.. .

3.2. Fractured Surfaces(a ) (b) Figure 7. ElongationElongation at atfracture fracture versus versus ligament ligament length length for: for: (a) n (aotched) notched specimens; specimens; (b) fatigue (b) fatigue pre- crackedpre-cracked specimens specimens..

3.2. Fractured Surfaces

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3.2.Metals Fractured 2020, 10 Surfaces, x FOR PEER REVIEW 8 of 12

ScanningScanning electron electron microscope microscope images images of of fractured fractured surfaces surfaces reveal reveal the the fracture fracture morphology morphology duringduring the the crack crack propagation. propagation. Figure Figure8 8shows shows thethe ductileductile fracture morphology morphology of of tested tested specimens, specimens, whichwhich means means that that micro micro voids voids nucleation nucleation and and coalescencecoalescence happened ahead ahead of of crack crack opening. opening. Necking Necking is minimalis minim atalthe at the beginning beginning of of crack crack growth growth andand gradually increases increases over over a short a short distance distance (transitional (transitional distance)distance) to ato uniform a uniform level. level. The The crack crack begins begins inin quasi-planequasi-plane strain strain condition condition and and sh shiftsifts to plane to plane stress stress afterafter the transitionalthe transitional distance distance [35 [35].]. The The transitional transitional distance distance is is the the same same for for all all the the ligament ligament lengths lengths and increasesand increases with thickness with thickness [27]. The [27]. presence The presence of a fatigue of a fatigue crack crack does does not significantlynot significantly change change the the stress statestress at the state crack at the tip crack or transitional tip or transitional distance. distance. A small A flatsmall ductile flat ductile fracture fracture is observed is observed in the in middle the middle of the fractured surface and a shear lipped slant fracture at the edges. The slant fracture of the fractured surface and a shear lipped slant fracture at the edges. The slant fracture proportion proportion increases along the crack path and becomes uniform after some distance. The relative increases along the crack path and becomes uniform after some distance. The relative proportion of proportion of flat and slant fracture depends on strain hardening before crack initiation, fracture flat and slant fracture depends on strain hardening before crack initiation, fracture strain and stress strain and stress state at the crack tip. The fractured surfaces show that the concept of pure plane statestress at the does crack not tip. exist The in fracturedthe ligament, surfaces plane show stress that and the plane concept strain of only pure exist plane in relative stress does proportions not exist in the ligament,to thickness. plane Dimples stress in and the planemiddle strain flat fracture only exist are in circular relative and proportions in mode-I tofracture. thickness. At the Dimples edge, in the middledimples flat are fracture mostly parabolic are circular and and in in shear mode-I mode fracture. fracture. At Dimples the edge, at dimples the extreme are mostly edges almost parabolic anddisappeared. in shear mode fracture. Dimples at the extreme edges almost disappeared.

(a) (b)

FigureFigure 8. Scanning 8. Scanning electron electron microscope microscope (SEM) (SEM) imagesimages of the the fractured fractured surface surface after after essential essential work work of of fracturefracture (EWF) (EWF testing:) testing: (a )(a Crack) Crack tip tip of of a a notched notched sample; ( (bb)) Crack Crack tip tip of of a fatigue a fatigue pre pre-cracked-cracked sample; sample; (c) Ductile(c) Ductile and and slant slant fracture fracture at at edge; edge; (d (d)) Flat Flat and and ductileductile fracture at at centre. centre.

3.3.3.3. Digital Digital Image Image Correlation Correlation Results Results TheThe distribution distribution of of strain strain during during EWF EWF testingtesting is evaluated using using the the digital digital image image correlation correlation technique.technique. One One of theof the fundamental fundamental requirements requirements of of the the EWF EWF test test is is limitinglimiting thethe plasticplastic deformation deformation to onlyto the only ligament the ligament and crack and initiation crack initiation after complete after complete yielding yielding of the ligament; of the ligament; it is veriﬁed it is successfully verified on everysuccessfully single teston every using single DIC systems.test using Aside DIC systems. from around Aside the from ligament around length,the ligament the rest length, of the the specimen rest

Metals 2020, 10, 1019 9 of 12 MetalsMetals 20202020,, 1010,, xx FORFOR PEERPEER REVIEWREVIEW 99 ofof 1212

