metals Article
A Simple and Efficient Method for Obtaining the Whole-Range Uniaxial Tensile Properties of Pipeline Steel Lingzhen Kong 1, * 1 2
*
ID
, Lingbo Su 1 , Xiayi Zhou 2 , Liqiong Chen 1 , Jie Chen 1 and Cheng Mao 1
School of Oil and Natural Gas Engineering, Southwest Petroleum University, Sichuan 610500, China;
[email protected] (L.S.);
[email protected] (L.C.);
[email protected] (J.C.);
[email protected] (C.M.) State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Sichuan 610500, China;
[email protected] Correspondence:
[email protected]; Tel.: +86-028-8303-7010
Received: 25 June 2018; Accepted: 17 July 2018; Published: 19 July 2018
Abstract: To obtain the whole-range true stress-true strain curves of API X65, a method is proposed based on the equal proportion principle and digital images. The tensile elongation was obtained by tracing the gauge points on the specimen surface, and the true strain and true stress of API X65 were calculated according to the formulae. The obtained true stress-true strain curves were validated by a 3-D finite element model. The true stress-true strain curve was set as the input data, while the engineering stress-engineering strain curve was set as the output data. The output data of the finite element model was the same as that of the experiment test. The findings imply that the proposed method could acquire reliable, whole-range true stress-true stain curves. These curves, which depict the material behavior of pipeline steel from initial elongation to fracture, could provide basic data for pipeline defect tolerance limit analysis and fracture assessment. Keywords: pipeline steel; true stress-true strain; gauge point; uniaxial tensile; finite element model
1. Introduction In pipeline safety evaluations, such as defect tolerance analysis and fracture assessment, the numerical finite element method is widely adopted [1–3]. The stress-strain curve of the pipeline forms the basic data for the full-size finite element simulation. The stress and strain data obtained by a traditional strain gauge could meet the requirements of ordinary strength evaluation, but it is not applicable for pipeline fracture assessments. Pipeline steel is a ductile material, and the crack tip will be in a large scale yielding and a large strain state, when crack propagation occurs. The traditional stress-strain curve only contains the data before the onset of necking, and the whole fracture process of the pipeline cannot be accurately described. Therefore, it is necessary to test the whole-range true stress-true strain curve of the pipeline steel. There are many methods for testing and calculating the true stress and true strain, which are divided into three types: the special strain gauge method, the numerical finite element method, and the DIC-based method. The specimens adopted in the special strain gauge method are mainly straight rectangular cross-section specimens. In a safety analysis of pipeline steel, Xin et al. [4] used displacement sensors to measure both axial and lateral displacements, and then obtained the true stress-true strain curves of X65, X80, and other pipeline steels. However, the study did not illustrate how to get the true stress-true strain curve through the axial and lateral displacements. Based on the principle of volume incompressibility, Wang [5] proposed a true stress-true strain calculation formula for round bar specimens. Zhang et al. [6] proposed a method to test the true stress-true strain curve
Metals 2018, 8, 555; doi:10.3390/met8070555
www.mdpi.com/journal/metals
Metals 2018, 2018, 8, 8, 555 555 Metals
22 of 12 of 12
strain curve of rectangular cross-section specimens. He quantified the relationship between the area of rectangular specimens. He quantified the relationship betweenspecimens the area reduction reduction rate cross-section and the thickness reduction rate for rectangular cross-section under a rate and the thickness reduction rate for rectangular cross-section specimens under a tensile load. tensile load. In the experiment, only three parameters (the load, displacement, and thickness) need In thetested. experiment, only three parameters (the thickness) need to tested. to be The thickness parameter could be load, testeddisplacement, by the specialand strain gauge shown in be Figure 1. The thickness parameter could be tested by the special strain gauge shown in Figure 1. On this basis, On this basis, Zhang et al. [7] also proposed a method to test the material properties of a weld area Zhang et aal.concave [7] also proposed a method to test the material properties of anot weld area through a concave through circular cross-section specimen. However, he did provide a way to get the circular cross-section specimen. However, he did not provide a way to get the strain either. strain either.
Figure 1. Special strain gauge for testing the specimen thickness variation. Figure 1. Special strain gauge for testing the specimen thickness variation.
Yao et al. [8] developed a method to obtain material uniaxial constitutive properties by combining Yaotest et and al. [8] developed methodcalling to obtain uniaxial properties by a tensile a finite elementamethod, it thematerial Test-Finite elementconstitutive method. Kamaya et al. [9] combining a tensile test and a finite element method, calling it the Test-Finite element method. and Joun and Kawakubo [10] also combined an experimental method and a finite element method to Kamaya al. [9] and Jounstrain and Kawakubo also combined experimental methodaimed and a at finite obtain theettrue stress-true curves. The[10] iterative process inanthe combined method the element method to obtain the true stress-true strain curves. The iterative process in the combined equivalence of the ultimate load-displacement curves for the experiment and finite element results. method aimed at the equivalence of the ultimate load-displacement curves for the experiment and However, the required iterative computation is tedious and time-consuming. finiteWith element results. However, the required iterative computation is tedious and time-consuming. the development of computer technology and the improvement of camera lens resolution, With the development of computer technology and the improvement of camera lens resolution, methods utilizing DIC (Digital Image Correlation) technology to test the material true stress-true methods utilizing DIC widely (Digitalused Image Correlation) technology to test the material strain curve have been [11–15]. Based on DIC technology, Poulain et al.true [16]stress-true proposed strain curve have been widely used [11–15]. Based on DIC technology, Poulain et al. [16] proposed three methods to get a true stress-true strain curve: VSE (Video-based Surface Extensometry), three methods to get a true stress-true strain curve: VSE (Video-based Surface Extensometry), VRE (Video-based Radial Extensometry), and local DIC. These three methods are all based onVRE the (Video-based Radial Extensometry), and local DIC. These three methods are all based on the principle of incompressible volume, and the