Final Report Summary - MIFACRIT (Methodology Toolbox for Accelerated Fatigue Testing of FRP Materials: <br/>Micro-structural Failure Criterion for Multi-axial Fatigue of FRP Structures)
Executive Summary:
The MIFACRIT project aimed at developing a failure criterion for fiber reinforced plastics (FRP). This criterion shall enable reliability and durability assessments of structural parts and systems of multiple stack-up structures. It shall be deduced from mechanical effects within the microstructure of the fiber reinforced polymer structures in order to cover various mechanical loading conditions. This ambitious goal is achieved through a symbiotic combination of experimental testing and analysis work based on numerical simulation using fracture/damage mechanic concepts. The material tests consist of visco-elastic characterization and stress tests applying constant strain rate and cyclic loads. Most importantly, they include a variety of loading situations such as tensile and bending loads and combinations of normal and shear components. The analyses determine the visco-elastic material properties and the micro-structural effects, which are responsible for damage and failure of the FRP structure in a comprehensive way. The detailed analysis of the damage and failure effects by means of numerical simulation will use a two-stage (global/local) sub-modeling strategy. The required model parameters are calibrated by measured data and the simulation results are confirmed by the experimental findings. Combining experiment and simulation in this way, the common link between the failure effects caused by different loading situations will be shown and described within the help of an objective mechanical criterion, which is identified and validated during the project MIFACRIT.
Project Context and Objectives:
The project MIFACRIT is continuing a development path. It seamlessly combine experimental work with numerical simulation for in-depth analysis and identification of a failure criterion that allows quantitative assessments of damage and reliability risk in FRP structures under multi-axial load conditions. The project is structured in five work packages (WP): WP 1 - Test, WP2 - Simulation, WP3 - Criterion, WP4 - Validation, WP5 - Management. WP1 and WP4 are dominated by experiments while the other two packages WP2 and WP3 are dominated by simulation and theoretical work.
MIFACRIT followed the 'V' approach of project structure. It started with the definition and specification phase in WP1, in which the inputs of the Clean Sky working group in terms of specific requirements were adopted and the material handed out was analyzed. Then, MIFACRIT proceeded via the simulation preparation, execution, and evaluation steps (WP2 & WP3) to finally arrived at the validation phase (WP4), which provided results that are readily implementable into the larger effort of the CleanSky working group, i.e. as substantial contribution to the expansion of the lifetime assessment methodology for FRP structures accounting for arbitrary multi-axial loadings.
1. WP: Experimental Tests - Experimental Investigation of the Damage and the Fatigue Effects
Main objectives:
o Sample characterization and preparation
o Specification of standard tests and design of new tests on mixed state loading
o Specification of the analysis techniques
o Design of experiment (DoE) and execution of the stress tests according to Miyano methodology
o Determination, analysis and documentation of the failure modes
The experimental studies performed in WP1 using the material handed out by the Clean Sky consortium - IS 400, as typical epoxy based material with woven fibre reinforcement. WP1 consisted of different material tests like visco-elastic characterizations and stress tests applying constant strain rate. Depending on the baseline of the test pyramid from the DoW the tests included a variety of loading situations such as tensile, bending and shear. In the first phase of the project, the fracture of the material was documented under 3 point bending loading and the fracture behaviour of IS400 has been studied. According to the pyramid of experiment the mixed mode loading as bending and shear as well as tension and shear were realized. For this purpose, a custom made sample holder has been designed and was used in order to introduce shear forces in the tension loading situation. In this work, we have defined an experimental procedure allowing us to determine the failure mechanism of the supplied IS400 laminate. Taking inspiration in the methodology of Miyano [2], the failure obtain during the constant strain rate (CSR) and fatigue tests for different loading scenario were investigated in order to verify that the same mechanism apply in all cases. Finally, the analysis of the failure modes were performed and documented according to the requirements of numerical simulation engineers concerning WP3.
2. WP: Numerical Simulation - In-depth Analysis of the Mechanical Situation at Global and Local Stage
Main objectives:
o Modeling of the specimen (geometric and material model of the ply stacks handed out by the Clean Sky consortium) and the load cases
o Simulation of the tests conducted
In parallel to the experimental work simulation approaches were carried out to comprehend the various mechanical loading situations based on numerical evaluations and utilization of fracture and damage mechanics concepts. Work package 2 comprises the numerical concept towards the in-depth analysis of the mechanical situation at global and local stage. Under different loading situations the damage and failure effect were investigated. For this purpose an appropriate geometric model of the specimen was created and material models (specifically, visco-elastic material data of the matrix material extracted in WP1), were included in the numerical calculation.
3. WP: Failure Criterion - Objectively Capturing the Effect of the Dominating Failure Mode
Main objectives:
o Fracture / damage mechanics analysis based on the leading edge concept according to the experimental findings on the failure mode
o Identification of a set of criteria candidates and determination of the favorite criterion
o Determination of quantitative thresholds characterizing fatigue and damage in FRP structures
This deliverable addresses the numerical simulation of fracture and damage in fibre reinforced laminates to determine the threshold values at which the tested FRP material fails. The determination of the ultimate strength is often based on macro-mechanical strength theories. Experimental investigations were performed to identify the failure mechanism and the strength values under combined load conditions. In the primary step the material data were extracted by tensile test and the visco-elastic matrix material data by DMA (Dynamic Mechanical Analysis). The effective material properties were determined by tensile tests and attendant FEA simulations in both in-plane directions. The damage/fracture threshold parameters were determined by evaluating the inelastic part of force vs. displacement behavior of the tensile tests under different fiber orientations.
4. WP: Result Validation - Summarizing and Proving the Outcome of the Study
Main objectives:
o Estimation of the response of known specimen structures to new loads
o Estimation of the response of new structures to load cases already studied
o Prognosis of the fatigue lifetime of FRP structures and comparison to real tests
While all previous steps utilized more or less uniaxial loading conditions, this work package addressed the verification step by applying a combined loading situation. Tensile loading of a specifically shaped sample leads to shear loading as well as pure tensile stresses in particular regions of the specimen at the same time. The utilization of the nonlinear damage model together with all its properties as determined in WP3 now reflect the experimentally observed crack propagation processes.
5. WP: Project Management
Main objectives:
o Planning, Coordination, Reporting of the Work as well as Dissemination and Exploitation of the results
o Control of the workflow in all tasks according to DoW and timeline
o Coordination of the interaction between the WPs
o Be the contact to the technical workgroup and the joint undertaking of Clean Sky
WP5 was dedicated to the project management. It controlled the work flow and the handover between the tasks within MIFACRIT as well as the interface activities to the outside world in terms of Clean Sky working group, Clean Sky Joint Undertaking, and dissemination and exploitation of the project results.
Project Results:
1 WP: Experimental Tests - Experimental Investigation of the Damage and the Fatigue Effects
The damage and failure effect under different orientation and loads have been investigated with the aim to deduce a failure criterion for fiber reinforced polymer structures. This work package covers all the remaining planed tests and the corresponding optical and physical analysis driven on the material samples provided by the Clean Sky consortium. The WP consisted of two complementary parts. One was the mechanical characterization of the delivered material, the second the extension of the tests to mix mode loading.
Figure 1: Test pyramid
This work package shows the experimental concept towards the in-depth analysis of the mechanical situation at global and local stage. Under different loading situations the damage and failure effect were investigated. For this purpose, a first set of experiment has been driven in order to validate the ability to drive the test and gather experience with the material. Chapter 1.1.2 presents the results obtain during DOE of experiment for 3PB and validate the feasibility of the overall experimental concept. In parallel, a sample holder for combined loading has been designed according to /3/ and custom made for our dynamic tester. The concept relies on a systematic study of the X direction of the sample and chosen conditions are then explored in the other directions.
1.1 Experimental base of the pyramid
1.1.1 Dynamic mechanical analysis
Visco-elastic properties of the material are obtained from frequency sweep temperature step measurement. This gives access to time dependent measurements of the storage modulus for various temperatures. Applying the time temperature superposition principle, the master curves are constructed by shifting the curves on the logarithmic frequency scale by the shift factor A /1/. The respective values for the shift function could be fitted with the Arrhenius function Equation 1.
Equation 1
Where R is the gas constant of 8.314 103 kJ/(K mol), H is the activation energy, TREF is the reference temperature, for which room temperature is chosen, and T is the actual temperature. The obtained visco-elastic master curve can be then fitted using Equation 2 to obtain Prony parameters that can be used to implement the time temperature dependency of the storage part of the Young's modulus E' in FEM simulation software.
Equation 2
Equation 2 where E∞ is the modulus at rubbery state, Ei and tau(i) denote the i(th) of N sets of Prony parameters (modulus and time constant, respectively), and t is the time.
According to Miyano et. Al. the obtained visco-elastic shift factors can be used on CSR and Creep data obtained for different temperatures to build the CSR and Creep master curves.
This master curves being used to build a fatigue master curve base on fatigue measurements obtained at various loading ratio and temperature. This fatigue master curve is then of great use as it allows to predict the lifetime of the FRP structure under consideration.
1.1.2 Static Tester (CSR)
CSR measurements where done on a static tester (DMA 2000+ from Metravib) using a similar method as describe by Miyano in /4/. Samples were placed in the tester in static 3 point bending mode and measured at different loading speeds for various temperatures. The master curve is then built by shifting the isothermal curves along the time axis. The same procedure was then applied on samples with different fiber orientation (0°, 90° and 45°). The resulting maximal strength is shown on Figure2. X and Y direction show some differences in the strength values but the failure observed after the test looks very similar. The 45° sample on the other hand shows little to no failure as the glass fibers are not perpendicular to the load direction and do not reach their rupture point.
Figure 2: CSR curves measured at different speed and temperature and resulting master curve for IS400, 5Ply.
Figure 3: Maximal strength different material orientation for IS400, 5 ply at measured at room temperature
1.2 Step two of the experimental pyramid
1.2.1 Realization of mix mode loading
Based on the previous results and in order to fulfil the proposed test pyramid, a specific sample holder was designed (Figure 4) and fabricated according to /3, 4/. Design and realization had been executed in parallel with the characterization work.
Figure 4: Engineering detail drawing and mounted sample holder for mix mode loading
The second kind of samples to realize mixed mode loading is depicted in Figure 5. The aim is to introduce shear loading by changing the sample geometry by drilling 10 mm holes in the sample that are placed 1,31 mm from each other on a 45° line on the sample.
Figure 5: Sample for tension-shear loading – sketch and mounted sample
1.2.2 Results I
Figure 4 depicts the experimental set-up with clamped IS400 test sample (see also Figure 5). The load angles 15°, 30° and 45° are realized in this test series.
Figure 6: Top view onto the 1-ply (left), cross section of 1-ply sample with tension direction in y (right)
Table 1 gives a review over the performed experiments. The tests were operated at room temperature with a displacement speed of 10-4, 10-5, 10-6 m/s and a preload of 3 N.
Table 1: Review over the performed experiments inclusive position of break
Table 2: Averaged force and displacement results
Figure 7: Force-displacement curves
Figure 8: View on fracture
1.2.3 Results II
In this test series samples with a width of 10 mm were investigated under optical observation and the loading angle was set to 45°. In this case 1-ply and 5-ply samples were included. The following image sequence (Figure 9) shows the progress of the crack through an 1-ply sample. To avoid cracks in the clamping region the samples have to provide with an initial crack with a length of the half of the width. In those conditions proper crack propagation could be observed.
Figure 9: Crack propagation in a 1-ply sample
The second image sequence (Figure 10) shows the progress of the crack through a 5-ply sample. Here, an initial crack of 2/3 of the sample’s width was necessary to reach crack propagation because of the machine’s load limit of 500 N.
Figure 10: Crack propagation in a 5-ply sample
The shear loading could be proved by digital image correlation (DIC). Pictures (Figure 11) show the displacement of the fiber texture. Picture 1 is the reference picture depicting the fabric in the unloading state and picture 2 the fabric under loading. The analysis of the two states by digital image correlation based on the difference between the grey scale values resulted in the in-plane displacement field as shown in picture 3.
Figure 11: Digital image correlation on a 1-ply sample during mixed mode loading
1.2.4 Results III
In this series, the tests were driven on samples with holes in order to induce shear component using the sample geometry in a tension test. For this purpose, the samples where specially prepared using laser cutting technics in order to minimize the edge effect on the holes. Samples were then placed in the tension clamps and force was applied until sample breaks.
Force displacement curves were recorded and in the same time the experiment was recorded using normal camera and high speed camera. The movies made with the normal camera were treated using image correlation software and correlate with the force displacement curve in order to obtain a 2D mapping of the displacement field on the sample. This was done for samples with fibber orientation 0° (Figure 12) and 45° (Figure 13).
Figure 12: Digital image correlation of tension shear sample with 0° fibber orientation
Figure 13: Digital image correlation of tension shear sample with 45° fibber orientation
Analysis of the high speed camera movies and optical analysis of the broken samples gives a unique picture of the fracture mechanism. As the force applied increase, the matrix will first fracture in many places, weakening the structure. After, the fracture will find its way to the nearest fibber bundle perpendicular to the applied tension and will follow this bundle. Ultimately, the fibbers in the direction of the applied force will rupture.
1.3 Conclusion
In the light of the latest experiments, it was possible to determine that the matrix fails first, then the fracture find its way through the nearest bundle of fibber perpendicular to the load. This failure mechanism can now be implemented in the simulation.
The detailed test DOE set up has been fulfilled within the scheduled timeframe and result delivered for simulation. This include: realization of a Mix-mode sample holder, samples with special geometry for tension-shear test, tension test and mixed mode loading test conditions according to the DoW and optical analysis of the fractured samples.
Therefore, Failure mode assessment - was achieved within the scheduled timetable according to the DoW.
2 WP: Numerical Simulation - In-depth Analysis of the Mechanical Situation at Global and Local Stage
This work package “Numerical models are finalized and input data is delivered” shows the numerical concept towards the in-depth analysis of the mechanical situation at global and local stage. Under different loading situations the damage and failure effect are investigated with the aim to deduce a failure criterion for fiber reinforced polymer (FRP) structures.
2.1 Failure simulation
The FE program ABAQUS provides numerical possibilities to investigate failure and damage in FRP structures /5/. Cohesive elements are used to model behavior of delamination and the ABAQUS damage model is used to predict behaviour of the fiber reinforced epoxy layer.
Figure 14: Unidirectional lamina
The modelling approach bases on a homogenized elastic orthotropic material model for fiber reinforced epoxy layers (non-woven) that takes into account 4 different modes of failure:
o fiber rupture in tension;
o fiber buckling and kinking in compression;
o matrix cracking under transverse tension and shearing; and
o matrix crushing under transverse compression and shearing
Figure 14 shows a single layer whereat the layer are modelled as crossed but non-woven.
The stiffness response regarding failure can be formulated as σ = Cd ε with Cd as in Equation 3.
Equation 3
The approach follows the work of Camanho et al., Hashin and Matzenmiller et al. /7-10/ and is implemented in the commercial FEM-code ABAQUSTM see the manual /6/.
2.1.1 Failure of Fiber-Reinforced Epoxy Layers – ABAQUS™ UMAT-material model
The approach is introduced into the FE-code via an extra user-material subroutine (Figure 15).
Figure 15: Failure of fiber reinforced epoxy layers – ABAQUS™ user routine /6/
This subroutine realizes damage initiation and evolution in the fiber and damage in the epoxy matrix.
Fiber
The damage in the fiber is initiated when the criterion in Equation 4 and Equation 5 is reached.
Equation 4
Equation 5
The fiber damage evolves with df as in formula (Equation 6):
Equation 6
Epoxy matrix
Similarly, damage initiation in the matrix is governed by the criterion (Equation 7).
Equation 7
The evolution law of the matrix damage is described by Equation 8.
Equation 8
The formulation (Equation 9) combines stiffness and stiffness degradation in an effective elasticity matrix and during progressive damage the effective elasticity matrix is reduced by the two damage variables df and dm, as follows:
Equation 9
2.1.2 Failure of Fiber-Reinforced Epoxy Layers – 3-Point Bending Example
The properties for the involved materials have been taken as in Table 3.
Table 3: material properties
The fiber orientation is defined by material orientation coordinate systems in alternating order. Figure 16 shows the symmetric model of the 3-point bending test.
Figure 16: Simulation model (10 plies) of the 3-point bending test
Following results ABAQUS delivers:
STRESSES/STRAINS etc.
STATEV(1) damage variable df
STATEV(2) damage variable dm
STATEV(3) regularized damage variable dfv
STATEV(4) regularized damage variable dmv
DAMAGE propagation
First results for a 10 ply lay-up plus upper and lower resin layer under 3-point bending show the damage parameters for both damage modes.
Figure 17 represents the damage parameter df. The elements in which the parameter df exceed a value of 0.96 are damaged (red colored elements). In this way, Figure 18 demonstrates the matrix damage.
Figure 17: Fiber damage occurs
Figure 18: Matrix damage occurs
One of the primary results – the force vs. displacement curves (Figure 19) – allow for adapting the damage initialization properties much better. These results should be seen as intermediate results in order to investigate and check the approach.
Figure 19: Failure of fiber reinforced epoxy layers – intermediate result
Figure 20: Element plot
Figure 21: Maximum principle stress
Omitting all elements with damage parameters greater than 0.96 clarifies the damage process but also the necessity of enhancing the damage properties as well as the specimen towards one of the 10-ply specimens investigated experimentally. These results give a better understanding about the damage evolution process and can be utilized to enhance the damage evolution description when compared to experimentally found damage zones/paths.
Figure 22: Maximum principle stress
2.2 Conclusion
It could be demonstrate that the commercial FE code ABAQUS employed in this work package affords the possibilities of providing the necessary methods and results. Global results as stress and strains extracted and damage occurs after adjustment of the damage parameters as observed in the experimental tests. Hence, the model setup was realized within the time frame defined in the DoW. The model calibration and simulation of the stress tests has been achieved within the frame of the project.
3 WP: Failure Criterion - Objectively Capturing the Effect of the Dominating Failure Mode
This work package addressed the numerical simulation of fracture and damage in fibre-reinforced laminates to determine the threshold values at which the tested FRP material fails. According to WP1 and the performed experiments, numerical investigations followed corresponding to the DoW.
3.1 Common characteristic of fracture and damage under different loads
The nature of composite material behavior when subjected to constant strain rate loading as performed in WP1 is of basic interest for predicting lifetime of the FRP (fiber reinforced plastics) structures. The failure simulation adopted in WP1 includes the prominent damage mechanism as fiber damage under tensile and compressive loading and matrix damage under combined tension/compression and shear loading situations.
In the attempt of finding a proper mechanical criterion for the crack initiation in IS-400 structures, the scenarios have been extracted from the observations - see Figure 23:
Figure 23: Crack propagation in a composite layup under bending load
3.2 Tensile experiments to determine common damage characteristics
Tensile tests (see specimen with sample and FE-model representation in Figure 24) with different specimen orientations regarding the tension axis with 1-ply specimens were performed up to the complete rupture point. Similar FE-models have been set up together with a DoE (Design of Experiment with 4 values per property) to determine:
1. Elastic constants (Young’s modulus in 1-direction (longitudinal), Young’s modulus in 2-direction (transversal), Poisson ration in plane of fibers, Poisson ration out of plane, shear modules in-plane and out of plane --> in FE-simulations a maximum of 0.1 mm elongation is used to stay in elastic, undamaged region. The DoE varied the Young’s modules as well as the in-plane shear modulus, 4 samples each and 4 loading angles.
