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Influence of high stress triaxiality on mechanical strength of ASTM A36, ASTM A572 and ASTM A992 steels
Construction and Building Materials 176 (2018) 129–134
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Technical note
Influence of high stress triaxiality on mechanical strength of ASTM A36, ASTM A572 and ASTM A992 steels Hizb Ullah Sajid, Ravi Kiran ⇑ Dept. of Civil & Env. Engg., North Dakota State University, ND 58105, United States
a r t i c l e
i n f o
Article history: Received 17 January 2018 Received in revised form 23 April 2018 Accepted 3 May 2018
Keywords: ASTM A36 steel ASTM A572 steel ASTM A992 steel Stress triaxiality Yield strength Ultimate tensile strength
a b s t r a c t This study aims at investigating the influence of high stress triaxiality on the yield strength and ultimate tensile strength of commonly used structural steels (ASTM A36, ASTM A572 and ASTM A992). To this end, axisymmetrically notched steel specimens are designed to generate a range of stress triaxialities. Yield strength and ultimate tensile strength of notched steel specimens are then determined using engineering stress-strain curves obtained from uniaxial tensile testing of notched specimens. Yield strength and ultimate tensile strength of all three types of structural steels are found to increase linearly with increase in stress triaxiality of test specimens. Based on experimental and complimentary finite element results, predictive equations are proposed to estimate increased yield strength and ultimate tensile strength as a function of stress triaxiality in structural steels. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction In service conditions, structural steels are routinely subjected to stress concentrations that arise from geometric discontinuities like holes, sharp corners, welds, etc. that are commonly observed in steel structures. Stress concentration is quantified by a dimensionless parameter referred to as stress triaxiality (Tr). Stress triaxiality is defined as the ratio between hydrostatic stress and von-Mises stress. Higher stress triaxiality aggravates the growth of microvoids in steel matrix [1], which in turn accelerates ductile fracture initiation in steels [2]. High stress triaxiality thus leads to reduction in ductility of steels [3]. Experimental and numerical studies on high strength low alloy structural steels (ASTM A992) have confirmed the adverse effects of stress triaxiality on ductility of structural steels [4,5]. However, the quantitative relationships between stress triaxiality and yield strength and ultimate tensile strength of structural steels that are important design parameters in structural design [6] are not currently addressed. Past studies conducted on different alloys and stainless steels have reported an increase in tensile strength with an increase in stress concentration [7–9]. Un-anticipated increase in yield strength and ultimate tensile strength of structural steels may lead to unintended consequences
⇑ Corresponding author. E-mail addresses: [email protected] (H.U. Sajid), [email protected] (R. Kiran). https://doi.org/10.1016/j.conbuildmat.2018.05.018 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.
in structural systems. For instance, stronger beams cause failure of columns leading to global collapse of the structure (strong beamweak column). Components like reduced beam sections, seismic fuse components should fail at pre-designed loads to protect the overall integrity and to avoid progressive collapse of structure. It is therefore, important to account for the increased yield strength and ultimate tensile strength due to high triaxiality in the design stage of steel structures [10]. With this objective in mind, the current study aims to establish a quantitative relationship between stress triaxiality, yield strength and ultimate tensile strength of structural steels (at a material level) that are widely used in construction industry. In this study, a mild steel (ASTM A36 [11]) along with two high strength low alloy (HSLA) steels (ASTM A572 [12] and ASTM A992 [13]) are investigated. ASTM A36 and ASTM A992 are predominantly used in construction of steel buildings in the United States whereas ASTM A572 steels are typically used in the construction of bridges [14–16]. ASTM A992 is currently the most common and preferred grade of structural steel used for wide flange shapes in the United States [16,17]. 2. Experimental study and finite element modeling Preliminary finite element analyses are conducted by choosing different geometries of notched tension specimens to generate a range of stress triaxialities. Based on the results obtained from preliminary study, six axisymmetrically notched tension specimens