true stress-true strain curves were tested through a virtual principle of incompressible volume, and theatrue stress-true strain were tested through strain gauge. Grytten et al. [17] also proposed method for testing the curves true stress-true strain curve ofa virtual strain gauge. Grytten et al. [17] also proposed a method for testing the true stress-true strain polymer materials based on DIC technology. curveMethods of polymer materials based on gauge DIC technology. using a special strain are difficult to implement because special equipment is Methods using a special strain gauge are difficult because special equipment is required [6,7], while the numerical finite element methodtoisimplement cumbersome because it requires iterative required [6,7], while the numerical finite element method is cumbersome because it requires calculation [10]. The DIC-based method could accurately obtain the true strain value of the material, iterative [10]. severe The DIC-based could accurately obtain the truethe strain valueofofDIC the even if it calculation has undergone necking. method However, it also has large drawbacks: erection material, even if it has undergone severe necking. However, it also has large drawbacks: the erection equipment requires certain space and conditions [18]; the specimens need to be sprayed with powder of DIC the equipment certain space directly and conditions [18]; the specimens needresults to be sprayed before test, andrequires the speckle’s quality affects the accuracy of the final [19]; andwith the powder before theequipment test, and the speckle’s quality directly the accuracy of the final [19]; operation of DIC requires specialized trainingaffects and learning. In addition, DICresults equipment and the operation of DICthousand equipment requires andis learning. In addition, DIC costs more than hundred dollars, andspecialized the general training laboratory likewise difficult to afford. equipmentbuilding costs more than hundred thousand dollars, the general laboratorytest is likewise Therefore, on the concept of DIC technology andand a traditional extensometer method, difficult to afford. Therefore, building on the concept of DIC technology and a traditional this paper develops a method to test the true stress and true strain of ductile material, pipeline steel, extensometer test method, paper a proportion method to principle. test the true stress and true using only a digital camera, this gauge pointdevelops and equal Digital imaging wasstrain used of to ductile material, pipeline steel, using only a digital camera, gauge point and equal proportion record the length during the stretching process, CAD (Computer Aided Design) software was used principle. Digital imaging was used record the length during stretching CAD to extract the real extension length, andtothe true stain and true stress the were calculatedprocess, according to (Computer Aided Design) software was used to extract the real extension length, and the true stain the formulae. and true stress were calculated according to the formulae. 2. Experiment Preparation 2. Experiment Preparation The experimental material is the pipeline steel API-5L X65, and the specimen design matches the The experimental is the pipeline steel API-5L X65,[21]. and The the specimen design matches international standardsmaterial ISO 6892-1-2009 [20] and GB/T 228-2002 specific specimen size for the international standards ISO 6892-1-2009 [20] and GB/T 228-2002 [21]. The specific specimen size the uniaxial tensile test is shown in Figure 2. The specimen’s thickness is 5 mm and the width is 20 mm. forthis the experiment, uniaxial tensile test specimens is shown inwere Figure 2. The specimen’s thickness is 5of mm the width In six L-T processed: L is the axial direction theand pipeline, and is T 20 mm. In this experiment, six L-T specimens were processed: L is the axial direction of the pipeline, is the hoop direction of the pipeline. Two specimens form a group, and three groups of specimens and Ttested: is theI1,hoop direction theO2. pipeline. Two specimens form a group, and three in groups of were I2, M1, M2, O1,ofand Two specimens in the same group were machined adjacent specimensI,were tested: I1, I2, M2, O1, and O2. Two specimens in the same group were machined positions. M, and O stand forM1, internal, middle, and outside, respectively, and indicate the position of in adjacent positions. M, and stand for outside, respectively, indicate material from the innerI,wall, theO middle, andinternal, the outermiddle, wall of and the pipeline. I1, M1 and O1and were tested the position of material from the inner wall, the middle, and the outer wall of the pipeline. I1, M1
Metals 2018, 8, 555 Metals 2018, 2018, 8, 8, 555 555 Metals
3 of 12 of 12 12 33 of
and O1method, were tested tested byI2,the the method, while I2, M2, M2,by and O2 were tested tested bygauge the traditional traditional strain gauge and O1 were method, I2, and were by the strain gauge by the whileby M2, and O2while were tested theO2 traditional strain method. Two kinds of method. Two kinds of results were used for comparison and analysis. method. Twoused kinds results wereand used for comparison and analysis. results were forofcomparison analysis.
Figure 2. Geometrical dimension of specimen. Figure 2. 2. Geometrical Geometrical dimension dimension of of specimen. specimen. Figure
After the specimen was machined, the gauge points were marked with marking pen; the distance After the the specimen specimen was was machined, machined, the the gauge gauge points points were were marked marked with with marking marking pen; pen; the the After between gauge points was 2 mm. These gauge points were distributed along the longitudinal symmetry distance between gauge points was 2 mm. These gauge points were distributed along the distance gauge mm.with These gauge points the line of thebetween specimen. After points that, thewas steel2ruler a scale was cut to a were shorterdistributed length, andalong the upper longitudinal symmetry symmetry line line of of the the specimen. specimen. After After that, that, the the steel ruler ruler with with aa scale scale was was cut to to aa longitudinal part of the steel ruler was fixed on the specimen surface with thesteel glue. The marked specimen iscut shown shorter length, and the upper part of the steel ruler was fixed on the specimen surface with the glue. shorter length, the upper the steel ruler was fixed on the specimen surface with glue. in Figure 3. Theand position of thepart steelofruler can be adjusted up and down or left and right, if it the does not The marked marked specimen specimen is is shown shown in in Figure Figure 3. 3. The The position position of of the the steel steel ruler ruler can can be be adjusted adjusted up up and and The block the gauge points and can be fixed firmly. down or or left left and and right, right, if if it it does does not not block block the the gauge gauge points points and and can can be be fixed fixed firmly. firmly. down
Figure 3. 3. Marked Marked specimen. specimen. Figure Figure 3. Marked specimen.
