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  • 1.
    Pakkam Gabriel, Vivek Richards
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Analysis of transverse cracking in cross-ply laminates: Weibull distribution based approach2022Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Fiber reinforced polymer composite laminates make up more than 50% of modern aircrafts. Such composite laminates are exposed to various environmental and in-service thermo-mechanical load conditions. Transverse/intralaminar cracking is usually the first form of damage appears in a composite laminate and they tend to increase in number during the service life. The growth in number of these cracks significantly degrades the thermo-elastic properties of the composite laminate and eventually leads to final failure. Thus, it is important to predict the crack density (number of cracks per unit length) growth in both non-interactive crack density region and interactive crack density region and its effect in thermo-elastic properties degradation. Non-interactive crack density region is the region where the cracks are far apart and stress perturbation between cracks do not overlap. Interactive crack density region is where the cracks are close to each other and stress perturbation between cracks overlaps and affects the formation of new cracks. In this study, transverse cracks in thick Glass Fiber Epoxy (GF/EP) cross-ply composite laminates under quasi-static tensile loading and tension-tension fatigue loading have been analyzed and predicted.

    In the first paper attached here, increase in number of transverse cracks in GF/EP cross-ply laminates under quasi-static tensile loading at room temperature (RT) are analyzed using 2 material systems. The failure stress distribution in 90° plies of the laminates is defined by Weibull distribution and the Weibull parameters are determined from crack density versus applied thermo-mechanical transverse stress in 90° layer (σTCLT) data points within the non-interactive crack density region. The crack density growth is then predicted versus the σTCLT and applied mechanical strain in the laminate from the determined Weibull parameters using Monte Carlo method and the stress distribution models between adjacent cracks. The predicted results using the novel stress distribution model introduced here were in good agreement with the non-interactive and interactive crack density regions of test results. The importance of using the Monte Carlo method and novel stress distribution model to predict the whole crack density region have been emphasized in the article, in addition to that it also redefined the interval of non-interactive crack density region. 

    The second paper expands the concept from the first paper, to address the tension-tension fatigue loading at RT. It deals with the crack density analysis and prediction in [0/90]s GF/EP laminate under fatigue loading at RT. The fatigue tests were performed at 3 maximum stress levels. Here the Weibull parameters were determined from the data points within the non-interactive crack density region in quasi-static and fatigue loading. From the determined Weibull parameters of each stress level and using Monte Carlo method and the novel stress distribution model, the crack density versus the number of fatigue cycles were predicted and in good agreement with the fatigue test results at the respective stress level. The intention here was to use Weibull parameters of one stress level to predict crack density at arbitrary stress levels. Based on it, the predicted results were not sufficiently good and suggested to revisit the Weibull parameter determination by performing fatigue tests at two stress levels. 

    In the attached paper 3, new methodology on crack density growth simulation and Weibull parameter determination in tension-tension fatigue loading has been developed. In the newly developed methodology, in detailed fatigue tests are performed at one maximum stress level to obtain all data points and at higher stress level to obtain one data point that is a crack density data point at certain number of cycles to determine Weibull parameters. Using the determined Weibull parameters from non-interactive crack density region, the whole crack density region was successfully predicted for other stress levels.

