# Comparison of Material Properties of Multilayered Laminates Determined by Testing and Micromechanics

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experiments

#### 2.1. Materials

^{2}(X-E-610-1270) were applied instead of 1200 g/m

^{2}(X-E-1210-1270).

#### 2.2. Methods

#### 2.3. Results and Discussion

_{1,c}/f

_{2,c}= 1.93) is lower because the compressive strength is not only dependent on the pure fiber volume fraction, but also on the parameters of the resin. The addition of fibers oriented in the ± 45 direction significantly increased the material strength in the shear mode. As compared to the bidirectional 0/90 laminate, this was an increase of 58% for shear strength and 33% for shear modulus. Due to the mixed fiber orientation, the failure mode of specimens was more complex as compared with the failure mode of laminas in previous stages of research.

## 3. Micromechanics Calculation

#### 3.1. Basic Assumptions

_{t}), compressive (f

_{c}) and shear strength (f

_{v}). In the case of heterogeneous laminates consisting of a series of laminas with different fiber orientations, the experimental determination of these parameters is a costly and time-consuming process. Alternatively, it is possible to conduct analytical calculations based on the properties of two basic laminate components: fibers and resin. In Table 6 the engineering constants and strength parameters for all types of fibers and epoxy resins are presented as given in the internal draft version of the new Eurocode on the design of fiber-reinforced polymer structures [29]. The values included in Table 6 are based on the material properties reported in the literature, and are not necessarily concomitant. Additionally, for the fibers, the reduction in tensile strength due to microdamage during the production of fibers was taken into account, following Ref. [36] (50% reduction for glass fibers, 31% for aramid and 20% for carbon) and Ref. [37] (41% reduction for basalt fibers). The reduced strength was named as the effective tensile strength, f

_{f,t}. The pure compressive strength of fibers is not decisive, as it is very unlikely that the failure of entire laminates is caused by the failure of compressed fibers alone. The loss of stability or shear failure in or out of the plane of the laminate occurs much more often. For this reason, the draft in Ref. [29] does not provide these values. The same explanation applies to the shear strength of the fibers, as the shear strength of the laminate is generally determined by the shear of the matrix, not the fibers.

_{f}) based on the Formula (1):

- ω
_{f}—the weight per unit area of all the fabric in the laminate; - ρ
_{f}—density of the fiber material;t—thickness of the laminate.

_{f}) values obtained for all specimens are presented in Table 7.

#### 3.2. Engineering Constants

_{1}, E

_{2}, ν

_{12}, G

_{12}), three models were applied: the linear model (otherwise known as rule of mixtures and inverse rule of mixtures), a combined model called the improved linear model (otherwise known as improved rule of mixtures) and the periodic microstructure model. The formulas used to determine the engineering constants according to three previously mentioned micromechanical models are given in Appendix A and the results are summarized in Table 8.

#### 3.3. Strength Parameters

## 4. Comparison between Experiment and Micromechanics

- The E
_{1}and E_{2}values for glass laminates (U-E, B-E, X-E and X-S-E) based on two analytical micromechanical models are in very good compliance with average test results (97–115% for ML, 104–117% for IL). The only exception was E_{2}for face laminate, which is 144% of the IL-calculated value. Besides this, 50% of the calculated values lay in the standard deviation range of test results; - The periodic microstructure approach gave higher values of 114–132% for all specimens except E
_{2}for U-E (175%). The calculation of face laminates showed wider scatter for both moduli E_{1}(75% for ML and IL, 81% for PM) and E_{2}(89%, 103% and 118% respectively). All calculated results lay outside of the range of the results’ standard deviation; - Comparisons of E
_{1}and E_{2}values for other types of fibers (B-A, B-B and B-C) were quite similar, with compliance in the range of 107–119% for analytical models LM and IL. Only one of the three results was in the range of the results’ standard deviation. The PM model was inappropriate for anisotropic fibers (B-A and B-C) because of its 44% and 29% compliance with test results for aramid and carbon fibers, respectively. For basalt fibers the compliance was satisfactory, i.e., 91%; - G
_{12}values for all laminates based on LM were only a little overestimated (115% on average). Two further models (IL and PM) overestimated G_{12}for all laminates much more, on average 167% for IML (111–201%) and 157% for PM (111–180%). Only 8% of the results lay in the standard deviation range of the test results (88% of the calculated results were overestimated); - The shear modulus values obtained in the tests were lower than those calculated on both micromechanical models: IL and PM. This could be the result of the adopted test method for the shear test. It is widely believed that the values obtained from tests following the procedures of the PN-EN ISO 14129 standard [34] are minimal. Other types of shear testing are not as popular and standardized because they require specialized overlays and equipment, as well as specific specimen forms. However, recent documents [38] and as-yet unpublished drafts of new Eurocode [29] indicate other methods as more realistic;
- The calculated values of Poisson’s ratio ν
_{12}were the most underestimated values among the engineering constants. Only PM values gave satisfactory result with an average of 96% compliance (in the range of 56–129%). The LM showed lower consistency with 52% compliance on average (in the range of 12–95%) and IL with 72% compliance on average (in the range of 24–114%). About 48% of the calculated values were in the standard deviation ranges of the test results, and 48% of the calculated results were underestimated.

