Macro-micro residual stress prediction and hot cracks formation mechanism during laser melt injection processing of ZrO2 particles into Ti6Al4V substrate

doi:10.21203/rs.3.rs-1534149/v1

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Macro-micro residual stress prediction and hot cracks formation mechanism during laser melt injection processing of ZrO2 particles into Ti6Al4V substrate

https://doi.org/10.21203/rs.3.rs-1534149/v1

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Laser melt injection (LMI) is a promising technology to produce ceramic particles reinforced metal matrix composites (MMCs) to achieve surface modification and performance upgrading. In this paper, the LMI process was conducted on Ti6Al4V substrate with ZrO₂particles (ZrO_2p) to produce functionally graded material for heat insulation. The track dimensions, particle distribution, and crack morphology of the MMC layer were studied, corresponding to varying laser power, and scanning velocity. The optical morphologies showed all outlines of MMC were in the shape of a lower lip, and there were cracks in the MMC layer. When the linear energy was lower than 6.0×10³J/m, the thickness of the MMC layer was under 0.4 mm, and the zirconia particles filled up the entire MMC layer. Then, a novel finite element model was proposed to calculate the thermal-mechanical characteristics during the LMI process, in both macro and micro scales, to expound on the crack formation mechanism. The simulated results showed that the distribution and volume fraction of ZrO_2p greatly influenced the magnitude and distribution of macro and micro residual stress. For the three LMI macro models, the transversal tensile stress was mainly located in the middle segment with 350 MPa. The longitudinal stress at the start and end of the top surface was close to 0 MPa, and the entire MMC layer was almost tensile stress. Besides, the most considerable transversal stress was spread over the heat affect zone, but the most significant longitudinal stress was distributed on the MMC top surface. The two-dimension micro-scale models revealed the residual stress distributed remarkably uniformly in the ZrO₂ particles, and the stress values were more significant than those of the Ti6Al4V substrate. Moreover, the particle spacing was more extensive, and the stress between particles got more significant with the volume fraction of ZrO_2p. In this study, the largest micro longitudinal stress was 891 MPa between particles C1 and C2, the location with the minor transverse stress with 561 MPa. Further, due to the solidification shrinkage of the metal, the ZrO_2p prevented the displacement of Ti6Al4V metal dislocation, which contributed to generating stress concentration points on the surface of ZrO_2p. At the same time, the gaps caused between the Ti6Al4V matrix and the ZrO_2p surface also provided the conditions for the formation of microcracks. Larger cracks would be generated after lots of microcracks were gathered.

laser melt injection

metal matrix composites

ZrO2p

residual stress

crack formation mechanism

The laser melt injection (LMI) process has been widely used in industry to reinforce the surface performances of metals, such as hardness, wear resistance, oxidation resistance, and heat insulation [1]. In this process, a specially modulated laser beam with reduced power density partially melts the top surface of the metal substrate while injecting additive-enhanced particles into the liquid metal pool via a stream of inert gas. Particles can be embedded in the metal after the rapid solidification of a laser-treated track, and a surface coating of metal-matrix composites (MMCs) can be achieved [2]. With the advantages of good controllability, limited interaction area, micro matrix damage, and complex shape adaptation, LMI has been considered another promising technique for surface modification and performance upgrading of conventional materials like magnesium[3], aluminum [4], steel[5][6][7] and titanium[8].

The titanium alloys processed by LMI with ceramic phases can yield functionally graded materials (MMC layers) with desirable surface capacities, high specific strength, toughness, good corrosion, and creep resistance. Due to the low laser reflectivity, the LMI of Ti alloys has an extensive process window and a wide choice of ceramic particles, e.g., carbides, nitrides, and oxides, sized from nanoscale to a micron order.

Pei et al. [9] produced the SiC_p/Ti6Al4V MMC layers by LMI and demonstrated the formation mechanism based on finite element calculations and experimental observations. The results showed that the positioning of the power stream behind the laser beam (without overlap) allowed for a graded distribution of SiCp and a limited reaction layer surrounded and, therefore, the crack-free MMC layer coatings.

Vreeling et al. [10] explored the macro dimensions, microstructure, and properties of the WC_p/Ti MMC layer created by the LMI process based on a Ti6Al4V substrate. A typical laser track with a lower crack tendency is about 1.8 mm at the width and 0.7 mm at depth. The WC particles inside were in a homogeneous distribution with a volume fraction of 0.25–0.3. The additive coatings result in a substantial improvement of wear resistance at the same contact stress.

