- Email: [email protected]
Hydrogen embrittlement susceptibility of prestressing steel wires: the role of the cold-drawing conditions
Available online at www.sciencedirect.com
ScienceDirect
Available online www.sciencedirect.com Available online at at www.sciencedirect.com Structural Integrity Procedia 00 (2016) 000–000
ScienceDirect ScienceDirect
Procedia Structural (2016) 626–631 Structural IntegrityIntegrity Procedia200 (2016) 000–000
www.elsevier.com/locate/procedia
www.elsevier.com/locate/procedia
21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy
Hydrogen embrittlement susceptibility of prestressing steel wires: XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal the role of the cold-drawing conditions Thermo-mechanical modeling of a high pressure turbine blade of an J. Toribioa,*, M. Lorenzoa, D. Vergaraa airplane gas turbine engine Fracture & Structural Integrity Research Group, University of Salamanca, Spain a a
P. Brandãoa, V. Infanteb, A.M. Deusc* a
AbstractDepartment of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,
Portugal IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,
b
Prestressing steel wires are highly susceptible to hydrogen embrittlement (HE). Residual stress-strain state, produced after wire Portugal c drawing, playsDepartment an essential role since Engineering, hydrogen damage certainTécnico, places of the material is directly affectedPais, by 1, stress and strain CeFEMA, of Mechanical InstitutoatSuperior Universidade de Lisboa, Av. Rovisco 1049-001 Lisboa, fields. Changes in wire drawing conditions modify the stress and strain fields and, consequently, the HE susceptibility and life in Portugal service of these structural components in the presence of a hydrogenating environment. This paper analyzes the distributions of residual stress and plastic strain obtained after diverse drawing conditions (inlet die angle, die bearing length, varying die angle andAbstract straining path) and their influence on HE susceptibility of the wires. The conditions for industrial cold drawing can thus be optimized, thereby producing commercial prestressing steel wires with improved performance against HE phenomena. During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, Copyright © 2016 The Authors. by Elsevier B.V.Such This isconditions an open access BY-NC-ND license especially the high pressurePublished turbine (HPT) blades. causearticle theseunder partsthe to CC undergo different types of time-dependent © 2016 The Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict Peer-review under responsibility of the Scientific Committee of ECF21. Peer-review responsibility of the Scientific Committee of ECF21. the creepunder behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model Keywords: hydrogen embrittlement; prestressing steel wires; cold drawing; die geometry; residual stresses and strains. needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The 1. overall Introduction expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data.
Cold drawing is a conforming process where a progressive reduction of wire diameter is performed in diverse stages © 2016 The Authors.to Published Elsevier B.V. drawing) producebycommercial prestressing steel wires. Plastic strains during drawing are not uniformly (multi-pass Peer-review under responsibility of the Committee of PCF 2016. Those plastic strains are the origin of a nondistributed through the wire radius, asScientific shown by Toribio et al. (2011a). negligible residual stress state, which directly affects the wire performance during its life in-service. Both fields Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. (residual stress and plastic strain states) produced after drawing play an essential role in hydrogen embrittlement (HE).
* Corresponding author. Tel.: +34 980 545 000 (ext. 3673); fax: +34 980 545 002. E-mail address: [email protected] 2452-3216 © 2016 The Authors. Published by Elsevier B.V. * Corresponding Tel.: +351of218419991. Peer-review underauthor. responsibility the Scientific Committee of ECF21. E-mail address: [email protected]
2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016.