3. Experimental Experimental Processes Processes 3.
experiments were were processed processed on MTS-810 type type universal universal material material testing testing Uniaxial tensile tensile experiments experiments were processed on the the MTS-810 Uniaxial ◦ C. The specimen (MTS System Corporation, Eden Prairie, MN, USA), at a temperature of 22 machine (MTS System Corporation, Eden Prairie, MN, USA), at a temperature of 22 °C. The machine (MTS System Corporation, Eden Prairie, MN, USA), at a temperature of 22 °C. The was fixed on the 250 KN tensile unit with a hydraulic unit. The stretching process was controlled by specimen was was fixed fixed on on the the 250 250 KN KN tensile tensile unit unit with with aa hydraulic hydraulic unit. unit. The The stretching stretching process process was wasa specimen displacement of 1 mm/min. Theof specimen was loaded until it broke. The displacement and load controlled bymode displacement mode of mm/min. The specimen specimen was loaded loaded until it it broke. broke. The controlled by aa displacement mode 11 mm/min. The was until The data were recorded and accessed through the MTS control software 793.10 multipurpose TestWare displacement and load data were recorded and accessed through the MTS control software 793.10 displacement and load data were recorded and accessed through the MTS control software 793.10 (4.0, MTS System Corporation, EdenSystem Prairie, Corporation, MN, USA). The traditional on multipurpose TestWare (4.0, MTS MTS System Corporation, Eden Prairie,strain MN, gauge USA).was Themounted traditional multipurpose TestWare (4.0, Eden Prairie, MN, USA). The traditional the middle ofwas the specimen wasmiddle fixed using rubber band.and Thewas gauge length of the strain gauge is strain gauge was mounted and on the the middle of the the specimen and was fixed using rubber band. The strain gauge mounted on of specimen fixed using rubber band. The 10 mm, and the strain range is ± 15%. gauge length of the strain gauge is 10 mm, and the strain range is ±15%. gauge length of the strain gauge is 10 mm, and the strain range is ±15%. the time interval to to store data was 2s To keep keep the theload loadand andthe thestrain strainofof ofdevice deviceinin insynchronization, synchronization, the time interval to store data was To keep the load and the strain device synchronization, the time interval store data was for MTS, and the time interval to take digital images was 30 s. The initial time for taking the image was 2 s for MTS, and the time interval to take digital images was 30 s. The initial time for taking the 2 s for MTS, and the time interval to take digital images was 30 s. The initial time for taking the set as the when the instrument to stretch. Into this way, the corresponding load data can image wasmoment set as as the the moment when the thebegan instrument began to stretch. In this this way, the the corresponding corresponding image was set moment when instrument began stretch. In way, easilydata be found according to theaccording moment ofto The first, second, and load data can easily easily be found found according toshooting. the moment moment of shooting. shooting. The third first, images second,correspond and third third load can be the of The first, second, and to row 1, 16, and 31, respectively, in the recorded MTS data. Finally, the true stress-true strain curve images correspond to row 1, 16, and 31, respectively, in the recorded MTS data. Finally, the true images correspond to row 1, 16, and 31, respectively, in the recorded MTS data. Finally, the true was obtained through subsequent data processing and calculation formulae. stress-true strain strain curve curve was was obtained obtained through through subsequent subsequent data data processing processing and and calculation calculation formulae. formulae. stress-true
Metals 2018, 8, 555 Metals 2018, 8, 555
4 of 12 4 of 12
4. Data Processing
4. Data Processing In the stretching process of the specimen, only the upside of steel ruler was connected to the specimen, so that the length was elongated when specimen stretched In the stretching processofofthe thegraduated specimen,part only thenot upside of steel rulerthe was connected to the (Figure 4). so Wethat defined the distance of the actual length mm) as the gauge and marked it as specimen, the length of the graduated part was(5 not elongated whenlength the specimen stretched L 0 . The length of the steel ruler, 5mm in the image, can be measured by CAD software (2007, (Figure 4). We defined the distance of the actual length (5 mm) as the gauge length and marked it as L0 . Autodesk, Rafael, CA, USA) to the obtain the can length data defined as LC0 . Similarly, theAutodesk, distance The length San of the steel ruler, 5mm in image, be measured by CAD software (2007, between theCA, twoUSA) points below data the necking can be measured by CAD software to San Rafael, to above obtain and the length definedposition as LC0 . Similarly, the distance between the two obtain the length data defined as L CS . The actual distance between the two points above and below points above and below the necking position can be measured by CAD software to obtain the length the LS, actual can bedistance obtainedbetween according thepoints principle ofand equal proportion: datanecking definedposition, as LCS . The theto two above below the necking position, LS , can be obtained according to the principle of equal L Lproportion:
Ls =
CS
0
(1) LCSL× C 0 L0 Ls = (1) LC0 The strain value at this moment can be obtained by Equation (2). This strain is the Green-Lagrange strain, or engineering which be This converted logarithmic strain The strain value at this moment can strain, be obtained bynee10ds Equationto(2). strain istothe Green-Lagrange according Equation (3). strain, or to engineering strain, which nee10ds to be converted to logarithmic strain according to Equation (3).
LS − LS 0 L − LL εeyy = S S 0 S0
yye =
(
LS0
(2) (2)
)
e ln 11++ εeyyyy εyyyy==ln
(3)(3)
Finally, the true stress value of the specimen can bebeobtained Finally, the true stress value of the specimen can obtainedaccording accordingtoto the the hypothesis hypothesis of byby Kong et al. In this way,way, the true incompressible volume volume and andthe thecalculation calculationformula formulaproposed proposed Kong et [12]. al. [12]. In this the stress-true strainstrain curvecurve of theofspecimen can be obtained: true stress-true the specimen can be obtained: σ==
F FF F ε yy == ee yy AA A A0
(4)(4)
0
Figure Figure 4. 4. Diagrammatic Diagrammatic sketch sketch of of measured measured range range on on the the specimen. specimen.
5. Results The first specimen of each group was tested by the proposed method, and the entire stretching process of specimen is shown in Figure 5. Figure 5 demonstrates that the specimen was stretched evenly at first, and then necking occurred between Figure 5c,d, with the position of the necking near the gauge point "0". As the load was continuously applied, Figure 5e–g show the rapid development stage of necking. Finally, the specimen fractured, fractured, as as shown shown in in Figure Figure 5h. 5h.
