Figure 1.
RVE model considering interphase for prestressed composites. (a) Geometrical model; (b) finite element model.
Figure 1.
RVE model considering interphase for prestressed composites. (a) Geometrical model; (b) finite element model.
Figure 2.
Illustrations for the distribution patterns of elastic modulus. (a) α = 1, β = 1, γ = 1; (b) α = 0.1, β = 1, γ = 1; (c) α = 1, β = 0.1, γ = 1; (d) α = 1, β = 0.1, γ = 0.5.
Figure 2.
Illustrations for the distribution patterns of elastic modulus. (a) α = 1, β = 1, γ = 1; (b) α = 0.1, β = 1, γ = 1; (c) α = 1, β = 0.1, γ = 1; (d) α = 1, β = 0.1, γ = 0.5.
Figure 3.
Illustration for the inter-fiber directions.
Figure 3.
Illustration for the inter-fiber directions.
Figure 4.
Manufacturing process of prestressed composites.
Figure 4.
Manufacturing process of prestressed composites.
Figure 5.
Multi-step methodology for the prediction of residual stress.
Figure 5.
Multi-step methodology for the prediction of residual stress.
Figure 6.
Residual axial stress induced by the prestress application (a) with the multi-step method and (b) with the modified equivalent thermal method.
Figure 6.
Residual axial stress induced by the prestress application (a) with the multi-step method and (b) with the modified equivalent thermal method.
Figure 7.
Transverse strain values in the fiber after prestress application (a) with the multi-step method and (b) with the modified equivalent thermal method.
Figure 7.
Transverse strain values in the fiber after prestress application (a) with the multi-step method and (b) with the modified equivalent thermal method.
Figure 8.
Radial stress distribution after prestress application (a) with the multi-step method and (b) with the modified equivalent thermal method.
Figure 8.
Radial stress distribution after prestress application (a) with the multi-step method and (b) with the modified equivalent thermal method.
Figure 9.
Circumferential stress distribution after prestress application (a) with the multi-step method and (b) with the modified equivalent thermal method.
Figure 9.
Circumferential stress distribution after prestress application (a) with the multi-step method and (b) with the modified equivalent thermal method.
Figure 10.
Thermal residual stress distribution patterns of composites (a) in the matrix and (b) in the fiber.
Figure 10.
Thermal residual stress distribution patterns of composites (a) in the matrix and (b) in the fiber.
Figure 11.
Residual stress distribution patterns of prestressed composites (a) in the matrix and (b) in the fiber.
Figure 11.
Residual stress distribution patterns of prestressed composites (a) in the matrix and (b) in the fiber.
Figure 12.
Residual axial stress distribution patterns in the RVE considering interphase (a) in the matrix before applying prestress; (b) in the matrix after applying prestress; (c) in the fiber before applying prestress; (d) in the fiber after applying prestress; (e) in the interphase before applying prestress; (f) in the interphase after applying prestress.
Figure 12.
Residual axial stress distribution patterns in the RVE considering interphase (a) in the matrix before applying prestress; (b) in the matrix after applying prestress; (c) in the fiber before applying prestress; (d) in the fiber after applying prestress; (e) in the interphase before applying prestress; (f) in the interphase after applying prestress.
Figure 13.
Stress distribution patterns along the radial direction (a) before applying prestress and (b) after applying prestress.
Figure 13.
Stress distribution patterns along the radial direction (a) before applying prestress and (b) after applying prestress.
Figure 14.
Stress distribution patterns along the circumferential direction (a) before applying prestress and (b) after applying prestress.
Figure 14.
Stress distribution patterns along the circumferential direction (a) before applying prestress and (b) after applying prestress.
Figure 15.
Axial stress distribution patterns with different prestress values. (a) 30 MPa; (b) 60 MPa; (c) 120 MPa.
Figure 15.
Axial stress distribution patterns with different prestress values. (a) 30 MPa; (b) 60 MPa; (c) 120 MPa.
Figure 16.
Radial stress distribution patterns with different prestress values. (a) 30 MPa; (b) 60 MPa; (c) 120 MPa.
Figure 16.
Radial stress distribution patterns with different prestress values. (a) 30 MPa; (b) 60 MPa; (c) 120 MPa.
Figure 17.
Circumferential stress distribution patterns with different prestress values. (a) 30 MPa; (b) 60 MPa; (c) 120 MPa.
Figure 17.
Circumferential stress distribution patterns with different prestress values. (a) 30 MPa; (b) 60 MPa; (c) 120 MPa.
Figure 18.
Radial stress distribution patterns. (a) αi = 0.1αm without prestress; (b) αi = 1.0αm without prestress; (c) αi = 10αm without prestress; (d) αi = 0.1αm with prestress; (e) αi = 1.0αm with prestress; (f) αi = 10αm with prestress.
Figure 18.
Radial stress distribution patterns. (a) αi = 0.1αm without prestress; (b) αi = 1.0αm without prestress; (c) αi = 10αm without prestress; (d) αi = 0.1αm with prestress; (e) αi = 1.0αm with prestress; (f) αi = 10αm with prestress.