Copyright © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer review under responsibility of the Scientific Committee of ECF21. 10.1016/j.prostr.2016.06.081
2
J. Toribio et al. / Procedia Structural Integrity 2 (2016) 626–631 Author name / Structural Integrity Procedia 00 (2016) 000–000
627
Hydrogen diffusion and accumulation in prospective damage places depends on the inwards gradients of hydrostatic stress and hydrogen solubility of the metal according to the model of hydrogen diffusion assisted by stress and strain described by Toribio et al. (2010), in which hydrogen diffusion is driven by the gradients of concentration, hydrostatic stress and cumulative plastic strain. Although several techniques are currently used to determine residual stress states (Martínez-Perez et al. (2005)), none of them provides information about plastic strains distributions. In this way, numerical simulation of the conforming process is an appropriate alternative to calculate both residual stress and plastic strain, as shown by He et al. (2003) and Luksza et al. (1998). Överstam (2004) proved that changes in residual stress state are produced by modifying process parameters such as the die geometry. This way, several studies analyzed the influence on the structural integrity (in terms of both the generation of residual stress and plastic strain and the HE susceptibility of cold drawn wires) of diverse drawing parameters that generate different residual stress and strain fields. Considering a one-step drawing: (i) Toribio et al. (2013) studied the inlet die angle; (ii) Toribio et al. (2014) analyzed the die bearing length; (iii) Toribio et al. (2011b) dealt with the wire diameter reduction at the first step of two commercial drawing chains and (iv) Toribio et al. (2015) explored the advantages of using a modified die geometry considering a varying die angle, i.e., two die angles within the same drawing die. With regard to continuous (multi-pass) drawing, Toribio et al. (2011a) studied the evolution of the residual stress and plastic strains and the influence on HE related phenomena and Toribio et al. (2012) considered diverse drawing paths, i.e., different sequences of wire diameter reductions (yielding history). The aim of this paper is to analyze the residual stresses and plastic strains obtained after diverse drawing conditions (inlet die angle, die bearing length, varying die angle and straining path) and their influence on HE susceptibility. This way, the optimal conditions (in terms of the drawing parameters, i.e., die geometry) for carrying out an industrial cold drawing process can be estimated, producing commercial prestressing steel wires with improved performance from the structural integrity point of view. 2. Residual stress-strain state after cold drawing Numerical finite element (FE) simulations of wire drawing allow one to obtain the residual stress and plastic strain states after drawing. The analysis is focused on the variables representing such states in the model of hydrogen diffusion assisted by stress and strains described by Toribio et al. (2010): hydrostatic stress () and equivalent plastic strain (P) for the following cases: (i) influence of the inlet die angle, (ii) influence of the die bearing length, (iii) influence of varying (double) die angle and (iv) influence of the straining path (yielding history). All simulations considered the same wire diameter reduction (from an initial diameter d0 = 12 mm to a final one d1 = 10.8 mm) and the same raw material (E = 199 GPa, Y = 696 MPa). The revolute geometry of both the die and the wire allows one to simplify the complete geometry to an axisymmetric case as explained by Toribio et al. (2011a). The constitutive model for the steel was chosen to be elastoplastic solid with von Mises yield surface, associated flow rule, and isotropic strain-hardening. The boundary condition of the prescribed axial displacement was imposed on the front extreme of the rod. Elastoplastic analysis was performed using large deformations and large strains, with updated lagrangian formulation. Several finite element meshes formed by four-node quadrilaterals were tried till the acceptable mesh-convergence of the result was ensured. Taking into account the simplicity of the wire geometry (a rectangle) in the 2D axisymmetric approach, the mesh of the wire was refined in the area next to the contact surface between the wire and the die. 2.1. Inlet die angle The influence of the drawing inlet die angle was analyzed by Toribio et al. (2013) considering several dies with different inlet die angle (): 5º, 7º and 9º. Fig. 1 shows the radial distribution of both hydrostatic stress and equivalent plastic strain obtained after drawing (r is the radial cylindrical coordinate throughout this paper). Thus, it can be noticed that: (i) main differences associated with the inlet die angles are located in the near surface zone; (ii) in such a zone, the higher the inlet die angle, the higher the hydrostatic stress and equivalent plastic strain.
J. Toribio et al. / Procedia Structural Integrity 2 (2016) 626–631 Author name / Structural Integrity Procedia 00 (2016) 000–000
628
500
3
0.35 º
0
0.3 P
º
(MPa)
º
º
-500
0.25
º º -1000
0
1
2
3 r (mm)
4
0.2
5
0
1
2
(a)
3 r (mm)
4
5
(b)
Fig. 1. Radial distribution of hydrostatic stress (a) and equivalent plastic strain (b) after three drawing processes with different inlet die angle.
2.2. Die bearing length Toribio et al. (2014) analyzed the role of die bearing length on the HE susceptibility of prestressing steel wires by considering several dies with different die bearing length (lz): d0, d0/2 and d0/4. The radial distribution of both hydrostatic stress and equivalent plastic strain generated for each case of study is shown in Fig. 2. Thus, it can be noticed that: (i) if the bearing length is equal or higher than the wire radius (d0/2), no significant changes are produced in the residual stress and strain states; (ii) if the bearing length is lower than the wire radius, linearly increases as the lz decreases, although only second order changes were found in the P fields. 1000
0.35 lz=d0/4
lz=d0/4
lz=d0/2 l =d z
0
l =d
0
z
0
0.25
-500 -1000
lz=d0/2
0.3
P
(MPa)
500
0
1
2
(a)
3 r (mm)
4
5
0.2
0
1
2
3 r (mm)
4
5
(b)
Fig. 2. Radial distribution of hydrostatic stress (a) and equivalent plastic strain (b) after three drawing processes with different die bearing length.
2.3. Varying die angle Toribio et al. (2015) explored the effect of varying die angle on the HE susceptibility of prestressing steel wires by means of several innovative cold drawing procedures using die geometries which considered two consecutive die angles: (i) 1 = 7º and 2 = 5º; (ii) 1 = 9º and 1 = 5º. The distribution of both hydrostatic stress and equivalent plastic strain generated by these two die geometries is represented in Fig. 3 for each case of study. Thus, according to the results obtained after the mechanical FE analysis of the different manufacturing techniques, the following effects were noticed: (i) wires drawn with a die with double angle of reduction exhibit a decrement of the stress state; (ii) such a reduction is strongly dependent on the angle used in the second reduction; (iii) the influence of the angle used in the first reduction can be considered as a second order effect; (iv) the plastic strain distribution is slightly increased by using varying die angle in drawing.
