Plastic injection molding will shrink inherently because density of polymer changes when process temperature drops to room temperature, causing shrinkage. Difference in shrinkage of the entire plastic part and cross section will cause internal residual stress, which has same effect as external force. If residual stress is higher than strength of plastic part structure during injection molding, plastic part will warp after demolding or break due to external force.

Residual stress is stress caused by flow of molten plastic (flow-induced) or thermal effect (thermal-induced) during plastic part molding, and is frozen in plastic part. If residual stress is higher than structural strength of plastic part, plastic part may warp during injection molding or break due to load later.
Residual stress is main cause of shrinkage and warpage of plastic parts. Good molding conditions and designs that can reduce shear stress caused by filling mold cavity can reduce residual stress caused by flow of molten plastic. Similarly, sufficient holding pressure and uniform cooling can reduce residual stress caused by thermal effects. For materials with added fibers, improving molding conditions of uniform mechanical properties can reduce residual stress caused by thermal effects.

Under stress, long-chain polymers are in a state of equilibrium with arbitrary curling at a temperature above melting point. During molding process, polymers are sheared and stretched, and molecular chains are oriented along flow direction.
If molecular chains solidify before they are completely relaxed and balanced, molecular chain orientation is frozen in plastic part. This stress freezing state is called flow-induced residual stress, which will cause uneven mechanical properties and shrinkage in flow direction and perpendicular to flow direction. In general, flow-induced residual stress is one power smaller than thermal-induced residual stress.
High orientation of surface of plastic part near mold wall will freeze immediately due to interaction of high shear stress and high cooling rate, as shown in Figure 1. If plastic part is stored in a high temperature environment, plastic part will release some stress, resulting in shrinkage and warping.
Heat insulation effect of solidified layer keeps polymer center layer at a higher temperature, which can release more stress, so molecular chains in the center layer have a lower orientation. Forming conditions that can reduce shear stress of melt will also reduce residual stress caused by flow, including: high melt temperature, high mold wall temperature, long filling time (low melt speed), reduced holding pressure, short flow path.

 

Figure 1 Molecular chain orientation frozen during filling and holding stages leads to flow-induced residual stress.
(1) Indicates high cooling rate, high shear stress or high orientation; (2) Indicates low cooling rate, low shear stress or low orientation.

Reasons for residual stress caused by thermal effect include following:
Plastic drops from set process temperature to room temperature, causing shrinkage.
When plastic solidifies, plastic part undergoes different thermal and mechanical processes from surface to the center, such as different cooling times and different holding pressures.
Pressure, temperature, molecular chain orientation and fiber orientation change due to changes in density and mechanical properties.
Design of mold limits shrinkage of plastic part in certain directions.
Shrinkage of plastic in injection molding can be illustrated by example of free cooling. If a plastic part with uniform temperature is suddenly clamped by cold mold walls on both sides, in the early stage of cooling, when surface of plastic part cools and begins to shrink, polymer inside plastic part is still in a high-temperature molten state and can shrink freely.
However, when temperature of center of plastic part drops, local thermal shrinkage is limited by solidified surface layer, resulting in a typical stress distribution with tensile stress in the center layer and compressive stress on the surface layer, as shown in Figure 2.
Difference in cooling rate from surface to the center of plastic part will induce residual stress of thermal effect. What's more, if cooling rates of mold walls on both sides of mold are different, asymmetric thermal effect residual stress will be caused. Tensile stress and compressive stress distributed asymmetrically in cross section of plastic part will cause bending moment, causing plastic part to warp, as shown in Figure 3.
Plastic parts with uneven thickness and areas with poor cooling effect will cause this unbalanced cooling, resulting in residual stress. Complex plastic parts have more complex distribution of residual stress caused by thermal effect due to factors such as uneven thickness, uneven mold cooling, and mold restrictions on free shrinkage.

 

Figure 2 Effect of uneven cooling of plastic parts and plastic temperature history leads to residual stress caused by thermal effect.

 

Figure 3 Uneven cooling in cross section of plastic part causes residual stress caused by asymmetric thermal effect, causing plastic part to warp.
Figure 4 illustrates change in specific volume of solidified layer caused by pressure history of holding pressure. Among them, left figure is temperature distribution curve of a cross section of plastic part. For convenience of explanation, plastic part is divided into 8 layers along thickness direction, and curve shows solidification time of each layer is t1~t8.
Note that plastic part solidifies from outermost layer, and the longer solidification time is, the closer to center layer.
Middle figure shows typical pressure history of each layer solidification, P1~P8. Pressure in filling stage usually rises gradually, reaching the highest pressure at the beginning of holding pressure, then gradually decreases due to cooling and gate solidification.
As a result, surface and center layers of plastic part solidify at low pressure, and the other middle layers solidify at high holding pressure. Right figure shows specific volume history of layer 5 on PvT diagram, specific volume of each layer at final solidification, and is marked with solid dots.

