[0001] This invention relates to a method for postweld heat treatment (hereinafter referred
to as PWHT) of a welded portion of, for example, a thick base metal, and more particularly
to a method for appropriately judging the time point for terminating the PWHT when
sufficient of the residual diffusible hydrogen in the welded metal has been dissipated
by the afterheating.
[0002] There sometimes occurs a problem of cold (or delayed) cracking when welding thick
low alloy steels. At present, it is the usual practice to resort to intermediate stress
relief annealing to prevent cracking of that sort. However, as seen in desulfurizing
reaction towers and coal liquefaction systems, there is a recent distinctive trend
in the chemical industries toward larger scale plants, which involve for an increased
number of times the intermediate stress relief annealing treatment after welding.
Repetitive intermediate stress relief annealing not only gives rise to deteriorations
in strength and toughness of the material but also hinders the fabrication process,
thus increasing the length of time of the process and the cost of the fabrication.
[0003] Under these circumstances, the present inventors have conducted research into multilayer
butt welds of thick 2¼Cr-1Mo steel and A508 Class 3 material and found that: (1) the
problematic cracks are mostly transverse cracks in a weld zone, that is to say, in
weld metal or in the heat affected zone (HAZ); (2) the cracks are apt to occur immediately
beneath the final layer due to the residual stress in the direction of weld line,
diffusible hydrogen and hard microstructure, propagating and growing toward the inner
and outer surfaces of a plate; and (3) the residual stress remains almost the same
independent of the plate thickness but the residual hydrogen decreases upon raising
the preheat and interpass temperature at the time of welding, thereby preventing the
occurrence of a crack. From these facts, it is deduced that an effective means for
preventing cracks is to decrease the diffusible hydrogen concentration in the weld
zone.
[0004] For this reason, our research was focussed on the so-called low-temperature PWHT
which prevents the cracking by decreasing the diffusible hydrogen concentration in
a weld zone by heating the weld zone to a relative low temperature immediately after
welding. Since this method is intended to prevent cracking solely through the diminution
of the diffusible hydrogen concentration in the weld zone, it is.necessary to clarify
the following items before its application.
[0005]
(1) 'The relation between the conditions of the welding operation for an actual structure
and the hydrogen concentration immediately after welding.
(2) The relation between the variations in the hydrogen concentration during low-temperature
PWHT and the treating conditions.
(3) The relation between the critical hydrogen concentration at which the possibility
of cracking is eliminated and the maximum Vicker's hardness number in the weld zone.
[0006] The present inventors clarified the items (1) to (3) by experiments on butt weldments
of thick 2¼Cr-1Mo steel and A508 Class 3 material and furthered their research on
the basis of the experimental data. As a result, they succeeded in preventing the
cracking by an appropriate PWHT, thereby permitting the omission of an intermediate
stress relief annealing step.
[0007] More particularly, one aspect of the present invention resides in:
(1) A step of obtaining the residual hydrogen concentration (Co)D and (Co) directly beneath the finally welded layer immediately after completion of
multilayer welding, where (Co)D and (Co)H are for weld metal and for heat affected zone, respectively.
(2) A step of obtaining the critical hydrogen concentration for the prevention of
cracking, that is to say, (Ccr)D and (Ccr)H for weld metal and HAZ, respectively, which depend upon the maximum residual stress
and maximum Vicker's hardness number of microstructure in weld zone.
(3) A step of obtaining the values of [Ccr/Co]D and [Ccr/Co]H, ratio of the critical hydrogen concentration [Ccr]D and [Ccr]H for the prevention of cracking both in the weld metal and HAZ to the residual hydrogen
concentration [Co]D for weld metal and [Co]H for HAZ.
(4) A step of obtaining the values of [C/Co]D and [C/Co]H for weld metal and HAZ, respectively, the ratios of the hydrogen concentration in
the weld zone [C]D and [C]H which are lessened by the low-temperature PWHT to the residual hydrogen concentration
[Co]D and [Co]H.
(5) A step of, from the relation of the sum [τ + Dp·tp]D for weld metal and [τ+ Dp·tp]H for HAZ of a hydrogen diffusion parameter [τ(cm2)] in a welding operation under given conditions

wherein
Di : a hydrogen diffusivity coefficient (cm2/sec) in an arbitrary weld zone of each unit layer;
th : the time required for welding each unit layer
and the product of a hydrogen diffusivity coefficient (
Dp(cm
2/sec)) during the
PWHT and the holding time (tp(sec)) and (C/Co)
D and (C/Co)
H, predetermining the values of (D
p·t
p)
D and (D
p·t
p)
H for weld metal and HAZ, respectively, where (C) is equal to (Ccr)
D or (Ccr)
H.
(6) A step of determining a larger value of (Dp·tp)D or (Dp·tp)H by comparing those values, namely, (Dp.tp) as a condition of PWHT.
(7) A step of measuring the temperature at a suitable portion of the weld during PWHT
to-terminate the heat treatment at a time point when the time integrated value of
the hydrogen diffusivity coefficient (Dpi(cm2/sec)) at the measured temperature exceeds the value of (Dp.tp).
[0008] By the way, when the maximum Vicker's hardness number of the microstructure in the
weld metal is higher than that in the HAZ, the estimation of above mentioned respective
values only for weld metal is sufficient because the hydrogen concentration in HAZ
is generally much lower than that in weld metal.
[0009] The present invention also provides a method for the low-temperature PWHT in multilayer
welding, comprising the steps of;
[0010] determining the residual hydrogen concentration Co (cc/100 g) directly beneath the
final welded layer immediately after completion of welding;
[0011] determining a crack-preventing critical hydrogen concentration Ccr (cc/100 g) to
obtain a ratio of Ccr/Co;
[0012] determining the value of a product D
p·t
p of a hydrogen diffusivity coefficient Dp (cm
2/sec.) during the heat treatment and a holding time tp (sec.) where a currently reached
hydrogen concentration C (cc/100 g) become equal to the critical hydrogen concentration
Ccr, on the basis of the relation of a ratio C/Co of the current hydrogen concentration
C (cc/100 g) to the residual hydrogen concentration Co and a sum of a parameter τ
(cm
2) of hydrogen diffusion of the formula given below and the product of D
p·t
p;
[0013] measuring the temperature of the heat treatment at a suitable position of the weld;
and
[0014] terminating the heat treatment at a time point when a time-integrated value of a
hydrogen diffusivity coefficient Dpi (cm
2/sec.) at the measured temperature exceeds the value of Dp.tp.

wherein, PWHT: postweld heat treatment,
D.: a hydrogen diffusivity coefficient (cm2/sec.) in an arbitrary weld portion during welding each unit layer; and
tn: time (sec.) required for welding each unit layer.
[0015] In the method of the present invention, for instance, the first step of obtaining
the value of (Co) can be realised by various means or procedures in practical applications.
The gist of the invention resides in the above mentioned steps and is not limited
to practical procedures employed therefor. The particular procedures developed in
the description are given only as typical examples and should not be construed as
limiting the present invention. In this regard, it is to be noted that the invention
includes all modifications and alterations as encompassed by the appended claims.
[0016] The present invention also provides a method for the low-temperature PWHT of a multilayer
weld, characterised by the steps of:
determining for a test weld similar to said multilayer weld the residual hydrogen
concentration Co (cc/lOOg) directly beneath the final welded layer immediately after
completion of welding;
determining for the test weld a crack-preventing critical hydrogen concentration Ccr
(cc/100 g) to obtain a ratio of Ccr/Co;
determining for the test weld the value of a product Dp.tp of a hydrogen diffusivity coefficient D (cm2/sec) during the heat treatment and a holding time tp(sec.) where a currently reached hydrogen concentration C (cc/100 g) becomes equal
to the critical hydrogen concentration Ccr, on the basis of the relation of a ratio
C/Co of the current hydrogen concentration C (cc/100 g) to the residual hydrogen concentration
Co and a sum of a parameter τ (cm2) of hydrogen diffusion of the formula given below and the product of Dp.tp;
measuring for said multilayer weld the temperature of the heat treatment at a suitable
position of the weld; and
terminating the heat treatment of said multi- layer weld at a time point when a time
integrated value of the previously determined hydrogen diffusivity coefficient Dpi
(cm2/sec.) at the measured temperature exceeds the previously determined value of Dp.tp.

wherein, PWHT: postweld heat treatment,
Di: a hydrogen diffusivity coefficient (cm2/sec.) in an arbitrary weld portion during welding each unit layer; and
tn: time (sec.) required for welding each unit layer.
[0017] The present invention also provides a method for the low-temperature postweld heat
treatment of a multi- layer weld, characterised by the steps of:
obtaining for a test weld similar to said multilayer weld, the residual hydrogen concentration
(Co)D and (Co)H (cc/100 g) directly beneath the finally welded layer immediately after completion
of multilayer welding, where (Co)D and (Co)H are for weld metal (deposited metal) and for heat affected zone, respectively;
obtaining for the test weld the critical hydrogen concentration for prevention of
cracking (Ccr)D and (Ccr)H for the weld metal and for the heat affected zone, respectively, which depend upon
the maximum residual stress and maximum Vicker's hardness number of the microstructure
in the weld zone;
obtaining for the test weld the values of (Ccr/Co)D and (Ccr/Co)H, the ratio of the critical hydrogen concentration (Ccr)D and Ccr)A for prevention of cracking both in the weld metal and the heat affected zone to the
residual hydrogen concentration (Co)D and (Co)H;
obtaining for the test weld the values of (C/CQ)D and (C/Co)H for the weld metal and for the heat affected zone, the ratio of the hydrogen concentration
(C)D and (C)H which are lessened by the low temperature postweld heat treatment to the residual
hydrogen concentration (Co)D and (Co)H;
obtaining for the test weld the values of (τ+Dp.tp)D and (τ + Dp.tp)H for the weld metal and for the heat affected zone where Dp is hydrogen diffusivity
coefficient during the postweld heat treatment and tp is the holding time, and τ (cm2) is a hydrogen diffusion parameter in a welding operation under given conditions

wherein Di is a hydrogen diffusivity coefficient (cm2/sec) in an arbitrary weld zone of each unit and tn is the time required for welding
each unit layer;
determining for the test weld a value (D .tp) which corresponds to the larger of (Dp.tp)D or (Dp.tp)H by comparing those values, as a condition of the postweld heat treatment;
measuring for said multilayer weld the temperature at a suitable portion of the weld
during the postweld heat treatment, and
terminating the heat treatment of said mult- layer weld at a time point when the time
integrated value of the previously determined hydrogen diffusivity coefficient (Dpi) (cm2/sec.) at the measured temperature exceeds the previously determined value of (Dp.tp).
[0018] In the accompanying drawings:
Figure 1 is a perspective view showing the conditions of test welding and a sampling
position of a test piece;
Figure 2 is a diagrammatic view explanatory of the way to divide a welded joint into
small elements for the analysis by the finite element method;
Figure 3 is a flow chart showing a programme for the analysis by the finite element
method;
Figure 4 is a diagram showing the dependency on temperature of various thermal constants;
Figure 5 is a diagram showing the relation between the hydrogen diffusivity coefficient
and the temperature;
Figure 6 is a schematic view explanatory of the restraint test specimen used in the
cracking tests,
Figure 7 is a schematic perspective view showing the method for measuring diffusible
hydrogen which is dissolved into weld metal by one pass of welding;
Fig. 8 is a diagram comparatively showing the actually measured and calculated values
of the hydrogen concentration distribution at a time point when the final bead reaches
can interpass tempprature;
Fig. 9-(a) and (b) are the diagrams showing the relations between the hydrogen concentration
immediately beneath the final pass of welds right after welding and the parameter
(τ) of hydrogen diffusion at the time of welding for weld metal of 2¼Cr-1Mo steel
weldments and for HAZ of A508 Class 3 weldments, respectively;
Fig. 10 is a schematic view of gas burners employed as auxiliary heating means for
maintaining an interpass temperature at the time of welding;
Figs. 11 and 12 are diagrams showing-the relation between welding conditions and the
parameter (τ) of hydrogen diffusion with auxiliary heating for 2¼Cr-1Mo steel weldments;
Fig. 13 is a diagram showing the same relation for A508 Class 3 weldments as Figs.
11 and 12.
Fig. 14-(a) is a diagram showing the influence of the hydrogen concentration distribution
immediately after welding on the relation between the variation in hydrogen concentration
in weld metal and treating conditions of the low temperature PWHT;
Fig. 14-(b) is the same diagram for HAZ as Fig. 14-(a);
Fig. 15-(a) is a diagram for weld metal showing the similar influence of the plate
thickness;
Fig. 15-(b) is the similar diagram for HAZ as Fig. 15-(a);
Fig. 16-(a) is a diagram for weld metal showing the similar influence of the beveling
width;
Fig. 16-(b) is the similar diagram for HAZ as Fig. 16-(b);
Fig. 17 is a diagram showing the relation between the variations in the hydrogen concentration
and PWHT conditions in a case where the beveling width exceeds 36mm;
Figs. 18-(a) and 18-(b) are the diagrams showing the results of cracking tests for
2¼Cr-1Mo steel and A508 Class 3 material along with the distribution of hydrogen concentration,
which were conducted for determining the crack-preventing critical hydrogen concentration;
Fig. 19 is a graph showing the relation between the crack-preyenting critical hydrogen
concentration in weld metal or in HAZ and maximum Vicker's hardness number of microstructure
in the respective region;
Fig. 20 is a flow chart illustrating procedures for determining the conditions of
the crack-preventing low temperature PWHT for various materials; and
Fig. 21 is a diagram showing the variations in the coefficient of hydrogen diffusion
against time.
PARTICULAR DESCRIPTION OF THE INVENTION:
[0019]
The method of the invention is hereafter described by way of fundamental tests conducted
on 2¼Cr-1Mo steel and A508 Class 3 material, results of the experiments and practical
procedures for the respective steps.
[Testing Method]
1. Test specimens and welding conditions
[0020] The base metal used in the tests was 200 mm thick rolled material of ASTM A387 GR22
Class 2 and a forged A508 Class 3 material. Those chemical compositions and mechanical
properties are shown in Table 1.