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are selected. These test specimens are classified as CN (circularnotched specimens), UN (U-notched specimens) and VN (V-notched specimens). The reference un-notched test specimens are labelled as SPR (reference un-notched test specimen). Detailed geometric illustrations of the un-notched and notched specimens are provided in Fig. 1. The chemical composition of all the three steels used in this study as specified by the manufacturer are summarized in Table 1. In total, 42 test specimens are tested as a part of this experimental study. These specimens are machined using computer numerically controlled (CNC) lath machine with a tolerance of ± 0.025 mm. The load-displacement behavior of all the test specimens are obtained by conducting uniaxial tension tests using servohydraulic MTS 809 system at a displacement rate of 0.02 mm/s. An Epsilon Model 3542 contact extensometer with 1-inch gage length is used to record the strains. The total load and elongation in the gage length are obtained at a sampling rate of 99 Hz, for both un-notched and notched test specimens. Engineering stress-strain curves of un-notched and notched test specimens are provided in Fig. 2. Near perfect repeatability of load-displacement curves is obtained for all the un-notched and notched test specimens. For the sake of clarity, stress-strain curve of only one representative specimen is provided for each un-notched and notched test specimen. Mechanical properties of test specimens evaluated from experimental stress strain curves are provided in Table 2. Nonlinear finite element analysis is conducted to obtain stress triaxiality profiles across critical cross-section at two different loading stages: a) initial stage of loading (corresponding to 1.35 ± 0.5% engineering strain), and b) ultimate load (strain corresponding to maximum stress in engineering stress-strain curve), as shown in Fig. 3. Maximum initial stress triaxiality (T ir;max ) ranges from 0.33 to 1.15. Finite element analyses are conducted using ABAQUSÒ finite element modeling software. All test specimens are modeled using four noded bilinear axisymmetric CAX4 elements and geometric non-linearity is considered. J2 plasticity model is used as the constitutive model. For all steels, the true stress strain curves obtained from the corresponding SPR specimens are used as the strain hardening curves in J2 plasticity model and are provided in Fig. 4. The applied boundary conditions and loading along with
Notch location
Table 1 Chemical composition of ASTM A36, ASTM A572, and ASTM A992 structural steels. Chemical composition (%)
ASTM A36
ASTM A572 Gr. 50
ASTM A992
Carbon (C) Manganese (Mn) Phosphorous (P) Sulphur (S) Silicon (Si) Copper (Cu) Chromium (Cr) Nickle (Ni) Molybdenum (Mo) Vanadium (V) Titanium (Ti) Niobium (Nb) Iron (Fe)
0.1500 0.6900 0.0180 0.0040 0.1800 0.2400 0.1500 0.0880 0.0195 0.0048 0.0012 0.0024 98.4521
0.0500 1.3400 0.0110 0.0040 0.1500 0.2800 0.1900 0.1300 0.0400 0.0830 0.0010 0.0030 97.7180
0.1000 0.9300 0.0160 0.0440 0.1900 0.2500 0.1400 0.0900 0.0200 0.0010 – 0.0210 98.1980
some typical finite element meshes used in the vicinity of the notches are provided in Fig. 5. 3. Results and discussion In this section, stress-strain curves, yield strength (ry) and ultimate tensile strength (ru) obtained from uniaxial tensile tests are discussed. Using engineering stress-strain curves, yield strength of each test specimen is determined based on 0.2% strain offset method [18]. The maximum engineering stress is taken as the ultimate tensile strength of steel. As observed in Fig. 2, stress-strain curves of notched specimens are characterized by significant reduction in ductility and increase in ultimate tensile strength as compared to un-notched specimens, for all three types of steels. A well-defined yield plateau is observed in un-notched specimens which diminishes in case of notched specimens with high stress triaxiality. It is observed that all notched specimens exhibited substantial increase in both yield strength and ultimate tensile strength as compared to un-notched steel specimens. Among notched steel specimens, highest yield strength and ultimate tensile strength is exhibited by specimens with highest average initial and average ultimate triaxialities (UN1 and VN1), respectively. In
D19
R 4.5
D10
19
10 25 25
25
50
Cross-section
SPR 10
R1.0
10
CN1
R2.0
R3.0
CN3
CN2
6.92
4 10
10
1
45°
R1.0
10
60°
10
2 UN1
VN1
SPR = Reference un-notched test specimen,
2 VN2
CN = C-notch, UN = U-notch, VN = V-notch
Fig. 1. Geometric details of axisymmetric test specimens (all dimensions are in mm.).
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VN2
CN2
VN1
VN1 UN1 VN2
(a) ASTM A36
UN1
(b) ASTM A572
CN3 SPR CN1
CN2
CN1
SPR
CN3
VN1 VN2 UN1
(c) ASTM A992 CN1 SPR
CN2 CN3
Fig. 2. Engineering stress-strain curves of un-notched and notched test specimens.