Ocelík et al. [11] found the intergranular crack of the conventional WC_p/Ti6Al4V system could be eliminated by using single-crystal ceramic particles during the LMI process. Li et al. [12] investigated the preparation of WC_p/Ti6Al4V layers using single-crystal WC particles. Firstly, a new W layer in the WCp/Ti reaction zone is observed, which can suppress further interfacial reactions. The tensile strength of the MMC layer was increased by 17% compared to the granular WC_p composite.

The ZrO₂ has low thermal conductivity, good thermal stability, and high thermal resistance against the metallic matrix, which has been considered an ideal ceramic phase to prepare the thermal barrier coatings based on titanium alloy matrix. The ZrO₂/Ti MMC layers, with heat protection and bearing function, have broad application prospects in various industrial manufacturing fields. However, compared to SiC_p/Ti and WC_p/Ti MMC layers, preparing ZrO_2p/Ti system via LMI is more challenging. The main problem is the hot crack occurring at ZrO_2p/Ti interface and Ti substrate, which can be easily caused by matrix alloying, rapid heating/cooling, and thermal stress mismatching. The solutions, including optimizing the injection position and reducing the heat input, can be helpful but fail to eliminate the cracks, especially in large-area MMCs coatings with multi-laser tracks overlapped. Accordingly, few literatures focus on ZrO₂/Ti LMI processing and representation. Recently, Zhao et al. [13]conducted the modeling and simulation of the dynamic process during LMI of ZrO_2p/Ti6Al4V. They revealed that the interactions between planted particles and molten metal largely determine the track dimensions and the internal ZrO_2p distribution. However, neither calculations on stain-stress behavior nor hot crack formation mechanism were reported in work.

In this paper, the ZrO₂ ceramic powder was implanted into the top surface of the Ti6Al4V substrate using the LMI method. The MMCs dimensions and ZrO_2p distribution under specific process parameters were discussed, and the features were extracted. To quantitatively study the thermal stress mismatching phenomenon in both macro (MMC layers structure) and micro (surrounding the particle) scales, the whole and local distributions of stress were calculated and analyzed concerning different laser power and scanning velocity.

A micro-scale finite element model with different volume fractions of the injected particles was designed to analyze the stresses between particles and the Ti6Al4V substrate. A thermal-cycle curve extracted from a macro numerical model was defined as the boundary condition to build this model. This research explained the crack formation mechanism for the titanium-based ZrO_2p/Ti6Al4V MMC layer.

The experimental setup of LMI has been documented in detail in Ref.[14], and the process of LMI is schematically depicted in Fig. 1. The Ti6Al4V plates sized 150×100×6 mm³ are employed as substrates. The ZrO₂ powder in a size range of 50–90 µm is utilized as a strengthening phase. The 4 kW IPG fiber laser (YLS 2000) is used to achieve surface melting of substrates, while the PF 2/2 powder feeder (made by GTV in Germany) is employed for particles injection. The processing parameters, including laser power, scanning velocity, laser-power distance, and power feeding rate, are listed in Table 1. The on-surface laser spot diameter keeps constant at 4 mm due to a positive defocus amount of 35 mm. To reduce the metallurgical reaction between ZrO_2p and Ti6Al4V, the power injection head is placed after the laser beam with 1 mm. In addition, the power feeding rate is set to 0.4 g·min^− 1.

Table 1

LMI processing parameters for ZrO₂/Ti6Al4V MMC layer system.
No.	Laser power P (kW)	Scanning velocity v (m/min)	Laser-powder distance D (mm)	Powder feeding rate R (g/min)	Linear energy Q (×10³ J/m)
#1	1.4	0.9	1	0.4	9.33
#2	1.3	0.9	1	0.4	8.67
#3	1.2	0.9	1	0.4	8.00
#4	1.1	0.9	1	0.4	7.33
#5	1.0	0.9	1	0.4	6.67
#6	0.9	0.9	1	0.4	6.00
#7	1.0	0.6	1	0.4	10.00
#8	1.0	0.7	1	0.4	8.57
#9	1.0	0.8	1	0.4	7.50
#10	1.0	0.9	1	0.4	6.67
#11	1.0	1.0	1	0.4	6.00
#12	1.0	1.1	1	0.4	5.46

3.1 Basic assumptions

The assumptions are made for macro-micro finite element modeling of the LMI process.

The MMC layer track made by LMI consists of several isotropy layers. The volume fraction of ZrO_2p is linearly decreased from the top MMC layer towards the MMCs layer/substrate interface.
The Ti6Al4V substrates are perfect (no defects), fully dense, and isotropic.
The ZrO₂ particles are in a shape of standard spherical with an equal diameter of 80 µm.
The flow of partially molten substrate during implantation is ignored.
The binding reaction between ZrO₂ particles and the metal matrix is not considered.
The phase transition stress due to temperature change is ignored.
The MMC layers are continuous materials without defects.

