Figure 1.
Test results of stiffness performance of H-GFRPs. (a) E11,t, (b) E11,c, (c) E22,t, (d) E22,c, (e) G12.
Figure 1.
Test results of stiffness performance of H-GFRPs. (a) E11,t, (b) E11,c, (c) E22,t, (d) E22,c, (e) G12.
Figure 2.
Coefficient of variation (CV) for the stiffness properties of the five H-GFRP batches.
Figure 2.
Coefficient of variation (CV) for the stiffness properties of the five H-GFRP batches.
Figure 3.
Longitudinal and transverse tensile–compression moduli of the five H-GFRP batches. (a) E11, (b) E22.
Figure 3.
Longitudinal and transverse tensile–compression moduli of the five H-GFRP batches. (a) E11, (b) E22.
Figure 4.
Test results of the strength properties of H-GFRPs. (a) Xt, (b) Xc, (c) Yt, (d) Yc, (e) S12.
Figure 4.
Test results of the strength properties of H-GFRPs. (a) Xt, (b) Xc, (c) Yt, (d) Yc, (e) S12.
Figure 5.
CV results for the strength properties of the five H-GFRP batches.
Figure 5.
CV results for the strength properties of the five H-GFRP batches.
Figure 6.
Fitting curves for the stiffness properties of H-GFRPs at RT. (a) E11,t, (b) E11,c, (c) E22,t, (d) E22,c, (e) v12, (f) G12.
Figure 6.
Fitting curves for the stiffness properties of H-GFRPs at RT. (a) E11,t, (b) E11,c, (c) E22,t, (d) E22,c, (e) v12, (f) G12.
Figure 7.
Probability function diagrams for the stiffness properties of H-GFRPs at RT. (a) E11,t, (b) E11,c, (c) E22,t, (d) E22,c, (e) v12, (f) G12.
Figure 7.
Probability function diagrams for the stiffness properties of H-GFRPs at RT. (a) E11,t, (b) E11,c, (c) E22,t, (d) E22,c, (e) v12, (f) G12.
Figure 8.
Fitting curves for the strength performance functions of H-GFRPs at RT. (a) Xt, (b) Xc, (c) Yt, (d) Yc, (e) S12.
Figure 8.
Fitting curves for the strength performance functions of H-GFRPs at RT. (a) Xt, (b) Xc, (c) Yt, (d) Yc, (e) S12.
Figure 9.
Probability distribution diagrams for the strength properties of H-GFRPs under the RTD condition. (a) Xt, (b) Xc, (c) Yt, (d) Yc, (e) S12.
Figure 9.
Probability distribution diagrams for the strength properties of H-GFRPs under the RTD condition. (a) Xt, (b) Xc, (c) Yt, (d) Yc, (e) S12.
Figure 10.
Functional fitting curves for the strength properties of H-GFRPs in a humid and hot environment. (a) E11,t, (b) E11,c, (c) E22,t, (d) E22,c, (e) G12.
Figure 10.
Functional fitting curves for the strength properties of H-GFRPs in a humid and hot environment. (a) E11,t, (b) E11,c, (c) E22,t, (d) E22,c, (e) G12.
Figure 11.
Probability distribution diagrams for the strength properties of H-GFRPs under the high-temperature equilibrium moisture absorption (ETW) condition. (a) E11,t, (b) E11,c, (c) E22,t, (d) E22,c, (e) G12.
Figure 11.
Probability distribution diagrams for the strength properties of H-GFRPs under the high-temperature equilibrium moisture absorption (ETW) condition. (a) E11,t, (b) E11,c, (c) E22,t, (d) E22,c, (e) G12.
Figure 12.
Functional fitting curves for the strength properties of H-GFRPs under the ETW condition. (a) Xt, (b) Xc, (c) Yt, (d) Yc, (e) S12.
Figure 12.
Functional fitting curves for the strength properties of H-GFRPs under the ETW condition. (a) Xt, (b) Xc, (c) Yt, (d) Yc, (e) S12.
Figure 13.
Probability distribution diagrams for the strength properties of H-GFRPs under the ETW condition. (a) Xt, (b) Xc, (c) Yt, (d) Yc, (e) S12.
Figure 13.
