Research on the deformation control for laser additive connection metal components based on the pre-deformation method

ABSTRACT

Laser additive connection is one of the main methods for additive manufacture of large-scale titanium alloy components. However, the connection deformation will seriously reduce the dimensional accuracy of large-scale components. By applying the methods of the finite-element simulation and the experiment, we analyzed the influence of different scanning strategies on the temperature field, stress and deformation of the connection components in this manuscript to effectively control the deformation of the laser additive connection metal component. The research results provide the basis for the laser additive connection scanning strategy selection. Then, based on the determined scanning strategy, the influence of different line energy density and connection area size on the laser additive connection angular deformation is further studied. Considering the influence of multiple parameters, a rapid prediction model for the angular deformation of laser additive connection was established, and the model error was less than 6%. The angular deformation of the laser additive connection is reduced by 80% by pre-deformation compensation. The deformation of the laser additive connection is effectively controlled.

Keywords:
Laser additive connection; Residual stress; Pre-deformation; Deformation control

1. INTRODUCTION

Laser additive manufacturing technology is an advanced manufacturing technology that relies on a laser heat source to melt metal powder/wire to form a molten pool, with point-by-point melting, line-by-line scanning, and layer-by-layer stacking to form a complex geometric entity [¹, ²]. With the growing maturity of laser additive manufacturing technology, its application in the aerospace field is gradually increasing [³]. Due to the size limitations of additive manufacturing equipment, large and complex integrated components used in the aerospace field are difficult to be formed as a single-piece, and are often formed by partitioning and then connected by additive technologies to complete the production of large-size components [⁴,⁵,⁶]. For high-performance alloys in the aerospace field, complex residual stresses can easily form during the connection process and cause deformation of the components, which seriously affects the molding quality of the components [⁷,⁸,⁹,¹⁰].

In additive connection, parameter optimization is a common way to improve forming quality. WANG [¹¹] investigated the influence of laser additive manufacture process parameters on residual stress by combining finite element simulation analysis and experiment. They observed that the residual stress in the top layer of the molded part decreased gradually with the increase of scanning speed, the decrease of laser power, and the increase of powder feeding rate. The simulation and measured results were well matched. DERAKHSHAN et al. [¹²] predicted the residual stresses and deformations of thin plate members after additive connection with SYSWELD finite element simulation software, and the results show that lower heat input significantly reduces the final deformation of the members.

Optimizing the bevel configuration is also often used to control the deformation of additive connection. YE et al. [¹³] compared the temperature cycling, residual stress distribution and deformation of three types of beveled connections, namely, V-type, K-type and X-type. They found that the type of bevel has a significant effect on the distribution of residual stress and the degree of deformation. JIANG et al. [¹⁴] investigated the effect of different bevel angles on the deformation of additive connection. The results showed that with the change of bevel angle, the transverse residual stress is more sensitive than the change of longitudinal residual stress. And the effect of bevel angle on the upper surface of the joint area is greater than that on the lower surface. In the study of Q345-316L dissimilar connection welding through a combination of finite element analysis and experimental methods, JIANG et al. [¹⁵] found that as the bevel angle increases and the deformation of the joint increases, the effect of the bevel angle on the residual stress and deformation of the member is very obvious. CHOOBI [¹⁶] investigated the effect of member geometry on the angular deformation by studying the angular deformation after arc welding of flat plates for different sizes. The results show that increasing the plate width will strengthen the plate stiffness and thus reduce the deformation of the connector.

In addition, deformation compensation is also an effective way to control the deformation of structural components. CHEON et al. [¹⁷] first proposed the concept of deformation compensation and applied this method to the deformation prediction of ship structural components. ZHANG et al. [¹⁸] proposed the structural constraint method, which was applied to the deformation compensation method to almost completely eliminate the angular deformation and reduce the final residual stresses. DAI et al. [¹⁹] applied this method to the additive connection process and investigated the longitudinal bending deformation for large linear structures of SUS304 stainless steel, and experimentally verified that the longitudinal bending deformation induced by the connection process was reduced by more than 90%.

All of the above studies can realize the deformation control of additive components to a certain extent. However, for the deformation control method based on the deformation compensation of the additive components, all of them fail to give the quantitative relationship between the process parameters, the connection area size and other factors on the deformation of the connected components. This seriously restricts the application of this technology in large components.

ABAQUS finite element analysis software and thermoelastic-plastic finite element calculation method are used in this paper. The influence of different process parameters (scanning strategy, line energy density) and connection area size (thickness, length, bevel angle) of laser additive connection on the temperature field, stress field and deformation of the connection components is investigated. The reliability of the simulation and analysis results is verified by experiments. In addition, according to the quantitative role of different process parameters and connection area size on the angular deformation of the connection, a rapid prediction model of angular deformation for laser additive connection with multi-parameter coupling was established. Finally, the deformation of the connectors was effectively controlled by the method of pre-deformation compensation.

2. EXPERIMENTAL AND FINITE ELEMENT SIMULATION PROCESS

2.1. Experimental details

This experiment was done on a laser additive manufacture equipment model LDM800. Two TC4 titanium alloy components were selected as the experimental objects. TC4 spherical powder with an average particle size of 90 µm was used as the connecting material. Argon was used as the protective gas during connection [²⁰]. Figure 1a shows the experimental equipment conditions and experimental environment. In order to prevent the dislocation of the connector during the connection, the fixture is placed on the surface of the connector without pre-tightening. The scanning strategy is shown in Figure 1b, where the red arrows indicate the scanning strategy. In this scanning strategy, the first two layers are long edge reciprocal scanning, and the short edge serpentine reciprocal scanning starts in the third layer.