3.2 LMI mesh model

As depicted in Fig. 2 (a), the ZrO₂/Ti6Al4V LMI domain for FEM calculation consists of a five mm-thick Ti6Al4V substrate without any implanted power and an MMCs domain. The green represents the MMCs domain in which the volume fraction of ZrO₂ particles is measured from experiments. In addition, the width and depth of MMCs were obtained from actual experimental results in different process parameters. Finally, the whole domain is meshed by transitional hexahedral elements. The finer mesh was adopted near the MMCs area to get more accurate numerical simulation results, which is shown in Fig. 2(b) and Fig. 2(c). The cross-section width (CW) and cross-section depth (CD) are measured in the experimental results.

3.3 Material properties

The LMI base metal used in the experiment is Ti6Al4V alloy, and the powder is ZrO₂ particle. The chemical composition of Ti6Al4V is shown in Table 2. The thermal physical properties and mechanical properties of Ti6Al4V are shown in Table 3 and Table 4. ZrO₂ is a ceramic material, and its performance vary less with temperature, as shown in Table 4.

Table 2

Chemical composition of Ti6Al4V as a mass percentage.
Al%	V%	Cr%	Cu	Fe%	Mn%	Mo%	Nb%	Sn%	Zr%	Si%	Ti%
6.50	4༎00	< 0.01	< 0.02	0.04	0.02	< 0.03	0.02	< 0.05	0.02	0.03	Base

Table 3

Thermal physical properties of Ti6Al4V [15].
Property	Symbol	Value
Density	ρ	4420 kg/m³
Special heat	c	c = (0.176T + 540) J/(kg·K)	T < = T_m
Special heat	c	c = 830.4 J/kg·K	T > = T_m
Thermal conductivity	k	k = (0.0156T + 7) W/m·C	T < = T_m
Thermal conductivity	k	k = 32.74 W/m·C	T > = T_m
Latent heat	L	418680 J/kg
Melt temperature	T_m	1650 K
Boiling temperature	T_b	3290 K

Table 4

Thermal and mechanical properties of ZrO₂ [16] and Ti6Al4V.
Temperature (K)	ZrO₂						Ti6Al4V
Temperature (K)	Density (kg/m³)	Modulus (GPa)	Poisson's ratio	Specific heat (J·kg^− 1·K^− 1)	Thermal conductivity (W·m^− 1·K^− 1)	Expansion coefficient (10^− 6K^− 1)	Modulus (GPa)	Poisson's ratio	Yield stress (MPa)
298	5900	206	0.29	460	2.2	10	112	0.34	887
473	5900	193	0.29	460	2.2	10	104	0.34	668
673	5900	182	0.29	460	2.2	10	92	0.37	508
873	5900	175	0.29	460	2.2	10.1	76	0.39	212
1073	5900	171	0.29	460	2.2	10.4	56	0.41	89
1273	5900	170	0.29	460	2.2	10.5	32	0.42	38

For MMC layer materials, the accurate determination of thermal property parameters can be pretty complicated. This paper employs the Eshelby method [17] to calculate the equivalent elastic modulus and Poisson's ratio of the ZrO₂/Ti6Al4V MMC layer in Fig. 2.

$$\left\{ \begin{gathered} \frac{{{G^*} - {G_0}}}{{{G_1} - {G_0}}}=\frac{{{c_1}{G_0}}}{{{G_0}+\alpha ({G_1} - {G_0})}} \hfill \\ \alpha =\frac{{(1+\gamma )}}{{3 \cdot (1 - \gamma )}} \hfill \\ \end{gathered} \right.$$

Where, ${G_0}$, ${G_1}$ are the elastic modulus of substrate and particles, respectively. ${G^{\text{*}}}$ is the equivalent elastic modulus. ${c_1}$ is the volume fraction of the particle phase. $\gamma$ and $\alpha$ are the Poisson's ratio of the substrate and the MMC layer, separately.

Other properties of the ZrO₂/Ti6Al4V, such as thermal conductivity and expansion coefficient, can be approximately calculated by the Voight model, which reads

$$p={p_c}{f_c}+{p_m}{f_m}$$

Where, ${p_c}$, ${p_m}$ denote specific property of Ti6Al4V and ZrO_2p, ${f_c}$, represent volume fraction of substrate/particle phase.

