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Heterogeneous strain responses of as-sintered cemented carbide
International Journal of Plasticity 121 (2019) 312–323
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Heterogeneous strain responses of as-sintered cemented carbide Yanan Li, Xuemei Liu, Chao Hou, Haibin Wang, Xiaoyan Song∗
T
College of Materials Science and Engineering, Key Laboratory of Advanced Functional Materials, Education Ministry of China, Beijing University of Technology, Beijing, 100124, China
ARTICLE INFO
ABSTRACT
Keywords: Strain response Residual stress Plastic deformation Cemented carbide
The heterogeneous interactions between the pre-existing thermal residual stress and external compression in the WC-Co cemented carbide are investigated, where the microstructural characteristics are taken into account simultaneously. A new method for creating three-dimensional finite element model based on real microstructure of the cemented carbides was proposed. The deformation behavior of the as-sintered cemented carbide was quantified and demonstrated in detail. The results indicate that among the heterogeneous distribution of strain responses in the dual-phase microstructure during compressive loading, the layer-like metal binder distributing in the transverse cross-section with respect to the direction of compression has the earliest strain response. The microcracks may preferentially nucleate at these regions due to the largest accumulation of plastic deformation. It is suggested that the activation sequence of dislocation slip systems in the metal binder can be changed by the anisotropic distribution of stress.
1. Introduction WC-Co cemented carbides are widely used as materials for cutting tools because of their excellent combination of hardness, wear resistance, and strength (Exner, 1979; Chang and Chen, 2014; Liu et al., 2018). This kind of materials contain two interpenetrating phases: WC and Co. The carbide phase (WC) mainly contributes to hardness while the binder phase (Co) mainly contributes to toughness. The physical and mechanical properties of these two phases, such as Young's modulus, yield strength, and thermal expansion, greatly differ. When the cemented carbide being cooled from the sintering temperature to ambient temperature, high thermal residual stresses may be generated due to the difference in the thermal expansion coefficients of WC and Co (Mari et al., 2002, 2009; Coats and Krawitz, 2003; Seol et al., 2005). Upon compression of the as-sintered WC-Co composite, the pre-existing thermal residual stress may interact with the applied external stress, which has previously been studied by neutron diffraction (Livescu et al., 2005a, 2005b; Paggett et al., 2007; Krawitz et al., 2009, 2010; Mari et al., 2015). The strain responses of WC and Co differ distinctly due to the different stress states (Livescu et al., 2005a). On the other hand, the applied strain was shown to be compressive in the axial direction while tensile in the transverse direction because of the Poisson ratio effect (Krawitz et al., 2010). Thus, for instance, in cobalt, which has tensile strain on average, the applied strain adds to the thermal residual strain in the transverse direction. This leads to a preferential yielding in the transverse direction, resulting in the anisotropic strain responses and plastic deformation. It has been confirmed by the numerical simulations such as the finite element method that the point-to-point distribution of thermal residual stresses in the cemented carbides varies dramatically (Spiegler et al., 1992; Weisbrook and Krawitz, 2002; Kayser et al., 2017, 2018; Zhong et al., 2017). The highest compressive stress exists in the regions of low dihedral carbide angles, while high
∗
Corresponding author. E-mail address: [email protected] (X. Song).
https://doi.org/10.1016/j.ijplas.2019.06.014 Received 4 April 2019; Received in revised form 12 June 2019; Accepted 26 June 2019 Available online 27 June 2019 0749-6419/ © 2019 Elsevier Ltd. All rights reserved.
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tensile stress exists in the regions with a low mean free path of the binder (Kayser et al., 2018). Moreover, both compressive and tensile stresses may exist in the two phases (Kayser et al., 2017). This indicates that the strain responses are heterogeneous among the phases, which has been revealed through the evolution of peak breadths from the neutron diffraction (Krawitz et al., 2009, 2010). Detailed phase responses with consideration of the complex spatial morphologies of both phases, are closely related with the exhibited toughness of the cemented carbides. Unfortunately, a quantitative description of the phase responses in the WC-Co cemented carbides during loading has not been reported in the literature yet. In this study, in order to examine the detailed interactions between the pre-existing thermal residual stress and the applied external stress, we firstly set up a new method for creating a three-dimensional (3D) finite element model based on the real microstructure of the WC-Co cemented carbide. Then, a process of uniaxial compression was simulated, with the loading applied immediately after the sintering and cooling treatment. The strain responses of the WC and Co phases during the compressive loading and unloading were studied, and their correlation with the plastic deformation behavior and fracture toughness of the cemented carbide materials was proposed. 2. Experimental A WC-8wt%Co sample was prepared by a sinter-hot isostatic pressure (HIP) process. The mean size of WC grains was approximately 400 nm, which was measured by the two-dimensional linear intercept method. A FEI Helios Nanolab 600i focused ion beam (FIB) coupled with field-emission scanning electron microscopy (FE-SEM) was utilized to acquire the image stacks for creating the three-dimensional finite element (FE) model. An area of interest in the sample, which was a cube of approximately 103 μm3, was subjected to the FIB milling. The step size of the milling process was set to 20 nm, according to the principle that at least 10 sections are needed through the smallest dimension of the WC grains (Groeber et al., 2008), which was underestimated at half of the mean grain size. 500 image stacks were acquired. Then, for the regions representative for the dual-phase structure of the cemented carbide, 20 image stacks were selected to build the 3D FE model, for which suitable computation time was also considered. The details of the FIB process can be found elsewhere (Borgh et al., 2013; Singh et al., 2016; Jiménez-Piqué et al., 2017). To gain the precise image stacks used in the model, a series of image processing were implemented on the raw images using the Visualization Sciences Group (VSG) Avizo software. Firstly, a sequential processing was employed, including alignment, cropping, shearing correction, and shading correction. Then, noises were reduced through the median filters and edge-preserving smoothing Gaussian filters. Finally, the WC and Co phases were segmented by histogram-based binarization. 3. Three-dimensional model and simulations Many simulation studies focused on the thermal residual stresses of WC-Co cemented carbide were carried out using 2D models or simple 3D models (so called as 2.5D models) (Kayser et al., 2018), which were reconstructed from the real microstructure. In these studies, the WC grain boundaries were outlined and vectorized after the segmentation of WC grains, as well as the WC/Co phase boundaries. However, discrepancy induced by the image algorithms was unavoidable, and manual corrections were required to eliminate the errors. These treatments can be well implemented for 2D or some 2.5D models. Intuitively, it seems to be impossible to reconstruct complex 3D models based on the real material microstructure by this approach. Thus, here we set up a new method for creating a 3D FE model based on the real microstructure of cemented carbide. The main idea was to convert the bitmaps directly into a FE model through the voxel distributions. Firstly, the bitmaps of image stacks were transformed into the distributions and attributions of the voxels, in which coordinates of the Co phase were collected. Additionally, the initial FE model with element distributions equivalent to the distributions of voxels was created and meshed in the ANSYS software. A 3-D 8-node hexahedron brick element (SOLID185 in ANSYS) was adopted in this work. The length and width of the element were the same as the actual size of one pixel, while the thickness was equivalent to the step size of milling mentioned above. Coordinates of the whole elements were obtained from the distributions of elements and nodes. Then, the list of elements attributed to the Co phase was achieved by comparing the coordinates between the Co phase and elements using an array lookup function. Finally, after attributing the properties of WC to the whole elements, the properties of elements that belonged to the Co phase were converted to those of Co according to the list. After finishing the above steps, the 3D FE model based on the real microstructure of the WC-Co cemented carbide was established. A FE model of WC-Co cemented carbide with the dimensions of 1.77 μm (axial) × 2.35 μm (long transverse) × 0.40 μm (short transverse) was utilized for the simulations on the thermal residual stress and the uniaxial compression process. Three adjacent faces were assigned to be symmetrical boundaries, while the other three faces were free boundaries. For the upper limit temperature at which the thermal residual stress is considered, in the literature researchers either used an absolute temperature, such as 800 °C (Zhong et al., 2017) and 1300 °C (Kayser et al., 2018), or a temperature drop, which was for example chosen as 800 K (Spiegler et al., 1992) or 600 K (Weisbrook and Krawitz, 2002). In this study, the initial temperature was set to 800 °C, and the final temperature was 25 °C, according to the real processing route. The initial stresses of both phases were assumed to be zero at 800 °C according to the results obtained by neutron diffraction (Mari et al., 2009). The uniaxial compression was carried out immediately after cooling. The compression load was applied on the free surface along the axial direction. The load circle was from 0 to −2000 MPa to 0 in an increment of 100 MPa. Throughout the modeling, the WC phase was considered as elastic, while the Co phase was elasto-plastic with linear isotropic hardening. The material properties derived and extrapolated from the data reported in the literature (Golovchan, 2007; Huang et al., 2008; Özden et al., 2015) were used in this study, as shown in Table 1. Due to the lack of the temperaturedependent plastic properties of Co phase, the parameters of Co phase plastic properties at the room temperature were used in this 313
