Civil Engineering Reference
In-Depth Information
FIGURE 6.3
Prototype transverse cross sections which show a high level of similarity but correspond to significantly
different welds.
temperature fields corresponding to identical energy sources and process parameters but for different
material properties (which are assumed independent of temperature). Referring to
Fig. 6.5
,
it can be seen
that the calculated transverse cross sections are relatively insensitive to reasonably large variations in
material properties. The insensitivity of calculated transverse cross sections to various weld process
parameters implies that it is important to adopt as constraints on the calculated temperature field some
type of information concerning the three-dimensional character of the weld. This information need not
represent detailed knowledge of the temperature field but rather bounds on its distribution of values in
three dimensions. Such information could be obtained by thermocouple measurements or from weld
cross sections other than those that are tranverse.
1, 2
6.6
Prototype Case Study Analyses of Welds
We present a set of case studies which are typical of a range of different welding processes, e.g., bead-in-
groove and bead-on-plate welding processes. This collection of prototype analyses serves to demonstrate
many of the properties of the geometric constraints method and issues associated with its application in
practice. Our analyses are based on the minimization of the objective function
T
p
N
s
N
S
q
0
V
B
3
()
l
------
------------
Z
()
T
C
p
T
()
d
T
Z
p
,
(6.32)
L
S
p
1
p
1
T
A
where
Z
p
is given by Eq. (6.17). Equation (6.32) is defined with reference to
Fig. 6.6
and represents a
restricted form of Eq. (6.26). Some of the weld data considered in our analyses are given in data sets 1
and 2 in the appendix and described in
Figs. 6.7
and
6.8
.
Included also in these data sets are model
parameters associated with our analyses. Shown in
Fig. 6.7
,
is a transverse cross-section for a bead-
on-plate weld having some reinforcement extending above the surface of the workpiece. The process