3.4 Heat source modeling

The volume heat source with a sizeable depth-width ratio, e.g., rotating Gaussian cone, has proved effective in the FEM simulation of deep-penetration laser beam welding [18]. However, for an LMI process with limited melting depth, the laser defocusing distance is usually increased to achieve a large spot diameter (several millimeters) and a lower energy density at the workpiece surface. Therefore, the double ellipsoid heat source model is employed in this paper, and the heat density can be expressed as [19]:

$$\begin{gathered} {q_f}(x,y,z)=\frac{{6\sqrt 3 {f_f}Q}}{{{a_f}bc\pi \sqrt \pi }}{e^{{{ - 3{x^2}} \mathord{\left/ {\vphantom {{ - 3{x^2}} {{a_f}^{2}}}} \right. \kern-0pt} {{a_f}^{2}}}}}{e^{{{ - 3{y^2}} \mathord{\left/ {\vphantom {{ - 3{y^2}} {{b^2}}}} \right. \kern-0pt} {{b^2}}}}}{e^{{{ - 3{z^2}} \mathord{\left/ {\vphantom {{ - 3{z^2}} {{c^2}}}} \right. \kern-0pt} {{c^2}}}}} \hfill \\ {q_r}(x,y,z)=\frac{{6\sqrt 3 {f_r}Q}}{{{a_r}bc\pi \sqrt \pi }}{e^{{{ - 3{x^2}} \mathord{\left/ {\vphantom {{ - 3{x^2}} {{a_r}^{2}}}} \right. \kern-0pt} {{a_r}^{2}}}}}{e^{{{ - 3{y^2}} \mathord{\left/ {\vphantom {{ - 3{y^2}} {{b^2}}}} \right. \kern-0pt} {{b^2}}}}}{e^{{{ - 3{z^2}} \mathord{\left/ {\vphantom {{ - 3{z^2}} {{c^2}}}} \right. \kern-0pt} {{c^2}}}}} \hfill \\ \end{gathered}$$

Where, ${q_f}$ and ${q_r}$ are the heat flux density in the front and rear quadrant, respectively. Q is the power efficiency of the heat source. The b and c describe the dimensions of the heat source, as presented in Fig. 3.

4.1 Macroscopic morphology analysis of ZrO₂/Ti6Al4V MMC layer

Figure 4 gives the transverse sections of ZrO₂/Ti6Al4V LMI specimens. The optical macroscopic morphologies obtained under the same laser scanning rate and different power numbered from case #1 to #12. It can be observed that the transverse cross-section morphologies of all samples are like lower lips. The thermal cracks are also present in all specimens, and the ZrO_2p distribution density decreases gradually from surface to inside of the MMC layer except in case #6. Besides, there is porosity in sample #5.

The bottom of the molten pool is almost entirely Ti6Al4V metal, and ZrO₂ particles are mainly distributed in the upper part and the edge area of the molten pool in case #1. The cracks in through-wall mode can be observed in cases #2 and #3, in which the linear energy input is 8.0×10³ J·m^− 1 and 8.67 ×10³ J·m^− 1, respectively. In comparison, lower laser power only causes micro-cracks near the interface between the MMC layer and Ti6Al4V substrate, as presented in cases #5 and #4. Furthermore, the higher the linear energy input, the lower the melting-mixing ratio between ZrO_2p and Ti6Al4V. Moreover, case #6 shows that ZrO₂ particles are uniformly distributed in the molten pool. Therefore, a larger linear energy input will not only increase the incidence of cracks but also reduce the implantation rate of ZrO₂ particles.

The combination of the same laser power and lower scanning velocity causes a more remarkable crack numbered from cases #7 to #12. Extending with an acute angle led to spallation shapes near the track surface, as shown in cases #7, #9, and #10. The smaller scanning velocity probably results in higher laser linear energy, which is more than 7.0 ×103 J·m-1, leading to strong interaction between the laser beam and the Ti6Al4V liquid in the molten pool. The increase of laser scanning velocity can reduce the size of the hot crack, which is probably due to the smaller thickness of the ZrO_2p injection layer, as shown in cases #10, #11, and #12.

4.2 Feature extraction of ZrO₂/Ti6Al4V track

It has been reported that no reaction layer is formed in ZrO₂/Ti interface, which means that the severe cracks produced during the LMI process are mainly caused by thermal stress mismatching between ZrO₂ and Ti6Al4V. To reveal the residual stress distribution within the LMI specimen, the finite element modeling is conducted based on specific process parameters and the resultant MMCs morphologies, including the track dimensions and the volume fraction of implanted ZrO_2p. One of the measurements is the modified circular segment in Ref [20], and the abridged general view as shown in Fig. 5(a).

The critical dimensions of the ZrO_2p/Ti6Al4V MMC layer presented in Fig. 5(a) include the cross-section width (CW), the reinforcement height RH, and the cross-section depth (CD). The MMC layer depicted in Fig. 5(b) is divided into three sublayers where the volume fraction of ZrO_2p decreases linearly from VF1 to VF3.

