*4.5. Joint Stiffness*

The effect of temperature on the properties of adhesives is evaluated through the change of adhesive joint stiffness. The stiffness of SLJs, 15◦ , 30◦ , 45◦ , 60◦ , 75◦ scarf joints and BJs varies with temperature, as shown in Figure 13. It can be clearly seen from the diagram that temperature has a significant effect on the stiffness of the joint. With the increase in temperature, the stiffness of the joint decreases gradually, and vice versa. For SLJs, when the temperature increases from RT to 80 ◦C, the stiffness of the joint decreases by 8.73%, and when the temperature of the joint decreases from RT to −40◦C, the stiffness of the joint increases by 3.83%. For 15◦ , 30◦ , 45◦ , 60◦ and 75◦ scarf joints, temperature increases from RT to 80 ◦C, and the joint stiffness decreases by 10.48%, 30.45%, 19.98%, 9.70% and 0.88%, respectively. When the temperature decreases from RT to −40 ◦C, the joint stiffness increases by 9.85%, 3.29%, 20.70%, 37.99% and 46.47%, respectively. When the temperature of BJs increases from RT to 80 ◦C, the stiffness of the joint decreases by 43.97%, while it increases by 8.35% from RT to −40 ◦C. Through the above analysis, it is found that in addition to the 15◦ scarf joint, the stiffness of the joint increases gradually with the increase of the specimen angle, or in other words, the greater the proportion of tensile load on the adhesive area of the joint, the greater the stiffness of the joint when the smallest SLJ stiffness appears, which can also explain this law. *Crystals* **2021**, *11*, x FOR PEER REVIEW 16 of 20 and 0.88%, respectively. When the temperature decreases from RT to −40 °C, the joint stiffness increases by 9.85%, 3.29%, 20.70%, 37.99% and 46.47%, respectively. When the temperature of BJs increases from RT to 80 °C, the stiffness of the joint decreases by 43.97%, while it increases by 8.35% from RT to −40 °C. Through the above analysis, it is found that in addition to the 15° scarf joint, the stiffness of the joint increases gradually with the increase of the specimen angle, or in other words, the greater the proportion of tensile load on the adhesive area of the joint, the greater the stiffness of the joint when the smallest SLJ stiffness appears, which can also explain this law.

**Figure 13.** Column diagram of joint stiffness varying with temperature. **Figure 13.** Column diagram of joint stiffness varying with temperature.

### *4.6. Energy Absorption 4.6. Energy Absorption*

and 125.23%, respectively.

The experimental results show that temperature significantly affects the adhesive strength, joint stiffness and joint failure displacement. The area surrounded by the experimental force-displacement curve of the joint is the energy absorbed in the failure process of the joint (called absorption energy). Temperature affects the fracture energy of adhesive joints in a way similar to the maximum load, or in other words, there is an ongoing reduction from low to high temperatures [28]. Temperature strongly affects the energy absorption of adhesive joints. The decrease of adhesive strength is accompanied by the decrease of energy absorption. From the absorption energy histogram, it can be seen that with the The experimental results show that temperature significantly affects the adhesive strength, joint stiffness and joint failure displacement. The area surrounded by the experimental force-displacement curve of the joint is the energy absorbed in the failure process of the joint (called absorption energy). Temperature affects the fracture energy of adhesive joints in a way similar to the maximum load, or in other words, there is an ongoing reduction from low to high temperatures [28]. Temperature strongly affects the energy absorption of adhesive joints. The decrease of adhesive strength is accompanied by the decrease of energy absorption. From the absorption energy histogram, it can be

reference of room temperature (RT), the fracture energy of all joints decreases with the

as shown in Figure 14. When the temperature of SLJs increases from RT to 40 °C, 60 °C and 80 °C, the fracture energy decreases from 4.811/J to 4.114/J, 3.292/J and 2.882/J, respectively, and when the temperature decreases from RT to 0 °C, −20 °C and −40 °C, the fracture energy increases to 6.46/J, 8.767/J and 10.836/J, with an increase of 34.276%, 82.23%

When the temperature of 15°, 30°, 45°, 60° and 75° scarf joints rises to 80 °C, the fracture energy of the joint decreases from 12.282/J, 8.063/J, 4.432/J, 3.328/J and 3.078/J to 7.513/J, 5.363/J, 1.899/J, 1.886/J and 1.505/J, respectively, and the attenuation rates are 38.83%, 33.49%, 57.15%, 43.33% and 51.10%, respectively. When the temperature drops to −40 °C, the fracture energy of the joint increases to 24.103/J, 17.368/J, 13.919/J, 7.806/J and 7.213/J, respectively, and the growth rates are 96.25%, 115.40%, 214.06%, 134.56% and 134.34%, respectively. In this case, it is found that the fracture energy of 45° scarf joints at the high temperature of 80 °C decreases the most, while the fracture energy of −40 °C joints increases to the greatest extent. The effect of temperature on the fracture energy of BJs is similar to that of other joints. When the temperature decreases to 0 °C, −20 °C and −40 °C, the fracture energy increases from 4.602/J to 5.245/J, 5.803/J and 7.479/J, respectively, or has an increase of 13.97%, 26.10% and 62.52%. When the temperature rises to 40 °C, 60 °C and 80 °C, the fracture energy decreases to 1.441/J, 2.031/J and 2.301/J, respectively; that is