- The average compliance for all 12 tensile strength values f
_{t}is 95%, but single values varied from 57% to 148%. The tensile strength for carbon fibers is the most overestimated (148%), and it may prove that the actual strength of carbon fibers is lower than assumed (Table 7) and that reduction is higher than the adopted 20%. In turn, the most underestimated of the calculations is the tensile strength of the X-S-E laminate, which may indicate a higher strength of the CSM layer than that which resulted from the adopted micromechanical model for the CSM layer. The tensile strength for the rest of the specimens did not differ significantly from the experimental results (about ±10%); - The compressive strength showed noticeably lower compliance. The average compliance for the 12 test values was 165% (Figure 14). The greatest overestimation by calculations occurred for aramid and basalt fibers (about 300% and 175%, respectively). The reasons can come both from the adopted material constants as well as from the adopted micromechanical models for these types of fibers. A similarly high overestimation of the compressive strength occurred for the face laminate. This is related to the fact that in-plane shear also contributes to the failure of the multilayer, thick, compressed laminate, which it was not possible to capture in the adopted micromechanical models. After omitting these two groups, the results for the remaining glass and carbon laminates showed a low average discrepancy of approximately 10%. For the U-E laminate the calculated compressive strength in both directions was lower than the results of the experiment;
- The shear strength values showed high compliance between calculation and experiment, with the average value for all specimens being as much as 90% for both micromechanical models. Significant discrepancies can be observed in the case of the X-S-E laminates with CSM layers, whose share in the shear strength was underestimated in both micromodels. A similar underestimation applies to the face laminate, and is related to the mismatch of micromechanical models (which are formulated generally to the individual, often unidirectionally reinforced lamina) to the analysis of multilayer laminates. Besides this, micromechanical models are based on the assumption that the material works linearly, while specimens subjected to shear showed a strong non-linearity. For X-S-E and face laminates, the τ-ε plots do not show initial linearity with a fracture point, as in the case of other types of fibers (Figure 5 and Figure 7). This proves the different nature of the behavior of this type of laminate, and therefore the need for a different calculation approach than with the others fibers is revealed.

## 5. Conclusions

_{1}) as compared to the respective values of the remaining composites. Aramid fiber composites showed a slightly lower shear modulus. Taking into account the obtained comparison as well as technological and economic factors, it was decided to conduct further research on glass fiber composites only, as the most promising material for the mass production of load-bearing deck panels.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Engineering Constants

_{ij}are elements of the stiffness tensor for lamina.

- E
_{1}, E_{2}—the elastic modulus of the virtually unidirectional layer with the same V_{f}as the real CSM layer, determined from, for example, the Formulas (A1) and (A2) or another micromechanical model.

## Appendix B. Strength Parameters

#### Appendix B.1. Longitudinal Tensile Strength

_{t}is calculated from Formula (A16):

- f
_{f,t}—tensile strength of fibers.

_{r}to E

_{f}) ranges from 1 to 4% (Table 7, depending on the type of fibers), the above equation can be simplified. Additionally, Formula (A16) can be expanded to multilayer laminates, if only fibers oriented in the direction of the tensile forces are considered. After these operations, the formula for strength in the i-direction will take the form (A17):

- ρ
_{f,i}—the weight of fibers in the i-direction, - ρ
_{f}—total weight of fibers.

#### Appendix B.2. Longitudinal Compressive Strength

_{f,c}instead of the tensile strength f

_{f,t}. However, this is not a real value, as most compressed laminates are failed by shearing or a fiber buckling. In addition, the perfect parallel alignment of the fibers is not possible in reality. The analytical solution, so-called the improved fiber buckling method [42], determines compressive strength f

_{1,c}by the Formula (A18):

- G
_{12}—shear modulus of laminate, - α
_{σ}—standard deviation of fiber misalignment, - f
_{12}—shear strength of the laminate.