Metals 2018, 8, 555 Metals 2018, 8, 555
5 of 12 5 of 12
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Figure Figure 5. 5. Stretching Stretching process process of of the the specimen. specimen. (a) (a) chuck chuck displacement displacement 1.3 1.3 mm; mm; (b) (b) chuck chuck displacement displacement 6.4 mm; (c) chuck displacement 15.6 mm; (d) chuck displacement 17.6 mm; (e) chuck displacement 6.4 mm; (c) chuck displacement 15.6 mm; (d) chuck displacement 17.6 mm; (e) chuck displacement 18.3 mm; mm; (f) (f) chuck chuck displacement displacement 19.3 19.3 mm; mm; (g) (g) chuck chuck displacement displacement 20.3 mm; (h) (h) chuck chuck displacement displacement 18.3 20.3 mm; 21.1 21.1 mm. mm.
The test results of the two methods for specimen I were compared, and the comparison shows that the the true truestress-true stress-truestrain strain curves obtained by two the methods two methods were essentially coincident curves obtained by the were essentially coincident before before necking. thestrain true strain was the 0.22,true the stress true stress byproposed the proposed method necking. When When the true value value was 0.22, testedtested by the method and and the strain gauge were 655.0 MPa and 673.3 MPa,respectively, respectively,and andthe theerror errorwas was 2.7%. 2.7%. Similarly, the strain gauge were 655.0 MPa and 673.3 MPa, Similarly, the engineering stress-engineering stress-engineering strain strain curves curves of of the two methods were also basically coincident before necking. necking. When When the theengineering engineeringstrain strainvalue valuewas was0.24, 0.24,the the engineering stress value measured engineering stress value measured by by proposed method strain gauge respectively, anderror the thethe proposed method andand the the strain gauge werewere 527.8527.8 MPaMPa and and 539.4539.4 MPa,MPa, respectively, and the error2.2%. was 2.2%. was After reaching reaching the the maximum maximum load load point, point, the the true true stress stress tested tested by by the the strain strain gauge began to decrease. The The true true stress stress obtained obtained through through the the proposed proposed method method continued continued to to increase increase with with the strain increase, until the specimen broke. This This result result is consistent consistent with with the the test test results results of of Xin Xin et et al. al. [4], [4], al. [8] [8] and and Kong Kong et et al. al. [12]. [12]. The true stress and true strain continued to increase with the Yao et al. displacement load after the necking of the specimen. The engineering engineering stress-engineering stress-engineering strain strain curves curves of of I1 I1 and and I2 I2 were were compared compared (Figure (Figure 6), 6), showing showing that that the the increase increase of the strain strain tested tested by by the the strain strain gauge gauge slowed slowed after after the the onset onset of of necking. necking. This is mainly because the strain gauge result is an average value. Although the strain at the necking thethe growth of the average strain value waswas not position increased increased rapidly rapidlyafter afterthe theonset onsetofofnecking, necking, growth of the average strain value obvious in the range of the strain gauge. In In addition, the not obvious in the range of the strain gauge. addition, thetest testresults resultswere werealso also affected affected by by the measuring range of the strain gauge, which means that the strain gauge cannot obtain accurate data when the deformation of the specimen exceeds the strain gauge range.
Metals 2018, 8, 555 Metals 2018, 8, 555
6 of 12 6 of 12
Metals 2018, 8, 555
6 of 12
measuring range of the strain gauge, which means that the strain gauge cannot obtain accurate data when the deformation of the specimen exceeds the strain gauge range.
Figure 6. Comparison of the test results of specimens I1 and I2. Figure 6. Comparison of the test results of specimens I1 and I2. 6. Comparison the and test results specimens in I1 and I2. 7 and 8. The results The test results ofFigure specimens M1, M2,ofO1, O2 areofpresented Figures
The test results M2,I2. O1, and O2 are presented inthe Figures 7 andof 8. specimen The results show the same law of asspecimens specimensM1, I1 and However, compared with test result I1, The test results ofspecimens specimensI1M1, M2, O1, and O2 are presented in Figures 7 and 8. The results show the same law as and I2. However, compared with the test result of specimen I1, there was a significantly lower end for the true stress-true strain curves of specimens M1 and O1. showwas the asame law as specimens I1for andthe I2.true However, compared the test result of specimen I1, there significantly end stress-true strain with curves and This is mainly because lower the initial distance between the gauge points of in specimens the middleM1 part ofO1. the there was a significantly lower end for the true stress-true strain curves of specimens M1 and O1. This is mainly initial distance the gauge pointsparts in theofmiddle part of theasspecimen specimen wasbecause 2 mm, the while it was 5 mmbetween at the upper and lower the specimens, shown in This is mainly because the initial distance between the gauge points in the middle part of the was 2 mm, while it wasthe 5 mm at the and upper lower partspositions of the specimens, as shown in Figure 9. Figure 9. Meanwhile, necking theand final fracture of specimens M1 and O1 were specimen was 2 mm, while itthe was 5 mm at thepositions upper and lower partsM1 of the specimens, as shown Meanwhile, the anddeviated final fracture of specimens and O1 were As either upperin either upper ornecking lower and from the center (dense markers) of the specimen. a result, at 9. Meanwhile, the necking and the final fracture positions of As specimens M1 and O1ofwere orFigure lower and deviated from the center (dense markers) of the specimen. a result, at the end the the end of the specimen stretching, the large distance between gauge points was unable to accurately either upper or lower and deviated from the center (dense markers) of thetospecimen. a result, specimen stretching, the large distance between gauge points was unable accuratelyAs capture theat capture the local strain of the severe necking part. the end of the specimen stretching, the large distance between gauge points was unable to accurately local strain of the severe necking part. capture the local strain of the severe necking part. 800
Specimen M 700 800
Specimen M
(MPa) (MPa) StressStress
600 700 500 600 400 500 300 400
True stress-true strain (M1) True stress-true strain (M2) Engineering stress-engineering strain (M1) True stress-true strain (M1) Engineering stress-engineering strain (M2) True stress-true strain (M2) Engineering stress-engineering strain (M1) Engineering stress-engineering strain (M2)
200 300 100 200 0 100 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.4
0.5
0.6
Strain (mm/mm)
0 0.0
0.1
0.2
0.3
Figure 7. Comparison of the Strain test results of specimens M1 and M2. (mm/mm) Figure 7. Comparison of the test results of specimens M1 and M2.