Figure 1
Schematic diagram of the experimental environment and scanning strategy. a) The experimental equipment conditions and experimental environment; b) the scanning strategy.

The process parameters used for experimental and simulation analysis are shown in Table 1.

Table 1
Laser additive joining process parameters.

PROCESS PARAMETER	LASER POWER (W)	SCAN SPEED (mm/s)	LASER BEAM DIAMETER (mm)	OVERLAP RATE	LAYER THICKNESS (mm)
value	2000	8	4	0.5	1

When connecting, the internal temperature of the plate is measured in real time using a type K thermocouple thermometer model DAM-3130F, and the temperature measurement position is indicated by the red dot (TCI) in Figure 2. After the connection is completed, the deformation of the bottom edge of the connector is measured by a Hexagon coordinate measuring instrument with a model of SF 4.5.4 and an accuracy of 8 μm. Connector size, bevel forms and deformation detection locations are shown in Figure 2.

Figure 2
Schematic diagram of connector size and measurement position.

2.2. Finite element simulation process

2.2.1. Finite element modeling

The ABAQUS finite element simulation software was utilized to establish a numerical model of the two connectors and the connection area. The laser additive connection process was simulated using the birth-death element technique to analyze the temperature field and deformation distribution of the connectors during the process. The simulation results were compared with experimental results to verify the accuracy of the simulation methodology and model. The simulation took into account that the thermal gradient is larger near the connection area and smaller away from it. Therefore, the mesh was refined near the connection area and coarsened in regions farther away. This approach balanced computational accuracy with efficiency. To verify mesh independence, three models with varying mesh sizes were compared, as illustrated in Figure 3. The element type selected was the reduced integration element C3D8RT, which enables direct coupled analysis of temperature and stress fields and mitigates the “locking phenomenon” commonly observed in full integration elements.

Figure 3
Finite element model diagram.

2.2.2. Material parameters

The material of the laser additive connection components is TC4 titanium alloy. In the connection, the nonlinear characteristics of the TC4 titanium alloy material are obvious, and its thermomechanical and thermophysical properties are shown in Tables 2 and 3.

Table 2
Mechanical parameters of TC4 titanium alloy.

TEMPERATURE (ºC)	THERMAL EXPANSION COEFFICIENT (1/°C)	ELASTIC MODULUS (Pa)	POISSON RATIO	YIELD STRENGTH (Pa)	PLASTIC STRAIN (Pa)
24	8.78 × 10-6	1.25e × 1011	0.345	1.00 × 109	7.00 × 108
205	1.00 × 10-5	1.00 × 1011	0.345	6.30 × 108	2.20 × 109
428	1.11 × 10-5	8.00 × 1010	0.345	5.00 × 108	1.90 × 109
539	1.12 × 10-5	7.40 × 1010	0.37	4.46 × 108	1.90 × 109
650	1.17 × 10-5	5.50 × 1010	0.37	3.00 × 107	1.90 × 109
872	1.23 × 10-5	2.00 × 1010	0.43	2.50 × 107	2.00 × 109
1094	1.24 × 10-5	5.00 × 109	0.43	5.00 × 106	2.00 × 109
1650	1.25 × 10-5	1.10 × 108	0.43	1.00 × 105	1.00 × 108

Table 3
TC4 thermophysical parameters.

TEMPERATURE (ºC)	DENSITY (kg/m3)	SPECIFIC HEAT (J/(kg·K))	THERMAL CONDUCTIVITY (W/(m·K))
25	4420	546	7
200	4395	584	10.15
400	4366	629	12.6
600	4336	673	14.2
995	4282	693	19.3
1300	4240	696	23.7
1650	3920	1007	27
1900	3750	831	24

2.2.3. Heat source modeling and boundary conditions

Laser additive connection is a high-speed transient process. The Gaussian body heat source is chosen as the simulated heat source, and the movement of the heat source is realized by the DFLUX subroutine in this simulation. The heat source expression is shown in Equation 1.

(1) $$q=\frac{2AP}{\pi R^2}{e}_{R²}^{2r²}$$

Where A, P and R are the absorption rate, laser power and laser spot radius, respectively. The calculation formula of convection and heat radiation loss is:

(2) $$q_c=h\left(T-T_S\right)$$

(3) $$q_r={\sigma }_B{\epsilon }_r\left(T^4-T_s^4\right)$$

Where h is the thermal convection heat transfer coefficient, set to 40 W·m⁻²·K⁻¹. σ_B is the Stefan- Boltzmann constant, set to 5.67 × 10^-8 W·m⁻²·K⁻¹. ε^r is the coefficient of thermal radiation, set to 0.6. T^S is the ambient temperature, set to 20°C.

The initial condition can be expressed as:

(4) $$T{\left(x,y,z\right)}_{t=0}=T_0$$

The boundary conditions can be expressed as:

(5) $$k\frac{\partial T}{\partial n}-q+q_c+q_r=0(x,y,z)ϵS$$

Where S denotes the boundary surface, T and n denote the temperature and normal vector of S, respectively [²¹, ²²].

In numerical simulation, reasonable constraints have a crucial impact on the accuracy of calculation results. In order to ensure that the connectors are smoothly connected without tampering, the displacements in the X, Y and Z directions at position 1, the displacements in the Y and Z directions at position 2 and the displacements in the Z direction at position 3 are limited [²³]. The boundary conditions are shown in Figure 3 above.