#### Appendix B.3. Transverse Tensile Strength

_{2,t}can be estimated from the Formulas (A19) and (A20):

- G
_{Ic}—fracture toughness in crack opening mode I based on fracture mechanics, - t
_{t}—transition thickness.

#### Appendix B.4. Transverse Compressive Strength

_{2,c}could be obtained from an analytical method based on the strain-magnification factor [43] and calculated from Formula (A21):

- ε
_{rc}—maximum shortening of a resin in compression, - E
_{f,2}—fiber’s elastic modulus in the transversal direction.

_{2,c}is empirical Formula (A22) [36,44]:

- σ
_{r,c}—compressive strength of the resin, - V
_{v}—void volume fraction.

#### Appendix B.5. In-Plane Shear Strength

_{12}of the unidirectional lamina (A23):

- G
_{IIc}—fracture toughness in crack opening mode II based on fracture mechanics.

- τ
_{r}—shear strength of resin.

#### Appendix B.6. CSM Layer

_{t,csm}can be determined from the Formulas (A25) and (A26) [36,45]:

_{1,t}, f′

_{2,t}and f′

_{12,v}—strength of a virtually unidirectional lamina with the same fiber volume fraction V

_{f}as the CSM layer.

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**Figure 1.**Geometry of typical tensile specimens (dimensions in mm); (

**a**) rectangular specimen according to the ISO 527-4 standard; (

**b**) dumbbell-shaped specimen according to the ASTM D638 standard.

**Figure 2.**Geometry of typical compression specimens (dimensions in mm); (

**a**) for the first and second stages of research, and (

**b**) for face laminate.

**Figure 3.**Representative curves for composite specimens with four types of reinforcement for tensile tests σ-ε (

**left**) and the shear by tensile test τ-ε (

**right**).

**Figure 4.**Typical failure modes of four types of reinforcement (from the top): B-A-470-1000 (aramid), B-B-345-1000 (basalt), B-C-600-1270 (carbon), and B-E-641-1300 (glass) for (

**a**) tensile, (

**b**) shear, and (

**c**) compression.

**Figure 5.**Representative curves for composite specimens with different glass fiber composites for tensile tests σ-ε (

**left**) and shear by tensile test τ-ε (

**right**).

**Figure 6.**Typical tensile failure modes of glass composite specimens (from the top): X-S-E-1109-1270, X-E-1210-1270, U-E-600-1200, and B-E-641-1300 for (

**a**) tensile, (

**b**) shear, and (

**c**) compression.

**Figure 7.**Representative curves for face laminate specimens at tension σ-ε (

**left**) perpendicularly (1 direction) and transversally to main reinforcement (two directions) and shear by tensile test τ-ε (

**right**).

**Figure 8.**Examples of failure modes of GFRP face specimens in tension (

**a**) perpendicularly and (

**b**) transversally to the main reinforcement; (

**c**) in shear (invisible to the naked eye) and compression (

**d**) perpendicularly and (

**e**) transversally to the main reinforcement.

**Figure 9.**Designations and orientations of the coordinate system for layers: unidirectional reinforced (

**a**), bidirectional reinforced (

**b**) and face laminate (

**c**).

**Figure 13.**Comparison of tensile strength f

_{1,t}and f

_{2,t}obtained by calculation and experiment.

**Figure 14.**Comparison of compression strength f

_{1,c}and f

_{2,c}obtained by calculation and experiment.

Stage | Fabric Type | Material | Fiber Direction | Unit Weight | Lamina Thickness |
---|---|---|---|---|---|

(g/m^{2}) | (mm) | ||||

1 | B-A-470-1000 (aramid) | Aramid 316 tex | 0/90 | 470 ± 5% | 2.46 ± 0.10 |

B-B-345-1000 (basalt) | Basalt 16/9 F/cm | 0/90 | 345 ± 25 | 2.01 ± 0.03 | |

B-C-600-1270 (carbon) | Carbon 800 tex | 0/90 | 600 ± 5% | 1.64 ± 0.06 | |

B-E-641-1300 (glass) | E-Glass 1200 tex E-Glass 600 tex | 0/90 | 641 ± 5% | 2.55 ± 0.04 | |

2 | X-S-E-1109-1270 (glass) | E-Glass 600 tex E-Glass 68 tex | ±45 | 1109 ± 5% | 2.53 ± 0.04 |

