# Progressive Failure Analysis of Thin-Walled Composite Structures Verified Experimentally

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## Abstract

**:**

_{s}. The composite structure was subjected to the process of axial compression. Experimental and numerical tests for the loss of stability and load-carrying capacity of the composite construction were carried out. The numerical buckling analysis was carried out based on the minimum potential energy criterion (based on the solution of an eigenvalue problem). The study of loss of load-carrying capacity was performed on the basis of a progressive failure analysis, solving the problem of non-linear stability based on Newton-Raphson’s incremental iterative method. Numerical results of critical and post-critical state were confronted with experimental research in order to estimate the vulnerable areas of the structure, showing areas prone to damage of the material.

## 1. Introduction

## 2. The Object of Study

## 3. Research Methodology

^{®}software (Abaqus 2019, Dassault Systemes Simulia Corporation, Velizy Villacoublay, France) based on the FEM. The work used a linear-elastic model, taking into account the orthotropic description of the material model. The discrete model is based on the use of shell elements (S8R) with six degrees of freedom at each of the eight nodes per finite element with reduced integration. The reduced integration technique makes it possible to remove false (erroneous) forms of deformation in finite elements [31]. In the case of non-deformable panels, linear shell elements R3D4 were used. In the process of discrete use, uniform thickening of the finite element grid was ensured by using the structural type of finite elements. The discrete numerical model consisted of 11,620 finite elements and 20,187 computational nodes.

#### 3.1. Damage Initiation

_{f}, d

_{m}and d

_{s}are the specific damage variables for fiber, matrix and shear failure modes, respectively.

^{T}= Y

^{C}/2 (where S

^{T}is transverse shear strength and Y

^{C}is transverse compressive strength). The essence of the presented procedure enables an independent assessment of the damage initiation of fibers and matrix of the composite material.

#### 3.2. Damage Evolution

_{ij}are stresses; τ

_{ij}are shear stresses; ε

_{ij}are strains; γ

_{ij}are shear strains; and parameter D is expressed as:

_{f}, d

_{m}and d

_{s}are the damage variables for fiber, matrix and shear failure modes, respectively.

^{®}is initially based on the damage initiation associated with fulfilment the Hashin’s criterion. The main principle of damage evolution assumes that the dissipation energy in the damage process is proportional to the volume of the damaged finite elements of numerical model. In FEM calculations, the damage evolution is strictly controlled by equivalent displacement; therefore, the calculation process itself is based on the constitutive compound “equivalent stress-equivalent displacement” [36]. As mentioned earlier, the progressive damage analysis includes five components, which in the context of numerical analysis are called tensile fiber damage—DAMAGEFT; compressive fiber damage—DAMAGEFC; tensile matrix damage—DAMAGEMT; compressive matrix damage—DAMAGEMC; and shear damage—DAMAGESHR. The algorithm of the progressive criterion is shown in Figure 6.

## 4. Results

_{cr}= 6903.4 N. The buckling mode obtained from experimental and numerical studies is presented in Figure 8.

^{2}≥ 0.95. Figure 9 shows the determined critical load values as the last components of the approximation functions from three tests.

_{ini}

_{(FEM)}= 4852 N. The value of the failure initiation load, which was determined experimentally based on the acoustic emission method, was P

_{ini}

_{(EXP)}= 5334 N. The discrepancy of presented results was only 9%. Additionally, a map of failure initiation due to tension of the matrix, and the results of experimental study, are presented in Figure 10.

_{f-FEM}= 19,723 N. For experimental tests, the load causing a sudden loss of stiffness was P

_{f-EXP}= 18,697 N. The discrepancy between the results of the limit loads was only 5.2%. After achieving one of the four parameters of the Hashin’s criterion, the stiffness of this parameter is gradually degraded according to the scheme shown in Figure 2. Further loads on the structure cause the damage parameter 1 to be achieved by successive parameters of the Hashin’s criterion, which also activates a gradual process of stiffness degradation of these parameters. As a consequence, there is a gradual loss of stiffness of the composite material until the moment of total loss of stiffness of the material. This is a long-term process carried out in numerical calculations using the incremental-iteration method until the moment of losing the ability to carry the load through the compressed structure. In the experimental studies (AEM), a sudden increase in the counts parameter (equal 350) was observed after 120 s of real time, which corresponded to the maximum load (loss of load-carrying capacity) recorded experimentally on a Universal Testing Machine—Figure 11b. An increase in counts may indicate progressive damage (complex state of damage) of the composite structure. The characteristics showing loss of load-carrying capacity in experimental (strain measurement, acoustic emission) and numerical tests are shown in Figure 11.