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  • 2.
    Pakkam Gabriel, Vivek Richards
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Transverse cracking in cross-ply composites during static and fatigue loading at different temperatures2024Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Polymer composite laminates are preferred in many load bearing applications for its tailorable mechanical properties while offering light-weight solution, corrosive resistance etc. Hence, polymer composites are attractive material choice for aircraft manufacturers to reduce weight and emissions. However, one of the challenges existing in composite laminates is accumulation of damage before final failure, that reduces mechanical properties of the composite laminates during service life. Hence it is crucial to develop a reliable model to predict damage and consequently mechanical properties degradation. The thesis focuses on transverse/intralaminar cracks, that are the first form of damage to appear in off-axis layers of composite laminates when subjected to tensile load and they increase in number with increase in load. Transverse crack growth in numbers was analyzed in terms of transverse crack density (= number of cracks / observed length) growth. Appended papers present methodologies developed using statistical transverse failure stress distribution approach to predict the transverse crack density growth when composite laminates subjected to quasi-static tensile and tension-tension fatigue loading at different temperatures. For that purpose, continuous fibers reinforced polymer composite cross-ply laminates containing different material systems were manufactured, and damage growth was studied in 90-layer in coupon scale specimens. In static tests, the crack density growth in specimens were analyzed against the thermo-mechanical transverse stress in the 90-layer. Distribution of transverse failure stress to initiate a crack along the transverse direction of the layer has been defined using 2 parameter Weibull distribution model. Paper 1 presents, methodology to predict crack density growth, using probability of failure stress distribution (based on Weibull model) in Monte Carlo simulation along with the developed stress distribution model between cracks, in specimens tested at room temperature (RT). The crack density was well predicted in both non-interactive and interactive crack density region using improved Weibull parameter determination routine. The presented Weibull model was extended to address the effect of iso-thermal heat treatment and test temperature in Paper 4. It was observed that both heat treatment and elevated test temperatures, in general, resulted in reduction of transverse cracking resistance. The effect of heat treatment and test temperature on transverse cracking was modelled as Weibull scale parameter dependency using polynomial expression. The developed model was validated against laminates with same material system but with different layups and fiber content.Fatigue tests were performed at different maximum stress levels and at RT and 150℃. Crack density growth was analyzed against number of fatigue cycles. The observed decrease in resistance to transverse cracking with every cycle of load was interpreted as monotonic decrease of Weibull scale parameter. Simple power function with respect to number of cycles was proposed to decrease the scale parameter. Paper 2 presents, fatigue test results at RT and methodology to predict crack density growth in different fatigue stress levels. The methodology, using maximum local transverse stress in a fatigue cycle in Weibull model and the Weibull parameters determined at a reference fatigue stress level, was limited in ability to predict the crack density growth at other stress levels. It was then found that the crack density growth not only depends on maximum local stress in a fatigue cycle, but also on the local stress ratio in the 90-layer, presented in Paper 3. Wherein, an equivalent stress was introduced to replace maximum local stress in Weibull model by addressing the combined effect of maximum local stress in a cycle and also the local stress ratio. Equivalent stress model was validated across different layups and fiber content with same material system. Paper 5 presents fatigue test results at different stress levels and temperatures. It was found that in fatigue tests at 150℃, in spite of lower thermal stress, crack density growth was more rapid than for RT fatigue tests. Methodology to predict crack density growth in 150℃ fatigue tests by combining the analytical model with the equivalent stress and with enhanced test temperature effect has been presented. 

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  • 3.
    Pakkam Gabriel, Vivek Richards
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Fernberg, Patrik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Fatigue Damage Model of High Temperature Polymer Composites in Aero-Engines2022In: ICAS Proceedings 33rd Congress of the International Council of the Aeronautical Sciences, Stockholm, Sweden, The International Council of the Aeronautical Sciences , 2022, Vol. 5, p. 3805-3812Conference paper (Refereed)
    Abstract [en]

    High Temperature Polymer Cross-ply (HTPC) laminate specimens are subjected to tension-tension fatigue loading at 3 different maximum stress levels at room temperature. Transverse cracking in 90° layer in the crossply laminate upon fatigue tests is analyzed. Based on probabilistic approach, using Weibull distribution, a prediction model for the increase in number of transverse cracks upon fatigue loading at different stress levelsis developed. The predicted crack density (number of cracks per unit length) development shows good agreement with the test results for fatigue at the higher stress levels considered. A slight overprediction is observed at lowest stress level.

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  • 4.
    Pakkam Gabriel, Vivek Richards
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Fernberg, Patrik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Prediction of transverse cracks in damaged layers of compositelaminates2022In: Svenska Mekanikdagar 2022 / [ed] Pär Jonsén; Lars-Göran Westerberg; Simon Larsson; Erik Olsson, Luleå tekniska universitet, 2022Conference paper (Refereed)
  • 5.
    Pakkam Gabriel, Vivek Richards
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Fernberg, Patrik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Tsampas, Spyros
    Huntsman Advanced Materials Gmbh, 4052 Basel, Switzerland.
    Varna, Janis
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science. Laboratory of Experimental Mechanics of Materials, Riga Technical University, Riga, Latvia.
    Transverse Cracking Characterization and Prediction in Heat Treated Polymer Composites under Quasi-Static Tensile Loading at Elevated Temperature2022In: ECCM 2022 - Proceedings of the 20th European Conference on Composite Materials: Composites Meet Sustainability / [ed] Anastasios P. Vassilopoulos; Véronique Michaud, EPFL Lausanne, Composite Construction Laboratory , 2022, Vol. 6, p. 23-30Conference paper (Other academic)
    Abstract [en]

