Fig。 1。 PVT diagram。

Uneven volumetric shrinkage can be induced by thermal effects, pressure, part geometry, and flowing orientation effects。 The details are presented as follows。

1。1。 Thermal effect

Temperature primarily causes the specific volume change in proc- essed polymers。 As depicted in the PVT diagram (Fig。 1), the specific volume of injection-molded parts cooled from high temperatures and surrounded by constant pressure change, causing a high shrinkage rate。 In thin-walled molding, molten polymer that enters cavities is quickly cooled with energy dissipated from cavity surfaces。 Conse- quently, polymer temperatures close to the mold surface are lower than those in the polymer's center, generating a relatively lower shrink- age rate。 Moreover, the thick portions shrink more than do the thin

portions。 Thus, injection-molded parts with uneven thicknesses under- go nonuniform shrinkage and subsequent  warpage。

In addition, differential cooling results in variations in sectional shrinkage。 The temperature difference between the upper and lower surfaces causes differential shrinkage between the cavity and core, pro- ducing a bending moment after the part is ejected from mold。 This bending moment creates warpage or residual stress, depending on the mechanical stiffness of the part [5,6]。 The cooling channel layout and the core and cavity material properties also affect the cooling rate uni- formity。 Basically, deviation in the cooling rate causes uneven shrink- age, particularly in thick parts that shrink substantially。 In addition, a hot mold surface shrinks more than does a cold surface。 The thermal effect contributes to generating internal stress in injection-molded parts during the cooling stage; the outer layer along the thickness direc- tion solidifies first and limits the shrinkage direction of the inner part that cools later。 Cooling channels are favorable to be placed close to the part whenever possible。 However, varying the distance between the cooling channels and the part can facilitate controlling the differen- tial cooling effects。

1。2。 Pressure effect

Pressure is another crucial factor affecting the specific volume of polymer。 As shown in the PVT diagram, injection-molded parts cooled under high pressure shrink less。 The pressure level is associated with the location of molten polymer in the cavities。 For example, the polymer near the gate is surrounded with high pressure, and therefore shrinks less。 By contrast, the polymer far from the gate and treated with low pressure shrinks more。 In thin-walled molding, molten polymer is rapidly cooled, generating a substantial pressure gradient along the thickness direction that produces nonuniform residual stress, and then creates uneven shrinkage after cooling, thereby generating part warp- age。 The molten polymer can efficiently release internal stress at a high temperature and shrinks less when sufficiently  cooled。

Packing profiles can be used to establish an approximately uniform distribution of volumetric shrinkage throughout a molded product。 In general, lower pressures cause volumetric shrinkage to increase, where- as higher pressures reduce volumetric shrinkage。 A constant packing pressure results in volumetric shrinkage and is maximal at the end  of

Fig。 2。 Geometry of the portable cover。

flow and minimal near the gate region。 A decayed pressure profile gen- erates an approximately uniform volumetric shrinkage by causing the parts of plastic cooling near the gate to freeze as effectively as if they were under the same pressure in regions further from the  gate。

1。3。 Geometry effect

Part geometry and mechanical properties of materials also play a crucial role in warpage; the final warpage of a part depends on mechan- ical stiffness, which is a function of the geometrical configuration and the material's mechanical properties。 If a part has greater mechanical stiffness, it will warp less because of high variations in the shrinkage; a part with less mechanical stiffness will warp more [6]。 In addition, the geometrical structure of parts may cause two flowing behaviors, the hysteresis effect and the race-tracking effect, that substantially affect the temperature and pressure distribution inside injection- molded parts。 These two effects are exerted when parts exhibit appar- ent thickness deviation。 During mold filling, molten polymer consistent- ly flows to the low resistance area first and then to the high resistance area。