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Plastic damage of additive manufactured aluminium with void defects
Accepted Manuscript
Plastic damage of additive manufactured aluminium with void defects Li-Ya Liu , Qing-Sheng Yang , Y.X. Zhang PII: DOI: Reference:
S0093-6413(18)30454-3 https://doi.org/10.1016/j.mechrescom.2018.12.002 MRC 3335
To appear in:
Mechanics Research Communications
Received date: Revised date: Accepted date:
14 September 2018 13 November 2018 4 December 2018
Please cite this article as: Li-Ya Liu , Qing-Sheng Yang , Y.X. Zhang , Plastic damage of additive manufactured aluminium with void defects, Mechanics Research Communications (2018), doi: https://doi.org/10.1016/j.mechrescom.2018.12.002
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Mechanics Research Communications. Year Editor-in-Chief: A. Rosato New Jersey Institute of Technology, Newark, New Jersey, USA [email protected]
Highlights The plastic deformation of the crystal firstly appears around the void, that is, the slip systems around the void start first.
The single crystal with the hard orientation and the bicrystal with the larger misorientation between the two grains are more difficult to slip.
The slip systems in crystal with a circular pore are more prone to start than with an elliptical pore.
The loading direction that is vertical to the grain boundary is more conducive to the slip of the crystal and the growth of the pore.
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Plastic damage of additive manufactured aluminium with void defects Li-Ya Liu1, Qing-Sheng Yang1,2*, Y. X. Zhang2 1
Dept. of Engineering Mechanics, Beijing University of Technology, Beijing 100124, China School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia
2
*Corresponding author, email: [email protected] Tel.: + 86-10-67396333; fax: + 86-10-67396333
Abstract
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Keywords: additive manufacturing, aluminium, void defects, crystal plasticity, plastic damage.
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Additive manufacturing technology is a novel approach for the development of the modern industry. Additive manufactured aluminium (Al) becomes the hotspot of current research in order to achieve the high-precision products. However, the additive manufactured Al parts easily generate void defects due to the poor fluidity and low density of the materials, which in turn affects the mechanical properties. This paper studies the damage behavior of additive manufactured Al parts with void defects under tensile load in a mesoscale by using a two-dimensional rate-dependent crystal plasticity theory. The stress-strain curves and the plastic damages of single crystal and bicrystal with void defects are determined with different combinations of crystal orientations and loading conditions. It is found that the mechanical properties of additive manufactured aluminium severely depend on the crystal orientations and shapes of void defects.
1. Introduction
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Aluminium parts play an extremely important role in aerospace, automobile and shipbuilding due to their excellent advantages of light weight and good plasticity as well as corrosion resistance [1]. When the traditional forging can not enable the manufacture of Al components with lightweight structure and composite performance, additive manufacturing (AM) technology emerges, which can achieve Al parts with high density, fine structure and design optimization [2]. Moreover, compared with Al parts manufactured by traditional forging, the mechanical property of additive manufactured Al is greatly improved while the cost is greatly reduced [3]. Howerer, there are still many problems in additive manufactured Al at present, such as oxidation, residual stress and void defects [4]. Yet, these problems, especially void defects, further affects the mechanical properties of additive manufactured Al parts [5]. As shown in Fig. 1, the distribution of these void defects can be observed by optical microscope images [6]. The slow development and lack of breakthroughs of additive manufactured Al are mainly caused by defects in the manufacturing process [7]. Yadollahi [8] found that if the voids are located outside the trimmed material layer, then polishing can not completely eliminate the void defects. Actually, optimization of manufactured parameters and adopting complex post-treatments can be never possible to totally eliminate void defects [9]. A catastrophic failure can be triggered by the individual void size and shape [10]. However, the experimental research of damage behavior of additive manufactured Al has some disadvantages, such as complicated experimental process, raw materials waste and high research cost, which seriously limits the further study of additive manufactured Al with void defects [11]. At present, the influence of void defects on mechanical properties of additive manufactured Al can be revealed by numerical simulation [12]. Many studies pay close attention to improve the technology of AM processes [13], however, there few efforts have been made to understand of the effect of defects on mechanical properties of the products. Therefore, the specific research of AM products with void defects in a mesoscale is necessary, which can provide a theoretical basis for the manufacture and safety evaluation of AM aluminum.
Fig. 1 OM images showing the Ti-6Al-4V voids under different magnifications.
The traditional elastoplastic mechanics mostly treat the metal as the isotropic material or use the improved constitutive model to study the influence of the void defects on the mechanical properties, so the whole process of the void deformation cannot be accurately described [14-15]. With the gradual improvement of the theoretical basis and enhancement of computer ability, the crystal plasticity theory and the finite element method have been combined to form the crystal plasticity finite element method (CPFEM) [16-17]. One of the main advantages of CPFEM is that it can solve crystal mechanical problems from mesoscopic scale with complex boundary conditions [18]. Recently, CPFEM have been employed to study the mechanical properties of metal. Orsini and Zikry [19] used a rate-dependent crystal plasticity model to investigate the growth of voids in FCC copper single crystals. The results showed that the rotation and plastic slip of the crystal concentrated in the region between the voids.
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Hereafter, based on the crystal plasticity model, Evers [20] considered the grain boundary action and the strengthening caused by dislocation density to predict the size dependence of flow stress. Kysar et al. [21] analyzed the circular void in a single crystal under plane strain condition by slip line theory, and found that the stress around the void was anisotropic. Liu [22] employed CPFEM to simulate the influence of crystal orientation on void growth and coalescence behavior. Subsequently, Li et al. [23] studied the effects of crystal orientation, grain shape and grain boundary on nanoindentation of aluminium alloy. Asim et al. [24] established a finite element model of aluminium alloy single crystal based on the crystal plasticity theory, and studied the potential physical mechanism of the tough failure process. Liu et al. [25] explored the relationship between indentation hardness and yield stress by a polycrystal tensile CPFEM. Liu et al. [26] investigated the effects of grain/phase boundary on mechanical properties by a CPFEM constitutive model combined with Bassani and Wu hardening law. In order to accurately predict the deformation mechanism under the complicated contact conditions between a billet and a die, Liu et al. [27] developed a 3D CPFEM of a real equal channel angular pressing process for the first time. Nevertheless, limited studies on the plastic damage behavior of the additive manufactured Al with void defects have been reported so far and the numerical studies by CPFEM are even less. In this paper, a two-dimensional rate-dependent crystal plasticity model using the numerical model is developed to study the plastic deformation and damage behavior of additive manufactured Al material with void defects under tensile load in a mesoscale. Then the effects of different orientations, loading conditions and void shapes for single crystal and bicrystal are investigated.
2. CPFE model of additive manufactured Al
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At present, the mechanical properties of additive manufactured Al are limited and depend on the manufacturing process. Considered here the material performance of additive manufactured Al is the same as that of Al manufactured by traditional process, but additive manufactured Al is more prone to occur a lot of void defects, thus the CPFEM can be used to study additive manufactured Al with void defects. Moreover, the mechanical response of single crystals or polycrystals can be obtained by responding to the stress generated by the dislocation slip process. The nature of metal deformation can be understood fundamentally at the grain scale from CPFEM [28]. The program used in the above article can only calculate the plastic problems of grain groups by combining with finite element software. In this paper, the program is modified to study the crystal plastic deformation with distinguishing the crystal grains. Crystal kinematic description is based on the multiplicative decomposition theory of the deformation gradient in the crystal plasticity theory. When analyzing the deformation of a single crystal, the total deformation gradient can be decomposed as
F FeF p
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p
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where F and F denote the elastic and plastic part of the total deformation gradient respectively. Also, the total velocity gradient can be decomposed into elastic and plastic parts of the velocity gradient expressed by (2) L F F 1 Le Lp The velocity gradient of plastic deformation can be expressed as N
(3)
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Lp s n 1
in which, is the slip rate on the α-th the slip system defined in the reference coordinates, s and n are the slip direction and
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the slip plane normal direction on the α-th slip system respectively. The constitutive relation in the current configuration can be described as
C e : d - e and,
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e P : C e B
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where, denotes the Jaumann derivative of the Cauchy stress tensor with the initial configuration as the reference state. C e is the elastic modulus tensor while d is the deformation rate. P and B are the plastic part of the deformation rate tensor and the rotation tensor, respectively. can be calculated according to the using hardening equation. 1
m 0 c c
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where is the shear stress on the α-th slip system (Schmid stress), 0 denotes the reference shear strain rate, c is the reference shear stress on the α-th slip system while m is the rate sensitivity coefficient. The expression of the slip hardening law is m
c h
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h q h0 1 c s
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1
where h is the hardening coefficient while h0 represents the initial hardening rate. s denotes the saturation flow stress and
q denotes the latent hardening matrix. The material parameters used in this work are listed in Table 1 [29].