2. Failure threshold values (failure stress in 1-direction and tension, failure stress in 1-direction and compression, same properties for 2-direction, failure stress in in-plane shear, fracture energy in matrix and fiber --> in FE-simulations additional loading points with elongations of 0.15 mm, 0,2 mm and 0.3 mm are to pick out for comparison. First results comparing the force vs. displacement curves for 4 specimen angles are shown in Figure 25.
Figure 24: Specimen and sample holder (left) and FE-model representation (right)
Figure 25: First results comparing the force vs. displacement curves for 4 specimen angles
3.3 Fracture and damage mechanics approach
The determination of the ultimate strength is often based on macro-mechanical strength theories such as maximum stress or strain theories for example the Tsai-Wu and Hashin Failure Criterion. The Tsai-Wu Criterion is a quadratic, interactive stress-based criterion that identifies a failure, but does not distinguish between different modes of failure. In contrast, the Hashin failure criterion indeed starts with the same terms of the stress tensor, but then decomposes into four different modes of failure tensile and compressive fiber failure as well as tensile and compressive matrix failure. Here, failure due to tension, compression and combinations with shear loading /7-10/ is considered – see also explanations of the underlying damage model in WP1.
A requirement in using these strength theories there is the definition of the strength parameters only by means of experiments on corresponding specimen. Another complicacy concerning the failure in FRPs is to predict both the failure mode and in which component the failure initiates /5/. Thereto, comprehensive experimental investigations were performed to identify the failure mechanism and the strength values under combined load conditions. In the primary step the material data extracted by tensile test and the visco-elastic matrix material data by DMA (Dynamic Mechanical Analysis).
3.3.1 Finite element model - material data
The FE (finite element) model using in the failure simulation is shown in Figure 24. Thereby, the fiber orientation follows the definition of the material orientation coordinate system in alternating order. An effective orthotropic material behavior of the fiber reinforced polymer composite is involved in the FE (finite element) simulations. The different distances of the fiber bundles in the plane directions are realized by corresponding effective orthotropic material properties of the ply.
The effective material properties were determined by tensile tests and attendant FEA-simulations in both in-plane directions.
Table 4: Orthotropic material data applied in the FE model
3.3.2 Finite element model - threshold properties
The damage/fracture threshold parameters are determined by evaluating the inelastic part of force vs. displacement behavior of the tensile tests under different fiber orientations – see Figure 25. Table 5 summarizes the resulting threshold parameter for use within the utilized material model.
Table 5: Orthotropic material data applied in the FE model
Figure 26: Force vs. displacement vs. angle of tension
Figure 27: Force at 0.1 mm displacement vs. angle of tension taking sample holder compliance into account
3.4 Conclusion
The work in WP3 consumed a huge amount of man power and computing resources. At least the man power could be reduced by:
o Setting up an automated procedure that includes the FE-modeling work, the sample holder compliance fitting procedure, the elastic and the fracture/damage property detection.
o The machine and sample holder compliance should be clearly determined prior to further experiments. Clamping conditions have to be enhanced, too. Initially, the large number of simulation experiments within the DoE did not reflect all initial stiffness’s – neither the highest force at a loading angle of 0 degree nor the lowest force for 45 degree oriented tension – see Figure 26. But, taking the sample holder compliance into account allowed to fit all the FEA results to the experimentally found forces at a displacement of 0.1 mm – see Figure 27. Adapted elastic properties see Table 4.
o A further DoE explaining the dependences of several points of the force vs. displacement curves (see Figure 25) on threshold values of fiber and matrix damage was performed with 3 sample values per threshold parameter, 3 loading points and 4 loading angles. The functional representation of these dependences allowed to find the wanted parameters whenever, with parameter associated different and not finally verified accuracy.
4 WP: Result Validation - Summarizing and Proving the Outcome of the Study
4.1 Combined loading within a double punched specimen
In order to better reflect the nature of composite material behavior when subjected to combined loading a double whole specimen was created, tailor-made and experimentally investigated under pure tensile loading conditions up to the full rupture load. The corresponding FE-model (see Figure 28) utilizes all the adopted material and damage properties as determined in WP 3 with 2 different fiber orientations: tension angle (y-axis) oriented fibers and 45 degree rotated fiber orientation. All geometrical and load settings have been adapted to the experimental conditions.
Figure 28: Clamped double punched specimen (left) and FE mesh with boundary condition hints
4.2 Results and discussion
As to see in Figure 29 for fiber orientation 0° and in Figure 31 for fiber orientation 45° for instance, the fiber and matrix failure measures indicate the same failure regions in experiment and FE-simulation. In FE-results SDV1 and SDV2 characterize the degree of damage. They range from 0 (undamaged) to 1 (completely damaged). A closer look onto the simulation results explains – that
1. The fibers are not completely disrupted (SDV1 >1) while
2. The matrix is completely broken within the red zones, the region between the wholes, especially.
3. The damaged zones do not completely follow the fiber orientations (as to see in experiment) which is acceptable a result of the underlying homogenized orthotropic material behaviour.
Figure 29: Damaged sample with 0° fiber orientation – experimentally observed damage pattern (upper picture), fiber failure measure in FEA (lower left picture) and matrix failure measure (lower right picture)
Figure 30: Tension-Shear samples with 0° fiber orientation after testing
The samples show a good reproducibility of the results and good agreement between simulation and reality. It also picture accurately the chronological fracture propagation (outside first, between the holes last) as observed on high speed movies. During experiment, the fracture goes through the fiber bundle on both sample sides, following a straight line whereas in the simulation, a random path is pictured (Figure 29). This could be due that in the model the fiber plies lie next to each other, whereas in reality the fiber bundles are tightly interwoven.
Figure 31: Damaged sample with 45° fiber orientation – experimentally observed damage pattern (upper picture), fiber failure measure in FEA (lower left picture) and matrix failure measure (lower right picture)
Figure 32: Tension-Shear samples for four 45° fiber orientation after testing
The samples show a good reproducibility of the results and a great agreement between simulation and reality even for the chronological appearance of the fractures (middle first outside last).
4.3 Conclusion
The realized procedure of capturing elastic properties as well as failure/damage properties of one-ply and multiply composites is in principal working. First testing samples showing combined loading stress situations in dedicated local areas have been experimentally investigated by simple tensile testing up to the point of complete rupture. Suitable FE-models have been set up and simulated taking into account the captured elastic properties as well as failure/damage properties from previous work packages. The final failure pattern and also the follow up of damage/crack propagation trough the specimens reflected by the simulation results. Whilst these results are in a good agreement with experiments further enhancements are necessary to improve the reliability of all captured parameters – the shear stress related properties especially. Dedicated experiments for shear loading could overcome the current uncertainties regarding this data.
