Numerical modeling of the progressive damage in the microstructure of WC-Co hardmetals under fatigue loading

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Procedia Structural Integrity 23 (2019) 451–456

9th International Conference on Materials Structure and Micromechanics of Fracture 9th International Conference on Materials Structure and Micromechanics of Fracture

Numerical modeling of the progressive damage in the Numerical modeling of the progressive damage in the microstructure of WC-Co hardmetals under fatigue loading microstructure of WC-Co hardmetals under fatigue loading a a

Keng Jianga,a,*, Alexander Bezoldaa, Christoph Broeckmannaa Keng Jiang *, Alexander Bezold , Christoph Broeckmann

Institute for Materials Applications in Mechanical Engineering, RWTH Aachen University, Augustinerbach 4, 52062 Aachen, Germany Institute for Materials Applications in Mechanical Engineering, RWTH Aachen University, Augustinerbach 4, 52062 Aachen, Germany

Abstract Abstract The study presents a framework of simulating the progressive damage under cyclic loading with the stress ratio R=0.1 in the WCThe study presents a framework of simulating theelement progressive damage under cyclic loading with the stress ratio R=0.1 WCCo hardmetals at mesoand microscale by finite method. A two-and-a-half-dimensional microstructure modelinisthe created Co hardmetals at mesoand microscale finite element A two-and-a-half-dimensional microstructure created based on electron backscatter diffraction by micrographs. It ismethod. able to capture the major microstructural characteristicsmodel of thisismaterial based on electron backscatter diffraction micrographs. It is able to capture major microstructural of this and preserve the local crystalline orientation. A set of anisotropic elasticitytheconstants is adopted for characteristics brittle WC phase, andmaterial elastoand preserve theparameters local crystalline A setmatrix of anisotropic elasticity constants is adopted fordynamic brittle WC phase, and elastoplastic material for theorientation. ductile binder are derived from fundamental static and testing conducted on plastic material parameters forspecimens. the ductile Proper binder failure matrix models are derived from fundamental static toand dynamictheir testing conducted on macroscopic binder-like alloy are applied for both phases represent respective failure macroscopic alloy specimens. failure modelsthe arestudy applied both phases to represent their respective failure mechanisms. binder-like Taking the residual stresses asProper an initial condition, alsofor introduces a method to investigate the influence of mechanisms. Taking thefatigue residual stresses as an initial condition, the study also introduces aismethod to with investigate the influence of residual stresses on the performance of hardmetals. The numerical implementation realized user subroutines in the residual stresses the fatigue performance commercial finiteonelement solver Abaqus. of hardmetals. The numerical implementation is realized with user subroutines in the commercial finite element solver Abaqus. © 2019 The Authors. Published by Elsevier B.V. © 2019 The Authors. Published by Elsevier B.V. B.V. © 2019 The Authors. by Elsevier This is an open accessPublished article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the ICorganizers MSMF organizers. Peer-review under responsibility of the scientific committee of the ICMSMF Peer-review under responsibility of the scientific committee of the IC MSMF organizers. Keywords: WC-Co hardmetals; microstructure; residual stress; fatigue; finit element method Keywords: WC-Co hardmetals; microstructure; residual stress; fatigue; finit element method

1. Introduction 1. Introduction Tungsten carbide-cobalt (WC-Co) hardmetal is an outstanding representative of cemented carbides alloys. Since (WC-Co) is an outstanding representative of cemented carbides Since its Tungsten invention carbide-cobalt in the early 20th century,hardmetal WC-Co hardmetal has become one of the most commercially andalloys. technically its inventionmaterial in the early 20th century, WC-Co hardmetal has becomedemand one of of theWC-based most commercially technically successful for engineering use. Driven by the increasing products and in automotive, successful material for engineering use. Driven by the increasing demand of WC-based products in automotive,

* Corresponding author. Tel.: +49-241-8090620; fax: +49-241-8092266. * E-mail Corresponding Tel.: +49-241-8090620; fax: +49-241-8092266. address:author. [email protected] E-mail address: [email protected] 2452-3216 © 2019 The Authors. Published by Elsevier B.V. 2452-3216 © 2019 Thearticle Authors. Published by Elsevier B.V. This is an open access under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the IC MSMF organizers. Peer-review under responsibility of the scientific committee of the IC MSMF organizers.