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Table 1. The material parameters of CPFEM. C11 (GPa)
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106.75
60.41
28.34
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12.5
75
60
3. Simulation process of additive manufactured Al
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There are two main reasons for the formation of void defects: (1) Due to the faster solidification rate, a part of the gas generated by the evaporation of water does not escape in time and remains in the molten pool, and thus the resulting void location is within the grain; (2) The powder is not completely melted or only partially melted, resulting in void on the grain boundary during fusion [30]. Therefore, there are different orientation combinations of the crystals and loading conditions in this work. As shown in Fig. 2(a), a two-dimensional Al single crystal model with a void was established with a size of 1×1 mm2, and the radius of 75 μm. To investigate the mechanical properties of Al single crystal under tensile conditions, an uniaxial tensile boundary condition was applied. During the simulation process, the maximum deformation of the model was set up to 25%. In those cases, 484 elements of CPE4R were employed for the simulation. These elements have been tested, and when the number of elements reaches a certain level, the calculation results tend to be stable, thus these elements are used to eliminate the mesh dependency.
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(a) (b) (c) Fig. 2 (a) Single crystal model and boundary conditions; (b) Bicrystal model and boundary conditions with load parallel to grain boundary; (c) Bicrystal model and boundary conditions with load vertical to grain boundary.
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In another case, as illustrated in Fig. 2(b)-(c), a two-dimensional Al bicrystal model with a void at grain boundary was established with a size of 1×1 mm2 and a radius of 75 μm. The crystal plasticity constitutive model considers the grain boundary as a purely geometrical interface, and taking into account only the differences in grain orientations on both sides of the grain boundary. To investigate the effect of grain boundaries on the mechanical properties of Al bicrystal under tensile conditions, uniaxial tensile boundary conditions were set, in which the tensile direction was parallel and vertical to the grain boundary respectively. Similarly, the maximum deformation of the model was set to be 25%.
4. The mechanical properties of Al single crystal At present the additive manufacturing technology is able to produce single crystal parts. It is necessary to study the void defects of single crystals with different orientations and shapes systematically in order to understand the influence of void defects on the mechanical behavior of additive manufactured Al. 4.1 Effect of the orientation of Al single crystal In this section, the effects of different initial crystal orientations (Cube {001}<100>, Goss {011}<100> and Brass {011}<211>) on the tensile mechanical properties of single crystals were investigated. As shown in Fig. 3, the total deformation
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process of the single crystal with a void under tensile loading were obtained. The voids within a crystal have varied shapes after deformation due to the anisotropic behavior of the crystal. For the elastic deformation stage, the slip systems are not started at this time. Afterward, there is an obvious yield point, which indicates that the slip system begins to start. Thereafter, the strain around the void is greater than the strain in other regions, which leads to a change in the shape of the void. The voids within Cube orientation and Goss orientation crystals grow along the loading direction due to the better symmetry in the sample coordinate system, while the growth direction of the void within Brass orientation crystal deviates from the loading direction. The plastic strain nephogram at different stages was obtained, as illustrated in Fig. 4. The plastic deformation of the single crystal with Cube orientation appears around the void initially and then extends along the loading direction gradually. That is, the slip systems around the void start first. Subsequently, the slip systems in other regions of the crystal begin to start. Thereafter, a large part of the crystal has plastic deformation after deformation, which indicates that the slip system has begun to start universally. Then gradient of the stress from the void to the boundary region is formed. Both the maximum stress and plastic strain appearing at the edge of the void are 45° from the horizontal direction. Similarly, the plastic deformation of the single crystal with Goss orientation occurs initially around the void. Then it gradually extends along the 45° direction of loading axis. The slip systems at the boundary region does not start after deformation, while the maximum plastic strain appearing at the edge of the void are also 45° from the horizontal axis. The void of the single crystal with Brass orientation is very irregular during the deformation process, and the plastic deformation gradually extends from the void to the boundary along the 30° direction of horizontal axis. Both the maximum stress and plastic strain appear at the edge of the void around the horizontal axis. From the above, the single crystal with Brass orientation is the most difficult to slip compared with the other two crystals.
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Fig. 3 Variation of deformation process of single crystal for different crystal orientations. (a) Void inside Cube crystal; (b) Void inside Goss crystal; (c) Void inside Brass crystal.
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(a) (b) (c) (d) (e) (f) Fig. 4 Equivalent plastic strain distributions. (a) Void inside Cube crystal at ε=0.15; (b) Void inside Cube crystal at ε=0.25; (c) Void inside Goss crystal at ε=0.2; (d) Void inside Goss crystal at ε=0.25; (e) Void inside Brass crystal at ε=0.2; (f) Void inside Brass crystal at ε=0.25;
Fig. 5 shows the variation of nominal stress of crystal with applied strain for different orientations. By observing the elastic stage and yield point, the critical slip stress increases in the order of the orientation of Goss, Cube and Brass in the same strain. That is, the single crystal with Brass orientation is the most difficult to slip. Then the single crystal with Brass orientation enters the linear hardening stage, while the single crystals with Cube orientation and Goss orientation directly enter the parabolic hardening stage. This indicates that the slip systems of Cube and Goss orientation start generally, and the crystal enter a largescale yield state. At the same time, most of the single crystal with Brass orientation are still in the elastic stage.
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4.2 Effect of the void shape In the above section, it is concluded that the single crystal with Brass orientation is the most difficult to slip. This is consistent with the conclusion from the literature [31]. In order to study the influence of initial void shapes on mechanical properties of single crystals, the axial ratios of the voids are assumed to be 1:2, 1:1 and 2:1 respectively. By observing the elastic deformation stage of the curves (Fig. 6), it is noticed that the location of the maximum strain and the deformation of the void are basically identical in the three cases. As the applied strain increases, the deformations of the three types of voids are gradually changed and become different. To be specific, for a larger axial ratio, the growth direction of the void deviates more from the yaxis while the location of the maximum strain is closer to the loading direction. The deformed shapes with different axial ratios of the void are shown in Fig. 7. The plastic strain of all three crystals appear around the void initially. That is, the slip systems around the void start first. In detail, the regions of the initial plastic deformation at the void axial ratios of 1:1 and 2:1 are basically identical, while the other is different. In addition, for the larger axis ratio, the localization of plastic deformation is more obvious. After deformation, the distribution of plastic strain in single crystal with different void shapes is different, which indicate that the void shape has a great influence on the damage behavior of single crystal with void defects.
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(c) Fig. 6 Variation of deformation process of single crystal with various axial ratios of void. (a) Void with axial ratio of 1:2 inside a Brass crystal; (b) Void with axial ratio of 1:1 inside a Brass crystal; (c) Void with axial ratio of 2:1 inside a Brass crystal.
(a) (b) (c) (d) (e) (f) Fig. 7 Equivalent plastic strain distributions. (a) Void with the axial ratio of 1:2 at ε=0.15; (b) Void with the axial ratio of 1:2 at ε=0.25; (c) Void with the axial ratio of 1:1 at ε=0.15; (d) Void with the axial ratio of 1:1 at ε=0.25; (c) Void with the axial ratio of 2:1 at ε=0.15; (d) Void with the axial ratio of 2:1 at ε=0.25.