References:
[1] S. Rzepka et al; Accelerated fatigue testing methodology for reliability assessments of fiber reinforced compo-site polymer materials in micro/nano systems; EuroSimE 2011
[2] Miyano, Y., Nakada, M., and Nishigaki, K., “Prediction of long-term fatigue life of quasi-isotropic CFRP laminates for aircraft use”. 3rd International Conference on Fatigue of Composites. International Journal of Fatigue 28, 10 (2006/10), 1217–1225
[3] Li Qing-fen, Qi Gui-ying, Yan Sheng-yuan, Buchholz F.-G. “Computational Fracture Analyses of a Compact Tension Shear (CTS) Specimen with an inclined Crack Plane.” Key engineering materials 385-387 (2008) 741-744
[4] El-Assal, A.M. Khashaba, U.A. “Fatigue analysis of unidirectional GFRP composites under combined bending and torsional loads”, Composite Structures 79 (2007) 599–605
[5] SIMULIA (ABAQUS) Manuals (V. 6.11) Dassault Systemes Simula Corp., Providence, RI, USA, 2011
[6] Mollenhauer D. et al., “Simulation of discrete damage in composite Overheight Compact Tension specimens”. Composites Part A 43 (2012), 1667–1679.
[7] Camanho, P. P., and C. G. Davila, “Mixed-Mode Decohesion Finite Elements for the Simulation of Delamination in Composite Materials,” NASA/TM-2002–211737, pp. 1–37, 2002
[8] Hashin, Z., “Failure Criteria for Unidirectional Fiber Composites,” Journal of Applied Mechanics, vol. 47, pp. 329–334, 1980
[9] Hashin, Z., and A. Rotem, “A Fatigue Criterion for Fiber-Reinforced Materials,” Journal of Composite Materials, vol. 7, pp. 448–464, 1973
[10] Matzenmiller, A., J. Lubliner, and R. L. Taylor, “A Constitutive Model for Anisotropic
Potential Impact:
The main final results comprise on the one hand the in depth understanding of typical failure modes in FRP and on the other hand the quantitative determination of a mechanical failure criterion. This mechanical criterion enables us in further projects to assess the fatigue status of a particular FRP structure and to predict its lifetime under more real loading situations. The acquired knowledge will be used to develop more realistic models, which will allow making more realistic lifetime predictions at a minimum time. The experimental and simulation knowledge gather throughout the project (combine loading test followed with high speed camera and in depth analysis using FEM simulation) are precious assets that will be further developed within our company. Moreover, based on our new experience, further synergies may arise, which will result in customer-specific requests or further R&D contracts. As a result of combining the experience of prior services provided to automotive industry with the technological requirements of energy-efficient sandwich composite structures for aerospace industry, an extension of AMITRONICS’ portfolio will further developed within BMWi project “moZat”.
List of Websites:
The development of a website wasn’t part of the project task. However, for dissemination purposes project results will be published under the beneficiary’s website at http://www.amitronics.de/unternehmensbereiche/Amitronics+Project(se abrirá en una nueva ventana).
The MIFACRIT project aimed at developing a failure criterion for fiber reinforced plastics (FRP). This criterion shall enable reliability and durability assessments of structural parts and systems of multiple stack-up structures. It shall be deduced from mechanical effects within the microstructure of the fiber reinforced polymer structures in order to cover various mechanical loading conditions. This ambitious goal is achieved through a symbiotic combination of experimental testing and analysis work based on numerical simulation using fracture/damage mechanic concepts. The material tests consist of visco-elastic characterization and stress tests applying constant strain rate and cyclic loads. Most importantly, they include a variety of loading situations such as tensile and bending loads and combinations of normal and shear components. The analyses determine the visco-elastic material properties and the micro-structural effects, which are responsible for damage and failure of the FRP structure in a comprehensive way. The detailed analysis of the damage and failure effects by means of numerical simulation will use a two-stage (global/local) sub-modeling strategy. The required model parameters are calibrated by measured data and the simulation results are confirmed by the experimental findings. Combining experiment and simulation in this way, the common link between the failure effects caused by different loading situations will be shown and described within the help of an objective mechanical criterion, which is identified and validated during the project MIFACRIT.
Project Context and Objectives:
The project MIFACRIT is continuing a development path. It seamlessly combine experimental work with numerical simulation for in-depth analysis and identification of a failure criterion that allows quantitative assessments of damage and reliability risk in FRP structures under multi-axial load conditions. The project is structured in five work packages (WP): WP 1 - Test, WP2 - Simulation, WP3 - Criterion, WP4 - Validation, WP5 - Management. WP1 and WP4 are dominated by experiments while the other two packages WP2 and WP3 are dominated by simulation and theoretical work.
MIFACRIT followed the 'V' approach of project structure. It started with the definition and specification phase in WP1, in which the inputs of the Clean Sky working group in terms of specific requirements were adopted and the material handed out was analyzed. Then, MIFACRIT proceeded via the simulation preparation, execution, and evaluation steps (WP2 & WP3) to finally arrived at the validation phase (WP4), which provided results that are readily implementable into the larger effort of the CleanSky working group, i.e. as substantial contribution to the expansion of the lifetime assessment methodology for FRP structures accounting for arbitrary multi-axial loadings.
1. WP: Experimental Tests - Experimental Investigation of the Damage and the Fatigue Effects
Main objectives:
o Sample characterization and preparation
o Specification of standard tests and design of new tests on mixed state loading
o Specification of the analysis techniques
o Design of experiment (DoE) and execution of the stress tests according to Miyano methodology
o Determination, analysis and documentation of the failure modes
The experimental studies performed in WP1 using the material handed out by the Clean Sky consortium - IS 400, as typical epoxy based material with woven fibre reinforcement. WP1 consisted of different material tests like visco-elastic characterizations and stress tests applying constant strain rate. Depending on the baseline of the test pyramid from the DoW the tests included a variety of loading situations such as tensile, bending and shear. In the first phase of the project, the fracture of the material was documented under 3 point bending loading and the fracture behaviour of IS400 has been studied. According to the pyramid of experiment the mixed mode loading as bending and shear as well as tension and shear were realized. For this purpose, a custom made sample holder has been designed and was used in order to introduce shear forces in the tension loading situation. In this work, we have defined an experimental procedure allowing us to determine the failure mechanism of the supplied IS400 laminate. Taking inspiration in the methodology of Miyano [2], the failure obtain during the constant strain rate (CSR) and fatigue tests for different loading scenario were investigated in order to verify that the same mechanism apply in all cases. Finally, the analysis of the failure modes were performed and documented according to the requirements of numerical simulation engineers concerning WP3.