4
J. Toribio et al. / Procedia Structural Integrity 2 (2016) 626–631 Author name / Structural Integrity Procedia 00 (2016) 000–000 1000
0.35
(MPa)
500
= 7º = 5º
= 7º, = 5º
= 9º = 5º
= 9º, = 5º
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1
2
P
0
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629
0
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3 r (mm)
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0.2
5
0
1
2
(a)
3 r (mm)
4
5
(b)
Fig. 3. Radial distribution of hydrostatic stress (a) and equivalent plastic strain (b) after two drawing processes with different varying die angle.
2.4. Drawing straining path Toribio et al. (2012) studied the effect of the straining path on the HE susceptibility of prestressing steel wires by means of a numerical simulation of two drawing processes: one of them with a heavy first reduction step (wire A) and the other one with a heavy last reduction step (wire B). The distribution of both hydrostatic stress and equivalent plastic strain after these two whole drawing procedures is plotted in Fig. 4, showing that: (i) hydrostatic distributions generated in wire B exhibit a positive gradient in the surface while in wire A the gradient is negative; (ii) a heavy reduction at the first step produces a smoother plastic strain profile than in wire B (heavy reduction at the last step). 1000 500
Heavy red. (1st step) Heavy red. (last step)
1.8 1.6
0
P
(MPa)
2
Heavy red. (1st step) Heavy red. (last step)
1.4 -500
-1000
1.2 0
0.5
1
1.5 2 r (mm)
2.5
3
(a)
3.5
1
0
0.5
1
1.5 2 r (mm)
2.5
3
3.5
(b)
Fig. 4. Radial distribution of hydrostatic stress (a) and equivalent plastic strain (b) after two drawing processes with different straining path.
3. Hydrogen embrittlement susceptibility HE phenomena can be analyzed in terms of hydrogen diffusion assisted by stress and strain, as discussed by Toribio et al. (2010). The stress-and-strain assisted diffusion equation (1) includes two key terms: (i) the inwards gradient of hydrostatic stress and (ii) the inwards gradient of strain-dependent hydrogen solubility, as follows: V C K Sε ( P ) D C DC H t RT K Sε ( P )
(1)
R being the universal gases constant, VH the partial volume of hydrogen, T the absolute temperature and Ks the hydrogen solubility which is linearly dependent on equivalent plastic strains according to Ksp.
J. Toribio et al. / Procedia Structural Integrity 2 (2016) 626–631 Author name / Structural Integrity Procedia 00 (2016) 000–000
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5
The equilibrium concentration of hydrogen (Ceq) can be obtained by the steady-state solution of equation (1) representing the long-time hydrogen accumulation in the metal.
V Ceq C0 K Sε ( P ) exp H RT
(2)
where C0 is the thermo-dynamical equilibrium hydrogen concentration for the considered material free of any stress and strain fields. Consequently, hydrogen diffuses from the wire surface towards those inner points depending, apart from the gradient of concentration itself given for the Fick´s term of the diffusion equation, on the negative inwards gradient of hydrostatic stress and the positive inwards gradient of hydrogen solubility, which is one-to-one related to the positive gradient of equivalent plastic strain due to the previously assumed linear dependence of Kswith the cumulative plastic strainP. Analysis is focused on the wire surface and its respective inwards gradient ( x), i.e., x being the depth from the surface, i.e., x = d/2 r, r being the radial cylindrical coordinate. The steady-state (long-time) distribution (t→∞) of hydrogen concentration can be obtained from the hydrostatic stress and equivalent plastic strain distributions trough equation (2). Using this procedure, Table 1 summarizes the values of the long-time hydrogen concentration (Ceq) at the wire surface representing the available hydrogen amount for diffusing toward the inner points. Table 1. Long-time hydrogen concentration at the wire surface for each case of study.