2.3. Simulation verification

To verify mesh independence, the deformation results and computational time of models with different mesh sizes were first compared, as shown in Figure 4 and Table 4.

Figure 4
Comparison of displacements among different mesh models.

Table 4
Comparison of results from different mesh models.

MESH GENERATION SCHEME	MAXIMUM DEFORMATION (mm)	COMPUTATIONAL TIME (h)
Case 1	2.54	4
Case 2	2.65	7
Case 3	2.69	18

As can be seen from Figure 4 and Table 4, the mesh size affects the prediction accuracy of the model but does not influence the final deformation trend. The maximum deformations of the models under the three mesh sizes are 2.54 mm, 2.65 mm and 2.69 mm, with computational time of 4 h, 7 h and 18 h, respectively. Therefore, given the balance between model accuracy and computational efficiency, the mesh generation scheme of Case 2 is adopted in this paper.

In order to verify the accuracy of the analysis methods and numerical models in this paper. Experimental and numerical simulation methods were used to obtain the temperature change during the connection process and the deformation distribution after connection of TC4 titanium alloy connectors. The experimental results are compared with the simulation results, as shown in Figure 5.

Figure 5
Comparison of temperature field and deformation distribution. a) The temperature history at the temperature monitoring point (TCI); b) the macroscopic deformation contrast diagram of the connector after cooling.

The temperature history at the temperature monitoring point (TCI) during the additive connection process is shown in Figure 5a. The results show that the overall trend of the temperature history curves obtained from experiment and simulation is consistent. During the connection, as the time of the laser beam acting on the connector increases, the peak temperature of each layer continues to increase. When it is connected to the fifth layer, the temperature of the temperature monitoring point (TCI) reaches the maximum. The R² value for the comparison between experimental and simulated temperatures is 0.91. The peak temperature deviations of each layer measured by experiment and simulation are 18%, 4%, 2%, 5%, and 6%, respectively. The simulated and experimental peak temperatures of the layers are in good agreement except for the first layer, where those between simulation and experiment exhibit a large deviation. Figure 5b is the macroscopic deformation contrast diagram of the connector after cooling. It can be seen from the figure that both the experimental and simulation connectors have obvious angular deformation.

In order to further compare the overall deformation of the connector after connection, the Hexagon coordinate measuring instrument with an accuracy of 8 μm was used to measure the displacement of the two paths shown in Figure 2 above. The results are shown in Figure 6.

Figure 6
Comparison of displacement results. a) The Z-direction displacements of paths 1; b) the Z-direction displacements of paths 2.

Figures 6a and 6b show the Z-direction displacements of paths 1 and 2, respectively. Comparing with Figure 6, it can be seen that the maximum vertical displacement of the connector along the transverse direction (Path 1) is 1.41 mm, and the maximum vertical displacement along the longitudinal direction (Path 2) is only 0.18 mm. The vertical displacement along the transverse direction is much larger than the vertical displacement along the longitudinal direction. Therefore, the deformation of the connected components after the connection is completed is mainly manifested as the angular deformation of the center depression and the ends warping. The deformation trend of the simulation results is consistent with that of the experimental results. The vertical displacement of the connector along the transverse side is equated to one side and the maximum displacement values of the experimental and simulation results are compared. Where the experimental result is 2.72 mm and the simulation result is 2.65 mm with an error of 2.57%. Coefficient of Determination (R²) and Relative Root Mean Square Error (RRMSE) of 0.989 and 8.9% for transverse vertical displacement.

In order to more accurately quantify the angular deformation of the connection, the amount of angular deformation of the connection was calculated using the following method, as shown in Figure 7. The formula is as follows:

Figure 7
Angular deformation calculation diagram.

(6) $${\alpha }_1=arctan\frac{z_1}{y_1}$$

(7) $${\alpha }_2=arctan\frac{z_2}{y_2}$$

(8) $$\alpha =\frac{{\alpha }_1+{\alpha }_2}{2}$$

Where a is the final angular deformation of the connector, and a¹ and a² are the angular deformation of the two sides of the connector, respectively. The final experimental and simulated angular deformations obtained by calculation are 2.68° and 2.6°, respectively, with an error of 2.99%, indicating that the accuracy of the simulation and analysis method and numerical model in this paper is high.

3. ANALYSIS OF INFLUENCING FACTORS

In laser additive connection, different process parameters and connection area size will affect the deformation of the connection components, thus affecting the molding accuracy of the additive connection components. And through the previous experiments and simulation results, it can be seen that for the open V-shaped bevel medium-thickness titanium alloy connectors in the laser additive connection, the deformation mode after is mainly angular deformation. Therefore, this paper utilizes the method of numerical simulation to comprehensively consider the influence of different process parameters and connection area size on the angular deformation of laser additive connectors. Establish the quantitative relationship between process parameters, connection area size and angular deformation of connectors.

3.1. Process parameters

3.1.1. Scanning strategy

In this paper, the effects of three commonly used scanning strategies, namely, long-side (L) reciprocating scanning, long-short interleaving (LS) reciprocating scanning, and short-side (S) reciprocating scanning on the temperature field, stress field, and deformation of the member are investigated. The different scanning strategies are shown in Figures 8a, 8b, and 8c, respectively.

Figure 8
Schematic diagram of the three scanning strategies. a) Long-side (L) reciprocating scanning; b) long-short interleaving (LS) reciprocating scanning; c) short-side (S) reciprocating scanning.