seen that with the reference of room temperature (RT), the fracture energy of all joints decreases with the increase in temperature, and that of all joints increases with the decrease in temperature, as shown in Figure 14. When the temperature of SLJs increases from RT to 40 ◦C, 60 ◦C and 80 ◦C, the fracture energy decreases from 4.811/J to 4.114/J, 3.292/J and 2.882/J, respectively, and when the temperature decreases from RT to 0 ◦C, −20 ◦C and −40 ◦C, the fracture energy increases to 6.46/J, 8.767/J and 10.836/J, with an increase of 34.276%, 82.23% and 125.23%, respectively. *Crystals* **2021**, *11*, x FOR PEER REVIEW 17 of 20 to say, 5.0%, 55.87% and 68.69%. Through the analysis of seven different stress forms of joints, it is found that the fracture energy of BJs is specially affected by temperature; the fracture energy attenuation at the high temperature of 80 °C is the largest, and the fracture energy at the low temperature of −40 °C increases the least.

**Figure 14.** Joint energy absorption histogram as a function of temperature. **Figure 14.** Joint energy absorption histogram as a function of temperature.

*4.7. Failure Criterion Surface of Adhesive Joint*  In order to predict the failure behavior of adhesive joints, realize safety design, and provide further reference and guidance for the practical application of adhesive structures in the automotive industry, it is necessary to establish reasonable failure criteria. The secondary stress criterion is widely used to predict the failure of adhesive joints, and its expressions are shown as Equation (2). ቀ ߪ ܰቁ ଶ + ቀ߬ ܵ ቁ ଶ = 1 (2) With tangential shear stress τ as the abscissa and normal stress σ as the ordinate, a coordinate system of adhesive positive shear stress was built. According to the experimental data shown in Tables 4–10, the least square method was adopted to fit the secondary stress failure criterion curve of adhesive joints at different temperatures (as shown in Figure 15). It can be seen from the figure that with the increase in temperature, the range between the failure criterion curve and the coordinate axis of the adhesive joint is gradually reduced, which indicates that the adhesive joint is more likely to be destroyed ܵ) and corresponding goodness of fit (R2) When the temperature of 15◦ , 30◦ , 45◦ , 60◦ and 75◦ scarf joints rises to 80 ◦C, the fracture energy of the joint decreases from 12.282/J, 8.063/J, 4.432/J, 3.328/J and 3.078/J to 7.513/J, 5.363/J, 1.899/J, 1.886/J and 1.505/J, respectively, and the attenuation rates are 38.83%, 33.49%, 57.15%, 43.33% and 51.10%, respectively. When the temperature drops to −40 ◦C, the fracture energy of the joint increases to 24.103/J, 17.368/J, 13.919/J, 7.806/J and 7.213/J, respectively, and the growth rates are 96.25%, 115.40%, 214.06%, 134.56% and 134.34%, respectively. In this case, it is found that the fracture energy of 45◦ scarf joints at the high temperature of 80 ◦C decreases the most, while the fracture energy of −40 ◦C joints increases to the greatest extent. The effect of temperature on the fracture energy of BJs is similar to that of other joints. When the temperature decreases to 0 ◦C, −20 ◦C and −40 ◦C, the fracture energy increases from 4.602/J to 5.245/J, 5.803/J and 7.479/J, respectively, or has an increase of 13.97%, 26.10% and 62.52%. When the temperature rises to 40 ◦C, 60 ◦C and 80 ◦C, the fracture energy decreases to 1.441/J, 2.031/J and 2.301/J, respectively; that is to say, 5.0%, 55.87% and 68.69%. Through the analysis of seven different stress forms of joints, it is found that the fracture energy of BJs is specially affected by temperature; the fracture energy attenuation at the high temperature of 80 ◦C is the largest, and the fracture energy at the low temperature of −40 ◦C increases the least.