2452-3216 © 2019 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 the ICMSMF organizers 10.1016/j.prostr.2020.01.128

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construction, mining, transportation, and oil industries, the tungsten carbide powder market is forecasted to reach two billion euros by 2023 (P&S Intelligence (2018)). Under most of operating conditions, hardmetal components are subjected to cyclic loading, and thus fatigue fracture is one of the most common types of failure. The study on fatigue behavior of hardmetals becomes popular among materials engineers and scientists. From a materials science point of view, the superior mechanical performance of WC-Co hardmetals benefits from combination of its constituents, i.e., the brittle WC phase contributes the high hardness and strength whereas the ductile Co phase compensates to the loss in toughness. It yields the fact that the fatigue performance of hardmetals strongly depends on its microstructure. Experimental investigations on the fatigue crack growth (FCG) indicated that the fatigue sensitivity of this material is significantly dependent upon binder content or carbide contiguity, while a monotonic correlation was not found between the FCG threshold and above microstructure features (Schleinkofer et al. (1996), Sailer et al. (2001), Llanes et al. (2002)). With the rise of finite element (FE) analysis, numerical method is also applied in investigating the microscopic damage and fracture of hardmetals. Fischmeister et al. (1988), Mishnaevsky et al. (1999), McHugh and Connolly (2003) carried out early efforts, implying that the fracture process in the microstructure of hardmetals can be numerically simulated by modeling the nucleation, growth and coalescence of microvoids in the binder phase. Recently, the numerical method applied by Özden et al. (2016) shows the possibility of simulating microscopic FCG of hardmetals with failure models of both phases for the case of cyclic loading. It is important to notice that most of current numerical work only focused on the failure behavior of the ductile binder phase, while brittle fracture in WC phase is omitted, and only the damage mechanism under monotonic loading was studied. Besides, realistic microstructure has been rarely reflected in created models. From the perspective in crystallography, local crystalline orientation, anisotropy and fracture strength of a single WC grain have never been modeled. Therefore, this study takes into account the morphology as well as local material parameters of single WC crystals. Benefiting from advanced electron backscatter diffraction (EBSD) characterization technique, the study is able to reconstruct more precise microstructure models. Finally yet importantly, the influence of micro- and mesoscopic residual stresses on the fatigue property is also considered for the first time in numerical simulation. 2. Materials characterization 2.1. WC phase Both the morphology and local material parameters must be properly characterized for the microstructure of hardmetals. Transmission electron microscopy (TEM) investigation shows that WC grains usually exist as truncated triangular prisms (Lay et al. (2008)). With scanning electron microscopy (SEM) as Fig. 1 shows, irregular polygons are usually observed as sections of polyhedra. The morphology comes from the nature of hexagonal lattice structure of WC crystals. The values of linear elasticity constants to connect the stress tensor 𝝈𝝈 and strain tensor 𝜺𝜺 of WC crystals have been determined by Lee and Gilmore (1982), Golovchan (1998). Referring to the microbeam testing introduced by Trueba et al. (2014), in which the fracture strength of individual WC grains was measured by in situ nanoindentation, it is assumed the brittle fracture is the form of failure for WC grains, thus the maximum principal stress strength theory is applied. The material is marked as failure as soon as the value of 𝜎𝜎1 exceeds its criterion 𝜎𝜎1,cr ,

0, if 1  1, cr D 1, if 1  1, cr

(1)

The material parameters for WC phase are summarized in Table 1. Table 1. Material parameters for WC phase (Lee et al. (1982), Golovchan (1998), Trueba et al. (2014)). 𝐶𝐶11 [MPa] 720 000

𝐶𝐶12 [MPa] 254 000

𝐶𝐶13 [MPa] 150 000

𝐶𝐶33 [MPa] 972 000

𝐶𝐶44 [MPa] 328 000

𝐶𝐶66 [MPa] 233 000

𝜎𝜎1,cr [MPa] 6 300



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(a)

453 3

(b)

[0001]

tungsten atom carbon atom

[1̅21̅0]

[21̅1̅0]

Fig. 1. (a) SEM micrograph of WC-Co hardmetals; (b) morphology of single ideal WC grain and lattice structure of WC unit cell.