X-E-1210-1270 (glass) | E-Glass 1200 tex | ±45 | 1210 ± 5% | 2.52 ± 0.03 | |

U-E-600-1200 (glass) | E-Glass 1200 tex E-Glass 68 tex | 0 | 600 ± 5% | 2.32 ± 0.02 |

Layer | Fabric Type | Fiber Direction | Fabric Thickness | Unit Weight | No. Fabrics | Layer Thickness | Unit Weight |
---|---|---|---|---|---|---|---|

(mm) | (g/m^{2}) | (mm) | (g/m^{2}) | ||||

1 | B-E-641-1300 | 0/90 | 0.45 | 641 | 6 | 2.70 | 3846 |

2 | X-E-610-1270 | ±45 | 0.43 | 610 | 1 | 0.43 | 610 |

3 | U-E-600-1200 | 0 | 0.42 | 600 | 5 | 2.10 | 3000 |

4 | X-E-610-1270 | ±45 | 0.43 | 610 | 1 | 0.43 | 610 |

5 | U-E-600-1200 | 0 | 0.42 | 600 | 5 | 2.10 | 3000 |

6 | X-E-610-1270 | ±45 | 0.43 | 610 | 1 | 0.43 | 610 |

7 | U-E-600-1200 | 0 | 0.42 | 600 | 5 | 2.10 | 3000 |

8 | X-E-610-1270 | ±45 | 0.43 | 610 | 1 | 0.43 | 610 |

9 | B-E-641-1300 | 0/90 | 0.45 | 641 | 6 | 2.70 | 3846 |

In total | 13.42 | 19,132 |

Laminate | Tensile | Shear | Compressive | ||||
---|---|---|---|---|---|---|---|

Strength f _{1,t} | Ult. Stain ε _{1,u} | Elastic Modulus E _{1,t} | Poisson’s Ratio ν _{12} | Strength f _{12,v} | Modulus G _{12} | Strength f _{1,c} | |

(MPa) | (%) | (GPa) | (-) | (MPa) | (GPa) | (MPa) | |

B-A-470-1000 (aramid) | 458.80 ± 37.85 | 2.33 ± 0.17 | 26.80 ± 4.07 | 0.29 ± 0.06 | 33.93 ± 1.78 | 1.65 ± 0.24 | 93.79 ± 13.10 |

B-B-345-1000 (basalt) | 399.13 ± 31.61 | 2.10 ± 0.21 | 23.72 ± 1.09 | 0.14 ± 0.04 | 40.49 ± 4.95 | 2.72 ± 0.17 | 217.24 ± 29.32 |

B-C-600-1270 (carbon) | 806.68 ± 62.01 | 1.65 ± 0.14 | 66.31 ± 4.31 | 0.17 ± 0.00 | 44.53 ± 1.09 | 3.17 ± 0.39 | 323.90 ± 43.39 |

B-E-641-1300 (glass) | 454.39 ± 23.11 | 2.29 ± 0.11 | 24.65 ± 3.03 | 0.15 ± 0.03 | 42.19 ± 4.63 | 2.83 ± 0.18 | 290.09 ± 36.88 |

Laminate/ Direction | Tensile | Shear | Compressive | |||||
---|---|---|---|---|---|---|---|---|

Strength f _{i,t} | Ult. Stain ε _{i,u} | Modulus E _{i,t} | Poisson’s Ratio ν _{12} | Strength f _{12,v} | Modulus G _{12} | Strength f _{i,c} | ||

(MPa) | (%) | (GPa) | (-) | (MPa) | (GPa) | (MPa) | ||

X-S-E-1109-1270 | 1, 2 | 408.55 ± 14.15 | 2.22 ± 0.08 | 22.97 ± 2.15 | 0.22 ± 0.06 | 75.62 ± 2.12 | 3.87 ± 0.27 | 305.48 ± 28.75 |

X-E-1210-1270 | 1, 2 | 477.39 ± 19.77 | 2.28 ± 0.12 | 24.25 ± 2.27 | 0.25 ± 0.03 | 30.82 ± 1.23 | 2.75 ± 0.16 | 346.48 ± 26.64 |

U-E-600-1200 | 1 | 765.92 ± 40.39 | 2.30 ± 0.13 | 35.48 ± 3.45 | 0.24 ± 0.02 | 34.24 ± 1.12 | 3.14 ± 0.12 | 482.89 ± 75.55 |