The bar graph in Fig. 6 exhibits different experimental parameters' cross-section width and depth. Figure 6(a) uncovers a principle that cross-section width and depth decrease with the reduction of linear energy input. Moreover, the injection depth decreased from 1.07 mm to 0.31 mm as the laser power decreased from 1.4 kW to 0.9 kW. However, the CW and CD of case #4 (laser power is 1.1kW and linear energy is 7.33 ×10³ J·m^− 1) are higher than case #3 (laser power is 1.2kW and linear energy is 8.0 ×10³ J·m^− 1). Comparing the through-wall cracks and distribution of ZrO₂ particles, it can be inferred that excessive laser heat input leads to the instant gasification of Ti6Al4V metal, which takes away a large amount of energy and reduces the content of Ti6Al4V in the MMC layer resulting in a decrease of the CW and CD, and forming penetrating cracks. Inconspicuous gasification occurs when the linear energy is lower than 8.0 ×10³ J·m^− 1 because of the fewer metals above boiling. It also illustrates that the CW and CD decrease as the scanning rate increases in Fig. 6(b).

Due to the fewer cracks of cases #1, #5, and #8 in the MMC layer, the three LMI cases are modeled for FEM simulation to analyze the residual stress. The values of CW, RH, and CD of the LMI experiments are measured. The VF value in different sublayers is averaged from three different location transversal sections of samples, as shown in Table 5.

Table 5

The MMC layer transverse cross-section parameters measured in three LMI cases.
Case No.	CW/mm	CD/mm	RH/mm	VF₁	VF₂	VF₃	VF-average	VF-approx.
#1	2.8	0.93	0.26	0.504	0.234	0.062	0.267	0.3
#5	2.47	0.44	0.21	0.652	0.486	0.432	0.523	0.5
#8	2.53	0.70	0.22	0.573	0.452	0.05	0.358	0.4

4.2.1 Heat source model verification

It is indispensable to check the heat source model due to the existence of ZrO₂ particles in the MMC layer. Table 6 gives the specific MMC layer dimensions between experimental and simulated. These comparisons certify the simulated cross-section morphology of the molten pool is in good agreement with the experimental results under the process parameters given in Table 1.

Table 6

The MMC layer transverse cross-section dimensions between experimental and simulated.
LMI cases	Result types	CW (mm)	CD (mm)
Case #1	Simulation	2.8	1.1
Case #1	Experiment	2.8	1.07
Case #5	Simulation	2.5	0.5
Case #5	Experiment	2.47	0.44
Case #8	Simulation	2.5	0.75
Case #8	Experiment	2.53	0.75

The temperature cycle curves at different distances from the centerline of the MMC layer are measured by a K-type thermocouple HP-DJ8X25. It is difficult to obtain an actual temperature history curve in the MMC layer center. The simulation can represent the experimental result of point C because the curves reveal the calculated thermal cycle curves of case #1 has an excellent agreement with the experiment in comparison, as shown in Fig. 8.

Figure 8. The temperature cycle curve resulted from experiment and simulation at (a) point A and point B; (b) the center of the MMC layer.

4.3 Analysis of macro residual stress characteristics

Due to the vast difference in the properties of Ti6Al4V and ZrO_2p materials, considerable residual stress will be generated under the laser beam, which has a significant influence on crack formation. Therefore, it is necessary to understand the distributions of residual stress. According to the LMI parameters given in Table 1 and the mesh model in Fig. 2, the finite element model of thermal elastoplastic is established to analyze residual stress characteristics in the MMC layer.

4.3.1 The transversal residual stresses analysis of the MMC layer

The transversal residual stress (σ_xx) contours in Fig. 8 manifest the maximum compressive stresses are all distributed at the start and ends of the LMI progress, and tensile stresses are mainly distributed in the middle region of the MMC layer and where the transition region to Ti6Al4V substrate. Additionally, the maximum compressive stresses are always higher than the ultimate tensile stress for three different process parameters. Though the order of linear energy from large to small is: case 1, case 8, and case5, the stress legends expose the maximum tensile residual stresses of case #1, case #5, and case #8 are 344 MPa, 348.5 MPa, and 352.4 MPa respectively. And the maximum compressive residual stress of case #1, case #5, and #8 are 818.3 MPa, 1369.8 MPa, and 1180.2 MPa, respectively. Combined with the volume fraction of zirconia in Table 5, it can be thereby deduced that the peak residual stress has a more significant correlation with the volume fraction of zirconia than with the heat input.