### at high temperature. The parameter values (ܰ, of the failure criterion formula at seven test temperatures are shown in Table 12. *4.7. Failure Criterion Surface of Adhesive Joint*

In order to predict the failure behavior of adhesive joints, realize safety design, and provide further reference and guidance for the practical application of adhesive structures in the automotive industry, it is necessary to establish reasonable failure criteria. The secondary stress criterion is widely used to predict the failure of adhesive joints, and its expressions are shown as Equation (2).

$$\left(\frac{\sigma}{N}\right)^2 + \left(\frac{\tau}{S}\right)^2 = 1\tag{2}$$

With tangential shear stress *τ* as the abscissa and normal stress *σ* as the ordinate, a coordinate system of adhesive positive shear stress was built. According to the experimental

data shown in Tables 4–10, the least square method was adopted to fit the secondary stress failure criterion curve of adhesive joints at different temperatures (as shown in Figure 15). It can be seen from the figure that with the increase in temperature, the range between the failure criterion curve and the coordinate axis of the adhesive joint is gradually reduced, which indicates that the adhesive joint is more likely to be destroyed at high temperature. The parameter values (*N*, *S*) and corresponding goodness of fit (R2) of the failure criterion formula at seven test temperatures are shown in Table 12. *Crystals* **2021**, *11*, x FOR PEER REVIEW 18 of 20

**Figure 15.** Failure criterion curves of adhesive joints at different temperatures. **Figure 15.** Failure criterion curves of adhesive joints at different temperatures.


**Table 12.** Parameters of failure criteria and corresponding goodness of fit at seven temperatures. **Table 12.** Parameters of failure criteria and corresponding goodness of fit at seven temperatures.

The parameters (ܰ, ܵ) in the failure criterion formula under different temperature conditions were extracted, the change law was fitted by the exponential function (0.9241 and 0.9827, respectively) according to their change characteristics with temperature, and Equation (3) and Equation (4) were obtained as follows. When Equation (3) and Equation (4) are brought in Equation (5), the failure criterion formula of the adhesive joint under the condition of the full temperature field is obtained. The parameters (*N*, *S*) in the failure criterion formula under different temperature conditions were extracted, the change law was fitted by the exponential function (0.9241 and 0.9827, respectively) according to their change characteristics with temperature, and Equations (3) and (4) were obtained as follows. When Equations (3) and (4) are brought in Equation (5), the failure criterion formula of the adhesive joint under the condition of the full temperature field is obtained.

$$N = 2.07 + 0.82 \times 0.98^T \tag{3}$$

$$S = 1.26 + 1.85 \times 0.99^T \tag{4}$$

$$\left(\frac{\sigma}{2.07 + 0.82 \times 0.98^T}\right)^2 + \left(\frac{\tau}{1.26 + 1.85 \times 0.99^T}\right)^2 = 1\tag{5}$$

where *T* represents any temperature value between −40 °C and 80 °C. When the ambient temperature is brought into Equations (3) and (4), the failure criterion of adhesive joints at this temperature can be obtained, which provides the basis for the failure prediction of the adhesive structure. In order to reflect the variation of failure criterion with temperature more intuitively, the failure criterion surface of adhesive joints is established by where *T* represents any temperature value between −40 ◦C and 80 ◦C. When the ambient temperature is brought into Equations (3) and (4), the failure criterion of adhesive joints at this temperature can be obtained, which provides the basis for the failure prediction of the adhesive structure. In order to reflect the variation of failure criterion with temperature more intuitively, the failure criterion surface of adhesive joints is established by

MATLAB software, as shown in Figure 16. Therefore, it can be seen that with the increase

in temperature, the failure criteria of adhesive joints shrink gradually.

**References** 

MATLAB software, as shown in Figure 16. Therefore, it can be seen that with the increase in temperature, the failure criteria of adhesive joints shrink gradually. *Crystals* **2021**, *11*, x FOR PEER REVIEW 19 of 20

**Figure 16.** ISR-7008 adhesive joint failure criterion surface. **Figure 16.** ISR-7008 adhesive joint failure criterion surface.

### **5. Conclusions 5. Conclusions**

In this paper, the influence of ambient temperature on the mechanical properties and joint strength of the adhesive body was studied, and the failure criterion surface under the full temperature field was also established. The specific research content is summarized as follows: In this paper, the influence of ambient temperature on the mechanical properties and joint strength of the adhesive body was studied, and the failure criterion surface under the full temperature field was also established. The specific research content is summarized as follows:


**Author Contributions:** Conceptualization, Y.F.; methodology, H.L.; writing—original draft preparation, Y.F.; writing—review and editing, Y.F.; project administration, H.P.; funding acquisition, Y.F. All authors have read and agreed to the published version of the manuscript. **Author Contributions:** Conceptualization, Y.F.; methodology, H.L.; writing—original draft preparation, Y.F.; writing—review and editing, Y.F.; project administration, H.P.; funding acquisition, Y.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Science and Technology Project of Henan Province, grant number 202102210044. **Funding:** This research was funded by the Science and Technology Project of Henan Province, grant number 202102210044.

**Data Availability Statement:** The datasets analyzed during the current study are available from the corresponding author on reasonable request. **Data Availability Statement:** The datasets analyzed during the current study are available from the corresponding author on reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest. **Conflicts of Interest:** The authors declare no conflict of interest.
