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S U P P L E M E N T TO T H E W E L D I N G J O U R N A L , J U N E , 1 9 7 2
ABSTRACT. A study was made of the effect on hot tearing in Al -Zn-Mg alloys when varying such properties as chemical composit ion, degree of purity of the aluminum base, casting temperature, aged condition of the alloy, dissolved gases and different amounts of zirconium as a grain refiner. For hot tearing evaluation, the parameter used was the area between the curves for comparative breaking elongation and l i near shrinkage as a funct ion of temperature in the solidification range.
High Temperature Elongation — Definition and Measurement
Aluminum is f inding ever increasing uses in industry. Because it lacks high mechanical properties alloying is necessary, although in many cases the alloying elements often create cracking and corrosion problems
in the present paper we shall consider the problem of hot cracking of Al-Zn-Mg alloys which frequently appears during casting and weld ing.
The term hot cracking involves two different though directly related phenomena: (a) the appearance of cracks formed during solidif ication as a result of normal contraction when solid grains coexist w i th the last remaining drops of l iquid and (b) the cracking which takesplace between the solidus temperature and room temperature either during subsequent cooling or similar heat cycles.
In this paper w e shall discuss the first of these points, designated "hot tearing, ' ' wh ich refers only to cracking produced by thermal contraction during solidif ication at temperatures ranging from the solidus to the l i quidus.
Archbutt, Grogin and Jenkins1
were the first authors to study these
problems. They observed the sharp variation in impact strength as the solidus temperature is reached and also that alloys which rapidly recover impact strength when the temperature falls below the solidus are less prone to cracking than other alloys where the increase is more gradual.
The f irst theory to elucidate these phenomena is due to Pumphrey2 and Jennings3 who established cracking temperatures between single points in the graphical representation of the ultimate tensile strength — temperature relationship. It is a theory that although it serves to explain such effects as grain size it does not clear up some others such as the effect of small additions on hot tearing.
In Pellini's much later theory 4 - 5 - 6
it is the solidified grains wh ich , as their volume is reduced, set up stresses on the liquid pockets which f inally break. By means of this theory7 the influence of each parameter on hot tearing can be established. A modification to this theory is that by Saveiko8. In Patterson's theory9 it is the liquid drops which act as notches facil i tating fracture of the solid grains.
The theories by Rogerson and Borland and that by Prokhorov are more recent.
Borland10 gathers the opinions of previous authors in that the shape of the liquid pockets has a decisive influence on the hot tearing phenomena and arrives at the conclusion that as the temperature of the alloy increases along the solidif ication range on account of the reduction of surface tension of the melt, the impingement angle '1 is reduced and the grain is f inally coated w i th a liquid layer wh ich causes total decohesion of the solid structure12 and resultant cracking.
Investigation of Hot Tearing in Al-Zn-Mg Alloys
Review of previous work leads to a method of separating the factors which do and do not affect hot tearing susceptibility
B Y J . HERNAEZ
A N D
A. M A D R O N E R O
This work was carried out in the laboratories of Centro Nacional de Investigaciones Metalurgicas (CENIM). Madrid, Spain.
W E L D I N G R E S E A R C H S U P P L E M E N T ! 281 -s
Temperature 'C
Fig. 1—Hot tearing tendency of an aluminum alloy. (1) Comparative breaking elongation versus temperature: (2) linear shrinkage versus temperature. Ts = solidus temperature of alloy: Tt = liquidus temperature of alloy: T, - lower limit temperature in brittle temperature range; T2 - upper limit temperature; t - transition temperature of rupture mechanism from Borland's to Prokhorov's (ref. 16). Shrinkage starts at this temperature
5I0 520 530 540 550 560 570 580 590 600 6I0
Temperature °C
Fig. 2—Hot tearing tendency of an ultra-high strength aluminum alloy (8.50% Zn and 3.05% Mg; 99.75 purity)
Prokhorov13*14 explains the fracture phenomenon as spinning of the grains wi th in the liquid envelope due to shrinkage stresses set up by solidif ication. When this spinning cannot take place, cracking results.
In a recent paper15 both of these mechanisms have been verif ied in Al -Sn alloys. Both theories are in our opinion true. Borland's theory is valid at temperatures just above the solidus whi le that by Prokhorov holds good somewhat below the liquidus.
These matters are dealt w i t h in greater detail in one of our previous studies16.
None of the above theories ful ly accounts for these phenomena nor do they explain quantitatively the influence of various parameters. In practice, tests designed to assess hot cracking of the various alloys ignore almost completely these theories and limit themselves to trying to reproduce the experimental condit ions under wh ich cracking occurs in practice by means of standard cast
ing or welding tests. The number of cracks formed is determined macro-scopically.
There are in the technical literature two classes of tests for hot cracking evaluation: (a) casting tests w i th restrained shrinkage and (b) we lding tests. On an evaluation of the test results, it should be noted that none take into account either the temperature at wh ich cracks are formed and propagated or their metallographic or micrographic appearance.
Pouring Tests
Pouring tests involve the casting of test bars in dies or sand molds in such a way that the bar cannot contract freely on freezing so that contraction stresses are set up, causing the test bars to crack.
There are two types of pouring tests according to the manner in which they are assessed. In the f irst the test bar dimensions are kept constant and the tests are repeated by varying the parameters whose influence is to determined, and the length of cracks wh ich appear under various circumstances is observed. In the other type one of the d imensions of the test bar is modified until incipient cracking is produced no matter how slight the contraction stresses may be. The maximum d i mension (when modifying the thickness of test bar) or min imum (when changing its length) for this tearing to start provides an evaluation index of the hot tearing tendency of the a l loy.
There are in the technical literature numerous instances of both types of test. Of those in which the test bar dimensions are unchanged the ring test bar by Singer and Jennings17 is a typical example and is, undoubtedly, the test most widely used for evaluating the hot tearing susceptibility of light alloys. When fixing the chemical composition for light alloys practically all procedures reduce the proportion of alloy elements until the hot cracking (tearing) produced in the Singer test is not excessive.