    Transverse cracking in high temperature polymer cross-ply composite laminate was experimentally studied. In the tests, pristine as well as heat treated cross-ply laminate specimens were subjected to quasi-static tensile loading at room temperature and 150°C. Microscopy studies revealed that manufacturing induced transverse cracks were present in 90° layer of pristine cross-ply laminates. An increase in number of transverse cracks were observed after the heat treatment. Transverse crack density (number of cracks/unit length) growth upon applied thermo-mechanical transverse stress in 90° layer was analyzed using 3-parameter Weibull failure stress distribution. The Weibull location parameter, in efforts to address the influence of temperature and heat treatment of crack density growth, is modified based on empirical data. The predicted results were in good agreement with the test results.

  • 6.
    Pakkam Gabriel, Vivek Richards
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Fernberg, Patrik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Varna, Janis
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Transverse cracking in cross-ply laminate under tension-tension fatigue loading at room and elevated temperatureManuscript (preprint) (Other academic)
  • 7.
    Pakkam Gabriel, Vivek Richards
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Loukil, Mohamed Sahbi
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Fernberg, Patrik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Varna, Janis
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Equivalent stress concept to account for the effect of local cyclic stress ratio on transverse cracking in tension-tension fatigueManuscript (preprint) (Other academic)
  • 8.
    Pakkam Gabriel, Vivek Richards
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Loukil, Mohamed Sahbi
    Department of Management and Engineering, Linköping University, Sweden.
    Fernberg, Patrik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Varna, Janis
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science. Laboratory of Experimental Mechanics, Riga Technical University, Latvia.
    Methodology for transverse cracking simulation in 90 plies of composite laminate under fatigue loading2022In: ECCM 2022 - Proceedings of the 20th European Conference on Composite Materials: Composites Meet Sustainability / [ed] Vassilopoulos, Anastasios P.; Michaud, Véronique, EPFL Lausanne, Composite Construction Laboratory , 2022, Vol. 6, p. 16-22Conference paper (Other academic)
    Abstract [en]

    Methodology for crack density evolution simulation in tension-tension fatigue and parameter determination in a model that relies on failure stress distribution (Weibull) in the 90 ply is presented. Cyclic loading is performed at one stress level to obtain detailed crack density dependence on the number of cycles. In addition, one data point (crack density at specified number of cycles) is necessary at a different stress level. Non-interactive crack density region is used to determine Weibull parameters. Then, crack density in a whole crack density range and for arbitrary stress level is predicted using the obtained Weibull parameters, the Monte Carlo method for failure stress distribution and a novel model for stress distribution between cracks. The predictions are in good agreement with test results.

  • 9.
    Pakkam Gabriel, Vivek Richards
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Loukil, Mohamed Sahbi
    RISE SICOMP, Sweden; Department of Management and Engineering, Linköping University, Linköping University, Sweden.
    Varna, Janis
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science. Laboratory of Experimental Mechanics of Materials, Riga Technical University, Riga Technical University, Latvia.
    Analysis of intralaminar cracking in 90-plies of GF/EP laminates with distributed ply strength2021In: Journal of composite materials, ISSN 0021-9983, E-ISSN 1530-793X, Vol. 55, no 26Article in journal (Refereed)
    Abstract [en]

    Intralaminar cracking in relatively thick 90-plies of [(Formula presented.)]s laminates is analyzed using experimental data for two Glass fiber/Epoxy (GF/EP) material systems. Weibull parameters for transverse failure stress of the 90-ply are obtained from experimental intralaminar crack density versus applied strain data, showing that a reliable analysis requires sufficient amount of data in so called noninteractive crack density region. Monte Carlo simulations of cracking were performed using stress distribution between two cracks calculated using two models: Hashin’s model and a novel model that ensures that the average stress is exactly the same as in FEM solution. Due to its features, the Hashin’s model predicts too low intralaminar crack density (it predicts too strong interaction between cracks). The results emphasize the importance of having a proper stress distribution model when performing Monte Carlo simulations. Simulations were used not only to simulate intralaminar cracking in high and very low crack density regions but also for improving the procedure of Weibull parameter determination.