 

Given solidification specific volume of each layer, shrinkage behavior of each layer of plastic part will shrink differently according to PvT curve. Assuming that layers are separated as shown in Figure 5, result is shrinkage to situation in the middle figure, middle layers such as 2, 5, 6, and 7 shrink less because of their low solidification specific volume (or high solidification density). In reality, layers are connected together, resulting in a compromise shrinkage distribution, with middle layer being compressed, outer and center layers being stretched.

 

Figure 5 Differences in specific volume of each solidified layer interact with each other, resulting in different residual stresses and deformation of plastic part.

For injection molding simulation, process-induced residual stress is more important than in-cavity residual stress. Following introduces definitions of these two terms and provides an example to illustrate their difference.
After the plastic part is ejected, constraint imposed by cavity on plastic part is released, plastic part can shrink and deform freely until it reaches a state of equilibrium.
At this time, stress remaining in plastic part is process-induced residual stress, or simply residual stress, which includes flow-induced residual stress and thermal effect-induced residual stress, with thermal effect being main influence.
When plastic part is still constrained by mold cavity, internal stress accumulated by solidification of plastic part is called mold cavity residual stress. This residual stress will drive plastic part to shrink and warp after ejection.
Upper left figure of Figure 6 shows mold cavity residual stress (usually tensile stress shown in figure) of formed plastic part before ejection, which is still constrained by mold.
Once ejected, mold is freed from constraint of plastic part, plastic part will release mold cavity residual stress, shrink and warp. Thermal effect residual stress distribution curve caused by shrinkage distribution of ejected plastic part is shown in the lower left figure of Figure 6. In absence of external force, tensile stress of plastic part section is equal to compressive stress and reaches a state of equilibrium. The lower right figure of Figure 6 shows that thickness of plastic part is subjected to uneven cooling, resulting in asymmetric residual stress and warping.

 

Figure 6 (upper) mold cavity residual stress distribution curve and (lower) process-induced residual stress distribution curve and plastic part shape after ejection.
Conditions that can create sufficient holding pressure and uniform mold wall temperature can reduce residual stress caused by thermal effects. These conditions include:
Appropriate holding pressure and holding time.
All surfaces of plastic part are uniformly cooled.
Plastic part has uniform cross-sectional thickness.

When injection molded plastic part drops from process temperature to room temperature, volume shrinkage rate (shrinkage) can be as high as 20%. When crystalline and semi-crystalline materials are cooled below glass transition temperature, molecules are arranged in a relatively regular manner and form crystals, which are particularly prone to thermal shrinkage;
Amorphous materials do not have microstructural changes during phase changes, and thermal shrinkage is relatively small. Therefore, specific volume difference between crystalline and semi-crystalline materials in molten phase and solid phase (crystallization) is greater than that of amorphous material, as shown in Figure 7. In addition, cooling rate will also affect PvT behavior of crystalline and semi-crystalline materials.

 

Figure 7 PvT curves of amorphous and crystalline polymers.
Specific volume changes △υ from process state (point A) to normal pressure and room temperature state.
Note: When pressure increases, specific volume decreases.
Reasons for excessive shrinkage of plastic parts include too low injection pressure, insufficient holding time or cooling time, too high melt temperature, too high mold temperature, too low holding pressure, relationship between shrinkage, process parameters and wall thickness is shown in Figure 8:
During injection molding, if volume shrinkage of plastic part is not compensated, it will cause dents on the surface of plastic part or internal pores. Therefore, shrinkage of plastic part must be considered when designing mold. Control of shrinkage rate of plastic part is very important for design of plastic parts, mold design, and process conditions, especially for combined plastic parts.
Holding pressure immediately after filling mold cavity can reduce/eliminate dents and pores to determine size of plastic part. Mold flow analysis software can predict shrinkage of plastic parts and provide guidelines for correct design of molds.

 

Figure 8 Process and design parameters that affect shrinkage of plastic parts
For further reading, please refer to How to solve shrinkage and warpage? Just read this article!.