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The effects of solid-state phase transformation upon stress evolution in laser metal powder deposition
Materials and Design 87 (2015) 807–814
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The effects of solid-state phase transformation upon stress evolution in laser metal powder deposition J.X. Fang a,b, S.Y. Dong b, Y.J. Wang b, B.S. Xu a,b, Z.H. Zhang a,b, D. Xia b, P. He a,⁎ a b
State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, Harbin 150001, China National Key Laboratory for Remanufacturing, Academy of Armored Forces Engineering, Beijing, 100072, China
a r t i c l e
i n f o
Article history: Received 8 May 2015 Received in revised form 11 August 2015 Accepted 14 August 2015 Available online 22 August 2015 Keywords: Laser metal powder deposition Residual stress Finite element analysis Martensitic transformation transformation induced plasticity
a b s t r a c t To investigate the influences of solid-state phase transformation on stress evolution during multi-pass laser metal powder deposition (LMPD) process, a 3D finite-element (FE) thermo-mechanical model considering phase transformation has been established. The influences of phase transformation such as mechanical properties changes, volume change and transformation induced plasticity (TRIP) are taken into account. Furthermore, the influences of high magnitude stress upon martensitic transformation characteristic temperature and TRIP are considered. The temperature and history (microstructure) dependent material properties used in the present research are obtained by experiments. The stress field during LMPD process is analyzed with and without solidstate phase transformation, respectively. Stress measurement of X-ray diffraction (XRD) method is applied to deposited samples, and the measuring data are compared with the computational predictions. The results show that phase transformation has a dominant effect on the stress evolution, longitudinal residual stresses significantly reduced as a result of solid-state phase transformation. In addition, the effect of stresses on martensitic transformation temperature is important for accurate prediction of residual stresses (stress state after cooling of the clad to ambient temperature). Residual stresses are lower when the phase transformation temperature is reduced. © 2015 Published by Elsevier Ltd.
1. Introduction Residual stress is one of the major issues affecting the large-scale commercial applications of laser metal powder deposition (LMPD). The complex thermal cycling of the process unavoidably relates to the evolution of stresses and strains and lead to cracks and distortion. Moreover, the magnitude and distribution of residual stresses may strongly influence the service behaviors, for example, the tensile residual stresses are often considered to reduce the strength of the material, induce stress corrosion and short the fatigue life [1–6]. Therefore, a valid approach to control the residual stresses is one of the most crucial problems to be solved in LMPD [7]. Using high-precision prediction calculation methods can assist in mitigating stress peaks and rearrange the stress distribution in favor of the product’s usage. Similar to ordinary welding process, the LMPD process parameters and material properties are the main factors affecting the evolution of stresses. With regard to some materials, phase transformation take place and greatly influence stress evolution during LMPD process. For example, the martensitic transformation in ferrous materials is often ⁎ Corresponding author at: State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, Harbin 150001, China. E-mail address: [email protected] (P. He).
http://dx.doi.org/10.1016/j.matdes.2015.08.061 0264-1275/© 2015 Published by Elsevier Ltd.
accompanied by the change of mechanical properties, volume growth and TRIP, etc., which will profoundly influence the development of residual stresses [8,9]. In order to improve the accuracy of predicting the residual weld stresses and strain, it has become the research focus for years to adopt the microstructure transformation effects into the weld thermal-mechanical simulation models [10–19]. Ghosh and Choi [10,11] have established a thermal-mechanicalmicrostructural model in which the effects of phase transformation are taken into account. It is found that stress evolution is sensitive to phase transformation. Phase transformation lead to the reduction of tensile stresses and even the emergence of compressive stresses. This model is very valuable. However, it can be improved because it is merely applied to single-pass welds, since it does not consider phase transformation induced by a new weld pass. Dean Deng et al. [13] have established a thermal-mechanical FE model. In his model, volume change as a result of martensitic transformation, mechanical properties variation due to microstructure change and TRIP have been take into account. It is concluded that the influence of phase transformation on welding residual stresses is important, the effect of TRIP should also be considered for accurate prediction of residual stresses. Lee and Chang [14,15] have developed a finite element model to predict the residual stresses of high carbon steel butt weld. The results show that phase transformation has significant effect on longitudinal tensile residual stresses due to volume change. In fact, many other valuable FE
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models considering phase transformation have been established by Ferro et al. [16], Wang and Felicelli [17], Shirish et al. [18], in the past few years. However, these models are similar as the model proposed by Ghosh and Choi, they do not consider phase transformation induced by the following weld pass. A thermal-kinetic model has been presented by Costa et al. [19,20] to simulate temperature field and microstructure in parts of AISI 420 tool steel built by LMPD. The effect of solid-state phase transformation upon temperature field is considered. This model can be applied to multi-pass weld and LMPD process, since the solid-state phase transformations induced by the thermal cycles are considered when a new layer of material is deposited. However, this model does not address the stress problem. Borjesson and Lindgren [21] have developed a valuable FE model to predict the residual stresses of multi-pass butt welding. But this two dimensions model can be extended to three dimensions. Residual stresses have been calculated and measured by Becker et al. [22] for multi-pass girth welds including post-weld heat treatment. However, the physical processes and computational process are only briefly detailed. In addition, the kinetic model of solid-state phase transformation and constitutive model considering phase transformation are the foundation for accurate prediction of stresses. The study of these nonlinear and strongly coupling problems continues to be a very active field [23–26], and further discussions on these subjects are essential. For example, the effects of stress on martensitic transformation are extremely complex, and the influence becomes significant under high magnitude stress [24,25]. TRIP increases very quickly when the tensile stresses exceed about a half of yield stress of high temperature phase. And it is well known that the magnitude of principal stresses is almost close to the yield strength of the clad material at certain temperature during LMPD process. As mentioned in the classical work by Francis et al. [27], however, the existing models of computational welding mechanics do not take into consider the nonlinearity of the TRIP versus the high magnitude stress. Moreover, the martensite starting and ending temperatures can be significantly influenced by high magnitude stress [28,29]. With regard to the material used in the present work, martensite start temperatue (Ms) can be increased by about 200 °C by stress comparable to the yield strength of austenite. Based on the above discussions, although considerable progress has been made to predict the residual stresses during welding or LMPD process, there are much left to do. In the present research, a FE model considering solid-state phase transformation has been developed to simulate the stress field during single-pass and multi-pass LMPD process. Not only the dependence of mechanical properties (yield strength) on phase volume fractions and temperature, but also the volume change and TRIP are taken into consideration. Furthermore, the influences of high magnitude stress upon TRIP and martensitic transformation characteristic temperatures are taken into account. The thermal and mechanical material parameters used in the present research are obtained by experiments. The stress fields of both single-pass and multi-pass LMPD process are predicted by the numerical simulation. The numerical results are validated by the experimental residual stress distributions of the XRD method.