Ceq Inlet die angle
Bearing length
Varying die angle
Straining path
=5º
2.44
lz = d0/4
3.07
=7º, =5º
2.63
Heavy red. (1st step)
=7º
2.70
lz = d0/2
2.68
=9º, =5º
2.82
Heavy red. (last step)
=9º
3.04
lz = d0
2.70
11.14 9.60
Taking into account the influence of the inlet die angle, the optimal wire drawing from the HE susceptibility point of view is obtained by using an inlet die angle as low as possible. Thus, in this case, the available hydrogen at the wire surface for diffusing towards inner points is the lowest one and, in addition, the inwards gradient of plastic strain is negligible in spite of the fact that wires drawn using high inlet die angles exhibit a higher negative inwards gradient acting against hydrogen diffusion towards the inner points. With regard to the influence of the die bearing length, the optimal wire drawing is obtained considering a value of such parameter equal or higher than the wire radius. Thus, the same radial distribution is achieved for hydrostatic stress and equivalent plastic strain, and consequently the same behaviour against HE is expected. However, if the die bearing length is lower than the wire radius, the hydrogen amount at the wire surface is higher and hence, more hydrogen is potentially diffusible towards the prospective damage zone. In the case of the modified die geometry considering double die angle, an improved behaviour against HE is achieved by using drawing dies with varying die angle instead of an equivalent conventional one, i.e., with the same values of 1 in the first one and in the last one. Thus, the radial distribution of hydrostatic stress is similar to the optimal one and consequently, the hydrogen amount at the wire surface is reduced. Nevertheless, an increment of the inwards gradient of equivalent plastic strain is achieved. Finally, an interesting behaviour is observed when two complete wire drawing chains (undergoing diverse drawing history) were compared. Thus, if a huge reduction is applied at the last step of the drawing chain, the inwards gradient of hydrostatic stress changes and now it promotes hydrogen diffusion towards the inner points. In addition, the inwards gradient of equivalent plastic strains is higher than a wire drawn using a huge reduction at the first step. However, the hydrogen amount at the wire surface is higher in the drawing chain using a high reduction at the first drawing step.
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J. Toribio et al. / Procedia Structural Integrity 2 (2016) 626–631 Author name / Structural Integrity Procedia 00 (2016) 000–000
631
4. Conclusions The optimal wire drawing consists of using a die angle as low as possible with a bearing length equal to or higher than the wire radius. If a low die angle is not possible, an alternative way for improving the structural integrity against HE is by using varying die geometry with a secondary die angle as low as possible. Finally, the yielding history is a key issue in the generation of residual stress and plastic strain since important changes are produced in the hydrostatic stress and equivalent plastic strains distributions, and consequently, a carefully design of the straining path undergone during multi-pass drawing is advisable. Ackowledgements The authors wish to acknowledge the financial support provided by the following Spanish Institutions: Ministry for Science and Technology (MCYT; Grant MAT2002-01831), Ministry for Education and Science (MEC; Grant BIA2005-08965), Ministry for Science and Innovation (MICINN; Grant BIA2008-06810), Ministry for Economy and Competitiveness (MINECO; Grant BIA2011-27870) and Junta de Castilla y León (JCyL; Grants SA067A05, SA111A07 and SA039A08). References He, S., Van Bael, A., Li, S.Y., Van Houtte, P., Mei, F., Sarban, A., 2003. Residual stress determination in cold drawn steel wire by FEM simulation and X-ray diffraction. Materials Science and Engineering A 346, 101–107. Luksza, J., Majta, J., Burdek, M., Ruminski, M., 1998. Modelling and measurement of mechanical behaviour in multi-pass drawing process. Journal of Material Processing Technology. 80-81, 398–405. Martínez-Perez, M.L., Borlado, C.R., Mompean, F.J., García-Hernández, M., Gil-Sevillano, J., Ruiz-Hervias, J., Atienza, J.M., Elices, M., Peng, R.L., Daymond, M.R., 2005. Measurement and modelling of residual stresses in straightened commercial eutectoid steel rods. Acta Materialia 53, 4415– 4425. Överstam, H., 2004. The influence of bearing geometry on the residual stress state in cold drawn wire by the FEM. Journal of Materials Processing Technology 171, 446–450. Toribio, J., Kharin, V., Vergara, D., Lorenzo, M., 2010. Two-dimensional numerical modelling of hydrogen diffusion assisted by stress and strain. Advanced Materials Research 138, 117–126. Toribio, J., Kharin, V., Lorenzo, M., Vergara, D., 2011a. Role of drawing-induced residual stresses and strains in the hydrogen embrittlement susceptibility of prestressing steels. Corrosion Science 53, 3346–3555. Toribio, J., Lorenzo, M., Vergara, D., Kharin, V., 2011b. Hydrogen degradation of cold-drawn wires: a numerical analysis of drawing-induced residual stresses and strains. Corrosion 67, 075001-1–075001-8. Toribio, J., Lorenzo, M., Vergara, D., 2012. Influence of drawing straining path on hydrogen damage of prestressing steel wires. Key Engineering Materials 488-489, 775–778. Toribio, J., Lorenzo, M., Vergara, D., Kharin, V., 2013. Hydrogen embrittlement of cold drawn prestressing steels: the role of the die inlet angle. Materials Science 49, 226–233. Toribio, J., Lorenzo, M., Aguado, L., Vergara, D., Kharin, V., 2014. Influence of the die bearing length on the hydrogen embrittlement of cold drawn wires. Key Engineering Materials 577-578, 553–556. Toribio, J., Lorenzo, M., Vergara, D., 2015. On the use of varying die angle for improving the resistance to hydrogen embrittlement of cold drawn prestressing steel wires. Engineering Failure Analysis 47, 273–282.