Figure 7. Comparison of the test results of specimens M1 and M2.
Metals 2018, 8, 555
7 of 12
Metals 2018, 8, 555
7 of 12
Metals 2018, 8, 555
7 of 12
Specimen O Specimen O
800 800
Stress (MPa) Stress (MPa)
600 600 400 400
True stress-true strain (O1) True stress-true strain (O2) True stress-true strain (O1) Engineering stress-engineering True stress-true strain (O2) strain (O1) Engineering stress-engineering strain (O2) Engineering stress-engineering strain (O1)
200 200
Engineering stress-engineering strain (O2) 0 0.0 0
0.2 0.0
0.4 0.2
Strain (mm/mm) 0.4
0.6
0.8 0.6
0.8
Strain (mm/mm)
Figure Figure8.8.Comparison Comparisonofofthe thetest testresults resultsofofspecimens specimensO1 O1and andO2. O2. Figure 8. Comparison of the test results of specimens O1 and O2.
Figure9.9.Distribution Distributiondiagram diagramofofgage gagepoints pointson onspecimen specimenO.O. Figure Figure 9. Distribution diagram of gage points on specimen O.
Verificationof ofthe theResults Results 6.6.Verification 6. Verification of the Results Toverify verifythe theresults resultsofofthe theproposed proposedmethod, method,an anFEM FEM(Finite (FiniteElement ElementMethod) Method)model modelofofI1I1was was To established using Abaqus 6.11 (Dassault Simulia Company, Providence, RI, USA)for for comparative To verify the results6.11 of the proposed method, an FEM (Finite Element Method) model of I1 was established using Abaqus (Dassault Simulia Company, Providence, RI, USA) comparative analysis. The 3D FEM was meshed with C3D8R element. In addition, theUSA) intermediate part established using Abaqus 6.11 (Dassault Simulia Company, Providence, for comparative analysis. The 3D FEM was meshed with thethe C3D8R element. In addition, the RI, intermediate part of theof the specimen was refined, as shown in Figure 10. The element size in the refines zone is 0.125 mm. analysis. The 3D FEM was meshed with the C3D8R element. In addition, the intermediate part of the specimen was refined, as shown in Figure 10. The element size in the refines zone is 0.125 mm. The The transition a coarse mesh away from middle region athe fine mesh the middle region specimen wasfrom as shown in Figure 10.the The element size refines zone is 0.125region mm. The transition from arefined, coarse mesh away from the middle region to atoin fine mesh in in the middle isis achieved byfrom using astructured structured transitional mesh pattern. Asthe theamesh mesh inthe thein middle section theis transition a acoarse mesh transitional away from mesh the middle region to fine in mesh the middle region achieved by using pattern. As middle section ofofthe specimen was refined, there geometric imperfection implied to induce Total number achievedwas by using a structured transitional mesh pattern. As the mesh inthe thenecking. middle section of the specimen refined, thereisisnono geometric imperfection implied to induce the necking. Total of elements and refined, nodes 8204are and specimen was there is no10,285, geometric imperfection implied to induce the necking. Total number of elements andare nodes 8204 and respectively. 10,285, respectively. GTNmodel waschosen chosen the material’s model.The Thefailure failurecriterion criterionisisEquation Equation(5) (5)[22]. [22]. number ofmodel elements and nodes arematerial’s 8204 andmodel. 10,285, respectively. GTN was asasthe GTN model was chosen as the !2 material’s model. The!failure criterion is Equation (5) [22]. σe 2 2 3 3q q2 σm 2 *∗ e ΦΦ== − + 2q f cosh q *( f ∗=)20= 0 (5) (5) + 2 q f cosh 32 q− −m −1−−1q− 1 1 3 f3 − 2 2 σ2 m * 2 (5) Φ = σ −e + 2q1 f * cosh =0 − − 1 − q3 f
2
( ) ( )
Metals 2018, 8, 555
8 of 12
Metals 2018, 8, x FOR PEER REVIEW
8 of 12
−
q2 is flow stress; m is the average normal stress;8qof1, 12 e − and where q3 are coefficients. Needleman [23]stress; proposed byaverage setting normal q1 = 1.5, stress; q2 = 1.0q1and equivalentand stress; is the , q2 is flow e is misesTvergaard m that Metalswhere 2018, 8, 555
is mises equivalent stress;
− could be achieved. f* is a function of the void volume fraction q = qq132 are a better fit to experimental data and coefficients. Tvergaard and [23] that by settingstress; q1 = 1.5, 1.0 and q where σe is mises equivalent stress; is flow stress; σmproposed is the average normal q1 ,qq22=and q3 are σ Needleman f and is defined as follows: 2 =coefficients. q12 a better fit to experimental data could be achieved. f* is a function of the void volume fraction Tvergaard and Needleman [23] proposed that by setting q1 = 1.5, q2 = 1.0 and q = q1 fa and is defined as follows: data could If f offthe better fit to experimental void volume fraction f and is f be achieved. f * is a function c
f u* − f c If f f f If f ≤Iff c f c cf f F f = f c + (6) * f ∗ ffcc f u − f c If f c ≤ f ≤ f F f ∗ = ffuF f−− * (6) + c f F − fc f = f c + If f c f f F (6) f If f f f − f F If f ≥ f F F F f F c f F If f f F For the API X65 pipeline steel, both Sandvik et al. [25] found that when Sandvik et al. [24] and Dybwad
defined as follows:
*
fcc ==0.13, the results numerical simulations experiments are ingood good agreement. 0.15when 0.13,the theAPI results of numerical andet experiments in f fFF ==that 0.15 ++ 2f 00.. For X65of pipeline steel, both Sandvik al. [24] andare Dybwad etagreement. al. [25] found In addition, f 00 was chosen as 0.00015 according to Han et al. [18]. was chosen as 0.00015 according to Han et al. [18]. fc = 0.13, the results of numerical simulations and experiments are in good agreement. fF = 0.15 + 2f0. The load is displacement-controlled. displacement-controlled. The specimen was loaded The to specimen was loaded by by applying applying aa load load on one end In addition, f0 was chosen as 0.00015 according Han et al. [18]. the other end was fixed. The stretching process is displayed in Figure 11. The processes of while other end was fixed. The stretching process is displayed in Figure 11. The The load is displacement-controlled. The specimen was loaded by applying a load onprocesses one end uniform stretching, necking, rapid necking development, and fracture are accurately simulated. The of uniform stretching, necking, rapid necking process development, and fracture are 11. accurately simulated. while the other end was fixed. The stretching is displayed in Figure The processes of engineering stress and the load are in a proportional relationship, as are the engineering strain and The engineering stress and the load are in a proportional relationship, as are the engineering strain uniform stretching, necking, rapid necking development, and fracture are accurately simulated. The the so the the engineering stress-engineering strain curves (as(as an the and displacement, the displacement, so the engineering stress-engineering strain curves analternative alternative ofand engineering stress and load are in a proportional relationship, as are the engineering strainof load-displacement curve) obtained by the FEM and the proposed method (Figure 12) were obtained bystress-engineering the FEM and the proposed method (Figure 12) were the displacement, socurve) the engineering strain curves (as an alternative of compared. the loadcompared. If the error is small, the test results of the proposed method are reliable. If the error is small, the test results of the proposed method are reliable. displacement curve) obtained by the FEM and the proposed method (Figure 12) were compared. If the error is small, the test results of the proposed method are reliable.