Ni-1.6 wt.% Mo-0.9 wt.% B-0.6 wt.% Mn-0.12 wt.% C. The particle size range of the powders was 45–100 μm. The wrought FV520 (B) plates with the size of 6 mm × 40 mm × 60 mm were used as substrate. Three single-pass samples and three multi-pass samples (Two layers, eight passes) were fabricated for residual stress tests. Two large bulks with the size of about 135 mm × 65 mm × 27 mm were made for the property parameters tests. XRD method was adopted for the residual stress measurement in which the XSTRESS3000 residual stress measuring instrument was used. Cobalt target was used in the present experiment. The residual stresses of the tested area were the average value of measurements. Specimens were cut from the large bulk to prepare for the property parameters tests. The high temperature properties with regard to material mechanics were obtained by an MTS810 mechanical testing machine according to the ASTME21-05 standard. Free dilatometric tests were carried out by DIL801 thermal expansion test instrument referring to Chinese National Standard of GB/T 4339–2008. The specific heat was obtained with Setaram Setsys Evo thermal analyzer according to the standard ASTME1269-11, while the thermal conductivity obtained with Netzsch LFA427 laser thermal conductivity meter according to the standard ASTME1461-11. 2.2. The process of solid-state phase transformation Fig. 1 is the schematic of phase transformation for the martensite stainless steel during the LMPD process [19]. Austenite is assumed to be the initial phase during solidification process. Moreover, the martensitic transformation rather than diffusion phase transformation occur during the cooling process due to the high cooling rates. As temperature decreases, the martensitic transformation starts at Ms and finishes at Mf, the martensite start and martensite finish temperatures, respectively. The volume fractions of martensite (fM) phase can be given by K-M equation [30]: f M ¼ 1−f γ0 ΦðT Þ 1; T ≥M s ΦðT Þ ¼ expð−0:011 ðMs −T ÞÞ; Tb M s
in which f γ0 is the initial austenitic volume percentage, and f γ0 ΦðTÞ is the proportion of austenitic at a given temperature T. When a new layer of material is deposited, the previously deposited material undergoes a new thermal cycle. Once the rising temperature is higher than Ac1, the transformation of martensite to austenite takes place. It is presently assumed that the initial and final austenitic ratio 0 is f γ0 and 100% when the temperature rise up to Ac1 and Ac3, respectively; the percentage of austenite phase increase linearly as temperature rise. 0
f γ ¼ f γ0 ðT−Ac1 Þ=ðAc3 −Ac1 Þ
2. Experiments and establishment of the FE model 2.1. Experiments A 6-axis robot equipped with continuous wave IPG fiber laser (4 kW, wavelength 1070 nm) was employed to fabricate the sample. The laser beam energy density was uniformly distributed of which the wavelength was 1070 nm. The parameters used for the process were: power of 2000 W with a defocused laser spot of 3 mm, overlapping rate of 50%, speed of 10 mm/s and powder flow rate of 29.5 g/min. The alloy powder used in the present experiment was martensitic stainless steel with the nominal chemical composition of 16 wt.% Cr-4.5 wt.%
ð1Þ
Fig. 1. Evolution of volume fraction of austenite during phase transformation.
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Once the temperature is lower than Ms, austenite will partially or totally transform into martensite during the subsequent cooling period. The martensite tempering and formation of interdendritic eutectic phases during solidification are neglected. Experiments have been carried out to obtain the thermal and mechanical material properties used in the present research as shown in Figs. 2, 3 and 4. The mechanical properties of most materials are both temperature and history (microstructure) dependent. The free dilatometry test enabled us to determine the thermomechanical characteristics, as shown in Fig. 5. With regard to the deposited material, we obtained from the tests the following characteristics: RT = 7 × 10−3, Ms = 200 °C, Mf = 30 °C, Ac1 = 630 °C, Ac3 = 850 °C. Δεαγ RT Δεαγ is the compactness variation between austenite and martensite phases at room temperature. If the high tensile stress characteristic of the LMPD process is taken into consideration, martensitic transformation will take place between Ms and Md. Based on the experiment investigation, the influence of stress upon martensitic transformation characteristic temperature is taken into account by making Mf and Ms equal to 150 °C and 310 °C, respectively. The Ac1 and Ac3 are marked up to 830 °C and 1050 °C, respectively, due to the high heating rate during the LMPD process [19]. RT are With regard to the base material, the Mf , Ms, Ac1, Ac3 and Δεαγ −3 60 °C, 185 °C, 630 °C, 850 °C and 7.0 × 10 , respectively. The influences of high temperature change rate upon Ac1 and Ac3 are taken into account.
Fig. 3. Thermal coefficient of expansion of the base meterial and cladding material.
σγy). However, the magnitude of principal stress is very high during LMPD process. Thus, the formulation can be extended as [23,32]: ΔεTrp ¼ −
eq 2Δε αγ σ ln ð f M ÞΔf M q Si j σy σ yγ εeff γ
ð5Þ
Where,
2.3. Constitutive relation To accurately predict stresses in LMPD, the constitutive equation for the state of material and loading condition during LMPD process must be obtained. The total strain increment Δε can be split into strain due to elastic ΔεE, plastic ΔεP, thermal loading ΔεT, volumetric change ΔεΔV and TRIP ΔεTrp, respectively [30,31]. Δε ¼ ΔεE þ Δε P þ Δε T þ Δε Trp þ Δε ΔV
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eq eq σ σ 1 ¼ 1 þ 3:5 q − y y σ σ 2
ð6Þ
ð3Þ
According to the classical work of Fisher [23], Leblond [32,33] and Inoue [34,35], the incremental TRIP can be written as: ΔεTrp ¼ −
2Δεαγ ln ð f M ÞΔf M Si j σ yγ εeff γ
ð4Þ
Δεαγ is the difference of thermal strain between the martensite and austenite, fM is the volume proportion of the product phase, σγy(εeff γ ) is the yield stress of weaker phase considering linear isotropic hardening, Sij is the deviatoric part of the applied stress tensor. This equation is applicable to relatively low applied stresses (does not exceed about a half of
Fig. 2. Thermal conductivity and specific heat of the base material and cladding material.
Fig. 4. (a) Yield strength and Young modulus of the base metal; (b)Yield strength and Young modulus of the cladding material.
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Fig. 5. The free dilatometry test of the base material and cladding material.
σ eq is the Von Mises norm of stress, σ y is the yield stress of the α + γ phases. For the sake of simplicity, q(σ eq/σ y) is equal to 2 in the present work according to the result by Taleb et al. [25]. The effect of strain hardening on TRIP is taken into account by the term σγy(εeff γ ) [23]. ¼ σ yγ ðT Þ þ hεeff σ yγ εeff γ γ
ð7Þ
σγy is the yield stress of the austenitic phases, the influence of temperature on σγy is omitted, since the martensitic transformation occurs in a rather small temperature range. h is the strain hardening modulus of the austenitic phase, in this model, h = 2800 MPa [23]. εeff γ is the accumulative plastic strain caused by martensitic transformation, its general expression was given by Leblond [33]. For simplicity, hεeff γ is equal to 39 MPa [23]. Δεαγ ¼ α α −α γ ΔT−ΔεRT αγ
ð8Þ
RT αα, αγ and Δεαγ were obtained from free dilatometric test. In the RT present work, Δεαγ = 7 × 10−3. RT ≈ ΔV/3V is made here for simplicity, The assumption of Δεαγ ≈ Δεαγ since the Mf is closer to room temperature. The strain increment due to volume change in the course of the austenite transformation is neglected. The increment of the strain due to volumetric dilatation during martensitic transformation can be written as [32–35]:
ΔεΔV ¼
Fig. 6. Flow chart showing the residual stresses calculation procedure with phase transformation taken into consideration.