  • 10.
    Pakkam Gabriel, Vivek Richards
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Loukil, Mohamed Sahbi
    Department of Management and Engineering, Linköping University, 581 83 Linköping, Sweden.
    Varna, Janis
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science. Laboratory of Experimental Mechanics of Materials, Riga Technical University, Riga, Latvia.
    Intralaminar cracking during cyclic loading in laminates with distributed failure stress in 90-plies2022In: International Journal of Fatigue, ISSN 0142-1123, E-ISSN 1879-3452, Vol. 161, article id 106909Article in journal (Refereed)
    Abstract [en]

    Methodology for cracking evolution simulation in 90-plies during cyclic loading is suggested in this paper. It includes using low crack density (where the neighboring cracks do not interact with each other) data from quasi-static and cyclic testing (at one load) to determine parameters in Weibull transverse failure stress distribution generalized for fatigue. Then, Monte Carlo process is used to assign failure stress to elements in the 90-ply. In the model, the failure stress of the element degrades with number of cycles and a crack appears when the failure stress becomes equal to the stress in the element, calculated with computationally efficient analytical method. The model is successfully used to predict cracking in the whole crack density range. In this model, data from cyclic test at one load is sufficient to predict damage at different load. The results suggest that the dependence on stress is slightly underestimated and the shape parameter in fatigue may be higher than in quasi-static tests. Therefore, fatigue tests at least at two load levels are recommended for reliable predictions.

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  • 11.
    Pakkam Gabriel, Vivek Richards
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Petkov, Valeri Ivanov
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Fernberg, Patrik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Varna, Janis
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science. Laboratory of Experimental Mechanics of Materials, Riga Technical University, LV-1048 Riga, Latvia.
    Effect of heat treatment and test temperature on transverse cracking in tensile loading2024In: Composites. Part A, Applied science and manufacturing, ISSN 1359-835X, E-ISSN 1878-5840, Vol. 181, article id 108149Article in journal (Refereed)
    Abstract [en]

    Accumulation of transverse cracks in carbon fiber heat resistant polymer (with bismaleimide formulation) cross-ply laminates during tensile loading at elevated temperatures and after long heat treatment is analysed. Data shows that both the iso-thermal heat treatment and testing at elevated temperatures reduce the transverse cracking resistance. A two-parameter Weibull failure stress distribution model with scale parameter degrading with heat treatment and elevated temperature is used for crack initiation analysis. The degradation is described by polynomial expansion including interaction terms. Data shows that the scale parameter dependence on the heat treatment time and the test temperature is rather linear. The same expansion parameters have been successfully used for laminates with the same constituents but with a different layup and fiber content.

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  • 12.
    Petkov, Valeri Ivanov
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Pakkam Gabriel, Vivek Richards
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Fernberg, Patrik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science.
    Semantic segmentation of progressive micro-cracking in polymer composites using Attention U-Net architecture2024In: Tomography of Materials and Structures, ISSN 2949-673X, Vol. 5, article id 100028Article in journal (Refereed)
    Abstract [en]

    The present study delivers a methodology for investigating the gradual damage development in a carbon fibre-reinforced cross-ply polymer composite during a sequence of thermo-mechanical loadings with the help of X-ray computed tomography. The procedure allows an in-depth analysis of the occurrence and nature of the multiple cracks that form within layers oriented perpendicular, or transverse, to the loading direction. This is achieved by using Attention U-Net architecture for semantic segmentation of the transverse cracks. The model shows promising results, through an ability to identify all the transverse cracks and reflect the damage progression. The described method provides a robust routine for analysing challenging polymer composite tomographic datasets.

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