When a bonding joint fails, our first steps typically involve assessing whether the adhesive strength is adequate, the surface treatment is proper, the impregnation is sufficient, and the materials have not aged.
However, in actual engineering applications, certain failures do not begin only upon commissioning; rather, potential risks are already present once the adhesive has fully cured.
This potential hazard is the presence of residual internal stress.
It is invisible and difficult to measure precisely directly, yet not mystical in nature. Simply put, adhesive undergoes shrinkage during curing and cooling; if the surrounding substrate restricts its free deformation, the unshrinkable portion becomes residual stress within the adhesive layer.
Today, I'll guide you all in thoroughly understanding this concept.
0 1 Why study it?
The hazards of internal stress are of an "energy-storage" nature.
Upon curing, the adhesive layer stores a portion of elastic strain energy. This energy serves as the underlying driving force for subsequent interfacial delamination, microcrack propagation, and warping deformation.
Take interface delamination and delamination as examples: internal stresses accumulate on top of the operational load, causing the actual interface stress to far exceed the design-calculated rating value. In other words, even before the adhesive layer begins formal service, the interface is already subjected to excessive pre-tensioning.
Another example is accuracy drift, which proves particularly detrimental to precision assemblies such as robots, motors, and optical components.
The position of the magnetic core in the motor, the alignment of optical components, and the dimensions of structural parts may all undergo long-term drift due to gradual release of internal stresses. If components are initially compliant during assembly but exhibit deviations after hundreds of hours of operation, such issues often stem from the presence of internal stresses.
Additionally, the fatigue life is reduced. Internal stress represents a long-term average stress level that collectively lowers the fatigue life curve. The combination of temperature cycling, humidity, and vibration often leads to situations where products pass initial testing but fail during mass production.
Therefore, internal stress is not a secondary issue but rather the fundamental prerequisite for bonding reliability. It determines not only whether adhesion can occur, but also how long the bond remains stable thereafter.
0 2 Where does internal stress originate?
To understand internal stress, one must first comprehend its origin.
The internal stress during adhesive curing fundamentally arises from two types of strains that exhibit a tendency to contract but cannot actually do so.
The first category is curing shrinkage, also known as chemical shrinkage.
In liquid monomers, molecules maintain contact through van der Waals forces (weak interactions). There are no chemical bonds between the atoms of the two molecules; they simply exist in close proximity, with a typical distance of approximately 0.3–0.4 nm (which represents the sum of the van der Waals radii of both molecules).
During the polymerization reaction, covalent bonds are formed between monomers. Taking the most common C–C single bond as an example, its bond length is approximately 0.154 nm. This means that two molecules originally separated by a loose distance of about 0.35 nm are now forcibly brought together by a covalent bond with a length of approximately 0.15 nm-resulting in a reduction of the intermolecular distance by more than half. (Figure)
At the macroscopic level, the simultaneous contraction of trillions of such molecular pairs manifests as volume reduction. This is a physical consequence that cannot be entirely avoided in any addition polymerization reaction.
The second category is thermal mismatch stress.
Many adhesives require heating to cure. After curing, when cooled from high temperature to room temperature, the thermal expansion coefficients of the adhesive and substrate differ.
The thermal expansion coefficient of the adhesive is typically significantly higher than that of base materials such as metals, magnets, and ceramics. During cooling, the adhesive tends to contract further, but the base material prevents its free contraction, thereby restraining the adhesive layer and inducing residual internal stress.
The most critical concept here is the gel point.
Prior to the gel point, the adhesive remains fluid and can flow. During this stage, even if contraction occurs, the material can dissipate such deformation through flow, reorganization, and filling, thereby minimizing the accumulation of internal stress.
After the gel point, the situation changes. A three-dimensional network begins to form within the adhesive, and the material gradually transitions from a liquid to a solid state. At this stage, the adhesive layer acquires load-bearing capacity and starts to "remember" subsequent shrinkage and deformation events.
In other words, the portion of contraction occurring after the gel point is truly prone to generating internal stress.
As time progresses, the material further solidifies, and its Tg continuously rises. When the Tg exceeds the current operating temperature, the adhesive layer transitions from a rubbery state to a glassy state.
Upon entering the glass state, the modulus of the adhesive layer increases rapidly, making chain segment movement more difficult; consequently, a portion of the stress that could previously be released becomes even harder to release.
Therefore, internal stress can be simply understood as:
Before the gel point: contraction can occur without readily inducing stress.
After the gel point: the gel layer begins to form a network, and subsequent shrinkage is prevented.
After vitrification: the material becomes rigid, with its molecular chains immobilized, making stress release more difficult.
As we all know:
Stress = Modulus × Strain
Final internal stress ≈ effective modulus × (post-gelation curing shrinkage + thermal mismatch deformation) − relaxation release
Heat mismatch deformation can be simply understood as:
Thermal mismatch deformation ≈ (thermal expansion coefficient of the adhesive − thermal expansion coefficient of the substrate) × effective temperature difference
Only the contraction and thermal mismatch occurring after the gel point, multiplied by the continuously increasing modulus, minus the portion released through relaxation during the process, constitutes the final net internal stress.
This is also the reason why internal stress is difficult to study: it does not arise abruptly at a single instant but accumulates gradually during the curing and cooling processes. Throughout this process, shrinkage, temperature, modulus, and the material's ability to release stress all undergo continuous changes.
03 How to characterize: First measure the "result," then measure the "cause."
It is now widely recognized that internal stress does not arise abruptly at a single instant, but rather accumulates gradually during the curing and cooling processes.
Every parameter here is constantly changing: the contraction rate, temperature, modulus, and even the material's ability to release stress all vary.
Therefore, the characterization of internal stress cannot rely solely on a single numerical value; it must simultaneously address two questions:
First, what amount of stress or deformation remains at the end?
Second, how are these stresses formed during the curing process?
When it comes to testing methods, they can generally be divided into two categories.
One category involves direct measurement of stress or deformation results, while the other measures material intrinsic parameters to establish models.
Category 1: Direct measurement of stress or deformation results
This approach focuses on determining the extent of deformation or residual stress induced in the structure after the adhesive has cured.
The most classical method is the cantilever beam or bimaterial beam bending approach. Adhesive is applied to thin metal sheets, silicon wafers, or other substrate materials; during curing, adhesive shrinkage causes the substrate to bend. By measuring curvature in real time and employing a method analogous to Stoney's equation, the average stress within the adhesive layer can be calculated. This approach offers the advantages of being intuitive and well-established, enabling the visualization of curves depicting how stress varies with curing time.
There is also the fiber Bragg grating (FBG) technique. By embedding optical fibers within a gel layer, strain within the gel can be measured in real time. This method provides a more accurate reflection of the gel's internal state compared to surface deformation measurements alone, though it entails higher costs and greater operational complexity.
Cure strain monitoring in composite laminates using a distributed optical sensor (Image source)
For transparent adhesives, photoelasticity or birefringence methods can also be employed to observe stress distribution via stress-induced birefringence.
Additionally, methods such as drilling, core sampling, X-ray diffraction (XRD), neutron scattering, and Raman shift analysis can also be employed under specific conditions for measuring residual stress or indirect strain.