[0021] ; The flux MF-29A or MF-27 was mainly used in the tests but the recently developed
flux MF-29AX of low hydrogen level was used in certain cases.
[0022] Table 3 shows the chemical composition and mechanical properties of the weld metals.
2. Measurement of hydrogen concentration distribution in thick plate weldsimmediately
after welding
[0023] 'Upon completion of welding, the distribution of hydrogen concentration in the direction
of plate thickness immediately after the final bead cooled to an interpass temperature
was measured, varying the preheating/ interpass temperature and the plate thickness
to clarify experimentally their influences on the distribution of hydrogen concentration
in the weld metals. The obtained hydrogen distributions were used as comparative data
against the calculated values to confirm the reliability of the program of finite
element method

for estimating the hydrogen distribution immediately after welding as described in
the next paragraph. The shape and dimensions of the welding joint used for the measurement
of diffusible hydrogen concentration are shown in Fig. 1(1), while the sampling position
of the test piece for its purpose is shown in Fig. 1(2) in which the various lengths
are in the unit of mm and indicated at 1 are trays for holding a cooling medium and
dry ice and at 2 is a cut of the weld metal test piece.
3. Analysis of hydrogen diffusion during welding by finite element method
[0024] For handling the hydrogen diffusion during the welding operation, it is preconditional
to reproduce the welding thermal cycle. However, our researches are directed to plates
of a thickness of 50 mm or greater which require welding in a relatively large number
of layers and the submerged arc welding process is generally utilized with high heat
input, so that it is almost impossible to simulate on the test piece the welding thermal
cycle which takes place when welding an actual structure. Therefore, the analysis
based on the finite element method was utilized.
[0025] Fig. 2 illustrates an element division of a weld zone into small triangles of I-beveling
welded with 2 passes per layer and having a penetration rate of 60%. In this figure,
the reference numeral 6 denotes the weld of the first pass consisting of a weld portion
4 and a penetrated portion 5. Indicated at 6' is the weld of the 12th pass consisting
of a weld portion 4' and a penetrated portion 5'. In this instance, the sum of residual
hydrogen in the penetrated portion and a predetermined amount of hydrogen dissolved
in the respective weld portion at the time of each weld is divided by the total weight
of the weld and penetrated portions, allotting the mean value uniformly thereto as
initial hydrogen concentration existing when welding each weld pass. The hydrogen
concentration at the nodes on the surfaces were considered as being constantly held
at zero throughout the analysis.
[0026] On the other hand, the calculation for the welding thermal history which is preconditional
to the analysis of the hydrogen diffusion was performed with a heat input of 4.0 KJ/cm
for 22:Cr-lMo steel welds and 37 KJ/cm for A508 Class 3 welds and a heat efficiency
of 65%, equivalently redistributing them to the weld and penetrated portions.
[0027] Fig. 3 is a flow chart of a program used for the analysis. The time increment for
each analysis was set in the range of 1 to 10 seconds to correspond with the cooling
rate. The shift to the next pass was effected when a predetermined temperature was
reached at a position located 10 mm inside the beveling face and 15 mm deep from the
plate surface, compiling that temperature as an interpass temperature. With a larger
plate thickness, the temperature was controlled by varying the measuring positions
for a.few times along the plate thickness in accordance with the progress of the welding
operation. In the various tests using a test specimen as shown in Fig. 1, the welding
thermal cycle was controlled by a CA thermocouple which was inserted at such measuring
positions for conformity with conditions of calculation.
[0028] Figs. 4 and 5 show the dependency on temperature of the various thermal constants
and the hydrogen diffusivity coefficient which were used in the calculations. With
regard to the thermal transfer coefficient A, thermal conductivity B and specific
heat C, the density was held constant in consideration of their dependency on temperature
shown. For the dependency on temperature of the hydrogen diffusivity coefficient,
the value indicated by solid lines in Fig. 5.was used.
4. Determination of hydrogen diffusivity coefficient of welded joints
[0029] Thy hydrogen diffusivity coefficient was determined by actually measuring the distributions
of hydrogen concentration immediately after welding and after the low-temperature
PWHT and comparing the measured values with calculated values as obtained under the
same conditions.
5. Cracking test for determining critical hydrogen concentration free from transverse
cracks
[0030] In order to know to which extent the concentration of residual hydrogen in the weld
zone immediately after welding has to be reduced for the prevention of cracking, namely,
in order to know the crack-free critical hydrogen concentration, cracking tests were
conducted with the use of restrained test specimens as shown in Fig. 6, in which the
respective dimensions are indicated in the unit of mm. The dimensions of h (plate
thickness) X° (angle of beveling) and R (radius of curvature at the root of beveling)
were varied in the cracking tests under the conditions shown in Table 4.