The stress-strain responses of a single crystal (Fig. 8) demonstrate that the critical slip stress increases in the order of the axial ratio of 1:1, 2:1, 1:2 in the same strain. In another word, the single crystal at the void axial ratio of 1:2 is the most difficult to slip. All the cases enter the parabolic hardening stage after deformation. To be specific, multiple sets of slip systems have started and the hardening phenomenon is obvious. It is also found that the single crystal at the void axial ratio of 1:2 has the best resistance to deformation compared to the other two cases.
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5. The mechanical properties of Al bicrystal
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When the polycrystal deforms, the single crystal forming polycrystal has complex deformation modes. Moreover, there is a problem of localization of stress and strain due to the existence of grain boundary. It is necessary to study the damage behavior of the void defects on the grain boundary by using a geometrically simple and easily analyzable bicrystal. The effects of different factors on the tensile mechanical properties of bicrystals with a void at grain boundary are investigated in this section. 5.1 Effect of the orientation of Al bicrystal Different combinations of bicrystal are studied in this work. The grain orientation of the bicrystal has the following two cases:
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(A) Goss ( 0 , 45 , 0 ) and Cube ( 0 , 0 , 0 ), denoting by Case GC ; (B) Goss ( 0 , 45 , 0 ) and Brass ( 35 , 45 , 0 ), denoting by Case GB. Fig. 9 is the deformation process under the first loading scenario, i.e., the loading direction parallel to the grain boundary and the second loading scenario, where the loading direction is vertical to the grain boundary, respectively. Different orientations of grains on both sides of the bicrystal lead to different slip systems activation. In turn, the deformation of the two grains is uncoordinated. The shape of the void is closer to symmetry and grows along the coordinate axis during the deformation process in the case GC because of the small misorientation between Goss and Cube. The deformation caused by misorientation is not obvious. On the contrary, the void has the irregular shape and deviates from the coordinate axis during the deformation process in case GB due to the large misorientation between Goss and Brass. 120
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The plastic deformation and von Mises stress of bicrystals are shown in Fig. 10-13. It is demonstrated that the slip systems around the void start first in every case. In turn, the started slip systems are concentrated around the void, which can lead to the localization of damage and failure. Stress concentration appears at the boundary of the void, and a gradient of the stress from the void to the boundary region is formed. To be specific, the stress concentration in case GC is relatively moderate due to the smaller misorientation between Goss and Cube. By observing the plastic distribution and the maximum stress value of nephograms, it is found that the damage behavior of the void whose loading direction is vertical to the grain boundary is more obvious than that of the void whose loading direction is parallel to the grain boundary. This result is consistent with the conclusion that metal tends to form void defects at vertical grain boundaries obtained from [32].
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(a) (b) (c) (d) Fig. 10 Equivalent plastic strain and equivalent stress distributions of the 1st loading for case GC. (a) strain at ε=0.2; (b) strain at ε=0.25; (c) stress at ε=0.2; (d) stress at ε=0.25.
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(a) (b) (c) (d) Fig. 11 Equivalent plastic strain and equivalent stress distributions of the 2nd loading for case GC. (a) strain at ε=0.2; (b) strain at ε=0.25; (c) stress at ε=0.2; (d) stress at ε=0.25.
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(a) (b) (c) (d) Fig. 12 Equivalent plastic strain and equivalent stress distributions of the 1st loading for case GB. (a) strain at ε=0.2; (b) strain at ε=0.25; (c) stress at ε=0.2; (d) stress at ε=0.25.
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(a) (b) (c) (d) Fig. 13 Equivalent plastic strain and equivalent stress distributions of the 2nd loading for case GB. (a) strain at ε=0.2; (b) strain at ε=0.25; (c) stress at ε=0.2; (d) stress at ε=0.25.
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As shown in Fig. 14, the critical slip stress of case GB is greater than that of the case GC for both loading situations. By observing the yield point, the slip systems of case GB is most difficult to start. It is also found that the resistance to deformation of case GB is higher than that of case GC, as illustrated in plastic stage of the curve. The mechanical properties of the bicrystal with a void depend not only on the grain orientation but also on the direction of loading. The stress in the first loading scenario is larger than that in the second loading scenario when the orientations of the two bicrystal models are identical, and this indicates that the void of the bicrystal whose loading direction is vertical to the grain boundary is easier to grow.
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Fig. 14 The Stress-strain response. (a) Different combinations of orientations in the first loading scenario; (b) Different combinations of orientations in the second loading scenario; (c) Different loadings for case GC; (d) Different loadings for case GB.
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5.2 Effect of the void shape As discussed in the above section, the bicrystal in case GB is most difficult to slip. To provide a numerical perspective, the influence of initial void shape on mechanical properties of bicrystal in case GB is studied. Similar to single crystal, the axial ratios of the voids in bicrystals are 1:2, 1:1 and 2:1 respectively. 140 120
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Fig. 15 Variation of deformation process for various axial ratios of void in different loadings. (a) The first loading scenario for the axial ratio of 1:2; (b) The first loading scenario for the axial ratio of 1:1; (c) The first loading scenario for the axial ratio of 2:1; (d) The second loading scenario for the axial ratio of 1:2; (e) The second loading scenario for the axial ratio of 1:1; (f) The second loading scenario for the axial ratio of 2:1.
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Fig. 15 shows the deformation process of the first loading scenario in the direction parallel to the grain boundary and the second loading scenario in the direction vertical to the grain boundary when the axial ratios of the voids in the bicrystal are 1:2, 1:1 and 2:1, respectively. By observing the elastic deformation stage of curves (Fig. 15(a)-(c)), it is noticed that the location of the maximum logarithmic strain of loading 1 are basically identical in the three cases. After deformation, the growth direction of the void deviates more from the loading axis for the larger axial ratios. The growth of void in the second loading scenario is more complex than that in the first loading scenario during the deformation process, as described in Fig. 15(d) to (f). To be specific, the growth direction of the void with the axial ratio of 1:2 is biased to the right of the loading axis, while the growth direction of the void with the axial ratio of 2:1 is on the contrary.
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(g) (h) (i) (j) (k) (l) Fig. 16 Equivalent plastic strain distributions. (a) The 1st loading for the axial ratio of 1:2 at ε=0.15; (b) The 1st loading for the axial ratio of 1:2 at ε=0.25; (c) The 1st loading for the axial ratio of 1:1 at ε=0.2; (d) The 1st loading for the axial ratio of 1:1 at ε=0.25; (e) The 1st loading for the axial ratio of 2:1 at ε=0.2; (f) The 1st loading for the axial ratio of 2:1 at ε=0.25; (g) The 2nd loading for the axial ratio of 1:2 at ε=0.2; (h) The 2nd loading for the axial ratio of 1:2 at ε=0.25; (i) The 2nd loading for the axial ratio of 1:1 at ε=0.2; (j) The 2nd loading for the axial ratio of 1:1 at ε=0.25; (k) The 2nd loading for the axial ratio of 2:1 at ε=0.2; (l) The 2nd loading for the axial ratio of 2:1 at ε=0.25.
The plastic deformation of the bicrystal appears around the void initially. That is, the slip systems at the boundary of the void start first. For larger axial ratios, the value of plastic strain in the first loading scenario is larger, and the localization of plastic deformation is more obvious. It is worth noting that the localization is easy to cause the formation and expansion of crack, and
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that localization of plastic deformation in the second loading scenario is most obvious when the axial ratio of void is 1:2. The bicrystal whose loading direction is parallel to the grain boundary has a greater strain gradient than that of the loading direction vertical to the grain boundary. Similar to the above section, the damage behavior of the void in the first loading scenario is more obvious than in the second loading scenario. Fig. 17 demonstrates that the critical slip stress of the first loading scenario increases in the order of the axial ratio of 1:1, 2:1, 1:2 in the same strain. Different from the first loading scenario, the critical slip stress of the second loading scenario increases in the order of the axial ratio of 1:1, 1:2, 2:1. In other words, the loading 1 at the void axial ratio of 1:2 is the most difficult to slip and has the best resistance to deformation, while the second loading scenario at the void axial ratio of 2:1 is the most difficult to slip and has the best resistance to deformation. It is also found that both bicrystal models at the void axial ratio of 1:1 are the easiest to slip. That is, the bicrystal with a circular void is most prone to plastic deformation compared to the other two shapes.