Probability distribution diagrams for the strength properties of H-GFRPs under the ETW condition. (a) Xt, (b) Xc, (c) Yt, (d) Yc, (e) S12.
Figure 14.
Comparison of the probability curves for the stiffness properties of H-GFRPs. (a) E11, (b) E22, (c) G12.
Figure 14.
Comparison of the probability curves for the stiffness properties of H-GFRPs. (a) E11, (b) E22, (c) G12.
Figure 15.
Comparison of the probability curves for the strength properties of H-GFRPs. (a) Xt, (b) Xc, (c) Yt, (d) Yc, (e) S12.
Figure 15.
Comparison of the probability curves for the strength properties of H-GFRPs. (a) Xt, (b) Xc, (c) Yt, (d) Yc, (e) S12.
Figure 16.
Probability function diagram for the elastic modulus of H-GFRP in the RTD state.
Figure 16.
Probability function diagram for the elastic modulus of H-GFRP in the RTD state.
Figure 17.
Function fitting curves for the stiffness of H-GFRPs under the RTD condition. (a) E11, (b) E22, (c) v12, (d) G12.
Figure 17.
Function fitting curves for the stiffness of H-GFRPs under the RTD condition. (a) E11, (b) E22, (c) v12, (d) G12.
Figure 18.
Probability distribution diagrams for the stiffness properties of H-GFRPs under RTD conditions. (a) E11, (b) E22, (c) v12, (d) G12.
Figure 18.
Probability distribution diagrams for the stiffness properties of H-GFRPs under RTD conditions. (a) E11, (b) E22, (c) v12, (d) G12.
Figure 19.
Correlations between the stiffness properties of H-GFRPs under the RTD condition. (a) E11 and E22, (b) E11 and v12, (c) E11 and G12, (d) E22 and v12, (e) E22 and G12, (f) v12 and G12.
Figure 19.
Correlations between the stiffness properties of H-GFRPs under the RTD condition. (a) E11 and E22, (b) E11 and v12, (c) E11 and G12, (d) E22 and v12, (e) E22 and G12, (f) v12 and G12.
Figure 20.
Probability distribution for the elastic modulus of H-GFRPs under the ETW condition.
Figure 20.
Probability distribution for the elastic modulus of H-GFRPs under the ETW condition.
Figure 21.
Function fitting curves for the stiffness of H-GFRPs under the ETW condition. (a) E11, (b) E22, (c) v12, (d) G12.
Figure 21.
Function fitting curves for the stiffness of H-GFRPs under the ETW condition. (a) E11, (b) E22, (c) v12, (d) G12.
Figure 22.
Probability distribution diagrams for the stiffness properties of H-GFRPs under the ETW condition. (a) E11, (b) E22, (c) v12, (d) G12.
Figure 22.
Probability distribution diagrams for the stiffness properties of H-GFRPs under the ETW condition. (a) E11, (b) E22, (c) v12, (d) G12.
Figure 23.
Diagrams of correlation between the stiffness properties of H-GFRPs under the ETW condition. (a) E11 and E22, (b) E11 and v12, (c) E11 and G12, (d) E22 and v12, (e) E22 and G12, (f) v12 and G12.
Figure 23.
Diagrams of correlation between the stiffness properties of H-GFRPs under the ETW condition. (a) E11 and E22, (b) E11 and v12, (c) E11 and G12, (d) E22 and v12, (e) E22 and G12, (f) v12 and G12.
Figure 24.
Comparison of the probability distribution curves for stiffness properties of H-GFRPs under different conditions. (a) E11, (b) E22, (c) G12.
Figure 24.
Comparison of the probability distribution curves for stiffness properties of H-GFRPs under different conditions. (a) E11, (b) E22, (c) G12.
Table 1.
Working conditions considered in the mechanical property test.
Table 1.
Working conditions considered in the mechanical property test.
No. | Temperature | Moisture Absorption | Code |
---|
I | −55 °C | dry state | CTD |
II | 23 °C | dry state | RTD |
III | 80 °C | dry state | ETD |
IV | 55 °C | equilibrium moisture absorption | ETW1 |
V | 70 °C | equilibrium moisture absorption | ETW |
Table 2.
Tests used to determine the basic mechanical properties.
Table 2.
Tests used to determine the basic mechanical properties.