In order to compare the effects of the three scanning strategies on the temperature field of the connector, the temperature-time course profile of the center point G on the upper surface of the first deposition layer of the connector was extracted. The cloud map of the temperature field distribution at this moment was intercepted when the connection was made to the middle position of the fifth layer. As shown in Figure 9.

Figure 9
Temperature field comparison of different scanning strategies. a) Temperature-time curve of point G on the upper surface of the 1st cladding layer of the connector; b) temperature field cloud map of the connector during connection at the middle of the 5th layer.

From the curves of Figure 9a, it can be seen that the required connection time for the three different scanning strategies are 150s, 187s, and 212s. When S scanning is adopted, the laser beam acts on the connection area for a longer period, and the peak temperatures of each layer are higher. This is because the laser head travels a longer trajectory during S scanning. Figure 9b shows the temperature field distribution of different scanning strategies during the connection process, where the gray-white area in the middle represents the current position of the melt pool. In L scanning, the temperature field distribution of the connector is more concentrated, with the high-temperature region mainly near the connection area. In contrast, the temperature field distribution is more uniform in LS and S scanning, with a wider high-temperature region that reduces the temperature gradient of the connector.

In order to compare the effects of the three scanning strategies on the stress field of the connectors, the transverse residual stress field and the longitudinal residual stress field cloud maps of the connectors are intercepted respectively. The transverse and longitudinal residual stresses on the upper surface of the connectors are extracted along the paths 3 and 4. As shown in Figure 10.

Figure 10
Stress comparison of different scanning strategies. a) Transverse residual stress field distribution of connectors under three scanning strategies; b) longitudinal residual stress field distribution of connectors under three scanning.

As shown in Figures 10a and 10b, the distribution of transverse residual stress field and longitudinal residual stress field of the connectors under the three scanning strategies are shown in the cloud diagrams, respectively. As can be seen from the figure, the trend of residual stress distribution of the connectors under the three scanning strategies is similar. The high stress areas in the connectors are mainly distributed in the center of the connection area and near the heat affected area. The transverse residual stresses in the connectors under the L scanning strategy are more widely distributed and have larger values than the other two scanning strategies. The longitudinal residual stresses are more concentrated in the center of the connection area and are distributed longer and narrower along the connection area compared to the other two scanning strategies. In addition, the peak transverse residual stress of the connector is significantly lower than the peak longitudinal residual stress. Figures 10c and 10d show the transverse and longitudinal residual stress profiles on the upper surface of the connector for the three scanning strategies, respectively. Along the direction of path 3, the peak values of transverse residual stresses on the surface of the connectors under the three scanning strategies are 88 MPa, 52 MPa, and 45 MPa, respectively, and the peak value of transverse residual stresses on the connectors under the L scanning strategy is 1.96 times higher than that under the S scanning strategy. The longitudinal residual stresses along the path 4 direction of the connector show a trend of high at the bottom of both ends and high in the middle. The peak values of the longitudinal residual stresses on the surface of the connector under the three scanning strategies are 649 MPa, 452 MPa, and 438 MPa, respectively, and the peak value of the longitudinal tensile residual stresses on the connector under the L scanning strategy is 1.48 times higher than that under the S scanning strategy.

Comparing the effects of the three scanning strategies on the residual stress field of the connectors, it is found that the transverse and longitudinal residual stresses of the connectors are minimized when the short-edge scanning is used, indicating that the short-edge scanning strategy can effectively discretize the residual stresses in the connectors.

In order to investigate the angular deformation of the connectors under the three scanning strategies, the Z-direction displacement distribution cloud map of the cooled connectors is intercepted, and the Z-direction displacements of the bottom surfaces of the connectors are extracted along Path 1 and Path 2, respectively, and the angular deformations of the connectors under the three scanning strategies are calculated as shown in Figure 11.

Figure 11
Comparison of deformation with different scanning Strategies. a) The cloud diagrams of Z-direction displacement distribution on the upper surface of the connectors under the three scanning strategies; b) the cloud diagrams of Z-direction displacement distribution on the lower surface of the connectors under the three scanning strategies; c) the Z-direction displacement curve extracted along path 1; d) the Z-direction displacement curve extracted along path 2; e) the Y-direction displacement (lateral contraction) of the bottom surface of the connector extracted along path 1; f) the angular deformation of the connector for the three scanning strategies.

As shown in Figures 11a and 11b, the cloud diagrams of Z-direction displacement distribution of the connectors under the three scanning strategies, the deformation trends of the connectors under the three scanning strategies are similar, but there are differences in the values. Combined with Figures 11c and 11d, it can be seen that the Z-direction displacement of the connectors under S scanning is the smallest among the three scanning strategies. In addition, when the L scanning strategy is adopted, the connector has a large bending along the connection direction, and the out-of-plane shows a slight anti-saddle deformation. The Y-direction displacement (lateral contraction) of the bottom surface of the connector is extracted along path 1 as shown in Figure 11e, and the angular deformation of the connector is calculated to be 3.51°, 2.71°, and 2.6° for the three scanning strategies, respectively, as shown in Figure 11f. Although the transverse shrinkage of the connectors was the largest among the three scanning strategies, the angular deformation of the connectors was the smallest under the S scanning strategy. The results show that the angular deformation of the connectors is more affected by the Z-direction displacement, while the transverse shrinkage has less effect on the angular deformation of the connectors.