ScienceDirect
Available online www.sciencedirect.com Available online at at www.sciencedirect.com Structural Integrity Procedia 00 (2016) 000–000
ScienceDirect ScienceDirect
Procedia Structural (2016) 626–631 Structural IntegrityIntegrity Procedia200 (2016) 000–000
www.elsevier.com/locate/procedia
www.elsevier.com/locate/procedia
21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy
Hydrogen embrittlement susceptibility of prestressing steel wires: XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal the role of the cold-drawing conditions Thermo-mechanical modeling of a high pressure turbine blade of an J. Toribioa,*, M. Lorenzoa, D. Vergaraa airplane gas turbine engine Fracture & Structural Integrity Research Group, University of Salamanca, Spain a a
P. Brandãoa, V. Infanteb, A.M. Deusc* a
AbstractDepartment of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,
Portugal IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,
b
Prestressing steel wires are highly susceptible to hydrogen embrittlement (HE). Residual stress-strain state, produced after wire Portugal c drawing, playsDepartment an essential role since Engineering, hydrogen damage certainTécnico, places of the material is directly affectedPais, by 1, stress and strain CeFEMA, of Mechanical InstitutoatSuperior Universidade de Lisboa, Av. Rovisco 1049-001 Lisboa, fields. Changes in wire drawing conditions modify the stress and strain fields and, consequently, the HE susceptibility and life in Portugal service of these structural components in the presence of a hydrogenating environment. This paper analyzes the distributions of residual stress and plastic strain obtained after diverse drawing conditions (inlet die angle, die bearing length, varying die angle andAbstract straining path) and their influence on HE susceptibility of the wires. The conditions for industrial cold drawing can thus be optimized, thereby producing commercial prestressing steel wires with improved performance against HE phenomena. During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, Copyright © 2016 The Authors. by Elsevier B.V.Such This isconditions an open access BY-NC-ND license especially the high pressurePublished turbine (HPT) blades. causearticle theseunder partsthe to CC undergo different types of time-dependent © 2016 The Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict Peer-review under responsibility of the Scientific Committee of ECF21. Peer-review responsibility of the Scientific Committee of ECF21. the creepunder behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model Keywords: hydrogen embrittlement; prestressing steel wires; cold drawing; die geometry; residual stresses and strains. needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The 1. overall Introduction expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data.
Cold drawing is a conforming process where a progressive reduction of wire diameter is performed in diverse stages © 2016 The Authors.to Published Elsevier B.V. drawing) producebycommercial prestressing steel wires. Plastic strains during drawing are not uniformly (multi-pass Peer-review under responsibility of the Committee of PCF 2016. Those plastic strains are the origin of a nondistributed through the wire radius, asScientific shown by Toribio et al. (2011a). negligible residual stress state, which directly affects the wire performance during its life in-service. Both fields Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. (residual stress and plastic strain states) produced after drawing play an essential role in hydrogen embrittlement (HE).
* Corresponding author. Tel.: +34 980 545 000 (ext. 3673); fax: +34 980 545 002. E-mail address: [email protected] 2452-3216 © 2016 The Authors. Published by Elsevier B.V. * Corresponding Tel.: +351of218419991. Peer-review underauthor. responsibility the Scientific Committee of ECF21. E-mail address: [email protected]
2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016.