Table 2 Experimental material properties of structural steels (obtained from un-notched test specimens) and comparison with ASTM standards. Steel type
Material property
ASTM specification
Experimental result
ASTM A36
Min. yield strength (MPa) Tensile strength (MPa) Min. elongation over 200 length (%) Min. yield strength (MPa) Min. tensile strength (MPa) Min. elongation over 200 length (%) Yield strength (MPa) Min. tensile strength (MPa) Min. elongation over 200 length (%) Max. yield to tensile strength ratio
250 400–550 23 345 450 21 345–450 450 21 0.85
386.48 517.09 40.65 (over 100 length) 389.15 502.40 44.81 (over 100 length) 354.46 484.47 45.07 (over 100 length) 0.74
ASTM A572 Gr. 50
ASTM A992
case of ASTM A36 steel, the yield strength of notched specimens increased by as much as 70% as compared to un-notched steel specimens. Both ASTM A572 and A992 steels exhibited almost similar increase (up to 57% and 60%, respectively) as compared to un-notched specimens. The ultimate tensile strength of notched specimens made of all three steels exhibited almost similar increase (ASTM A36-51%, ASTM A572-54%, ASTM A992-53%) when compared to ultimate tensile strength of corresponding unnotched specimens. Average yield strength (ry) of (two) test specimens for a given geometry is plotted as a function of spatially averaged initial triaxiality (T iavg ), as shown in Fig. 6. The spatially averaged initial triaxiality (T iavg ) is evaluated by averaging the triaxiality over the critical cross section of the notched test specimen at a total strain of 1.35 ± 0.5%. The average ultimate tensile strength (ru) of two test specimens for a given geometry is plotted against spatially averaged triaxiality evaluated at a
strain corresponding to ultimate load (T uavg ), as shown in Fig. 7. Triaxiality is dependent on the shape of the notch and material properties. The notches in the test specimens may undergo significant shape change before the ultimate tensile strength is achieved. This shape change in the notch is accounted by choosing T uavg which is obtained by evaluating the spatial average of triaxiality across the critical cross section at the strain corresponding to ultimate tensile strength. From Fig. 6, it is clear that the yield strength increases linearly with increase in stress triaxiality for all the three steels. Similarly, the ultimate tensile strength is observed to increase linearly with increase in stress triaxiality, for all three types of steels, as shown in Fig. 7. Based on experimental and finite element results, the following predictive equations are proposed to estimate yield strength and ultimate tensile strength as a function of spatially averaged initial stress triaxiality, and spatially averaged ultimate stress triaxiality, respectively.
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VN1 UN1
UN1
CN2 VN2
VN1
CN3
VN2
CN2
CN1 SPR
CN1
CN3
(a) SPR = Reference un-notched test specimen,
SPR
(b) CN = C-notch, UN = U-notch, VN = V-notch
Fig. 3. (a) Initial stress triaxiality profiles, (b) stress triaxiality profiles at ultimate load.
ASTM A572 steel
ry ¼ 407:33T iavg þ 266:41
ð3Þ
ru ¼ 489:10T uavg þ 334:41
ð4Þ
ASTM A992 steel
Fig. 4. Strain hardening curves of un-notched test specimens used in finite element analysis.
ASTM A36 Steel
ry ¼ 498:59T iavg þ 218:28
ð1Þ
ru ¼ 482:50T uavg þ 351:26
ð2Þ
ry ¼ 403:75T iavg þ 227:78
ð5Þ
ru ¼ 473:96T uavg þ 323:57
ð6Þ
The authors hypothesize that the strain localization in the vicinity of the notch leads to high strain hardening which ultimately results in increased yield strength and ultimate tensile strength. Increase in the yield strength with increase in triaxiality is also reported for AISI 1080 steel and Al T6061 alloys [9,19]. Currently, there is no clear consensus on the exact cause for the increase in yield strength/ultimate tensile strength of notched specimens and further microscale experimentation is needed to investigate the root cause behind this phenomena.
Boundary Conditions: @ x = 0; uz = 0 @ z = 0; ux = 0
(a) (b)
(c)
z
x (d) Fig. 5. (a) Applied boundary and loading conditions, (b) typical C-notch mesh, (c) typical U-notch mesh, and (d) typical V-notch mesh.