Figure 19.
Radial stress values with different CTEs (a) along path-1 and (b) along path-2.
Figure 19.
Radial stress values with different CTEs (a) along path-1 and (b) along path-2.
Figure 20.
Circumferential stress distribution patterns. (a) αi = 0.1αm without prestress; (b) αi = 1.0αm without prestress; (c) αi = 10αm without prestress; (d) αi = 0.1αm with prestress; (e) αi = 1.0αm with prestress; (f) αi = 10αm with prestress.
Figure 20.
Circumferential stress distribution patterns. (a) αi = 0.1αm without prestress; (b) αi = 1.0αm without prestress; (c) αi = 10αm without prestress; (d) αi = 0.1αm with prestress; (e) αi = 1.0αm with prestress; (f) αi = 10αm with prestress.
Figure 21.
Circumferential stress values with different CTEs (a) along path-1 and (b) along path-2.
Figure 21.
Circumferential stress values with different CTEs (a) along path-1 and (b) along path-2.
Figure 22.
Axial stress distribution patterns. (a) αi = 0.1αm without prestress; (b) αi = 1.0αm without prestress; (c) αi = 10αm without prestress; (d) αi = 0.1αm with prestress; (e) αi = 1.0αm with prestress; (f) αi = 10αm with prestress.
Figure 22.
Axial stress distribution patterns. (a) αi = 0.1αm without prestress; (b) αi = 1.0αm without prestress; (c) αi = 10αm without prestress; (d) αi = 0.1αm with prestress; (e) αi = 1.0αm with prestress; (f) αi = 10αm with prestress.
Figure 23.
Axial stress values with different CTEs (a) along path-1 and (b) along path-2.
Figure 23.
Axial stress values with different CTEs (a) along path-1 and (b) along path-2.
Figure 24.
Radial stress distribution patterns. (a) Ei = 1.9 GPa without prestress; (b) Ei = 5 GPa without prestress; (c) Ei = 50 GPa without prestress; (d) Ei = 1.9 GPa with prestress; (e) Ei = 5 GPa with prestress; (f) Ei = 50 GPa with prestress.
Figure 24.
Radial stress distribution patterns. (a) Ei = 1.9 GPa without prestress; (b) Ei = 5 GPa without prestress; (c) Ei = 50 GPa without prestress; (d) Ei = 1.9 GPa with prestress; (e) Ei = 5 GPa with prestress; (f) Ei = 50 GPa with prestress.
Figure 25.
Radial stress values with different elastic modulus values (a) along path-1 and (b) along path-2.
Figure 25.
Radial stress values with different elastic modulus values (a) along path-1 and (b) along path-2.
Figure 26.
Circumferential stress distribution patterns. (a) Ei = 1.9 GPa without prestress; (b) Ei = 5 GPa without prestress; (c) Ei = 50 GPa without prestress; (d) Ei = 1.9 GPa with prestress; (e) Ei = 5 GPa with prestress; (f) Ei = 50 GPa with prestress.
Figure 26.
Circumferential stress distribution patterns. (a) Ei = 1.9 GPa without prestress; (b) Ei = 5 GPa without prestress; (c) Ei = 50 GPa without prestress; (d) Ei = 1.9 GPa with prestress; (e) Ei = 5 GPa with prestress; (f) Ei = 50 GPa with prestress.
Figure 27.
Circumferential stress values with different elastic modulus values (a) along path-1 and (b) along path-2.
Figure 27.
Circumferential stress values with different elastic modulus values (a) along path-1 and (b) along path-2.
Figure 28.
Axial stress distribution patterns. (a) Ei =1.9 GPa without prestress; (b) Ei =5 GPa without prestress; (c) Ei =50 GPa without prestress; (d) Ei = 1.9 GPa with prestress; (e) Ei = 5 GPa with prestress; (f) Ei = 50 GPa with prestress.
Figure 28.
Axial stress distribution patterns. (a) Ei =1.9 GPa without prestress; (b) Ei =5 GPa without prestress; (c) Ei =50 GPa without prestress; (d) Ei = 1.9 GPa with prestress; (e) Ei = 5 GPa with prestress; (f) Ei = 50 GPa with prestress.
Figure 29.
Axial stress values with different elastic modulus values (a) along path-1 and (b) along path-2.
Figure 29.
Axial stress values with different elastic modulus values (a) along path-1 and (b) along path-2.
Figure 30.
Radial stress distribution patterns of the model with heterogeneous elastic modulus (a) before applying prestress and (b) after applying prestress.
Figure 30.
Radial stress distribution patterns of the model with heterogeneous elastic modulus (a) before applying prestress and (b) after applying prestress.
Figure 31.
Circumferential stress distribution patterns of the model with heterogeneous elastic modulus (a) before applying prestress and (b) after applying prestress.
Figure 31.
