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Characterization of cast stainless steel weld pools by using ball indentation technique
Materials Science and Engineering A 513–514 (2009) 389–393
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Characterization of cast stainless steel weld pools by using ball indentation technique Gautam Das a,b , Mousumi Das a,b , Subhasis Sinha a,b,1 , Kalyan Kumar Gupta a,b , Sanchita Chakrabarty a,b , Ashok Kumar Ray a,b,∗ a b
National Metallurgical Laboratory, Jamshedpur 831007, India Department of Metallurgy, Jadavpur University, Kolkata 700032, India
a r t i c l e
i n f o
Article history: Received 3 October 2008 Received in revised form 5 February 2009 Accepted 6 February 2009 Keywords: Weld pool Flow properties Ball indentation technique Microstructure Mechanical properties Ferrite
a b s t r a c t Ball indentation technique (BIT) was used to characterize two weld pools of cast stainless steel. Yield strength, ultimate tensile strength, strength coefficient, strain hardening exponent and fracture toughness (KJC ) were determined through BIT. The concept of continuum damage mechanics was employed to evaluate the KJC of the weld pools. Weld pool having higher Cr content shows superior YS and UTS, but KJC was slightly lower. This is agreed by the presence of higher amount of ferrite in the weld pool with higher Cr. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Ball indentation technique (BIT) has become an important method to evaluate fracture toughness (KJC ) and a few mechanical properties of ductile materials [1–7]. Spherical balls of tungsten carbide of varying diameters (0.7–1.57 mm) are employed for indentation. The idea of estimating the mechanical properties of metallic materials using a simple method, such as hardness measurement, rather than the tensile tests has been the subject of considerable attention over the past few decades. There have been several attempts to characterize the stresses and strains in the region under the indenter. When the load is applied to the indenter, the metal surface and the indenter both will deform elastically according to the classical theory of Hertz [8]. With further increment in the load the metal surface will deform plastically. At the point of contact, the stresses generated are infinite, which are known as Hertizian stresses [8]. However, when the metal surface is in elastic state, the contact region increases from a point to a defined region as the
∗ Corresponding author at: Materials Science and Technology Division, National Metallurgical Laboratory (CCSIR), PO-Burmamines, Jamshedpur 831007, India. Tel.: +91 657 2345197; fax: +91 657 2270527/2271159. E-mail addresses: [email protected], [email protected] (A.K. Ray). 1 Tel: +91 657 2346061. 0921-5093/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2009.02.007
applied load increases. As the load continues to increase, a stage is reached at which the maximum shear stress in the metal exceeds its elastic limit and it sets about the onset of plastic deformation. The present analysis of determining the fracture toughness of a ductile material is based on the assumption that stress tri-axiality beneath the indenter is similar to that ahead of a crack tip in a conventional fracture toughness test sample. Indentation deformation energy to a certain depth can be correlated with energy required to initiate a crack i.e. the characteristic features of fracture initiation point. The challenge lies to determine this characteristic fracture initiation point (at a certain indentation depth) correctly. This was done by using the concepts of continuum damage mechanics (CDM). Initially proposed by Lemaitre [9], the CDM approach was modified by Bonora [10]. This model matches well with the damage evolution of various metals. But this model mainly focused on materials behavior under tensile state of stress. The related mechanism under compressive state of stress is still in dilemma. Further, Pirondi and Bonora [11] have shown that this model can be applied under multi-axial state of stress and predicted the crack initiation point correctly. This [11] was confirmed with the experimental results. Recently Lee et al. [12] have successfully introduced the continuum damage mechanics for determining the KJC of ductile materials. The concept of void volume fraction beneath the indenter has been applied to determine the characteristic point of crack initiation during indentation.
