ing the first stage of solidification, a coherent network does not form and hot tears do not occur. As the dendrites grow and come into contact, a coherent network forms. Further solidification produces a stress such that alloy contraction is restrained by the mold. Verö clarified the importance of the influence of eutectic constituents. If the remaining eutectic liquid were sufficient in volume and available, it would feed and ‘heal’ the incipient tears.


Pumphrey et al.13 proposed that hot tears could develop as


long as a small amount of residual liquid remained. Note that the strength of a metal increases with decreasing so- lidification temperatures. Pumphrey hypothesized that an alloy has a “brittle temperature range” between the tem- perature at which a coherent dendrite structure first devel- ops and the solidus temperature. In this temperature range, the metal possesses little ductility and is prone to hot tear. These early studies all considered that hot tearing was in- duced by the stress buildup in the metal during solidifica- tion and cooling due to the hindered contraction. The im- portance of the “healing effects” of the remaining liquid was also addressed.


In 1952, Pellini et al. studied the initiation of hot tears by using radiography and thermal analysis of solidifying cast- ings, and introduced the concept of liquid film during the last stages of solidification.14


Campbell2


postulated that hot tears are due to uniaxial ten-


sile failure in the weak portion of the casting, and suggest- ed that theories based on feeding difficulties be dismissed, since the hydrostatic (i.e. triaxial) stress resulted from feed- ing is associated with porosity formation between dendrites. He quantified Pellini’s theory and expressed the strain (ε) in the hot spot as:


ε = α ∆T L / l


α: coefficient of thermal expansion; ∆T: length of mushy zone; L: the length of the casting; l: length of a hot spot.


From this equation it is clear that strain can be reduced by refining the grains, reducing lengths between hot spots, and minimizing temperature differences.


Recently, Davidson and coworkers conducted experiments to confirm the hot tearing temperature.17


They used a hot tear Pellini et al. noted that a tear


started when the metal temperature was above the solidus (when there was a thin continuous liquid film remaining be- tween the solidified dendrites). He suggested that the mecha- nism of hot tearing consisted of separation of the film during solidification and when the solidus was being approached while a minute amount of liquid remained. It is at this stage when Pellini15


published his strain theory of hot tear-


ing based on strain accumulation and the concept of liquid films. Pellini suggested that hot tearing is a strain-controlled phenomenon: it occurs when the strain accumulated in a hot spot and reaches a critical value. At the onset of the film stage, the film is relatively thick and continuous throughout. At this point, the load required to deform the hot spot (the liquid film) should be near zero; but the deformation or ex- tension needed to open the liquid film and to initiate a hot tear should be relatively high. During the latter stages of so- lidification, the film is thinner and thinner and the deforma- tion is localized on a few remaining hot zones, giving rise to high strains. Total strain developed during film life depends on two factors: strain rate and film life. According to Pelli- ni14


the liquid film provided the condition that permitted hot


tearing, and the actual occurrence of hot tearing was deter- mined by mechanical factors inherent to the rate of deforma- tion. Hot tearing of semisolid metal was not possible unless the strain rate was high enough. Pellini and coworkers14-16 conducted quite elegant experiments at the Naval Research Laboratory and confirmed that the hot tearing temperature was above the solidus temperature of the alloy. Their work confirmed that temperature interval is crucial for hot tearing.


24


test rig, which was equipped with a window over the hot spot region, in an effort to measure the load imposed on the mushy zone and simultaneously observe the hot tear forma- tion and growth. They found that in Al-Cu alloys, hot tears started at very low loads and at temperatures between 93% and 96% solid.


Metz and Flemings6 conducted a fundamental study of hot


tearing using a shear test. They suggested that the strain rate was critical to hot tearing formation. They proposed that hot tearing is the result of progressive separation of dendrites to accommodate strain.


Theories Based on Other Principles


In 1961, Saveiko developed a theory based on interdendritic liquid film,18


whereby surface tension of the liquid film was


deemed to be critical in hot tearing. Saveiko’s model for hot tearing is shown in Figure 1. As can be seen, the grains were simplified and assumed to be cubical in shape. As shrinkage progresses, grains at locations A and B move in opposite directions, and the extension between them increases. If the movement reaches a certain value, a tear may form along one of the liquid films. To separate the liquid film to form two new surfaces, work must be done to overcome the mo- lecular adhesion force. The force required to tear apart the liquid film is:


P = 2αF / 1000gb


Where α is surface tension of the liquid, erg/cm2 area of contact between the plates and liquid, cm2


.


Equation 2 ; F is the


; b is the


thickness of the liquid layer between the plates, cm; and g is gravitational acceleration constant, cm/s2


Equation 1


International Journal of Metalcasting/Winter 11


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