In summary, among the three scanning strategies, the temperature field distribution of the connectors under the S scanning strategy is more uniform, the temperature gradient is smaller, the residual stress is smaller, and the final angular deformation is minimized. Therefore, compared with the other two scanning strategies, the S reciprocating scanning is undoubtedly a better scanning strategy in the same size.

3.1.2. Line energy density

The process parameters affecting the forming of laser additive connection components are mainly laser power and scanning speed. Due to the complexity of the heat input process of laser additive connection, the process parameters are not independent, but have a large coupling relationship with each other. Therefore, this paper converts the laser power and scanning speed into line energy density. From the perspective of line energy density, the effects of different line energy densities on the temperature field, stress field and deformation of laser additive connectors are explored.

The specific parameters of different line energy densities are shown in Table 5, and the line energy density formula is as follows:

(9) $$K=P\text{/}v$$

Table 5
Parameter setting of different line energy density.

LASER POWER (W)	SCAN SPEED (mm/s)	LINE ENERGY DENSITY (J/mm)
2000	8	250
2750	10	275
3000	10	300
2600	8	325
2800	8	350

where P denotes the laser power in W, v denotes the scanning speed in mm/s.

In order to compare the influence of different line energy densities on the temperature field of the connector, the temperature-time history curve of the center point G on the upper surface of the first layer of the connector is extracted, as shown in Figure 12.

Figure 12
Comparison of temperature field of different line energy density.

Figure 12 shows the temperature-time history curve of the connector point G under different line energy densities. When the scanning strategy is kept unchanged, the overall thermal cycle trend of the connector under different line energy densities is basically the same. However, when the scanning speed is different, the time required to complete the connection is also different. Increasing the scanning speed can shorten the connection time. The line energy density mainly affects the peak temperature of each layer during connection. When the line energy density is increased, the peak temperature of each layer during connection will increase.

In order to compare the influence of different line energy densities on the stress field of the connector, the transverse and longitudinal residual stresses on the upper surface of the connector are extracted along paths 3 and 4, as shown in Figure 13.

Figure 13
Comparison of different line energy density stress. a) Extraction of stress field distribution under different line energy densities along path 3; b) extraction of stress field distribution under different line energy densities along path 4.

Figures 13a and 13b reflect the distribution of transverse residual stress and longitudinal residual stress on the upper surface of the connector under different line energy densities. It can be seen from the figure that the line energy density does not affect the distribution trend of the residual stress of the connector, but with the increase of the line energy density, the transverse and longitudinal residual stresses of the connector will increase.

In order to explore the angular deformation of the connector under different line energy densities, the Z-direction displacement of the bottom surface of the connector is extracted along paths 1 and 2, and the angular deformation of the connector under different line energy densities is calculated, as shown in Figure 14.

Figure 14
Deformation comparison of different line energy density. a) The Z-direction displacement of the bottom surface of the connector is extracted along paths 1; b) the Z-direction displacement of the bottom surface of the connector is extracted along paths 2; c) the Y-direction displacement curve of the connector under different line energy densities; d) the variation curve of angular deformation with line energy density.

Figures 14a and 14b are the Z-direction displacement curves of the connector along path 1 and path 2 under different line energy densities, respectively. Increasing the line energy density will increase the deformation of the connector along the thickness direction (Z-direction displacement). When the linear energy density is 250 J/mm, the maximum displacement of the connector along the thickness direction is 1.33 mm. When the linear energy density increases to 350 J/mm, the maximum displacement of the connector also increases to 1.58 mm. Figure 14c is the Y-direction displacement curve of the connector under different line energy densities. Under the scanning strategy of short-side reciprocating scanning, the line energy density has a greater impact on the transverse shrinkage of TC4 titanium alloy connectors. When the line energy density is 250 J/mm, the maximum transverse shrinkage of the connector is 0.74 mm, and when the line energy density is 350 J/mm, the maximum transverse shrinkage of the connector can reach 1.17 mm. Figure 14d shows the variation curve of angular deformation with line energy density. The results show that with the increase of line energy density, the angular deformation of the connector will also increase.

3.2. Connection area size

3.2.1. Connection area thickness

In order to study the influence of the thickness of the connection area on the temperature field, stress field and deformation of the component, TC4 titanium alloy components with thicknesses of 3 mm, 5 mm, 7 mm, 9 mm and 11 mm were studied. The process parameters, scanning strategy and boundary conditions of the whole simulation process are exactly the same as those of the above experiments.

In order to compare the influence of different thicknesses of the connecting area on the temperature field of the connecting piece, the temperature-time history curve of the center point G on the upper surface of the first layer of the connecting piece is extracted, as shown in Figure 15.

Figure 15
Comparison of temperature field of different thickness connectors.

Figure 15 shows the temperature-time history curve of the connector point G with different thickness. It can be seen from the curve that as the thickness of the connecting area increases, the overall heat input time during the connection increases exponentially, resulting in the final cooling rate of the connector gradually decreasing and the required cooling time gradually increasing.

In order to compare the influence of different thicknesses of the connecting area on the stress field of the connecting piece, the transverse and longitudinal residual stresses on the upper surface of the connecting piece are extracted along paths 3 and 4, as shown in Figure 16.

Figure 16
Comparison of stress field of connectors with different thickness. a) Extract residual stress along path 3; b) extract residual stress along path 4.