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Table 1 Plastic properties of Co and elastic properties of WC and Co. Material
Young's modulus (GPa)
Thermal expansion coefficient (°C−1)
Poisson's ratio
Yield stress (MPa)
Hardening modulus (GPa)
WC
20 °C 400 °C 800 °C
719.0 700.0 680.0
3.2 × 10−6 4.0 × 10−6 6.0 × 10−6
0.19
–
–
Co
20 °C 400 °C 800 °C
213.5 194.5 174.5
8.0 × 10−6 14.0 × 10−6 16.0 × 10−6
0.31
683.0
52.4
study. The yield stress and hardening modulus of Co phase were taken from the same literature (Özden et al., 2015), in which the features of the Co binder phase were similar with those in the present WC-Co cemented carbide material. 4. Results and discussion 4.1. Thermal residual stress The main purpose of this study was to examine the interaction between the pre-existing thermal residual stress and applied external stress. Thus, the distribution of thermal residual stresses was simulated at first to build up the initial state of stress before compression. Fig. 1 shows the 3D topographies of the FE model of the WC-Co composite and the contour plots of the thermal residual stress in the material after cooling. It can be seen that the cobalt phase (Fig. 1c) was homogeneously distributed in the WC-Co composite (Fig. 1d). The axial-component and transverse-component of the thermal residual stresses, which are illustrated in Fig. 1e and f, respectively, show that high tensile stresses exist in the Co phase, while the compressive stresses exist in the WC phase. In addition, tensile stresses can also be found in the WC phase near the WC/Co interfaces. 4.2. Stress-strain curve of cemented carbide The macroscopic stress-strain curve of the WC-Co cemented carbide in the process of compression is illustrated in Fig. 2. For comparison, an experimental result of macroscopic stress-strain curve from literature (Livescu et al., 2005b) is also shown in Fig. 2, which was obtained from a WC-10 wt%Co sample with cobalt content a little higher than that in the present material. It can be seen that the simulation results exhibit nearly a same trend as that of the experimental results. A distinct deviation from a linear relationship between stress and strain is found starting from −500 MPa, which indicates that the yielding occurs at the early stage of loading. After unloading, a negative plastic deformation of 0.035% was produced, which is slightly larger than that reported in the experiments (Livescu et al., 2005b). The elastic modulus (E) evaluated from the early stage of the stress-strain curve is 519.1 GPa in the simulations, which is close to the elastic modulus measured by the extensometer (571.2 GPa) in Ref. (Livescu et al., 2005b). Therefore, the results obtained by simulations are reasonable to be used for subsequent analyses related with the stress-strain curves. 4.3. Heterogeneous strain responses within the microstructure To investigate the strain responses in the microstructure of the cemented carbide, which consists of WC and Co phases, a typical cross-section that is representative of the random distribution of the dual-phase constitution was cut from the three-dimensional model, as shown in Fig. 3. The locations taken for analysis are marked in the figure, where seven of them are located in the Co phase and three are located in the WC phase, respectively. According to the microstructure, three representative regions of the Co phase are examined: the zone with a nearly round shape, indexed as 1, 2 and 3; the layer-like zone along the transverse direction, indexed as 4 and 5; and the layer-like zone along the axial direction, indexed as 6 and 7. In Fig. 3b, the above representative regions are highlighted in the real microstructure with different colors respectively. Apparently, the Co phase mainly exhibits a moderate strain response due to the mixed characteristics. The stress-strain curves of different locations in the Co phase are shown in Fig. 4. The strain was extracted from the node at each location. The initial thermal strains are offset to zero for the intuitive comparison between locations 1 to 7. It is shown in Fig. 3a that before compression, the cobalt undergoes tensile stress either in the axial direction or in the transverse direction, i.e. the Co phase has positive thermal strain. Upon loading, the applied strain opposes the thermal residual strain in the axial direction. However, in the transverse direction, the applied strain adds to the thermal residual strain due to the Poisson ratio effect, leading to an earlier yielding in this direction. This results in the reduction of the initial thermal strain in the cemented carbide along the transverse direction, while the initial strain in the axial direction increases. Therefore, the strain presents a negative deviation in the transverse direction but a positive deviation in the axial direction, implying that the initial stress decreases in the transverse direction but increases in the axial direction. The stress-strain responses distinct from one another in different directions and the directional yielding suggest that the stress state has significant influence on the plastic deformation behavior of the material. In addition, the statistical stress-strain response in Co binder is also shown in Fig. 4, which exhibits a similar trend with that reported by experiments (Livescu et al., 2005b; Krawitz et al., 2010; Mari et al., 2015). 314
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Fig. 1. Topographies of the FE model of the WC-Co composite and distribution contours of initial thermal residual stress: (a) schematic diagram and dimensions, (b) 3D distribution of WC, (c) 3D distribution of Co, (d) 3D topography of WC-Co, (e) axial-component of initial thermal residual stress, (f) transverse-component of initial thermal residual stress.
As seen in Fig. 4, the interactions between the thermal residual strain and the applied strain vary significantly in different locations of Co phase, which depends on the combination effect of the initial thermal residual stress and the microstructural feature. Transversal yielding is a main consequence due to the release of thermal residual stresses, which implies that a higher initial thermal stress will lead to a larger strain deviation upon the complete unloading. For the initial transversal stresses in cobalt shown in Fig. 3a, the highest tensile stress existed in the layer-like Co along the transverse direction, followed by the stress existing in the near-round shaped Co phase. The layer-like Co along the axial direction had the lowest initial stress. Corresponding to the various local initial stress states, the yielding strengths of different locations in Co differ greatly, indicating that the yield strength is strongly affected by the initial stress. Their relationship will be discussed in detail in Section 4.4. The microstructural features also have a significant effect on the strain responses. To understand this mechanism, compression simulations without considering the initial thermal residual stresses were studied, and the transverse strain responses of the three representative regions are shown in Fig. 5. The near-round shaped Co exhibits the earliest strain response. However, the yielding occurs firstly in the layer-like Co along the transverse direction due to the stress concentration. Consequently, the strain responses of different locations in the Co phase are obviously heterogeneous (Fig. 4). In the near-round shaped Co, a moderate strain response with a yield external stress of approximately 1000–1500 MPa was observed. The yield stresses were slightly different as a consequence of the variable initial thermal stress. An extreme strain response was found in the layer-like Co along the transverse direction (locations 4 and 5), where the yielding occurred at the beginning of loading and finally the thermal strain was greatly released. The yielding occurred in these locations caused indistinct deviation of the macroscopic stress-strain curve from the linear 315
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Fig. 2. Macroscopic stress-strain responses in the WC-Co cemented carbides, which are obtained from the present simulations and previous experimental studies (Livescu et al., 2005b).
Fig. 3. Representative cross-section of the three-dimensional microstructure of WC-Co cemented carbide: (a) distribution of Co phase and locations (indexed by numbers) selected for analysis, the axial-component (A) and transverse-component (T) of the initial thermal residual stress (with unit of MPa and positive indicating tensile stress) are shown correspondingly, (b) typical Co regions in the real microstructure.
relationship as the stress is lower than −500 MPa, as shown in the inset of Fig. 2. In contrast, along the axial direction in the layerlike Co (locations 6 and 7), the strain responses were inconspicuous. In addition, a deviation from the linear relationship was observed in locations 4 and 5 at the end of unloading, indicating that these regions also yielded due to the stress transfer during the unloading process. Apparently, after unloading, the plastic strains in the layer-like Co along the transverse direction are much larger than those at other locations, which indicates that the plastic deformation behavior of Co is heterogeneous in the cemented carbide. In previous studies, the peak breadth of the neutron diffractions was used to reveal the stress variance within the Co phase (Krawitz et al., 2010). In the present study, alternatively, the evolution of the standard deviation of thermal residual stresses at 316
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Fig. 4. Microscopic stress-strain responses of various locations in Co phase (as marked by 1–7 in Fig. 3a) and the wide-ranging statistical stress-strain response.
different locations was examined to analyze the heterogeneous stress state, and was compared with the neutron diffraction results. It can be seen from Fig. 6 that the simulation results have very similar trend with those of the measured results. In the axial direction, the stress variance increases during loading and decreases during unloading. However, in the transverse direction, the deviation 317
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Fig. 5. Microscopic transverse stress-strain responses of locations 1, 4, and 6 in Co phase without considering the initial thermal residual stress.
Fig. 6. Stress variances within Co during loading and unloading processes: (a) Comparison between the present simulations and experimental results in Ref. (Krawitz et al., 2009), (b) Variances of maximum and minimum stresses at the studied locations in the axial direction, (c) Variances of maximum and minimum stresses at the studied locations in the transverse direction.
decreases with loading before −1000 MPa and then reverses to increase until completion of loading. In the unloading process, the deviation decreases monotonously. Upon unloading, in both the axial and transverse directions, the deviations have a net reduction due to the yielding occurred at specific regions. This indicates that the stress field tends to be more homogeneous after compressive deformation, and is inherently related with the plastic deformation behavior. The evolution of the maximum and minimum stresses at the studied locations during the compression process is illustrated in Fig. 6b and c, corresponding to different directions. In the axial direction, the rapid decrease in the minimum stress dominates the increase of stress variance during loading, as well as the decrease of that during unloading. The minimum stress exists in the layer-like Co along the transverse direction, which undergoes the most yielding during compression. In the transverse direction, the stress variance decreases at first because the maximum stress rapidly decreases at the beginning of loading, and then conversely increases because of the rapid decline of the minimum stress. This change has never been further examined and explained by experimental studies. Moreover, the rapid decreases of the maximum stress at the beginning and the minimum stress at the final stage both occur at location 4 (Fig. 6c). Actually, this region experienced a continuous stress reduction from the maximum to minimum throughout the 318
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Fig. 7. Microscopic stress-strain responses of various locations in WC phase (as marked by 8–10 in Fig. 3a). The coordinate ranges of the figures are consistent with those in Fig. 4.
loading process, corresponding to the continuous plastic deformation of location 4 in Fig. 4. The accumulated plastic deformation may result in microcracks occurring in this region, which will be discussed in Section 4.4. Fig. 7 shows the strain responses of different locations in the WC phase upon loading and unloading. There is only a slight difference in the stress-strain responses of different locations in the WC phase. It is obvious that the strain deviation in WC upon unloading is much smaller than that in Co. Because the WC phase was assumed to be elastic in the model, the change in the elastic strain of WC is merely due to the strain relaxation in Co. In the dual-phase microstructure of the cemented carbide, the load can be transferred to WC from Co, and the strain field is thus redistributed during the compression process. The simulation shows that during the uniaxial compression, the strain responses are clearly different between the axial and transverse directions, i.e. with the external stress, the strain response is anisotropic. It is known that the thermal residual stresses are in principle hydrostatic (Krawitz et al., 2009), which indicates that the stresses are equivalent in any physical direction throughout the microstructure. Therefore, a two-dimensional simulation of the thermal residual stress for the state after cooling from the sintering temperature is reasonable. However, as a result of the anisotropic plastic flow in Co during compression, the hydrostatic stress state transforms into a cylindrical stress state (Livescu et al., 2005a,b). This indicates that a three-dimensional simulation is indispensable to understand the interactions between the pre-existing thermal residual stress and the applied stress; otherwise, the twodimensional simulation results may be misleading. Moreover, in the present study, our attention is focused on the strain responses during deformation, the stress distribution, and the interaction between the thermal residual stress and the applied stress. Thus, the deformation state of the materials was simulated till the stage of plastic deformation before occurrence of fracture. 4.4. Correlation between strain response and plastic deformation behavior of cemented carbide In the simulations, the WC and Co phases were assumed to be elastic and elasto-plastic, respectively. The plastic deformation of the cemented carbide mainly occurred in the Co phase. However, previous studies show that the plastic properties of Co can be very different, especially the yield strength of Co was reported ranging from 279 to 2950 MPa (Herd et al., 2018). There are many factors that affect the yield strength of Co phase on the microscopic scale, such as solid solution of W and C in Co (Roebuck et al., 1984), grain size and orientation (Roebuck, 2006; Csanádi et al., 2015; Kim et al., 2016), crystal structure transformation (Liu et al., 2012), and the stress state as well as its evolution, which is the focused issue in this study. The plastic deformation is, on the microscale, generated by the motion of dislocations, which needs to overcome the resistance of crystal lattice that is inversely related to the lattice spacing. The microscopic residual stress is essentially lattice distortion (Hu et al., 2016; Salvati and Korsunsky, 2017); in other words, the increase in the lattice spacing results in tensile stress within the crystal, and conversely the compressive stress. According to the Peierls stress from the lattice (Liu et al., 2016, 2017a), plastic deformation is more likely to occur in regions which have higher tensile stress with lower lattice resistance, thus in these locations a relatively lower yield 319
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Fig. 8. Cumulative plastic deformation at locations 1, 4, and 6 with loading up to −5000 MPa in an increment of 100 MPa. The inset is an experimental result in our previous work (Liu et al., 2017b), showing the crack nucleation in the layer-like Co along the transverse direction with respect to the loading direction.
strength is shown. As seen in Fig. 4, the layer-like Co along the transverse direction (locations 4 and 5) that undergo the highest tensile stresses (Fig. 2) yield at the initial stage of loading, exhibiting an extreme low yield strength. It is shown in Fig. 4 that the layer-like Co along the transverse direction yielded the earliest during compression, indicating that the stress was heavily concentrated in this region. After unloading, the plastic deformation of Co varies significantly at different locations. To quantify this phenomenon, the cumulative plastic deformation of each region was calculated for the load in a range up to −5000 MPa, and the results are shown in Fig. 8. The plastic deformation was accumulated faster in the regions of stress concentration than in other regions, which implies that massive dislocations were triggered to coordinate the stress concentration. As a result, work hardening may occur when the motion of dislocations is stagnated in these regions, and microcracks can nucleate due to the rapid accumulation of plastic deformation. Moreover, crack nucleation and propagation may also occur at the WC/Co interfaces when the Co phase cannot effectively relax the stress concentration due to work hardening. To verify the above statement, the results from the molecular dynamics (MD) simulations for the WC-Co cemented carbide under uniaxial compression are provide in Fig. 9. The details for the setup of the simulation model were described in our previous work (Fang et al., 2019). It is observed in Fig. 9 that the first two microcracks initiated at the WC/Co phase boundaries, which were adjacent to the layer-like Co along the transverse direction of the compression. The MD simulation results confirmed the present simulation results on the microscale. In summary, the layer-like Co distributing in the transverse cross-section with respect to the direction of compression is detrimental to the deformation behavior of the cemented carbides, hence is undesirable for the fracture toughness and strength of the material. The simulation results suggest that design and modification of the dual-phase microstructure of the cemented carbides are significant to improve the mechanical properties, particularly, the dense distribution of the layer-like Co should be avoided. Moreover, as there are different characteristics of WC morphologies and WC skeletons in the cemented carbides (García et al., 2019), other parameters such as WC grain shape factor, WC contiguity, and Co mean free path may be introduced in the simulations to extend the model application to complex deformation behavior of the cemented carbides. The present study indicates that plastic deformation results in the relaxation of thermal residual stress after unloading. Moreover, the external stress provides a higher driving force for the motion of dislocations in the stress concentration regions, while the residual stress changes the resistance from the lattice against the motion of dislocations. Actually, both the thermal residual stress and the applied stress affect the motion of dislocations by changing the distortion extent of the lattice. After migration of the dislocations, the
Fig. 9. MD simulation result of the WC-Co cemented carbide under uniaxial compression, showing nucleation of microcracks at the WC/Co phase boundaries adjacent to the layer-like Co along the transverse direction of the compression (Fang et al., 2019). 320
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Fig. 10. Von Mises stress distribution contours of the representative cross-section: (a) initial stress state, (b) stress state after compression.
lattice distortion decreases, which macroscopically appears as the release of the thermal residual stress. It is worth noting that under tension, the stress concentration occurs at the crack tip, and the crack may expand continuously due to the accumulation and release of the stored energy, with almost no plastic deformation away from the cracks (Mingard et al., 2013). In contrast, as shown in Fig. 8, non-simultaneous plastic deformations occur in various regions of Co during compression. When a certain degree of plastic deformation occurs in the stress concentration region, plastic deformation can also initiate in other regions of Co to accommodate a homogeneous stress field throughout the cemented carbide, which results in a much higher compressive strength than the tensile strength (Golovchan and Litoshenko, 2010). To form a homogeneous stress field, as indicated in Fig. 6, dislocations will migrate towards the direction with lower lattice resistance; hence, the distortion of lattice tends to be uniform. On the macroscopic scale, the stress field is homogenized. As shown in Fig. 10, compared with the initial distribution of the von Mises stress, which is usually utilized as a criterion for evaluating the yield, after compression the initially higher stress decreases while the lower stress increases. This implies that the residual stress may be an additional factor affecting the activation sequence of the slip systems. Generally, the activation sequence of dislocation slip systems is determined by the crystal lattice resistance, i.e. the Peierls stress, which is expressed as (Hertzberg, 1989) P
=
2G 1
exp
2 a (1
(1)
)b
where a is the interplanar spacing of the slip plane, b is the interatomic spacing along the slip direction, and is the Poisson's ratio, G is the shear modulus. According to the relationship between the Peierls stress and the lattice distortion, a certain slip system is easier to activate with the existence of residual stress as compared with the non-stress state. It is predicted that an anisotropic stress state can change the activation sequence of the dislocation slip systems. It is worth noting that the present simulation method is applicable to other type dual-phase materials and can also be extended for multiphase materials. As the method is based on the SEM image stacks taken from the FIB-SEM experiments, it implies that if the multiple phases can be distinguished in the SEM images by contrasts, this method can be used to analyze the stress-strain behavior of the material. 5. Conclusions In the present work, a three-dimensional FE model based on the real microstructure of WC-Co cemented carbide was set up to study the interaction between the pre-existing thermal residual stress and the applied compressive stress. The heterogeneous strain responses of Co and WC phases upon compressive loading and unloading were illustrated in detail, and the effects of the thermal residual stress combined with the microstructural features on the mechanical behavior of the cemented carbide were shown. The main conclusions are drawn as follows. 321
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(1) A new method was developed for creating a three-dimensional finite element model based on the real microstructure of the WCCo cemented carbide through conversion of bitmaps of the dual-phase structure. The accuracy of the model was confirmed by comparing the macroscopic stress-strain curve and the stress variance during compression obtained from simulations with those from the experimental results. Simulations based on this model can precisely exhibit the characteristics of the stress distribution and strain response in the cemented carbide as a typical cermet material. Furthermore, this modeling method can be extended to be applied in a variety of composite materials with dual-phase and also multiphase microstructures. (2) The strain responses of the WC-Co cemented carbide in the process of compression are obviously heterogeneous throughout the microstructure. The layer-like Co distributing on the transverse cross-section with respect to the direction of compression, where the highest thermal residual stress pre-exists, exhibits the earliest strain response during compression. The plastic deformation is more likely to occur in these regions due to the low lattice resistance, and a relatively low yield strength is presented. Furthermore, plastic deformations in these regions are cumulated faster than in other regions. Under uniaxial compressive loading microcracks may preferentially nucleate in the layer-like Co along the transverse direction and WC/Co phase boundaries adjacent to Co layers. To achieve high fracture toughness and strength, dense directional distribution of the layer-like Co should be eliminated in the design and modification of the dual-phase microstructures. (3) The stress variance during compression indicates the interaction between the applied stress and the pre-existing thermal residual stress at different locations in the microstructure. Upon unloading, the stress variance decreases, suggesting partial release of the thermal residual stress due to the plastic deformation occurred in certain regions of the cemented carbide. As a result, a more homogeneous stress field is obtained. On the microscopic scale, dislocations may migrate towards the direction with low lattice resistance to accommodate the distortion of lattice. Thus, the residual stress, as well as the anisotropic stress state, may change the activation sequence of the dislocation slip systems in the composite materials. Acknowledgements This work was supported by the National Key Program of Research and Development (2018YFB0703902, 2016YFB0700501 and 2016YFB0700503), the National Natural Science Foundation of China (51631002, 51425101 and 51621003) and the Postdoctoral Research Foundation of Chaoyang District (2018ZZ0129). References Borgh, I., Hedström, P., Odqvist, J., Borgenstam, A., Ågren, J., Gholinia, A., Winiarski, B., Withers, P.J., Thompson, G.E., Mingard, K., Gee, M.G., 2013. On the threedimensional structure of WC grains in cemented carbides. Acta Mater. 61, 4726–4733. https://doi.org/10.1016/j.actamat.2013.05.008. Chang, S.H., Chen, S.L., 2014. Characterization and properties of sintered WC-Co and WC-Ni-Fe hard metal alloys. J. Alloy. Comp. 585, 407–413. https://doi.org/10. 1016/j.jallcom.2013.09.188. Coats, D.L., Krawitz, A.D., 2003. Effect of particle size on thermal residual stress in WC-Co composites. Mater. Sci. Eng. A 359, 338–342. https://doi.org/10.1016/ S0921-5093(03)00379-4. 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Heterogeneous strain responses of as-sintered cemented carbide Yanan Li, Xuemei Liu, Chao Hou, Haibin Wang, Xiaoyan Song∗
T
College of Materials Science and Engineering, Key Laboratory of Advanced Functional Materials, Education Ministry of China, Beijing University of Technology, Beijing, 100124, China
ARTICLE INFO
ABSTRACT
Keywords: Strain response Residual stress Plastic deformation Cemented carbide
The heterogeneous interactions between the pre-existing thermal residual stress and external compression in the WC-Co cemented carbide are investigated, where the microstructural characteristics are taken into account simultaneously. A new method for creating three-dimensional finite element model based on real microstructure of the cemented carbides was proposed. The deformation behavior of the as-sintered cemented carbide was quantified and demonstrated in detail. The results indicate that among the heterogeneous distribution of strain responses in the dual-phase microstructure during compressive loading, the layer-like metal binder distributing in the transverse cross-section with respect to the direction of compression has the earliest strain response. The microcracks may preferentially nucleate at these regions due to the largest accumulation of plastic deformation. It is suggested that the activation sequence of dislocation slip systems in the metal binder can be changed by the anisotropic distribution of stress.
1. Introduction WC-Co cemented carbides are widely used as materials for cutting tools because of their excellent combination of hardness, wear resistance, and strength (Exner, 1979; Chang and Chen, 2014; Liu et al., 2018). This kind of materials contain two interpenetrating phases: WC and Co. The carbide phase (WC) mainly contributes to hardness while the binder phase (Co) mainly contributes to toughness. The physical and mechanical properties of these two phases, such as Young's modulus, yield strength, and thermal expansion, greatly differ. When the cemented carbide being cooled from the sintering temperature to ambient temperature, high thermal residual stresses may be generated due to the difference in the thermal expansion coefficients of WC and Co (Mari et al., 2002, 2009; Coats and Krawitz, 2003; Seol et al., 2005). Upon compression of the as-sintered WC-Co composite, the pre-existing thermal residual stress may interact with the applied external stress, which has previously been studied by neutron diffraction (Livescu et al., 2005a, 2005b; Paggett et al., 2007; Krawitz et al., 2009, 2010; Mari et al., 2015). The strain responses of WC and Co differ distinctly due to the different stress states (Livescu et al., 2005a). On the other hand, the applied strain was shown to be compressive in the axial direction while tensile in the transverse direction because of the Poisson ratio effect (Krawitz et al., 2010). Thus, for instance, in cobalt, which has tensile strain on average, the applied strain adds to the thermal residual strain in the transverse direction. This leads to a preferential yielding in the transverse direction, resulting in the anisotropic strain responses and plastic deformation. It has been confirmed by the numerical simulations such as the finite element method that the point-to-point distribution of thermal residual stresses in the cemented carbides varies dramatically (Spiegler et al., 1992; Weisbrook and Krawitz, 2002; Kayser et al., 2017, 2018; Zhong et al., 2017). The highest compressive stress exists in the regions of low dihedral carbide angles, while high
∗
Corresponding author. E-mail address: [email protected] (X. Song).
https://doi.org/10.1016/j.ijplas.2019.06.014 Received 4 April 2019; Received in revised form 12 June 2019; Accepted 26 June 2019 Available online 27 June 2019 0749-6419/ © 2019 Elsevier Ltd. All rights reserved.
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tensile stress exists in the regions with a low mean free path of the binder (Kayser et al., 2018). Moreover, both compressive and tensile stresses may exist in the two phases (Kayser et al., 2017). This indicates that the strain responses are heterogeneous among the phases, which has been revealed through the evolution of peak breadths from the neutron diffraction (Krawitz et al., 2009, 2010). Detailed phase responses with consideration of the complex spatial morphologies of both phases, are closely related with the exhibited toughness of the cemented carbides. Unfortunately, a quantitative description of the phase responses in the WC-Co cemented carbides during loading has not been reported in the literature yet. In this study, in order to examine the detailed interactions between the pre-existing thermal residual stress and the applied external stress, we firstly set up a new method for creating a three-dimensional (3D) finite element model based on the real microstructure of the WC-Co cemented carbide. Then, a process of uniaxial compression was simulated, with the loading applied immediately after the sintering and cooling treatment. The strain responses of the WC and Co phases during the compressive loading and unloading were studied, and their correlation with the plastic deformation behavior and fracture toughness of the cemented carbide materials was proposed. 2. Experimental A WC-8wt%Co sample was prepared by a sinter-hot isostatic pressure (HIP) process. The mean size of WC grains was approximately 400 nm, which was measured by the two-dimensional linear intercept method. A FEI Helios Nanolab 600i focused ion beam (FIB) coupled with field-emission scanning electron microscopy (FE-SEM) was utilized to acquire the image stacks for creating the three-dimensional finite element (FE) model. An area of interest in the sample, which was a cube of approximately 103 μm3, was subjected to the FIB milling. The step size of the milling process was set to 20 nm, according to the principle that at least 10 sections are needed through the smallest dimension of the WC grains (Groeber et al., 2008), which was underestimated at half of the mean grain size. 500 image stacks were acquired. Then, for the regions representative for the dual-phase structure of the cemented carbide, 20 image stacks were selected to build the 3D FE model, for which suitable computation time was also considered. The details of the FIB process can be found elsewhere (Borgh et al., 2013; Singh et al., 2016; Jiménez-Piqué et al., 2017). To gain the precise image stacks used in the model, a series of image processing were implemented on the raw images using the Visualization Sciences Group (VSG) Avizo software. Firstly, a sequential processing was employed, including alignment, cropping, shearing correction, and shading correction. Then, noises were reduced through the median filters and edge-preserving smoothing Gaussian filters. Finally, the WC and Co phases were segmented by histogram-based binarization. 3. Three-dimensional model and simulations Many simulation studies focused on the thermal residual stresses of WC-Co cemented carbide were carried out using 2D models or simple 3D models (so called as 2.5D models) (Kayser et al., 2018), which were reconstructed from the real microstructure. In these studies, the WC grain boundaries were outlined and vectorized after the segmentation of WC grains, as well as the WC/Co phase boundaries. However, discrepancy induced by the image algorithms was unavoidable, and manual corrections were required to eliminate the errors. These treatments can be well implemented for 2D or some 2.5D models. Intuitively, it seems to be impossible to reconstruct complex 3D models based on the real material microstructure by this approach. Thus, here we set up a new method for creating a 3D FE model based on the real microstructure of cemented carbide. The main idea was to convert the bitmaps directly into a FE model through the voxel distributions. Firstly, the bitmaps of image stacks were transformed into the distributions and attributions of the voxels, in which coordinates of the Co phase were collected. Additionally, the initial FE model with element distributions equivalent to the distributions of voxels was created and meshed in the ANSYS software. A 3-D 8-node hexahedron brick element (SOLID185 in ANSYS) was adopted in this work. The length and width of the element were the same as the actual size of one pixel, while the thickness was equivalent to the step size of milling mentioned above. Coordinates of the whole elements were obtained from the distributions of elements and nodes. Then, the list of elements attributed to the Co phase was achieved by comparing the coordinates between the Co phase and elements using an array lookup function. Finally, after attributing the properties of WC to the whole elements, the properties of elements that belonged to the Co phase were converted to those of Co according to the list. After finishing the above steps, the 3D FE model based on the real microstructure of the WC-Co cemented carbide was established. A FE model of WC-Co cemented carbide with the dimensions of 1.77 μm (axial) × 2.35 μm (long transverse) × 0.40 μm (short transverse) was utilized for the simulations on the thermal residual stress and the uniaxial compression process. Three adjacent faces were assigned to be symmetrical boundaries, while the other three faces were free boundaries. For the upper limit temperature at which the thermal residual stress is considered, in the literature researchers either used an absolute temperature, such as 800 °C (Zhong et al., 2017) and 1300 °C (Kayser et al., 2018), or a temperature drop, which was for example chosen as 800 K (Spiegler et al., 1992) or 600 K (Weisbrook and Krawitz, 2002). In this study, the initial temperature was set to 800 °C, and the final temperature was 25 °C, according to the real processing route. The initial stresses of both phases were assumed to be zero at 800 °C according to the results obtained by neutron diffraction (Mari et al., 2009). The uniaxial compression was carried out immediately after cooling. The compression load was applied on the free surface along the axial direction. The load circle was from 0 to −2000 MPa to 0 in an increment of 100 MPa. Throughout the modeling, the WC phase was considered as elastic, while the Co phase was elasto-plastic with linear isotropic hardening. The material properties derived and extrapolated from the data reported in the literature (Golovchan, 2007; Huang et al., 2008; Özden et al., 2015) were used in this study, as shown in Table 1. Due to the lack of the temperaturedependent plastic properties of Co phase, the parameters of Co phase plastic properties at the room temperature were used in this 313
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Table 1 Plastic properties of Co and elastic properties of WC and Co. Material
Young's modulus (GPa)
Thermal expansion coefficient (°C−1)
Poisson's ratio
Yield stress (MPa)
Hardening modulus (GPa)
WC
20 °C 400 °C 800 °C
719.0 700.0 680.0
3.2 × 10−6 4.0 × 10−6 6.0 × 10−6
0.19
–
–
Co
20 °C 400 °C 800 °C
213.5 194.5 174.5
8.0 × 10−6 14.0 × 10−6 16.0 × 10−6
0.31
683.0
52.4
study. The yield stress and hardening modulus of Co phase were taken from the same literature (Özden et al., 2015), in which the features of the Co binder phase were similar with those in the present WC-Co cemented carbide material. 4. Results and discussion 4.1. Thermal residual stress The main purpose of this study was to examine the interaction between the pre-existing thermal residual stress and applied external stress. Thus, the distribution of thermal residual stresses was simulated at first to build up the initial state of stress before compression. Fig. 1 shows the 3D topographies of the FE model of the WC-Co composite and the contour plots of the thermal residual stress in the material after cooling. It can be seen that the cobalt phase (Fig. 1c) was homogeneously distributed in the WC-Co composite (Fig. 1d). The axial-component and transverse-component of the thermal residual stresses, which are illustrated in Fig. 1e and f, respectively, show that high tensile stresses exist in the Co phase, while the compressive stresses exist in the WC phase. In addition, tensile stresses can also be found in the WC phase near the WC/Co interfaces. 4.2. Stress-strain curve of cemented carbide The macroscopic stress-strain curve of the WC-Co cemented carbide in the process of compression is illustrated in Fig. 2. For comparison, an experimental result of macroscopic stress-strain curve from literature (Livescu et al., 2005b) is also shown in Fig. 2, which was obtained from a WC-10 wt%Co sample with cobalt content a little higher than that in the present material. It can be seen that the simulation results exhibit nearly a same trend as that of the experimental results. A distinct deviation from a linear relationship between stress and strain is found starting from −500 MPa, which indicates that the yielding occurs at the early stage of loading. After unloading, a negative plastic deformation of 0.035% was produced, which is slightly larger than that reported in the experiments (Livescu et al., 2005b). The elastic modulus (E) evaluated from the early stage of the stress-strain curve is 519.1 GPa in the simulations, which is close to the elastic modulus measured by the extensometer (571.2 GPa) in Ref. (Livescu et al., 2005b). Therefore, the results obtained by simulations are reasonable to be used for subsequent analyses related with the stress-strain curves. 4.3. Heterogeneous strain responses within the microstructure To investigate the strain responses in the microstructure of the cemented carbide, which consists of WC and Co phases, a typical cross-section that is representative of the random distribution of the dual-phase constitution was cut from the three-dimensional model, as shown in Fig. 3. The locations taken for analysis are marked in the figure, where seven of them are located in the Co phase and three are located in the WC phase, respectively. According to the microstructure, three representative regions of the Co phase are examined: the zone with a nearly round shape, indexed as 1, 2 and 3; the layer-like zone along the transverse direction, indexed as 4 and 5; and the layer-like zone along the axial direction, indexed as 6 and 7. In Fig. 3b, the above representative regions are highlighted in the real microstructure with different colors respectively. Apparently, the Co phase mainly exhibits a moderate strain response due to the mixed characteristics. The stress-strain curves of different locations in the Co phase are shown in Fig. 4. The strain was extracted from the node at each location. The initial thermal strains are offset to zero for the intuitive comparison between locations 1 to 7. It is shown in Fig. 3a that before compression, the cobalt undergoes tensile stress either in the axial direction or in the transverse direction, i.e. the Co phase has positive thermal strain. Upon loading, the applied strain opposes the thermal residual strain in the axial direction. However, in the transverse direction, the applied strain adds to the thermal residual strain due to the Poisson ratio effect, leading to an earlier yielding in this direction. This results in the reduction of the initial thermal strain in the cemented carbide along the transverse direction, while the initial strain in the axial direction increases. Therefore, the strain presents a negative deviation in the transverse direction but a positive deviation in the axial direction, implying that the initial stress decreases in the transverse direction but increases in the axial direction. The stress-strain responses distinct from one another in different directions and the directional yielding suggest that the stress state has significant influence on the plastic deformation behavior of the material. In addition, the statistical stress-strain response in Co binder is also shown in Fig. 4, which exhibits a similar trend with that reported by experiments (Livescu et al., 2005b; Krawitz et al., 2010; Mari et al., 2015). 314
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Fig. 1. Topographies of the FE model of the WC-Co composite and distribution contours of initial thermal residual stress: (a) schematic diagram and dimensions, (b) 3D distribution of WC, (c) 3D distribution of Co, (d) 3D topography of WC-Co, (e) axial-component of initial thermal residual stress, (f) transverse-component of initial thermal residual stress.