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G. Das et al. / Materials Science and Engineering A 513–514 (2009) 389–393
Fracture toughness of a few RPV steel was determined by Byun et al. [13] through indentation technique. In his model he adopted critical mean contact pressure as a fracture criterion for ductile materials. In the last decade many researchers [14–18] have successfully shown on various materials that BIT could be used for determining mechanical properties and fracture toughness. Recently Mukhopadhayay and Paufler [19] have shown that indentation technique has proved to be indispensable compared to conventional technique either for field application or from small amount of test materials. Therefore, the objective of the present work is to evaluate a few mechanical properties and fracture toughness of two weld pools (WP1 and WP2) using BIT as due to insufficient test coupons the conventional mechanical test method cannot be applied. Microstructure of the weld pools has been studied to estimate the amount of ferrite present in the weld pools. 1.1. Methodology The basic principle of the ball indentation technique is multiple indentations by a spherical indenter at a single test location on the test sample with intermediate partial unloading. Here a spherical ball with a specific rate of loading indents the test materials and multiple indentations in a single position is made through loading–unloading–reloading sequence as it facilitates the separation of the elastic and plastic components of indentation at each step and is able to take account of the usually ignored phenomenon of piling up and sinking-in. Spherical balls of different diameters have been used to get multiple stress–strain data points. Here, the load increases approximately linearly with penetration depth. This is due to two non-linear but opposing processes occur simultaneously, i.e. the non-linear increase in the applied load with indentation depth due to the spherical geometry of the indenter and non-linear increase of load with indentation depth due to the work hardening of the test pieces. During each subsequent loading, fresh materials beneath the indenter experiences increased plastic deformation, so continuous yielding and strain hardening occurs simultaneously. In contrast, for the case of a uni-axial tensile test the plastic deformation is confined only to the limited volume of test sample of gauge section. For each loading cycle the total indentation depth (ht ) is obtained corresponding to the maximum load and the plastic indentation depth (hp ) is obtained after completing unloading. The computer program determines the slope of each unloading cycle. Then the intersection of this line with the zero load line determines the value of hp . The ht , hp and the corresponding maximum loads are the raw data for determining the mechanical properties like UTS, YS, K, n and t –εt curves. The details of the theory are given elsewhere [20]. Fracture toughness was determined on the concept of continuum damage mechanics which is based on the formation of voids beneath the indenter during indentation. Indentation with a small spherical indenter generated concentrated stress field near and beneath the indenter and it is similar to the concentrated stress field ahead of a crack tip. Elastic theory and finite element analysis [10] show that the stress tri-axiality present on the tip of a crack in a fracture toughness specimen is similar to those at the centre of contact surface beneath the indenter. The deformation energy at the centre of the impression is hence comparable to that at the front of a crack tip. Therefore, it has been postulated that the indentation energy per unit contact area up to a critical fracture stress is related to the so-called ‘indentation energy to fracture’ (Wf ). The Wf can be correlated with the KJC of a ductile material
as follows [12]: KJC =
2 EWf
(1)
where E = elastic modulus of the test specimen, in GPa. Wf can be related to critical indentation energy and can be calculated from the indentation load–depth curve as follows:
h
2 Wf = lim
h→h∗ f
0
4P mLD dh = ln ˘ d2
D D − hf
(2)
where P = mLD h and d=2
(3)
Dh − h2
(4)
where hf = critical indentation depth, in mm, D = diameter of the indenter, in mm, P = load, in N and mLD = slope of the load–indentation depth curve. Damage of a ductile material means the progressive deterioration of microstructure and it (damage variable) can be defined in terms of relative reduction of net resisting section of a reference volume element as [9]: D=
SD S
(5)
where S = cross-sectional area of the loaded region, in mm2 and SD = reduced area due to micro-defects, in mm2 . Considering the isotropic damage and using the effective stress concept, initially proposed by Kachanov, Lemaitre and Chaboche have developed the CDM and the damage variable (D) can be presented as [9,11,22]: D=1−
ED = ED = E(1 − D) E
(6)
where ED = elastic modulus of the damaged material, in GPa and E = elastic modulus of the undamaged material, in GPa. The Young’s Modulus value of standard stainless steel (193 GPa) [26], was used for BIT to determine the mechanical properties of the weld pools. ED can be represented with indentation parameters as: ED =
(2
1 − 2 √ AC / ˘S − 1 − i2 /Ei )
(7)
where and i Poisson’s ratio of the material and indenter, respectively, Ei = elastic modulus of the indenter, AC = contact area between indenter and material and S = unloading slope. Damage variable can also be defined as [12]: D=
˘ 4((4/3)˘)
2/3
f 2/3
(8)
where f = critical void volume fraction beneath the indenter. 2. Experimental procedure Two electrodes of cast stainless steel with varying composition were considered for the present investigation. Two weld pools (WP) were made on Cu substrate under similar condition. The two weld pools are designated as WP1 and WP2. The elemental composition of the two weld pools is given in Table 1. The mechanical properties of both the weld pools have been determined through non-conventional BIT only as the availability of test materials is too less for conducting conventional mechanical test. The detail of the set-up is given elsewhere [23,24]. The tests have been conducted with a tungsten carbide spherical ball of 1.57 mm diameter. The crosshead velocity has been chosen at
G. Das et al. / Materials Science and Engineering A 513–514 (2009) 389–393
391
Table 2 Mechanical properties obtained through BIT.