Type of Test | Specimen Size (Length × Width × Thickness) | Stiffness Properties | Strength Properties |
---|
Tensile test (0°) | 250 mm × 15 mm × 1 mm | Longitudinal tensile modulus E11,t, Poisson’s ratio v12 | Longitudinal tensile strength Xt |
Compression test (0°) | 140 mm × 12 mm × 2 mm | Longitudinal compression modulus E11,c | Longitudinal compressive strength Xc |
Tensile test (90°) | 175 mm × 25 mm × 2 mm | Transverse tensile modulus E22,t | Transverse tensile strength Yt |
Compression test (90°) | 140 mm × 12 mm × 2 mm | Transverse compression modulus E22,c | Transverse compressive strength Yc |
In-plane shear test | 250 mm × 25 mm × 3.6 mm | Longitudinal and transverse shear modulus G12 | Longitudinal and transverse shear strength G12 |
Table 3.
Batches of high-strength glass fibre composites (H-GFRPs).
Table 3.
Batches of high-strength glass fibre composites (H-GFRPs).
Batch | Date |
---|
1 | 4 November 2017 |
2 | 27 November 2017 |
3 | 29 November 2017 |
4 | 30 November 2017 |
5 | 22 January 2018 |
Table 4.
Statistical values of stiffness properties of five batches of H-GFRP.
Table 4.
Statistical values of stiffness properties of five batches of H-GFRP.
No. | E11,t/GPa | E11,c/GPa | E22,t/GPa |
Mean | SD | CV/% | Mean | SD | CV/% | Mean | SD | CV/% |
I | 58.5 | 2.71 | 4.63 | 61.0 | 1.32 | 2.17 | 17.7 | 1.29 | 7.29 |
II | 60.0 | 1.72 | 2.87 | 61.1 | 0.51 | 0.84 | 16.3 | 1.26 | 7.72 |
III | 55.4 | 0.29 | 0.53 | 59.6 | 1.10 | 1.85 | 13.5 | 0.82 | 6.06 |
IV | 57.1 | 1.75 | 3.07 | 59.4 | 0.58 | 0.97 | 10.6 | 0.25 | 2.36 |
V | 56.3 | 2.34 | 4.15 | 58.4 | 0.71 | 1.21 | 8.90 | 0.19 | 2.19 |
No. | E22,c/GPa | G12/GPa | v12 |
Mean | SD | CV/% | Mean | SD | CV/% | Mean | SD | CV/% |
I | 19.8 | 0.76 | 3.83 | 5.43 | 0.357 | 6.58 | / | / | / |
II | 17.7 | 0.88 | 4.96 | 4.30 | 0.211 | 4.90 | 0.283 | 0.0067 | 2.36 |
III | 15.3 | 0.76 | 4.93 | 3.51 | 0.152 | 4.32 | / | / | / |
IV | 14.9 | 0.43 | 2.91 | 3.18 | 0.172 | 5.40 | / | / | / |
V | 13.4 | 0.25 | 1.86 | 2.76 | 0.074 | 2.69 | / | / | / |
Table 5.
Statistical values of strength properties of five batches of H-GFRP.
Table 5.
Statistical values of strength properties of five batches of H-GFRP.
No. | Xt/MPa | Xc/MPa | Yt/MPa |
Mean | SD | CV/% | Mean | SD | CV/% | Mean | SD | CV/% |
I | 2151 | 144 | 6.71 | 1392 | 83 | 5.95 | 91.8 | 6.45 | 7.02 |
II | 1961 | 103 | 5.26 | 1216 | 55 | 4.54 | 73.3 | 3.06 | 4.17 |
III | 1683 | 74 | 4.38 | 1014 | 108 | 10.60 | 61.5 | 2.57 | 4.18 |
IV | 1102 | 40 | 3.66 | 975 | 77 | 7.85 | 51.9 | 1.67 | 3.22 |
V | 1009 | 66 | 6.49 | 859 | 62 | 7.21 | 43.5 | 1.72 | 3.97 |
NO. | Yc/MPa | S12/MPa | / | / | / |
Mean | SD | CV/% | Mean | SD | CV/% | / | / | / |
I | 310 | 15.01 | 4.85 | 88.0 | 3.21 | 3.65 | / | / | / |
II | 223 | 5.96 | 2.67 | 65.8 | 1.50 | 2.27 | / | / | / |
III | 164 | 5.61 | 3.42 | 50.1 | 1.52 | 3.03 | / | / | / |
IV | 141 | 4.04 | 2.86 | 42.0 | 2.52 | 6.00 | / | / | / |
V | 123 | 1.30 | 1.06 | 35.2 | 1.05 | 2.99 | / | / | / |
Table 6.