Figures 16a and 16b are the transverse residual stress and longitudinal residual stress on the upper surface of the connectors with different thicknesses, respectively. It can be clearly seen from the figure that the change of the thickness of the connecting area has a great influence on the transverse residual stress of the connecting piece. When the thickness of the connecting area exceeds 7mm, the transverse residual stress of the connecting piece will increase sharply with the increase of the thickness. The peak transverse tensile residual stress of the connecting piece with a thickness of 11 mm is 362 MPa, and when the thickness is 3 mm–7 mm, the peak transverse tensile residual stress of the connecting piece does not exceed 60 MPa. The thickness of the connection area has a relatively small effect on the longitudinal residual stress of the connector. With the increase of the thickness, the longitudinal residual stress of the connector decreases first and then increases. However, because the first two layers adopt the scanning strategy of long edge scanning, and the long edge scanning will increase the residual stress of the connector, when the thickness is small, the longitudinal residual stress of the connector will be affected by the scanning strategy to a certain extent, and then when the thickness of the connection area is 3 mm, the longitudinal residual stress of the connector is larger.

In order to explore the angular deformation of connectors with different thicknesses, the Z-direction displacement of the bottom surface of the connector is extracted along paths 1 and 2, and the angular deformation of connectors with different thicknesses is calculated, as shown in Figure 17.

Figure 17
Comparison of deformation of connectors with different thicknesses. a) The Z-direction displacement of the bottom surface of the connector is extracted along paths 1; b) the Z-direction displacement of the bottom surface of the connector is extracted along paths 2; c) the Y-direction displacement curve of path 1; d) the curve of angular deformation with the thickness of the connection area.

Figures 17a and 17b are the Z-direction displacement values of the connectors with different thicknesses perpendicular to the connection direction (path 1) and along the connection direction (path 2), respectively. The connectors with different thicknesses eventually undergo obvious angular deformation, and with the increase of thickness, the deformation increases as a whole. In Figure 17b, because the 3mm plate is relatively thin compared with other thickness plates and the stiffness is small, it has a large bending deformation in the horizontal direction due to the influence of scanning strategy and stiffness. When the thickness of the plate gradually increases, the stiffness of the plate increases, and the bending deformation in the horizontal direction gradually disappears. Figure 17c is the Y-direction displacement curve of path 1, which reflects the transverse shrinkage of the bottom surface of the connector. With the increase of the thickness of the connecting area, the transverse shrinkage of the connector increases first and then decreases. When the thickness is 9 mm, the transverse shrinkage of the bottom surface of the connector reaches the maximum value close to 1 mm, and when the thickness is 11 mm, the transverse shrinkage of the bottom surface of the connector is only about 0.6 mm, even lower than that of the connector with 5 mm thickness.

The curve of angular deformation with the thickness of the connection area is shown in Figure 17d. Combined with the temperature history curve and the final residual stress curve of the connectors with different thicknesses in Figures 15 and 16, it can be seen that with the increase of the thickness of the connection area, the overall heat accumulation time during the connection increases continuously, and the longer heat accumulation time will produce larger angular deformation. Therefore, when the thickness of the connection area is 3–9 mm, the angular deformation of the connector increases with the increase of the thickness of the connection area.

However, when the thickness increases to a certain extent, the heat accumulation for a long time will remain in the connector in the form of residual stress, and cannot be released well by deformation. Therefore, when the thickness of the connection area increases to 11 mm, the growth rate of the angular deformation of the connector does not continue to rise, but gradually slows down.

3.2.2. Connection area length

In order to study the influence of the length of the connection area on the temperature field, stress field and deformation of the connector, TC4 titanium alloy components with plate lengths of 60 mm, 70 mm, 80 mm, 90 mm and 100 mm were taken as the research object, and other parameters were kept completely consistent.

In order to compare the influence of different connection area lengths on the temperature field of the connector, the temperature-time history curve of the center point G on the upper surface of the first layer of the connector is extracted, as shown in Figure 18.

Figure 18
Comparison of temperature field of connectors with different lengths.

Figure 18 is the temperature-time history curve of the connector point G with different lengths. With the increase of the length of the connection area, the heat input time of the connector increases continuously, but the peak temperature of each layer is very small.

In order to compare the influence of different connection area lengths on the stress field of the connector, the transverse and longitudinal residual stresses on the upper surface of the connector are extracted along path 3 and 4, respectively, as shown in Figure 19.

Figure 19
Comparison of stress fields of connectors with different lengths. a) Extract residual stress along path 3; b) extract residual stress along path 4.

Figures 19a and 19b are the distributions of transverse residual stress and longitudinal residual stress on the upper surface of connectors with different lengths, respectively. The length of the connection area has a significant effect on the transverse and longitudinal residual stresses of the connector. When the length of the connection area increases, the transverse residual stress of the connector decreases gradually, while the longitudinal residual stress of the connector increases.

In order to explore the angular deformation of connectors with different lengths, the Z-direction displacement of the bottom surface of the connector is extracted along path 1 and path 2, and the angular deformation of connectors with different lengths is calculated, as shown in Figure 20.

Figure 20
Comparison of deformation of connectors with different lengths. a) The Z-direction displacement of the bottom surface of the connector is extracted along paths 1; b) the Z-direction displacement of the bottom surface of the connector is extracted along paths 2; c) the Y-direction displacement curve of path 1; d) the variation curve of angular deformation with the length of the connection area.