Among the tests that measure hot tearing susceptibility by the min imum test bar diameter wi thstanding the test wi thout signif icant cracking, mention should be made of the Za-kharov test18. Among tests wh ich measure the maximum elongation sustained without cracking are those by Gamber19 and Rosemberg20. More recently, tests have been developed in which several test bars of increasing length are poured s immultan-eously and the hot tearing susceptibility of the alloy is measured by eval-
282 -s I J U N E 1 9 7 2
Table 1 —Three
Type of alloy
Weldable Intermediate Ultra-high
strength
Alloy types invest igated
Chemical composit ion, percent
Zn
3 6 8.5
Mg
1.7 2.5 3
Solidif ication range, deg C
Solidus Liquidus temperature temperature
6 2 0 645 585 637 550 632
Pouring temperature,
deg C
745 737 730
Table 2—Indexes of hot tearing strength fo
Al loy
Ultra-high strength Intermediate Weldable
Fig-
2
3 4
T2 , °C
602
624 631
T , °C
542
573 619
r Figs. 2
(T2 -T), °C
60
51 12
3 and 4
h taken
°C
572
598 625
h,
mm
12
22 26
c= h
VT 0.200
0.431 2.166
5 8 0 590 6 0 0
Temce ro t u re
Fig. 3—Hot tearing tendency of an intermediate alloy (6.30% Zn and 2.31% Mg). Aluminum-base. 99.75%, purity
uating the amount of cracks formed in various lengths, in accordance w i th a previously established table giving the hot tearing susceptibility values. The tests by Tatur21 and Prokhorov13 are typical examples of this type.
Welding Tests
Welding tests can be said to have started wi th the restrained plates of Singer and Jennings1 7 wh ich have been discussed by numerous authors. The next phase was to replace the two restrained plates by a single one in which weld metal was deposited in a groove on the axis of symmetry. Mudrack22 proposed an original criterion for assessing these tests. He defined as hot tearing sus
ceptibility the quotient between the length of crack produced and 80 percent of the groove containing the weld; that is, when the crack reaches a length equivalent to 8 0 percent of the groove length, hot tearing susceptibility is 100 percent. For longer cracks, the hot tearing susceptibility is over 100 percent. This author made an attempt to improve the test by adding transverse cuts in the test bar to provide uniform cooling condit ions along the weld bead.
On this line Houldcroft23 proposed his " f ishbone" test wh ich has been widely discussed. This test was developed by Evrard24 w h o established more suitable test bar dimensions for each plate thickness. The sensitivity of this test is so marked that it
has enabled the influence of very small amounts of grain refiners as wel l as other factors to be established by means of rigid statistical analysis.25*26*27 This test should not be considered decisive despite its excellent sensitivity because it does not possess the required proportionality between length of crack and hot tearing tendency of the alloy. The work of Rogerson, Cotterell and Borland28 give good evidence of this.
From calculations in the latter report the so-called function " inherent crack sensit ivi ty" is defined which does truly express hot tearing of the alloy and accounts for the fact that the proportionality between the crack and the hot tearing tendency of the alloy does not hold. They also explain the influence of welding rate and other welding conditions on the results. In spite of this we consider the " f ishbone" test the most thorough of all. Some attempts to improve this test have been made, among which is the test by Hirsch-field and Scilley29. In the work by Borland30 some twenty examples are given.
The latest trend in these tests makes use of two plates which are welded together and tested using highly automated equipment. These plates are subjected to tension stresses whi le being welded simultaneously under severe condit ions. 3 1 . 3 2 . 3 3* 3 4 In fact these tests attempt to measure not only the cracking produced during solidification but also the cracking which appears on welding. A more exhaustive bibliographical review is given by Madronero.35
Summing up, it can be said that no universally accepted test is available to estimate the hot tearing tendency of the various alloys.
Evaluation Of Hot Tearing By Ductility Measurement In The Solidification Range
As indicated the usual tests for determining the hot tearing tendency of light alloys consist of welding or casting test bars of various sizes in which cracking is measured. Cracks that could have been formed at temperatures below the solidus are not taken into account, nor is a distinct ion made between cracks that are due more to the embrit t lement of the alloy than to particular conditions of the test. Furthermore, at the t ime of evaluation only the length of the cracks produced are taken into account.
Hot tearing is a fracture phenomenon which appears in metals due to the solidification process producing some contraction stresses which can exceed the ability of the alloy to w i t h -
W E L D I N G R E S E A R C H S l l P P i P M C M T I O O O
stand them. To determine the hot tearing susceptibility inherent in each alloy, in the least arbitrary manner and wi th in the solidification range, a test should relate the ability to sustain stresses w i th the tendency of the alloy to set up contraction stresses. The relation should clearly indicate the variations in the values of both characteristics of t h e m a t e r i a l throughout the entire solidif ication range.
The immediate problem is to consider which measurable properties are more apt to represent, in the solidification range, the ability of the material to wi thstand stresses w i t h out fracture and to set up contraction stresses. Both should be homologous since the objective is to establish their difference throughout t he whole solidif ication range.
The first step is to evaluate the tendency of the alloy to set up contract ion stresses by suitably varying the
temperature. It is wel l known that in the temperature range just above the solidus, there is a correct proport ionality between the relative elongations and the stresses wh ich produce them. Since in the casting of an alloy the effect of a reduction in temperature is a shortening of the length of test bar, it is just this shortening wh ich sets up the contraction stresses when the movement of the test bar is restricted. We therefore consider a graphical representation of linear shrinkage versus temperature to be appropriate for representing the inherent tendency of the alloy to set up contraction stresses throughout the entire solidif ication range.
The curve provided by a high precision dilatometer has the shape (particularly w h e n the solidus temperature is reached during a quick cooling started at a temperature very slightly below the liquidus) of a parab-
£ o o
580 5 9 0 6 0 0 610 620 630 640 650
"em pe ra ture , °C
Fig. 4—Hot tearing tendency of a weldable alloy (2.60%> Zn and 1.75%> Mg). Aluminum-base, 99.75%o purity
Table 3—Purity of three of four aluminum bases used in preparing weldable alloy specimens. Chemical compositions of the aluminum with different grades of purity*
Element
Fe Cu Si Zn Mg Cr Pb M n Ni
Aluminum, 99.3-4%
0.30 0.02 0.065 0.019 0.004 0.01 0.02 0.01 0.01
Aluminum, 99.5%
0.20 0.005 0.065 0.0065 0.001 5 0.01 0.01 0.01 0.01
*The chemical composition of the 99.75%> purity aluminum was
Aluminum, 99.99%
0.001 0.005 0.001 0.002 0.001 0.0003 0.001 0.001 0.0005
given previously. .
ola whose slope can he determined by straight lines tangent to it, especially at temperatures slightly above the solidus where hot tearing takes place.16 Thus, we correlate linear shrinkage to a straight line whose slope is the tangent of the curve recorded by a precision absolute dilatometer. in 3 6 can be seen a more detailed justi f ication of these reasons as wel l as a description of a device for the appropriate measurement of linear shrinkage.