H.U. Sajid, R. Kiran / Construction and Building Materials 176 (2018) 129–134
Fig. 6. Average initial stress triaxiality versus yield strength.
Fig. 7. Average ultimate stress triaxiality versus ultimate tensile strength.
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4. Conclusions Following are important conclusions drawn from this study: 1. Yield strength of structural steels increased linearly with increase in stress triaxiality. About 70% increase in yield strength is observed in ASTM A36 steel when the triaxiality is changed from T iavg ¼ 0:32 to T iavg ¼ 0:84. For a similar change in triaxiality, ASTM A572 and ASTM A992 recorded 57% and 60% increase in yield strength, respectively. 2. Ultimate tensile strength of structural steels also increased linearly with increase in stress triaxiality. An increase up to 54% in ultimate tensile strength is observed for all the three structural steels considered in this study when the T uavg is increased from 0.34 to 0.88. Conflict of interest No conflict of interest. Acknowledgements The financial support from NDSU Research and Creative Activity and NDSU Department of Civil and Environmental Engineering is gratefully acknowledged by the authors. References [1] R. Kiran, K. Khandelwal, A micromechanical model for ductile fracture prediction in ASTM A992 steels, Eng. Fract. Mech. 102 (2013) 101–117.
[2] T.L. Anderson, Fracture Mechanics: Fundamentals and Applications, third ed., Taylor & Francis, 2005. [3] A.M. Agogino, Notch effects, stress state, and ductility, J. Eng. Mater. Technol. 100 (1978) 348–355. [4] R. Kiran, K. Khandelwal, Experimental studies and models for ductile fracture in ASTM A992 steels at high triaxiality, J. Struct. Eng. 140 (2013) 04013044. [5] R. Kiran, K. Khandelwal, A triaxiality and Lode parameter dependent ductile fracture criterion, Eng. Fract. Mech. 128 (2014) 121–138. [6] American Institute of Steel Construction (AISC), AISC 360-05-Specification for Structural Steel Buildings, ANSI/AISC, Chicago, 2005. [7] W.D. Jenkins, W.A. Willard, Effect of temperature and notch geometry on the tensile behavior of a titanium alloy, NBS J. Eng. Instrum. 73 (1966) 5–11. [8] J. Ganesh Kumar, M. Nandagopal, P. Parameswaran, K. Laha, M. Mathew, Effect of notch root radius on tensile behaviour of 316L (N) stainless steel, Mater. High Temp. 31 (2014) 239–248. [9] X. Lei, C. Li, X. Shi, X. Xu, Y. Wei, Notch strengthening or weakening governed by transition of shear failure to normal mode fracture, Sci. Rep. 5 (2015) 10537. [10] American Institute of Steel Construction, Manual of Steel Construction, thirteenth ed., AISC, Chicago, 2005. [11] ASTM International, A36/A36M-14 Standard Specification for Carbon Structural Steel, ASTM International, West Conshohocken, PA, 2014. [12] ASTM International, Standard Specification for High-Strength Low-Alloy Columbium-Vanadium Structural Steel, ASTM International, West Conshohocken, PA, 2015. [13] ASTM International, Standard Specification for Structural Steel Shapes, ASTM International, West Conshohocken, PA, 2015. [14] R. Bjorhovde, Development and use of high performance steel, J. Constr. Steel Res. 60 (2004) 393–400. [15] E.M. Aziz, V.K. Kodur, Effect of temperature and cooling regime on mechanical properties of high-strength low-alloy steel, Fire Mater. 40 (2016) 926–939. [16] K. Gustafson, P. SE, Evaluation of existing structures, Mod. Steel Constr. 47 (2007) 41. [17] G. Hu, M.A. Morovat, J. Lee, E. Schell, Elevated Temperature Properties of ASTM A992 Steel, in: Structures Congress 2009, American Society of Civil Engineers, 2009, pp. 1067–1076. [18] ASTM International, ASTM A6/A6M-17a Standard Specification for General Requirements for Rolled Structural Steel Bars, Plates, Shapes, and Sheet Piling, ASTM International, West Conshohocken, PA, 2017. [19] R.W. Hertzberg, R.P. Vinci, J.L. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, fifth ed., John Wiley and Sons, 2012.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Technical note
Influence of high stress triaxiality on mechanical strength of ASTM A36, ASTM A572 and ASTM A992 steels Hizb Ullah Sajid, Ravi Kiran ⇑ Dept. of Civil & Env. Engg., North Dakota State University, ND 58105, United States
a r t i c l e
i n f o
Article history: Received 17 January 2018 Received in revised form 23 April 2018 Accepted 3 May 2018
Keywords: ASTM A36 steel ASTM A572 steel ASTM A992 steel Stress triaxiality Yield strength Ultimate tensile strength
