\input texp.tex

\rightline{\it Short Communication} \bigskip\bigskip

\centerline {\large The Bruscato Factor in the Temper Embrittlement of
Welds}

\centerline{S. H. Lalam,  H. K. D. H. Bhadeshia and D. J. C. MacKay$^{\dag}$}\medskip
\centerline{ University of Cambridge}

\centerline{ Department of Materials Science and Metallurgy} 
 \centerline{ Pembroke Street, Cambridge CB2 3QZ, U.K.}

\medskip

\centerline{ $^{\dag}$Cavendish Laboratory}

\centerline{Madingley Road, Cambridge CB3 0HE, U.K.}

\bigskip \singlespace

\sec {Abstract}

{\parindent=20pt \narrower \medskip 

Published experimental data on the tendency for ${\rm 2{1\over4}Cr1Mo}$
to undergo impurity--induced temper embrittlement have been analysed
quantitatively. The results indicate strong effects due to the
phosphorus, silicon, manganese and molybdenum concentrations, but the
influence of tin, antimony and arsenic cannot be perceived because of
the overwhelming effects of the other elements. A computer model for the
calculations is obtainable freely over the world wide web.

 \medskip} 
  
  
\sec {Introduction}

Welding alloys designed for creep--resistant steels  frequently
have to be tempered in a temperature range where they are susceptible to
embrittlement by impurity elements such as antimony or phosphorus. The
segregation of these deleterious elements to the prior austenite grain
boundaries leads to intergranular failure and consequently, a reduction
in toughness. Whereas this mechanism of embrittlement is well--understood
from a vast amount of research published over the last five decades,
there are no quantitative methods capable of estimating the degree of
embrittlement as a function of the chemical composition and heat
treatment.

It was in this context that Bruscato [1] reported a large number of
experiments, based on the classical ${\rm 2{1\over4}Cr1Mo}$ composition,
but with variations in the phosphorus, antimony, tin and arsenic
concentrations. There were also some   variations in the
concentrations of the major alloying additions including C, Mn, Si, Cr and
Mo. The tendency to embrittlement was monitored by comparing the impact
toughness of both post--weld heat treated (PWHT) and step--aged samples.
The latter heat treatment exaggerates the extent of embrittlement.

Bruscato used an embrittlement factor to interpret his data:
$$ \overline X = {\rm {10P + 5Sb + 4Sn + As}\over{100}} \numeqn $$ where
the concentrations of the elements are in parts per million by weight. A
large value of $\overline X$ implies a greater tendency to temper
embrittlement. This led him to conclude that the embrittlement of  ${\rm
2{1\over4}Cr1Mo}$ welds is directly related to the manganese, silicon,
phosphorus, tin, arsenic and antimony concentrations, with the first
four being of greatest significance. The derivation of
$\overline X$ was not presented in the original paper, although it is
stated that the equation is based on data from chromium--steels. In the
present work we analyse Bruscato's original data using neural network
analysis [2, 3], and examine his conclusions in more detail. The neural
network method has already been explained in previous publications [2, 3] and so
is not reproduced here. Suffice it to say that neural networks are
parameterized non--linear models used for   regression or classification
modelling. Their flexibility makes them able to discover more complex
relationships in data than traditional linear statistical models. The particular method used here also has the advantage of indicating an error bar which depends on the position in the input space.

\sec {The Data}

Bruscato published results on thirty separate weld deposits; the range
of parameters is listed in \tablaa. The Charpy toughness of the
step--aged samples represents the output to be modelled as a function
of all the other variables listed in \tablee. All of the thirty welds
had been given an identical heat treatment. For the purposes of the
analysis, the data were all normalised in the range
$\pm 0.5$ in order to compare the significance of each of the input
variables. 