Circumferential stress distribution patterns of the model with heterogeneous elastic modulus (a) before applying prestress and (b) after applying prestress.
Figure 32.
Axial stress distribution patterns of the model with heterogeneous elastic modulus (a) before applying prestress and (b) after applying prestress.
Figure 32.
Axial stress distribution patterns of the model with heterogeneous elastic modulus (a) before applying prestress and (b) after applying prestress.
Figure 33.
Stress values along path-1 with elastic modulus distribution case one. (a) Radial stress values; (b) circumferential stress values; (c) axial stress values.
Figure 33.
Stress values along path-1 with elastic modulus distribution case one. (a) Radial stress values; (b) circumferential stress values; (c) axial stress values.
Figure 34.
Stress values of the models with heterogeneous elastic modulus along path-1. (a) Radial stress values; (b) circumferential stress values; (c) axial stress values.
Figure 34.
Stress values of the models with heterogeneous elastic modulus along path-1. (a) Radial stress values; (b) circumferential stress values; (c) axial stress values.
Table 1.
Elastic parameters for the fiber and matrix [
19].
Table 1.
Elastic parameters for the fiber and matrix [
19].
Glass Fiber | Matrix |
---|
Modulus, Ef (GPa) | 74 | Modulus, Em (GPa) | 3.35 |
Poisson’s ratio, vf | 0.2 | Poisson’s ratio, vm | 0.35 |
Coefficient of Thermal Expansion, CTEf (/°C) | 4.9 × 10−6 | Coefficient of Thermal Expansion, CTEm (/°C) | 58 × 10−6 |
Table 2.
Axial stress values predicted with only prestress application considered.
Table 2.
Axial stress values predicted with only prestress application considered.
Constituents | Analytical Method [27] | Multi-Step Method | Modified Equivalent Thermal Method |
---|
Fiber (MPa) | 3.8 | 3.930 | 3.935 |
Matrix (MPa) | −2.5 | −2.641 | −2.645 |
Table 3.
Axial stress values predicted with both polymer curing and prestress application considered.
Table 3.
Axial stress values predicted with both polymer curing and prestress application considered.
Constituents | Analytical Method [11] | Numerical Method Developed in This Study |
---|
Fiber (MPa) | 3.2 | 3.17 |
Matrix (MPa) | −2.14 | −2.11 |
Table 4.
Axial stress values predicted with interphase considered.
Table 4.
Axial stress values predicted with interphase considered.
Constituents | Fiber (MPa) | Matrix (MPa) | Interphase (MPa) |
---|
Modified analytical method | 3.03 | −2.14 | −1.22 |
Numerical method | 3.06 | −2.12 | −1.24 |
Table 5.
Max and min stress values in the interphase with different interphase CTE.
Table 5.
Max and min stress values in the interphase with different interphase CTE.
Interphase CTE | αi = 0.1αm | αi = αm | αi = 10αm |
---|
Prestress Application | Before | After | Before | After | Before | After |
---|
Max radial stress | −0.06651 | −0.01377 | −0.05936 | −0.01935 | 0.06374 | 0.2751 |
Max circumferential stress | −0.06842 | −0.3614 | 0.3167 | 0.02148 | 4.194 | 3.988 |
Min circumferential stress | −0.2169 | −0.4227 | 0.1841 | −0.02173 | 3.931 | 3.684 |
Max axial stress | −0.07208 | −1.607 | 0.3138 | −1.221 | 4.202 | 2.764 |
Min axial stress | −0.2339 | −1.672 | 0.1693 | −1.268 | 4.173 | 2.638 |
Table 6.
Max and min stress values in the interphase with different interphase elastic modulus.
Table 6.
Max and min stress values in the interphase with different interphase elastic modulus.
| Ei = 1.9 GPa | Ei = 5 GPa | Ei = 50 GPa |
---|
MPa | Before | After | Before | After | Before | After |
---|
Max radial stress | −0.05936 | −0.01935 | −0.05274 | −0.01739 | −0.04885 | −0.01848 |
Max Circumferential stress | 0.3167 | 0.02148 | 0.919 | 0.08883 | 9.374 | 1.549 |
Min Circumferential stress | 0.1841 | −0.02173 | 0.7943 | 0.04928 | 8.693 | 1.409 |
Max axial stress | 0.3138 | −1.221 | 0.9051 | −3.168 | 8.808 | −29.06 |
Min axial stress | 0.1693 | −1.268 | 0.7602 | −3.216 | 8.745 | −29.09 |
Table 7.
Average stress values in interphases for the models with heterogeneous elastic modulus.
Table 7.
Average stress values in interphases for the models with heterogeneous elastic modulus.
Direction | Circumferential Stress | Axial Stress |
---|
Prestress Application | Before | After | Before | After |
---|
Heterogenous elastic modulus (MPa) | 4.391225 | 0.566071 | 4.233318 | −14.2137 |
Uniform elastic modulus (MPa) | 4.268806 | 0.556931 | 4.157911 | −14.2131 |