Figure 9 (a) presents the σ_xx curves of the top, middle, and bottom layers of the MMC region from the start to the end. These curves reveal the top surface distributes transversal compressive stresses, but the middle and bottom areas disseminate tensile stress. The reason is the presence of zirconia particles in the MMC layer, and the upper surface is in a free state without any constraint. At the same time, the bottom region is constrained by the unmelted Ti6Al4V substrate. In addition, the σ_xx fluctuates between 2mm and 4mm from the starting point of the laser beam. That is because of the faster melting rate of Ti6Al4V under the action of the laser beam. However, in the initial stage of LMI, the initial temperature of the substrate is room temperature, which leads to a fast thermal conduction rate and rapid solidification of the molten metal.

Figure 9 (b) shows the σ_xx values from MMC upper surface to the bottom region of the Ti6Al4V in the thickness direction. Their specific perpendiculars are marked in Fig. 8. The distances from the vertical lines L-A, L-B, and L-C to the starting point are L/2, in which L is the length of the Ti6Al4V substrate. These curves disclose that the transverse stress exhibits a compression-tension-compression-tension distribution in the thickness direction. The smaller the volume fraction of zirconia particles, the greater the compressive stress on the upper surface, as shown in the L-A line. Moreover, the maximum tensile stress is mainly distributed in the heat-affected zone of the Ti6Al4V substrate. And the maximum compressive stress is primarily concentrated in the base metal area under the Ti6Al4V heat-affected zone. The three curves show that although case #1 LMI has the largest heat input, its maximum compressive stress is 221.5 MPa, which is smaller than 245.6 MPa for cases #8 and 263.4 MPa for case #5. However, case #5, with the largest zirconia volume fraction, has maximum tensile stress of 328.6 MPa, greater than that of cases #1 and #8. Comparing curves L-C and L-B, it can be inferred that the effect of decreasing heat input on the transverse residual stress is far less than that of increasing the volume fraction of zirconia. Therefore, it concluded that the main factor affecting the macroscopic residual transverse stress is the volume fraction of zirconia particles. Further, two crests of the L-A line indicate that inhomogeneous dispersion of ZrO_2p and the remelted Ti6Al4V have more significant influences on the distribution and magnitude of residual stress, combined with the optical topography analysis.

4.3.2 The longitudinal residual stress analysis of the MMC layer

Figure 10 makes clear the longitudinal tensile stress is in the MMC layer, and the compressive stress distributes other sections. The maximum tensile stress of three LMI cases is more than 1800 MPa, which is much higher than the yield strength of Ti6Al4V titanium alloy. This phenomenon may be the vast difference in the properties between Ti6Al4V and ZrO_2p materials and the FEM model assumption in section 3.1. In addition, the most considerable tensile stress is always higher than maximum compressive stresses. The peak tensile stress of case #8 is higher than the other two LMI cases, reaching 1811.7 MPa. However, the tensile stresses of case #5 with minimum linear energy are higher 246.4 MPa than case #1 with maximum heat input. It indicates that the effect of increasing the volume fraction of zirconia on the residual longitudinal stress is much greater than that caused by the decrease in heat input.

Figure 11(a) uncovers the fact that the residual longitudinal stress (σ_zz) at the start and end of the MMC layer on the top surface are close to 0 MPa, and the tensile stress distributes the entire MMC layer since the endpoints are free boundaries resulting in no constraints beyond the endpoints. In addition, the σ_zz on the upper surface of a whole MMC layer is always larger than that in the middle region and then larger than the bottom area. The peak residual stress of case #1 is the smallest, which does not exceed 1500 MPa.

Figure 11 (b) reflects the σ_zz variation regulation from the MMC upper surface to the bottom surface of the Ti6Al4V substrate along the centerline in the thickness direction. These curves show the tensile stresses gradually decrease from the upper surface to the inside of the MMC layer. However, there are trough points near the fusion lines, and there are stable transition zones in the heat-affected zone. The maximum tensile stresses are located on the upper surface of the MMC layer, and minimum tensile stresses are lay on the bottom surface of TI6Al4V. Moreover, the largest compressive stresses are concentrated in the base metal under the heat-affected zone. In addition, the σ_zz of the entire MMC layer exceeds the yield strength of Ti6Al4V, which indicates that the presence of zirconia particles has a significant influence on the increase of residual stress, which is also the reason why the MMC layer is susceptible to cracks. The three curves also indicate that the larger the volume fraction of zirconia is, the larger the residual stress is near the fusion line.

4.4 Analysis of microcosmic residual stress characteristics

For different LMI macro models, the implant layers are layered according to the different content of ZrO₂ ceramic particles. The two-dimension microscopic model is designed to study the interaction between ZrO_2p particles and Ti6Al4V substrate where the computation domain is 250×250 um². The diameter of ZrO₂ ceramic particles is assumed to be 80 um, and they are randomly distributed in Ti6Al4V titanium alloy.