The next step is to describe the method chosen to measure the capacity of an alloy to sustain stresses wi thout fracture. It seems logical to apply a tensile test to the alloy and to choose a parameter wh ich would show us how near the alloy is to breaking point. The tensile test measures stresses and elongations. Stresses as measured show an excessive degree of dispersion2*3 ; they are also of different dimensions than the linear shrinkage. It is, therefore, logical to choose the relative elongation as this is measured in the same units as linear shrinkage. As at these temperatures it is impossible accurately to determine from the tensi le-stress plot the elastic l imit, although the ult imate tensile strength is determined, w e choose the relative breaking elongation to represent the ability of the alloy to sustain stresses without fracture.
At temperatures at wh ich the relative breaking elongation is lower than the linear shrinkage, tearing of the material wi l l take place, whi le at temperatures where the relative breaking elongation is higher than the linear shrinkage the alloy wi l l be able to wi thstand the stresses w i t h out tearing, w i t h a probability proportional to the difference between these two values. Thus the not tearing tendency of an alloy w i l l be given by the difference between the relative breaking strength and the l inear contraction throughout t he whole solidif ication range.
From the foregoing it appears that the probability for an alloy to sustain this state wi thout fracture is proportional to surface area S 0 in Fig. 1. The correct procedure for a study of the influence of each of the parameters which affect the hot tearing tendency of an alloy is to observe how they alter values of S0 , bearing in mind that any increase in this surface area created by an increase in the relative breaking strength or a reduction in the slope of the linear shrinkage wi l l be considered to favor the hot tearing strength of the alloy so that they must be added to S 0 , whi le increases in surface produced by a rise in temperature T2 or a reduction in temperature T should be
284 -s | J U N E 1 9 7 2
subtracted from So since they increase the probability of the alloy to undergo hot tearing.
Thus the initial hot plasticity coefficient of the alloy is defined as:
P = S 0
When the characteristics of the alloy are modified, its hot tearing ten-denci diagram also undergoes modif ication, so that the value of *P becomes
P = S0 + AS, + AS2 + AS3 + AS4
TheAS values are either positive or negative depending on whether they represent an increase or reduct ion in the ability of alloy to w i th stand hot tearing, as shown in Fig. 9.
Wi th this we can study the development of the hot tearing tendency of an alloy w h e n its ductil ity changes due to the variation of a given factor (grain size, gas content, proportion of stabilizers, such as Cr, etc.).
To compare the hot tearing of completely different alloys (more correctly, of alloys which have a quite different hot tearing diagram) it is more convenient to use the coefficient resistivity to hot tearing:
9 10
Z i n c %
<T2 T,)2 T2 - T
Fig. 5—Hot cracking curves in Singer test of Al-Zn-Mg alloys (ref. 38). W - weldable alloy (2.60% Zn and 1.75% Mg); I = intermediate alloy (6.30% Zn and 2.31% Mg); U = ultra-high strength alloy (8.50% Zn and 3.05% Mg)
The lower the value of C in a alloy, the greater w i l l be its hot tearing susceptibility in the solidification range.
The reader wi l l f ind this criterion fully justif ied in our previous paper36
together w i th a complete description of the operational procedures developed for their use.
We wish to point out that by using this criterion we measure the inherent hot tearing tendency of the alloy, regardless of the particular welding or casting conditions wh ich give rise to the fact that the alloy undergoes a certain amount of cracking in these processes.
Evaluation of Hot Tearing In A -Zn-Mg Alloys
General. Once the criterion to be observed and the operational procedures have been developed we go on to determine hot tearing in A l -Zn-Mg alloys. To this end we select three alloys in the Al-Zn-Mg system, each representing the three large groups into which these alloys are divided; namely, ultra-high strength alloys, weldable or self-hardening alloys and intermediate type alloys as shown in Table 1. The ultra-high strength alloys contain a high proport ion of alloying elements, their strength is very high and when they
Table 4—Comparison of test results obtained from weldable alloy specimens prepared from four levels of aluminum base purity
Diagram of Fig.
6 7 4 8
Purity of aluminum base, %
99.35% 99.5 99.75 9999
Chemical | i composition % |
Zn
2.84 3.23 2.60 2.85
Mg
1.75 1.72 1.75 1.75
Zn-Mg
4.59 4.95 4.35 4.60
T 2
°C
629.5 628.5 631 629.5
T °C
615 612 619 616
h, mm.
25 22 26 25
C = ^ T T2-T,
1.724 1.333 2.166 1.293
Brittle area. mm 2
679 682 537 652
also contain copper possess the highest mechanical strength values in light alloys. To represent this group we have chosen an alloy whose chemical composition is 8.5 Zn-3.0 Mg. The weldable or self-hardening alloys are unique in that they do not lose the mechanical properties obtained through heat treatments on air cooling, that is, they are self-hardening. They have some interesting cryogenic uses and are undoubtedly the group of alloys in the Al -Zn-Mg family showing more promise for the future. As representative of this group we selected an alloy of composition 3.0 Zn-1.7 Mg. Finally, we chose an alloy of composition 6.0 Zn-2.5 Mg to represent the intermediate type.
Apart f rom the case discussed later under the influence of pouring temperature, these alloys wi l l be cast w i th a pouring temperature 100 C higher than its liquidus temperature which together w i th the fact that none of these alloys possess in termediate phases as they are included in the aluminum solubility corner of the equil ibrium phase diagram for the Al-Zn-Mg system, make them have an homogeneous structure so that the results of the measurements are perfectly comparable.
To prepare the alloys two master alloys were produced, one containing 20 percent Zn and the other, 10 percent Mg, pure aluminum being added to the crucible. This aluminum was of the same degree of purity as
W E L D I N G R E S E A R C H S U P P L E M E N T ! 285 -s
E o o
580 590 600 610 620 630
Temperatu re , °C
6 4 0 6 5 0
Fig. 6~Hot tearing tendency of a weldable alloy (2.84%, Zn and 1.75%, Mg). Remelt aluminum base
5 •
\
\
- \
1
E o o
580 590 6 0 0 610 620 6 3 0
Te mperature, °C
5 4 0
Fig. 7—Hot tearing tendency of a weldable alloy (3.23%, Zn and 1.72%, Mg). Aluminum base, 99.5%, purity
Table 5—Values of the coefficient P for Figs. 6, 7, 4 and 8* Diagram Brittle ASj AS 2 AS3 AS* 'P = S o + s A S , of Fig. Area, mm2
6 679 — — — — 679 7 682 - 2 0 + 1 7 - 1 3 8 538 4 537 — - 2 8 — + 200 851 8 652 — — — + 48 727
* AS signs and values have been taken according to Fig. 9.
that used in the preparation of the master alloys.