Copyright © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer review under responsibility of the Scientific Committee of ECF21. 10.1016/j.prostr.2016.06.081
2
J. Toribio et al. / Procedia Structural Integrity 2 (2016) 626–631 Author name / Structural Integrity Procedia 00 (2016) 000–000
627
Hydrogen diffusion and accumulation in prospective damage places depends on the inwards gradients of hydrostatic stress and hydrogen solubility of the metal according to the model of hydrogen diffusion assisted by stress and strain described by Toribio et al. (2010), in which hydrogen diffusion is driven by the gradients of concentration, hydrostatic stress and cumulative plastic strain. Although several techniques are currently used to determine residual stress states (Martínez-Perez et al. (2005)), none of them provides information about plastic strains distributions. In this way, numerical simulation of the conforming process is an appropriate alternative to calculate both residual stress and plastic strain, as shown by He et al. (2003) and Luksza et al. (1998). Överstam (2004) proved that changes in residual stress state are produced by modifying process parameters such as the die geometry. This way, several studies analyzed the influence on the structural integrity (in terms of both the generation of residual stress and plastic strain and the HE susceptibility of cold drawn wires) of diverse drawing parameters that generate different residual stress and strain fields. Considering a one-step drawing: (i) Toribio et al. (2013) studied the inlet die angle; (ii) Toribio et al. (2014) analyzed the die bearing length; (iii) Toribio et al. (2011b) dealt with the wire diameter reduction at the first step of two commercial drawing chains and (iv) Toribio et al. (2015) explored the advantages of using a modified die geometry considering a varying die angle, i.e., two die angles within the same drawing die. With regard to continuous (multi-pass) drawing, Toribio et al. (2011a) studied the evolution of the residual stress and plastic strains and the influence on HE related phenomena and Toribio et al. (2012) considered diverse drawing paths, i.e., different sequences of wire diameter reductions (yielding history). The aim of this paper is to analyze the residual stresses and plastic strains obtained after diverse drawing conditions (inlet die angle, die bearing length, varying die angle and straining path) and their influence on HE susceptibility. This way, the optimal conditions (in terms of the drawing parameters, i.e., die geometry) for carrying out an industrial cold drawing process can be estimated, producing commercial prestressing steel wires with improved performance from the structural integrity point of view. 2. Residual stress-strain state after cold drawing Numerical finite element (FE) simulations of wire drawing allow one to obtain the residual stress and plastic strain states after drawing. The analysis is focused on the variables representing such states in the model of hydrogen diffusion assisted by stress and strains described by Toribio et al. (2010): hydrostatic stress () and equivalent plastic strain (P) for the following cases: (i) influence of the inlet die angle, (ii) influence of the die bearing length, (iii) influence of varying (double) die angle and (iv) influence of the straining path (yielding history). All simulations considered the same wire diameter reduction (from an initial diameter d0 = 12 mm to a final one d1 = 10.8 mm) and the same raw material (E = 199 GPa, Y = 696 MPa). The revolute geometry of both the die and the wire allows one to simplify the complete geometry to an axisymmetric case as explained by Toribio et al. (2011a). The constitutive model for the steel was chosen to be elastoplastic solid with von Mises yield surface, associated flow rule, and isotropic strain-hardening. The boundary condition of the prescribed axial displacement was imposed on the front extreme of the rod. Elastoplastic analysis was performed using large deformations and large strains, with updated lagrangian formulation. Several finite element meshes formed by four-node quadrilaterals were tried till the acceptable mesh-convergence of the result was ensured. Taking into account the simplicity of the wire geometry (a rectangle) in the 2D axisymmetric approach, the mesh of the wire was refined in the area next to the contact surface between the wire and the die. 2.1. Inlet die angle The influence of the drawing inlet die angle was analyzed by Toribio et al. (2013) considering several dies with different inlet die angle (): 5º, 7º and 9º. Fig. 1 shows the radial distribution of both hydrostatic stress and equivalent plastic strain obtained after drawing (r is the radial cylindrical coordinate throughout this paper). Thus, it can be noticed that: (i) main differences associated with the inlet die angles are located in the near surface zone; (ii) in such a zone, the higher the inlet die angle, the higher the hydrostatic stress and equivalent plastic strain.
J. Toribio et al. / Procedia Structural Integrity 2 (2016) 626–631 Author name / Structural Integrity Procedia 00 (2016) 000–000
628
500
3
0.35 º
0
0.3 P
º
(MPa)
º
º
-500
0.25
º º -1000
0
1
2
3 r (mm)
4
0.2
5
0
1
2
(a)
3 r (mm)
4
5
(b)
Fig. 1. Radial distribution of hydrostatic stress (a) and equivalent plastic strain (b) after three drawing processes with different inlet die angle.
2.2. Die bearing length Toribio et al. (2014) analyzed the role of die bearing length on the HE susceptibility of prestressing steel wires by considering several dies with different die bearing length (lz): d0, d0/2 and d0/4. The radial distribution of both hydrostatic stress and equivalent plastic strain generated for each case of study is shown in Fig. 2. Thus, it can be noticed that: (i) if the bearing length is equal or higher than the wire radius (d0/2), no significant changes are produced in the residual stress and strain states; (ii) if the bearing length is lower than the wire radius, linearly increases as the lz decreases, although only second order changes were found in the P fields. 1000
0.35 lz=d0/4
lz=d0/4
lz=d0/2 l =d z
0
l =d
0
z
0
0.25
-500 -1000
lz=d0/2
0.3
P
(MPa)
500
0
1
2
(a)
3 r (mm)
4
5
0.2
0
1
2
3 r (mm)
4
5
(b)
Fig. 2. Radial distribution of hydrostatic stress (a) and equivalent plastic strain (b) after three drawing processes with different die bearing length.
2.3. Varying die angle Toribio et al. (2015) explored the effect of varying die angle on the HE susceptibility of prestressing steel wires by means of several innovative cold drawing procedures using die geometries which considered two consecutive die angles: (i) 1 = 7º and 2 = 5º; (ii) 1 = 9º and 1 = 5º. The distribution of both hydrostatic stress and equivalent plastic strain generated by these two die geometries is represented in Fig. 3 for each case of study. Thus, according to the results obtained after the mechanical FE analysis of the different manufacturing techniques, the following effects were noticed: (i) wires drawn with a die with double angle of reduction exhibit a decrement of the stress state; (ii) such a reduction is strongly dependent on the angle used in the second reduction; (iii) the influence of the angle used in the first reduction can be considered as a second order effect; (iv) the plastic strain distribution is slightly increased by using varying die angle in drawing.
