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Modeling and numerical simulation of welding dynamic displacement field

preface

as an important part of advanced manufacturing technology, the development of welding technology in the future will move from "technology" to "science". EPS board (expandable polystyrene board) has the advantages of light weight, low price, low thermal conductivity, small water absorption, good electrical insulation performance, sound insulation, shock resistance, moisture resistance, simple molding process, etc., so it is widely used in buildings, ships, automobiles The development of welding process simulation technology is an important symbol of thermal insulation, sound insulation and seismic materials such as trains, refrigerators and freezers. Since Rosenthal's moving heat source solid heat conduction model and the establishment of analytical solutions of welding temperature field, many welding workers have made great efforts to study the computer simulation technology of welding process, such as Yukio Ueda of Japan, who first analyzed the stress and strain of welding process by using finite element technology

at present, the simulation objects in the welding field mainly include temperature, displacement, strain, stress, etc. Among them, the real impact on the overall structural performance is the stress and strain, which is the ultimate object of simulation. However, the stress and strain are difficult to be tested and verified (most of the existing detection methods are not resistant to high temperature or destructive), so from the perspective of whether it is suitable for the result verification, the displacement field should be used as the direct analog quantity. After verifying the correctness of the analog quantity, the stress and strain results should be derived for analysis

The establishment of constitutive equationthe establishment of constitutive relationship is closely related to the state of materials. Metal components in the welding process go through two stages: heating and cooling. At a certain time, there will be solid-phase zone, liquid-phase zone and solid-liquid coexistence zone on the components, which affects the equation used in the calculation. There is a lot of viscosity in the solid-liquid coexistence zone, which conforms to the viscoelastic plastic finite element method. However, due to the fast cooling speed and the short existence time of the solid-liquid zone under the welding condition, it can be ignored, so the solid-phase zone and the liquid-phase zone are mainly considered. The stress and strain in the solid region obey the THERMOELASTIC-PLASTIC theory. According to the isotropic strengthened von Mises yield criterion and Prandtl Reuss flow increment theory, the corresponding experimental installation is based on the THERMOELASTIC-PLASTIC incremental stress-strain relationship that the material properties depend on temperature of the pure mechanical testing mechanism in the mid-19th century, namely the incremental constitutive equation, as shown in Formula 1

d{ σ}= [D]d{ ε}- {C} DT (1)

where:

[d]: elastoplastic matrix, in the elastic region [d]=[de],

in the plastic region [d]=[d]ep=[de]-[d]p

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where [de]: elastic matrix

[d]ep- elastoplastic matrix

{ α}- The linear expansion coefficient vector

for thermoelastoplasticity, its detailed expansion is:

where H: strain hardening index

t: equivalent stress

according to the principle of virtual displacement, the incremental expression of the finite element equation is established as shown in equation 3

[K]e△{ δ}= △ {r}e (3)

where: [k]e: element stiffness matrix

[k]e= ∫ e[b]t[d][b]dxdy

{ δ}： Displacement increment caused by this loading (or temperature increment)

{r}e: element equivalent nodal force vector

△ {r}e= ∫ ∫ e[b]t{c} △ tdxdy

the above is obtained under certain theoretical assumptions, and the assumptions are as follows: the behavior in the plastic zone obeys the flow law, showing strain hardening; Elastic strain, plastic strain and temperature strain are separable; The mechanical properties of materials change with temperature; The effects of viscosity and creep are not considered; The material is isotropic

2 establishment of displacement field analysis model

2.1 establishment of geometric model

the geometric model of displacement field is consistent with the temperature field. After completing the temperature field calculation in this step, the element is converted from temperature field element to structural field element through element transformation, and the division of element is consistent with the temperature field, as shown in Figure 1