Figures 20a and 20b are the Z-direction displacement curves of path 1 and path 2 of connectors with different lengths, respectively. With the increase of the length of the connection area, the deformation of the connector along the thickness direction gradually increases. However, compared with the thickness of the connection area, the length of the connection area has a relatively small effect on the deformation of the connector. Combined with Figure 18, it can be seen that one of the reasons for this phenomenon is that the overall heat input gap between connectors of different lengths is small. Figure 20c is the Y-direction displacement curve of connectors with different lengths, and the final transverse shrinkage of connectors with different lengths is approximately the same. Therefore, compared with the influence along the thickness direction, the length of the connection area has little effect on the transverse shrinkage of the connector. Figure 20d shows the variation curve of angular deformation with the length of the connection area. When the length of the connection area is in the range of 60–100 mm, the angular deformation of the connector increases approximately linearly with the increase of the length of the connection area.

3.2.3. Bevel angle

In order to study the influence of the bevel angle of the connection area on the temperature field, stress field and deformation of the connection, TC4 titanium alloy components with bevel angles of 70°, 80°, 90°, 100° and 110° were taken as the research object, and other parameters were kept completely consistent.

In order to compare the influence of different bevel angles on the temperature field of the connector, the temperature-time history curve of the center point G on the upper surface of the first layer of the connector is extracted, as shown in Figure 21.

Figure 21
Comparison of temperature field of connectors with different bevel angles.

Figure 21 shows the temperature-time history curve of the connector point G with different bevel angles. As the bevel angle increases, the heat input time of the connector will gradually increase, and increasing the bevel angle of the connection area will increase the peak temperature of each layer during the connection.

In order to compare the influence of different bevel angles on the stress field of the connector, the transverse and longitudinal residual stresses on the upper surface of the connector are extracted along paths 3 and 4, as shown in Figure 22.

Figure 22
Comparison of stress field of connectors with different groove angles. a) Extract residual stress along path 3; b) extract residual stress along path 4.

Figures 22a and 22b are the distributions of transverse residual stress and longitudinal residual stress on the surface of the connector with different bevel angles. With the increase of the bevel angle of the connection area, the transverse and longitudinal residual stresses of the connector decrease continuously. When the bevel angle is 70°, the peak transverse tensile residual stress of the connector is 64 MPa, and the peak longitudinal tensile residual stress is 651 MPa. When the bevel angle is 110°, the peak transverse tensile residual stress of the connector is 30 MPa, and the peak longitudinal tensile residual stress is only 300 MPa.

In order to explore the angular deformation of connectors with different bevel angles, the Z-direction displacement of the bottom surface of connectors is extracted along paths 1 and 2, and the angular deformation of connectors with different groove angles is calculated, as shown in Figure 23.

Figure 23
Deformation comparison of connectors with different groove angles. a) The Z-direction displacement of the bottom surface of the connector is extracted along paths 1; b) the Z-direction displacement of the bottom surface of the connector is extracted along paths 2; c) the Y-direction displacement curve of path 1; d) the curve of angular deformation with the change of the bevel angle of the connection area.

Figures 23a and 23b are the Z-direction displacement curves of path 1 and path 2 of connectors with different bevel angles. As the bevel angle of the connection area increases, the displacement of the connector along the thickness direction becomes more and more obvious. The maximum displacement difference between the connector with a bevel angle of 80° and the connector with a bevel angle of 70° is 0.25 mm, while the maximum displacement difference between the connector with a bevel angle of 110° and the connector with a bevel angle of 100° is 0.36 mm. Figure 23c is the Y-direction displacement curve of the connector with different bevel angles. When the bevel angle is 70°, the maximum transverse shrinkage of the connector is 0.27 mm. When the bevel angle increases to 110°, the maximum transverse shrinkage of the connector reaches 1.16 mm. The bevel angle has a great influence on the transverse shrinkage of the connector.

Figure 23d is the curve of angular deformation with the change of the bevel angle of the connection area. When the groove angle of the connection area is in the range of 70°–110°, the angular deformation of the connector increases exponentially with the increase of the bevel angle. Combined with the temperature history curve of G point in Figure 21, it can be seen that with the increase of bevel angle, the difference of heat accumulation time during connection will become larger and larger, and it will increase in an approximate exponential form, which eventually leads to the approximate exponential growth of angular deformation of connectors.

4. DEFORMATION CONTROL

4.1. Deformation prediction model

The pre-deformation method is one of the most simple and efficient methods to control the angular deformation, and the accurate prediction of the deformation compensation of the component before the connection is the key to the pre-deformation method.

First convert the connection area dimensions (connection area thickness, connection area length, bevel angle) to connection area volume:

(10) $$V=\frac{1}{2}LDH$$

(11) $$D=2Htan\frac{\alpha }{2}$$

Substituting Equation 11 into Equation 10 gives:

(12) $$V=L{H}^{2}tan\frac{\alpha }{2}$$

As shown in Figure 24, where V is the volume of the connection area in (mm³), L is the length of the connection area in (mm), D is the width of the connection area in (mm), H is the thickness of the connection area in (mm), α is the angle of the bevel in (°).

Figure 24
Schematic diagram of the dimensions of the connection area.

Using the quantitative relationship between the factors in the above research and the angular deformation of the additive connection component, the line energy density, the volume of the connection area and the angular deformation of the connector are fitted to establish a multi-parameter coupled rapid prediction model for the deformation of the additive connection component, so as to realize the rapid prediction of the connection deformation of the additive component, as shown in Figure 25.

Figure 25
Deformation prediction model.