MARC was used in this study. Microstructure calculations and mechanical behavior were made using the external user subroutines. The birth-death element method was used to simulate the filling process of deposited powder. In the present work, the single-pass model is composed of 36120 elements with 41140 nodes, while the multi-pass model is composed of 46680 elements with 67880 nodes. Mesh independence studies were conducted prior to the final simulation results. The finer mesh did similar results for temperature and stress fields. The geometries of single-layer and multi-layer deposition model are shown in Fig. 7. The following settings are proposed in the presented model: (1) Thermal material properties (specific heat, heat conductivity) obtained during temperature-rise period is used in present
n o ΔV Δf M ¼ −0:011 f γ0 expð−0:011 ðM s −T ÞÞ ΔT ΔεV αγ 3V ð9Þ
Where fM is the martensite fraction, ΔT is the increment of temperature during cooling, ΔεVαγ∗ is the strain due to volume change with full martensite transformation. 2.4. Establishment of the FE model As we know, the LMPD process is described by a set of nonlinear coupled equations. The FE method is an available and convenient option for solving such a coupled equations problem. As shown in Fig. 6, prediction of phase transformation is obtained by the calculation result of temperature field, based on which the influence of phase transformation on material properties is defined. So, the temperature evolution, phase transformation and evolution of properties are adopted into the model of stress evolution. Mechanical material properties of every node in the elements are updated at the end of every increment step, which finished the preparation for the next increment step. The commercial code
Fig. 7. (a) Geometry of single-layer laser clad sample; (b) Geometry of multilayer laser clad sample.
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(2)
(3)
(4) (5) (6)
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research, one reason is that solid-state phase transformation has a limited contribution to temperature field, another reason is that it is easy to implement. Molten pool convection is simulated indirectly by elevated thermal conductivity coefficient (twice as large as that of room temperature) and the double ellipsoid heat source. Latent heat (283 J/g) is taken into consideration only when melting and solidification take place, since latent heats of solid-state phase transformations do not have a large effect [21]. The emissivity, ε is defined to be 0.5, and the convection coefficient, hc, is set at 30 W/m2K [36]. The deposition process is regarded as quasi-steady process, the materials are assumed isotropic. The initial temperature is room temperature (25 °C).
Experiments have been carried out to obtain the thermal and mechanical material properties used in the model.
3. Simulation and experiment results Fig. 8 shows the longitudinal (Z direction, along the laser travel) residual stress distribution under the condition of single-pass deposition. Three kinds of conditions are analyzed in comparation, two cases for phase transformation (one considering stresses) and one with no phase transformation at all. The stress distribution is almost the same in the area away from the clad bead. For the case with phase transformation considered, the stresses are obviously lower in the clad bead and the adjacent area. Moreover, the stresses are even lower in the interface between the cladding and substrate than that in the clad bead. The maximum tensile stress is observed at about 3 mm from the surface of the clad bead. This may be because of there is no solid-state phase transformation in this area during LMPD process, since the maximum temperature is colder than AC1; the tensile stresses gradually decrease and turn to compressive stresses as the distance increase. When the phase transformation is ignored, the residual stresses in the clad bead are close to the yield strength; the maximum tensile stress is found in the interface between the substrate plate and the clad bead; the tensile stresses decrease and turn to compressive stresses as the distance to the clad bead increase. In addition the maximum compressive stress is shown to be higher when the phase transformation is ignored. When the phase transformation are taken into account, the case with and without stress effect taken into consideration show similar characteristics. But the influence of stress seems to reduce the magnitude of the longitudinal stresses.
Fig. 9. Comparison of longitudinal stress at midpoint of single-layer laser clad sample with, without phase transformation and with the stress influence.
Figs. 9 and 10 show the evolution of longitudinal (Z direction) and transverse (X direction, parallel to top surface of substrate) residual stresses for the midpoint (41077 node) of the clad bead. Three kinds of cases are analyzed in comparation. The numeric simulation results are compared with the test results. When the phase transformation is ignored, the residual longitudinal stress is almost equal to the yield strength with the transverse residual stress of about 192 MPa. When the phase transformation is considered, the maximum longitudinal stress is close to 600 MPa, gradually decreased as the temperature decreased, and finally stabilized at about 200 MPa. The transverse residual stress is lower than 100 MPa. When the stress influence is considered, the residual longitudinal stress is closer to the experimental results (394 MPa) than the other two cases. Generally, phase transformation have an obvious effect on the residual stresses and make it comparatively lower giving birth to a more accurate simulation result. Further discussions can be carried out with the help of temperature evolution. Fig. 11 shows temperature evolution of the midpoint (41077 node) in the single-pass model. The laser spot reached this point at the 3rd second resulting to a molten pool of 1833 °C, which is consistent with the experimental value (1760 °C). Tensile stresses are produced as the laser spot passed. When phase transformation is taken into consideration, both the stress increasing speed and the maximum stress are limited by the strength of austenite phase. The temperature dropped to 200 °C at 8.7 s. Then the longitudinal stress reached the maximum; solid-state phase transformation started leading to the release of tensile stresses, which resulted in the decline of the longitudinal stresses and the discounted increasing speed of transverse stresses to the final
Fig. 8. Comparison of longitudinal stress distribution in cross-section of single-layer laser clad sample: (a) without phase transformation; (b) with phase transformation; (c) with the stress influence.
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Fig. 10. Comparison of transverse stress at midpoint of single-layer laser clad sample with, without phase transformation and with the stress influence.
Fig. 12. Comparison of longitudinal stress at the midpoint of the sample over the depth with, without phase transformation and with the stress influence.