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(a) (b) Fig. 17 The Stress-strain responses of the bicrystal for different axial ratios of void. (a) The first loading scenario; (b) The second loading scenario.
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6. Conclusions
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In this paper, a rate-dependent crystal plasticity theory was applied to characterize the damage behavior of additive manufactured Al materials with void defects under tension. The effects of different orientations and voids for single crystal and bicrystal are discussed. The findings can be summarized as follows. (1) The plastic deformation of the crystal firstly appears around the void, that is, the slip systems around the void start first. Moreover, the single crystal with the hard orientation is more difficult to slip and has a better resistance to deformation. (2) The void shape has a great influence on the damage behavior of crystals of additive manufacturing Al with void defects. The slip systems in crystal with a circular void are more prone to start than with an elliptical void. (3) For the larger misorientation between the two grains on both sides of the bicrystal, the deformation of the crystal is more uncoordinated, and the stress concentration of the void is more obvious. Besides, the localization of plastic deformation in the bicrystal with a circular void is more obvious than in the bicrystal with an elliptical void. The shear localization easily causes the formation and expansion of the crack. (4) The damage behavior of additive manufacturing Al with void defect at grain boundary also depends on the loading direction. To be specific, the loading direction that is vertical to the grain interface is more conducive to the slip of the crystal and the growth of the void.
References
[2] [3] [4] [5] [6] [7] [8] [9]
Li X P, O’Donnell K M, Sercombe T B. Selective laser melting of Al-12Si alloy: Enhanced densification via powder drying. Additive Manufacturing, 2016, 10:10-14. Wang X J, Zhang L C, Fang M H, et al. The effect of atmosphere on the structure and properties of a selective laser melted Al–12Si alloy. Materials Science & Engineering A, 2014, 597(597):370-375. Shangguan H L, Kang J W, Yi J H, et al. Controlled cooling of an aluminium alloy casting based on 3D printed rib reinforced shell mold. China Foundry, 2018, 15(3):210-215. Maskery I, Aboulkhair N T, Corfield M R, et al. Quantification and characterisation of porosity in selectively laser melted Al-Si10-Mg using X-ray computed tomography. Materials Characterization, 2016, 111:193-204. Xue Y, Li T. Micromechanical simulations for fatigue damage incubation mechanisms of processed steel. Procedia Engineering, 2010, 2(1):1165-1172. Wang P, Tan X, He C, et al. Scanning optical microscopy for porosity quantification of additively manufactured components. Additive Manufacturing, 2018, 21:350-358. Weingarten C, Buchbinder D, Pirch N, et al. Formation and reduction of hydrogen porosity during selective laser melting of AlSi10Mg. Journal of Materials Processing Tech, 2015, 221:112-120. Bagherifard S, Beretta N, Monti S, et al. On the fatigue strength enhancement of additive manufactured AlSi10Mg parts by mechanical and thermal postprocessing. Materials & Design, 2018, 145:28-41. Romano S, Brückner-Foit A, Brandão A, et al. Fatigue properties of AlSi10Mg obtained by additive manufacturing: Defect-based modelling and prediction of fatigue strength. Engineering Fracture Mechanics, 2018, 187:165-189.
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[1]
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This work was supported by the National Natural Science Foundation of China (Grant No. 11472020, 11520007, 11572109 and 11632005) and Hong Kong Scholars Program (Grant XJ2016021) is gratefully acknowledged.
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[21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]
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[19] [20]
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[18]
M
[16] [17]
ED
[13] [14] [15]
PT
[12]
CE
[11]
AC
[10]
Author name / Mechanics Research Communications 00 (2015) 000–000 Felix H. Kim, Shawn P. Moylan. Literature Review of Metal Additive Manufacturing Defects. Advanced Manufacturing Series (NIST AMS) - 100-16, 2018. Noah H. Paulsona, Matthew W. Priddyb, David L. McDowell, et al. Reduced-order microstructure-sensitive protocols to rank-order the transition fatigue resistance of polycrystalline microstructures. International Journal of Fatigue, 2019, 119:1-10. Schoinochoritis B, Chantzis D, Salonitis K. Simulation of metallic powder bed additive manufacturing processes with the finite element method: A critical review. Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture, 2015, 231(1): 1-22. Vayre B, Vignat F, Villeneuve F. Designing for Additive Manufacturing. Procedia Cirp, 2012, 3(1):632-637. Rice J R, Tracey D M. On the ductile enlargement of voids in triaxial stress fields. Journal of the Mechanics & Physics of Solids, 1969, 17(3):201-217. Gurson A L. Continuum Theory of Ductile Rupture by Void Nucleation and Growth : Part 1-Yield Criteria and Flow Rules for Porous Ductilr Media. Journal of Engineering Materials & Technology, 1977, 99(1):297-300. Goh C H, Wallace J M, Neu R W, et al. Polycrystal plasticity simulations of fretting fatigue. International Journal of Fatigue, 2001, 23(01):423-435. He S, Van Bael A, Li S Y, et al. Residual stress determination in cold drawn steel wire by FEM simulation and X-ray diffraction. Materials Science & Engineering A, 2002, 346(1):101-107. Roters F, Eisenlohr P, Hantcherli L, et al. Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finiteelement modeling: Theory, experiments, applications. Acta Materialia, 2010, 58(4):1152-1211. Orsini V C, Zikry M A. Void growth and interaction in crystalline materials. International Journal of Plasticity, 2001, 17(10):1393-1417. Evers L P, Brekelmans W A M, Geers M G D. Non-local crystal plasticity model with intrinsic SSD and GND effects. Journal of the Mechanics & Physics of Solids, 2004, 52(10):2379-2401. Kysar J W, Gan Y X, Mendez-Arzuza G. Cylindrical void in a rigid-ideally plastic single crystal. Part I: Anisotropic slip line theory solution for facecentered cubic crystals. International Journal of Plasticity, 2005, 21(8):1481-1520. Liu W H, Zhang X M, Tang J G, et al. Simulation of void growth and coalescence behavior with 3D crystal plasticity theory. Computational Materials Science, 2007, 40(1):130-139. . Li L, Shen L, Proust G, et al. Three-dimensional crystal plasticity finite element simulation of nanoindentation on aluminium alloy 2024. Materials Science & Engineering A, 2013, 579:41-49. Asim U, Siddiq M A, Demiral M. Void growth in high strength aluminium alloy single crystals: a CPFEM based study. Modelling Simul.Mater.Sci.Eng, 2017, 25(3):35010. Mao L, Cheng L, Anh T K, et al. A combined experimental-numerical approach for determining mechanical properties of aluminum subjects to nanoindentation. Scientific Reports, 2015, 5:15072. Liu M, Lu C, Tieu K A, et al. Crystal plasticity FEM study of nanoindentation behaviors of Cu bicrystals and Cu-Al bicrystals. Journal of Materials Research, 2015, 30(16):2485-2499. Liu M, Nambu S, Koseki T, et al. Three-dimensional quantification of texture heterogeneity in single-crystal aluminium subjected to equal channel angular pressing. Philosophical Magazine, 2017, 97(11):799-819. Groh S, Marin E B, Horstemeyer M F, et al. Multiscale modeling of the plasticity in an aluminium single crystal. International Journal of Plasticity, 2009, 25(8):1456-1473. Roters F, Wang Y, Kuo J ‐, et al. Comparison of Single Crystal Simple Shear Deformation Experiments with Crystal Plasticity Finite Element Simulations. Advanced Engineering Materials, 2004, 6(8):653-656. Gorsse S, Hutchinson C, Gouné M, et al. Additive manufacturing of metals: a brief review of the characteristic microstructures and properties of steels, Ti6Al-4V and high-entropy alloys. Science & Technology of Advanced Materials, 2017, 18(1):584-610. Mei, YANG, Xianghuai, et al. Simulation of lattice orientation effects on void growth and coalescence by crystal plasticity. Acta Metallurgica Sinica (English Letters), 2009, 22(1):40-50. Wan J S, Yue Z F. Stress distribution near grain boundary in anisotropic bicrystals and tricrystals. Applied Mathematics and Mechanics, 2004, 25(1):3946.