[0031] The low-temperature PWHT was performed in an annealing furnace. Leaving the test
specimen at room temperature for two weeks after the low-temperature PWHT, vertical
sections of the weld were cut out to check the existence of cracks by magnaflux detection
and by naked eyes after etching.
[0032] Nextly, the hydrogen diffusion during PWHT was analyzed by the use of the thermal
history which was obtained in the cracking test during the time interval from the
completion of welding to the time point when the temperature of the test specimen
cooled down to 100°C after the low temperature PWHT, thereby determining the hydrogen
distribution in the weld zone at the temperature of 100°C. Thereafter, the crack-preventing
critical hydrogen concentration was determined on the basis of the results of the
cracking test and the corresponding distribution of hydrogen concentration.
6. Measurement of initial hydrogen content necessary for determining conditions of
low temperature PWHT in accordance with the combination of base metal and welding
materials
[0033] A test piece as shown in Fig. 7(1) (in which all the dimensions are indicated in
the unit of mm) was welded with one pass in the arrowed direction which was, immediately
after being quenched in a water bath with crashed ice, put in liquid nitrogen to fix
hydrogen. Thereafter, four test pieces were cut off as shown in Fig. 7(2) for the
determination of hydrogen. These test pieces were sealed in a vacuum container for
about 20 days at room temperature and then subjected to determination of diffusible
hydrogen by a vacuum extraction apparatus.
[Test results and practical procedures]
1. Relation between hydrogen concentration immediately after welding and conditions
of welding operation
[0034] Fig. 8 shows actually measured and calculated values of the hydrogen distribution
in the weld metal of 2¼Cr-1Mo steel weldments when the final pass of the weld is cooled
down to the interpass temperature. In this figure, the marks " O ", " Δ " and " □
" represent the actually measured values and the curves indicate the results of analysis.
Both the actually measured and calculated values have peaks in the vicinity of a point
immediately beneath the final layer, showing a higher value with a greater plate thickness.
Generally, the calculated values coincide with the actually measured values indicatively
of the reliability of the analyzing computer program. As mentioned hereinbefore, it
is necessary to employ a large test specimen in order to simulate the cooling rate
in actual welding involving a thick and wide plate. However, the hydrogen distribution
in such a case can easily be obtained by the use of the analysing program.
[0035] Nextly, it is important to determine the relation between the hydrogen concentration
immediately beneath the final bead and the conditions of welding - operation for the
prevention of transverse cracking induced in weld metal. With regard to the hydrogen
concentration immediately beneath the newest bead after its pass of welding, it is
determined by dissolved hydrogen from the arc column and residual hydrogen in the
vicinity of the penetrated portion of the bead. It is easily conceivable that the
latter is determined by dissolved hydrogen from the arc column during each pass of
welding and residual hydrogen in the vicinity of the penetrated portion and the welding
thermal history until that pass. In this instance, it is known that the dissolved
hydrogen from the arc column in each pass welding is constant and according to the
results of the study in the regard, the thermal history in each pass of welding is
considered to be substantially the same. Therefore, the hydrogen concentration immediately
beneath the penetrated portion after welding the final bead in multi- layer welding
can be determined from the mean hydrogen concentration in the weld immediately after
welding the initial layer and one welding thermal history in the proximity of the
final layer.
[0036] As to the hydrogen concentration in HAZ, the same consideration can be accepted because
it becomes a function of hydrogen concentration in weld metal.
[0037] It is known from Fick's Second Law that a variation in hydrogen concentration during
a small time - period Ati at a certain point is proportional to Di·Δti where Di is
the diffusivity coefficient at that point. It follows that the quantity of hydrogen
which is dif- fusingly released from the weld zone in one welding thermal cycle is
considered to be determined by

which is obtained by dividing the thermal cycle into the small time periods Ati and
adding Di·Δti corresponding to the respective Ati.
[0038] In view of the fact that the transverse cracking is most susceptible to occur in
weld metal of 2¼Cr-1Mo steel weldment or in HAZ of A508 Class 3 weldments immediately
beneath the final layer, the value of

was determined on the basis of the thermal history of the final pass of welds, determining
its relation with the hydrogen concentration in weld metal or in HAZ immediately beneath
the penetrated portion of the final pass of welds. In Fig. 9-(a) for 2¼Cr-1Mo steel
weldments, the abscissa represents r for

while the ordinate represents the hydrogen concentration in weld metal directly beneath
the.final bead immediately after welding the final pass, non-dimensionally in terms
of the mean hydrogen concentration in the weld metal immediately after the initial
welding. Here, the discussion is based on welding of one layer with one pass. In a
case where one layer is welded with n-number of passes, this relation can be generalized
by graduating the abscissa on the scale of n (the same applies hereafter). The results
of calculation shown in Fig. 9-(a) were obtained by varying the conditions of the
welding operation over a wide range, including the thickness and width of plates and
preheating and interpass temperatures. As clear from the figure, the relation between
the hydrogen concentration in weld metal directly beneath the final pass immediately
after welding and the parameter τ of hydrogen diffusion determined from the welding
thermal history depending upon welding conditions can be expressed by a single curve.
The same relation was obtained for HAZ of A508, Class 3 weldments as shown in Fig.
9-(b).
[0039] By the use of the diagram of Fig. 9-(a) or 9-(b), it becomes possible to dispense
with the calculations which would otherwise be necessitated by variations in the mean
hydrogen concentration Co,o in the weld immediately after welding the first layer,
as a result of use of a flux of a different hydrogen level or a variation in the coefficient
of hydrogen diffusion due to use of a different material. The hydrogen concentration
directly beneath the final pass can be readily obtained as long as the value of Co,o
or one welding thermal cycle in the vicinity of the final layer and the coefficient
of hydrogen diffusion are known.
[0040] We now consider the relation between the parameter τ of hydrogen diffusion and the
conditions of welding operations.
[0041] The foregoing description has dealt with the results where the next pass of welding
is proceeded at a time point when the bead temperature reaches the level of the interpass
temperature. However, in actual operation, there sometimes occurs a temperature drop
during the pass interval which is elongated depending upon the size of a pressure
vessel or the like. In such a case, the interpass temperature is maintained by an
auxiliary heating means like gas burners as shown in Fig. 10. In this figure, indicated
at 7 is a turning roller, at 8 a welding torch, at 9 a gas burner and at 10 a shell
course of a pressure vessel. While the welding bead temperature which has reached
the interpass temperature is maintained at that level by the auxiliary heating means
until the subsequent weld bead is deposited, it is now necessary to consider the influence
of the auxiliary heating on the parameter τ of hydrogen diffusion.
[0042] With the auxiliary heating, the value of the parameter T which is determined by one
welding thermal cycle consists of the value of τ shown in Fig. 9 plus the contribution
of the auxiliary heating, that is to say, the product D.Ata of the time interval Δta
at which the welding of a next bead is deposited after the bead temperature reaching
the interpass temperature and the coefficient D of hydrogen diffusion at the temperature.
The value of Δta varies depending upon the welding conditions such as the interpass
temperature, welding speed, dimensions of the base metal, for example, the diameter
of a vessel when a girth welding to join the shell courses of a pressure vessel is
performed.
[0043] Fig. 11 shows the relation between the pass interval and the parameter τ in a case
where a joint of infinitely wide plate of 2¼Cr-1Mo steel is welded at an interpass
temperature of 200°C and, when the bead temperature reaches the interpass temperature
at the time of welding each pass, it is maintained constantly at the interpass temperature
by the auxiliary heating until the commencement of welding of the next pass. In this
figure, the broken line indicates the relation between the time in which the bead
temperature cools off to the interpass temperature after the welding of the bead and
the value of τ as determined by the welding thermal cycle at that time, namely, the
value of

