Figure 6-7 shows the computed carbon concentration vs. distance from the internal wall at a point on the internal wall of the pipe.

Figure 6-8 shows the thickness of the carburized film layer on several cross-sections vs. time. The dip in carbon concentration seen in Figure 6-8 corresponds to higher temperatures that shift the carbon concentration on the liquidus line to lower carbon values.

The following test results show that useful estimates of the risk of bum-through can be achieved by using the FEM methodologies.

Figure 6-9 shows some typical results of the thermal analysis.

Figure 6-10: The temperature and thickness of the liquid layer versus time is shown for a point on the inside wall of the pipe.

Figure 6-10 shows a typical transient temperature distribution with geometry deformed by stress analysis.

The peak at the liquid-solid interface is caused by the temperature dropping to the eutectic temperature and that shifts the carbon level to the eutectic value. The results of our analysis are consistent with anecdotal evidence of a liquid carburized film forming on the inner wall of the pipe.

The thickness of the liquid layer and the concentration of carbon as a function of distance from the inner wall of the pipe have been computed. A 3D transient temperature, displacement, stress and strain have been computed and coupled to the model of growth of the carburized layer.

Figure 6-11 shows also results of the thermal analysis.

The accuracy of the thermal analyses is considered to be limited primarily by the values chosen for the convection coefficient on the internal surface of the pipe. By setting the weld pool cross-section size and power input from data given in [8] and choosing an arc efficiency factor of 0.65, we find the best agreement with data from [8] with the convection coefficient in the range 1000 to 2000 W/m2 °K. We consider 1500 W/m2 °K to be the best estimate of the value of the convection coefficient.

We first note that the stress state in the machined slot is rather different from that of a thin walled pipe with internal pressure. The thin walled slot actually deforms more like a bubble than a thin walled pipe. See Figure 6-12, curve A would be constant in a thin - walled pipe. The bending changes the stress distribution from that of a thin-walled pipe. Instead of a constant hoop stress, the hoop stress is higher on the outer surface where bending adds a tensile component and lower on the internal surface where bending adds a compressive component. Some of the hoop stress load is shunted around the slot as it would be shunted around a crack.

The agreement between experiment and FEM analysis for the total displacement of the deformed cross-sections in welds H, J and E is quite good. This suggests the FEM model is reasonably accurate. All welds that experiment showed had less risk of bum - through than weld G also had less thinning in the FEM analysis.

Kiefner [1 and 2] states that by the Battelle model, ”It has been shown that for certain welding process, the level of 980 °С (1800 °F, 1255 °K) at the inside surface is a safe upper limit for avoiding bum through”. Figure 6-11 clearly shows that the difference in peak temperature on the internal wall of the pipe is not a sensitive measure of risk of bum through. This is not surprising because the peak temperature criterion ignores time and bum through is a time dependent phenomena. We argue that a much better model is obtained by CWM because, in addition to the peak temperature, it includes several additional parameters that are critical to the bum - through phenomena. These include the value of the internal pressure, the pipe diameter and wall thickness, the weld pool geometry and speed, convection coefficient, the area of the internal surface at temperatures above temperatures of 900°C, and the time spent at high temperatures. The CWM FEM analyses of bum-through presented in this chapter do consider all of these factors. We argue that this is a significant advance in modeling bum-through when welding on pressurized pipelines, Figures 6-13 to 6-18.

It should be noted that almost no use has been made of adjustable or tuning parameters in the FEM analysis described in this section. Certainly there is some uncertainty in the convection coefficient on the internal surface of the pipe. However, the values used are in the range expected for a water filled pipe. There is also some uncertainty in the value of the high temperature viscosity for steel. Again the values used are in the range expected for thermal activated dislocation motion, i. e., high temperature creep in steels.

To simulate the actual bum-through, i. e., the formation of a hole, we conjecture that a dynamic analysis including inertial forces would be required.

Figure 6-16: Computed cross-section for weld E cross-sections show excellent agreement between the predicted and experimental deformation of weld E.

If internal surface temperatures could be measured

experimentally, the convection coefficient could be estimated more accurately. If deformation of the internal surface could be measured more accurately, then even higher accuracy comparisons could be made with FEM simulations.