Machinery's Handbook, 31st Edition
1494 SOLIDIFICATION AND COOLING OF METALS Within the temperature range where solidification begins ( T l ) and solidification ends ( T S ) , the alloy is in a “mushy” state, with columnar dendrites. The mushy metal is present between the dendrite arms. The width of this mushy zone is an important factor during solidification. It is described by the freezing range as: (6) Pure metals have no freezing range, and the solidification front moves in a plane without forming a mushy zone. In alloys with a nearly symmetrical phase diagram, the structure generally is lamellar, with two or more solid phases present, depending on the alloy system. For alloys, a short freezing range generally involves a temperature difference less than 122°F (50°C) and a long freezing range higher than 230°F (110°C). Ferrous castings generally have narrow mushy zones, whereas aluminum and magnesium alloys have wide mushy zones. Slow cooling rates approximately 10 2 K/s result in coarse dendritic structures with large spac- ing between the dendrite arms. For higher cooling rates, from 10 6 to 10 8 K/s, the structures developed are amorphous. Solidification Time.—Total solidification time is the time required for the casting to so - lidify from molten metal after pouring. Casting geometry, material, and process deter- mine solidification time. Chvorinov’s rule states that under the same conditions, a casting with a large surface area and small volume will cool more rapidly than a casting with a small surface area and large volume. Therefore, a large sphere solidifies and cools to ambient temperature at a much slower rate than a smaller sphere. The reason is that the volume of a sphere is proportional to the cube of its diameter, and its surface area is proportional to the square of its diameter. Similarly, molten metal in a cube-shaped mold will solidify faster than in a spherical mold of the same volume. According to this rule, solidification time is a function of the volume of a casting and its surface area: (7) where V is the volume of the casting; A is the surface area of the casting; k is the mold constant; and n is the exponent ( 1.5 2 < ≤ n , but usually taken as 2). The mold constant k depends on the properties of the cast metal (heat of fusion, specific heat, and thermal conductivity), mold material, and pouring temperature. The value of k for a given casting operation can be based on experimental data from previous operations carried out using the same mold material, metal, and pouring temperature, even though the shape of the workpiece might be complex. During the early stages of solidification, a thin, solidified skin begins to form at the cool mold walls; as times passes, the skin thickens. With flat mold walls, this thickness is pro - portional to the square root of time. Shrinkage.—Most materials contract or shrink during solidification and cooling. Shrink - age is the result of contraction of the liquid as it cools prior to solidification; contraction during the phase change from liquid to solid; and contraction of the solid as it continues to cool to ambient temperature. Sometimes, shrinkage can cause cracking in a component as it solidifies. Since the cool - est area of a volume of liquid is where it contacts a mold or die, solidification usually begins first at this surface. As the crystals grow inward, the material continues to shrink. If the solid surface is too rigid and will not deform to accommodate the internal shrink- age, the stresses can exceed the tensile strength of the material and cause a crack to form. Shrinkage cavitation also may occur as a material solidifies inward and shrinks to such an extent that not enough atoms are present to fill the available space, and a void is left. The amount of contraction during the solidification of metals is shown in Table 1. Note that gray cast iron expands, because graphite has a relatively high specific volume, and when it precipitates as graphite flakes during solidification, it causes a net expansion of the metal. Freezing range = T l – T S Solidification time = k ( V / A ) n
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