Statistical values of the longitudinal and transverse tensile−compression moduli of the five H-GFRP batches.
Table 6.
Statistical values of the longitudinal and transverse tensile−compression moduli of the five H-GFRP batches.
No. | E11/GPa | E22/GPa |
---|
Mean | SD | CV/% | Mean | SD | CV/% |
---|
I | 59.8 | 1.25 | 2.09 | 18.76 | 0.535 | 2.85 |
II | 60.5 | 0.95 | 1.56 | 17.03 | 0.845 | 4.96 |
III | 57.5 | 0.59 | 1.02 | 14.43 | 0.478 | 3.31 |
IV | 58.3 | 1.07 | 1.83 | 12.76 | 0.182 | 1.42 |
V | 57.4 | 1.28 | 2.23 | 11.15 | 0.150 | 1.35 |
Table 7.
Statistical distribution parameters for the stiffness properties of H-GFRPs at RT.
Table 7.
Statistical distribution parameters for the stiffness properties of H-GFRPs at RT.
Model | Normal | Lognormal | Weibull |
---|
μ | σ | Adj. R2 | μ | σ | Adj. R2 | λ | κ | Adj. R2 |
---|
E11,t/GPa | 59.50 | 2.40 | 0.996 | 4.09 | 0.040 | 0.996 | 60.43 | 29.24 | 0.992 |
E11,c/GPa | 60.92 | 1.39 | 0.980 | 4.11 | 0.023 | 0.979 | 61.47 | 50.50 | 0.986 |
E22,t/GPa | 16.09 | 1.28 | 0.983 | 2.78 | 0.079 | 0.986 | 16.59 | 14.22 | 0.971 |
E22,c/GPa | 17.49 | 1.07 | 0.997 | 2.86 | 0.061 | 0.997 | 17.92 | 18.75 | 0.989 |
v12 | 0.281 | 0.015 | 0.995 | −1.27 | 0.053 | 0.994 | 0.286 | 22.44 | 0.993 |
G12/GPa | 4.28 | 0.229 | 0.988 | 1.45 | 0.053 | 0.985 | 4.37 | 21.95 | 0.995 |
Table 8.
Values of the three statistical distribution parameters for the strength properties of H-GFRPs at RT.
Table 8.
Values of the three statistical distribution parameters for the strength properties of H-GFRPs at RT.
Model | Normal | Lognormal | Weibull |
---|
μ | σ | R | μ | σ | R | λ | κ | R |
---|
Xt/MPa | 1926 | 171 | 0.993 | 7.56 | 0.088 | 0.990 | 1992 | 13.1 | 0.997 |
Xc/MPa | 1183 | 89 | 0.994 | 7.08 | 0.076 | 0.996 | 1217 | 15.5 | 0.985 |
Yt/MPa | 72.53 | 5.45 | 0.989 | 4.28 | 0.075 | 0.986 | 74.62 | 15.75 | 0.997 |
Yc/MPa | 222 | 7.15 | 0.986 | 5.40 | 0.032 | 0.987 | 225 | 35.40 | 0.967 |
S12/MPa | 65.90 | 2.87 | 0.930 | 4.19 | 0.043 | 0.922 | 66.95 | 28.21 | 0.955 |
Table 9.
Values of the three statistical distribution parameters for the stiffness properties of H-GFRPs in a humid and hot environment.
Table 9.
Values of the three statistical distribution parameters for the stiffness properties of H-GFRPs in a humid and hot environment.
