Updated, May 2007
The calculation accuracy of welding cooling time was improved.
The boundary condition at the plate surface in SAW was changed to the adiabatic condition.
(The thermal reflection rate was changed from 0.9 to 1.0)
Any input exceeding the limit is rejected and replaced by the limit value.

Master code by N. Y.

1. Formulae of carbon equivalent and steel transition temperature

Transformation temperatures (oC)

Ac₃=937.2-436.5C+56Si-19.7Mn-16.3Cu-26.6Ni-4.9Cr+38.1Mo

+124.8V+136.3Ti-19.1Nb+198.4Al+3315B

Ac₁=750.8-26.6C+17.6Si-11.6Mn-22.9Cu-23Ni+24.1Cr+22.5Mo

-39.7V-5.7Ti+232.4Nb-169.4Al-894.7B

Ms=521-353C-22Si-24.3Mn-7.7Cu-17.3Ni-17.7Cr-25.8Mo

Carbon equivalents(wt%)
          The unit of chemical composition is wt%.

CE(IIW)=C+Mn/6+(Cu+Ni)/15+(Cr+Mo+V)/5

CE(WES)=C+Si/24+Mn/6+Ni/40+Cr/5+Mo/4+V/14

Pcm=C+Si/30+Mn/20+Cu/20+Ni/60+Cr/20+Mo/15+V/10+5B

CEn=C+f(C){Si/24+Mn/6+Cu/15+Ni/20+(Cr+Mo+Nb+V)/5}

where, f(C)=0.75+0.25tanh{20(C-0.12)}

.2. Equation of welding thermal history

The calculation is based on the following equation in which the effects of
finite plate thickness and heat transfer on the plate surfaces are considered
on the original Rosenthal equation.

where,

T: temperature (oC)

Tph: preheat & interpass temperature (oC)

: ambient temperature (oC)

Tw: temperature increase due to a moving point heat source(oC)

x: coordinate in the welding direction (cm)

z: coordinate in the plate thickness direction (cm)

y: coordinate in the direction perpendicular to the welding direction (cm)

w: moving coordinate in the welding direction, w = x - v*t

v: welding velocity (cm/s)

t: time elapsed after the point heat source passed the static coordinate
    origin (x = y = z = 0), (s)

R:

Rn:

Rn':

Qp: energy of heat source   (cal/s)

h: plate thickness (cm)

: arc thermal efficiency, = 1.0 (SAW),  0.80 (SMAW, GMAW),  0.60 (GTAW)

: heat transfer coefficient at the plate surface = 0.0005cm/s (SAW)
                                                 = 0.0020cm/s (SMAW, GMAW, GTAW)

: heat transfer coefficient at the surface except the weld part
                                                 = 0.0020cm/s

r: heat reflection rate at the plate surface = 1.00 (SAW), = 0.80 (SMAW, GMAW, GTAW)

: thermal conductivity = 0.06 + 0.000012 * HI (cal/cm s)

: thermal diffusively = 0.042 + 0.000016 * HI (cm cm/s)

E: arc energy, E = 60 * A * V / v (J/cm)

HI: heat input, HI = * E (J/cm)

A: welding current (A)

V: welding voltage (V)

The above heat conduction equatiion is mathematically incorrect since the heat reflction rate, r is contained.
"r" was introduced so that the prediction could be more precisely made.
The accuracy of the prediction is shown in
      N. Yurioka. "Prediction of weld metal strength", IIW Doc. IX-2058-03

3. Equation of HAZ maximum hardness

HAZ maximum hardness is estimated by equations described in the following paper:

N. Yurioka et al., "Prediciton of HAZ hardness of ferritic steels", Metal Construction, vol19 (1987), p.217R

where,

t8/5: welding cooling time between 800 and 500oC (s)
The unit of chemical compostion is wt%.

f(B): an increase in HAZ hardenability due to boron, (C <= 0.8%, N <= 0.01%)

4. Prediction of minimum necessary preheat temperature

The minimum necessary preheat temperature is predicted based on a method described in
the following paper:

  N. Yurioka and T. Kasuya: "A chart method to determine necessary preheat in steel welding"

     Welding in the World, vol. 35 (1995), p. 327-334

The validity of this method is compared with the British Standard and American Welding Society
method:

   N. Yurioka: "Comparison of preheat predictive methods"

     Welding in the World, vol. 48 (2004), p. 21-27

The objective of preheating is to effuse diffusible hydrogen out of welds to prevent hydrogen-assisted
cold cracking. The occurrence of cold cracking is influenced by the following factors:
  1) Chemical composition of steel;
  2) Plate thickness or wall thickness;
  3) Weld metal diffusible hydrogen content
  4) Welding heat input
  5) Welding residual stresses or weld metal yield strength
  6) Weld joint restraint
  7) Notch concentration factor at weld toe and weld root or groove shape
  8) Weld pass number
  9) Preheating method (Heating rate, heating width)
10) Ambient temperature
11) Immediate postheating

The present predictive method considers most of the factors above mentioned.