Table 1 Elemental analysis of the investigated alloys. Sample
C
Mn
Cr
Si
Ni
P
S
Fe
Sample
UTS (MPa)
YS (MPa)
K (MPa)
n
HBN
WP1 WP2
0.05 0.07
2.38 0.46
25.54 33.0
1.23 1.17
9.3 11.57
0.03 0.028
0.007 0.006
Balance Balance
Weld pool WP1 WP2
651 842
303 390
1101 1209
0.213 0.121
171 227
Virgin of WP1 Conventional BIT
696 673
358 349
1233 1164
0.23 0.216
190 195
Virgin of WP2 Conventional BIT
890 885
420 415
1333 1313
0.132 0.14
235 240
Table 3 Fracture toughness (KJC ) obtained through conventional and BIT.
Fig. 1. Load–deflection curves showing the differences of the two samples investigated.
1 mm/min. The total experiment was of eight intermediate partial unloading cycles. The sample was in cylindrical shape of 1 cm diameter and 0.5 cm in thickness. The samples were ground for proper flatness using up to 1000 grade emery papers for ball indentation test. For microstructural studies the samples polished by the standard metallographic techniques. The polished samples were etched using aqua-regia as etchant and the microstructure was observed under optical microscope, attached with Image Analyzer. 3. Results and discussion The multiple load–deflection (P–ı) curves, obtained through BIT, are shown in Fig. 1. The curves obtained from both the weld pool are placed in the same figures for comparison. For each sample five (5 tests) P–ı curves were taken for better average, but only one from each of the case is shown in Fig. 1. It is observed from the curves that for WP2 higher load is required for same indentation depth compare to WP1, indicating more resistance to deformation for WP2.
Fig. 2. Comparison of true stress–true plastic strain curve of two samples, obtained through BIT.
Sample
Fracture toughness (KJC )
WP1 WP2
304 MPa m1/2 278 MPa m1/2
To determine the mechanical properties of materials though indentation technique the requirement is to determine the indentation diameters at each step from the LVDT measured indentation depth. But due to the formation of pile-up of materials surrounding the indentation, the LVDT measured contact area differs from the actual contact area of the indented surface. It has been found by various researchers, including the present authors [6,20,21] that a correction factor is necessary for conversion of the LVDT measured depth to get the actual contact area between the indenter and the test material. Ignoring bulging surrounding the indentation, results in an error in estimating the contact area which was found to be as much as 60% for conical indentation on aluminium [6]. Therefore, an attempt to determine the mechanical properties due consideration of pileup/sink-in is of utmost importance. The details of the approach for taking care of pile-up/sink-in have been discussed in details by the present authors [20]. This correction factors are found to vary as per the work hardening characteristic of the materials and also it depends on prior mechanical working of the specimen. Fig. 2 represents the true stress–true plastic strain ( t –εt ) curves for both the samples. The mechanical properties were determined after analyzing the t –εt plots. The mechanical properties determined through BIT are listed in Table 2. It is observed from Table 2 that the YS, UTS, n and K values differ from each other. The YS, UTS and K have higher values for WP2 compare to WP1, whereas lower
Fig. 3. Variation of Young’s Modulus (ED ) along the indentation depth (hc ).
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G. Das et al. / Materials Science and Engineering A 513–514 (2009) 389–393
Fig. 4. Log–log plot ED and hc . Fig. 5. Engineering stress vs engineering strain curve of the virgin material, using conventional technique.
Fig. 6. Optical micrographs of the sample WP1, revealing the distribution of ferrites in the matrix of austenite.
Fig. 7. Optical micrographs of the sample WP2, revealing the distribution of ferrites in the matrix of austenite.
G. Das et al. / Materials Science and Engineering A 513–514 (2009) 389–393
n is observed for sample WP2. These are due to higher amount of Cr and consequently higher percentage of ferrite present in the sample WP2. This was confirmed by quantitative metallography for the two samples. The KJC was determined for both the weld pools. The ED values at each cycle were determined and it was plotted against the indentation depth (plastic). The ED vs indentation depth (h) plot is shown in Fig. 3 for the sample WP1. The same data has been plotted in ln–ln scale (Fig. 4) and by extrapolation the plot, the critical depth was determined. It is the initiation point of stable crack growth. The critical damage value was determined by considering the critical void volume fraction as 0.25 [25]. The fracture toughness values, determined through BIT for both the sample are listed in Table 3. It is found that the KJC is slightly higher for WP1 than WP2. A typical engineering stress–strain curve of the virgin material of WP1 is revealed in Fig. 5. It was found that the strength of the virgin material is slightly higher than that of the weld pool, which agreed well with the test results of BIT (Table 2). The optical micrographs of the two weld pools at two magnifications have been shown in Figs. 6 and 7. It is observed that the microstructures are dendritic in natures which are ferrite in a matrix of austenite. The amounts of ferrite was however different for the two samples. On observing the microstructures, it was found by calculation of area fraction (using an image analyzer) that the amount of ferrite was more in case of sample WP2 than in WP1. Ferrite is the strengthening phase. The amount of ferrite in WP1 was around 16% while that in WP2 was around 23%, hence explaining the higher strength of sample WP2 compare to WP1. Using the Schaeffler diagram, the amount of ferrite on the basis elemental composition is calculated for the two samples and found closed agreement with the results from the quantitative analysis by Image Analyzer. 4. Conclusions On summarization, the following major conclusions are drawn from the present work: (1) BI technique can be effectively employed to evaluate mechanical properties including fracture toughness of weld pools. It has potential for evaluating mechanical properties particularly where there is a constrained of test materials.