The melt was poured into a bento-nite-bonded green sand mold. From each cast enough melt was obtained to fi l l three molds, eight identical ingots being obtained from each mold. These ingots were later machined and a tensile test specimen was produced from each one of them. From each mold ten dilatometry test specimens and chippings for chemical analyses were also obtained. The chemical analyses were made by atomic absorption. The Zn and Mg used for making the master alloys were of high commercial purity.
Under these operational conditions practically all of the ingots w e obtained had an equiaxed as-cast structure. This is of great significance as " . . . w i th the columnar structure . . . conditions are less favorable for intergranular deformation than w i th the equiaxed structure. Accordingly, the solid-liquid ductil ity of the equiaxed structure is at all temperatures higher than that of the columnar structure."37
When plotting the relative breaking elongation and linear shrinkage on the hot tearing diagrams we made sure of always using the same scale so that comparable results would be obtained at all t imes.
Hot Tearing Susceptibility of the alloys shown in Table 1
The three alloys were prepared wi th an aluminum base which f rom now onwards wi l l be known as 99.75 aluminum. Its chemical composition (in weight percent) according to the analyses carried out in our laboratories was as fol lows: 0.09 FE, 0.01 Mn, 0.01 Ni, 0.03 Zn, 0.085 Si, 0.01 Cr, 0.01 Pb, 0.005 Cu, 0.002 Mg.
Hot tearing diagrams are given in Figs. 2, 3 and 4 and indexes of hot tearing strength in Table 2.
These results show that the ultra-high alloy is much less resistant to hot tearing during solidification than the weldable alloy whi le the hot tearing susceptibility of the alloy designated intermediate lies between that of the other two. It can easily been seen that the difference between the various values of C is basically due to the amplitude of the britt le temperature range and to the height of the comparative elongation plateau. L ineal shrinkage is practically the same for the three alloys.
These results are logically predictable since, as the amount of alloy elements added to the aluminum base increases, it can be expected that the possibilities for undergoing hot tearing wi l l increase.
Figure 5 gives the results obtained
286-s I J U N E 1 9 7 2
by Patterson38 w i th the Singer test. It w i l l be seen that his results differ considerably from ours, in particular so far as the ultra-high strength alloy is concerned. We believe this is due to the fact that, we explained in our previous paper16, the cracks which appear in the Singer test of A l -Zn-Mg alloys do not form at temperatures above the solidus but under it. As the ultra-high strength alloy has a greater strength than either the weldable or the intermediate alloy it w i l l , in spite of its higher hot tearing susceptibility, resist hot cracking at temperatures under the solidus better than the other two.
Owing to the great similari ty between the diagrams for the hot tearing tendency of these three alloys, we shall f rom here on study the influence of the various parameters on one of them and shall extrapolate the results to the other two. Of the three alloys we shall select the weldable one since it represents the most important group of these alloys and also because its range of solidif icat ion temperature is the narrowest, so that a smaller number of tests are required in order to determine its ducti l i ty throughout that range. We shall assume the results obtained in these tests to be valid for the other two alloys, the ultra-high strength and the intermediate ones.
Effect Of Aluminum Base Purity On Hot Tearing Susceptibility
The influence of the grade of purity of the base alumimun on the hot tearing susceptibility of A l -Zn-Mg alloys was considered from the viewpoint of cost to determine whether the use of high purity and expensive aluminum would relieve th is great technical inconvenience of A l -Zn-Mg alloys.
We therefore investigated the hot tearing susceptibility of the weldable alloy prepared w i th aluminum of four different grades of purity, as shown in Figs. 6, 7, 4 and 8. The chemical compositions of the aluminum bases are given in Table 3. Test results are shown in Table 4.
The problem is to deduce from the results of Table 4 whether the variation in britt le area (area between the curves for relative breaking elongation and linear shrinkage and the ordinates corresponding to T, andT 2 ) is due to the purity of the base aluminum or to the chemical composit ion. Of course, the ideal would have been to test four alloys of exactly identical chemical composition. That was impossible since (a) the base aluminums differed and (b) the alloys were prepared in different casts making it practically impossible to obtain identical composit ion.
5 •
3 -\
580 590 600 6I0 620 630 640 650
T e m p e r a t u re , °C
Fig. 8—Hot tearing tendency of a weldable alloy (2.85%, Zn and 1.75% Mg). Aluminum base, 99.99%,purity
P= S0± A S , - A S 2 - flS3i A S 4
o a
u Te m p e r a t u r e , ° C
Fig. 9—Rule for applying positive or negative sign to values of S and A S in determining P from hot-cracking diagram
Comparing the Data of Table 4 w i th Table 2, it seems at first that the differences are simply due to variations in chemical composition.
It can be seen that in the alloys of Table II the variation in chemical composition influences the value of C. The average amount of alloying elements (% Zn + % Mg : 11.55, 8.61 and 4.35) is 8.17 t 2.08 ( 1 25%). Average value of C is (0.200, 0.431
and 2.166), 0.932 ± 0 . 6 2 (+_66.50%). The relationship between both percentage errors is
66.5 = 2.66
25 Let us do this same thing for re
sults in Table IV. The average amount of alloying elements (% Zn + % Mg: 4.59, 4.95, 4.35 and 4.60) is 4.62 ± 0.12 ( ± 3%). The mean
W E L D I N G R E S E A R C H S U P P L E M E N T ! 287 -s
c o
4 -
_. N
580 590 600 610 620 630 640 650
Due to the small difference existing between both relationships, it may be presumed that the influence of the degree of purity of the aluminum base is completely masked by the small variations in the chemical composition, unavoidable when having to make various casts.
To operate even more strictly Figs. 6, 7, 4 and 8 should be interpreted by means of coefficient P, as we are dealing w i th very similar britt le diagrams.36
Table 5 gives the coefficient P for the britt le diagrams of Figs. 6, 7, 4 and 8, taking as S 0 values corresponding to Fig. 6.
