Thixoforming : Semi-solid Metal Processing

have to form a network to absorb the forces. The average contact quantity to other
particles per particle is referred to as convectivity, whereas the contiguity (Cfs)
characterizes the steric arrangement or rather the cohesion of solid-phase particles
and can be described by the average proportion of solid–solid and solid–liquid
boundary surfaces. The contiguity has a major influence on the dimensional stability
of a partial liquid billet and, therefore, also on the viscosity of the material. Simplified,
contiguity can be understood as the degree of carcass formation of neighbouring
particles, where three different types of particle contacts are distinguished: not wetted
grain boundaries, partially wetted grain boundaries and completely wetted grain
boundaries [39–42]. For the characterization of neighbouring relationships of partial
liquid suspensions, the network character of a material is defined by means of the
degree of carcass formation or rather the contiguity of the solid phase or the matrix
character (M fl) of the liquid phase. The contiguity is characterized by the proportion
of common boundary surfaces within one component compared with all boundary
surfaces. The contiguity results for partial liquid metals according to Equation 3.7
from the proportion of the grain boundary surface in the solid phase to its complete
surface [39]:
Cf s ¼ 2Sss v
2S ss
v
þ Ssl
v
ð3:7Þ
where Cfs is the contiguity value of the solid phase, S ss
v is the boundary surface of the
solid-phase particles, Ssl v is the boundary surface of the solid (s ¼ solid) and the
liquid phase (l ¼ liquid). The determination of the contiguity takes place on
metallographic images by measuring the solid–solid and solid–liquid boundary
surfaces. It can take values between 0 and 1. If Cfs takes the value zero, the particles
of the solid phase are completely surrounded by melt and are isolated from the
liquid matrix.
As the carcass strength of the solid phases depends on both the contiguity and
the volume fraction of the solid phase, the product Csfs might be used instead of
the contiguity. This factor is referred to as the contiguity volume and describes the
volume of connected phase areas [41]:
Csf s ¼ V sCf s
3.2 Backgroundj59
ð3:8Þ
where Csfs is the contiguity volume, Vs is the volume fraction of the solid phase and
Cfs is the contiguity value of the solid phase. Examinations of the aluminium alloy
AA6082 showed that the contiguity volume is an important factor for
thixoforming [43].
The matrix character can be established according to the following equations [44]:
Mfs ¼ Lf s P ; Mfl ¼
Li
Lfl
P ;
Li
X Mi ¼ 1 ð3:9Þ
where Mfs is the matrix character of the solid phase, Mfl is the matrix character of the
liquid phase, L fs is the carcass line length of the solid phase, L fl is the carcass line
length of the liquid phase, P Li is the sum of the carcass line lengths and P Mi is the
sum of the matrix characters of the two phases. For the matrix character, by definition,