2. WP: Numerical Simulation - In-depth Analysis of the Mechanical Situation at Global and Local Stage
Main objectives:
o Modeling of the specimen (geometric and material model of the ply stacks handed out by the Clean Sky consortium) and the load cases
o Simulation of the tests conducted
In parallel to the experimental work simulation approaches were carried out to comprehend the various mechanical loading situations based on numerical evaluations and utilization of fracture and damage mechanics concepts. Work package 2 comprises the numerical concept towards the in-depth analysis of the mechanical situation at global and local stage. Under different loading situations the damage and failure effect were investigated. For this purpose an appropriate geometric model of the specimen was created and material models (specifically, visco-elastic material data of the matrix material extracted in WP1), were included in the numerical calculation.
3. WP: Failure Criterion - Objectively Capturing the Effect of the Dominating Failure Mode
Main objectives:
o Fracture / damage mechanics analysis based on the leading edge concept according to the experimental findings on the failure mode
o Identification of a set of criteria candidates and determination of the favorite criterion
o Determination of quantitative thresholds characterizing fatigue and damage in FRP structures
This deliverable addresses the numerical simulation of fracture and damage in fibre reinforced laminates to determine the threshold values at which the tested FRP material fails. The determination of the ultimate strength is often based on macro-mechanical strength theories. Experimental investigations were performed to identify the failure mechanism and the strength values under combined load conditions. In the primary step the material data were extracted by tensile test and the visco-elastic matrix material data by DMA (Dynamic Mechanical Analysis). The effective material properties were determined by tensile tests and attendant FEA simulations in both in-plane directions. The damage/fracture threshold parameters were determined by evaluating the inelastic part of force vs. displacement behavior of the tensile tests under different fiber orientations.
4. WP: Result Validation - Summarizing and Proving the Outcome of the Study
Main objectives:
o Estimation of the response of known specimen structures to new loads
o Estimation of the response of new structures to load cases already studied
o Prognosis of the fatigue lifetime of FRP structures and comparison to real tests
While all previous steps utilized more or less uniaxial loading conditions, this work package addressed the verification step by applying a combined loading situation. Tensile loading of a specifically shaped sample leads to shear loading as well as pure tensile stresses in particular regions of the specimen at the same time. The utilization of the nonlinear damage model together with all its properties as determined in WP3 now reflect the experimentally observed crack propagation processes.
5. WP: Project Management
Main objectives:
o Planning, Coordination, Reporting of the Work as well as Dissemination and Exploitation of the results
o Control of the workflow in all tasks according to DoW and timeline
o Coordination of the interaction between the WPs
o Be the contact to the technical workgroup and the joint undertaking of Clean Sky
WP5 was dedicated to the project management. It controlled the work flow and the handover between the tasks within MIFACRIT as well as the interface activities to the outside world in terms of Clean Sky working group, Clean Sky Joint Undertaking, and dissemination and exploitation of the project results.
Project Results:
1 WP: Experimental Tests - Experimental Investigation of the Damage and the Fatigue Effects
The damage and failure effect under different orientation and loads have been investigated with the aim to deduce a failure criterion for fiber reinforced polymer structures. This work package covers all the remaining planed tests and the corresponding optical and physical analysis driven on the material samples provided by the Clean Sky consortium. The WP consisted of two complementary parts. One was the mechanical characterization of the delivered material, the second the extension of the tests to mix mode loading.
Figure 1: Test pyramid
This work package shows the experimental concept towards the in-depth analysis of the mechanical situation at global and local stage. Under different loading situations the damage and failure effect were investigated. For this purpose, a first set of experiment has been driven in order to validate the ability to drive the test and gather experience with the material. Chapter 1.1.2 presents the results obtain during DOE of experiment for 3PB and validate the feasibility of the overall experimental concept. In parallel, a sample holder for combined loading has been designed according to /3/ and custom made for our dynamic tester. The concept relies on a systematic study of the X direction of the sample and chosen conditions are then explored in the other directions.
1.1 Experimental base of the pyramid
1.1.1 Dynamic mechanical analysis
Visco-elastic properties of the material are obtained from frequency sweep temperature step measurement. This gives access to time dependent measurements of the storage modulus for various temperatures. Applying the time temperature superposition principle, the master curves are constructed by shifting the curves on the logarithmic frequency scale by the shift factor A /1/. The respective values for the shift function could be fitted with the Arrhenius function Equation 1.
Equation 1
Where R is the gas constant of 8.314 103 kJ/(K mol), H is the activation energy, TREF is the reference temperature, for which room temperature is chosen, and T is the actual temperature. The obtained visco-elastic master curve can be then fitted using Equation 2 to obtain Prony parameters that can be used to implement the time temperature dependency of the storage part of the Young's modulus E' in FEM simulation software.
Equation 2
Equation 2 where E∞ is the modulus at rubbery state, Ei and tau(i) denote the i(th) of N sets of Prony parameters (modulus and time constant, respectively), and t is the time.
According to Miyano et. Al. the obtained visco-elastic shift factors can be used on CSR and Creep data obtained for different temperatures to build the CSR and Creep master curves.
This master curves being used to build a fatigue master curve base on fatigue measurements obtained at various loading ratio and temperature. This fatigue master curve is then of great use as it allows to predict the lifetime of the FRP structure under consideration.
1.1.2 Static Tester (CSR)
CSR measurements where done on a static tester (DMA 2000+ from Metravib) using a similar method as describe by Miyano in /4/. Samples were placed in the tester in static 3 point bending mode and measured at different loading speeds for various temperatures. The master curve is then built by shifting the isothermal curves along the time axis. The same procedure was then applied on samples with different fiber orientation (0°, 90° and 45°). The resulting maximal strength is shown on Figure2. X and Y direction show some differences in the strength values but the failure observed after the test looks very similar. The 45° sample on the other hand shows little to no failure as the glass fibers are not perpendicular to the load direction and do not reach their rupture point.
Figure 2: CSR curves measured at different speed and temperature and resulting master curve for IS400, 5Ply.
Figure 3: Maximal strength different material orientation for IS400, 5 ply at measured at room temperature
1.2 Step two of the experimental pyramid
1.2.1 Realization of mix mode loading
Based on the previous results and in order to fulfil the proposed test pyramid, a specific sample holder was designed (Figure 4) and fabricated according to /3, 4/. Design and realization had been executed in parallel with the characterization work.
Figure 4: Engineering detail drawing and mounted sample holder for mix mode loading
The second kind of samples to realize mixed mode loading is depicted in Figure 5. The aim is to introduce shear loading by changing the sample geometry by drilling 10 mm holes in the sample that are placed 1,31 mm from each other on a 45° line on the sample.