393
(2) It was found that weld pools with higher amount Cr showed higher strength however the fracture toughness and n is having lower value. This may be attributed by the presence of higher amount of ferritic phases in the test sample WP2 compare to WP1. Acknowledgements The authors are grateful to Prof. S.P. Mehrotra, Director, National Metallurgical Laboratory (NML) for his given encouragement and permission to publish this work. The authors would like to thank Dr. S. Sivaprasad, Sri P.K. Dey for their keen interest and useful discussion. References [1] J.-Y. Kim, K.-W. Lee, J.-S. Lee, D. Kwon, Surf. Coat. Technol. 201 (2006) 4278. [2] M.D. Mathew, K.L. Murty, K.B.S. Rao, S.L. Mannan, Mater. Sci. Eng. A 264 (1999) 159. [3] F.M. Haggag, T.S. Byun, J.H. Hong, P.Q. Miraglia, K.L. Murty, Scripta Mater. 38 (1998) 645. [4] T.S. Byun, J.H. Hong, F.M. Haggag, K. Farrell, F.H. Lee, Int. J. Pres. Ves. Pip. 74 (1997) 231. [5] B. Taljat, G.M. Pharr, Int. J. Solid Struct. 41 (2004) 3891. [6] H. Habbab, B.G. Mclor, S. Syngcllakis, Acta Mater. 54 (2006) 1965. [7] J.S. Field, M.V. Swain, J. Mater. Res. 10 (1995) 101. [8] D. Tabor, The Hardness of Metals, Clarendon Press, Oxford, 1951, p. 15. [9] J. Lemaitre, J. Eng. Mater. Technol. 107 (1985) 83. [10] N. Bonora, Eng. Frac. Mech. 58 (1/2) (1997) 11. [11] A. Pirondi, N. Bonora, Comput. Mater. Sci. 26 (2003) 129. [12] J.-S. Lee, J-i. Jang, B.-W. Lee, Y. Choi, S.G. Lee, D. Kwon, Acta Mater. 54 (2006) 1101. [13] T.S. Byun, S.H. Kim, B.S. Lee, I.S. Kim, J.H. Hong, J. Nucl. Mater. 277 (2000) 263. [14] Y. Choi, W.Y. Choo, D. Kwon, Scripta Mater. 45 (2001) 1401. [15] K.L. Murty, M.D. Mathew, Trans. SMiRT 16 (2001) 1. [16] C.-S. Seok, J.-M. Koo, Mater. Sci. Eng. A 395 (2005) 141. [17] S. Ghosh, S.K. Sahay, G. Das, J. Metall. Mater. Sci. 46 (2) (2004) 95. [18] G. Das, S. Ghosh, S.K. Sahay, V.R. Ranganath, K.K. Vaze, Int. J. Mater. Res. Adv. Technol., Metallkunde 95 (2004) 1120. [19] N.K. Mukhopadhyay, P. Paufler, Int. Mater. Rev. 51 (4) (2006) 1. [20] G. Das, S. Ghosh, S. Ghosh, R.N. Ghosh, Mater. Sci. Eng. A 408 (2005) 158. [21] X. Hernot, O. Bartier, Y. Bekouche, R.El. Abdi, G. Mauvoisin, Int. J. Solids Struct. 43 (2006) 4136–4153. [22] G. Rousselier, J. Mech. Phys. Solids 49.8 (2001) 1727. [23] G. Das, S. Ghosh, S.K. Sahay, Mater. Lett. 59 (2005) 2246. [24] G. Das, S. Ghosh, S. Ghosh, NDT & D Inter. 39 (2006) 155. [25] H. Andersson, J. Mech. Phys. Solid 25 (1977) 217. [26] J.R. Davis (Ed.), Handbook on Stainless Steel, ASM International, 1994, p. 489.