As may be seen, the mean of P values (679, 538, 851 and 727) i s , 6 9 9 + 64 (+9.1 5%), so that
^ l 5 - = 3.05
T e m p e r a t u re, °C
Fig. 10—Hot tearing tendency of a weldable alloy (3.00% Zn and 1.80%, Mg). Aluminum base, 99.75%, purity. Pouring temperature 700 C.
Tem p e r a t u r e , °C
Fig. 11—Hot-cracking tendency of a weldable alloy (3.00%, Zn and 1.60%, Mg). Aluminum base, 99.75%, purity. Pouring temperature 800C
value of C is (1.724, 1.333, 2.166 and 1.923) is 1.786 + 0.17 (+9.51%). The relationship between both mean
square errors is: 9.51 3.17
is valid since it f i ts in perfectly w i th ourforegoing conclusion.
It therefore appears justif iable to interpret the variations wh ich the hot tearing susceptibility of an alloy can experience due to the variation in the purity of the base aluminum as being negligible in terms of the variation it undergoes due to the least minimum change in its chemical composition. That is, the influence of the purity of the base aluminum may be considered of no importance.
The only tests we know of performed in th is respect are those by Guilhaudis and Develay39 who tested Al-Zn-Mg alloys using the welding test on restrained plates. They showed it was likely that when the base aluminum passed from 99.5 to 99.7% the hot tearing susceptibility seemed to increase and this increase was of such litt le importance that the authors did not venture to state categorically that this slight increase be significant. We further believe that the dispersion in their results was higher than in ours.
Effect of change in grain size due to variation in pouring temperature.
In order to determine the influence of grain size we measured the hot tearing susceptibility of the weldable alloy w i th 99.75 base aluminum and
Table 6—Comparison of test results obtained from weldable alloy specimens poured at three different temperatures
Diagram of Fig.
10 4
11
Chemica % Zn
3.00 2.60 3.00
composit ion % Mg
1.80 1.75 1.60
Pouring temperature,
°C 7 0 0 745 8 0 0
T, °C
618.5 619 621
B ittle range T5
°C 630.5 631 632.5
T; —T °C 12 12 11.5
h measured at (°C)
624.5 625 627
h, mm
34 26 20
Parameter C
2.833 2.166 1.739
288-s I J U N E 1 9 7 2
va r i ous g r a i n s izes. G r a i n s ize is u s u a l l y c o n t r o l l e d by a d d i n g g r a i n r e f i n e r s o r v a r y i n g t h e p o u r i n g t e m p e r a tu re . To o b s e r v e t h e i n f l u e n c e of g ra i n s ize w i t h o u t i n t e r f e r e n c e s f r o m o the r e f fec ts , w e p r e f e r r e d v a r y i n g t h e p o u r i n g t e m p e r a t u r e o n l y b e cause g r a i n r e f i n e r s can at f i r s t a l t e r t h e p r o p e r t i e s of t h e l i qu i d p h a s e apa r t f r o m r e d u c i n g g r a i n s ize.
W e t h e r e f o r e c a r r i e d ou t t h e t e s t s , us i ng t h e c o n d i t i o n s d e s c r i b e d in F igs. 10 , 4 a n d 11 ( the a l l o y c o r r e s p o n d i n g to F ig. 4 w a s p o u r e d at 7 4 5 C). The resu l t s a re g i v e n in Tab le 6.
The i n c r e a s e in t h e b r i t t l e r a n g e of t h e a l loy is d u e to t h e r i se in t h e p l a teau of t h e re la t i ve b r e a k i n g e l o n g a t i o n .
A s c a n be s e e n t h e r e s u l t s a g r e e c o m p a r a t i v e l y w e l l w i t h t h o s e g i v e n by Ta tur 2 1 (page 2 2 5 5 ) . In ou r case it is poss ib le to o b s e r v e no t o n l y h o w t h e ho t t e a r i n g t e n d e n c y of t h e a l l oy va r i es bu t a lso t h e r e a s o n fo r it. In t h e f i r s t p lace (Fig. 10) it w i l l be a p p r e c i a t ed t h a t w h e n t h e p o u r i n g t e m p e r a t u r e is ve r y l o w ho t t e a r i n g is g r e a t l y r e d u c e d d u e t o t h e h i g h d u c t i l i t y ex h i b i t ed by t h e a l l oy at t h e ho t t e a r i n g range t e m p e r a t u r e s . If w e i n c r e a s e t h e p o u r i n g t e m p e r a t u r e t h i s d u c t i l i t y w i l l dec rease bu t if w e i n c r e a s e it ex cess ive ly , apa r t f r o m d i m i n i s h i n g , t h e g r a i n u n l o c k i n g zone w i l l d i s a p pear ( w e re fe r t o t h e s h a r p d r o p i n duc t i l i t y w h i c h s e p a r a t e s t h e P ro k h o r o v zone f r o m t h a t of B o r l a n d ) b e cause due to t h e i r s ize t h e y ve r y eas i l y i n te r l ock , P r o k h o r o v ' s zone t h u s be ing r e d u c e d to a m i n i m u m . 1 6
Al l t h e s e resu l t s c o n f i r m t h e usua l ru le in m e t a l l u r g y t h a t a m a t e r i a l w i l l e xh ib i t i ts bes t p r o p e r t i e s w h e n i ts g r a i n s ize is t h e m i n i m u m poss ib le .
Ef fec t of Grain Ref iners, Especial ly Z i rcon ium
S p e c i a l a t t e n t i o n s h o u l d be g i v e n to t h e w a y g r a i n r e f i n e r s a t t e n u a t e t h e ho t t e a r i n g t e n d e n c y of l i gh t a l loys. A l t h o u g h eve ry a u t h o r a g r e e s t ha t t hey reduce ho t t e a r i n g e f f i c i e n t ly, it is no t c lea r h o w a n d w h y t h e y d o so . A l t h o u g h t h e m a j o r i t y i m p u t e t h e e f fec t s i m p l y t o a r e d u c t i o n in g r a i n s ize, t h e r e a r e o t h e r s w h o c o n s ider it due to a v a r i a t i o n in t h e a m o u n t of gas d i sso l ved in t h e me l t . 4 0 S t i l l o t h e r s f i n d i n s t e a d t h a t t he e f fec t is due m o r e to t h e i m p r o v e m e n t m a d e in m i c r o p o r o s i t y a n d t h e d i s t r i b u t i o n of t h e i n t e r m e t a l l i c c o m -
A
- \
E o
CJ
5 8 0 5 9 0 6 0 0 610 6 2 0 6 3 0 6 4 0
Tem p e r o t u r e , °C
Fig. 12—Hot tearing tendency of a weldable alloy (2.63%, Zn and 1.61% Mg) with 0.1% Zr. Aluminum base, 99.75% purity
\
\
\ .