value. Considerable contrasts can be found as phase transformation is ignored including the sharply increase stress and the delay growth. The increasing speed is decreased after the 10th second and reached the stable value finally. When the stress influence is considered, the Ms is marked up to 310 °C. The longitudinal stress reached the maximum at 7 s. The results imply that lower Ms lead to smaller residual stress. The residual longitudinal stress distribution along depth in the single-pass deposited sample is shown in Fig. 12. Three kinds of conditions are analyzed in comparation. When the phase transformation is ignored, the residual stresses in the deposited layer and the interface between the substrate plate and the deposited layer are indicated to be comparatively higher and close to the yield strength of the material. The stresses gradually decrease as the distance from the top point increase. The stresses turn to be zero at 4 mm away from the top point and change to be compressive stresses when the distance exceeded 4 mm. When the phase transformation is considered, the stress in the interface between the deposited layer and the substrate plate is only 20% of the yield strength. The tensile stresses gradually increase as the distance from the top point increase and reach the peak value close to the yield strength with the depth of 3 mm. The stresses start to decrease and transfer to compressive stresses with the continuously increase distance, which show the same evolution process as the phasetransformation-ignored condition with the neglectable difference of lower stress value. The residual longitudinal stress distribution along the symmetric line in the upper surface of the single-pass deposited sample is shown in Fig. 13. Three kinds of cases are analyzed in comparation. Consistent
residual regularity is indicated by the stress distribution in the area further than 3 mm away from the center of the clad bead. However, the residual stresses are comparatively lower with phase transformation considered in the area within 3 mm from the weld center. The stress is lower than 100 MPa in the clad center. Compressive stresses gradually increase as the distance from the clad bead center increase and approach the peak at the boundary of the clad bead. Then the stresses transfer from tensile state to compressive state and approach the peak at the area of about 2.5-3 mm away from the clad bead center. When phase transformation is ignored, the stress is maximum at the clad bead center and close to the yield strength; the residual stress is about 500 MPa which is comparatively lower at the boundary of the clad bead; it increase to about 1000 MPa at the area about 3 mm away from the clad bead center; the residual stresses remain low compressive stresses and gradually decrease as the distance from the weld center increase. When the stress influence is considered, the stresses are slightly lower in the clad bead and the adjacent area. With respect to multi-pass LMPD process, complexity is introduced by thermal cycling and solid-state phase transformation. The stress evolutions of multi-pass LMPD process (Fig. 7, two layers, eight passes) are predicted by the numerical simulation. The longitudinal and transverse stress evolutions at the midpoint (40233 node) of the first pass are shown in Figs. 14 and 15, respectively. The predicted stress evolutions under three conditions are provided together with the experimental results of residual stresses. The longitudinal residual stress is about 1100 MPa with phase transformation ignored, while it is just about 253 MPa with phase transformation considered. The measured residual longitudinal stress is 390 MPa. When the stress influence is considered,
Fig. 11. Temperature variation at midpoint of single-layer laser clad sample.
Fig. 13. Comparison of longitudinal stress over the midperpendicular with, without phase transformation and with the stress influence.
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decreasing of temperature, and lead to a larger decrease of stresses. During the fifth pass of cladding, the rising temperature is higher than austenitizing temperature, the transformation of martensite to austenite takes place. When the stress influence is ignored, there is no solidstate phase transformation at all before the final cladding, since no change in phase until the temperature dropped to 200 °C. 4. Discussion
Fig. 14. Comparison of longitudinal stress at the midpoint of the first pass of muti-layer laser clad sample with, without phase transformation and with the stress influence: (a) the first fifty six seconds; (b) 1100 seconds.
the longitudinal residual stress is about 296 MPa, closer to the experimental data. The measured residual transverse stress is about 168 MPa, closer to the simulated result with phase transformation considered. There is no significant difference in the magnitude of the residual stresses between the two simulation results, with and without stress influence. However, the evolution of stresses is very different in two different situations. This is mainly because of the phase transformation temperature becoming higher, when the stress influence is taken into account. Thus, before the second pass of cladding, the stress assisted or strain induced martensitic transformation take place with the
Fig. 15. Comparison of transverse stress at the midpoint of the first pass of muti-layer laser clad sample with, without phase transformation and with the stress influence.
Better correspondence to the experimental results can be obtained from the prediction model when phase transformation is taken into consideration. However, the prediction accuracy can be further improved because of the following reasons. Firstly, the influences of stress upon starting and ending temperature of martensitic transformation are taken into account in the presented research. Also, the effect of high magnitude stress on TRIP is taken into consideration. However, the influences of stress on phase transformation are extremely complex. In this work, the contribution of Magee effect [23,37] to TRIP is ignored for the sake of simplicity. However, the preferred orientations of the martensite plate have been observed in our previous work. It means that the Magee effect is also very important in LMPD process. This effect is neglected by the existing models to the best of our knowledge. In the future work, further investigation is necessary to deal with the coupled problem between the stress and solid-state phase transformation. Secondly, it is difficult to get accurate high-temperature material properties, meaning the inevitable inaccuracy of the tested value. For example, the samples should be heated above Ac3 temperature and cooled to the test temperature when the properties of the material after austenization are tested within Ms and Ac1 temperature. According to the TEM microstructure of the tested samples, the intergranular eutectic phase in the testes samples is spheroidized to a small extent, besides of the appearance of nano-precipitation phase in matrix. The differences of microstructure inevitably lead to differences in properties. Thirdly, as to austenitization, this model assumes that the percentage of austenite phase increased linearly with the increasing temperature, the kinetics of austenitization [38] has been neglected. Moreover, the Ac1 and Ac3 are considered to be constant in the present work, although they depend both on the heating rate and the initial microstructure [39]. Fourthly, accurate measurement of residual stresses is still very difficult. The error is comparatively small when the tested stress is high. But the stress may be so small that the error get close to or exceed the true residual stress when the residual stress is low enough. In the present model, the results reveal that phase transformation can lead to a lower residual stresses, which can reasonably be expected. During the LMPD process, the stresses are strongly limited by mechanical material parameters (yield stress, hardening parameters, etc.) of high temperature phase before the formation of martensite. The high temperature phase (austenite) is the weaker phase. With the decreasing of temperature, the stresses assisted or strain induced martensitic transformation take place. The density change and TRIP lead to a larger decrease of stresses. Sometimes phase transformation even resulted in formation of compressive residual stresses. It is worth mentioning that the residual stresses are slightly lower when the transformation temperature is reduced. This result is reasonable, since the martensite is so tough that there is a less relaxation of stresses by plastic strain, while volume expansion due to phase transformation is larger at lower temperature. What have been discussed above show the potential of controlling phase transformation to minimize the residual stresses in LMPD process. Theoretically, the residual stresses of deposits can be controlled and minimized to a low level, if the martensitic transformation in LMPD is controlled to take place at certain temperature and timespace domain. It can be achieved by optimizing process parameters
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and adjusting chemical composition of clad material. Practically the complexity is extremely high. To implement this task, it is essential to reveal the evolution laws of stress by quantitative simulation under different processing conditions and different material composition. 5. Conclusions In this work, a FE model considering solid-state phase transformation has been developed to simulate the stresses during LMPD. The model reported in this work includes several improvements, which help to improve the predication accuracy of residual stresses. This model can be applied to multi-pass LMPD process, since the phase transformations induced by the new thermal cycles, when a new layer of material is deposited, are considered. The nonlinearity of the TRIP versus the high magnitude stress is taken into account. Also, the influence of stress upon martensitic transformation characteristic temperature is taken into consider by setting Ms and Mf equal to 310 °C and 150 °C, respectively. In addition, the thermal and mechanical material parameters used in the presented model are obtained by experiments. As we know, the reliability of the temperature and process history dependent material properties is one of the most crucial problems in computational welding mechanics. The presented study reveals that phase transformation has a significant influence on the stress evolution. Taking phase transformation into consideration can assure a better accuracy in predicting the residual stresses. The influence of stress upon martensitic transformation characteristic temperatures is not ignorable. The residual stresses become smaller when the phase transformation temperature is reduced. In the present work, martensitic transformation has a major affect in reducing the residual stresses (especially longitudinal stresses) in LMPD. The presented work show the potential of residual stresses control during LMPD or welding by phase transformation, though further research is essential. Acknowledgements This work was financially supported from 973 Project of China, No. 2011CB013403. The authors thank Fengyuan Shu for his great help in finite element simulation and Pengfei Zhao for his assistance in experiments.