1) Chemical composition of steel

The following carbon equivalent has been long used as an index representing the susceptibility to
cold cracking. or weldability.

   CE(IIW) = C + Mn/6 + (Cu + Ni)/15 + (Cr + Mo + V)/5 [wt%]

This carbon equivalent satisfactorily evaluates weldability whose carbon content is higher than 0.12%.
Modern low alloy steel is mostly of a carbon reduced type (C <= 0.12wt%). Weldability of this type of steel is more
adequately evaluated by the following carbon equivalent.

   Pcm = C + Si/30 + Mn/20 + Cu/20 + Ni/60 + Cr/20 + Mo/15 +V/10 + 5B [wt%]

Susceptibility to cold cracking is determined by hardness of welds (HAZ and weld metal). The weld hardness is
determined by an interactive effect of weld hardenability and carbon content.. The following carbon equivalent
considers this effect and can evaluates weldability of steel with a wide range of carbon.

CEn = C + f(C) { Si/24 + Mn/6 + Cu/15 + Ni/20 + (Cr + Mo + Nb + V)/5 } [wt%]

       where, f(C) = 0.5 + 0.25 tanh { 20 (C - 0.12) } [wt%]

With decreasing carbon content, f(C) decreases from 1.0 to 0.5. Therefore, CEn is close to CE(IIW)
when C is higher than 0.15wt% and CEn approaches to Pcm as a carbon content decreases.
The present preheat predictive method uses CEn carbon equivalent. CEn is stipulated in ASTM A1005/A-00
and ASME B16.49-2000.

2) Plate thickness and wall thickness

With increasing plate thickness, 1) the welding cooling rate increases (welding cooling time, t8/5 decreases)
and thus, weld hardenability is raised; 2) the welding cooling time to 100oC, t100 decrease and thus, an
opportunity of effusion of diffusible hydrogen from weld metal decreases; 3) the welding pass (layer) increases
and thus the amount of hydrogen accumulated in weld metal is raised. These effects raises a risk of the
occurrence of cold cracking.

3) Weld metal diffusible hydrogen

Weld metal hydrogen is one of the important factor in hydrogen-assisted cold cracking.
It is desired to use welding materials of low hydrogen types. A care must be taken to prevent welding
materials from being moistened and to clean weld grooves before welding.

The following is an example of the diffusible hydrogen content, H(IIW) for various welding materials:

Rutile electrode : 30ml/100g;
Cellulosic electrode : 60ml/100g;
Low hydrogen electrode : 5 - 8ml/100g
Ultra low hydrogen electrode : 2 - 5ml/100g

TIG, Solid wire GMAW : 2ml/100g;
Flux cored wire GMAW : 6 - 10ml/100g
SMAW : 2 - 8ml/100g

4) Welding heat input

With increasing heat input, the cooling rate decreases (the welding cooling time between 800 and 500oC, t8/5
and welding cooling time to 100oC, t100 increases) and thus, a risk of the occurrence of cold cracking is reduced. Roughly speaking, cold cracking is a matter of concern only when heat input is not higher than 3kJ/mm.

5) Welding residual stresses or weld metal yield strength

Welding residual stresses are one of the important factors in cold cracking. The welding residual stresses often
attain the yield strength of weld metal. Hydrogen-assisted cold cracking is more likely occur in welding of
high strength steel with using high strength welding materials.

6) Weld joint restraint

The weld joint restraint affects the cold cracking occurrence in one-pass welding.. In multi-pass welding, the
joint restraint influences cold cracking to much lesser extent because a joint has been restrained after root-
pass welding. Very low restraint may cause bending distortion leading to high bending stresses in weld root.
As a result, root cracking may be caused.
The present predictive method does not consider the effect of joint restraint.

7) Notch concentration factor at weld toe and weld root or groove shape

Cold cracking is more likely to occur at the root pass in the first side of double bevel groove (K groove, X
groove) because of a high notch concentration factor at the root. However, the root weld of the first side is
generally gouged before the start of second side welding. In welding with V groove and single-bevel groove,
a notch concentration factor at the root is far less than that in double bevel groove welding. Therefore,
the present predictive method does not consider the effect of a notch concentration factor.

In partial penetration welding with Y groove or single bevel groove, it is difficult to detect root cracking.
Therefore, it is desired to employ the preheat temperature for repair welding.