a b s t r a c t This study aims at investigating the influence of high stress triaxiality on the yield strength and ultimate tensile strength of commonly used structural steels (ASTM A36, ASTM A572 and ASTM A992). To this end, axisymmetrically notched steel specimens are designed to generate a range of stress triaxialities. Yield strength and ultimate tensile strength of notched steel specimens are then determined using engineering stress-strain curves obtained from uniaxial tensile testing of notched specimens. Yield strength and ultimate tensile strength of all three types of structural steels are found to increase linearly with increase in stress triaxiality of test specimens. Based on experimental and complimentary finite element results, predictive equations are proposed to estimate increased yield strength and ultimate tensile strength as a function of stress triaxiality in structural steels. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction In service conditions, structural steels are routinely subjected to stress concentrations that arise from geometric discontinuities like holes, sharp corners, welds, etc. that are commonly observed in steel structures. Stress concentration is quantified by a dimensionless parameter referred to as stress triaxiality (Tr). Stress triaxiality is defined as the ratio between hydrostatic stress and von-Mises stress. Higher stress triaxiality aggravates the growth of microvoids in steel matrix [1], which in turn accelerates ductile fracture initiation in steels [2]. High stress triaxiality thus leads to reduction in ductility of steels [3]. Experimental and numerical studies on high strength low alloy structural steels (ASTM A992) have confirmed the adverse effects of stress triaxiality on ductility of structural steels [4,5]. However, the quantitative relationships between stress triaxiality and yield strength and ultimate tensile strength of structural steels that are important design parameters in structural design [6] are not currently addressed. Past studies conducted on different alloys and stainless steels have reported an increase in tensile strength with an increase in stress concentration [7–9]. Un-anticipated increase in yield strength and ultimate tensile strength of structural steels may lead to unintended consequences
⇑ Corresponding author. E-mail addresses: [email protected] (H.U. Sajid), [email protected] (R. Kiran). https://doi.org/10.1016/j.conbuildmat.2018.05.018 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.
in structural systems. For instance, stronger beams cause failure of columns leading to global collapse of the structure (strong beamweak column). Components like reduced beam sections, seismic fuse components should fail at pre-designed loads to protect the overall integrity and to avoid progressive collapse of structure. It is therefore, important to account for the increased yield strength and ultimate tensile strength due to high triaxiality in the design stage of steel structures [10]. With this objective in mind, the current study aims to establish a quantitative relationship between stress triaxiality, yield strength and ultimate tensile strength of structural steels (at a material level) that are widely used in construction industry. In this study, a mild steel (ASTM A36 [11]) along with two high strength low alloy (HSLA) steels (ASTM A572 [12] and ASTM A992 [13]) are investigated. ASTM A36 and ASTM A992 are predominantly used in construction of steel buildings in the United States whereas ASTM A572 steels are typically used in the construction of bridges [14–16]. ASTM A992 is currently the most common and preferred grade of structural steel used for wide flange shapes in the United States [16,17]. 2. Experimental study and finite element modeling Preliminary finite element analyses are conducted by choosing different geometries of notched tension specimens to generate a range of stress triaxialities. Based on the results obtained from preliminary study, six axisymmetrically notched tension specimens
