The existing attenuation models for the durability of FRP (fiber-reinforced polymer) composites in hydrothermal environments were compared, and a new coupled strength attenuation model with a temperature parameter was proposed in this paper. A series of durability experiments on GFRP sheets in hydrothermal environments were conducted to validate the accuracy and rationality of the new model. A comparison between experimental data and the calculation results of the coupled model indicated that the new model can fit better with the experimental data and effectively reflect the convergence phenomenon in the strength attenuation of GFRP in hydrothermal environments. With a temperature parameter included, the new model can better predict the service life of GFRP composites at different aging temperatures. According to the coupled attenuation model proposed in this paper, a concept and calculation method of the slow-aging time point are put forward, which can be convenient for the evaluation and design of GFRP structures with long-term durability.

Research shows that FRP (fiber-reinforced polymer) composites possess great durability performance [

A few researchers have already proposed strength attenuation models of FRPs in hydrothermal environments. Williams et al. [

Gunyaev et al. [

Guo [

A comparison of the existing attenuation models indicates that Williams’s model fits the experimental data well, but there is some error in the data of the later aging process. It is widely confirmed that Gunyaev et al.’s model fits better with the experimental data, while the complexity caused by a large number of parameters in the model makes it inconvenient to use. Guo bilinear model is easy to calculate, but it cannot reflect the nonlinear law of the performance degradation of FRPs. Zhang parabolic-linear model has a good prediction capability at early aging times, but the second stage of the linear part of the model cannot reflect the gradual convergence of the degradation. In addition, none of the models above contain a temperature parameter. Williams’s model has to translate data of the strength reduction under different temperatures into that of the same temperature and then calculate a single-factor model that is only related to the aging time factor. The other three models lack consideration of the influence of temperature, as the parameters are different for the same material at different temperatures, making it inconvenient to predict the strength attenuation of FRPs under conditions of a specific temperature. Therefore, a more convenient and reasonable model is urgently needed. This paper proposes a new model for the strength attenuation of GFRP containing a temperature parameter. The parameters of the model remain unchanged for a single material or product. The coupled model was proposed based on previous studies and a mechanism analysis. A series of durability experiments under hydrothermal environments were conducted to verify the accuracy of the proposed model.

According to the Arrhenius formula, the relationship between the strength reduction and temperature presents as the higher the temperature, the greater the strength reduction (within a certain temperature range). The slope of the tangent of the strength reduction curve as a function of temperature is gradually increasing. This indicates that the relationship between the strength reduction and temperature may be exponential or multinomial. Many scholars [

Relationship between strength reduction rate and temperature.

Therefore, assume that the strength reduction shows a natural exponential growth relationship with the temperature, and the attenuation model of the temperature can be expressed as

According to (

To verify the accuracy of the model, a series of durability experiments on GFRP sheets under different temperatures was conducted. The specimens for the tests were made of glass fiber fabric embedded in epoxy matrix and then cured for 24 h in laboratory environment (a temperature of 23°C and a humidity of 50%) before the experiments. The aging temperatures of the experiments were set to 25°C, 50°C, and 75°C, and the environmental humidity was 95%. Figure

Experimental pictures: (a) samples of GFRP sheet and (b) the hydrothermal aging box.

The average strength of the GFRP sheets before the aging tests (after curing for 24 h) is 1011 MPa. The strengths of the samples were tested after different aging times. The results of the tensile tests after aging are summarized in Table

Strength of the samples after aging tests (MPa).

Tem. | Time | ||||
---|---|---|---|---|---|

42 d | 83 d | 124 d | 185 d | 250 d | |

25°C | 982 | 960 | 942 | 927 | 922 |

50°C | 1034 | 940 | 922 | 895 | 898 |

75°C | 958 | 912 | 890 | 856 | 854 |

Based on the original data in Table

Strength reduction rates of the samples (%).

Tem. | Time | ||||
---|---|---|---|---|---|

42 d | 83 d | 124 d | 185 d | 250 d | |

25°C | 2.87 | 5.06 | 6.82 | 8.31 | 8.51 |

50°C | −2.28 | 7.02 | 8.80 | 11.47 | 11.18 |

75°C | 5.12 | 9.79 | 11.97 | 15.33 | 15.53 |

It can be observed from Table

Extensive research has been conducted to study the attenuation law of strength for the GFRPs. Most of the studies [

The experimental data under the temperature of 50°C (Table

Comparison of models and experimental data at 50°C.

Generally speaking, the strength of the GFRPs decreases rapidly at first and then slowly, and the aging rate becomes slower and slower over the aging time with a trend of convergence. It could be learned from the experimental data that, at a condition of 50°C, the decrease of the strength began to slow down after exposure to a hydrothermal environment for 185 days, which indicates that the aging model proposed in this paper can better reflect this convergence phenomenon and can better fit the experimental data.

From the analysis of the single-factor model, the relationship between the strength reduction and temperature could be expressed by (

Equation (

For the material used in our experiments, the value of parameter

Values of material parameter

Tem. | Time | ||||
---|---|---|---|---|---|

42 d | 83 d | 124 d | 185 d | 250 d | |

25°C | 0.054 | 0.063 | 0.070 | 0.076 | 0.074 |

50°C | −0.032 | 0.062 | 0.067 | 0.078 | 0.072 |

75°C | 0.053 | 0.064 | 0.067 | 0.077 | 0.074 |

According to the results shown in Table

Strength decline rates under different temperatures.

From the aging experimental data and the strength attenuation curve given in Figure

The paper proposes a coupled model of strength attenuation for GFRP composites in hydrothermal environments. Although the aging mechanism has not yet been confirmed, single-factor models of the temperature and aging time were proposed based on the existing research results, and the coupled model was then obtained. A series of durability experiments on GFRP sheets in hydrothermal environments were conducted to validate the accuracy and rationality of the model. On the basis of the coupled model, the concept and calculation method of the slow-aging time point were presented. The following conclusions can be drawn from this study:

A temperature-factor model was proposed based on the Arrhenius formula and existing studies, and it indicated that the strength reduction rate shows a natural exponential growth relationship with the temperature. The accuracy and rationality of the temperature were verified by the results of durability experiments, based on which the calculated values of influence factor

A new strength attenuation model with aging time factor was proposed based on the data of previous studies. Experimental data were used to support the new model, and it was shown that the new model can fit the experimental data better than the parabolic-linear model. The new model can also reflect the convergence phenomenon found in the experimental data.

A coupled model for the strength attenuation of GFRP was obtained based on the single-factor models. According to the coupled model, the degradation curves of the strength of GFRP under 25°C, 50°C, and 75°C were obtained. Despite the abnormal data after 42 days of aging, the experimental data can basically fit the coupled model proposed by the paper.

According to the coupled model, the concept and calculation method of the slow-aging time point

The authors declare that there are no competing interests regarding the publication of this paper.

The authors gratefully acknowledge the financial support provided by the China 973 Program (Project no. 2012CB026205) and the Project of Water Conservancy Scientific Research and Technical Extension in Shandong Province (Project no. SDSLKY201407).