## 5. Conclusions

^{®}software. The tests were performed on the full range of loads—until the total failure of the composite structure. As part of the numerical simulation, a progressive failure criterion was used for calculations, which allowed for the degradation of material stiffness due to compression. In numerical studies, non-linear stability analysis of the structure until failure was carried out by using progressive failure analysis-energy criterion (PFA) based on Hashin’s damage initiation criterion. The progressive failure model is a specialized model dedicated in numerical calculations for the analysis of the failure processes of composite materials, allowing for a detailed analysis of the damage of each individual component of the composite material, excluding the debonding process. On the basis of the tests conducted, it was stated that:

- It is possible to determine the values of critical load during buckling of the composite columns;
- Achievement of damage initiation (using Hashin’s criterion) in a given area does not mandate further degradation of material stiffness (progressive failure analysis) in the same structural area;
- It is possible to conduct experimental failure tests based on the measurement of strain gauges and acoustic emission parameters, and numerical damage analysis based on the progressive criterion of material damage.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 9.**Experimental post-buckling path and approximation line used for determining critical load by Koiter’s method: (

**a**) first attempt; (

**b**) second attempt; (

**c**) third attempt.

**Figure 10.**The damage initiation: (

**a**) FEM–HSNMTCRT (matrix tension); (

**b**) experimental results (first peak of energy—damage initiation, and second peak of energy—damage evolution).

**Figure 11.**Post-critical equilibrium paths: (

**a**) experimental study—strain measurement (strain gauges); (

**b**) experimental test—acoustic emission (AMSY-5); (

**c**) numerical analysis (FEM).

**Figure 12.**Damage evolution parameters—progressive failure analysis: (

**a**) compressed fiber damage; (

**b**) tensile fiber damage; (

**c**) compressed matrix damage; (

**d**) tensile matrix damage; (

**e**) shear damage.

**Figure 13.**Comparison of the results of failure study: (

**a**) experimental test—front side; (

**b**) numerical analysis—front side; (

**c**) experimental test—back side; (

**d**) numerical analysis—back side.

Mechanical Properties | Strength Properties | ||
---|---|---|---|

Young’s modulus E_{1} [MPa] | 130,710 | Tensile Strength (0°) F_{T1} [MPa] | 1867 |

Young’s modulus E_{2} [MPa] | 6360 | Compressive Strength (0°) F_{C1} [MPa] | 1531 |

Poisson’s ratio [-] | 0.32 | Tensile Strength (90°) F_{T2} [MPa] | 26 |

Kirchhoff modulus G_{12} [MPa] | 4180 | Compressive Strength (90°) F_{C2} [MPa] | 214 |

Shear Strength F_{12} [MPa] | 100 |

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**MDPI and ACS Style**

Rozylo, P.; Ferdynus, M.; Debski, H.; Samborski, S. Progressive Failure Analysis of Thin-Walled Composite Structures Verified Experimentally. *Materials* **2020**, *13*, 1138.
https://doi.org/10.3390/ma13051138

**AMA Style**

Rozylo P, Ferdynus M, Debski H, Samborski S. Progressive Failure Analysis of Thin-Walled Composite Structures Verified Experimentally. *Materials*. 2020; 13(5):1138.
https://doi.org/10.3390/ma13051138

**Chicago/Turabian Style**

Rozylo, Patryk, Miroslaw Ferdynus, Hubert Debski, and Sylwester Samborski. 2020. "Progressive Failure Analysis of Thin-Walled Composite Structures Verified Experimentally" *Materials* 13, no. 5: 1138.
https://doi.org/10.3390/ma13051138