The angular deformation of TC4 titanium alloy connection specimens after laser additive connection conforms to the following formula:

(13) $$z=ax+by+c{x}^2+d{y}^2+fxy+z_0$$

where z represents the angular deformation of the connector, unit (°), x is the line energy density of the connection, unit (J/mm), y is the volume of the connection area, unit (m³), a = 0.0124, c = 0.0000206, a and c are the influence factors of linear energy density on the angular deformation of the connector, b = 0.0012, d = -0.00000007, b and d are the influence factors of the volume of the connection area on the angular deformation of the connector, f = 0.000000321, f is the influence factor of the line energy density and the volume of the connection area on the angular deformation, when y ≤ 5000, Z⁰ = −5.21, when y > 5000, Z⁰ = −5.84.

To validate the accuracy of the pre-deformation prediction model, this study employs a connector with a groove angle of 90°, a thickness of 8 mm, a length of 80 mm, and a linear energy density of 250 J/mm for experimental verification. The experimental and simulation results are shown in Figure 26 and Table 6.

Figure 26
Comparison of deformations between experiment and simulation.

Table 6
Comparison of prediction results.

METHOD	GROOVE ANGLE (°)	ERROR WITH THE PREDICTION MODEL (%)
Experiment	3.72	3.88
Simulation	3.66	5.74
Prediction Model	3.87	0

Under experimental and simulation conditions, the angular deformations of the connector with a groove angle of 90°, thickness of 8 mm, and length of 80 mm are 3.72° (experimental) and 3.66° (simulation). The angular deformation obtained by the prediction model for the connector under the same conditions is 3.87°, with errors of 3.88% (prediction vs. experiment) and 5.74% (prediction vs. simulation), respectively. This indicates that the prediction model established in this paper can accurately predict the angular deformation of laser additive connection components.

4.2. Pre-deformation control

In this paper, the influence of pre-deformation method on the forming quality of connectors is explored by combining experiment and simulation.

The principle of the pre-deformation method is shown in Figure 27. Firstly, the angular deformation of the connecting member after the additive connection is simulated and predicted, and then the deformation of the connecting member is compensated before the connection, and finally the deformation of the component is reduced.

Figure 27
Schematic diagram of pre-deformation principle.

In order to explore the influence of pre-deformation method on the forming quality of connectors, the deformation distribution of pre-deformed connectors and non-pre-deformed connectors is compared. The results are shown in Figure 28.

Figure 28
Comparison of pre-deformation results. a) The overall deformation results of the connectors before and after pre-deformation are compared; b) the curve comparing the overall deformation results of the connector before and after pre-deformation; c) the angular deformation results of the connector after applying the pre-deformation method.

As shown in Figures 28a and 28b, the overall deformation results of the connectors before and after pre-deformation are compared. The figure clearly and intuitively reflects that the pre-deformation method can effectively reduce the overall deformation of the connectors. It can be seen from Figure 28c that before the pre-deformation method is applied, the angular deformation experimental result of the connector is 2.63°, and the simulation result is 2.6°. When the pre-deformation method is used for additive connection, the angular deformation experimental result of the connector is 0.57°, and the simulation result is 0.6°. Comparing these four sets of data, it can be found that the application of pre-deformation reduces the angular deformation of the connecting sample by up to 80%, realizes the effective control of the angular deformation of the connecting piece, greatly improves the forming accuracy of the laser additive connecting member, and also verifies the accuracy of the numerical simulation in this paper.

This study provides a theoretical basis for deformation prediction and control of large-scale additively manufactured components. However, in industrial practices, challenges such as deviations in deformation prediction of components with complex geometric features and difficulty in applying the pre-deformation method may arise. In subsequent research, introducing machine learning (such as neural networks and genetic algorithms) to establish a “geometric feature-pre-deformation amount” mapping model is worth considering. Such a model can fit the compensation laws of complex geometries through training data to improve the applicability of the rapid deformation prediction model. Complex components can be decomposed into several simple geometric units, with independent pre-deformation designs for each unit, followed by finite element simulation to verify the overall compensation effect after unit splicing. Ultimately, these strategies achieve the deformation control of large-scale complex additively manufactured components and promote the application of the pre-deformation method in practical engineering.

5. CONCLUSION

In this paper, the effects of process parameters and connection area size on the deformation of TC4 titanium alloy connectors were studied by means of experiment and simulation. By comparing the results of the temperature field, stress field and deformation with the different scanning strategies, it is found that when the short-edge reciprocating scanning strategy is adopted, more uniform temperature field and smaller temperature gradient lead to smaller residual stress and deformation for laser additive connecting metal components. In addition, by analyzing the influence of different line energy density and different connection area size on the angular deformation, the rapid deformation prediction model is established for laser additive connecting metal components. By randomly selecting the determined line energy density and connecting area size, the angle deformations are acquired by the numerical simulation of the rapid deformation prediction model established in this paper. The deformation results are compared and the error is only 3.88%. The accuracy of the deformation prediction model is verified. Finally, according to the deformation predicting results of laser additive connecting metal components, the pre-deformation method is used to effectively control the metal component’s deformation. Applying the pre-deformation method, the laser additive connecting component’s deformation is reduced by 80%.

6. ACKNOWLEDGMENTS

This work was supported by the National Key Research and Development Program (2022YFB4600901), the Liaoning Provincial Natural Science Foundation (2025-MS-123), the Project of Liaoning Provincial Education Department (LJ232510143005), the Aviation Science Foundation Program (2023M049054001).

DATA AVAILABILITY

The data supporting the reported results in this study are available on request from the corresponding author.

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Publication Dates

• Publication in this collection
  07 Nov 2025
• Date of issue
  2025

History

• Received
  13 Feb 2025
• Accepted
  14 July 2025