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are selected. These test specimens are classified as CN (circularnotched specimens), UN (U-notched specimens) and VN (V-notched specimens). The reference un-notched test specimens are labelled as SPR (reference un-notched test specimen). Detailed geometric illustrations of the un-notched and notched specimens are provided in Fig. 1. The chemical composition of all the three steels used in this study as specified by the manufacturer are summarized in Table 1. In total, 42 test specimens are tested as a part of this experimental study. These specimens are machined using computer numerically controlled (CNC) lath machine with a tolerance of ± 0.025 mm. The load-displacement behavior of all the test specimens are obtained by conducting uniaxial tension tests using servohydraulic MTS 809 system at a displacement rate of 0.02 mm/s. An Epsilon Model 3542 contact extensometer with 1-inch gage length is used to record the strains. The total load and elongation in the gage length are obtained at a sampling rate of 99 Hz, for both un-notched and notched test specimens. Engineering stress-strain curves of un-notched and notched test specimens are provided in Fig. 2. Near perfect repeatability of load-displacement curves is obtained for all the un-notched and notched test specimens. For the sake of clarity, stress-strain curve of only one representative specimen is provided for each un-notched and notched test specimen. Mechanical properties of test specimens evaluated from experimental stress strain curves are provided in Table 2. Nonlinear finite element analysis is conducted to obtain stress triaxiality profiles across critical cross-section at two different loading stages: a) initial stage of loading (corresponding to 1.35 ± 0.5% engineering strain), and b) ultimate load (strain corresponding to maximum stress in engineering stress-strain curve), as shown in Fig. 3. Maximum initial stress triaxiality (T ir;max ) ranges from 0.33 to 1.15. Finite element analyses are conducted using ABAQUSÒ finite element modeling software. All test specimens are modeled using four noded bilinear axisymmetric CAX4 elements and geometric non-linearity is considered. J2 plasticity model is used as the constitutive model. For all steels, the true stress strain curves obtained from the corresponding SPR specimens are used as the strain hardening curves in J2 plasticity model and are provided in Fig. 4. The applied boundary conditions and loading along with
Notch location
Table 1 Chemical composition of ASTM A36, ASTM A572, and ASTM A992 structural steels. Chemical composition (%)
ASTM A36
ASTM A572 Gr. 50
ASTM A992
Carbon (C) Manganese (Mn) Phosphorous (P) Sulphur (S) Silicon (Si) Copper (Cu) Chromium (Cr) Nickle (Ni) Molybdenum (Mo) Vanadium (V) Titanium (Ti) Niobium (Nb) Iron (Fe)
0.1500 0.6900 0.0180 0.0040 0.1800 0.2400 0.1500 0.0880 0.0195 0.0048 0.0012 0.0024 98.4521
0.0500 1.3400 0.0110 0.0040 0.1500 0.2800 0.1900 0.1300 0.0400 0.0830 0.0010 0.0030 97.7180
0.1000 0.9300 0.0160 0.0440 0.1900 0.2500 0.1400 0.0900 0.0200 0.0010 – 0.0210 98.1980
some typical finite element meshes used in the vicinity of the notches are provided in Fig. 5. 3. Results and discussion In this section, stress-strain curves, yield strength (ry) and ultimate tensile strength (ru) obtained from uniaxial tensile tests are discussed. Using engineering stress-strain curves, yield strength of each test specimen is determined based on 0.2% strain offset method [18]. The maximum engineering stress is taken as the ultimate tensile strength of steel. As observed in Fig. 2, stress-strain curves of notched specimens are characterized by significant reduction in ductility and increase in ultimate tensile strength as compared to un-notched specimens, for all three types of steels. A well-defined yield plateau is observed in un-notched specimens which diminishes in case of notched specimens with high stress triaxiality. It is observed that all notched specimens exhibited substantial increase in both yield strength and ultimate tensile strength as compared to un-notched steel specimens. Among notched steel specimens, highest yield strength and ultimate tensile strength is exhibited by specimens with highest average initial and average ultimate triaxialities (UN1 and VN1), respectively. In
D19
R 4.5
D10
19
10 25 25
25
50
Cross-section
SPR 10
R1.0
10
CN1
R2.0
R3.0
CN3
CN2
6.92
4 10
10
1
45°
R1.0
10
60°
10
2 UN1
VN1
SPR = Reference un-notched test specimen,
2 VN2
CN = C-notch, UN = U-notch, VN = V-notch
Fig. 1. Geometric details of axisymmetric test specimens (all dimensions are in mm.).
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VN2
CN2
VN1
VN1 UN1 VN2
(a) ASTM A36
UN1
(b) ASTM A572
CN3 SPR CN1
CN2
CN1
SPR
CN3
VN1 VN2 UN1
(c) ASTM A992 CN1 SPR
CN2 CN3
Fig. 2. Engineering stress-strain curves of un-notched and notched test specimens.