2 | 58.29 ± 4.77 | 1.15 ± 0.23 | 10.46 ± 0.90 | 0.22 ± 0.05 | 114.16 ± 14.72 | |||

B-E-641-1300 | 1 | 454.39 ± 23.11 | 2.29 ± 0.11 | 24.65 ± 3.03 | 0.15 ± 0.03 | 42.19 ± 4.63 | 2.83 ± 0.18 | 290.09 ± 36.88 |

2 | 325.95 ± 19.71 | 1.98 ± 0.10 | 21.44 ± 1.26 | 0.15 ± 0.06 | 283.02 ± 34.86 |

Laminate/ Direction | Tensile | Shear | Compressive | ||||
---|---|---|---|---|---|---|---|

Strength f _{i,t} | Ult. Stain ε _{i,u} | Modulus E _{i,t} | Strength f _{12,v} | Modulus G _{12} | Strength f _{i,c} | ||

(MPa) | (%) | (GPa) | (MPa) | (GPa) | (MPa) | ||

GFRP laminate | 1 | 434.08 ± 14.20 | 1.71 ± 0.13 | 30.67 ± 0.71 | 66.80 ± 6.32 | 3.75 ± 0.19 | 187.70 ± 14.50 |

2 | 177.47 ± 5.08 | 1.83 ± 0.15 | 13.26 ± 0.44 | 96.91 ± 11.01 |

**Table 6.**The material constants and strength parameters for all types of fibers and epoxy resin [29].

Component | Material Constants | Strength Parameters | |||||
---|---|---|---|---|---|---|---|

Elastic Modulus | In-Plane Shear Modulus | Poisson’s Ratio | Nominal Tensile Strength | Effective Tensile Strength | Compressive Strength | ||

E_{1} | E_{2} | G_{12} | ν_{12} | f_{t,brutto} | f_{t} | f_{c} | |

(GPa) | (GPa) | (GPa) | (-) | (MPa) | (MPa) | (MPa) | |

Glass fibers | 74 | 74 | 30 | 0.25 | 2500 | 1250 | - |

Aramid fibers | 130 | 10 | 12 | 0.35 | 3600 | 2484 | - |

Basalt fibers | 90 | 90 | 22 | 0.31 | 3000 | 1773 | - |

Carbon fibers | 230 | 20 | 16 | 0.20 | 4900 | 3920 | - |

Epoxy resin | 3.0 | 3.0 | 1.6 | 0.40 | 35 | 35 | 80 |

Series Identifier (Fiber’s Material) | ||||||||
---|---|---|---|---|---|---|---|---|

B-A-470-1000 | B-B-345-1000 | B-C-600-1270 | B-E-641-1300 | X-S-E-1109-1270 | X-E-1210-1270 | U-E-600-1200 | Face Laminate | |

Aramid | Basalt | Carbon | Glass | Glass | Glass | Glass | Glass | |

V_{f} | 39 | 50 | 61 | 58 | 56 ^{1}/43 ^{2} | 56 | 60 | 41 |

^{1}—laminate with continuous fibers,

^{2}—laminate with chopped fibers (chopped strand mat, CSM).

Laminate | Longitudinal Elastic Modulus | Transverse Elastic Modulus | In-Plane Shear Modulus | Poisson’s Ratio | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

E_{1} (GPa) | E_{2} (GPa) | G_{12} (GPa) | ν_{12} (-) | |||||||||

LM ^{1} | IL ^{2} | PM ^{3} | LM ^{1} | IL ^{2} | PM ^{3} | LM ^{1} | IL ^{2} | PM ^{3} | LM ^{1} | IL ^{2} | PM ^{3} | |

B-A-470-1000 (aramid) | 28.57 | 28.67 | 11.91 | 28.57 | 28.67 | 11.91 | 2.42 | 3.31 | 2.97 | 0.06 | 0.07 | 0.25 |

B-B-345-1000 (basalt) | 26.42 | 28.10 | 21.59 | 26.42 | 28.10 | 21.59 | 2.98 | 4.37 | 4.05 | 0.08 | 0.13 | 0.18 |

B-C-600-1270 (carbon) | 74.08 | 75.40 | 19.17 | 74.08 | 75.40 | 19.17 | 3.55 | 5.69 | 4.82 | 0.02 | 0.04 | 0.16 |

B-E-641-1300 (glass) | 27.07 | 28.95 | 31.29 | 23.36 | 25.83 | 28.34 | 3.49 | 5.27 | 5.03 | 0.09 | 0.14 | 0.15 |