8) The number of weld passes

In muti-pass welding, a root pass is reheated by subsequent passes so that residual stresses as well as
hydrogen in the root bead are reduced. As a result, root cracking is less likely to occur in multi-pass welding
than in one-pass welding..

This predictive method firstly gives the preheat temperature necessary to avoid root cracking in y-groove
restraint testing in which a one-pass short bead is deposited with high restraint as well as high notch
concentrations. This testing is so sever that much higher preheat is required than in normal welding practices.
For normal welding, this predictive method gives preheating temperatures much lower than that for y-groove testing.. For instance, the necessary preheating temperature for normal welding is 75oC less than that for y-groove testing when YP380MPa class steel is welded.

9) Welding residual stress

This predictive method considers the effect of welding residual stresses. The maximum welding residual stress is considered to be close to the yield strength of the weld metal. For higher strength steel, HAZ toe cracking, HAZ under bead cracking and weld metal transverse cracking are more likely other than root cracking. As mentioned above, the necessary preheat can be decreased from that obtained by y-groove testing. However, the amount of this temperature reduction decreases as the steel strength increases (the weld metal strength also increases and welding residual stress increases as well). For instance, the temperature reduction is 75oC for YP360 steel and 0oC for YP700 steel.
In this predictive method, the yield strength of weld metal has to be input. When it is unknown, the specified minimum yield strength of the steel may be input.

10) Preheating method

The objective of preheating is to enhance the hydrogen evolution from a weld. The effect of preheating increases as the width of preheating increases and the heating rate of preheating decrease. The preheating width over 200mm each side of the groove is desired. The preheating temperature has to be increased in the case of rapid preheating and narrow local preheating.

11) Ambient temperature

The occurrence of cold cracking is significantly affected by the ambient temperature. The cracking is more likely at the lower temperatures. As for the determination of preheat at lower ambient temperatures, the following paper should be referred to.

T. Kasuya and N. Yuiroka: "Determination of necessary preheat temperature to avoid cold cracking under various ambient temperatures", ISIJ International, vol. 35 (1995), No.10, p.1183-1189

12) Immediate post heating

Post heating immediately after welding is very effective for the hydrogen evolution. When the predicted necessary preheating temperature is excessively high, immediate post heating should be employed so that the necessary preheating temperature could be reduced.

150 oC for 95 hrs, or 200 oC for 29 hrs, or 250 oC for 12 hrs, or 300 oC for 2 hrs.

　5. Prediction of weld metal tensile strength

This predictive method is base on the following paper.
      N. Yruioka: Perdition of weld metal strength, IIW Doc. IX-2058-03

This method first predicts the weld metal hardness, Hv from weld metal chemical composition (C, Si, Mn, Cu, Ni, Cr, Mo, V, Nb, Ti[wt%]) and the welding cooling time (t85[s]).

      Hv = (HM + HB)/2 - (HM-HB) arctan(x)/2.2

      x = 4 log(t85/tM)/log(tB/tM) - 2

      HM = 884C + 294

      tM (s)= exp(10.6CEI - 4.8)

      CEI (wt%)= C + Si/24 + Mn/(2.88(1 +Mn)) + Ni/30 + Cr/16 + Mo/8

      HB = 145 + 130 tanh(2.65CEII - 0.69)

      CEII(wt%) = C + Si/24 + Mn/(2.16(1 + Mn)) + Cu/10 + Ni/45 + Cr/10 + Mo/5 +2V + 2.2Nb/(1 + 5Nb) + Ti/10

      tB (s)= exp(6.2CEIII + 0.74)

      CEIII (wt%)= C + Mn/(1.68(1 + Mn)) + Ni/15 + Cr/10 + Mo/8

      Then, Hv thus obtained is converted to the weld metal tensile strength, TS.

      TS(MPa) = 3.0Hv + 22.3

6. Prediction of weld metal toughness

This perdition is preformed by a neural network analysis of the database of low alloy weld metal from the University of Cambridge
(http://www.msm.cam.ac.uk/map/data/materials/)

The weld metal in the database is all-weld-metal obtained under a constant welding condition of arc energy of 1kJ/mm (heat input of 0.8kJ/mm), interpass temperature of 200oC and plate thickness of 20mm. The toughness is given by the transition temperature for the Charpy impact value of 28J.

A software developed by D. J. C. Mackay at the University of Cambridge was used for the neural network analysis. The prediction gives the degree of the prediction error. When the difference between the max and min predicted values is over 30oC, the prediction may be unreliable.

The following figure shows the relation between the estimation (vertical axis) and the database (horizontal axis).

Ver. 1.5 - Updated, June 2008