Using the center (the Point C in Fig. 8) of the MMC layer thermal cycle curve (as shown in Fig. 12) as the thermal boundary conditions of the micro model, the contents of ZrO₂ ceramic particles are 30%, 40%, and 50%, as shown in Fig. 13. The lower-left corner of the calculation domain is the origin coordinates.

Due to the different contents of ZrO_2p resulting in different distances between particles from Fig. 14, the residual stress of the substrate located between particles is complicated. The micro transversal stress (m-σ_xx) and longitudinal stress (m-σ_yy) in particles are more than the Ti6Al4V substrate. And the stress at the edge of the particle is the least. Even though the volume fractions of ZrO₂ are different in the computational domain, the residual stress is uniformly distributed in the ZrO₂ particles. After that, the average residual stress at various locations in the computational domain is extracted, as depicted in Fig. 15.

Four particles are distributed in a rhombus for the model with a 30% volume fraction of ZrO2, and particle A4 is at the edge of the computational domain. The m-σ_xx inside the particles is almost equal and around the particles is less than the Ti6Al4V substrate. The average m-σ_xx at region P1 is 781MPa, which is higher than region P2, which is 689 MPa. In contrast, the average m-σ_yy at region P1 is 790 MPa, which is less than region P2, which is 861 MPa. This is because P1 is surrounded by particles A1, A2, A3, and A4, so it is affected by four particles. Besides, the P2, just between particles A2 and A3, is only affected by two particles. The average m-σ_xx and m-σ_yy of particles A1, A2, and A3 are close to 930 MPa, as shown in Fig. 15 (b).

Five particles are distributed in a centrosymmetric manner in a model with the 40% volume fraction of ZrO_2p. Therefore, areas P3, P4, P5, and P6 are influenced severally by three particles resulting in the m-σ_xx and m-σ_yy at the symmetric region (P3-P5 and P4-P6) being similar. The m-σ_xx and m-σ_yy of P3 and P5 are about 780 MPa and 800 MPa, respectively. The m-σ_xx and m-σ_yy values of P4 and P6 are about 803 MPa and 774 MPa, respectively. Furthermore, the phenomenon of low m-σ_xx around the particle is more noticeable. Still, the low m-σ_xx areas between particle B3 and other particles are narrower than the rest of the region around the particle. What’s more, the average m-σ_xx and m-σ_yy of these five particles are close to A1.

There are six particles randomly distributed in a model with a 50% volume fraction of ZrO_2p. The average m-σ_xx and m-σ_yy in every particle are severally about 925MPa and 930 MPa, which access A1. However, there are also low transversal stress areas between particles, such as points P9 and P10, as shown in Fig. 14. The m-σ_xx of P9 and P10 are 590MPa and 561 MPa, respectively. The m-σ_yy of P9 and P10 are 886 MPa and 891 MPa, respectively. However, there is an interesting occurrence in which the micro residual stresses of P7 are similar to P3, and that of P8 is close to P4. That is because the positions of P7 and P8 are severally identical to those of P3 and P4 in the computational domain, influenced by the three surrounding particles.

It concludes that the micro residual stresses between particles are affected by the particle spacing. The distance is more adjacent between the particles in the direction of the coordinate axis, the more significant residual stress is along this direction.

4.5 Analysis of crack formation mechanism in MMC layer

It can be inferred that the accumulation of micro residual stress leads to more enormous macro residual stress, leading to the formation of cracks. The ZrO₂ is a ceramic material, in which the melting point (2700℃) is much higher than Ti6Al4V. Therefore, the melted Ti6Al4V metal solution will coat the ZrO₂, as shown in Fig. 16(a). And the thermal expansion coefficient of ZrO₂ particles hardly changes during the process, but that of Ti6Al4V is greatly affected by temperature. Thereby, a gap, as shown in Fig. 16(b), is generated between ZrO₂ particles and Ti6Al4V substrate when the Ti6Al4V metal solidifies, because of the vast difference in the two material properties resulting in the metal surrounding the particle being partially under tensile stress and partially under compressive stress. A mass of ZrO₂ particles is equivalent to many inclusions present in Ti6Al4V metal. During the solidification process of Ti6Al4V, the metal dislocations move to contact with the ZrO₂ particles resulting in a stress concentration effect at a point (SCP), thereby transferring the stresses to the ZrO₂ particles. That is why the residual stresses in the ZrO₂ particle are more prominent than that in the Ti6Al4V substrate. A micro fissure will be formed when the stress at this point exceeds the yield stress limit of Ti6Al4V, and the gap will be further expanded, as shown in Fig. 16(c). As the cooling goes on, the initial micro- fissures gradually develop under the action residual stresses until the crack forms, and two gaps also merge, as shown in Fig. 16(d). Finally, several micro-cracks and gaps grow, forming cracks visible to the naked eye.