i / \
E o u
580 590 600 6I0 620 630 640 650
T e m p e r a t u r e , ° c
Fig. 13—Hot tearing tendency of a weldable alloy (2.84% Zn and 1.62%, Mg) with 0.2% Zr. Aluminum base, 99.75% purity
pounds 4 1 (p. 72 ) . The f i r s t p r o b l e m is to c h o o s e fo r
s tudy t h e m o s t su i t ab le g r a i n re f i ne r . The l i t e ra tu re p rov ides n u m e r o u s ex a m p l e s m a i n l y f o r t h e use of Zr , T i , M n a n d B.
E n o u g h is n o w k n o w n abou t t h e m a n n e r in w h i c h g r a i n r e f i n e r s b e have. H a v i n g d i s c a r d e d t h e h y p o t h es is of t h e c o n c e n t r a t i o n g r a d i e n t , 4 2
it is b e l i e v e d t h a t g r a i n r e f i n e r s b e l o n g i n g to t h e t r a n s i t i o n e l e m e n t s
Table 7—Ef fec t o f Zr addi t ions to we ldab le al loys having 9 9 . 7 5 % pure al loy base
Diagram Chemical composit ion of Fig. % Zn % Mg % Zr
4 2.60 1.75 12 2.63 1.61 0.1 13 2.84 1.62 0.2
Britt le range °C T, T2
619 631 618 631 617 631
T 2 - T , 12 13 14
h measured at °C 625C 624C 624C
h in mm 26 26 37
: = h
T2— T, 2.166 2.000 2.642
W E L D I N G R E S E A R C H S U P P L E M E N T ! 2 8 9 - s
and to the lanthanides, due to their electronic layers,43 form some few degrees above their liquidus temperature "quasi-molecules."These molecular aggregates of grain refiner atoms are related to aluminum atoms and behave as solidification nuclei. According to this theory grain refiners are, in order of efficiency, Zr, Ti , Hf, Ta, V, W, Nb, Mo, Re, Fe, M n , Cr, Co and Ni. As some of these bodies are "donors" and others "acceptors," it is possible that two of them in a certain amount could nullify their effect as grain refiners. Thus, for instance, Ti + Zr, Ti + Fe and Ti + Cr may be cancelled. Other times, on the contrary, their effects are additive and this explains the known results44: that by relating two of them (Ti and B) an optimum reduction in grain size is achieved.
The effect of grain refiners on hot tearing has been examined traditionally by means of welding tests. Ti and Zr are undoubtedly the two grain refiners more often studied. Zirconium was studied by Schoer and Gruhl45
who recommend 0.20% as an optimum ratio, by Dudas46 who suggests its use in a ratio of 0.10-0.15% and by Sugiyama and Fukui.26 The latter give a curve of the variation in hot tearing which seems to show that up to a ratio of 0 . 1 % , Zr does not have any influence on cracking; f rom this ratio onwards the hot tearing susceptibility starts to diminish, until f rom 0.2% upwards its influence does not increase further. They also found that Ti and B, although they refine the grain, exert only a very slight influence on hot tearing susceptibility.
Chevigny and Develay go so far as to eliminate the hot tearing of an A l -Zn-Mg alloy by putting the Zn and Mg into an approximate relationship of 2 and by the use of Zr in a 0.1 to 0.5% ratio.
The effect of Zr is perhaps better studied in a paper by Develay and Croutzeilles.26 In this paper it is shown that Ti produces similar effects and that when -it is added together w i th Zr there is an optimum reduction in the hot tearing susceptibility.
In the light of the foregoing w e chose Zr for study as the exclusive grain refiner in the ratios of 0.1 and 0.2%. The hot cracking diagrams are
given in Figs. 12 and 13. The coefficients resulting from the diagrams in Figs. 4, 12 and 13 are shown in Table 7.
The data in Table 7 are highly significant. They clearly show that the effect an 0 . 1 % Zr addition can have is below the measurement error, so that we consider it has no influence. Observing the effect of an 0.2% Zr addition we see a reduction in the hot tearing susceptibility and if we compare Figs. 13 and 10 it w i l l be seen that the difference is due to an increase in the height of the plateau typical of a fine size grain. This increase could have been greater if the chemical composition instead of being 2.80% Zn and 1.70% Mg had been 2.60% Zn and 1.75% Mg.
There is a special effect in the Zr addition which is seen on studying Fig. 13. There is a broadening of the Prokhorov zone which is hardly perceptible in the alloy w i th 0 . 1 % Zr and wh ich seems to be produced by an increase in the liquidus temperature, this being in perfect agreement w i th the Al-Zr diagram shown in Fig. 14.
Thus the effect of Zr appears to be accounted for. When the ratio of Zr is less than 0 . 1 % it does not influence significantly the hot tearing susceptibility of the alloy. But when its proportion is higher (when there is enough Ar so that, according to Sam-somov's theory43 some molecular aggregates are formed in a con-siderableamountand, therefore, grain refining takes place) apart from increasing the ductil ity of the alloy, a widening of Prokhorov's zone is produced due to the increase in the l iquidus temperature. We believe this broadening bears no influence on the hot tearing susceptibility as in this zone the alloy can sustain significant elongation without cracking and should th is happen there are many probabilities that at lower temperatures the cracks could be "cured."4 8
Novikov37 obtained similar conclusions when he showed that small amounts of M n and Ti increased the relative elongation of an AI-7.5% Cu alloy.
That a reduction in grain size always produces an increase in plateau height, whether it is caused by a reduction in the pouring temperature or whether it is produced by
the addition of grain refiners, suggests that this increase in ductil ity is due to the cracks being "cured" 4 9
more readily by the remaining molten metal in Borland's zone. This can occur for two reasons: (a) because the cracks to be fil led are smaller (we must remember that a crack is the space left by two adjacent grains which have been torn apart and, therefore, the finer the grains the shorter w i l l be the cracks) or (b) because the surface tension of the melt remaining is reduced by the addition of the grain refiner. If the two effects are added the influence of the grain refiners wi l l be strikingly great. In the technical literature we f ind, for instance, that Saveiko50 supposes that Cr attenuates hot tearing of steels by reducing the surface tension of melt.