of Fig. 9-(a). In this instance, the preheating zones on opposite sides of the weld
were locally preheated to 200°C over a width corresponding to the plate thickness
of 50 mm or 100 mm.. The value of τ thus obtained was 0.041 cm
2 with a plate thickness of 50 mm and 0.022 cm
2 with a plate thickness of 100 mm. The value of τ resulting from overall preheating
was 0.041 cm2 with a plate thickness of 50 mm and 0.023 cm
2 with a plate thickness of 100 mm, which were substantially the same as the values
in the case,
.of local preheating. It is known therefrom that, in the multilayer welding for plates
of extremely great thickness, the preheating in the initial stage imposes almost no
influence on the welding thermal cycle of the final layer due to dissipation of heat
over a long time period before completion of the welding. Therefore, the relation
between the cooling time to the interpass temperature after the final pass of welding
and

for a plate thickness of 250 mm was determined on the welding of the final ten passes
alone without preheating.
[0044] In Fig. ll, the straight line which extends out of the broken line indicates the
relation between the time Δta in which the welding of the next pass is initiated .after
the bead temperature reaching the interpass temperature and the increase in τ due
to the auxiliary heating, namely, the relation of D·Δta. Therefore, the' gradient
of the straight line equals the coefficient of hydrogen diffusivity at the interpass
temperature. It is clear therefrom that the pass interval imposes a great influence
on the parameter τ in consideration of the auxiliary heating. Fig. 12 shows their
relation in both cases where the interpass temperature is 150°C and 250°C. Upon comparing
this figure with Fig. 11, it is observed that the influence of the auxiliary'heating
on the parameter τ becomes greater with a higher interpass temperature although its
effect is unexpectable at the temperature of 150°C.
[0045] Thus, the hydrogen concentration in weld metal of 2¼Cr-1Mo steel weldments immediately
after welding under given conditions can readily be obtained from the diagram of Fig.
9-(a) by equivalently substituting thereinto the value of τ as determined by Fig.
11 or Fig. 12.
[0046] As for the hydrogen concentration in HAZ of A508 Class 3 weldments, relationship
shown in Fig. 13 was obtained. So, its value immediately after welding can be obtained
by combining Fig. 9-(b) and Fig. 13.
2. Relation between variations in hydrogen concentration during low temperature PWHT
and treating conditions
2-1 Influence of initial hydrogen distribution
[0047] Since the transverse weld cracking is most susceptible to occur in the vicinity of
the peak of the hydrogen concentration, it is important to clarify the relation between
the variations in the peak values of the hydrogen concentration both in weld metal
and in HAZ during the low temperature PWHT and the treating conditions in order to
prevent the transverse cracking. This paragraph deals with the influence of the hydrogen
concentration distribution immediately after welding on that relation.
[0048] Fig. 14-(a) illustrates the relation between the peak value of the hydrogen concentration
in weld metal during the low temperature PWHT (LTPNHT) and the treating con- ditions.
In the diagram of Fig. 14-(a), the ordinate represents the ratio of the peak value
C of the hydrogen concentration in the low temperature PWHT in weld metal to the hydrogen
concentration Co immediately beneath the final bead after welding, while the abscissa
represents the sum of the value of the parameter T of hydrogen diffusion during welding
and the product D
p.t
p of the coefficient of hydrogen diffusivity at the temperature of the PWHT and the
holding time. Thus, the diagram of Fig. 14-(a) shows, by way of the relation between
C/Co and (τ+D
p·t
p), the influence of the initial hydrogen distribution on the relation between the
variation in the peak value of the hydrogen concentration in the low temperature PWHT
and the. treating conditions, namely, the influence of the hydrogen distribution immediately
after the bead temperature reaching the level of the interpass temperature upon completion
of welding. The initial hydrogen concentration distribution was varied by changing
the preheating and interpass temperatures in various ways. It is observed therefrom
that, even if the initial hydrogen distribu- .tion is varied, it is possible to express
the relation between the variations in the peak value of the hydrogen concentration
and the treating conditions substantilly by a single curve based on the relation of
C/Co and (τ + D
p·t
p).
[0049] The similar relation was obtained for HAZ as shown in Fig. 14-(b). The change of
hydrogen concentration in HAZ through PWHT except for the early stage of it can also
be expressed by a single curve regardless of hydrogen concentration distribution immediately
after welding.
2-2 Influences of plate thickness
[0050] The diagram of Fig. 15-(a) shows the influence of the plate thickness on the relation
between the peak values in weld metals and the treating conditions. As clear therefrom,
no influence of the plate thickness is observed in the initial stage of the low temperature
PWHT. This is because the peak value of the hydrogen concentration is located immediately
beneath the final bead and the hydrogen diffusion at that position is greatly influenced
by the plate surfaces Further, as the heat treatment proceeds, the influence of the
plate thickness is gradually manifested due to inward shift of the peak position of
the hydrogen concentration. Judging from the conditions of low temperature PWHT which
prevent the cracking, the value of (τ + D
p·t
p) should be smaller than 1.5 cm
2 at largest in the case of 2¼Cr-1Mo steel weldments by submerged arc welding process
with the heat input of 40 KJ/cm. Therefore, with a plate thickness in excess of 100
mm, the preventing condition for a cold cracking induced in weld metal of 2¼Cr-1Mo
steel weldments can be obtained from the relation between C/Co and (T + D
p·t