As seen in Fig. 4, the interactions between the thermal residual strain and the applied strain vary significantly in different locations of Co phase, which depends on the combination effect of the initial thermal residual stress and the microstructural feature. Transversal yielding is a main consequence due to the release of thermal residual stresses, which implies that a higher initial thermal stress will lead to a larger strain deviation upon the complete unloading. For the initial transversal stresses in cobalt shown in Fig. 3a, the highest tensile stress existed in the layer-like Co along the transverse direction, followed by the stress existing in the near-round shaped Co phase. The layer-like Co along the axial direction had the lowest initial stress. Corresponding to the various local initial stress states, the yielding strengths of different locations in Co differ greatly, indicating that the yield strength is strongly affected by the initial stress. Their relationship will be discussed in detail in Section 4.4. The microstructural features also have a significant effect on the strain responses. To understand this mechanism, compression simulations without considering the initial thermal residual stresses were studied, and the transverse strain responses of the three representative regions are shown in Fig. 5. The near-round shaped Co exhibits the earliest strain response. However, the yielding occurs firstly in the layer-like Co along the transverse direction due to the stress concentration. Consequently, the strain responses of different locations in the Co phase are obviously heterogeneous (Fig. 4). In the near-round shaped Co, a moderate strain response with a yield external stress of approximately 1000–1500 MPa was observed. The yield stresses were slightly different as a consequence of the variable initial thermal stress. An extreme strain response was found in the layer-like Co along the transverse direction (locations 4 and 5), where the yielding occurred at the beginning of loading and finally the thermal strain was greatly released. The yielding occurred in these locations caused indistinct deviation of the macroscopic stress-strain curve from the linear 315
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Fig. 2. Macroscopic stress-strain responses in the WC-Co cemented carbides, which are obtained from the present simulations and previous experimental studies (Livescu et al., 2005b).
Fig. 3. Representative cross-section of the three-dimensional microstructure of WC-Co cemented carbide: (a) distribution of Co phase and locations (indexed by numbers) selected for analysis, the axial-component (A) and transverse-component (T) of the initial thermal residual stress (with unit of MPa and positive indicating tensile stress) are shown correspondingly, (b) typical Co regions in the real microstructure.
relationship as the stress is lower than −500 MPa, as shown in the inset of Fig. 2. In contrast, along the axial direction in the layerlike Co (locations 6 and 7), the strain responses were inconspicuous. In addition, a deviation from the linear relationship was observed in locations 4 and 5 at the end of unloading, indicating that these regions also yielded due to the stress transfer during the unloading process. Apparently, after unloading, the plastic strains in the layer-like Co along the transverse direction are much larger than those at other locations, which indicates that the plastic deformation behavior of Co is heterogeneous in the cemented carbide. In previous studies, the peak breadth of the neutron diffractions was used to reveal the stress variance within the Co phase (Krawitz et al., 2010). In the present study, alternatively, the evolution of the standard deviation of thermal residual stresses at 316
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Fig. 4. Microscopic stress-strain responses of various locations in Co phase (as marked by 1–7 in Fig. 3a) and the wide-ranging statistical stress-strain response.
different locations was examined to analyze the heterogeneous stress state, and was compared with the neutron diffraction results. It can be seen from Fig. 6 that the simulation results have very similar trend with those of the measured results. In the axial direction, the stress variance increases during loading and decreases during unloading. However, in the transverse direction, the deviation 317
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Fig. 5. Microscopic transverse stress-strain responses of locations 1, 4, and 6 in Co phase without considering the initial thermal residual stress.
Fig. 6. Stress variances within Co during loading and unloading processes: (a) Comparison between the present simulations and experimental results in Ref. (Krawitz et al., 2009), (b) Variances of maximum and minimum stresses at the studied locations in the axial direction, (c) Variances of maximum and minimum stresses at the studied locations in the transverse direction.
decreases with loading before −1000 MPa and then reverses to increase until completion of loading. In the unloading process, the deviation decreases monotonously. Upon unloading, in both the axial and transverse directions, the deviations have a net reduction due to the yielding occurred at specific regions. This indicates that the stress field tends to be more homogeneous after compressive deformation, and is inherently related with the plastic deformation behavior. The evolution of the maximum and minimum stresses at the studied locations during the compression process is illustrated in Fig. 6b and c, corresponding to different directions. In the axial direction, the rapid decrease in the minimum stress dominates the increase of stress variance during loading, as well as the decrease of that during unloading. The minimum stress exists in the layer-like Co along the transverse direction, which undergoes the most yielding during compression. In the transverse direction, the stress variance decreases at first because the maximum stress rapidly decreases at the beginning of loading, and then conversely increases because of the rapid decline of the minimum stress. This change has never been further examined and explained by experimental studies. Moreover, the rapid decreases of the maximum stress at the beginning and the minimum stress at the final stage both occur at location 4 (Fig. 6c). Actually, this region experienced a continuous stress reduction from the maximum to minimum throughout the 318
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Fig. 7. Microscopic stress-strain responses of various locations in WC phase (as marked by 8–10 in Fig. 3a). The coordinate ranges of the figures are consistent with those in Fig. 4.
loading process, corresponding to the continuous plastic deformation of location 4 in Fig. 4. The accumulated plastic deformation may result in microcracks occurring in this region, which will be discussed in Section 4.4. Fig. 7 shows the strain responses of different locations in the WC phase upon loading and unloading. There is only a slight difference in the stress-strain responses of different locations in the WC phase. It is obvious that the strain deviation in WC upon unloading is much smaller than that in Co. Because the WC phase was assumed to be elastic in the model, the change in the elastic strain of WC is merely due to the strain relaxation in Co. In the dual-phase microstructure of the cemented carbide, the load can be transferred to WC from Co, and the strain field is thus redistributed during the compression process. The simulation shows that during the uniaxial compression, the strain responses are clearly different between the axial and transverse directions, i.e. with the external stress, the strain response is anisotropic. It is known that the thermal residual stresses are in principle hydrostatic (Krawitz et al., 2009), which indicates that the stresses are equivalent in any physical direction throughout the microstructure. Therefore, a two-dimensional simulation of the thermal residual stress for the state after cooling from the sintering temperature is reasonable. However, as a result of the anisotropic plastic flow in Co during compression, the hydrostatic stress state transforms into a cylindrical stress state (Livescu et al., 2005a,b). This indicates that a three-dimensional simulation is indispensable to understand the interactions between the pre-existing thermal residual stress and the applied stress; otherwise, the twodimensional simulation results may be misleading. Moreover, in the present study, our attention is focused on the strain responses during deformation, the stress distribution, and the interaction between the thermal residual stress and the applied stress. Thus, the deformation state of the materials was simulated till the stage of plastic deformation before occurrence of fracture. 4.4. Correlation between strain response and plastic deformation behavior of cemented carbide In the simulations, the WC and Co phases were assumed to be elastic and elasto-plastic, respectively. The plastic deformation of the cemented carbide mainly occurred in the Co phase. However, previous studies show that the plastic properties of Co can be very different, especially the yield strength of Co was reported ranging from 279 to 2950 MPa (Herd et al., 2018). There are many factors that affect the yield strength of Co phase on the microscopic scale, such as solid solution of W and C in Co (Roebuck et al., 1984), grain size and orientation (Roebuck, 2006; Csanádi et al., 2015; Kim et al., 2016), crystal structure transformation (Liu et al., 2012), and the stress state as well as its evolution, which is the focused issue in this study. The plastic deformation is, on the microscale, generated by the motion of dislocations, which needs to overcome the resistance of crystal lattice that is inversely related to the lattice spacing. The microscopic residual stress is essentially lattice distortion (Hu et al., 2016; Salvati and Korsunsky, 2017); in other words, the increase in the lattice spacing results in tensile stress within the crystal, and conversely the compressive stress. According to the Peierls stress from the lattice (Liu et al., 2016, 2017a), plastic deformation is more likely to occur in regions which have higher tensile stress with lower lattice resistance, thus in these locations a relatively lower yield 319
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Fig. 8. Cumulative plastic deformation at locations 1, 4, and 6 with loading up to −5000 MPa in an increment of 100 MPa. The inset is an experimental result in our previous work (Liu et al., 2017b), showing the crack nucleation in the layer-like Co along the transverse direction with respect to the loading direction.