Figure 10. Specimen′s Figure 10. Specimen0 s finite finite element element model. model. Figure 10. Specimen′s finite element model.
(a) (a)
(b)
(c)
(b)
(c) Figure 11. Cont.
(d) (d)
Metals 2018, 8, 555 Metals2018, 2018,8,8,x 555 Metals FOR PEER REVIEW
9 of 12 9 9ofof1212
(e)
(f)
(g)
(h)
Figure 11. Stretching in finite element (e) process of the specimen (f) (g) simulation. (a) chuck (h) displacement 1.3 mm; (b) chuck displacement 6.4 mm; (c) chuck displacement 15.6 mm; (d) chuck displacement 17.6 Figure 11. Stretching process the specimen ininfinite element simulation. (a) chuck displacement 1.3 Figure 11.chuck Stretching processofof the specimen finite element simulation. chuck displacement mm; (e) displacement 18.3 mm; (f) chuck displacement 19.3 mm; (g) (a) chuck displacement 20.3 mm;mm; (b) chuck displacement 6.4 mm; (c) chuck displacement 15.6 15.6 mm;mm; (d) chuck displacement 17.6 1.3 chuck displacement mm; (c) chuck displacement (d) chuck displacement mm; (h)(b) chuck displacement 21.16.4 mm. mm;mm; (e) chuck displacement 18.3 18.3 mm;mm; (f) chuck displacement 19.3 19.3 mm;mm; (g) chuck displacement 20.3 17.6 (e) chuck displacement (f) chuck displacement (g) chuck displacement mm; (h) chuck displacement 21.1 mm. 20.3 mm; (h) chuck displacement 21.1 mm. 600 600 500
Stress (MPa) Stress (MPa)
500 400 400 300
the new method finite element method strain gauge method the new method finite element method strain gauge method
300 200 200 100 100
0 0.0
0.2
0.4
0.6
0.8
1.0
Strain (mm/mm)
0 0.0
0.2
0.4
0.6
0.8
1.0
Strain stress-engineering (mm/mm) Figure 12. Comparison of the engineering strain of three methods.
Figure 12. Comparison of the engineering stress-engineering strain of three methods.
Before necking occurs, the three results are basically coincident. After the onset of necking, Figure 12. strain Comparison ofdecreased the engineering stress-engineering strain of three the test results of the gauge rapidly, while the results ofAfter the proposed and the Before necking occurs, the three results are basically coincident. the methods. onsetmethod of necking, the FEM gently. Before thedecreased engineering strain reached 0.8, the engineering stress of the proposed test decreased results of the strain gauge rapidly, while the results of the proposed method and the Before occurs, therelatively three results areWhen basically coincident. After the onset0.74, of necking, the method andnecking the FEM wereBefore still close. the engineering reached the error of FEM decreased gently. the engineering strain reached 0.8,strain the engineering stress of the test results of the strain gauge decreased rapidly, while the results of the proposed method and the the engineering stresses between two methods was 3.5%,When whichthe is still within anstrain acceptable range. proposed method and the FEM the were still relatively close. engineering reached 0.74, FEMcomparison decreased results gently.show Before the engineering strain is reached 0.8, the engineering stress of the The that the proposed method feasible. the error of the engineering stresses between the two methods was 3.5%, which is still within an proposed method and the FEM wereof still relatively close. When thetest engineering strain reached 0.74, For further illustrating the effect gauge point on the results, seven values of gauge acceptable range. The comparison results show thatdistance the proposed method is feasible. the error of the engineering stresses two 3.5%, which still within an point distance (GPD) were studied. Thebetween values ofthe GPD aremethods 0.25 mm,was 0.75the mm, mm,is2.0 mm, 2.5 mm, For further illustrating the effect of gauge point distance on test1.75 results, seven values of acceptable range. The comparison results show that the proposed method is feasible. 3.5 mm, and 5 mm, respectively. The engineering strain-engineering stress curves for different GPD gauge point distance (GPD) were studied. The values of GPD are 0.25 mm, 0.75 mm, 1.75 mm, 2.0 For further illustrating the effect of gauge distance on that the test of gauge values are presented in Figure Asrespectively. shown in point Figure 13, except the results, GPD is seven 5mm, values the engineering mm, 2.5 mm, 3.5 mm, and 5 13. mm, The engineering strain-engineering stress curves for point distance (GPD) werecurves studied. valuesGPD of GPD are 0.25 almost mm, 0.75 mm, 1.75 mm, 2.0when mm, the 2.5 stress-engineering strain of The different different GPD values are presented in Figure 13. Asvalues shown are in Figure 13,coincident. except that Even the GPD is 5mm, mm, 3.5 mm, and 5 mm, respectively. The engineering strain-engineering stress curves for different engineering strainstress-engineering reached 0.92, the strain differences between thoseGPD engineering stress-engineering strain the engineering curves of different values are almost coincident. Even GPD values are presented in Figure 13. As shown in Figure 13, except that the GPD is 5mm, the curves veryengineering small. Thus, strain the GPDreached should be less than equal to 3 mm (2 mm are recommended) when are the 0.92, the or differences between those engineering engineering stress-engineering strain curves of different GPD values are almost coincident. Even when the proposedstrain method is used for obtaining thethe whole-range tensile properties of stress-engineering curves are very small. Thus, GPD shoulduniaxial be less than or equal to 3 mm when the engineering strain reached 0.92, the differences between those engineering stresspipeline steel. (2 mm are recommended) when the proposed method is used for obtaining the whole-range uniaxial engineering strain curves are very small. Thus, the GPD should be less than or equal to 3 mm (2 mm tensile properties of pipeline steel. are recommended) when the proposed method is used for obtaining the whole-range uniaxial tensile properties of pipeline steel.