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Materials and Design journal homepage: www.elsevier.com/locate/jmad
The effects of solid-state phase transformation upon stress evolution in laser metal powder deposition J.X. Fang a,b, S.Y. Dong b, Y.J. Wang b, B.S. Xu a,b, Z.H. Zhang a,b, D. Xia b, P. He a,⁎ a b
State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, Harbin 150001, China National Key Laboratory for Remanufacturing, Academy of Armored Forces Engineering, Beijing, 100072, China
a r t i c l e
i n f o
Article history: Received 8 May 2015 Received in revised form 11 August 2015 Accepted 14 August 2015 Available online 22 August 2015 Keywords: Laser metal powder deposition Residual stress Finite element analysis Martensitic transformation transformation induced plasticity
a b s t r a c t To investigate the influences of solid-state phase transformation on stress evolution during multi-pass laser metal powder deposition (LMPD) process, a 3D finite-element (FE) thermo-mechanical model considering phase transformation has been established. The influences of phase transformation such as mechanical properties changes, volume change and transformation induced plasticity (TRIP) are taken into account. Furthermore, the influences of high magnitude stress upon martensitic transformation characteristic temperature and TRIP are considered. The temperature and history (microstructure) dependent material properties used in the present research are obtained by experiments. The stress field during LMPD process is analyzed with and without solidstate phase transformation, respectively. Stress measurement of X-ray diffraction (XRD) method is applied to deposited samples, and the measuring data are compared with the computational predictions. The results show that phase transformation has a dominant effect on the stress evolution, longitudinal residual stresses significantly reduced as a result of solid-state phase transformation. In addition, the effect of stresses on martensitic transformation temperature is important for accurate prediction of residual stresses (stress state after cooling of the clad to ambient temperature). Residual stresses are lower when the phase transformation temperature is reduced. © 2015 Published by Elsevier Ltd.
1. Introduction Residual stress is one of the major issues affecting the large-scale commercial applications of laser metal powder deposition (LMPD). The complex thermal cycling of the process unavoidably relates to the evolution of stresses and strains and lead to cracks and distortion. Moreover, the magnitude and distribution of residual stresses may strongly influence the service behaviors, for example, the tensile residual stresses are often considered to reduce the strength of the material, induce stress corrosion and short the fatigue life [1–6]. Therefore, a valid approach to control the residual stresses is one of the most crucial problems to be solved in LMPD [7]. Using high-precision prediction calculation methods can assist in mitigating stress peaks and rearrange the stress distribution in favor of the product’s usage. Similar to ordinary welding process, the LMPD process parameters and material properties are the main factors affecting the evolution of stresses. With regard to some materials, phase transformation take place and greatly influence stress evolution during LMPD process. For example, the martensitic transformation in ferrous materials is often ⁎ Corresponding author at: State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, Harbin 150001, China. E-mail address: [email protected] (P. He).
http://dx.doi.org/10.1016/j.matdes.2015.08.061 0264-1275/© 2015 Published by Elsevier Ltd.
accompanied by the change of mechanical properties, volume growth and TRIP, etc., which will profoundly influence the development of residual stresses [8,9]. In order to improve the accuracy of predicting the residual weld stresses and strain, it has become the research focus for years to adopt the microstructure transformation effects into the weld thermal-mechanical simulation models [10–19]. Ghosh and Choi [10,11] have established a thermal-mechanicalmicrostructural model in which the effects of phase transformation are taken into account. It is found that stress evolution is sensitive to phase transformation. Phase transformation lead to the reduction of tensile stresses and even the emergence of compressive stresses. This model is very valuable. However, it can be improved because it is merely applied to single-pass welds, since it does not consider phase transformation induced by a new weld pass. Dean Deng et al. [13] have established a thermal-mechanical FE model. In his model, volume change as a result of martensitic transformation, mechanical properties variation due to microstructure change and TRIP have been take into account. It is concluded that the influence of phase transformation on welding residual stresses is important, the effect of TRIP should also be considered for accurate prediction of residual stresses. Lee and Chang [14,15] have developed a finite element model to predict the residual stresses of high carbon steel butt weld. The results show that phase transformation has significant effect on longitudinal tensile residual stresses due to volume change. In fact, many other valuable FE
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models considering phase transformation have been established by Ferro et al. [16], Wang and Felicelli [17], Shirish et al. [18], in the past few years. However, these models are similar as the model proposed by Ghosh and Choi, they do not consider phase transformation induced by the following weld pass. A thermal-kinetic model has been presented by Costa et al. [19,20] to simulate temperature field and microstructure in parts of AISI 420 tool steel built by LMPD. The effect of solid-state phase transformation upon temperature field is considered. This model can be applied to multi-pass weld and LMPD process, since the solid-state phase transformations induced by the thermal cycles are considered when a new layer of material is deposited. However, this model does not address the stress problem. Borjesson and Lindgren [21] have developed a valuable FE model to predict the residual stresses of multi-pass butt welding. But this two dimensions model can be extended to three dimensions. Residual stresses have been calculated and measured by Becker et al. [22] for multi-pass girth welds including post-weld heat treatment. However, the physical processes and computational process are only briefly detailed. In addition, the kinetic model of solid-state phase transformation and constitutive model considering phase transformation are the foundation for accurate prediction of stresses. The study of these nonlinear and strongly coupling problems continues to be a very active field [23–26], and further discussions on these subjects are essential. For example, the effects of stress on martensitic transformation are extremely complex, and the influence becomes significant under high magnitude stress [24,25]. TRIP increases very quickly when the tensile stresses exceed about a half of yield stress of high temperature phase. And it is well known that the magnitude of principal stresses is almost close to the yield strength of the clad material at certain temperature during LMPD process. As mentioned in the classical work by Francis et al. [27], however, the existing models of computational welding mechanics do not take into consider the nonlinearity of the TRIP versus the high magnitude stress. Moreover, the martensite starting and ending temperatures can be significantly influenced by high magnitude stress [28,29]. With regard to the material used in the present work, martensite start temperatue (Ms) can be increased by about 200 °C by stress comparable to the yield strength of austenite. Based on the above discussions, although considerable progress has been made to predict the residual stresses during welding or LMPD process, there are much left to do. In the present research, a FE model considering solid-state phase transformation has been developed to simulate the stress field during single-pass and multi-pass LMPD process. Not only the dependence of mechanical properties (yield strength) on phase volume fractions and temperature, but also the volume change and TRIP are taken into consideration. Furthermore, the influences of high magnitude stress upon TRIP and martensitic transformation characteristic temperatures are taken into account. The thermal and mechanical material parameters used in the present research are obtained by experiments. The stress fields of both single-pass and multi-pass LMPD process are predicted by the numerical simulation. The numerical results are validated by the experimental residual stress distributions of the XRD method.