4
J. Toribio et al. / Procedia Structural Integrity 2 (2016) 626–631 Author name / Structural Integrity Procedia 00 (2016) 000–000 1000
0.35
(MPa)
500
= 7º = 5º
= 7º, = 5º
= 9º = 5º
= 9º, = 5º
1
2
1
2
0.3
1
2
1
2
P
0
0.25
-500 -1000
629
0
1
2
3 r (mm)
4
0.2
5
0
1
2
(a)
3 r (mm)
4
5
(b)
Fig. 3. Radial distribution of hydrostatic stress (a) and equivalent plastic strain (b) after two drawing processes with different varying die angle.
2.4. Drawing straining path Toribio et al. (2012) studied the effect of the straining path on the HE susceptibility of prestressing steel wires by means of a numerical simulation of two drawing processes: one of them with a heavy first reduction step (wire A) and the other one with a heavy last reduction step (wire B). The distribution of both hydrostatic stress and equivalent plastic strain after these two whole drawing procedures is plotted in Fig. 4, showing that: (i) hydrostatic distributions generated in wire B exhibit a positive gradient in the surface while in wire A the gradient is negative; (ii) a heavy reduction at the first step produces a smoother plastic strain profile than in wire B (heavy reduction at the last step). 1000 500
Heavy red. (1st step) Heavy red. (last step)
1.8 1.6
0
P
(MPa)
2
Heavy red. (1st step) Heavy red. (last step)
1.4 -500
-1000
1.2 0
0.5
1
1.5 2 r (mm)
2.5
3
(a)
3.5
1
0
0.5
1
1.5 2 r (mm)
2.5
3
3.5
(b)
Fig. 4. Radial distribution of hydrostatic stress (a) and equivalent plastic strain (b) after two drawing processes with different straining path.
3. Hydrogen embrittlement susceptibility HE phenomena can be analyzed in terms of hydrogen diffusion assisted by stress and strain, as discussed by Toribio et al. (2010). The stress-and-strain assisted diffusion equation (1) includes two key terms: (i) the inwards gradient of hydrostatic stress and (ii) the inwards gradient of strain-dependent hydrogen solubility, as follows: V C K Sε ( P ) D C DC H t RT K Sε ( P )
(1)
R being the universal gases constant, VH the partial volume of hydrogen, T the absolute temperature and Ks the hydrogen solubility which is linearly dependent on equivalent plastic strains according to Ksp.
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5
The equilibrium concentration of hydrogen (Ceq) can be obtained by the steady-state solution of equation (1) representing the long-time hydrogen accumulation in the metal.
V Ceq C0 K Sε ( P ) exp H RT
(2)
where C0 is the thermo-dynamical equilibrium hydrogen concentration for the considered material free of any stress and strain fields. Consequently, hydrogen diffuses from the wire surface towards those inner points depending, apart from the gradient of concentration itself given for the Fick´s term of the diffusion equation, on the negative inwards gradient of hydrostatic stress and the positive inwards gradient of hydrogen solubility, which is one-to-one related to the positive gradient of equivalent plastic strain due to the previously assumed linear dependence of Kswith the cumulative plastic strainP. Analysis is focused on the wire surface and its respective inwards gradient ( x), i.e., x being the depth from the surface, i.e., x = d/2 r, r being the radial cylindrical coordinate. The steady-state (long-time) distribution (t→∞) of hydrogen concentration can be obtained from the hydrostatic stress and equivalent plastic strain distributions trough equation (2). Using this procedure, Table 1 summarizes the values of the long-time hydrogen concentration (Ceq) at the wire surface representing the available hydrogen amount for diffusing toward the inner points. Table 1. Long-time hydrogen concentration at the wire surface for each case of study.