X-S-E-1109-1270 (glass) | 22.20 | 23.87 | 26.24 | 22.20 | 23.87 | 26.24 | 4.08 | 5.42 | 5.56 | 0.19 | 0.22 | 0.22 |

X-E-1210-1270 (glass) | 24.65 | 26.68 | 29.08 | 24.65 | 26.68 | 29.08 | 3.38 | 5.07 | 4.84 | 0.08 | 0.14 | 0.14 |

U-E-600-1200 (glass) | 40.94 | 40.76 | 42.44 | 10.37 | 15.11 | 18.31 | 3.59 | 5.48 | 5.23 | 0.21 | 0.25 | 0.24 |

Face laminate (glass) | 22.87 | 23.06 | 24.96 | 11.74 | 13.60 | 15.64 | 3.30 | 4.18 | 4.17 | 0.20 | 0.24 | 0.24 |

^{1}—Linear Model,

^{2}—Improved Linear Model,

^{3}—Periodic Microstructure Model.

**Table 9.**Strength parameters for all specimens calculated according to different micromechanical theories.

Laminate | Longitudinal Direction | Transverse Direction | In-Plane | ||||||
---|---|---|---|---|---|---|---|---|---|

Tensile | Comp. | Tensile | Compressive | Shear | |||||

f_{1,t} (MPa) | f_{1,c} (MPa) | f_{2,t} (MPa) | f_{2,c} (MPa) | f_{12,v} (MPa) | |||||

LM ^{1} | IFB ^{2} | LM ^{1} | FM ^{3} | IFB ^{2} | SA ^{4} | EF ^{5} | FM ^{6} | EF ^{7} | |

B-A-470-1000 (aramid) | 484 | 289 | 484 | - | 289 | - | - | 29.1 | 38.1 |

B-B-345-1000 (basalt) | 443 | 366 | 443 | - | 366 | - | - | 37.3 | 37.6 |

B-C-600-1270 (carbon) | 1196 | 374 | 1196 | - | 374 | - | - | 35.3 | 37.9 |

B-E-641-1300 (glass) | 391 | 407 | 320 | - | 407 | - | - | 40.4 | 37.5 |

X-S-E-1109-1270 (glass) | 234 | 451 | 234 | - | 451 | - | - | 43.6 | 41.5 |

X-E-1210-1270 (glass) | 348 | 398 | 348 | - | 398 | - | - | 39.7 | 37.5 |

U-E-600-1200 (glass) | 671 | 414 | 69.0 | 56.2 | - | 44.6 | 49.8 | 40.9 | 37.5 |

Face laminate (glass) | 323 | 392 | 113 | - | 392 | - | - | 39.3 | 37.2 |

^{1}—Linear model,

^{2}—Improved fiber buckling method, α

_{σ}assumed to be 3 deg,

^{3}—Fracture mechanics, adopted values according to Ref. [36]: G

_{Ic}= 360 J/m

^{2}; t

_{t}= 0.6 (glass and basalt) or 0.8 mm (carbon and aramid); material constants from Table 8 (LM),

^{4}—Strain amplification method,

^{5}—Empirical formulas, adopted values: V

_{u}= 0.02, σ

_{r,c}= 80 MPa from Table 6,

^{6}—Fracture mechanics, adopted values according to Ref. [36]: G

_{2c}= 220 J/m

^{2}; t

_{t}= 0.6 (glass and basalt) or 0.8 mm (carbon and aramid); G

_{12}from Table 8 (LM),

^{7}—Empirical formulas, V

_{u}assumed to be 2%; τ

_{r}was calculated on test results and was adopted as 60.1 MPa.

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**MDPI and ACS Style**

Kulpa, M.; Wiater, A.; Rajchel, M.; Siwowski, T.
Comparison of Material Properties of Multilayered Laminates Determined by Testing and Micromechanics. *Materials* **2021**, *14*, 761.
https://doi.org/10.3390/ma14040761

**AMA Style**

Kulpa M, Wiater A, Rajchel M, Siwowski T.
Comparison of Material Properties of Multilayered Laminates Determined by Testing and Micromechanics. *Materials*. 2021; 14(4):761.
https://doi.org/10.3390/ma14040761

**Chicago/Turabian Style**

Kulpa, Maciej, Agnieszka Wiater, Mateusz Rajchel, and Tomasz Siwowski.
2021. "Comparison of Material Properties of Multilayered Laminates Determined by Testing and Micromechanics" *Materials* 14, no. 4: 761.
https://doi.org/10.3390/ma14040761