Figure 5: Sample for tension-shear loading – sketch and mounted sample
1.2.2 Results I
Figure 4 depicts the experimental set-up with clamped IS400 test sample (see also Figure 5). The load angles 15°, 30° and 45° are realized in this test series.
Figure 6: Top view onto the 1-ply (left), cross section of 1-ply sample with tension direction in y (right)
Table 1 gives a review over the performed experiments. The tests were operated at room temperature with a displacement speed of 10-4, 10-5, 10-6 m/s and a preload of 3 N.
Table 1: Review over the performed experiments inclusive position of break
Table 2: Averaged force and displacement results
Figure 7: Force-displacement curves
Figure 8: View on fracture
1.2.3 Results II
In this test series samples with a width of 10 mm were investigated under optical observation and the loading angle was set to 45°. In this case 1-ply and 5-ply samples were included. The following image sequence (Figure 9) shows the progress of the crack through an 1-ply sample. To avoid cracks in the clamping region the samples have to provide with an initial crack with a length of the half of the width. In those conditions proper crack propagation could be observed.
Figure 9: Crack propagation in a 1-ply sample
The second image sequence (Figure 10) shows the progress of the crack through a 5-ply sample. Here, an initial crack of 2/3 of the sample’s width was necessary to reach crack propagation because of the machine’s load limit of 500 N.
Figure 10: Crack propagation in a 5-ply sample
The shear loading could be proved by digital image correlation (DIC). Pictures (Figure 11) show the displacement of the fiber texture. Picture 1 is the reference picture depicting the fabric in the unloading state and picture 2 the fabric under loading. The analysis of the two states by digital image correlation based on the difference between the grey scale values resulted in the in-plane displacement field as shown in picture 3.
Figure 11: Digital image correlation on a 1-ply sample during mixed mode loading
1.2.4 Results III
In this series, the tests were driven on samples with holes in order to induce shear component using the sample geometry in a tension test. For this purpose, the samples where specially prepared using laser cutting technics in order to minimize the edge effect on the holes. Samples were then placed in the tension clamps and force was applied until sample breaks.
Force displacement curves were recorded and in the same time the experiment was recorded using normal camera and high speed camera. The movies made with the normal camera were treated using image correlation software and correlate with the force displacement curve in order to obtain a 2D mapping of the displacement field on the sample. This was done for samples with fibber orientation 0° (Figure 12) and 45° (Figure 13).
Figure 12: Digital image correlation of tension shear sample with 0° fibber orientation
Figure 13: Digital image correlation of tension shear sample with 45° fibber orientation
Analysis of the high speed camera movies and optical analysis of the broken samples gives a unique picture of the fracture mechanism. As the force applied increase, the matrix will first fracture in many places, weakening the structure. After, the fracture will find its way to the nearest fibber bundle perpendicular to the applied tension and will follow this bundle. Ultimately, the fibbers in the direction of the applied force will rupture.
1.3 Conclusion
In the light of the latest experiments, it was possible to determine that the matrix fails first, then the fracture find its way through the nearest bundle of fibber perpendicular to the load. This failure mechanism can now be implemented in the simulation.
The detailed test DOE set up has been fulfilled within the scheduled timeframe and result delivered for simulation. This include: realization of a Mix-mode sample holder, samples with special geometry for tension-shear test, tension test and mixed mode loading test conditions according to the DoW and optical analysis of the fractured samples.
Therefore, Failure mode assessment - was achieved within the scheduled timetable according to the DoW.
2 WP: Numerical Simulation - In-depth Analysis of the Mechanical Situation at Global and Local Stage
This work package “Numerical models are finalized and input data is delivered” shows the numerical concept towards the in-depth analysis of the mechanical situation at global and local stage. Under different loading situations the damage and failure effect are investigated with the aim to deduce a failure criterion for fiber reinforced polymer (FRP) structures.
2.1 Failure simulation
The FE program ABAQUS provides numerical possibilities to investigate failure and damage in FRP structures /5/. Cohesive elements are used to model behavior of delamination and the ABAQUS damage model is used to predict behaviour of the fiber reinforced epoxy layer.
Figure 14: Unidirectional lamina
The modelling approach bases on a homogenized elastic orthotropic material model for fiber reinforced epoxy layers (non-woven) that takes into account 4 different modes of failure:
o fiber rupture in tension;
o fiber buckling and kinking in compression;
o matrix cracking under transverse tension and shearing; and
o matrix crushing under transverse compression and shearing
Figure 14 shows a single layer whereat the layer are modelled as crossed but non-woven.
The stiffness response regarding failure can be formulated as σ = Cd ε with Cd as in Equation 3.
Equation 3
The approach follows the work of Camanho et al., Hashin and Matzenmiller et al. /7-10/ and is implemented in the commercial FEM-code ABAQUSTM see the manual /6/.
2.1.1 Failure of Fiber-Reinforced Epoxy Layers – ABAQUS™ UMAT-material model
The approach is introduced into the FE-code via an extra user-material subroutine (Figure 15).
Figure 15: Failure of fiber reinforced epoxy layers – ABAQUS™ user routine /6/
This subroutine realizes damage initiation and evolution in the fiber and damage in the epoxy matrix.
Fiber
The damage in the fiber is initiated when the criterion in Equation 4 and Equation 5 is reached.
Equation 4
Equation 5
The fiber damage evolves with df as in formula (Equation 6):
Equation 6
Epoxy matrix
Similarly, damage initiation in the matrix is governed by the criterion (Equation 7).
Equation 7
The evolution law of the matrix damage is described by Equation 8.
Equation 8
The formulation (Equation 9) combines stiffness and stiffness degradation in an effective elasticity matrix and during progressive damage the effective elasticity matrix is reduced by the two damage variables df and dm, as follows:
Equation 9
2.1.2 Failure of Fiber-Reinforced Epoxy Layers – 3-Point Bending Example
The properties for the involved materials have been taken as in Table 3.
Table 3: material properties
The fiber orientation is defined by material orientation coordinate systems in alternating order. Figure 16 shows the symmetric model of the 3-point bending test.
Figure 16: Simulation model (10 plies) of the 3-point bending test
Following results ABAQUS delivers:
STRESSES/STRAINS etc.
STATEV(1) damage variable df
STATEV(2) damage variable dm
STATEV(3) regularized damage variable dfv
STATEV(4) regularized damage variable dmv
DAMAGE propagation
First results for a 10 ply lay-up plus upper and lower resin layer under 3-point bending show the damage parameters for both damage modes.
Figure 17 represents the damage parameter df. The elements in which the parameter df exceed a value of 0.96 are damaged (red colored elements). In this way, Figure 18 demonstrates the matrix damage.