Metals 2018, 8, 555
10 of 12
Metals 2018, 8, 555
10 of 12
600
Engineering Stress (MPa)
500
400
GPD=0.25 GPD=0.75 GPD=1.75 GPD=2.0 GPD=2.5 GPD=3.5 GPD=5
300
200
100
0 0.0
0.5
1.0
Engineering strain (mm/mm)
Figure 13. Comparison of engineering strain-engineering stress curves for different gauge point displacements.
Figure 13. Comparison of engineering strain-engineering stress curves for different gauge point displacements. 7. Conclusions
In a traditional uniaxial tensile experiment, a strain gauge is generally used to measure the strain 7. Conclusions value, with a gauge distance of 10 mm. In this paper, a method for testing the true stress-true strain traditional uniaxial tensile experiment, strain gauge is generally usedcapture to measure the curvesInofapipeline steel was proposed using a scaleadistance of 2 mm, which could subtler strain value, with a gauge distance of 10 mm. In this paper, a method for testing the true stress-true stress and strain values. The proposed method and the traditional strain gauge method were both strain pipeline steel was proposed using scale distance 2 mm, which used to curves test theofengineering stress-engineering strain acurves and true of stress-true strain could curvescapture of six subtler stress and strain values. proposed method andcurves the traditional method were specimens in three groups. Next, The the true stress-true strain obtainedstrain by thegauge proposed method both used to test the engineering stress-engineering strain curves and true stress-true strain curves were verified and checked by the established finite element model. Finally, the test results of both of six specimens in threeand groups. Next,The themain true conclusions stress-true strain obtained by the proposed methods were compared analyzed. are ascurves follows: method were verified and checked by the established finite element model. Finally, the test results of (1) The true stress-true strain curve and engineering stress-engineering strain curve are basically both methods were compared and analyzed. The main conclusions are as follows: coincident in the results of the proposed method and the traditional strain gauge method before the (1)necking. The true strain and engineering strainiscurve are onset of Thisstress-true indicates that the curve pre-necking data obtainedstress-engineering by the proposed method effective basically coincident in the results of the proposed method and the traditional strain gauge method and reliable. before the onset of necking. This obtained by the the proposed proposed (2) After the onset of necking, theindicates true stressthat andthe truepre-necking strain valuesdata obtained through methodcontinued is effective reliable. method toand increase with load displacement. However, the true strain value obtained by the (2) After the onset of necking, the the true stress and trueshowed strain values obtained through traditional strain gauge grew slowly and true stress value a decreasing trend, which the is proposedillogical. method The continued to increase withcould load not displacement. true strain value obviously traditional strain gauge get effectiveHowever, data after the the onset of necking, obtained by the traditional strain grew and and the true stress value showed a decreasing but the proposed method could stillgauge capture theslowly true stress the true strain. trend, which is obviously illogical. The traditional strain gauge could not get data after the (3) The true stress-true strain curve of the proposed method was verified byeffective the established finite onset ofmodel. necking, the proposed method could strain still capture true two stress and thewere true compared, strain. element Thebut engineering stress-engineering curves the of these methods (3) The true stress-true strain curve of the proposed method was verified by the established and the results show that they are very close when the strain is less than 0.74. finite model. The engineering of these on twothe methods were (4)element The layout of gauge points in thestress-engineering proposed methodstrain has a curves great influence accuracy of compared, andand the the results show that they are very close when the strain is less than 0.74. the test results, smaller the distance between gauge points, the more accurate the test results (4)The Thegauge layoutpoints of gauge points the proposed method a great influence on the the distance accuracyisof will be. should bein evenly distributed alonghas a symmetric line, and the test results, the than smaller the distance between gauge points, the more accurate the test results recommended toand be less 3 mm. will be. The gauge points should be evenly distributed along a symmetric line, and the distance is Author Contributions: recommended to be Conceptualization, less than 3 mm. L.K. and L.S.; Methodology, X.Z.; Software, L.C.; Validation, X.Z., J.C.
and C.M.; Formal Analysis, L.C.; Investigation, L.K.; Resources, L.S.; Data Curation, L.C.; Writing-Original Draft Preparation, L.K.; Writing-Review and Editing, X.Z.; Visualization, J.C.; Supervision, X.Z.; Project Administration, Author Contributions: L.K. and L.S.; Methodology, X.Z.; Software, L.C.; Validation, X.Z., L.C.; Funding Acquisition,Conceptualization, L.K. J.C. and C.M.; Formal Analysis, L.C.; Investigation, L.K.; Resources, L.S.; Data Curation, L.C.; Writing-Original Acknowledgments: The authors gratefully acknowledge the sponsorship of this work by the Young Scholars Draft Preparation, L.K.; Writing-Review and Editing, X.Z.; Visualization, J.C.; Supervision, X.Z.; Project Development Fund of SWPU (Grant No. 201699010002), PetroChina Innovation Foundation (Grant No. Administration, L.C.; Funding Acquisition, L.K. 2016D-5007-0602), Scientific Research Starting Project of SWPU (No. 2017QHZ003), and National Key R&D Program of China (Grant No. 2016YFC0802100). Acknowledgments: The authors gratefully acknowledge the sponsorship of this work by the Young Scholars Development Fund of SWPU (Grant No. 201699010002), PetroChina Innovation Foundation (Grant No.