p) for the plate thickness of 100 mm.
[0051] The similar relation for HAZ was obtained as indicated in Fig. 15-(b).
2-3 Influence of beveling width
[0052] Fig. 16-(a) shows the influence of the beveling width of the weld on the relation
between C/Co in weld metal and (T + D
p.t
p). Fig. 16-(b) is for HAZ. It is clear therefrom that the change of the hydrogen concentration
is delayed with a larger beveling width since the gradient of hydrogen concentration
in a direction perpendicular to the weld line becomes smaller as the vebeling width
is increased. When considering the hydrogen diffusion in the weld, it is often discussed
as a one-dimensional diffusion in the direction of plate thickness, ignoring the diffusion
from the weld to the base metal. However, in view of Figs. 15 and 16 which show the
influence of the beveling width rather than that of the plate thickness, such a discussion
is obviously meaningless. Although Fig. 16-(a) shows the influence of the beveling
width of up to 36 mm, it is the general practice in the welding in flat position to
design the beveling in a constant width taking into account the transverse contraction
of the weld, for ensuring a high welding efficiency. Therefore, the beveling width
for plates of a thickness of about 300 mm may be taken as about 36 mm at maximum.
On the other hand, in horizontal position, the beveling width is increased with a
greater plate thickness and may exceed 36 mm in some cases. Therefore, nextly considered
is the relation between C/Co in weld metal and (T + Dp-tp) in a case where the beveling
width is greater than 36 mm.
[0053] With a heavier plate thickness, the diffusion takes place in a greater degree in
the direction of plate width than in the direction of plate thickness. Now, assuming
that the diffusion occurs only in the direction of plate width according to Fick's
Second Law, the ratio of the hydrogen concentration C at the center of the weld during
the low temperature PWHT to the initial hydrogen concentration Co can be expressed
simply as C/Co = Φ (W/4√τ + D
p·t
p), in which Φ is an error function. The influence-of a beveling width greater than
36 mm can thus be approximately expressed by arranging the results of the case of
h = 150 mm and W = 36 mm of Fig. 16-(a) into the relation between C/Co and 4 √τ +
D
p·t
p /W.
[0054] The solid line in Fig. 17 is a plot of the thus obtained relation between the variation
in the hydrogen concentration in the low temperature PWHT, treating conditions and
beveling width. However, this relation fails to sufficiently take into account the
diffusion in the direction of plate thickness except for the case where W = 36 mm,
underestimating the diffusion in an increasing degree as the beveling width becomes
larger than 36 mm. As a result, C/Co is given a value which is greater than its actual
value. However, as mentioned hereinbefore, the diffusion in the direction of plate
thickness is considered to take place in a small degree as compared with that in the
direction of plate width in a case where the plate thickness is sufficiently large
relative to the beveling width, approximately establishing the relation shown. Therefore,
the relation of C/Co and (T + D
p·t
p) in the case where h = 150 mm and W = 30 mm of Fig. 16 was arranged into the relation
of C/Co and 4√τ + D
p.t
p /W as indicated by a curve of broken line in Fig. 17. Upon comparing the curves of
solid and broken lines, it will be clear that the relation between C/Co and 4 √τ +
Dp.tp /W undergoes almost no changes in spite of variations in W. Thus, it is possible
to obtain safe and approximately correct conditions for the low temperature PWHT for
weld metal by applying the curve of solid line to beveling widths greater than 36
mm.
[0055] The same relation with regard to the change of hydrogen concentration in HAZ where
a beveling width . is greater than 37 mm, can easily be obtained by making use of
the relation in case of plate thickness and beveling width being 150 mm and 37 mm,
which is shown in Fig. 16-(b).
3. Critical hydrogen concentration for preventing trans- verse cracking in weld zone
in butt welding
[0056] Fig. 18-(a) shows the results of cracking tests under different conditions of welding
and low temperature PWHT along with hydrogen distributions in the respective test
conditions. Since prevention of the cold cracking is considered to depend on the cooling
rate to the level of 100°C, the critical hydrogen concentration for the prevention
of cracking is expressed by values at the time when the test pieces are cooled to
100°C. The curves in this figure indicate the hydrogen concentration distributions
in the cooled test pieces at 100°C, of which curves of broken lines are of test pieces
with a crack and the curves of solid lines are of test pieces without a crack. It
will be clear therefrom that the crack-preventing critical hydrogen concentration
in the weld in butt welding of 2¼Cr-1Mo steel is about 3.3 cc/100gr at a peak value.
[0057] On the other hand, as for A508 Cl.3 weldments, its susceptibility to the transverse
weld cracking induced in HAZ depends upon the extent of the segregation of alloying
elements and impure elements, such as C, Mn, Si, Mo, S, and so forth. In other words,
the critical hydrogen concentration changes depending upon whether HAZ contains a
so-called inverse V segregation zone, or not, as shown in Fig. 18-(b). This is because
such a segregation hardens the microstructure of HAZ to a high degree.
[0058] From these data, we can introduce a relation practically useful to determine the
critical hydrogen concentration under which any transverse weld cracking will not
occur either in weld metal or in HAZ. Fig. 19 shows the relation between the hydrogen
concentration and the microstructure in weld zone in terms of maximum Vicker's hardness
number with regard to the occurrence of the crack. So, a straight line in the figure
shows the relation between the critical hydrogen concentration [Ccr] and maximum Vicker's
hardness number in weld zone [Hv], as is represented by an equation:

where [Hv] is in the range of 300 to 500. Using this relationship, we can easily determine
the critical hydrogen concentration depending upon base metal and welding conditions,
such as welding materials, weld heat input, and so forth, through the maximum Vicker's
hardness number in weld zone produced under the respective conditions.
[0059] As a result, using the value of [Ccr] obtained from the above equation, we can determine
the minimum condition of low-temperature PWHT required to prevent the transverse crack
induced in multi-layer welds. Of course, in order to determine the practical condition
.of PWHT, the value of [Ccr] should be estimated lower to a certain extent than the
value obtained from the equation because the factor of safety should be modified depending
upon the importance of the structure, accuracy of non-destructive inspection employed
for weld zone, and so forth.
4. Condition for preventing cracking through low temperature PWHT
[0060] As mentioned hereirbefore, the conditions for preventing cracking through low temperature
PWHT depend on factors such as the shape and dimensions of the weld, the hydrogen
level of the flux, sort of the base metal or its conb ination with welding materials
and the conditions of the welding operation. As an example the conditions for a particular
operation for 2¼Cr-1Mo steel weldments are determined by the following procedures.
[0061] (1) For given plate thickness at the weld, preheating and interpass temperatures,
nunb er of weld passes per layer, and pass intervals, decide the parameter which governs
the hydrogen diffusion at the time of welding by the use of the diagram of Fig. 11
or Fig. 12.
[0062] (2) Find in Fig. 9 (a) the value of the hydrogen concentration Co which is determined
by the parameter . Here, Co,o represents the mean hydrogen concentration in the weld
immediately after welding the first pass and is 4.74 cc/100 g in the case of sub merged
arc welding using the flux MF-29A.
[0063] (3) Of tain the values of the crack-preventing critical hydrogen concentration Ccr
from the relation between Ccr and maximum Vicker's hardness nunber in weld metal mentioned
in the preceding paragraph and its ratio Ccr/Co to the hydrogen concentration Co immediately
after welding.
[0064] (4) Plot the values of Ccr/Co of the preceding step (3) on the ordinate of the diagram
of Fig. 16-(a) or Fig. 17, reading out the necessary treating conditions (τ + D
p·t
p) on the abscissa according to the given plate thickness and beveling width.
[0065] (5) Subtract the value of Tof the step (1) from the value of (τ + D
p·t
p) of the step (4) to obtain the low temperature PWHT conditions D
P. *t
p suitable for the plate thickness, preheating and interpass temperatures, number of
weld passes per layer, pass intervals, maximum Vicker's hardness number in weld zone,
and beveling width as specified in the steps (1) through (4). Here, the values of
Dp and tp represent the hydrogen diffusivity coefficient and the holding time at the
treating temperature, respectively, so that the holding time for a given treating
temperature can be obtained according to the relation between the hydrogen diffusivity
coefficient and the temperature. The same condition of PWHT required to prevent the
occurrence of a cold cracking in other low alloy steel weldments can be evaluated
by following the procedure presented in Fig. 20.
[0066] Fig. 21 schematically shows the PWHT in multi- layer welding of a circumferential
joint of a pressure vessel, wherein a shell course of a vessel 1 which is rotated
on turning rollers 7 in the arrowed direction is heated at two positions by burners
9A and 9B while measuring the temperature'of the shell course 1 at six different positions
T
1 to T
6. There are no restrictions on the numbers of the burners and measuring points or
on the measuring positions or method. However, it is preferred to provide the burners
and measuring points as many positions as possible in order to enhance the accuracy
of the heat control. The dissipation of diffusible hydrogen is improved all the more
in a case where the shell course is heated on both the inner and outer sides thereof.
[0067] The diagram of Fig. 22 shows the relation between the lapse of time in the course
of measurement at the respective measuring points of the temperatures of the shell
course 1 heated by burners 9A and 9B and the hydrogen diffusivity coefficient (Dp
i) at the respective temperatures. In order to assist understanding, the diagram shows
the positions of the burners 9A and 9B relative to the measuring points. It will be
seen therefrom that the hydrogen diffusivity coefficient (Dp
i) has a pattern of declining from T
1 to T
3 and from T
4 to T
6.
[0068] While rotating the vessel for the LTPWHT in the above-described manner, the value
of Dpi which varies with lapses of time is time-integrated until its cumulative value
reaches Dp.tp determined in the step (5). Upon detection of the time point when the
time-integration of Dpi reaches D
p·t
p, the LTPWHT is terminated since the concentration of diffusible hydrogen at the peak
position is smaller than the critical hydrogen concentration Ccr at that time point.
[0069] In a welding operation other than the circumferential welding of a vessel, for instance,
in an operation for a seam welding or for welding a nozzle to a pressure vessel, the
weld line is uniformly heated along the entire length thereof so that the temperatures
measured only at one arbitrary point may be used for the control of the PWHT.
[0070] It will be appreciated from the foregoing description that, according to the method
of the present invention, it becomes possible to judge the terminating point of the
LTPWHT correctly and to improve the quality control by precluding the cracking due
to insufficient LTPWHT or uneconomical excessive PWHT, so called inter- . mediate
stress relief annealing.
1. A method for the low-temperature PWHT in multilayer welding, comprising the steps
of;
determining the residual hydrogen concentration Co (cc/100 g) directly beneath the
final welded layer immediately after completion of welding;
determining a crack-preventing critical hydrogen concentration Ccr (cc/100 g) to obtain
a ratio of
Ccr/Co; determining the value of a product Dp·tp of a hydrogen diffusivity coefficient Dp (cm2/sec.) during the heat treatment and a holding time tp (sec.) where a currently reached
hydrogen concentration C (cc/100 g) become equal to the critical hydrogen concentration
Ccr, on the basis of the relation of a ratio C/Co of the current hydrogen concentration
C (cc/100 g) to the residual hydrogen concentration Co and a sum of a parameter τ
(cm2) of hydrogen diffusion of the formula given below and the product of Dp.tp;
measuring the temperature of the heat treatment at a suitable position of the weld;
and
terminating the heat treatment at a time point when a time-integrated value of a hydrogen
diffusivity coefficient Dpi (cm2/sec.) at the measured temperature exceeds the value of Dp·tp.

wherein, PWHT: postweld heat treatment,
Di: a hydrogen diffusivity coefficient (cm2/sec.) in an arbitrary weld portion during welding each unit layer; and
tn: time (sec.) required for welding each unit layer.
2. A method for the low-temperature PWHT as set forth in claim 1, comprising determining
the parameter τ of hydrogen diffusion and the dissolved hydrogen concentration Co,o
(cc/100 g) under given welding conditions, and determining Co on the basis of the
relation between the parameter τ and Co/Co,o.
3. A method for the low-temperature PWHT as set .forth in claim 1 or 2, comprising
heating a circumferential weld of a rotated heavily thick vessel by more than one
burner, measuring the temperature of said weld at an arbitrary point thereof to obtain
variations in a hydrogen diffusivity coefficient Dpi against time, and detecting the
time point when the time-integrated value of said coefficient Dpi exceeds the value
of Dp.tp.
4. A method for the low-temperature PWHT as set forth in claim 1 or 2, comprising
heating a butt weld line from one side thereof by a plural number of fixed burners
while measuring temperatures at arbitrary different points on the other side of said
weld line to obtain variation in the hydrogen diffusivity coefficient Dpi against
time, and detecting a time point when the time-integrated value of Dpi exceeds the
value of Dp·tp.
5. A method for the low-temperature postweld heat treatment as set forth in claim
1, 2 or 3, wherein the critical hydrogen concentration [Ccr] has the following relation
with maximum Vicker's hardness number in the weld zone [Hv]; [Ccr] = -0.0096 [Hv]
+ 6.76 where [Hv] is in the range of 300 to 500.
6. A method for the low-temperature postweld heat treatment in multilayer welding,
comprises the steps of;
obtaining the residual hydrogen concentration [Co]D and [Co]H (cc/100 g) directly beneath the finally welded layer immediately after completion
of multilayer welding, where [Co]D and [Co]H are for weld metal (deposited metal) and for heat affected zone, respectively;
obtaining the critical hydrogen concentration for prevention of cracking [Ccr]D and [Ccr]H for the weld metal and for the heat affected zone, respectively, which depend upon
the maximum residual stress and maximum Vicker's hardness number of microstructure
in weld zone;
obtaining the values of [Ccr/Co]D and [Ccr/Co]g, ratio of the critical hydrogen concentration [Ccr]D and [Ccr]H for prevention of cracking both in the weld metal and the heat affected zone to the
residual hydrogen concentration [Co]D and [Co]H;
obtaining the values of [C/Co]D and [C/Co]H for the weld metal and for the heat affected zone, the ratio of the hydrogen concentration
in the weld zone [C]D and [C]H which are lessen by the low-temperature postweld heat treatment to the residual hydrogen
concentration [Co]D and [Co]H;
obtaining the values of [τ + Dp·tp]D and [τ + Dp·tp]H for the weld metal and for the heat affected zone where Dp is hydrogen diffusivity
coefficient during the postweld heat treatment and tp is the holding time, and T (cm2) is a hydrogen diffusion parameter in a welding operation under given conditions

wherein Di is a hydrogen diffusivity coefficient (cm2/sec.) in an arbitrary weld zone of each unit and tn is the time required for welding
each unit layer;
determining a larger value [Dp.tp] of [Dp·tp]D or [Dp.tp]H by comparing those values, as a condition of the postweld heat treatment;
measuring the temperature at a suitable portion of the weld during the postweld heat
treatment, and
terminate the heat treatment at a time point when the time-integrated value of the
hydrogen diffusivity coefficient [Dpi] (cm2/sec.) at the measured temperature exceeds the value of [Dp.tp].
7. The method as set forth in claim 6, wherein the critical hydrogen concentration
[Ccr]
D and [Ccr]
D are obtained by the following equations

and

where [Hv]
D and [Hv]
H are maximum Vicker's hardness number in the weld metal and in the heat affected zone.
8. A method for the low temperature PWHT of a multi- layer weld characterised by the
steps of:
determining for a test weld similar to said multilayer weld the residual hydrogen
concentration Co (cc/100 g) directly beneath the final welded layer immediately after
completion of welding;
determining for the test weld a crack-preventing critical hydrogen concentration Ccr
(cc/100 g) to obtain a ratio of Ccr/Co;
determining for the test weld the value of a product D .t of a hydrogen diffusivity
coefficient Dp (cm2/sec.) during the heat treatment and a holding time tp (sec.) where a currently reached hydrogen concentration C (cc/100 g) becomes equal
to the critical hydrogen concentration Ccr, on the basis of the relation of a ratio
C/Co of the current hydrogen concentration C (cc/100 g) to the residual hydrogen concentration
Co and a sum of a parameter τ (cm2) of hydrogen diffusion of the formula given below and the product of Dp.tp;
measuring for said multilayer weld the temperature of the heat treatment at a suitable
position of the weld; and
terminating the heat treatment of said multi- layer weld at a time point when a time-integrated
value of the previously determined hydrogen diffusivity coefficient Dpi (cm2/sec.) at the measured temperature exceeds the previously determined value of Dp·tp.

wherein, PWHT: postweld heat treatment,
Di: a hydrogen diffusivity coefficient (cm2/sec) in an arbitrary weld portion during
welding each unit layer; and
tn: time (sec.) required for welding each unit layer.
9. A method for the low temperature postweld heat treatment of a multilayer weld,
characterised by the steps of;
obtaining for a test weld similar to said multilayer weld, the residual hydrogen concentration
(Co)D and (Co)H (cc/100 g) directly beneath the finally welded layer immediately after completion
of multilayer welding, where (Co)D and (Co)H are for weld metal (deposited metal) and for heat affected zone, respectively;
obtaining for the test weld the critical hydrogen concentration for prevention of
cracking (Ccr)D and (Ccr)H for the weld metal and for the heat affected zone, respectively, which depend upon
the maximum residual stress and maximum Vicker's hardness number of the microstructure
in the weld zone;
obtaining for the test weld the values of (Ccr/Co)D and (Ccr/Co)H, the ratio of the critical hydrogen concentration (Ccr)D and (Ccr)- for prevention of cracking both in the weld metal and the heat affected zone to the
residual hydrogen concentration (Co)D and (Co)H;
obtaining for the test weld the values of (C/Co)D and (C/Co)H for the weld metal and for the heat affected zone, the ratio of the hydrogen concentration
in the weld zone and the heat affected zone (C)D and (C)H which are lessened by the low temperature postweld heat treatment to the residual
hydrogen concentration (Co)D and (Co)H;
obtaining for the test weld the values of τ + Dp·tp)D and (τ + Dp·tp)H for the weld metal and for the heat affected zone where Dp is hydrogen diffusivity coefficient during the postweld heat treatment and t is the
holding time, and τ (cm2) is a hydrogen diffusion parameter in a welding operation under given conditions

wherein Di is a hydrogen diffusivity coefficient (cm2/sec.) in an arbitrary weld zone of each unit and tn is the time required for welding
each unit layer;
determining for the test weld a value (Dp·tp) which corresponds to the larger of (Dp·tp)D or (Dp·tp)H by comparing those values, as a condition of the postweld heat treatment;
measuring for said multilayer weld the temperature at a suitable portion of the weld
during the postweld heat treatment, and
terminating the heat treatment of said multi- layer weld at a time point when the
time integrated value of the previously determined hydrogen diffusivity coefficient
(Dpi) (cm2/sec.) at the measured temperature exceeds the previously determined value of (Dp·tp).