Metals 2020, 10, x FOR PEER REVIEW 9 of 12 ofof thethe specimenspecimen hashas closeclose toto zerozero strain.strain. Generally,Generally, crackcrack initiationinitiation happenshappens nearnear peakpeak loadload (notched(notched has close to zero strain. Generally, crack initiation happens near peak load (notched samples) and samples)samples) and and loading loading in in the the ligament ligament decreases decreases as as the the crack crack propagates. propagates. For For fatigue fatigue pre pre--crackedcracked loadingof the specimen in the ligament has close decreases to zero strain. as the Generally, crack propagates. crack initiation For fatigue happens pre-cracked near peak samples, load (notched the crack samples,samples, thethe crackcrack initiatedinitiated beforebefore reachingreaching thethe peakpeak load.load. GeneGenerally,rally, inin allall tests,tests, thethe crackcrack propagatedpropagated initiatedsamples) before and loadingreaching in the the peak ligament load. Generally,decreases as in the all tests, crack the propagates. crack propagated For fatigue at the pre same-cracked speed atat thethe samesame speedspeed inin eithereither direction.direction. TheThe highesthighest strainstrain concentrationconcentration cancan bebe foundfound atat notchesnotches andand insamples, either direction. the crack initiated The highest before strain reaching concentration the peak load. can Gene be foundrally, in at all notches tests, the and crack advances propagated as the advancesadvances asas thethe crackcrack propagatespropagates (Figure(Figure 9).9). TheThe shapeshape ofof thethe plasticplastic deformationdeformation aroundaround thethe ligamentligament crackat the propagates same speed (Figure in either9). Thedirection. shape The of thehighest plastic strain deformation concentration around can thebe found ligament at notches is circular and for isis circularcircular forfor lowerlower lengthlength ligamentsligaments andand becomesbecomes moremore ellipticalelliptical forfor longerlonger ligamentligament lengths.lengths. FigureFigure loweradvances length as ligamentsthe crack propagates and becomes (Figure more 9). ellipticalThe shape for of longerthe plastic ligament deformation lengths. around Figure the 10 ligament shows the 1010is shows showscircular thethe for VonVon lower--MisesMises length strainstrain ligaments justjust beforebefore and becomes crackcrack initiationinitiation more elliptical forfor variousvarious for longer ligamentligament ligament lengthslengths lengths. (scaling(scaling Figure factorfactor Von-Mises strain just before crack initiation for various ligament lengths (scaling factor is set between isis10 setset shows betweenbetween the Von zerozero-Mises andand logstrainlog 0.1).0.1). just TheThe before maximummaximum crack initiation strainstrain is isfor onlyonly various concentratedconcentrated ligament lengths inin thethe fracture(scalingfracture factor processprocess zero and log 0.1). The maximum strain is only concentrated in the fracture process zone and the strain is zonezoneis set andand between thethe strainstrain zero isandis distributeddistributed log 0.1). The inin incrementalmaximumincremental strain bandsbands is onlyconnectingconnecting concentrated twotwo notches.notches. in the fracture InIn FigureFigure process 11,11, thethe distributed in incremental bands connecting two notches. In Figure 11, the major strain along a section majormajorzone strainstrainand the alongalong strain aa sectionsectionis distributed lineline isis plottedinplotted incremental atat aa differentdifferent bands timetimeconnecting interval.interval. two TheThe notches. peakpeak strain strainIn Figure atat thethe 11, middlemiddle the line is plotted at a diﬀerent time interval. The peak strain at the middle of the sectional line is the ofofmajor thethe sectionalsectional strain along lineline a is issection thethe indicationindication line is plotted ofof extensiveextensive at a different neckingnecking time beforebefore interval. fracturefracture The peak inin FPZ. FPZ.strain TheThe at the majormajor middle strainstrain indication of extensive necking before fracture in FPZ. The major strain distribution is mostly uniform distributiondistributionof the sectional is is mostly mostly line is uniform uniformthe indication along along of the the extensive sectional sectional necking line line until until before reaching reaching fracture the the in peakFPZ. peak The load load major and and severelystrain severely along the sectional line until reaching the peak load and severely increasing in FPZ during necking. increasincreasdistributioninging inin FPZ isFPZ mostly duringduring uniform necking.necking. along the sectional line until reaching the peak load and severely increasing in FPZ during necking.