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Characterization of cast stainless steel weld pools by using ball indentation technique Gautam Das a,b , Mousumi Das a,b , Subhasis Sinha a,b,1 , Kalyan Kumar Gupta a,b , Sanchita Chakrabarty a,b , Ashok Kumar Ray a,b,∗ a b
National Metallurgical Laboratory, Jamshedpur 831007, India Department of Metallurgy, Jadavpur University, Kolkata 700032, India
a r t i c l e
i n f o
Article history: Received 3 October 2008 Received in revised form 5 February 2009 Accepted 6 February 2009 Keywords: Weld pool Flow properties Ball indentation technique Microstructure Mechanical properties Ferrite
a b s t r a c t Ball indentation technique (BIT) was used to characterize two weld pools of cast stainless steel. Yield strength, ultimate tensile strength, strength coefficient, strain hardening exponent and fracture toughness (KJC ) were determined through BIT. The concept of continuum damage mechanics was employed to evaluate the KJC of the weld pools. Weld pool having higher Cr content shows superior YS and UTS, but KJC was slightly lower. This is agreed by the presence of higher amount of ferrite in the weld pool with higher Cr. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Ball indentation technique (BIT) has become an important method to evaluate fracture toughness (KJC ) and a few mechanical properties of ductile materials [1–7]. Spherical balls of tungsten carbide of varying diameters (0.7–1.57 mm) are employed for indentation. The idea of estimating the mechanical properties of metallic materials using a simple method, such as hardness measurement, rather than the tensile tests has been the subject of considerable attention over the past few decades. There have been several attempts to characterize the stresses and strains in the region under the indenter. When the load is applied to the indenter, the metal surface and the indenter both will deform elastically according to the classical theory of Hertz [8]. With further increment in the load the metal surface will deform plastically. At the point of contact, the stresses generated are infinite, which are known as Hertizian stresses [8]. However, when the metal surface is in elastic state, the contact region increases from a point to a defined region as the
∗ Corresponding author at: Materials Science and Technology Division, National Metallurgical Laboratory (CCSIR), PO-Burmamines, Jamshedpur 831007, India. Tel.: +91 657 2345197; fax: +91 657 2270527/2271159. E-mail addresses: [email protected], [email protected] (A.K. Ray). 1 Tel: +91 657 2346061. 0921-5093/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2009.02.007
applied load increases. As the load continues to increase, a stage is reached at which the maximum shear stress in the metal exceeds its elastic limit and it sets about the onset of plastic deformation. The present analysis of determining the fracture toughness of a ductile material is based on the assumption that stress tri-axiality beneath the indenter is similar to that ahead of a crack tip in a conventional fracture toughness test sample. Indentation deformation energy to a certain depth can be correlated with energy required to initiate a crack i.e. the characteristic features of fracture initiation point. The challenge lies to determine this characteristic fracture initiation point (at a certain indentation depth) correctly. This was done by using the concepts of continuum damage mechanics (CDM). Initially proposed by Lemaitre [9], the CDM approach was modified by Bonora [10]. This model matches well with the damage evolution of various metals. But this model mainly focused on materials behavior under tensile state of stress. The related mechanism under compressive state of stress is still in dilemma. Further, Pirondi and Bonora [11] have shown that this model can be applied under multi-axial state of stress and predicted the crack initiation point correctly. This [11] was confirmed with the experimental results. Recently Lee et al. [12] have successfully introduced the continuum damage mechanics for determining the KJC of ductile materials. The concept of void volume fraction beneath the indenter has been applied to determine the characteristic point of crack initiation during indentation.