2.2. Co phase The metallic binder phase is treated as an elastoplastic material. A group of binder like alloy specimens were produced via hot isostatic pressing (HIP) technique with 85.69 ± 1 wt.-% Co, 14.18 ± 1 wt.-% W and 0.13 ± 0.02 wt.-% C. The energy dispersive X-ray (EDX) measurement validated the successful production of 100 % 𝛾𝛾-Co without undesirable presence of graphite or 𝜂𝜂-phase (Özden et al. (2015)). The specimens were then tested under both monotonic and cyclic loading to determine elastoplastic material parameters. In this study, the cyclic strain hardening behavior is represented by Chaboche plasticity model (Chaboche et al. (1979)). This model decomposes the backstress 𝑿𝑿 into three parts, and the evolution of each part 𝑿𝑿𝑘𝑘 is produced by Armstrong-Fredrick hardening model (Armstrong and Frederick (1966)), 3

X = Xk

(2)

k1

Xk 

Ck

0

   X    pl   k  Xk   pl

(3)

where 𝜎𝜎 0 is the equivalent stress defined the size of the yield surface at zero plastic strain and remains constant, 𝐶𝐶𝑘𝑘 , 𝛾𝛾𝑘𝑘 are material constants, and 𝜀𝜀̅̇pl is the equivalent plastic strain rate. The basic idea of this superposition is to represent the initial hardening modulus, transient nonlinear stage and quasi-linear part by three components, respectively. The ductile damage evolution for Co phase is described by Lemaitre damage model: 2 eq R   2E1-D2 dp, if D  Dcr D=   1, if D  Dcr 

(4)

where 𝜎𝜎eq is the equivalent von Mises stress, 𝑅𝑅𝜈𝜈 is the stress triaxiality function and 𝑝𝑝 is the accumulated equivalent plastic strain. The model relates the accumulative damage in a material to its internal stress and strain state. When the level of damage 𝐷𝐷 exceeds its critical value 𝐷𝐷cr (Lemaitre and Desmorat (2005)), the material fails. The material parameters for Co phase are summarized in Table 2. Table 2. Material parameters for Co phase. 𝐸𝐸 [MPa] 227 280

𝜈𝜈

0.3

𝜎𝜎 0 [MPa] 198

𝐶𝐶1 [MPa] 210 000

𝛾𝛾1

1 900

𝐶𝐶2 [MPa] 85 000

𝛾𝛾2

400

𝐶𝐶3 [MPa] 22 000

𝛾𝛾3

30

𝐷𝐷cr 0.3

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3. FE modeling and simulation To prepare FE models, the EBSD-based modeling approach proposed by Kayser et al. (2018) is applied in this work. Fig. 2 shows a 50 μm × 50 μm × 1 μm sample model of a WC-6 wt.% (weight percentage) Co hardmetal, which is subjected to a cyclic loading. The stress ratio 𝑅𝑅 equals 0.1 and the maximum applied stress is 800 MPa. The model captures more details of the microstructure when compared to previous SEM-based reconstruction. Individual WC grains are separated by WC-WC grain boundaries, and each grain is assigned the realistic local orientation exported from EBSD analysis system. The application of two-and-a-half-dimensional model by extruding two-dimensional morphology by 1 μm in the thickness direction aims at suppressing side effects, e.g. the under- or overestimation because of the plane stress or strain state assumption (Chen et al. (2016)). (a)

(b)

(c) applied effective stress 𝛴𝛴𝑥𝑥

10 µm

Fig. 2. (a) Morphology of the microstructure of studied hardmetal sample; (b) boundary condition of FE model; (c) cyclic loading profile.

The computational formulation of damage and failure is realized by introducing a field variable. At the end of each time increment, the updated damage according to equation (1) and equation (4) is assigned to the field variable. When the predefined failure criterion is reached, its stiffness parameters listed in Table 1 and Table 2 (except Poisson’s ratio) are set to minimal values. The material is tagged as failed and nearly loses its bearing capacity. The virtual element elimination technique allows modeling the incubation and evolution of microcracks. The functionality is realized by composing the user subroutine USDFLD and connecting with the commercial FE solver Abaqus/Standard. 4. Results and discussion (a)

(b)

(c)

Fig. 3. Simulated damage evolution process without residual stress over loading cycles 𝑁𝑁: (a) 𝑁𝑁 = 25; (b) 𝑁𝑁 = 70; (b) 𝑁𝑁 = 142.



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Fig. 3 plots the damage and failure state over loading cycles, from which the FCG behavior in the microstructure can be described. The simulated count of cycles to failure is 142. At the beginning, weak regions are usually found close to WC-Co phase interfaces, which can be assigned to incompatible strain due to large stiffness gradients. The damage evolution are more common in binder phase than WC phase. It can be interpreted from the fact that accumulation of plastic strain in Co binder increases the damage level simultaneously according to the equation (4). In contrast, the relatively low stress level is not able to split WC grains. These previously formed microcracks tends to form a main crack or multiple subcritical microcracks, and finally the stable growth reaches a limit. To investigate the influence of local thermal residual stress on the fatigue resistance of hardmetals, the simulation of the thermal contraction step before the mechanical loading step is executed. The respective thermal expansion coefficients 𝛼𝛼WC = 5.8 × 10−6 K −1 and 𝛼𝛼Co = 12 × 10−6 K −1 are applied (Spiegler et al (1992)). The distribution of residual stresses in the microstructure after cooling from 825 ℃ to the room temperature is given in Fig. 4, accompanied by a histogram plot as a summary. The positive sign of the hydrostatic stress 𝜎𝜎H indicates a tensile state in general. The higher tensile stresses appears in binder regions where crucial microstructural morphologies are found, e.g. narrow sites with tiny binder mean free path. The region near the WC-Co interface commonly hold higher order of magnitude than the interior domain does. On the contrary, WC phase mainly bears compression. (a)

(b)

𝜎𝜎H [MPa] Fig. 4. The distribution of simulated residual stresses in the microstructure as: (a) a contour plot; (b) a histogram plot.

Simulation results of the damage evolution with residual stress are shown in Fig. 5 and compared with ones from previous residual stress-free simulation. The damage and failure state in the microstructure after same counts of loading cycles for both simulations are displayed. By comparing microcracks at the same time, more damage spots appear in the microstructure from the new simulation. Besides, the simulated lifetime is also reduced by about 40%. A preliminary conclusion can be drawn that the thermal residual stresses decrease the fatigue resistance in hardmetals because the tensile state of stress in binder region accelerates the plastic strain accumulation and damage evolution. (a)

(b)

(c)

Fig. 5. Simulated damage evolution process with residual stress over loading cycles 𝑁𝑁: (a) 𝑁𝑁 = 25; (b) 𝑁𝑁 = 70; (b) 𝑁𝑁 = 86.