Plastic damage of additive manufactured aluminium with void defects Li-Ya Liu , Qing-Sheng Yang , Y.X. Zhang PII: DOI: Reference:
S0093-6413(18)30454-3 https://doi.org/10.1016/j.mechrescom.2018.12.002 MRC 3335
To appear in:
Mechanics Research Communications
Received date: Revised date: Accepted date:
14 September 2018 13 November 2018 4 December 2018
Please cite this article as: Li-Ya Liu , Qing-Sheng Yang , Y.X. Zhang , Plastic damage of additive manufactured aluminium with void defects, Mechanics Research Communications (2018), doi: https://doi.org/10.1016/j.mechrescom.2018.12.002
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Highlights The plastic deformation of the crystal firstly appears around the void, that is, the slip systems around the void start first.
The single crystal with the hard orientation and the bicrystal with the larger misorientation between the two grains are more difficult to slip.
The slip systems in crystal with a circular pore are more prone to start than with an elliptical pore.
The loading direction that is vertical to the grain boundary is more conducive to the slip of the crystal and the growth of the pore.
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Plastic damage of additive manufactured aluminium with void defects Li-Ya Liu1, Qing-Sheng Yang1,2*, Y. X. Zhang2 1
Dept. of Engineering Mechanics, Beijing University of Technology, Beijing 100124, China School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia
2
*Corresponding author, email: [email protected] Tel.: + 86-10-67396333; fax: + 86-10-67396333
Abstract
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Keywords: additive manufacturing, aluminium, void defects, crystal plasticity, plastic damage.
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Additive manufacturing technology is a novel approach for the development of the modern industry. Additive manufactured aluminium (Al) becomes the hotspot of current research in order to achieve the high-precision products. However, the additive manufactured Al parts easily generate void defects due to the poor fluidity and low density of the materials, which in turn affects the mechanical properties. This paper studies the damage behavior of additive manufactured Al parts with void defects under tensile load in a mesoscale by using a two-dimensional rate-dependent crystal plasticity theory. The stress-strain curves and the plastic damages of single crystal and bicrystal with void defects are determined with different combinations of crystal orientations and loading conditions. It is found that the mechanical properties of additive manufactured aluminium severely depend on the crystal orientations and shapes of void defects.
1. Introduction
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Aluminium parts play an extremely important role in aerospace, automobile and shipbuilding due to their excellent advantages of light weight and good plasticity as well as corrosion resistance [1]. When the traditional forging can not enable the manufacture of Al components with lightweight structure and composite performance, additive manufacturing (AM) technology emerges, which can achieve Al parts with high density, fine structure and design optimization [2]. Moreover, compared with Al parts manufactured by traditional forging, the mechanical property of additive manufactured Al is greatly improved while the cost is greatly reduced [3]. Howerer, there are still many problems in additive manufactured Al at present, such as oxidation, residual stress and void defects [4]. Yet, these problems, especially void defects, further affects the mechanical properties of additive manufactured Al parts [5]. As shown in Fig. 1, the distribution of these void defects can be observed by optical microscope images [6]. The slow development and lack of breakthroughs of additive manufactured Al are mainly caused by defects in the manufacturing process [7]. Yadollahi [8] found that if the voids are located outside the trimmed material layer, then polishing can not completely eliminate the void defects. Actually, optimization of manufactured parameters and adopting complex post-treatments can be never possible to totally eliminate void defects [9]. A catastrophic failure can be triggered by the individual void size and shape [10]. However, the experimental research of damage behavior of additive manufactured Al has some disadvantages, such as complicated experimental process, raw materials waste and high research cost, which seriously limits the further study of additive manufactured Al with void defects [11]. At present, the influence of void defects on mechanical properties of additive manufactured Al can be revealed by numerical simulation [12]. Many studies pay close attention to improve the technology of AM processes [13], however, there few efforts have been made to understand of the effect of defects on mechanical properties of the products. Therefore, the specific research of AM products with void defects in a mesoscale is necessary, which can provide a theoretical basis for the manufacture and safety evaluation of AM aluminum.
Fig. 1 OM images showing the Ti-6Al-4V voids under different magnifications.
The traditional elastoplastic mechanics mostly treat the metal as the isotropic material or use the improved constitutive model to study the influence of the void defects on the mechanical properties, so the whole process of the void deformation cannot be accurately described [14-15]. With the gradual improvement of the theoretical basis and enhancement of computer ability, the crystal plasticity theory and the finite element method have been combined to form the crystal plasticity finite element method (CPFEM) [16-17]. One of the main advantages of CPFEM is that it can solve crystal mechanical problems from mesoscopic scale with complex boundary conditions [18]. Recently, CPFEM have been employed to study the mechanical properties of metal. Orsini and Zikry [19] used a rate-dependent crystal plasticity model to investigate the growth of voids in FCC copper single crystals. The results showed that the rotation and plastic slip of the crystal concentrated in the region between the voids.
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Hereafter, based on the crystal plasticity model, Evers [20] considered the grain boundary action and the strengthening caused by dislocation density to predict the size dependence of flow stress. Kysar et al. [21] analyzed the circular void in a single crystal under plane strain condition by slip line theory, and found that the stress around the void was anisotropic. Liu [22] employed CPFEM to simulate the influence of crystal orientation on void growth and coalescence behavior. Subsequently, Li et al. [23] studied the effects of crystal orientation, grain shape and grain boundary on nanoindentation of aluminium alloy. Asim et al. [24] established a finite element model of aluminium alloy single crystal based on the crystal plasticity theory, and studied the potential physical mechanism of the tough failure process. Liu et al. [25] explored the relationship between indentation hardness and yield stress by a polycrystal tensile CPFEM. Liu et al. [26] investigated the effects of grain/phase boundary on mechanical properties by a CPFEM constitutive model combined with Bassani and Wu hardening law. In order to accurately predict the deformation mechanism under the complicated contact conditions between a billet and a die, Liu et al. [27] developed a 3D CPFEM of a real equal channel angular pressing process for the first time. Nevertheless, limited studies on the plastic damage behavior of the additive manufactured Al with void defects have been reported so far and the numerical studies by CPFEM are even less. In this paper, a two-dimensional rate-dependent crystal plasticity model using the numerical model is developed to study the plastic deformation and damage behavior of additive manufactured Al material with void defects under tensile load in a mesoscale. Then the effects of different orientations, loading conditions and void shapes for single crystal and bicrystal are investigated.
2. CPFE model of additive manufactured Al
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At present, the mechanical properties of additive manufactured Al are limited and depend on the manufacturing process. Considered here the material performance of additive manufactured Al is the same as that of Al manufactured by traditional process, but additive manufactured Al is more prone to occur a lot of void defects, thus the CPFEM can be used to study additive manufactured Al with void defects. Moreover, the mechanical response of single crystals or polycrystals can be obtained by responding to the stress generated by the dislocation slip process. The nature of metal deformation can be understood fundamentally at the grain scale from CPFEM [28]. The program used in the above article can only calculate the plastic problems of grain groups by combining with finite element software. In this paper, the program is modified to study the crystal plastic deformation with distinguishing the crystal grains. Crystal kinematic description is based on the multiplicative decomposition theory of the deformation gradient in the crystal plasticity theory. When analyzing the deformation of a single crystal, the total deformation gradient can be decomposed as
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where is the shear stress on the α-th slip system (Schmid stress), 0 denotes the reference shear strain rate, c is the reference shear stress on the α-th slip system while m is the rate sensitivity coefficient. The expression of the slip hardening law is m
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q denotes the latent hardening matrix. The material parameters used in this work are listed in Table 1 [29].