Model | Normal | Lognormal | Weibull |
---|
μ | σ | Adj. R2 | μ | σ | Adj. R2 | λ | κ | Adj. R2 |
---|
E11,t/GPa | 55.48 | 2.88 | 0.990 | 4.02 | 0.052 | 0.991 | 56.64 | 21.70 | 0.977 |
E11,c/GPa | 58.30 | 1.13 | 0.995 | 4.07 | 0.019 | 0.994 | 58.75 | 59.61 | 0.995 |
E22,t/GPa | 8.83 | 0.38 | 0.976 | 2.18 | 0.043 | 0.976 | 8.98 | 26.36 | 0.971 |
E22,c/GPa | 13.33 | 0.45 | 0.992 | 2.59 | 0.034 | 0.992 | 13.51 | 34.19 | 0.986 |
G12/GPa | 2.76 | 0.097 | 0.971 | 1.01 | 0.035 | 0.969 | 2.79 | 33.18 | 0.988 |
Table 10.
Values of the three statistical distribution parameters for the strength properties of H-GFRPs under the ETW condition.
Table 10.
Values of the three statistical distribution parameters for the strength properties of H-GFRPs under the ETW condition.
Model | Normal | Lognormal | Weibull |
---|
μ | σ | Adj. R2 | μ | σ | R | λ | κ | Adj. R2 |
---|
Xt/MPa | 988 | 93 | 0.993 | 6.89 | 0.094 | 0.990 | 1024 | 12.3 | 0.997 |
Xc/MPa | 829 | 99 | 0.998 | 6.72 | 0.119 | 0.998 | 867 | 9.7 | 0.996 |
Yt/MPa | 42.99 | 3.26 | 0.986 | 3.76 | 0.076 | 0.984 | 44.24 | 15.40 | 0.987 |
Yc/MPa | 122 | 2.71 | 0.995 | 4.81 | 0.022 | 0.996 | 124 | 52.19 | 0.985 |
S12/MPa | 35.19 | 1.62 | 0.980 | 3.56 | 0.045 | 0.978 | 35.80 | 24.63 | 0.989 |
Table 11.
Comparison of the probability distribution characteristics of the stiffness properties of H-GFRPs.
Table 11.
Comparison of the probability distribution characteristics of the stiffness properties of H-GFRPs.
Stiffness Property | RTD | ETW |
---|
μ (λ) | σ (κ) | Distribution | μ (λ) | σ (κ) | Distribution |
---|
E11,t/GPa | 4.09 | 0.040 | Lognormal | 4.02 | 0.052 | Lognormal |
E11,c/GPa | 61.47 | 50.50 | Weibull | 58.75 | 59.61 | Weibull |
E22,t/GPa | 2.78 | 0.079 | Lognormal | 8.83 | 0.38 | Normal |
E22,c/GPa | 2.86 | 0.061 | Lognormal | 2.59 | 0.034 | Lognormal |
v12 | 0.281 | 0.015 | Normal | / | / | / |
G12/GPa | 4.37 | 21.95 | Weibull | 2.79 | 33.18 | Weibull |
Table 12.
Comparison of the probability distributions of the strength properties of H-GFRPs.
Table 12.
Comparison of the probability distributions of the strength properties of H-GFRPs.
Stiffness Property | RTD | ETW |
---|
μ (λ) | σ (κ) | Distribution | μ (λ) | σ (κ) | Distribution |
---|
Xt/MPa | 1992 | 13.1 | Weibull | 1024 | 12.3 | Weibull |
Xc/MPa | 7.08 | 0.076 | Lognormal | 829 | 99 | Normal |
Yt/MPa | 74.62 | 15.75 | Weibull | 44.24 | 15.40 | Weibull |
Yc/MPa | 5.40 | 0.032 | Lognormal | 4.81 | 0.022 | Lognormal |
S12/MPa | 66.95 | 28.21 | Weibull | 35.80 | 24.63 | Weibull |
Table 13.
Performance parameters of H-GFRPs components under the RT condition.
Table 13.
Performance parameters of H-GFRPs components under the RT condition.
Volume | Elastic Parameter of Fibre | Elastic Parameter of Matrix |
---|
| | /GPa | | /GPa | /GPa | | /GPa |
0.6 | 0.4 | 93 | 0.25 | 37.2 | 3.0 | 0.35 | 1.11 |
Table 14.
Statistical model of the material properties in the RTD state.
Table 14.
Statistical model of the material properties in the RTD state.
Parameter | Mean | CV | Distribution Type |
---|
/GPa | 93 | 0.05 | Normal |
| 0.25 | 0.05 | Normal |
/GPa | 3.0 | 0.05 | Normal |
| 0.35 | 0.05 | Normal |
| 0.6 | 0.05 | Normal |
Table 15.