390
G. Das et al. / Materials Science and Engineering A 513–514 (2009) 389–393
Fracture toughness of a few RPV steel was determined by Byun et al. [13] through indentation technique. In his model he adopted critical mean contact pressure as a fracture criterion for ductile materials. In the last decade many researchers [14–18] have successfully shown on various materials that BIT could be used for determining mechanical properties and fracture toughness. Recently Mukhopadhayay and Paufler [19] have shown that indentation technique has proved to be indispensable compared to conventional technique either for field application or from small amount of test materials. Therefore, the objective of the present work is to evaluate a few mechanical properties and fracture toughness of two weld pools (WP1 and WP2) using BIT as due to insufficient test coupons the conventional mechanical test method cannot be applied. Microstructure of the weld pools has been studied to estimate the amount of ferrite present in the weld pools. 1.1. Methodology The basic principle of the ball indentation technique is multiple indentations by a spherical indenter at a single test location on the test sample with intermediate partial unloading. Here a spherical ball with a specific rate of loading indents the test materials and multiple indentations in a single position is made through loading–unloading–reloading sequence as it facilitates the separation of the elastic and plastic components of indentation at each step and is able to take account of the usually ignored phenomenon of piling up and sinking-in. Spherical balls of different diameters have been used to get multiple stress–strain data points. Here, the load increases approximately linearly with penetration depth. This is due to two non-linear but opposing processes occur simultaneously, i.e. the non-linear increase in the applied load with indentation depth due to the spherical geometry of the indenter and non-linear increase of load with indentation depth due to the work hardening of the test pieces. During each subsequent loading, fresh materials beneath the indenter experiences increased plastic deformation, so continuous yielding and strain hardening occurs simultaneously. In contrast, for the case of a uni-axial tensile test the plastic deformation is confined only to the limited volume of test sample of gauge section. For each loading cycle the total indentation depth (ht ) is obtained corresponding to the maximum load and the plastic indentation depth (hp ) is obtained after completing unloading. The computer program determines the slope of each unloading cycle. Then the intersection of this line with the zero load line determines the value of hp . The ht , hp and the corresponding maximum loads are the raw data for determining the mechanical properties like UTS, YS, K, n and t –εt curves. The details of the theory are given elsewhere [20]. Fracture toughness was determined on the concept of continuum damage mechanics which is based on the formation of voids beneath the indenter during indentation. Indentation with a small spherical indenter generated concentrated stress field near and beneath the indenter and it is similar to the concentrated stress field ahead of a crack tip. Elastic theory and finite element analysis [10] show that the stress tri-axiality present on the tip of a crack in a fracture toughness specimen is similar to those at the centre of contact surface beneath the indenter. The deformation energy at the centre of the impression is hence comparable to that at the front of a crack tip. Therefore, it has been postulated that the indentation energy per unit contact area up to a critical fracture stress is related to the so-called ‘indentation energy to fracture’ (Wf ). The Wf can be correlated with the KJC of a ductile material
as follows [12]: KJC =
2 EWf
(1)
where E = elastic modulus of the test specimen, in GPa. Wf can be related to critical indentation energy and can be calculated from the indentation load–depth curve as follows:
h
2 Wf = lim
h→h∗ f
0
4P mLD dh = ln ˘ d2
D D − hf
(2)
where P = mLD h and d=2
(3)
Dh − h2
(4)
where hf = critical indentation depth, in mm, D = diameter of the indenter, in mm, P = load, in N and mLD = slope of the load–indentation depth curve. Damage of a ductile material means the progressive deterioration of microstructure and it (damage variable) can be defined in terms of relative reduction of net resisting section of a reference volume element as [9]: D=
SD S
(5)
where S = cross-sectional area of the loaded region, in mm2 and SD = reduced area due to micro-defects, in mm2 . Considering the isotropic damage and using the effective stress concept, initially proposed by Kachanov, Lemaitre and Chaboche have developed the CDM and the damage variable (D) can be presented as [9,11,22]: D=1−
ED = ED = E(1 − D) E
(6)
where ED = elastic modulus of the damaged material, in GPa and E = elastic modulus of the undamaged material, in GPa. The Young’s Modulus value of standard stainless steel (193 GPa) [26], was used for BIT to determine the mechanical properties of the weld pools. ED can be represented with indentation parameters as: ED =
(2
1 − 2 √ AC / ˘S − 1 − i2 /Ei )
(7)
where and i Poisson’s ratio of the material and indenter, respectively, Ei = elastic modulus of the indenter, AC = contact area between indenter and material and S = unloading slope. Damage variable can also be defined as [12]: D=
˘ 4((4/3)˘)
2/3
f 2/3
(8)
where f = critical void volume fraction beneath the indenter. 2. Experimental procedure Two electrodes of cast stainless steel with varying composition were considered for the present investigation. Two weld pools (WP) were made on Cu substrate under similar condition. The two weld pools are designated as WP1 and WP2. The elemental composition of the two weld pools is given in Table 1. The mechanical properties of both the weld pools have been determined through non-conventional BIT only as the availability of test materials is too less for conducting conventional mechanical test. The detail of the set-up is given elsewhere [23,24]. The tests have been conducted with a tungsten carbide spherical ball of 1.57 mm diameter. The crosshead velocity has been chosen at
G. Das et al. / Materials Science and Engineering A 513–514 (2009) 389–393
391
Table 2 Mechanical properties obtained through BIT.
