from the mold wall to its center can cause thermal-induced residual stress. Furthermore, asymmetrical thermal-induced residual stress can occur if the cooling rate of the two surfaces is unbalanced. Such unbalanced cooling will result in an asymmetric tension-compression pattern across the part, causing a bending moment that tends to cause part warpage. This is illustrated in Figure 3 below. Consequently, parts with non-uniform thickness or poorly cooled areas are prone to unbalanced cooling, and thus to residual thermal stresses. For moderately complex parts, the thermal-induced residual stress distribution is further complicated by non-uniform wall thickness, mold cooling, and mold constraints to free contraction.
FIGURE 3. Asymmetrical thermal-induced residual stress caused by unbalanced cooling across the molded part thickness introduces part warpage
Variable frozen-in densities
The figure below illustrates the variation in frozen-in densities caused by the packing pressure history.
The left figure plots the temperature profile at one location on the part. For the purpose of illustration, the part is divided into eight equal layers across the part thickness. The profile shows the temperature at the solidification (freeze-off) time instant for each layer (t1 to t8). Note that the material starts solidifying from the outer layers and the frozen interface moves inwards with time.
The center figure plots a typical pressure history, showing the pressure levels (P1 to P8) as each layer solidifies. In general, the pressure gradually increases during filling, reaching a maximum in the early packing stage, and then starts to decay due to cooling and gate freeze-off. Accordingly, the material at the outer layers and center layers solidify when the pressure level is low, whereas the intermediate layers freeze under high packing pressure.
Frozen-in specific volume
The right figure depicts the specific volume trace for layer 5 on a pvT plot and the final frozen-in specific volumes for all the layers, marked by the numbered solid circles.
FIGURE 4. Factors that influence the development of “frozen-in” specific volume
Given the frozen-in specific volumes, the various layers will shrink differently, according to the pvT curves that govern the material shrinkage behavior. Hypothetically, if each layer were detached from others (as shown in Figure 5) then material elements in the left figure below would have shrunk like those in the center figure. In this case, the intermediate layers tend to shrink less than the others because of lower frozen-in specific volume (or, equivalently, higher frozen-in density). In reality, all the layers are bound together. Therefore, the end result will be a compromised shrinkage distribution with intermediate layers being compressed and outer and center layers being stretched.