Ni-1.6 wt.% Mo-0.9 wt.% B-0.6 wt.% Mn-0.12 wt.% C. The particle size range of the powders was 45–100 μm. The wrought FV520 (B) plates with the size of 6 mm × 40 mm × 60 mm were used as substrate. Three single-pass samples and three multi-pass samples (Two layers, eight passes) were fabricated for residual stress tests. Two large bulks with the size of about 135 mm × 65 mm × 27 mm were made for the property parameters tests. XRD method was adopted for the residual stress measurement in which the XSTRESS3000 residual stress measuring instrument was used. Cobalt target was used in the present experiment. The residual stresses of the tested area were the average value of measurements. Specimens were cut from the large bulk to prepare for the property parameters tests. The high temperature properties with regard to material mechanics were obtained by an MTS810 mechanical testing machine according to the ASTME21-05 standard. Free dilatometric tests were carried out by DIL801 thermal expansion test instrument referring to Chinese National Standard of GB/T 4339–2008. The specific heat was obtained with Setaram Setsys Evo thermal analyzer according to the standard ASTME1269-11, while the thermal conductivity obtained with Netzsch LFA427 laser thermal conductivity meter according to the standard ASTME1461-11. 2.2. The process of solid-state phase transformation Fig. 1 is the schematic of phase transformation for the martensite stainless steel during the LMPD process [19]. Austenite is assumed to be the initial phase during solidification process. Moreover, the martensitic transformation rather than diffusion phase transformation occur during the cooling process due to the high cooling rates. As temperature decreases, the martensitic transformation starts at Ms and finishes at Mf, the martensite start and martensite finish temperatures, respectively. The volume fractions of martensite (fM) phase can be given by K-M equation [30]: f M ¼ 1−f γ0 ΦðT Þ 1; T ≥M s ΦðT Þ ¼ expð−0:011 ðMs −T ÞÞ; Tb M s
in which f γ0 is the initial austenitic volume percentage, and f γ0 ΦðTÞ is the proportion of austenitic at a given temperature T. When a new layer of material is deposited, the previously deposited material undergoes a new thermal cycle. Once the rising temperature is higher than Ac1, the transformation of martensite to austenite takes place. It is presently assumed that the initial and final austenitic ratio 0 is f γ0 and 100% when the temperature rise up to Ac1 and Ac3, respectively; the percentage of austenite phase increase linearly as temperature rise. 0
f γ ¼ f γ0 ðT−Ac1 Þ=ðAc3 −Ac1 Þ
2. Experiments and establishment of the FE model 2.1. Experiments A 6-axis robot equipped with continuous wave IPG fiber laser (4 kW, wavelength 1070 nm) was employed to fabricate the sample. The laser beam energy density was uniformly distributed of which the wavelength was 1070 nm. The parameters used for the process were: power of 2000 W with a defocused laser spot of 3 mm, overlapping rate of 50%, speed of 10 mm/s and powder flow rate of 29.5 g/min. The alloy powder used in the present experiment was martensitic stainless steel with the nominal chemical composition of 16 wt.% Cr-4.5 wt.%
ð1Þ
Fig. 1. Evolution of volume fraction of austenite during phase transformation.
ð2Þ
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Once the temperature is lower than Ms, austenite will partially or totally transform into martensite during the subsequent cooling period. The martensite tempering and formation of interdendritic eutectic phases during solidification are neglected. Experiments have been carried out to obtain the thermal and mechanical material properties used in the present research as shown in Figs. 2, 3 and 4. The mechanical properties of most materials are both temperature and history (microstructure) dependent. The free dilatometry test enabled us to determine the thermomechanical characteristics, as shown in Fig. 5. With regard to the deposited material, we obtained from the tests the following characteristics: RT = 7 × 10−3, Ms = 200 °C, Mf = 30 °C, Ac1 = 630 °C, Ac3 = 850 °C. Δεαγ RT Δεαγ is the compactness variation between austenite and martensite phases at room temperature. If the high tensile stress characteristic of the LMPD process is taken into consideration, martensitic transformation will take place between Ms and Md. Based on the experiment investigation, the influence of stress upon martensitic transformation characteristic temperature is taken into account by making Mf and Ms equal to 150 °C and 310 °C, respectively. The Ac1 and Ac3 are marked up to 830 °C and 1050 °C, respectively, due to the high heating rate during the LMPD process [19]. RT are With regard to the base material, the Mf , Ms, Ac1, Ac3 and Δεαγ −3 60 °C, 185 °C, 630 °C, 850 °C and 7.0 × 10 , respectively. The influences of high temperature change rate upon Ac1 and Ac3 are taken into account.
Fig. 3. Thermal coefficient of expansion of the base meterial and cladding material.
σγy). However, the magnitude of principal stress is very high during LMPD process. Thus, the formulation can be extended as [23,32]: ΔεTrp ¼ −
eq 2Δε αγ σ ln ð f M ÞΔf M q Si j σy σ yγ εeff γ
ð5Þ
Where,
2.3. Constitutive relation To accurately predict stresses in LMPD, the constitutive equation for the state of material and loading condition during LMPD process must be obtained. The total strain increment Δε can be split into strain due to elastic ΔεE, plastic ΔεP, thermal loading ΔεT, volumetric change ΔεΔV and TRIP ΔεTrp, respectively [30,31]. Δε ¼ ΔεE þ Δε P þ Δε T þ Δε Trp þ Δε ΔV
809
eq eq σ σ 1 ¼ 1 þ 3:5 q − y y σ σ 2
ð6Þ
ð3Þ
According to the classical work of Fisher [23], Leblond [32,33] and Inoue [34,35], the incremental TRIP can be written as: ΔεTrp ¼ −
2Δεαγ ln ð f M ÞΔf M Si j σ yγ εeff γ
ð4Þ
Δεαγ is the difference of thermal strain between the martensite and austenite, fM is the volume proportion of the product phase, σγy(εeff γ ) is the yield stress of weaker phase considering linear isotropic hardening, Sij is the deviatoric part of the applied stress tensor. This equation is applicable to relatively low applied stresses (does not exceed about a half of
Fig. 2. Thermal conductivity and specific heat of the base material and cladding material.
Fig. 4. (a) Yield strength and Young modulus of the base metal; (b)Yield strength and Young modulus of the cladding material.
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Fig. 5. The free dilatometry test of the base material and cladding material.
σ eq is the Von Mises norm of stress, σ y is the yield stress of the α + γ phases. For the sake of simplicity, q(σ eq/σ y) is equal to 2 in the present work according to the result by Taleb et al. [25]. The effect of strain hardening on TRIP is taken into account by the term σγy(εeff γ ) [23]. ¼ σ yγ ðT Þ þ hεeff σ yγ εeff γ γ
ð7Þ
σγy is the yield stress of the austenitic phases, the influence of temperature on σγy is omitted, since the martensitic transformation occurs in a rather small temperature range. h is the strain hardening modulus of the austenitic phase, in this model, h = 2800 MPa [23]. εeff γ is the accumulative plastic strain caused by martensitic transformation, its general expression was given by Leblond [33]. For simplicity, hεeff γ is equal to 39 MPa [23]. Δεαγ ¼ α α −α γ ΔT−ΔεRT αγ
ð8Þ
RT αα, αγ and Δεαγ were obtained from free dilatometric test. In the RT present work, Δεαγ = 7 × 10−3. RT ≈ ΔV/3V is made here for simplicity, The assumption of Δεαγ ≈ Δεαγ since the Mf is closer to room temperature. The strain increment due to volume change in the course of the austenite transformation is neglected. The increment of the strain due to volumetric dilatation during martensitic transformation can be written as [32–35]:
ΔεΔV ¼
Fig. 6. Flow chart showing the residual stresses calculation procedure with phase transformation taken into consideration.