Ceq Inlet die angle
Bearing length
Varying die angle
Straining path
=5º
2.44
lz = d0/4
3.07
=7º, =5º
2.63
Heavy red. (1st step)
=7º
2.70
lz = d0/2
2.68
=9º, =5º
2.82
Heavy red. (last step)
=9º
3.04
lz = d0
2.70
11.14 9.60
Taking into account the influence of the inlet die angle, the optimal wire drawing from the HE susceptibility point of view is obtained by using an inlet die angle as low as possible. Thus, in this case, the available hydrogen at the wire surface for diffusing towards inner points is the lowest one and, in addition, the inwards gradient of plastic strain is negligible in spite of the fact that wires drawn using high inlet die angles exhibit a higher negative inwards gradient acting against hydrogen diffusion towards the inner points. With regard to the influence of the die bearing length, the optimal wire drawing is obtained considering a value of such parameter equal or higher than the wire radius. Thus, the same radial distribution is achieved for hydrostatic stress and equivalent plastic strain, and consequently the same behaviour against HE is expected. However, if the die bearing length is lower than the wire radius, the hydrogen amount at the wire surface is higher and hence, more hydrogen is potentially diffusible towards the prospective damage zone. In the case of the modified die geometry considering double die angle, an improved behaviour against HE is achieved by using drawing dies with varying die angle instead of an equivalent conventional one, i.e., with the same values of 1 in the first one and in the last one. Thus, the radial distribution of hydrostatic stress is similar to the optimal one and consequently, the hydrogen amount at the wire surface is reduced. Nevertheless, an increment of the inwards gradient of equivalent plastic strain is achieved. Finally, an interesting behaviour is observed when two complete wire drawing chains (undergoing diverse drawing history) were compared. Thus, if a huge reduction is applied at the last step of the drawing chain, the inwards gradient of hydrostatic stress changes and now it promotes hydrogen diffusion towards the inner points. In addition, the inwards gradient of equivalent plastic strains is higher than a wire drawn using a huge reduction at the first step. However, the hydrogen amount at the wire surface is higher in the drawing chain using a high reduction at the first drawing step.
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4. Conclusions The optimal wire drawing consists of using a die angle as low as possible with a bearing length equal to or higher than the wire radius. If a low die angle is not possible, an alternative way for improving the structural integrity against HE is by using varying die geometry with a secondary die angle as low as possible. Finally, the yielding history is a key issue in the generation of residual stress and plastic strain since important changes are produced in the hydrostatic stress and equivalent plastic strains distributions, and consequently, a carefully design of the straining path undergone during multi-pass drawing is advisable. Ackowledgements The authors wish to acknowledge the financial support provided by the following Spanish Institutions: Ministry for Science and Technology (MCYT; Grant MAT2002-01831), Ministry for Education and Science (MEC; Grant BIA2005-08965), Ministry for Science and Innovation (MICINN; Grant BIA2008-06810), Ministry for Economy and Competitiveness (MINECO; Grant BIA2011-27870) and Junta de Castilla y León (JCyL; Grants SA067A05, SA111A07 and SA039A08). References He, S., Van Bael, A., Li, S.Y., Van Houtte, P., Mei, F., Sarban, A., 2003. Residual stress determination in cold drawn steel wire by FEM simulation and X-ray diffraction. Materials Science and Engineering A 346, 101–107. Luksza, J., Majta, J., Burdek, M., Ruminski, M., 1998. Modelling and measurement of mechanical behaviour in multi-pass drawing process. Journal of Material Processing Technology. 80-81, 398–405. Martínez-Perez, M.L., Borlado, C.R., Mompean, F.J., García-Hernández, M., Gil-Sevillano, J., Ruiz-Hervias, J., Atienza, J.M., Elices, M., Peng, R.L., Daymond, M.R., 2005. Measurement and modelling of residual stresses in straightened commercial eutectoid steel rods. Acta Materialia 53, 4415– 4425. Överstam, H., 2004. The influence of bearing geometry on the residual stress state in cold drawn wire by the FEM. Journal of Materials Processing Technology 171, 446–450. Toribio, J., Kharin, V., Vergara, D., Lorenzo, M., 2010. Two-dimensional numerical modelling of hydrogen diffusion assisted by stress and strain. Advanced Materials Research 138, 117–126. Toribio, J., Kharin, V., Lorenzo, M., Vergara, D., 2011a. Role of drawing-induced residual stresses and strains in the hydrogen embrittlement susceptibility of prestressing steels. Corrosion Science 53, 3346–3555. Toribio, J., Lorenzo, M., Vergara, D., Kharin, V., 2011b. Hydrogen degradation of cold-drawn wires: a numerical analysis of drawing-induced residual stresses and strains. Corrosion 67, 075001-1–075001-8. Toribio, J., Lorenzo, M., Vergara, D., 2012. Influence of drawing straining path on hydrogen damage of prestressing steel wires. Key Engineering Materials 488-489, 775–778. Toribio, J., Lorenzo, M., Vergara, D., Kharin, V., 2013. Hydrogen embrittlement of cold drawn prestressing steels: the role of the die inlet angle. Materials Science 49, 226–233. Toribio, J., Lorenzo, M., Aguado, L., Vergara, D., Kharin, V., 2014. Influence of the die bearing length on the hydrogen embrittlement of cold drawn wires. Key Engineering Materials 577-578, 553–556. Toribio, J., Lorenzo, M., Vergara, D., 2015. On the use of varying die angle for improving the resistance to hydrogen embrittlement of cold drawn prestressing steel wires. Engineering Failure Analysis 47, 273–282.