((aa)) ((bb)) ((cc)) (a) (b) (c) FigureFigureFigure 9.9.9. VonVon--MiMisesses strainstrain aroundaround thethe ligamentligament atat differentdifferent stagesstages duringduring EWFEWF testingtesting forfor aa ligamentligament Figure 9.Von-Mises Von-Misesstrain strain aroundaround the ligament at at different diﬀerent stages stages during during EWF EWF testing testing for fora ligament a ligament length of 7.89 mm: (a) 50 s; (b) 70 s; (c) 98 s. lengthlengthlength ofof of 7.897.89 7.89 mm:mm: mm: ( (aa)) 50 50 s; s; ( (bb)) 70 70 s; ( c)) 98 98 ss s...

(((aaa))) (((bbb)) ) (c()(c c))

FigureFigureFigureFigure 10. 10.10. 10. Von-Mises Von VonVon--Mises-MisesMises strain strainstrain around aroundaround the thethe ligament ligamentligament for for forfor various various variousvarious ligament ligament ligamentligament lengths: lengths: lengths:lengths: ( a()a ( 5.85)(a a5.85)) 5.855.85 mm; mm; mm;mm; (b ()b 8.79)(( b8.79b)) 8.798.79 mm; (mcm)mm;m; 13m; (( mm. cc()c) )1313 13 mmmm mm.. .

Figure 11. Major strain development along the section line in incremental stage time.

Metals 2020, 10, 1019 10 of 12

4. Conclusions Fracture toughness analysis of DP450 steel using essential work of fracture methodology has been e completed successfully. Fatigue crack presence strongly influences the we and δc values and has a relatively low impact on ψe values. For a quick comparison between two materials, the presence of fatigue crack is not essential, but the results do not truly represent the actual fracture resistance. e Since we and δc values are obtained from extrapolating the curves to zero ligament length, values are not extremely precise in repetition and influenced by the choice of lower ligament lengths. Fractured surfaces have a small flat ductile fracture at the middle and shear lipped slant fracture at the edges. Energy consumed to fracture increases linearly with ligament length; good linearity is observed for notched and fatigue pre-cracked samples. Constant transitional distance is observed in all fractured specimens irrespective of the ligament length. Fracture strain in the FPZ is far higher than the rest of the plastic zone, due to extensive necking before final separation. Comparing the specific essential work of fracture and J-integral at various stages, such as crack initiation and yielding, may give a comprehensive link between two parameters.

Author Contributions: Conceptualization, S.K.M.R. and E.S.; Methodology, S.K.M.R., E.S., F.B. and N.V.L.; Investigation, S.K.M.R., E.S., P.K. and D.M.; Resources, E.S., P.K. and D.M.; Data curation, S.K.M.R., E.S., P.K., D.M. and F.B.; Writing—original draft preparation, S.K.M.R. and E.S.; Writing—review and editing, E.S., N.V.L. and F.B.; Visualization, S.K.M.R., E.S. and N.V.L. All authors have read and agreed to the published version of the manuscript. Funding: This study has been accomplished by support of the Grant No: SGS_2020_009. Acknowledgments: We would like to thank Jakub Zajíc, Research Assistant, University of Pardubice, for his support during testing. We would like to thank Skoda Auto, Czech Republic, for providing materials. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Nomenclature

Ag elongation at ultimate stress A50 elongation at the fracture Jc critical J-integral We essential work of fracture W f total work of fracture Wp non-essential work of fracture u f elongation at fracture we specific essential work of fracture wp specific non-essential work of fracture w f specific work of fracture L length of the ligament n strain hardening exponent W specimen width (DENT) e δc crack tip opening displacement from EWF test ρc critical notch tip radius σu ultimate tensile strength σy yield strength ψe crack tip opening angle from EWF test t thickness of the specimen β shape factor of plastic deformation Metals 2020, 10, 1019 11 of 12

Abbreviations

AHSS Advanced high strength steels CTOA Crack tip opening angle CTOD Crack tip opening displacement DENT Double edge notch tension DIC Digital image correlation EDM Electrical discharge machining EWF Essential work of fracture FLD Forming limit diagram FPZ Fracture process zone

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