We do not believe this happens in the case of light alloys, since if the two effects (reduction in grain size and variation in the surface tension of remaining melt) were to be added the increase in height of the plateau of the relative elongation would be much greater in Fig. 13 than in Fig. 10 which, in spite of the differences in chemical composition does not happen. We believe that, should the variation in surface tension bear an influence, it would be insignificant in terms of the effect of grain size reduction (or, in other words, of size of cracks).
This is difficult to prove by means of accurate mathematical calculations, for in order to calculate the variation in the surface tension of an aluminum melt containing Zn and Mg w i th Zr additions, an exact knowledge of Eotvos's constant would be required and, although w e have carried out an exhaustive bibliographical review we have been unable to f ind it. It was also impossible to f ind data on experimental measurements concerning the influence of Zr additions; in addition his experimental determination is beyond the scope of the present work due to its excessive complexity.51
Nevertheless, it is not surprising that the additions of Zr in these proportions hardly reduce the surface tension of melt, since in an early paper by Pelzel52, in wh ich a experimental study of the variation in surface tension of Al due to individual
Table 8—Effect of Cr Addition to Weldable Alloys Disregarding Purity of Aluminum Base
Diagram of fig.
4 17 18
Chemical composition, % Zn Mg Cr
2.60 268 2.70
1.75 1.74 1.71
0.24 0.24
Range of brittle temperatures, °C T, 72 T, —T2
619 608 609
631 632 632
12 24 23
h taken at °C
I 625 620 621
h in mm.
26 22 22
2.166 0.916 0.956
290-s I J U N E 1972
and simultaneous additions of Zn and Mg is made, the Zn and Mg alter little the surface tension of melt, particularly when in small proportions. Moreover we noted earlier that small variations in the proportion of Zn and Mg have greater effects on the ductil ity of the alloy than small additions of Zr.
In a more recent work by Korol-kov53 it is shown that the effect of an alloying element on the surface tension of A l is almost proportional to the difference between the atomic volumes of the alloying element and of the aluminum (at. vol. of A l = 10, of Mg = 16 .21 , of Zn = 9.90 and of Zr = 14.1). According to this, Zr should have a lesser influence than Mg and almost the same as Zn. It has been proved experimentally52, however, that Zn has an almost negligible influence and that of Mg is very small . In any case, even if the Zr did influence the surface tension of the molten aluminum considerably, it would not affect the surface tension of the last alloy drops in the liquid state located among the grains of the alloy under consideration. Since the Zr atoms remain almost "bu r ied " in the core of the grains due to their grouping into "quas i -mo lecu les " grain embryos (according to Samso-mov's theory43 cited previously), it wi l l be difficult for them to influence the remaining melt when there is not much of it as is the case in Borland's zone. They wi l l only have an effect on the melt when the grains are almost decomposed. Because of proximity to the liqffidus temperature the nuclei of the most minute grains, on dissolving, provide a considerable proportion of Zr to the remaining melt. This agrees wel l w i th the
9 50
660,5°
AI+ Zr A l 3
400 0,2 0,4 0,6 0,8
ZIRCONIUM (Wt % )
Fig. 14—Equilibrium diagram of Al-Zr alloys
l,0 1,2 l,6
z- \
^ t
• r \
T
{ j l
=̂=7*
•r
• ft. '. •
f
1 h r
W' *
Fig 15—Structure of weldable alloy with 0.24%, Cr; Aluminum base, 99.5%, purity. As-cast condition (100X) (a) Magnesia polished. Unetched, (b) Mechanically polished and electrolytically etched.
W E L D I N G R E S E A R C H S U P P L E M E N T ! 291-s
y
J,
/r ~-^s \.
i*** ~7 / Fig. 16 — Structure of weldable alloy with 0.24%, Cr after an ageing heat treatment at 450C for 4 hr, (a) Magnesia polished. Unetched (b) Mechanically polished and electro-lytically etched.
3 2
\
\ \
630 640 650
Fig. 17-Cr. Non
Tern peratu re . °C
-Hot tearing tendency ot a weldable alloy (2.68%, Zn and 1.74%, Mg) with 0.24%, aged. Aluminum-base, 99.5%, purity
breakdown zone of the solid structure16 of the curve in Fig. 13 (last part of the curve, at temperatures just below the liquidus).
Thus we conclude by stating that grain refiners produce an increase in the strength of Al -Zn-Mg alloys to sustain hot tearing due only to their reducing the mean grain size. The possible variation they may produce in the surface tension of the melt does not appear to have any appreciable influence at all. They also produce a broadening of Prokhorov's zone which does not influence the hot tearing tendency of the alloys significantly. The minimum amount of grain refiner required to produce this effect can be deduced from the phase diagram of the system.
Effect of Stabilizers, Especially Chromium
One of the main drawbacks of A l -Zn-Mg alloys that sometimes restricts their use is the tendency to sustain stress corrosion. Ageing these alloys is the best remedy for stress corrosion. It is easy to do and is also advantageous because the mechanical properties of the alloys can thus be increased. The alloying elements most widely used for this are Ge, M n and above all, Ag and Cr. Thus, for instance, the effect of Cr and Mn are compared in references 54,55,56 a n c j that of Cr, Zr and Ag in 57.
However, monographs on a single stabilizer are more abundant; for example, the effect of Ge is studied in 58 and that of Ag in 59 to 63 But the one which has been more widely investigated is, undoubtedly, Cr.64
Therefore we are famil iar w i th the phenomena which take place on the ageing 65 to 69 of these alloys wi th various Cr additions. The ageing kinetics can be seen in 76*70 and the influence of the point defects of the material on ageing when there are Cr additions present is to be found in 71 *72. There are also various papers which report on optical and electron microscopy, and X-ray observations of the precipitates whose formation is due toCr 7 3 80,
Because the ageing process of A l -Zn-Mg alloys is better known when the alloy containsCr additions it seems appropriate to choose this stabilizer study. There are two reports wh ich induce this selection. In 67 it is said that Cr has a much more considerable effect on the ageing of these alloys than Mn and Cu. Baba81 is even more explicit. He makes an exhaustive study of the effect of possible additions on the ageing of Al -Zn-Mg alloys and reaches the conclusion that the most active is Cr, fo l lowed at quite a distance by Mo, V, Zr, Mn ,
292-s I J U N E 1 9 7 2
Cd, Ag, and Cu. We consider it appropriate to study it in the weldable a l loy as it is the type in which the annealing temperatures and heating rates have a lesser influence on ageing.82 Besides we need not worry about the purity of the base of aluminum because, as it appears to have been proved, it does not influence ageing.83
We have studied the hot tearing tendency of the weldable alloy w i th U.24% Cr in the as-cast condit ion ana after it had been subjected to an anneal-ageing treatment at 450 C tor four hours. Figs. 1o and 16 are micrographs of the alloys prior to and fol lowing the ageing treatment; the electrolytic etchant used was Herenguel's.84 As can be easily seen ageing is complete. The diagrams for the alloys before and after ageing are shown in Figs. 17 and 18 whi le the results of the determination are given in Table 8.