Table 2 Experimental material properties of structural steels (obtained from un-notched test specimens) and comparison with ASTM standards. Steel type
Material property
ASTM specification
Experimental result
ASTM A36
Min. yield strength (MPa) Tensile strength (MPa) Min. elongation over 200 length (%) Min. yield strength (MPa) Min. tensile strength (MPa) Min. elongation over 200 length (%) Yield strength (MPa) Min. tensile strength (MPa) Min. elongation over 200 length (%) Max. yield to tensile strength ratio
250 400–550 23 345 450 21 345–450 450 21 0.85
386.48 517.09 40.65 (over 100 length) 389.15 502.40 44.81 (over 100 length) 354.46 484.47 45.07 (over 100 length) 0.74
ASTM A572 Gr. 50
ASTM A992
case of ASTM A36 steel, the yield strength of notched specimens increased by as much as 70% as compared to un-notched steel specimens. Both ASTM A572 and A992 steels exhibited almost similar increase (up to 57% and 60%, respectively) as compared to un-notched specimens. The ultimate tensile strength of notched specimens made of all three steels exhibited almost similar increase (ASTM A36-51%, ASTM A572-54%, ASTM A992-53%) when compared to ultimate tensile strength of corresponding unnotched specimens. Average yield strength (ry) of (two) test specimens for a given geometry is plotted as a function of spatially averaged initial triaxiality (T iavg ), as shown in Fig. 6. The spatially averaged initial triaxiality (T iavg ) is evaluated by averaging the triaxiality over the critical cross section of the notched test specimen at a total strain of 1.35 ± 0.5%. The average ultimate tensile strength (ru) of two test specimens for a given geometry is plotted against spatially averaged triaxiality evaluated at a
strain corresponding to ultimate load (T uavg ), as shown in Fig. 7. Triaxiality is dependent on the shape of the notch and material properties. The notches in the test specimens may undergo significant shape change before the ultimate tensile strength is achieved. This shape change in the notch is accounted by choosing T uavg which is obtained by evaluating the spatial average of triaxiality across the critical cross section at the strain corresponding to ultimate tensile strength. From Fig. 6, it is clear that the yield strength increases linearly with increase in stress triaxiality for all the three steels. Similarly, the ultimate tensile strength is observed to increase linearly with increase in stress triaxiality, for all three types of steels, as shown in Fig. 7. Based on experimental and finite element results, the following predictive equations are proposed to estimate yield strength and ultimate tensile strength as a function of spatially averaged initial stress triaxiality, and spatially averaged ultimate stress triaxiality, respectively.
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VN1 UN1
UN1
CN2 VN2
VN1
CN3
VN2
CN2
CN1 SPR
CN1
CN3
(a) SPR = Reference un-notched test specimen,
SPR
(b) CN = C-notch, UN = U-notch, VN = V-notch
Fig. 3. (a) Initial stress triaxiality profiles, (b) stress triaxiality profiles at ultimate load.
ASTM A572 steel
ry ¼ 407:33T iavg þ 266:41
ð3Þ
ru ¼ 489:10T uavg þ 334:41
ð4Þ
ASTM A992 steel
Fig. 4. Strain hardening curves of un-notched test specimens used in finite element analysis.
ASTM A36 Steel
ry ¼ 498:59T iavg þ 218:28
ð1Þ
ru ¼ 482:50T uavg þ 351:26
ð2Þ
ry ¼ 403:75T iavg þ 227:78
ð5Þ
ru ¼ 473:96T uavg þ 323:57
ð6Þ
The authors hypothesize that the strain localization in the vicinity of the notch leads to high strain hardening which ultimately results in increased yield strength and ultimate tensile strength. Increase in the yield strength with increase in triaxiality is also reported for AISI 1080 steel and Al T6061 alloys [9,19]. Currently, there is no clear consensus on the exact cause for the increase in yield strength/ultimate tensile strength of notched specimens and further microscale experimentation is needed to investigate the root cause behind this phenomena.
Boundary Conditions: @ x = 0; uz = 0 @ z = 0; ux = 0
(a) (b)
(c)
z
x (d) Fig. 5. (a) Applied boundary and loading conditions, (b) typical C-notch mesh, (c) typical U-notch mesh, and (d) typical V-notch mesh.