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There are two main reasons for the formation of void defects: (1) Due to the faster solidification rate, a part of the gas generated by the evaporation of water does not escape in time and remains in the molten pool, and thus the resulting void location is within the grain; (2) The powder is not completely melted or only partially melted, resulting in void on the grain boundary during fusion [30]. Therefore, there are different orientation combinations of the crystals and loading conditions in this work. As shown in Fig. 2(a), a two-dimensional Al single crystal model with a void was established with a size of 1×1 mm2, and the radius of 75 μm. To investigate the mechanical properties of Al single crystal under tensile conditions, an uniaxial tensile boundary condition was applied. During the simulation process, the maximum deformation of the model was set up to 25%. In those cases, 484 elements of CPE4R were employed for the simulation. These elements have been tested, and when the number of elements reaches a certain level, the calculation results tend to be stable, thus these elements are used to eliminate the mesh dependency.
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(a) (b) (c) Fig. 2 (a) Single crystal model and boundary conditions; (b) Bicrystal model and boundary conditions with load parallel to grain boundary; (c) Bicrystal model and boundary conditions with load vertical to grain boundary.
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In another case, as illustrated in Fig. 2(b)-(c), a two-dimensional Al bicrystal model with a void at grain boundary was established with a size of 1×1 mm2 and a radius of 75 μm. The crystal plasticity constitutive model considers the grain boundary as a purely geometrical interface, and taking into account only the differences in grain orientations on both sides of the grain boundary. To investigate the effect of grain boundaries on the mechanical properties of Al bicrystal under tensile conditions, uniaxial tensile boundary conditions were set, in which the tensile direction was parallel and vertical to the grain boundary respectively. Similarly, the maximum deformation of the model was set to be 25%.
4. The mechanical properties of Al single crystal At present the additive manufacturing technology is able to produce single crystal parts. It is necessary to study the void defects of single crystals with different orientations and shapes systematically in order to understand the influence of void defects on the mechanical behavior of additive manufactured Al. 4.1 Effect of the orientation of Al single crystal In this section, the effects of different initial crystal orientations (Cube {001}<100>, Goss {011}<100> and Brass {011}<211>) on the tensile mechanical properties of single crystals were investigated. As shown in Fig. 3, the total deformation
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process of the single crystal with a void under tensile loading were obtained. The voids within a crystal have varied shapes after deformation due to the anisotropic behavior of the crystal. For the elastic deformation stage, the slip systems are not started at this time. Afterward, there is an obvious yield point, which indicates that the slip system begins to start. Thereafter, the strain around the void is greater than the strain in other regions, which leads to a change in the shape of the void. The voids within Cube orientation and Goss orientation crystals grow along the loading direction due to the better symmetry in the sample coordinate system, while the growth direction of the void within Brass orientation crystal deviates from the loading direction. The plastic strain nephogram at different stages was obtained, as illustrated in Fig. 4. The plastic deformation of the single crystal with Cube orientation appears around the void initially and then extends along the loading direction gradually. That is, the slip systems around the void start first. Subsequently, the slip systems in other regions of the crystal begin to start. Thereafter, a large part of the crystal has plastic deformation after deformation, which indicates that the slip system has begun to start universally. Then gradient of the stress from the void to the boundary region is formed. Both the maximum stress and plastic strain appearing at the edge of the void are 45° from the horizontal direction. Similarly, the plastic deformation of the single crystal with Goss orientation occurs initially around the void. Then it gradually extends along the 45° direction of loading axis. The slip systems at the boundary region does not start after deformation, while the maximum plastic strain appearing at the edge of the void are also 45° from the horizontal axis. The void of the single crystal with Brass orientation is very irregular during the deformation process, and the plastic deformation gradually extends from the void to the boundary along the 30° direction of horizontal axis. Both the maximum stress and plastic strain appear at the edge of the void around the horizontal axis. From the above, the single crystal with Brass orientation is the most difficult to slip compared with the other two crystals.
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Fig. 3 Variation of deformation process of single crystal for different crystal orientations. (a) Void inside Cube crystal; (b) Void inside Goss crystal; (c) Void inside Brass crystal.
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(a) (b) (c) (d) (e) (f) Fig. 4 Equivalent plastic strain distributions. (a) Void inside Cube crystal at ε=0.15; (b) Void inside Cube crystal at ε=0.25; (c) Void inside Goss crystal at ε=0.2; (d) Void inside Goss crystal at ε=0.25; (e) Void inside Brass crystal at ε=0.2; (f) Void inside Brass crystal at ε=0.25;
Fig. 5 shows the variation of nominal stress of crystal with applied strain for different orientations. By observing the elastic stage and yield point, the critical slip stress increases in the order of the orientation of Goss, Cube and Brass in the same strain. That is, the single crystal with Brass orientation is the most difficult to slip. Then the single crystal with Brass orientation enters the linear hardening stage, while the single crystals with Cube orientation and Goss orientation directly enter the parabolic hardening stage. This indicates that the slip systems of Cube and Goss orientation start generally, and the crystal enter a largescale yield state. At the same time, most of the single crystal with Brass orientation are still in the elastic stage.
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4.2 Effect of the void shape In the above section, it is concluded that the single crystal with Brass orientation is the most difficult to slip. This is consistent with the conclusion from the literature [31]. In order to study the influence of initial void shapes on mechanical properties of single crystals, the axial ratios of the voids are assumed to be 1:2, 1:1 and 2:1 respectively. By observing the elastic deformation stage of the curves (Fig. 6), it is noticed that the location of the maximum strain and the deformation of the void are basically identical in the three cases. As the applied strain increases, the deformations of the three types of voids are gradually changed and become different. To be specific, for a larger axial ratio, the growth direction of the void deviates more from the yaxis while the location of the maximum strain is closer to the loading direction. The deformed shapes with different axial ratios of the void are shown in Fig. 7. The plastic strain of all three crystals appear around the void initially. That is, the slip systems around the void start first. In detail, the regions of the initial plastic deformation at the void axial ratios of 1:1 and 2:1 are basically identical, while the other is different. In addition, for the larger axis ratio, the localization of plastic deformation is more obvious. After deformation, the distribution of plastic strain in single crystal with different void shapes is different, which indicate that the void shape has a great influence on the damage behavior of single crystal with void defects.
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(c) Fig. 6 Variation of deformation process of single crystal with various axial ratios of void. (a) Void with axial ratio of 1:2 inside a Brass crystal; (b) Void with axial ratio of 1:1 inside a Brass crystal; (c) Void with axial ratio of 2:1 inside a Brass crystal.
(a) (b) (c) (d) (e) (f) Fig. 7 Equivalent plastic strain distributions. (a) Void with the axial ratio of 1:2 at ε=0.15; (b) Void with the axial ratio of 1:2 at ε=0.25; (c) Void with the axial ratio of 1:1 at ε=0.15; (d) Void with the axial ratio of 1:1 at ε=0.25; (c) Void with the axial ratio of 2:1 at ε=0.15; (d) Void with the axial ratio of 2:1 at ε=0.25.
The stress-strain responses of a single crystal (Fig. 8) demonstrate that the critical slip stress increases in the order of the axial ratio of 1:1, 2:1, 1:2 in the same strain. In another word, the single crystal at the void axial ratio of 1:2 is the most difficult to slip. All the cases enter the parabolic hardening stage after deformation. To be specific, multiple sets of slip systems have started and the hardening phenomenon is obvious. It is also found that the single crystal at the void axial ratio of 1:2 has the best resistance to deformation compared to the other two cases.
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100 80 60 40 20 0 0.00
0.00 0.01 Strain 0.05
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Fig. 8 The stress-strain responses of single crystal for various axial ratios of void.
