Analysis of Fatigue Life of PMMA at Different Frequencies Based on a New Damage Mechanics Model

Table 2

Comparison of equation and 𝑅² of three models.

	Model 1	Model 2	Model 3
Equations	Initial 𝑁=0, 𝐷𝑓=0, 𝐷𝑐=0	Initial 𝑁=0, 𝐷tot=1	Initial 𝑁=0, 𝐷tot(𝑁)=0
	End 𝐷tot(𝑁)=1	End 𝐷tot(𝑁)=1	End 𝐷tot(𝑁)=1
	Δ𝐷𝑓=𝜎𝑎^2𝑠+1𝐵𝑓^𝑚1−𝐷𝑓	Δ𝐷𝑓=𝜎𝑎^2𝑠+1𝐵𝑓^𝑚1−𝐷tot	Δ𝐷𝑓=𝜎𝑎^2𝑠+1𝐵1−𝐷tot
	Δ𝐷𝑐=()𝑇^𝑁𝑇𝑁−1𝐴𝜎1−𝐷c^𝑟d𝑡	Δ𝐷𝑐=()𝑇^𝑁𝑇𝑁−1𝐴𝜎1−𝐷tot^𝑟d𝑡	Δ𝐷𝑐=()𝑇^𝑁𝑇𝑁−1𝐴𝜎1−𝐷tot^𝑟d𝑡
	𝐶=𝑐^′expΔ𝐷𝑐+Δ𝐷𝑓0.5(Δ𝐷𝑐+Δ𝐷𝑓)	𝐷tot=𝐷tot+Δ𝐷𝑓+Δ𝐷𝑐	𝐷tot=𝐷tot+Δ𝐷𝑓+Δ𝐷𝑐
	𝐷𝑓=𝐷𝑓+Δ𝐷𝑓+𝐶⋅Δ𝐷𝑐
	𝐷𝑐=𝐷𝑐+Δ𝐷𝑐+𝐶⋅Δ𝐷𝑓
	𝐷tot=𝐷𝑐+𝐷𝑓
Parameters	For three models: 𝐴=9.198𝐸−26, 𝑟=14.216 units: (𝜎,𝜎𝑎: MPa 𝑇,𝑡: hour)
	𝑠=1.1497,  𝑚=0.3316	𝑠=1.0592,  𝑚=0.34047	𝑠=1.1436
	𝐵=190990790, 𝑐^′=0.9964	𝐵=99955327	𝐵=99767982
𝑅^2	0.98	0.95	0.66