H.U. Sajid, R. Kiran / Construction and Building Materials 176 (2018) 129–134
Fig. 6. Average initial stress triaxiality versus yield strength.
Fig. 7. Average ultimate stress triaxiality versus ultimate tensile strength.
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H.U. Sajid, R. Kiran / Construction and Building Materials 176 (2018) 129–134
4. Conclusions Following are important conclusions drawn from this study: 1. Yield strength of structural steels increased linearly with increase in stress triaxiality. About 70% increase in yield strength is observed in ASTM A36 steel when the triaxiality is changed from T iavg ¼ 0:32 to T iavg ¼ 0:84. For a similar change in triaxiality, ASTM A572 and ASTM A992 recorded 57% and 60% increase in yield strength, respectively. 2. Ultimate tensile strength of structural steels also increased linearly with increase in stress triaxiality. An increase up to 54% in ultimate tensile strength is observed for all the three structural steels considered in this study when the T uavg is increased from 0.34 to 0.88. Conflict of interest No conflict of interest. Acknowledgements The financial support from NDSU Research and Creative Activity and NDSU Department of Civil and Environmental Engineering is gratefully acknowledged by the authors. References [1] R. Kiran, K. Khandelwal, A micromechanical model for ductile fracture prediction in ASTM A992 steels, Eng. Fract. Mech. 102 (2013) 101–117.
[2] T.L. Anderson, Fracture Mechanics: Fundamentals and Applications, third ed., Taylor & Francis, 2005. [3] A.M. Agogino, Notch effects, stress state, and ductility, J. Eng. Mater. Technol. 100 (1978) 348–355. [4] R. Kiran, K. Khandelwal, Experimental studies and models for ductile fracture in ASTM A992 steels at high triaxiality, J. Struct. Eng. 140 (2013) 04013044. [5] R. Kiran, K. Khandelwal, A triaxiality and Lode parameter dependent ductile fracture criterion, Eng. Fract. Mech. 128 (2014) 121–138. [6] American Institute of Steel Construction (AISC), AISC 360-05-Specification for Structural Steel Buildings, ANSI/AISC, Chicago, 2005. [7] W.D. Jenkins, W.A. Willard, Effect of temperature and notch geometry on the tensile behavior of a titanium alloy, NBS J. Eng. Instrum. 73 (1966) 5–11. [8] J. Ganesh Kumar, M. Nandagopal, P. Parameswaran, K. Laha, M. Mathew, Effect of notch root radius on tensile behaviour of 316L (N) stainless steel, Mater. High Temp. 31 (2014) 239–248. [9] X. Lei, C. Li, X. Shi, X. Xu, Y. Wei, Notch strengthening or weakening governed by transition of shear failure to normal mode fracture, Sci. Rep. 5 (2015) 10537. [10] American Institute of Steel Construction, Manual of Steel Construction, thirteenth ed., AISC, Chicago, 2005. [11] ASTM International, A36/A36M-14 Standard Specification for Carbon Structural Steel, ASTM International, West Conshohocken, PA, 2014. [12] ASTM International, Standard Specification for High-Strength Low-Alloy Columbium-Vanadium Structural Steel, ASTM International, West Conshohocken, PA, 2015. [13] ASTM International, Standard Specification for Structural Steel Shapes, ASTM International, West Conshohocken, PA, 2015. [14] R. Bjorhovde, Development and use of high performance steel, J. Constr. Steel Res. 60 (2004) 393–400. [15] E.M. Aziz, V.K. Kodur, Effect of temperature and cooling regime on mechanical properties of high-strength low-alloy steel, Fire Mater. 40 (2016) 926–939. [16] K. Gustafson, P. SE, Evaluation of existing structures, Mod. Steel Constr. 47 (2007) 41. [17] G. Hu, M.A. Morovat, J. Lee, E. Schell, Elevated Temperature Properties of ASTM A992 Steel, in: Structures Congress 2009, American Society of Civil Engineers, 2009, pp. 1067–1076. [18] ASTM International, ASTM A6/A6M-17a Standard Specification for General Requirements for Rolled Structural Steel Bars, Plates, Shapes, and Sheet Piling, ASTM International, West Conshohocken, PA, 2017. [19] R.W. Hertzberg, R.P. Vinci, J.L. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, fifth ed., John Wiley and Sons, 2012.