MARC was used in this study. Microstructure calculations and mechanical behavior were made using the external user subroutines. The birth-death element method was used to simulate the filling process of deposited powder. In the present work, the single-pass model is composed of 36120 elements with 41140 nodes, while the multi-pass model is composed of 46680 elements with 67880 nodes. Mesh independence studies were conducted prior to the final simulation results. The finer mesh did similar results for temperature and stress fields. The geometries of single-layer and multi-layer deposition model are shown in Fig. 7. The following settings are proposed in the presented model: (1) Thermal material properties (specific heat, heat conductivity) obtained during temperature-rise period is used in present
n o ΔV Δf M ¼ −0:011 f γ0 expð−0:011 ðM s −T ÞÞ ΔT ΔεV αγ 3V ð9Þ
Where fM is the martensite fraction, ΔT is the increment of temperature during cooling, ΔεVαγ∗ is the strain due to volume change with full martensite transformation. 2.4. Establishment of the FE model As we know, the LMPD process is described by a set of nonlinear coupled equations. The FE method is an available and convenient option for solving such a coupled equations problem. As shown in Fig. 6, prediction of phase transformation is obtained by the calculation result of temperature field, based on which the influence of phase transformation on material properties is defined. So, the temperature evolution, phase transformation and evolution of properties are adopted into the model of stress evolution. Mechanical material properties of every node in the elements are updated at the end of every increment step, which finished the preparation for the next increment step. The commercial code
Fig. 7. (a) Geometry of single-layer laser clad sample; (b) Geometry of multilayer laser clad sample.
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(2)
(3)
(4) (5) (6)
811
research, one reason is that solid-state phase transformation has a limited contribution to temperature field, another reason is that it is easy to implement. Molten pool convection is simulated indirectly by elevated thermal conductivity coefficient (twice as large as that of room temperature) and the double ellipsoid heat source. Latent heat (283 J/g) is taken into consideration only when melting and solidification take place, since latent heats of solid-state phase transformations do not have a large effect [21]. The emissivity, ε is defined to be 0.5, and the convection coefficient, hc, is set at 30 W/m2K [36]. The deposition process is regarded as quasi-steady process, the materials are assumed isotropic. The initial temperature is room temperature (25 °C).
Experiments have been carried out to obtain the thermal and mechanical material properties used in the model.
3. Simulation and experiment results Fig. 8 shows the longitudinal (Z direction, along the laser travel) residual stress distribution under the condition of single-pass deposition. Three kinds of conditions are analyzed in comparation, two cases for phase transformation (one considering stresses) and one with no phase transformation at all. The stress distribution is almost the same in the area away from the clad bead. For the case with phase transformation considered, the stresses are obviously lower in the clad bead and the adjacent area. Moreover, the stresses are even lower in the interface between the cladding and substrate than that in the clad bead. The maximum tensile stress is observed at about 3 mm from the surface of the clad bead. This may be because of there is no solid-state phase transformation in this area during LMPD process, since the maximum temperature is colder than AC1; the tensile stresses gradually decrease and turn to compressive stresses as the distance increase. When the phase transformation is ignored, the residual stresses in the clad bead are close to the yield strength; the maximum tensile stress is found in the interface between the substrate plate and the clad bead; the tensile stresses decrease and turn to compressive stresses as the distance to the clad bead increase. In addition the maximum compressive stress is shown to be higher when the phase transformation is ignored. When the phase transformation are taken into account, the case with and without stress effect taken into consideration show similar characteristics. But the influence of stress seems to reduce the magnitude of the longitudinal stresses.
Fig. 9. Comparison of longitudinal stress at midpoint of single-layer laser clad sample with, without phase transformation and with the stress influence.
Figs. 9 and 10 show the evolution of longitudinal (Z direction) and transverse (X direction, parallel to top surface of substrate) residual stresses for the midpoint (41077 node) of the clad bead. Three kinds of cases are analyzed in comparation. The numeric simulation results are compared with the test results. When the phase transformation is ignored, the residual longitudinal stress is almost equal to the yield strength with the transverse residual stress of about 192 MPa. When the phase transformation is considered, the maximum longitudinal stress is close to 600 MPa, gradually decreased as the temperature decreased, and finally stabilized at about 200 MPa. The transverse residual stress is lower than 100 MPa. When the stress influence is considered, the residual longitudinal stress is closer to the experimental results (394 MPa) than the other two cases. Generally, phase transformation have an obvious effect on the residual stresses and make it comparatively lower giving birth to a more accurate simulation result. Further discussions can be carried out with the help of temperature evolution. Fig. 11 shows temperature evolution of the midpoint (41077 node) in the single-pass model. The laser spot reached this point at the 3rd second resulting to a molten pool of 1833 °C, which is consistent with the experimental value (1760 °C). Tensile stresses are produced as the laser spot passed. When phase transformation is taken into consideration, both the stress increasing speed and the maximum stress are limited by the strength of austenite phase. The temperature dropped to 200 °C at 8.7 s. Then the longitudinal stress reached the maximum; solid-state phase transformation started leading to the release of tensile stresses, which resulted in the decline of the longitudinal stresses and the discounted increasing speed of transverse stresses to the final
Fig. 8. Comparison of longitudinal stress distribution in cross-section of single-layer laser clad sample: (a) without phase transformation; (b) with phase transformation; (c) with the stress influence.
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Fig. 10. Comparison of transverse stress at midpoint of single-layer laser clad sample with, without phase transformation and with the stress influence.
Fig. 12. Comparison of longitudinal stress at the midpoint of the sample over the depth with, without phase transformation and with the stress influence.