5. The mechanical properties of Al bicrystal
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When the polycrystal deforms, the single crystal forming polycrystal has complex deformation modes. Moreover, there is a problem of localization of stress and strain due to the existence of grain boundary. It is necessary to study the damage behavior of the void defects on the grain boundary by using a geometrically simple and easily analyzable bicrystal. The effects of different factors on the tensile mechanical properties of bicrystals with a void at grain boundary are investigated in this section. 5.1 Effect of the orientation of Al bicrystal Different combinations of bicrystal are studied in this work. The grain orientation of the bicrystal has the following two cases:
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(A) Goss ( 0 , 45 , 0 ) and Cube ( 0 , 0 , 0 ), denoting by Case GC ; (B) Goss ( 0 , 45 , 0 ) and Brass ( 35 , 45 , 0 ), denoting by Case GB. Fig. 9 is the deformation process under the first loading scenario, i.e., the loading direction parallel to the grain boundary and the second loading scenario, where the loading direction is vertical to the grain boundary, respectively. Different orientations of grains on both sides of the bicrystal lead to different slip systems activation. In turn, the deformation of the two grains is uncoordinated. The shape of the void is closer to symmetry and grows along the coordinate axis during the deformation process in the case GC because of the small misorientation between Goss and Cube. The deformation caused by misorientation is not obvious. On the contrary, the void has the irregular shape and deviates from the coordinate axis during the deformation process in case GB due to the large misorientation between Goss and Brass. 120
80
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60
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0 0.25 (b) 0.00
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(c)
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100
60
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0.25
(d)
GB 0.05
0.10 0.15 Strain
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Fig. 9 Variation of deformation process of bicrystal for various cases. (a) The first loading scenario for case GC; (b) The first loading scenario for case GB; (c) The second loading scenario for case GC; (d) The second loading scenario for case GB.
The plastic deformation and von Mises stress of bicrystals are shown in Fig. 10-13. It is demonstrated that the slip systems around the void start first in every case. In turn, the started slip systems are concentrated around the void, which can lead to the localization of damage and failure. Stress concentration appears at the boundary of the void, and a gradient of the stress from the void to the boundary region is formed. To be specific, the stress concentration in case GC is relatively moderate due to the smaller misorientation between Goss and Cube. By observing the plastic distribution and the maximum stress value of nephograms, it is found that the damage behavior of the void whose loading direction is vertical to the grain boundary is more obvious than that of the void whose loading direction is parallel to the grain boundary. This result is consistent with the conclusion that metal tends to form void defects at vertical grain boundaries obtained from [32].
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(a) (b) (c) (d) Fig. 10 Equivalent plastic strain and equivalent stress distributions of the 1st loading for case GC. (a) strain at ε=0.2; (b) strain at ε=0.25; (c) stress at ε=0.2; (d) stress at ε=0.25.
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(a) (b) (c) (d) Fig. 11 Equivalent plastic strain and equivalent stress distributions of the 2nd loading for case GC. (a) strain at ε=0.2; (b) strain at ε=0.25; (c) stress at ε=0.2; (d) stress at ε=0.25.
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(a) (b) (c) (d) Fig. 12 Equivalent plastic strain and equivalent stress distributions of the 1st loading for case GB. (a) strain at ε=0.2; (b) strain at ε=0.25; (c) stress at ε=0.2; (d) stress at ε=0.25.
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(a) (b) (c) (d) Fig. 13 Equivalent plastic strain and equivalent stress distributions of the 2nd loading for case GB. (a) strain at ε=0.2; (b) strain at ε=0.25; (c) stress at ε=0.2; (d) stress at ε=0.25.
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parallel vertical 46
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As shown in Fig. 14, the critical slip stress of case GB is greater than that of the case GC for both loading situations. By observing the yield point, the slip systems of case GB is most difficult to start. It is also found that the resistance to deformation of case GB is higher than that of case GC, as illustrated in plastic stage of the curve. The mechanical properties of the bicrystal with a void depend not only on the grain orientation but also on the direction of loading. The stress in the first loading scenario is larger than that in the second loading scenario when the orientations of the two bicrystal models are identical, and this indicates that the void of the bicrystal whose loading direction is vertical to the grain boundary is easier to grow.
44 0.000
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0.001 Strain
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Fig. 14 The Stress-strain response. (a) Different combinations of orientations in the first loading scenario; (b) Different combinations of orientations in the second loading scenario; (c) Different loadings for case GC; (d) Different loadings for case GB.
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5.2 Effect of the void shape As discussed in the above section, the bicrystal in case GB is most difficult to slip. To provide a numerical perspective, the influence of initial void shape on mechanical properties of bicrystal in case GB is studied. Similar to single crystal, the axial ratios of the voids in bicrystals are 1:2, 1:1 and 2:1 respectively. 140 120
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Fig. 15 Variation of deformation process for various axial ratios of void in different loadings. (a) The first loading scenario for the axial ratio of 1:2; (b) The first loading scenario for the axial ratio of 1:1; (c) The first loading scenario for the axial ratio of 2:1; (d) The second loading scenario for the axial ratio of 1:2; (e) The second loading scenario for the axial ratio of 1:1; (f) The second loading scenario for the axial ratio of 2:1.
(a)
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Fig. 15 shows the deformation process of the first loading scenario in the direction parallel to the grain boundary and the second loading scenario in the direction vertical to the grain boundary when the axial ratios of the voids in the bicrystal are 1:2, 1:1 and 2:1, respectively. By observing the elastic deformation stage of curves (Fig. 15(a)-(c)), it is noticed that the location of the maximum logarithmic strain of loading 1 are basically identical in the three cases. After deformation, the growth direction of the void deviates more from the loading axis for the larger axial ratios. The growth of void in the second loading scenario is more complex than that in the first loading scenario during the deformation process, as described in Fig. 15(d) to (f). To be specific, the growth direction of the void with the axial ratio of 1:2 is biased to the right of the loading axis, while the growth direction of the void with the axial ratio of 2:1 is on the contrary.
(b)
(c)
(d)
(e)
(f)
(g) (h) (i) (j) (k) (l) Fig. 16 Equivalent plastic strain distributions. (a) The 1st loading for the axial ratio of 1:2 at ε=0.15; (b) The 1st loading for the axial ratio of 1:2 at ε=0.25; (c) The 1st loading for the axial ratio of 1:1 at ε=0.2; (d) The 1st loading for the axial ratio of 1:1 at ε=0.25; (e) The 1st loading for the axial ratio of 2:1 at ε=0.2; (f) The 1st loading for the axial ratio of 2:1 at ε=0.25; (g) The 2nd loading for the axial ratio of 1:2 at ε=0.2; (h) The 2nd loading for the axial ratio of 1:2 at ε=0.25; (i) The 2nd loading for the axial ratio of 1:1 at ε=0.2; (j) The 2nd loading for the axial ratio of 1:1 at ε=0.25; (k) The 2nd loading for the axial ratio of 2:1 at ε=0.2; (l) The 2nd loading for the axial ratio of 2:1 at ε=0.25.
The plastic deformation of the bicrystal appears around the void initially. That is, the slip systems at the boundary of the void start first. For larger axial ratios, the value of plastic strain in the first loading scenario is larger, and the localization of plastic deformation is more obvious. It is worth noting that the localization is easy to cause the formation and expansion of crack, and
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that localization of plastic deformation in the second loading scenario is most obvious when the axial ratio of void is 1:2. The bicrystal whose loading direction is parallel to the grain boundary has a greater strain gradient than that of the loading direction vertical to the grain boundary. Similar to the above section, the damage behavior of the void in the first loading scenario is more obvious than in the second loading scenario. Fig. 17 demonstrates that the critical slip stress of the first loading scenario increases in the order of the axial ratio of 1:1, 2:1, 1:2 in the same strain. Different from the first loading scenario, the critical slip stress of the second loading scenario increases in the order of the axial ratio of 1:1, 1:2, 2:1. In other words, the loading 1 at the void axial ratio of 1:2 is the most difficult to slip and has the best resistance to deformation, while the second loading scenario at the void axial ratio of 2:1 is the most difficult to slip and has the best resistance to deformation. It is also found that both bicrystal models at the void axial ratio of 1:1 are the easiest to slip. That is, the bicrystal with a circular void is most prone to plastic deformation compared to the other two shapes.
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Stress/MPa
Stress/MPa
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160 140 120 100 80 60 40 20 0 0.00
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(a) (b) Fig. 17 The Stress-strain responses of the bicrystal for different axial ratios of void. (a) The first loading scenario; (b) The second loading scenario.