strength is shown. As seen in Fig. 4, the layer-like Co along the transverse direction (locations 4 and 5) that undergo the highest tensile stresses (Fig. 2) yield at the initial stage of loading, exhibiting an extreme low yield strength. It is shown in Fig. 4 that the layer-like Co along the transverse direction yielded the earliest during compression, indicating that the stress was heavily concentrated in this region. After unloading, the plastic deformation of Co varies significantly at different locations. To quantify this phenomenon, the cumulative plastic deformation of each region was calculated for the load in a range up to −5000 MPa, and the results are shown in Fig. 8. The plastic deformation was accumulated faster in the regions of stress concentration than in other regions, which implies that massive dislocations were triggered to coordinate the stress concentration. As a result, work hardening may occur when the motion of dislocations is stagnated in these regions, and microcracks can nucleate due to the rapid accumulation of plastic deformation. Moreover, crack nucleation and propagation may also occur at the WC/Co interfaces when the Co phase cannot effectively relax the stress concentration due to work hardening. To verify the above statement, the results from the molecular dynamics (MD) simulations for the WC-Co cemented carbide under uniaxial compression are provide in Fig. 9. The details for the setup of the simulation model were described in our previous work (Fang et al., 2019). It is observed in Fig. 9 that the first two microcracks initiated at the WC/Co phase boundaries, which were adjacent to the layer-like Co along the transverse direction of the compression. The MD simulation results confirmed the present simulation results on the microscale. In summary, the layer-like Co distributing in the transverse cross-section with respect to the direction of compression is detrimental to the deformation behavior of the cemented carbides, hence is undesirable for the fracture toughness and strength of the material. The simulation results suggest that design and modification of the dual-phase microstructure of the cemented carbides are significant to improve the mechanical properties, particularly, the dense distribution of the layer-like Co should be avoided. Moreover, as there are different characteristics of WC morphologies and WC skeletons in the cemented carbides (García et al., 2019), other parameters such as WC grain shape factor, WC contiguity, and Co mean free path may be introduced in the simulations to extend the model application to complex deformation behavior of the cemented carbides. The present study indicates that plastic deformation results in the relaxation of thermal residual stress after unloading. Moreover, the external stress provides a higher driving force for the motion of dislocations in the stress concentration regions, while the residual stress changes the resistance from the lattice against the motion of dislocations. Actually, both the thermal residual stress and the applied stress affect the motion of dislocations by changing the distortion extent of the lattice. After migration of the dislocations, the
Fig. 9. MD simulation result of the WC-Co cemented carbide under uniaxial compression, showing nucleation of microcracks at the WC/Co phase boundaries adjacent to the layer-like Co along the transverse direction of the compression (Fang et al., 2019). 320
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Fig. 10. Von Mises stress distribution contours of the representative cross-section: (a) initial stress state, (b) stress state after compression.
lattice distortion decreases, which macroscopically appears as the release of the thermal residual stress. It is worth noting that under tension, the stress concentration occurs at the crack tip, and the crack may expand continuously due to the accumulation and release of the stored energy, with almost no plastic deformation away from the cracks (Mingard et al., 2013). In contrast, as shown in Fig. 8, non-simultaneous plastic deformations occur in various regions of Co during compression. When a certain degree of plastic deformation occurs in the stress concentration region, plastic deformation can also initiate in other regions of Co to accommodate a homogeneous stress field throughout the cemented carbide, which results in a much higher compressive strength than the tensile strength (Golovchan and Litoshenko, 2010). To form a homogeneous stress field, as indicated in Fig. 6, dislocations will migrate towards the direction with lower lattice resistance; hence, the distortion of lattice tends to be uniform. On the macroscopic scale, the stress field is homogenized. As shown in Fig. 10, compared with the initial distribution of the von Mises stress, which is usually utilized as a criterion for evaluating the yield, after compression the initially higher stress decreases while the lower stress increases. This implies that the residual stress may be an additional factor affecting the activation sequence of the slip systems. Generally, the activation sequence of dislocation slip systems is determined by the crystal lattice resistance, i.e. the Peierls stress, which is expressed as (Hertzberg, 1989) P
=
2G 1
exp
2 a (1
(1)
)b
where a is the interplanar spacing of the slip plane, b is the interatomic spacing along the slip direction, and is the Poisson's ratio, G is the shear modulus. According to the relationship between the Peierls stress and the lattice distortion, a certain slip system is easier to activate with the existence of residual stress as compared with the non-stress state. It is predicted that an anisotropic stress state can change the activation sequence of the dislocation slip systems. It is worth noting that the present simulation method is applicable to other type dual-phase materials and can also be extended for multiphase materials. As the method is based on the SEM image stacks taken from the FIB-SEM experiments, it implies that if the multiple phases can be distinguished in the SEM images by contrasts, this method can be used to analyze the stress-strain behavior of the material. 5. Conclusions In the present work, a three-dimensional FE model based on the real microstructure of WC-Co cemented carbide was set up to study the interaction between the pre-existing thermal residual stress and the applied compressive stress. The heterogeneous strain responses of Co and WC phases upon compressive loading and unloading were illustrated in detail, and the effects of the thermal residual stress combined with the microstructural features on the mechanical behavior of the cemented carbide were shown. The main conclusions are drawn as follows. 321
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(1) A new method was developed for creating a three-dimensional finite element model based on the real microstructure of the WCCo cemented carbide through conversion of bitmaps of the dual-phase structure. The accuracy of the model was confirmed by comparing the macroscopic stress-strain curve and the stress variance during compression obtained from simulations with those from the experimental results. Simulations based on this model can precisely exhibit the characteristics of the stress distribution and strain response in the cemented carbide as a typical cermet material. Furthermore, this modeling method can be extended to be applied in a variety of composite materials with dual-phase and also multiphase microstructures. (2) The strain responses of the WC-Co cemented carbide in the process of compression are obviously heterogeneous throughout the microstructure. The layer-like Co distributing on the transverse cross-section with respect to the direction of compression, where the highest thermal residual stress pre-exists, exhibits the earliest strain response during compression. The plastic deformation is more likely to occur in these regions due to the low lattice resistance, and a relatively low yield strength is presented. Furthermore, plastic deformations in these regions are cumulated faster than in other regions. Under uniaxial compressive loading microcracks may preferentially nucleate in the layer-like Co along the transverse direction and WC/Co phase boundaries adjacent to Co layers. To achieve high fracture toughness and strength, dense directional distribution of the layer-like Co should be eliminated in the design and modification of the dual-phase microstructures. (3) The stress variance during compression indicates the interaction between the applied stress and the pre-existing thermal residual stress at different locations in the microstructure. Upon unloading, the stress variance decreases, suggesting partial release of the thermal residual stress due to the plastic deformation occurred in certain regions of the cemented carbide. As a result, a more homogeneous stress field is obtained. On the microscopic scale, dislocations may migrate towards the direction with low lattice resistance to accommodate the distortion of lattice. Thus, the residual stress, as well as the anisotropic stress state, may change the activation sequence of the dislocation slip systems in the composite materials. 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