value. Considerable contrasts can be found as phase transformation is ignored including the sharply increase stress and the delay growth. The increasing speed is decreased after the 10th second and reached the stable value finally. When the stress influence is considered, the Ms is marked up to 310 °C. The longitudinal stress reached the maximum at 7 s. The results imply that lower Ms lead to smaller residual stress. The residual longitudinal stress distribution along depth in the single-pass deposited sample is shown in Fig. 12. Three kinds of conditions are analyzed in comparation. When the phase transformation is ignored, the residual stresses in the deposited layer and the interface between the substrate plate and the deposited layer are indicated to be comparatively higher and close to the yield strength of the material. The stresses gradually decrease as the distance from the top point increase. The stresses turn to be zero at 4 mm away from the top point and change to be compressive stresses when the distance exceeded 4 mm. When the phase transformation is considered, the stress in the interface between the deposited layer and the substrate plate is only 20% of the yield strength. The tensile stresses gradually increase as the distance from the top point increase and reach the peak value close to the yield strength with the depth of 3 mm. The stresses start to decrease and transfer to compressive stresses with the continuously increase distance, which show the same evolution process as the phasetransformation-ignored condition with the neglectable difference of lower stress value. The residual longitudinal stress distribution along the symmetric line in the upper surface of the single-pass deposited sample is shown in Fig. 13. Three kinds of cases are analyzed in comparation. Consistent
residual regularity is indicated by the stress distribution in the area further than 3 mm away from the center of the clad bead. However, the residual stresses are comparatively lower with phase transformation considered in the area within 3 mm from the weld center. The stress is lower than 100 MPa in the clad center. Compressive stresses gradually increase as the distance from the clad bead center increase and approach the peak at the boundary of the clad bead. Then the stresses transfer from tensile state to compressive state and approach the peak at the area of about 2.5-3 mm away from the clad bead center. When phase transformation is ignored, the stress is maximum at the clad bead center and close to the yield strength; the residual stress is about 500 MPa which is comparatively lower at the boundary of the clad bead; it increase to about 1000 MPa at the area about 3 mm away from the clad bead center; the residual stresses remain low compressive stresses and gradually decrease as the distance from the weld center increase. When the stress influence is considered, the stresses are slightly lower in the clad bead and the adjacent area. With respect to multi-pass LMPD process, complexity is introduced by thermal cycling and solid-state phase transformation. The stress evolutions of multi-pass LMPD process (Fig. 7, two layers, eight passes) are predicted by the numerical simulation. The longitudinal and transverse stress evolutions at the midpoint (40233 node) of the first pass are shown in Figs. 14 and 15, respectively. The predicted stress evolutions under three conditions are provided together with the experimental results of residual stresses. The longitudinal residual stress is about 1100 MPa with phase transformation ignored, while it is just about 253 MPa with phase transformation considered. The measured residual longitudinal stress is 390 MPa. When the stress influence is considered,
Fig. 11. Temperature variation at midpoint of single-layer laser clad sample.
Fig. 13. Comparison of longitudinal stress over the midperpendicular with, without phase transformation and with the stress influence.
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decreasing of temperature, and lead to a larger decrease of stresses. During the fifth pass of cladding, the rising temperature is higher than austenitizing temperature, the transformation of martensite to austenite takes place. When the stress influence is ignored, there is no solidstate phase transformation at all before the final cladding, since no change in phase until the temperature dropped to 200 °C. 4. Discussion
Fig. 14. Comparison of longitudinal stress at the midpoint of the first pass of muti-layer laser clad sample with, without phase transformation and with the stress influence: (a) the first fifty six seconds; (b) 1100 seconds.
the longitudinal residual stress is about 296 MPa, closer to the experimental data. The measured residual transverse stress is about 168 MPa, closer to the simulated result with phase transformation considered. There is no significant difference in the magnitude of the residual stresses between the two simulation results, with and without stress influence. However, the evolution of stresses is very different in two different situations. This is mainly because of the phase transformation temperature becoming higher, when the stress influence is taken into account. Thus, before the second pass of cladding, the stress assisted or strain induced martensitic transformation take place with the
Fig. 15. Comparison of transverse stress at the midpoint of the first pass of muti-layer laser clad sample with, without phase transformation and with the stress influence.
Better correspondence to the experimental results can be obtained from the prediction model when phase transformation is taken into consideration. However, the prediction accuracy can be further improved because of the following reasons. Firstly, the influences of stress upon starting and ending temperature of martensitic transformation are taken into account in the presented research. Also, the effect of high magnitude stress on TRIP is taken into consideration. However, the influences of stress on phase transformation are extremely complex. In this work, the contribution of Magee effect [23,37] to TRIP is ignored for the sake of simplicity. However, the preferred orientations of the martensite plate have been observed in our previous work. It means that the Magee effect is also very important in LMPD process. This effect is neglected by the existing models to the best of our knowledge. In the future work, further investigation is necessary to deal with the coupled problem between the stress and solid-state phase transformation. Secondly, it is difficult to get accurate high-temperature material properties, meaning the inevitable inaccuracy of the tested value. For example, the samples should be heated above Ac3 temperature and cooled to the test temperature when the properties of the material after austenization are tested within Ms and Ac1 temperature. According to the TEM microstructure of the tested samples, the intergranular eutectic phase in the testes samples is spheroidized to a small extent, besides of the appearance of nano-precipitation phase in matrix. The differences of microstructure inevitably lead to differences in properties. Thirdly, as to austenitization, this model assumes that the percentage of austenite phase increased linearly with the increasing temperature, the kinetics of austenitization [38] has been neglected. Moreover, the Ac1 and Ac3 are considered to be constant in the present work, although they depend both on the heating rate and the initial microstructure [39]. Fourthly, accurate measurement of residual stresses is still very difficult. The error is comparatively small when the tested stress is high. But the stress may be so small that the error get close to or exceed the true residual stress when the residual stress is low enough. In the present model, the results reveal that phase transformation can lead to a lower residual stresses, which can reasonably be expected. During the LMPD process, the stresses are strongly limited by mechanical material parameters (yield stress, hardening parameters, etc.) of high temperature phase before the formation of martensite. The high temperature phase (austenite) is the weaker phase. With the decreasing of temperature, the stresses assisted or strain induced martensitic transformation take place. The density change and TRIP lead to a larger decrease of stresses. Sometimes phase transformation even resulted in formation of compressive residual stresses. It is worth mentioning that the residual stresses are slightly lower when the transformation temperature is reduced. This result is reasonable, since the martensite is so tough that there is a less relaxation of stresses by plastic strain, while volume expansion due to phase transformation is larger at lower temperature. What have been discussed above show the potential of controlling phase transformation to minimize the residual stresses in LMPD process. Theoretically, the residual stresses of deposits can be controlled and minimized to a low level, if the martensitic transformation in LMPD is controlled to take place at certain temperature and timespace domain. It can be achieved by optimizing process parameters
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and adjusting chemical composition of clad material. Practically the complexity is extremely high. To implement this task, it is essential to reveal the evolution laws of stress by quantitative simulation under different processing conditions and different material composition. 5. Conclusions In this work, a FE model considering solid-state phase transformation has been developed to simulate the stresses during LMPD. The model reported in this work includes several improvements, which help to improve the predication accuracy of residual stresses. This model can be applied to multi-pass LMPD process, since the phase transformations induced by the new thermal cycles, when a new layer of material is deposited, are considered. The nonlinearity of the TRIP versus the high magnitude stress is taken into account. Also, the influence of stress upon martensitic transformation characteristic temperature is taken into consider by setting Ms and Mf equal to 310 °C and 150 °C, respectively. In addition, the thermal and mechanical material parameters used in the presented model are obtained by experiments. As we know, the reliability of the temperature and process history dependent material properties is one of the most crucial problems in computational welding mechanics. The presented study reveals that phase transformation has a significant influence on the stress evolution. Taking phase transformation into consideration can assure a better accuracy in predicting the residual stresses. The influence of stress upon martensitic transformation characteristic temperatures is not ignorable. The residual stresses become smaller when the phase transformation temperature is reduced. In the present work, martensitic transformation has a major affect in reducing the residual stresses (especially longitudinal stresses) in LMPD. The presented work show the potential of residual stresses control during LMPD or welding by phase transformation, though further research is essential. Acknowledgements This work was financially supported from 973 Project of China, No. 2011CB013403. The authors thank Fengyuan Shu for his great help in finite element simulation and Pengfei Zhao for his assistance in experiments.
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