Metals 2018, 8, 555
11 of 12
Conflicts of Interest: The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.
References 1. 2. 3.
4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
17. 18. 19. 20. 21. 22.
Shuai, J.; Tu, S.; Wang, J.; Ren, X.; He, J.; Zhang, Z. Determining critical CTOA from energy-load curves with DWTT specimen. Eng. Fract. Mech. 2017, 186, 47–58. [CrossRef] Paredes, M. Plastic limit load and its application to the fracture toughness testing for heterogeneous single edge notch tension specimens. Fatigue Fract. Eng. Mater. Struct. 2014, 37, 265–279. [CrossRef] Dadfarnia, M.; Sofronis, P.; Somerday, B.P.; Balch, D.K.; Schembri, P.; Melcher, R. On the environmental similitude for fracture in the SENT specimen and a cracked hydrogen gas pipeline. Eng. Fract. Mech. 2011, 78, 2429–2438. [CrossRef] Xin, X.X.; Yao, Y.Z.; Zhang, K.L.; Fan, Y.G. Analysis on security of pipeline steel with high yield ratio. Weld. Pipe Tube 2006, 29, 36–39. (In Chinese) Wang, C.L. The calculation model and test system for true stress-true strain. CN 101319977A, 10 December 2008. Zhang, Z.L.; Hauge, M.; Ødegård, J.; Thaulow, C. Determining material true stress–strain curve from tensile specimens with rectangular cross-section. Int. J. Solids Struct. 1999, 36, 3497–3516. [CrossRef] Zhang, Z.L.; Hauge, M.; Thaulow, C.; Ødegård, J. A notched cross weld tensile testing method for determining true stress–strain curves for weldments. Eng. Fract. Mech. 2002, 69, 353–366. [CrossRef] Yao, D.; Cai, L.X.; Bao, C. An approach for full-range uniaxial constitutive relationships of ductile materials. Chin. Meas. Test 2014, 40, 5–13. (In Chinese) Joun, M.S.; Eom, J.G.; Min, C.L. A new method for acquiring true stress–strain curves over a large range of strains using a tensile test and finite element method. Mech. Mater. 2008, 40, 586–593. [CrossRef] Kamaya, M.; Kawakubo, M. A procedure for determining the true stress–strain curve over a large range of strains using digital image correlation and finite element analysis. Mech. Mater. 2011, 43, 243–253. [CrossRef] Kong, L.; Shuai, J.; Zhou, X.; Chao, Y.; Han, K. A Universal Method for Acquiring the Constitutive Behaviors of API-5 L X90 Welds. Exp. Mech. 2016, 56, 165–176. [CrossRef] Kong, L.Z.; Shuai, J.; Zhou, X.Y.; Huang, K.; Yu, G.J. True stress-logarithmic strain curves test of pipeline steels using 3D digital image correlation. Optoelectron. Adv. Mater. Rapid Commun. 2015, 9, 1380–1388. Devivier, C.; Pierron, F.; Wisnom, M.R. Impact damage detection in composite plates using deflectometry and the Virtual Fields Method. Composites Part A 2013, 48, 201–218. [CrossRef] Brown, R.; Tang, W.; Reynolds, A.P. Multi-pass friction stir welding in alloy 7050-T7451: Effects on weld response variables and on weld properties. Mater. Sci. Eng. A 2009, 513, 115–121. [CrossRef] Scintilla, L.D.; Tricarico, L.; Brandizzi, M.; Satriano, A.A. Nd:YAG laser weldability and mechanical properties of AZ31 magnesium alloy butt joints. J. Mater. Process. Technol. 2010, 210, 2206–2214. [CrossRef] Poulain, X.; Kohlman, L.W.; Binienda, W.; Roberts, G.D.; Goldberg, R.K.; Benzerga, A.A. Determination of the intrinsic behavior of polymers using digital image correlation combined with video-monitored testing. Int. J. Solids Struct. 2013, 50, 1869–1878. [CrossRef] Grytten, F.; Daiyan, H.; Polanco-Loria, M.; Dumoulin, S. Use of digital image correlation to measure large-strain tensile properties of ductile thermoplastics. Polym. Test. 2009, 28, 653–660. [CrossRef] Han, K.J.; Shuai, J.; Deng, X.M.; Kong, L.Z.; Zhao, X.; Sutton, M. The effect of constraint on CTOD fracture toughness of API X65 steel. Eng. Mech. Fract. 2014, 124, 167–181. [CrossRef] Boyce, B.L.; Reu, P.L.; Robino, C.V. The constitutive behavior of laser welds in 304L stainless steel determined by digital image correlation. Metall. Mater. Trans. A 2006, 37, 2481–2492. [CrossRef] ISO 6892-1-2009. Metallic Materials—Tensile Testing—Part 1: Method of Test at Room Temperature; ISO: Geneva, Switzerland, 2009. GB/T 228-2002. Metallic Materials—Tensile Testing at Ambient Temperature; General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China: Beijing, China, 2002. Tvergaard, V. Influence of Voids on Shear Band Instabilities Under Plane Strain Conditions. Int. J. Fract. 1981, 17, 389–407. [CrossRef]
Metals 2018, 8, 555
23. 24. 25.
12 of 12
Tvergaard, V.; Needleman, A. Analysis of the Cup-Cone Fracture in a Round Tensile bar. Acta Metall. 1984, 32, 157–169. [CrossRef] Sandvik, A.; Østby, E.; Thaulow, C. A probabilistic fracture mechanics model including 3D ductile tearing of bi-axially loaded pipes with surface cracks. Eng. Fract. Mech. 2008, 75, 76–96. [CrossRef] Dybwad, J.; Østby, E.; Törnqvist, R.; Thaulow, C. Simulations of Ductile Tearing at Large Strains of Biaxially Loaded Pipes. In Proceedings of the 28th International Conference on Ocean, Offshore and Arctic Engineering, Honolulu, HI, USA, 31 May–5 June 2009. © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