Table 8 compares the weldable alloy containing Cr w i th the alloy of Fig. 4 (99.75% purity) instead of comparing it w i th that of Fig. 7 whose base aluminum is of the same purity as those in Fig. 17 and 18. This comparison was selected because (a) the quantities of Zn and Mg are in more similar proportion and (b) it was previously shown8 3 that the purity of the aluminum base does not influence the effect of chromium on the ageing of these alloys.
The results in Table 8 are easy to interpret. In Figs. 4, 17 and 18 it is seen that the three curves have their plateau almost at the same height and that all the chromium addition has really done is to change the extent of the solidification range. Further, there is a very slight linear shrinkage increase of the alloy.
These results indicate tnat chromium does not alter the ductil ity of the alloys. However, because it widens the range of britt le temperatures, it increases the hot tearing susceptibility slightly. This effect is independent of whether the alloy is aaed or not.
Effect of Gas Content on Hot Tearing
On this topic the bibliographical data are more contradictory. On one hand there is the general belief that gases reduce the hot tearing susceptibility of light alloys, as expressed by Lees85 and recently by Scheuer, W i l l iams and Wood8 6 and Novikov37
who ascribe it to the fact that the gas content reduces linear shrinkage. There are some, however, who consider that the gases increase the hot tearing susceptibility of these alloys87 and there is always someone who finds that gases have no inf luence 21
lo
A \
M E o o
5 8 0 5 9 0 6 0 0 6 I 0 6 2 0 6 3 0 6 4 0
Te m peratu re
Fig. 18—Hot tearing tendency of a weldable alloy (2.70% Zn and 1.74%, Mg) with 0.24% Cr. Aged at 450 C for 4 hr. Aluminum-base, 99.5% purity
580 590 600 6I0 620 630 640 650
Temperatu re, °C
Fig. 19—Hot tearing tendency of a weldable alloy (2.80%, Zn and 1.75% Mg. remelted). Gas content- 22cm3/100g
The result of our test can be seen in Fig. 19. The amount of gas existing in the alloys tested previously was about 15 c m 3 / 1 0 0 g. The procedure in pouring tor this test was s imply to take no precaution whatsoever to avoid the dissolution of the gases in the melt whi le in all other previous alloys we had used some degas-ifying products.88 The gas content includes not only hydrogen but all gases that could be produced during the fusion casting process.
Comparing Figs. 6 and 19 it seems that hot tearing susceptibility clearly increases due to the step wh ich the
plateau makes in the zone of the higher temperatures of the Borland range. We believe, however, that this increase is less signif icant than is shown by these figures, for a l though at this step the cracking probability is greater, " cu r i ng " of the cracks may take place at the lower temperatures.
It must be noted that the effect of gas content is the most difficult to study w i th these tests, as we can only examine specimens w i th a smaller quantity of gas than would produce porosity; that is, only gassed specimens of zero type and another
W E L D I N G R E S E A R C H S U P P L F M F W T l i>a->-
from the range of gassed specimens by of zero type and another from the range of gassed specimens by Scheuer.86 Even so it was seen that the dispersion of tensile test results was higher than in those made in the preceding tests, to such an extent that we had to repeat this curve many t imes and our tests had to be more carefully controlled. As the gas content is increased, the distr ibution of porosity is never perfectly homogeneous, and as at testing temperatures fracture is fully britt le, dispersion wi l l be excessive on account of the variation in the cross-section of the test specimens. Another disadvantage is that in the dilatometry tests heating takes place slowly and it is possible that some of the gases may escape from the test bar during the linear shrinkage measurement. It may be for these reasons we never found the amount of gases to influence linear shrinkage, contrary to Novikov's opinion.37
We are therefore inclined towards the belief expressed87 that the hot tearing tendency of Al -Zn-Mg alloys increases w i th gas content, although the tests performed for this determination were the least satisfactory of all.
Conclusions
1. The hot tearing tendency of A l -Zn-Mg alloys can best be studied by measuring their ductility and linear shrinkage along their solidif ication range than by using the welding or pouring tests of a somewhat arbitrary design wh ich are usual in technical literature.
2. The variation in ductil ity is what determines the influence of a given factor on the hot tearing tendency of Al-Zn-Mg alloys. The variations in linear shrinkage are negligible in terms of the observed differences in ductility.
3. The hot tearing susceptibility of these alloys seems to grow wi th the proportion of alloying elements. On this account, of the three alloy-types studied the one more prone to sustain hot tearing is the ultra-high strength alloy type and the less prone to tearing is the weldable alloy type.
4. The degree of purity of the base aluminum does not appear to bear any influence on the hot tearing susceptibility of the alloys examined in this work.
5. Wi th increasing pouring temperature the hot tearing susceptibility of the alloys increases.
6. The addition of Cr alters somewhat the hot tearing susceptibility of these alloys; it modifies only to a scarcely noticeable degree their
solidification range. We believe to have proved that this effect is independent of whether the alloy has or has not aged.
7. Grain refiners reduce the hot tearing susceptibility on account of the grain size reduction they originate, wi thout it seems, at least in the particular case of Zr, its possible influence on the surface tension of the molten alloy making up the intergranular layers, being significant. They also produce a broadening of Prokhorov's zone which does not influence the hot tearing tendency during solidification of the alloy.
8. It seems that the amount of gases in these alloys increases their hot tearing susceptibility although this effect is more difficult to study wi th our procedures due to the dispersion in the tensile tests.
A cknowledgments Part of this paper is contained in the Doctoral Thesis by one of the authors (AM ) who wishes to express his thanks to the "Juan March" foundation for an allowance granted for carrying it out at CENIM
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