Table 1 Elemental analysis of the investigated alloys. Sample
C
Mn
Cr
Si
Ni
P
S
Fe
Sample
UTS (MPa)
YS (MPa)
K (MPa)
n
HBN
WP1 WP2
0.05 0.07
2.38 0.46
25.54 33.0
1.23 1.17
9.3 11.57
0.03 0.028
0.007 0.006
Balance Balance
Weld pool WP1 WP2
651 842
303 390
1101 1209
0.213 0.121
171 227
Virgin of WP1 Conventional BIT
696 673
358 349
1233 1164
0.23 0.216
190 195
Virgin of WP2 Conventional BIT
890 885
420 415
1333 1313
0.132 0.14
235 240
Table 3 Fracture toughness (KJC ) obtained through conventional and BIT.
Fig. 1. Load–deflection curves showing the differences of the two samples investigated.
1 mm/min. The total experiment was of eight intermediate partial unloading cycles. The sample was in cylindrical shape of 1 cm diameter and 0.5 cm in thickness. The samples were ground for proper flatness using up to 1000 grade emery papers for ball indentation test. For microstructural studies the samples polished by the standard metallographic techniques. The polished samples were etched using aqua-regia as etchant and the microstructure was observed under optical microscope, attached with Image Analyzer. 3. Results and discussion The multiple load–deflection (P–ı) curves, obtained through BIT, are shown in Fig. 1. The curves obtained from both the weld pool are placed in the same figures for comparison. For each sample five (5 tests) P–ı curves were taken for better average, but only one from each of the case is shown in Fig. 1. It is observed from the curves that for WP2 higher load is required for same indentation depth compare to WP1, indicating more resistance to deformation for WP2.
Fig. 2. Comparison of true stress–true plastic strain curve of two samples, obtained through BIT.
Sample
Fracture toughness (KJC )
WP1 WP2
304 MPa m1/2 278 MPa m1/2
To determine the mechanical properties of materials though indentation technique the requirement is to determine the indentation diameters at each step from the LVDT measured indentation depth. But due to the formation of pile-up of materials surrounding the indentation, the LVDT measured contact area differs from the actual contact area of the indented surface. It has been found by various researchers, including the present authors [6,20,21] that a correction factor is necessary for conversion of the LVDT measured depth to get the actual contact area between the indenter and the test material. Ignoring bulging surrounding the indentation, results in an error in estimating the contact area which was found to be as much as 60% for conical indentation on aluminium [6]. Therefore, an attempt to determine the mechanical properties due consideration of pileup/sink-in is of utmost importance. The details of the approach for taking care of pile-up/sink-in have been discussed in details by the present authors [20]. This correction factors are found to vary as per the work hardening characteristic of the materials and also it depends on prior mechanical working of the specimen. Fig. 2 represents the true stress–true plastic strain ( t –εt ) curves for both the samples. The mechanical properties were determined after analyzing the t –εt plots. The mechanical properties determined through BIT are listed in Table 2. It is observed from Table 2 that the YS, UTS, n and K values differ from each other. The YS, UTS and K have higher values for WP2 compare to WP1, whereas lower
Fig. 3. Variation of Young’s Modulus (ED ) along the indentation depth (hc ).
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Fig. 4. Log–log plot ED and hc . Fig. 5. Engineering stress vs engineering strain curve of the virgin material, using conventional technique.
Fig. 6. Optical micrographs of the sample WP1, revealing the distribution of ferrites in the matrix of austenite.
Fig. 7. Optical micrographs of the sample WP2, revealing the distribution of ferrites in the matrix of austenite.
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n is observed for sample WP2. These are due to higher amount of Cr and consequently higher percentage of ferrite present in the sample WP2. This was confirmed by quantitative metallography for the two samples. The KJC was determined for both the weld pools. The ED values at each cycle were determined and it was plotted against the indentation depth (plastic). The ED vs indentation depth (h) plot is shown in Fig. 3 for the sample WP1. The same data has been plotted in ln–ln scale (Fig. 4) and by extrapolation the plot, the critical depth was determined. It is the initiation point of stable crack growth. The critical damage value was determined by considering the critical void volume fraction as 0.25 [25]. The fracture toughness values, determined through BIT for both the sample are listed in Table 3. It is found that the KJC is slightly higher for WP1 than WP2. A typical engineering stress–strain curve of the virgin material of WP1 is revealed in Fig. 5. It was found that the strength of the virgin material is slightly higher than that of the weld pool, which agreed well with the test results of BIT (Table 2). The optical micrographs of the two weld pools at two magnifications have been shown in Figs. 6 and 7. It is observed that the microstructures are dendritic in natures which are ferrite in a matrix of austenite. The amounts of ferrite was however different for the two samples. On observing the microstructures, it was found by calculation of area fraction (using an image analyzer) that the amount of ferrite was more in case of sample WP2 than in WP1. Ferrite is the strengthening phase. The amount of ferrite in WP1 was around 16% while that in WP2 was around 23%, hence explaining the higher strength of sample WP2 compare to WP1. Using the Schaeffler diagram, the amount of ferrite on the basis elemental composition is calculated for the two samples and found closed agreement with the results from the quantitative analysis by Image Analyzer. 4. Conclusions On summarization, the following major conclusions are drawn from the present work: (1) BI technique can be effectively employed to evaluate mechanical properties including fracture toughness of weld pools. It has potential for evaluating mechanical properties particularly where there is a constrained of test materials.