Figure 1 Division of finite element calculation unit

2.2 treatment of molten pool

when the metal in the molten pool area melts under the action of arc heat, the molten pool area will enter the state of zero mechanical properties, that is, all stress and strain will disappear; When the molten pool changes from liquid to solid, it enters the initial state of strain free history. In addition, the force exerted by the liquid molten pool metal on the surrounding solids is very small, and has little effect on the stress-strain distribution in the area around the molten pool. Therefore, in order to correctly simulate the stress-strain distribution in the high-temperature zone, the emergence and disappearance of the molten pool must be considered, otherwise the displacement field simulation will be invalid due to the pseudo deformation of the molten pool. In this regard, the "unit alive and dead" method is adopted. The principle is as follows: the numerical results of the temperature field of each sub step are selected: the unit beyond the melting point will die, and the unit below the melting point will be "activated"

2.3 nonlinear treatment

there is great nonlinearity in the welding process. It is shown in the following aspects:

① geometric nonlinearity: Welding belongs to large strain problem. Large strain refers to that the strain produced is large enough to cause the change of element shape and stiffness,

② material nonlinearity: refers to the nonlinear relationship between stress and strain, for example, plasticity has a nonlinear stress-strain relationship; Viscoplasticity and creep are the relationship between strain and other factors (time, temperature). In order to comprehensively consider the properties of plastic materials in the analysis, the unification of yield criterion, flow criterion and hardening law must be considered

to solve the above problems, the following methods are adopted:

① the full Newton Raphson method is adopted, and the stiffness matrix is modified every time the equilibrium iteration is carried out,

② the bilinear isotropic strengthening model provided by ANSYS is used to simulate material nonlinearity. This type is applicable to isotropic materials. Von Mises yield criterion and Prandtl Reuss flow equation are applied together (but Bauschinger effect is not considered)

2.4 analysis process

in this paper, ANSYS software is used for finite element calculation. ANSYS provides two coupling methods for the analysis of different physical fields: direct coupling and indirect coupling. Strictly speaking, the temperature field analysis and displacement field analysis are directly coupled, but because the test shows that this coupling effect is very small, it is ignored. The indirect coupling method based on sub step level is adopted in the calculation. That is, divide the time into enough small areas (sub steps), conduct transient thermal analysis in each area first, and store the results of the maximum time of heat flow gradient in the unit table after the solution is completed; Then carry out element transformation, carry out structural analysis with the same geometric model and element division, import the result data of the element table as the boundary condition of structural analysis, and carry out structural analysis of static free deformation. In this process, the welding heating process is simulated for 5 seconds, and then the cooling process is simulated for about 60 seconds. The command flow in the heating phase is shown in Figure 2

Figure 2 Calculation and analysis flow chart

3 verification of displacement field calculation results of argon arc fixed-point welding

the material used in this experiment is LY2 aluminum alloy, and the size of the specimen is 120 × one hundred and twenty × 2mm. The welding method is tig fixed-point welding. The welding current is 80A. It is suitable for relatively large tension welding voltage of 12.8v. The measurement method of welding displacement field is laser electronic speckle interferometry. The experimental fixture is shown in Figure 3

Fig. 3 Schematic diagram of experimental fixture

Fig. 4 Comparison of test results of TIG spot welding laser speckle method and finite element calculation results

Fig. 4 is the comparison between the calculation results of TIG spot welding displacement field and the actual measurement results obtained by laser electronic speckle interferometry (the figure shows 1/4 of the total displacement field). It can be seen from the figure that there is a certain error between the experimental results and the calculation results, which may be caused by the following reasons:

1 The high temperature thermophysical and mechanical property data of materials are obtained by extrapolation method, which is inconsistent with the actual data, resulting in calculation errors

2. In the numerical simulation, the heat source is strictly applied to the center of the plate, but in the actual experiment, due to the inability to accurately locate and ensure that the arc is strictly perpendicular to the workpiece. Therefore, the calculation results of displacement field are affected

4 conclusion

the actual measured welding dynamic displacement field using laser electronic speckle interferometry is compared with the finite element calculation results, and the results show that the calculated results are in good agreement with the measured results. This shows that the model of dynamic displacement field in welding process established by using elastoplastic theory in this paper is correct. (end)

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