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6. Conclusions
Acknowledgments
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In this paper, a rate-dependent crystal plasticity theory was applied to characterize the damage behavior of additive manufactured Al materials with void defects under tension. The effects of different orientations and voids for single crystal and bicrystal are discussed. The findings can be summarized as follows. (1) The plastic deformation of the crystal firstly appears around the void, that is, the slip systems around the void start first. Moreover, the single crystal with the hard orientation is more difficult to slip and has a better resistance to deformation. (2) The void shape has a great influence on the damage behavior of crystals of additive manufacturing Al with void defects. The slip systems in crystal with a circular void are more prone to start than with an elliptical void. (3) For the larger misorientation between the two grains on both sides of the bicrystal, the deformation of the crystal is more uncoordinated, and the stress concentration of the void is more obvious. Besides, the localization of plastic deformation in the bicrystal with a circular void is more obvious than in the bicrystal with an elliptical void. The shear localization easily causes the formation and expansion of the crack. (4) The damage behavior of additive manufacturing Al with void defect at grain boundary also depends on the loading direction. To be specific, the loading direction that is vertical to the grain interface is more conducive to the slip of the crystal and the growth of the void.
References
[2] [3] [4] [5] [6] [7] [8] [9]
Li X P, O’Donnell K M, Sercombe T B. Selective laser melting of Al-12Si alloy: Enhanced densification via powder drying. Additive Manufacturing, 2016, 10:10-14. Wang X J, Zhang L C, Fang M H, et al. The effect of atmosphere on the structure and properties of a selective laser melted Al–12Si alloy. Materials Science & Engineering A, 2014, 597(597):370-375. Shangguan H L, Kang J W, Yi J H, et al. Controlled cooling of an aluminium alloy casting based on 3D printed rib reinforced shell mold. China Foundry, 2018, 15(3):210-215. Maskery I, Aboulkhair N T, Corfield M R, et al. Quantification and characterisation of porosity in selectively laser melted Al-Si10-Mg using X-ray computed tomography. Materials Characterization, 2016, 111:193-204. Xue Y, Li T. Micromechanical simulations for fatigue damage incubation mechanisms of processed steel. Procedia Engineering, 2010, 2(1):1165-1172. Wang P, Tan X, He C, et al. Scanning optical microscopy for porosity quantification of additively manufactured components. Additive Manufacturing, 2018, 21:350-358. Weingarten C, Buchbinder D, Pirch N, et al. Formation and reduction of hydrogen porosity during selective laser melting of AlSi10Mg. Journal of Materials Processing Tech, 2015, 221:112-120. Bagherifard S, Beretta N, Monti S, et al. On the fatigue strength enhancement of additive manufactured AlSi10Mg parts by mechanical and thermal postprocessing. Materials & Design, 2018, 145:28-41. Romano S, Brückner-Foit A, Brandão A, et al. Fatigue properties of AlSi10Mg obtained by additive manufacturing: Defect-based modelling and prediction of fatigue strength. Engineering Fracture Mechanics, 2018, 187:165-189.
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[1]
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This work was supported by the National Natural Science Foundation of China (Grant No. 11472020, 11520007, 11572109 and 11632005) and Hong Kong Scholars Program (Grant XJ2016021) is gratefully acknowledged.
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[21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]
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[19] [20]
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[18]
M
[16] [17]
ED
[13] [14] [15]
PT
[12]
CE
[11]
AC
[10]
Author name / Mechanics Research Communications 00 (2015) 000–000 Felix H. Kim, Shawn P. Moylan. Literature Review of Metal Additive Manufacturing Defects. Advanced Manufacturing Series (NIST AMS) - 100-16, 2018. Noah H. Paulsona, Matthew W. Priddyb, David L. McDowell, et al. Reduced-order microstructure-sensitive protocols to rank-order the transition fatigue resistance of polycrystalline microstructures. International Journal of Fatigue, 2019, 119:1-10. Schoinochoritis B, Chantzis D, Salonitis K. Simulation of metallic powder bed additive manufacturing processes with the finite element method: A critical review. Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture, 2015, 231(1): 1-22. Vayre B, Vignat F, Villeneuve F. Designing for Additive Manufacturing. Procedia Cirp, 2012, 3(1):632-637. Rice J R, Tracey D M. On the ductile enlargement of voids in triaxial stress fields. Journal of the Mechanics & Physics of Solids, 1969, 17(3):201-217. Gurson A L. Continuum Theory of Ductile Rupture by Void Nucleation and Growth : Part 1-Yield Criteria and Flow Rules for Porous Ductilr Media. Journal of Engineering Materials & Technology, 1977, 99(1):297-300. Goh C H, Wallace J M, Neu R W, et al. Polycrystal plasticity simulations of fretting fatigue. International Journal of Fatigue, 2001, 23(01):423-435. He S, Van Bael A, Li S Y, et al. Residual stress determination in cold drawn steel wire by FEM simulation and X-ray diffraction. Materials Science & Engineering A, 2002, 346(1):101-107. Roters F, Eisenlohr P, Hantcherli L, et al. Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finiteelement modeling: Theory, experiments, applications. Acta Materialia, 2010, 58(4):1152-1211. Orsini V C, Zikry M A. Void growth and interaction in crystalline materials. International Journal of Plasticity, 2001, 17(10):1393-1417. Evers L P, Brekelmans W A M, Geers M G D. Non-local crystal plasticity model with intrinsic SSD and GND effects. Journal of the Mechanics & Physics of Solids, 2004, 52(10):2379-2401. Kysar J W, Gan Y X, Mendez-Arzuza G. Cylindrical void in a rigid-ideally plastic single crystal. Part I: Anisotropic slip line theory solution for facecentered cubic crystals. International Journal of Plasticity, 2005, 21(8):1481-1520. Liu W H, Zhang X M, Tang J G, et al. Simulation of void growth and coalescence behavior with 3D crystal plasticity theory. Computational Materials Science, 2007, 40(1):130-139. . Li L, Shen L, Proust G, et al. Three-dimensional crystal plasticity finite element simulation of nanoindentation on aluminium alloy 2024. Materials Science & Engineering A, 2013, 579:41-49. Asim U, Siddiq M A, Demiral M. Void growth in high strength aluminium alloy single crystals: a CPFEM based study. Modelling Simul.Mater.Sci.Eng, 2017, 25(3):35010. Mao L, Cheng L, Anh T K, et al. A combined experimental-numerical approach for determining mechanical properties of aluminum subjects to nanoindentation. Scientific Reports, 2015, 5:15072. Liu M, Lu C, Tieu K A, et al. Crystal plasticity FEM study of nanoindentation behaviors of Cu bicrystals and Cu-Al bicrystals. Journal of Materials Research, 2015, 30(16):2485-2499. Liu M, Nambu S, Koseki T, et al. Three-dimensional quantification of texture heterogeneity in single-crystal aluminium subjected to equal channel angular pressing. Philosophical Magazine, 2017, 97(11):799-819. Groh S, Marin E B, Horstemeyer M F, et al. Multiscale modeling of the plasticity in an aluminium single crystal. International Journal of Plasticity, 2009, 25(8):1456-1473. Roters F, Wang Y, Kuo J ‐, et al. Comparison of Single Crystal Simple Shear Deformation Experiments with Crystal Plasticity Finite Element Simulations. Advanced Engineering Materials, 2004, 6(8):653-656. Gorsse S, Hutchinson C, Gouné M, et al. Additive manufacturing of metals: a brief review of the characteristic microstructures and properties of steels, Ti6Al-4V and high-entropy alloys. Science & Technology of Advanced Materials, 2017, 18(1):584-610. Mei, YANG, Xianghuai, et al. Simulation of lattice orientation effects on void growth and coalescence by crystal plasticity. Acta Metallurgica Sinica (English Letters), 2009, 22(1):40-50. Wan J S, Yue Z F. Stress distribution near grain boundary in anisotropic bicrystals and tricrystals. Applied Mathematics and Mechanics, 2004, 25(1):3946.