A Ti6Al4V- ZrO2p MMC layer was obtained by the LMI process. A finite element method was proposed that coupled thermo-mechanical to forecast the macroscope residual stress for a single-pass laser melted injection process and the microscope residual stresses between Ti6Al4V substrate and ZrO2 particles. Finally, the macro-crack formation mechanism was explained. The major conclusions are listed as follows:

According to MMC layer macroscopic morphologies, when the linear energy input was greater than 7.5×10³ J·m^-1, the cracks could go across the whole MMC layer. Besides, the linear energy greatly affected the cross-section width and depth of the MMC layer.

By comparing simulated and experimental MMC layer dimensions and the temperature cycle curve of measurement, we demonstrated a reliable model predicting residual stress and deformation of the MMC layer by using double ellipsoid thermogenic.

The macro transversal residual stress (σ_xx) of the MMC layer on the Ti6Al4V substrate was mainly featured with tensile stress, which in HAZ of the MMC layer was greater than that in other areas. The compressive stress was distributed at the ends of the MMC layer for all LMI processes. The most considerable tensile and compressive stresses were more than 355 MPa and 1300 MPa, respectively. Besides, the tensile stress increases at first and then decreases gradually from the upper surface to the inside of the MMC layer.

There were mainly macro residual tensile stresses in the MMC layer. Laser power and volume fraction of ZrO2p greatly influenced longitudinal residual stress (σ_zz). When the volume fraction of ZrO_2p was more than 50%, the σ_zz could exceed 1800 MPa.

The micro transversal and longitudinal stresses in ZrO_2p were larger than Ti6Al4V substrate. The stress at the edge of the particles was lower than 900 MPa. The residual stress differences were small between different particles, and all stress was above 900 MPa.

The zirconia volume fraction significantly affected the residual stress. A ZrO₂ particle, which acted as the inclusion phase of MMC, hindered dislocation movement during MMC solidification, resulting in the formation of cracks. The volume fraction of ZrO₂ particles was the main factor affecting the crack generation. It was concluded that the powder feeding rate and laser process parameters must be controlled strictly to improve the quality of MMC layer formation.

Acknowledgments The authors gratefully acknowledged projects funded by China Postdoctoral Science Foundation (No. 2020M671479) and Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

Funding This work was supported by China Postdoctoral Science Foundation (No. 2020M671479) and Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

Ethics approval Not applicable.

Consent to participate The authors declare their consent to participate.

Consent for publication The authors declare their consent for publication.

Conflict of interest The authors declare no competing interest.

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Editorial decision: Minor Revisions Needed
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You are reading this latest preprint version

Macro-micro residual stress prediction and hot cracks formation mechanism during laser melt injection processing of ZrO2 particles into Ti6Al4V substrate

Status:

Version 1

Abstract

Figures

1 Introduction

2 Experimental Process

3 Lmi Macroscopic Finite Element Modeling

3.1 Basic assumptions

3.2 LMI mesh model

3.3 Material properties

3.4 Heat source modeling

4 Results And Discussion

4.1 Macroscopic morphology analysis of ZrO₂/Ti6Al4V MMC layer

4.2 Feature extraction of ZrO₂/Ti6Al4V track

4.2.1 Heat source model verification

4.3 Analysis of macro residual stress characteristics

4.3.1 The transversal residual stresses analysis of the MMC layer

4.3.2 The longitudinal residual stress analysis of the MMC layer

4.4 Analysis of microcosmic residual stress characteristics

4.5 Analysis of crack formation mechanism in MMC layer

5 Conclusions

Declarations

References

Status:

Version 1

Macro-micro residual stress prediction and hot cracks formation mechanism during laser melt injection processing of ZrO2 particles into Ti6Al4V substrate

Status:

Version 1

Abstract

Figures

1 Introduction

2 Experimental Process

3 Lmi Macroscopic Finite Element Modeling

3.1 Basic assumptions

3.2 LMI mesh model

3.3 Material properties

3.4 Heat source modeling

4 Results And Discussion

4.1 Macroscopic morphology analysis of ZrO2/Ti6Al4V MMC layer

4.2 Feature extraction of ZrO2/Ti6Al4V track

4.2.1 Heat source model verification

4.3 Analysis of macro residual stress characteristics

4.3.1 The transversal residual stresses analysis of the MMC layer

4.3.2 The longitudinal residual stress analysis of the MMC layer

4.4 Analysis of microcosmic residual stress characteristics

4.5 Analysis of crack formation mechanism in MMC layer

5 Conclusions

Declarations

References

Status:

Version 1

4.1 Macroscopic morphology analysis of ZrO₂/Ti6Al4V MMC layer

4.2 Feature extraction of ZrO₂/Ti6Al4V track