Values of the three statistical distribution parameters for the stiffness properties of H-GFRPs under the RTD condition.
Table 15.
Values of the three statistical distribution parameters for the stiffness properties of H-GFRPs under the RTD condition.
Model | Normal | Lognormal | Weibull |
---|
μ | σ | Adj. R2 | μ | σ | Adj. R2 | λ | κ | Adj. R2 |
---|
E11/GPa | 56.45 | 3.89 | 0.99998 | 4.03 | 0.069 | 0.99992 | 57.96 | 17.01 | 0.99765 |
E22/GPa | 16.15 | 1.56 | 0.99966 | 2.78 | 0.097 | 0.99999 | 16.75 | 12.1 | 0.99649 |
v12 | 0.289 | 0.011 | 0.99999 | −1.24 | 0.037 | 0.99996 | 0.294 | 31.8 | 0.99743 |
G12/GPa | 3.96 | 0.384 | 0.99961 | 1.38 | 0.097 | 0.99998 | 4.11 | 12.05 | 0.99651 |
Table 16.
Correlation coefficients between the stiffness properties of H-GFRPs under the RTD condition.
Table 16.
Correlation coefficients between the stiffness properties of H-GFRPs under the RTD condition.
Correlation Coefficient | E11 | E22 | v12 | G12 |
---|
E11 | 1 | / | / | / |
E22 | 0.717 | 1 | / | / |
v12 | −0.196 | −0.189 | 1 | / |
G12 | 0.662 | 0.970 | −0.338 | 1 |
Table 17.
Statistical model parameters of materials under the ETW condition.
Table 17.
Statistical model parameters of materials under the ETW condition.
Parameter | μ | CV | Model |
---|
/GPa | 90 | 0.05 | Normal |
| 0.25 | 0.05 | Normal |
/GPa | 2.08 | 0.05 | Normal |
| 0.35 | 0.05 | Normal |
| 0.6 | 0.05 | Normal |
Table 18.
Values of the three statistical distribution parameters for the stiffness properties of H-GFRPs under the ETW condition.
Table 18.
Values of the three statistical distribution parameters for the stiffness properties of H-GFRPs under the ETW condition.
Model | Normal | Lognormal | Weibull |
---|
μ | σ | Adj. R2 | μ | σ | Adj. R2 | λ | κ | Adj. R2 |
---|
E11/GPa | 54.28 | 3.75 | 0.99996 | 3.99 | 0.069 | 0.99997 | 55.73 | 16.95 | 0.99775 |
E22/GPa | 11.85 | 1.20 | 0.99945 | 2.47 | 0.102 | 0.99995 | 12.31 | 11.50 | 0.99602 |
v12 | 0.289 | 0.011 | 0.99999 | −1.24 | 0.037 | 0.99996 | 0.294 | 32.18 | 0.99753 |
G12/GPa | 2.81 | 0.282 | 0.99946 | 1.03 | 0.101 | 0.99995 | 2.92 | 11.64 | 0.99618 |
Table 19.
Correlation coefficients between the stiffness properties of H-GFRPs under the ETW condition.
Table 19.
Correlation coefficients between the stiffness properties of H-GFRPs under the ETW condition.
Correlation Coefficient | E11 | E22 | v12 | G12 |
---|
E11 | 1 | / | / | / |
E22 | 0.695 | 1 | / | / |
v12 | −0.193 | −0.191 | 1 | / |
G12 | 0.647 | 0.972 | −0.335 | 1 |
Table 20.
Comparison of the probability distribution characteristics of the stiffness properties of H-GFRPs.
Table 20.
Comparison of the probability distribution characteristics of the stiffness properties of H-GFRPs.
Stiffness | RTD | ETW |
---|
μ | σ | Distribution | μ | σ | Distribution |
---|
E11/GPa | 56.45 | 3.89 | Normal | 3.99 | 0.069 | Lognormal |
E22/GPa | 2.78 | 0.097 | Lognormal | 2.47 | 0.102 | Lognormal |
v12 | 0.289 | 0.011 | Normal | 0.289 | 0.011 | Normal |
G12/GPa | 1.38 | 0.097 | Lognormal | 1.03 | 0.101 | Lognormal |