Residual stress


A culprit in shrinkage and warpage problems

Residual stress is a process-induced stress, frozen in a molded part. It can be either flow-induced or thermal-induced. Residual stresses affect a part similarly to externally applied stresses. If they are strong enough to overcome the structural integrity of the part, the part will warp upon ejection, or later crack, when external service load is applied. Residual stresses are the main cause of part shrinkage and warpage. The process conditions and design elements that reduce shear stress during cavity filling will help to reduce flow-induced residual stress. Likewise, those that promote sufficient packing and uniform mold cooling will reduce thermal-induced residual stress. For fiber-filled materials, those process conditions that promote uniform mechanical properties will reduce thermal-induced residual stress.

Flow-induced residual stress
Unstressed, long-chain polymer molecules tend to conform to a random-coil state of equilibrium at temperatures higher than the melt temperature (i.e., in a molten state). During processing the molecules orient in the direction of flow, as the polymer is sheared and elongated. If solidification occurs before the polymer molecules are fully relaxed to their state of equilibrium, molecular orientation is locked within the molded part. This type of frozen-in stressed state is often referred to as flow-induced residual stress. Because of the stretched molecular orientation in the direction of flow, it introduces anisotropic, non-uniform shrinkage and mechanical properties in the directions parallel and perpendicular to the direction of flow.


Frozen-in molecular orientation
Due to a combination of high shear stress and a high cooling rate adjacent to the mold wall, there is a highly oriented layer frozen immediately below the part surface. This is illustrated in Figure 1. Subsequent exposure of a part with high residual flow stresses (or frozen-in orientation) to high temperature may allow some of the stresses to relieve. This typically results in part shrinkage and warpage. Due to the thermal insulating effect of the frozen layers, polymer melt in the hot core is able to relax to a higher degree, leading to a low molecular orientation zone.


FIGURE 1. The development of residual flow stresses due to frozen-in molecular orientation during the filling and packing stages. (1) High cooling, shear, and orientation zone (2) Low cooling, shear, and orientation zone


Reducing flow-induced residual stress
Process conditions that reduce the shear stress in the melt will reduce the level of flow-induced residual stresses. In general, flow-induced residual stress is one order of magnitude smaller than the thermal-induced residual stress.

Thermal-induced residual stress
Thermal-induced residual stress occurs due to the following reasons:


Free quenching example
Material shrinkage during injection molding can be conveniently demonstrated with a free quenching example, in which a part of uniform temperature is suddenly sandwiched by cold mold walls. During early cooling stages, when the external surface layers cool and start to shrink, the bulk of the polymer at the hot core is still molten and free to contract. However, as the internal core cools, local thermal contraction is constrained by the already-rigid external layers. This results in a typical state of stress distribution with tension in the core balanced by compression in the outer layers, as illustrated Figure 2 below.


FIGURE 2. The development of residual thermal stress in a "free-quenching" part due to variations in cooling across the molded part and the material's response to the temperature history.


Unbalanced cooling
Variation in the cooling rate 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.

Temperature profile  
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.

Pressure trace  
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



Differential shrinkage
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.


FIGURE 5. Variable residual stresses arise and the part deforms as layers of different frozen-in specific volume interact with each other

Process-induced vs. in-cavity residual stress
Process-induced residual stress data are much more useful than in-cavity residual stress data for molding simulation. Following are definitions of the two terms, along with an example that illustrates the difference between them.


Process-induced residual stress
After part ejection, the constraints from the mold cavity are released, and the part is free to shrink and deform. After it settles to an equilibrium state, the remaining stress inside the part is called process-induced residual stress, or simply, residual stress. Process-induced residual stress can be flow-induced or thermal-induced, with the latter being the dominant component.


In-cavity residual stress
While the part is still constrained in the mold cavity, the internal stress that accumulates during solidification is referred to as in-cavity residual stress. This in-cavity residual stress is the force that drives post-ejection part shrinkage and warpage.


Example
The shrinkage distribution described in Warpage due to differential shrinkage leads to a thermal-induced residual stress profile for an ejected part, as shown in the lower-left figure below. The stress profile in the upper-left figure is the in-cavity residual stress, in which the molded part remains constrained within the mold prior to ejection. Once the part is ejected and the constrained force from the mold is released, the part will shrink and warp to release the built-in residual stress (generally tensile stress, as shown) and reach an equilibrium state. The equilibrium state means that there is no external force exerting on the part and the tensile and compressive stresses over the part cross-section should balance with each other. The figures on the right side correspond to the case with a non-uniform cooling across the part thickness and, thereby, causing an asymmetric residual-stress distribution.


FIGURE 6. In-cavity residual stress profile (top) vs. process-induced residual stress profile and part shape after ejection (bottom).


Reducing thermal-induced residual stress
Conditions that lead to sufficient packing and more uniform mold-wall temperatures will reduce the thermal-induced residual stresses. These include: