Experimental Validation of Residual Stress Simulations in Welded Steel Tubes with Digital Image Correlation

As each production process introduces residual stresses in the material, cold-rolled steel tubes are not delivered stress-free. The motivation of this research can be traced back to the laser cutting of tubes. During the cutting process, residual stresses are relieved, which causes deformation of the tube and a reduction of the precision of cut. Residual stresses also play a role in stress corrosion and sudden collapse of tubular structures.

This work concentrates on the residual stresses in cold-rolled steel tubes due to the welding process. Insight into the origin, influencing parameters, distribution and magnitude is gained with a finite element (FE) simulation of the welding process. An FE model allows for the visualisation of these aspects in the entire tube. A welding simulation requires the quantification of numerous input parameters: thermal and thermomechanical material properties (and their evolution at elevated temperatures), thermal and mechanical boundary conditions, and a model for the heat-input of the welding torch. The simulation is split up into a thermal analysis which calculates the temperature field in the tube during the welding and subsequent cooling and a thermomechanical simulation which calculates the deformation and stress.

Since welding simulations require an appropriate value for numerous parameters, validation of the simulation results is of utmost importance. For this purpose, a laboratory setup which allows measuring the temperatures and deformations during the welding of the tube is built. The temperatures are measured with 5 thermocouples. The deformation is measured with strain gauges and the digital image correlation (DIC) technique.

Although DIC has some advantages over other techniques measuring deformations during welding, to the author's knowledge it is the first time that DIC is used in a welding application. First, it is investigated whether it is possible to measure the thermal expansion of the types of stainless steel used in this work (austenitic SS304 and ferritic SS409) on 3D objects. It is shown that this is possible up to 600°C. From these measurements the thermal expansion coefficient is determined, and this is used as input in the thermomechanical simulations. Although the strain that occurs in the welding is rather small compared to common DIC applications, the strain evolution during the welding and subsequent cooling of the tube can be recognised easily. These strain evolutions are in agreement with the strain evolution measured with the strain gauges. Strain gauges have in this application the disadvantage that the measured strain must be compensated for the actual material temperature, which makes their result dependent on this temperature measurement.

In the thermal simulation, the predicted temperature field is brought in agreement with the measured temperature field. For this purpose, the value of three poorly known input parameters was optimised: (i) the efficiency of the welding process; (ii) the actual room temperature around the setup; and (iii) the convection film coefficient. This procedure results in physically acceptable values for these parameters. The difference between the measured and the simulated temperature curves at the thermocouple points is minimised, but they are certainly not yet coincident, which is directly reflected in the simulated strain evolutions.

In the thermomechanical simulation, the thermal field is combined with the thermal dilatation of the material to calculate the stress and strain evolution during the welding process. The tube in the experiments was subjected to a stress relief treatment before the experiment was started and also the simulations start from a stress-free tube. The simulated strain evolutions are compared with the measured ones. The residual stress profile in the middle section of the tube is compared to an X-ray diffraction residual stress measurement. A sensitivity analysis shows that parameter variations are visible in both the strain evolution and in the residual stress profile. Validating the simulations with the strain evolution is preferred to a residual stress measurement as in this way the whole process is checked and not just the final state.

The methodology developed for a SS304 tube with a diameter of 60mm and wall thickness of 1.5mm is applied to a SS409 tube with a diameter of 60mm and wall thickness of 2mm. Especially the larger heat input and the lower thermal expansion coefficient define this case study. The results are similar to the SS304 tube, but a better material characterisation of the SS409 steel is necessary to improve the results.

Finally, the effect of an initial residual stress field on the strain evolution during and the residual stress after the welding is investigated. For that reason the stress/strain state inferred from exploratory rolling simulations was implemented as initial field in the welding simulations. From these simulations it is concluded that the final residual stress pattern is mainly determined by the welding process.