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5. Conclusion In this paper, a numerical approach to study the microscopic progressive fatigue damage evolution of WC-Co hardmetals is presented. The developed modeling technique allows a precise reconstruction of the microstructure. Suitable material models are adopted to simulate the fatigue process at a microlevel. FE simulation result implies that, under a fatigue regime, microcracks are usually initiated in the ductile phase due to the accumulation of plastic strain after several cycles. Consequently, the coalescence of these microdefects results in the formation of subcritical cracks. This process is consistent with experimental observations, in which the susceptibility of the ductile binder to the fatigue property are usually discovered (Llanes et al. (2002)). The effect of micro- and mesoscopic residual stresses due to the cooling history in production process on the fatigue property is also studied. Although corresponding experiments on hardmetals cannot be identified by now, the reduction in fatigue resistance due to the tensile residual stress in the ductile phase still shows a satisfactory agreement with empirical experience (Doremus et al. (2015)). References Armstrong, P. J., and Frederick, C. O., 1966. A mathematical representation of the multiaxial Bauschinger effect (Vol. 731). Berkeley: Central Electricity Generating Board and Berkeley Nuclear Laboratories, Research & Development Department. Chaboche, J. L., Dang Van, K., and Cordier, G., 1979. Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel. Chen, G., Weichert, D., and Broeckmann, C., 2016. Strength prediction of particulate reinforced metal matrix composites. Dissertation, RWTH Aachen University, 2016. Doremus, L., Cormier, J., Villechaise, P., Henaff, G., Nadot, Y., and Pierret, S., 2015. Influence of residual stresses on the fatigue crack growth from surface anomalies in a nickel-based superalloy. Materials Science and Engineering: A, 644, 234–246. Fischmeister, H. F., Schmauder, S., and Sigl, L. S., 1988. Finite element modelling of crack propagation in WC-Co hard metals. Materials Science and Engineering: A, 105, 305–311. Golovchan, V. T. (1998). Elastic moduli of a tungsten monocarbide crystal. International applied mechanics, 34(8), 755-757. Kayser, W., Bezold, A., and Broeckmann, C., 2018. EBSD-based FEM simulation of residual stresses in a WC6wt.-% Co hardmetal. International Journal of Refractory Metals and Hard Materials, 73, 139–145. Lay, S., Allibert, C. H., Christensen, M., and Wahnström, G., 2008. Morphology of WC grains in WC–Co alloys. Materials Science and Engineering: A, 486(1–2), 253–261. Lee, M., and Gilmore, R. S., 1982. Single crystal elastic constants of tungsten monocarbide. Journal of Materials Science, 17(9), 2657–2660. Lemaitre, J., and Desmorat, R. 2005. Engineering damage mechanics: ductile, creep, fatigue and brittle failures. Springer Science & Business Media. Llanes, L., Torres, Y., and Anglada, M., 2002. On the fatigue crack growth behavior of WC–Co cemented carbides: kinetics description, microstructural effects and fatigue sensitivity. Acta Materialia, 50(9), 2381–2393. Mishnaevsky Jr, L., Dong, M., Hönle, S., and Schmauder, S., 1999. Computational mesomechanics of particle-reinforced composites. Computational Materials Science, 16(1–4), 133–143. McHugh, P. E., and Connolly, P. J., 2003. Micromechanical modelling of ductile crack growth in the binder phase of WC–Co. Computational Materials Science, 27(4), 423–436. Özden, U. A., Mingard, K. P., Zivcec, M., Bezold, A. and Broeckmann, C., 2015. Mesoscopical finite element simulation of fatigue crack propagation in WC/Co-hardmetal. International Journal of Refractory Metals and Hard Materials, 49, 261–267. Özden, U. A., Jiang, K., Bezold, A., and Broeckmann, C., 2016. Evaluation of Fatigue Crack Growth Performance in different Hardmetal Grades based on Finite Element Simulation. Procedia Structural Integrity, 2, 648–655. Prescient & Strategic (P&S) Intelligence Private Limited. Tungsten Carbide Powder Market by Grain Size, by Grade, by Application, by EndUse Industry, by Geography—Global Market Size, Share, Development, Growth, and Demand Forecast, November 2018. Sailer, T., Herr, M., Sockel, H. G., Schulte, R., Feld, H., and Prakash, L. J., 2001. Microstructure and mechanical properties of ultrafine-grained hardmetals. International Journal of Refractory Metals and Hard Materials, 19(4–6), 553–559. Schleinkofer, U., Sockel, H. G., Go, K., and Heinrich, W., 1996. Microstructural processes during subcritical crack growth in hard metals and cermets under cyclic loads. Materials Science and Engineering: A, 209(1–2), 103–110. Spiegler, R., Schmauder, S. and Exner, H. E., 1992. Finite element modelling of the thermal residual stress distribution in a WC-10wt%Co Alloy. Journal of Hard Materials, 3(2), 143–151. Trueba, M., Aramburu, A., Rodríguez, N., Iparraguirre, I., Elizalde, M. R., Ocaña, I., Sánchez, J. M., and Martínez-Esnaola, J. M., 2014. “In-situ” mechanical characterisation of WC-Co hardmetals using microbeam testing. International Journal of Refractory Metals and Hard Materials, 43, 236–240.