Once reserved for the aerospace and automotive industries, Finite Element Analysis (FEA) has become ubiquitous in general industrial applications because of its effectiveness in digitally modeling real-world situations. FEA accelerates the necessary but often time-consuming job of evaluating performance variables for good outcomes. Using FEA dramatically reduces design cycle time and cost by decreasing the number of experiments and materials used to optimize joint design. It works by rapidly screening adhesives, substrates and joint geometries to design the best possible joint for the application. In short, FEA minimizes the variables and cuts to the chase.
3M offers structural adhesives with a wide range of properties, and different adhesive types respond to loads differently. For example, a flexible adhesive undergoes much larger deformations than a stiff adhesive under the same load. The relationship between the stresses and strains is referred to as the material model and defines the adhesive behavior. Needless to say, it is imperative to select the correct adhesive for a joint design at the outset. The good news is that 3M has extensive data on our products and can provide adhesive material models to customers in the form of material data cards (MDCs), which can be imported directly into most FEA software packages.
There are many complex variables at play when it comes to selecting the right adhesive for an application. Let’s take a look at some of those, and how FEA modelling can help determine the right solution while detecting options that pose red flags down the road.
FEA modeling can predict non-uniform stresses and strains
Adhesives can be modeled using several different material models, with varying degrees of complexity and accuracy. The simplest material model is linear elastic:
𝜎 = 𝐸𝜀
Here 𝜎 is the stress, 𝜀 is the strain, and 𝐸 is Young’s Modulus. Young’s Modulus is a material property that describes the adhesive stiffness and must be measured experimentally. More sophisticated material models including elastic-plastic and cohesive zone models that can simulate adhesive behavior more accurately, but they also require the measurement of more material properties. The ideal material model is the simplest model that generates results with the necessary degree of accuracy.
FEA modeling can predict the stresses and strains in an adhesive joint when a load is applied. For example, consider an overlap shear sample with a 1” overlap width and ½” overlap length subjected to 350 lbf. The stress is the force divided by the overlap area:
𝜎 = 𝐹/(𝐿𝑒𝑛𝑔𝑡ℎ ∗ 𝑊𝑖𝑑𝑡ℎ) = 350 𝑙𝑏𝑓/(1" ∗ 0.5") = 700 𝑝𝑠𝑖
This, however, describes the average stress, whereas the local stress varies throughout the bond line. An FEA model of this joint is shown in Figure 1. Note that the stress is concentrated at the ends of the joint and the maximum stress is much higher than the average stress. Adhesive bonds fail when the maximum stress reaches a critical value, so the information generated by the FEA model is much more meaningful than the average stress calculation. The model also shows that the adhesive is not in a state of uniform shear, and large peel stresses occur at the ends of the bond.
Figure 1: Shear and peel stress distributions in an overlap shear joint.
Different adhesives exhibit different properties and 3M technology helps pinpoint the right one
Manufacturers can model 3M adhesives in their joints to help determine which adhesive is best for the application. Modeling will show how toughened epoxy adhesives resist deformation resulting in small strains and large stress concentrations, while flexible urethanes undergo larger strains resulting in more uniform stress distributions. The implication is clear: stiff adhesives should be used to transfer and hold large loads, and flexible adhesives should be used when joint movement is required. Even joints with substrate CTE (coefficient of thermal expansion) mismatches can be modeled, and running an FEA model using 3M data enables manufacturers to identify an adhesive with enough flexibility to allow movement and sufficient strength to withstand the required loads.
Changing the parameters in the model to drive better performance
FEA modeling can be used to evaluate and optimize joint geometry to increase adhesive performance. It enables the identification of peel and cleavage forces and predicts what happens when they are reduced or eliminated. Joint design parameters including the bond overlap, bond line thickness, and substrate properties can be optimized to meet the application requirements without overengineering the joint. For example, doubling the overlap length might be expected to double the bond strength, but stress concentrations at the ends of the bond (Figure 1) cause the strength to increase by less than a factor of two. Additionally, substrate properties have a significant effect on the performance of joints, with thinner and more flexible substrates generally resulting in higher stresses and lower bond strengths. Finally, increasing the bond line thickness might cause the strength to increase or decrease, depending on the specific properties of the adhesive.
As these examples demonstrate, the strength of one joint design cannot be used to accurately predict the strength of another design with a different geometry because the stress distribution is not uniform. While it is not feasible to test all possible joint geometries and substrates, material models can predict adhesive behavior in a wide range of joint designs, which ultimately eliminates time-consuming manual calculations and expedites the process, while giving design engineers confidence to proceed with the optimal adhesives for their project.
All in all, FEA has emerged as a powerful tool for digitally modeling real-world behaviors, but like any predictive technique, results are subject to errors and misinterpretation if the assumptions and limitations are not properly understood. This is where 3M’s expertise and industry leading knowledge can make all the difference when partnering with customers and sharing best practices. One important consideration is that models typically assume a perfect bond, with a cohesive failure mode, meaning that failure occurs within the adhesive layer and not by clean removal of the adhesive from a substrate. It is also important to understand that adhesives are viscoelastic materials, and their behavior is strain rate and temperature dependent. While FEA modeling is an excellent way to test many situations digitally, all 3M material models should be validated by the customer on the assembly line.