\midinsert  
  \thicksize=0.7pt \thinsize=0.5pt 
 \tablewidth=6.4truein {\smalltype  
 \begintable 
 {\bf Input element  } | {\bf Minimum  } |{\bf  Maximum  } | {\bf Mean  } | {\bf Standard Deviation } \cr  
  Silicon    (wt\%) \hfill  |  0.32 \hfill  | 1.19 \hfill  | 0.64 \hfill  | 0.20\nr 
  Manganese  (wt\%) \hfill  | 0.54 \hfill  | 0.79 \hfill  | 0.69 \hfill  | 0.06 \nr 
  Phosphorus (wt\%) \hfill  | 0.004 \hfill  | 0.018 \hfill  | 0.009 \hfill  | 0.003 \nr 
  Molybdenum (wt\%) \hfill  | 0.9 \hfill  | 1.27 \hfill  | 1.10 \hfill  | 0.10 \nr 
  Tin     (ppm wt.) \hfill  | 70 \hfill  |  300 \hfill  | 109 \hfill  | 39 \nr 
  Antimony (ppm wt.) \hfill  | 0.9 \hfill  | 22 \hfill  | 5 \hfill  | 4 \nr 
  Arsenic  (ppm wt.) \hfill  | 0.0 \hfill  |  130 \hfill  | 59 \hfill  | 28 \cr 

 Charpy toughness after step aging (J) \hfill  |  7 \hfill  | 137 \hfill  | 60 \hfill  | 29 
 \endtable }
  {\tabtit{\tablee : } {The range of values reported by Bruscato, and
used in the present work.}} 
 \endinsert 

The data were  divided at random into two parts, a training and a
test dataset. The neural network models were then created using just the
training data [3]. The resulting models were assessed on their ability to
generalise on the unseen test data.  From the models created, a committee
of three models was found to give the best generalisation on unseen
data.  These three models had 13, 11 and 11 hidden units with
$\sigma_\nu$ values of 0.083293, 0.083149 and 0.083118 respectively; 
$\sigma_\nu$ is the perceived level of noise in the normalised output. An
increase in the number of hidden units enables the network to recognise
more complex relationships. The details of the network have been
reported previously [2, 3]. The committee members were finally optimised
on the entire dataset. The performance of the committee is illustrated in
\fagg.

\fagg\ shows the significance $\sigma_w$ of each of the input variables.
The value of $\sigma_w$ for a particular input variable indicates the
ability of that input to explain variations in the output (Charpy
toughness). Three $\sigma_w$ values are presented for each input,
corresponding to each of the three members of the committee of models. A
consistent value of $\sigma_w$, for a given input, indicates
that there exists a well--defined relationship between that
input and the output. \figg\ shows that tin, antimony and arsenic have
very little effect on the embrittlement of the ${\rm 2{1\over4}Cr1Mo}$
welds studied, whereas phosphorus has a very large effect.

These observations can be illustrated further by making predictions.
Calculations were done using the base set of input values listed in
\tablaa, while varying each input individually.


 \midinsert 
  \thicksize=0.7pt \thinsize=0.5pt 
 \tablewidth=3.0truein {\smalltype \begintable  
 Silicon    (wt\%) \hfill  |  0.58 \nr 
  Manganese  (wt\%) \hfill  | 0.78  \nr 
  Phosphorus (wt\%) \hfill  | 0.008  \nr 
  Molybdenum (wt\%) \hfill  | 1.05  \nr 
  Tin     (ppm wt.) \hfill  | 120  \nr 
  Antimony (ppm wt.) \hfill  | 1.6  \nr 
  Arsenic  (ppm wt.) \hfill  | 36    
 \endtable} 

 \tabtit{\tablee : } {Base input values used in the application of the 
embrittlement model. The values correspond to weld~Q in [1].} 
 \endinsert 

\fagg\ shows the effects of molybdenum, silicon, manganese and
phosphorus concentrations. As expected, phosphorus has a strong and very
significant tendency to embrittle the weld metal; as stated earlier, the
mechanism of phosphorus embrittlement is well--understood, involving its
segregation to prior austenite grain boundaries. On the other hand,
molybdenum actually improves the resistance to embrittlement. This is
also expected, because molybdenum and phosphorus atoms tend to associate
so that the latter is prevented from segregating to the prior austenite grain
surfaces [4]. 

It is exciting that significant trends are recognised also for manganese
and silicon. The manganese effect is consistent with work which suggests
that it reduces the intergranular fracture strength [5].
Silicon is known to promote the segregation of
phosphorus to the austenite grain boundaries [6].

By contrast, there are no significant trends notable for arsenic, tin
or antimony (\fagg). Based on these observations, we do not find that
As, Sn and Sb are important contributors to embrittlement in the
particular alloy system studied here. It is possible that this result is
a consequence of the fact that the welds all contain phosphorus in
concentrations large enough to swamp the much smaller effects of As, Sn
and Sb. Thus, the mean phosphorus concentration is 90~p.p.m, with a
standard deviation of 30~p.p.m. 

\sec {CONCLUSIONS}

It is found that phosphorus, silicon and manganese all make ${\rm
2{1\over4}Cr1Mo}$ welds susceptible to temper embrittlement, with the
embrittling potency decreasing in that order. Molybdenum decreases the
tendency to impurity induced embrittlement. These observations are all
expected from published work. By contrast, As, Sb and Sn have no
perceptible effect on the welding alloys studied, probably because of the
overwhelming influence of phosphorus. It follows that any attempt to reduce the effects of temper embrittlement should focus primarily on reduction in the phosphorus. The computer model produced to make these predictions can be obtained from:

 $$http://www.msm.cam.ac.uk/map/mapmain.html$$



 \sec{REFERENCES} 
  
\def\ref#1#2#3#4#5#6#7{\hoffset=6.0mm \parindent=-6.0mm 
\singlespace \rightskip=6.0mm \singlespace {#1.} #2: {\it 
#4} {\bf #5} (#3) #6\vskip 0.5truemm} 

{\parskip=0mm \parindent=10pt \narrower 

\ref{1} {Robert Bruscato} {April, 1970} {Welding Research Supplement} {} {148s--156s} {Temper Embrittlement and Creep Embrittlement of 2$1\over4$Cr - 1Mo Shielded Metal Arc Weld Deposits}

\ref{2}  {MacKay, D. J. C.} {1997} {Mathematical Modelling of Weld Phenomena 3, Ed. by  H. Cerjak} {} {359--389} {The Institute of Materials, London, U.K.}


\ref{3} {Bhadeshia, H. K. D. H.} {1999} {ISIJ International} {39} {966--979} {Neural Networks in Materials Science} 
 
\ref{4} {Powers, A. E.} {1956} { Trans. ASM} {48} {149--164} {The influence of molybdenum and tungsten on temper embrittlement}

\ref{5} {Grabke, H. J., Hennesen, K., M$\ddot{o}$ller, R. and Wei, W.} {1987} {Scripta Metallurgica} {21} {1329--1334} {Effects of manganese on the grain boundary segregation, bulk and grain boundary diffusivity of P in ferrite}

\ref{6} {Smith, J. F., Reynolds, J. H. and Southworth, H. N.} {1980} { Acta Metallurgica} {28} {1555--1564} {The role of Mn in the temper embrittlement of A 3.5Ni--Cr--Mo--V steel}

\medskip}



\topinsert
\vskip 3.5 in
\special{psfile=COM_RESULT.eps hoffset=80 voffset=-80 hscale=45 vscale=45}

 {\tabtit{Fig. 1 : }{Comparison of the predicted and measured values 
 of the Charpy toughness. The predictions are made using the committee
of three models.}}

\vskip 3.5 in
\special{psfile=sigma_w5.eps hoffset=0 voffset=-50 hscale=80 vscale=80}

 {\tabtit{Fig. 2 : }{The perceived significance $\sigma_w$ values of three committee models for each of the inputs.}}

\endinsert

\topinsert
\vskip 3.5 in
\special{psfile=RMo.eps hoffset=-20 voffset=0 hscale=50 vscale=50}
\special{psfile=RSi.eps hoffset=190 voffset=0 hscale=50 vscale=50}
\smallskip

\vskip 3.5 in
\special{psfile=RMn.eps hoffset=-40 voffset=0 hscale=50 vscale=50}
\special{psfile=RP.eps hoffset=190 voffset=0 hscale=50 vscale=50}

  {\tabtit{Fig. 3 : }{Analysing the effects of molybdenum, silicon, manganese and phosphorus on toughness after step aging.}}

\endinsert



\topinsert
\vskip 3.5 in
\special{psfile=RSn.eps hoffset=-40 voffset=0 hscale=50 vscale=50}
\special{psfile=RSb.eps hoffset=190 voffset=0 hscale=50 vscale=50}

\vskip 3.5 in
\special{psfile=RAs.eps hoffset=90 voffset=0 hscale=50 vscale=50}
\smallskip
  {\tabtit{Fig. 4 : }{The effects of tin, antimony and arsenic on toughness after step aging.}}
\endinsert


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 \end 
  