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(2) It was found that weld pools with higher amount Cr showed higher strength however the fracture toughness and n is having lower value. This may be attributed by the presence of higher amount of ferritic phases in the test sample WP2 compare to WP1. Acknowledgements The authors are grateful to Prof. S.P. Mehrotra, Director, National Metallurgical Laboratory (NML) for his given encouragement and permission to publish this work. The authors would like to thank Dr. S. Sivaprasad, Sri P.K. Dey for their keen interest and useful discussion. References [1] J.-Y. Kim, K.-W. Lee, J.-S. Lee, D. Kwon, Surf. Coat. Technol. 201 (2006) 4278. [2] M.D. Mathew, K.L. Murty, K.B.S. Rao, S.L. Mannan, Mater. Sci. Eng. A 264 (1999) 159. [3] F.M. Haggag, T.S. Byun, J.H. Hong, P.Q. Miraglia, K.L. Murty, Scripta Mater. 38 (1998) 645. [4] T.S. Byun, J.H. Hong, F.M. Haggag, K. Farrell, F.H. Lee, Int. J. Pres. Ves. Pip. 74 (1997) 231. [5] B. Taljat, G.M. Pharr, Int. J. Solid Struct. 41 (2004) 3891. [6] H. Habbab, B.G. Mclor, S. Syngcllakis, Acta Mater. 54 (2006) 1965. [7] J.S. Field, M.V. Swain, J. Mater. Res. 10 (1995) 101. [8] D. Tabor, The Hardness of Metals, Clarendon Press, Oxford, 1951, p. 15. [9] J. Lemaitre, J. Eng. Mater. Technol. 107 (1985) 83. [10] N. Bonora, Eng. Frac. Mech. 58 (1/2) (1997) 11. [11] A. Pirondi, N. Bonora, Comput. Mater. Sci. 26 (2003) 129. [12] J.-S. Lee, J-i. Jang, B.-W. Lee, Y. Choi, S.G. Lee, D. Kwon, Acta Mater. 54 (2006) 1101. [13] T.S. Byun, S.H. Kim, B.S. Lee, I.S. Kim, J.H. Hong, J. Nucl. Mater. 277 (2000) 263. [14] Y. Choi, W.Y. Choo, D. Kwon, Scripta Mater. 45 (2001) 1401. [15] K.L. Murty, M.D. Mathew, Trans. SMiRT 16 (2001) 1. [16] C.-S. Seok, J.-M. Koo, Mater. Sci. Eng. A 395 (2005) 141. [17] S. Ghosh, S.K. Sahay, G. Das, J. Metall. Mater. Sci. 46 (2) (2004) 95. [18] G. Das, S. Ghosh, S.K. Sahay, V.R. Ranganath, K.K. Vaze, Int. J. Mater. Res. Adv. Technol., Metallkunde 95 (2004) 1120. [19] N.K. Mukhopadhyay, P. Paufler, Int. Mater. Rev. 51 (4) (2006) 1. [20] G. Das, S. Ghosh, S. Ghosh, R.N. Ghosh, Mater. Sci. Eng. A 408 (2005) 158. [21] X. Hernot, O. Bartier, Y. Bekouche, R.El. Abdi, G. Mauvoisin, Int. J. Solids Struct. 43 (2006) 4136–4153. [22] G. Rousselier, J. Mech. Phys. Solids 49.8 (2001) 1727. [23] G. Das, S. Ghosh, S.K. Sahay, Mater. Lett. 59 (2005) 2246. [24] G. Das, S. Ghosh, S. Ghosh, NDT & D Inter. 39 (2006) 155. [25] H. Andersson, J. Mech. Phys. Solid 25 (1977) 217. [26] J.R. Davis (Ed.), Handbook on Stainless Steel, ASM International, 1994, p. 489.