Figure 17: Fiber damage occurs
Figure 18: Matrix damage occurs
One of the primary results – the force vs. displacement curves (Figure 19) – allow for adapting the damage initialization properties much better. These results should be seen as intermediate results in order to investigate and check the approach.
Figure 19: Failure of fiber reinforced epoxy layers – intermediate result
Figure 20: Element plot
Figure 21: Maximum principle stress
Omitting all elements with damage parameters greater than 0.96 clarifies the damage process but also the necessity of enhancing the damage properties as well as the specimen towards one of the 10-ply specimens investigated experimentally. These results give a better understanding about the damage evolution process and can be utilized to enhance the damage evolution description when compared to experimentally found damage zones/paths.
Figure 22: Maximum principle stress
2.2 Conclusion
It could be demonstrate that the commercial FE code ABAQUS employed in this work package affords the possibilities of providing the necessary methods and results. Global results as stress and strains extracted and damage occurs after adjustment of the damage parameters as observed in the experimental tests. Hence, the model setup was realized within the time frame defined in the DoW. The model calibration and simulation of the stress tests has been achieved within the frame of the project.
3 WP: Failure Criterion - Objectively Capturing the Effect of the Dominating Failure Mode
This work package addressed the numerical simulation of fracture and damage in fibre-reinforced laminates to determine the threshold values at which the tested FRP material fails. According to WP1 and the performed experiments, numerical investigations followed corresponding to the DoW.
3.1 Common characteristic of fracture and damage under different loads
The nature of composite material behavior when subjected to constant strain rate loading as performed in WP1 is of basic interest for predicting lifetime of the FRP (fiber reinforced plastics) structures. The failure simulation adopted in WP1 includes the prominent damage mechanism as fiber damage under tensile and compressive loading and matrix damage under combined tension/compression and shear loading situations.
In the attempt of finding a proper mechanical criterion for the crack initiation in IS-400 structures, the scenarios have been extracted from the observations - see Figure 23:
Figure 23: Crack propagation in a composite layup under bending load
3.2 Tensile experiments to determine common damage characteristics
Tensile tests (see specimen with sample and FE-model representation in Figure 24) with different specimen orientations regarding the tension axis with 1-ply specimens were performed up to the complete rupture point. Similar FE-models have been set up together with a DoE (Design of Experiment with 4 values per property) to determine:
1. Elastic constants (Young’s modulus in 1-direction (longitudinal), Young’s modulus in 2-direction (transversal), Poisson ration in plane of fibers, Poisson ration out of plane, shear modules in-plane and out of plane --> in FE-simulations a maximum of 0.1 mm elongation is used to stay in elastic, undamaged region. The DoE varied the Young’s modules as well as the in-plane shear modulus, 4 samples each and 4 loading angles.
2. Failure threshold values (failure stress in 1-direction and tension, failure stress in 1-direction and compression, same properties for 2-direction, failure stress in in-plane shear, fracture energy in matrix and fiber --> in FE-simulations additional loading points with elongations of 0.15 mm, 0,2 mm and 0.3 mm are to pick out for comparison. First results comparing the force vs. displacement curves for 4 specimen angles are shown in Figure 25.
Figure 24: Specimen and sample holder (left) and FE-model representation (right)
Figure 25: First results comparing the force vs. displacement curves for 4 specimen angles
3.3 Fracture and damage mechanics approach
The determination of the ultimate strength is often based on macro-mechanical strength theories such as maximum stress or strain theories for example the Tsai-Wu and Hashin Failure Criterion. The Tsai-Wu Criterion is a quadratic, interactive stress-based criterion that identifies a failure, but does not distinguish between different modes of failure. In contrast, the Hashin failure criterion indeed starts with the same terms of the stress tensor, but then decomposes into four different modes of failure tensile and compressive fiber failure as well as tensile and compressive matrix failure. Here, failure due to tension, compression and combinations with shear loading /7-10/ is considered – see also explanations of the underlying damage model in WP1.
A requirement in using these strength theories there is the definition of the strength parameters only by means of experiments on corresponding specimen. Another complicacy concerning the failure in FRPs is to predict both the failure mode and in which component the failure initiates /5/. Thereto, comprehensive experimental investigations were performed to identify the failure mechanism and the strength values under combined load conditions. In the primary step the material data extracted by tensile test and the visco-elastic matrix material data by DMA (Dynamic Mechanical Analysis).
3.3.1 Finite element model - material data
The FE (finite element) model using in the failure simulation is shown in Figure 24. Thereby, the fiber orientation follows the definition of the material orientation coordinate system in alternating order. An effective orthotropic material behavior of the fiber reinforced polymer composite is involved in the FE (finite element) simulations. The different distances of the fiber bundles in the plane directions are realized by corresponding effective orthotropic material properties of the ply.
The effective material properties were determined by tensile tests and attendant FEA-simulations in both in-plane directions.
Table 4: Orthotropic material data applied in the FE model
3.3.2 Finite element model - threshold properties
The damage/fracture threshold parameters are determined by evaluating the inelastic part of force vs. displacement behavior of the tensile tests under different fiber orientations – see Figure 25. Table 5 summarizes the resulting threshold parameter for use within the utilized material model.
Table 5: Orthotropic material data applied in the FE model
Figure 26: Force vs. displacement vs. angle of tension
Figure 27: Force at 0.1 mm displacement vs. angle of tension taking sample holder compliance into account
3.4 Conclusion
The work in WP3 consumed a huge amount of man power and computing resources. At least the man power could be reduced by:
o Setting up an automated procedure that includes the FE-modeling work, the sample holder compliance fitting procedure, the elastic and the fracture/damage property detection.
o The machine and sample holder compliance should be clearly determined prior to further experiments. Clamping conditions have to be enhanced, too. Initially, the large number of simulation experiments within the DoE did not reflect all initial stiffness’s – neither the highest force at a loading angle of 0 degree nor the lowest force for 45 degree oriented tension – see Figure 26. But, taking the sample holder compliance into account allowed to fit all the FEA results to the experimentally found forces at a displacement of 0.1 mm – see Figure 27. Adapted elastic properties see Table 4.
o A further DoE explaining the dependences of several points of the force vs. displacement curves (see Figure 25) on threshold values of fiber and matrix damage was performed with 3 sample values per threshold parameter, 3 loading points and 4 loading angles. The functional representation of these dependences allowed to find the wanted parameters whenever, with parameter associated different and not finally verified accuracy.
4 WP: Result Validation - Summarizing and Proving the Outcome of the Study
4.1 Combined loading within a double punched specimen
In order to better reflect the nature of composite material behavior when subjected to combined loading a double whole specimen was created, tailor-made and experimentally investigated under pure tensile loading conditions up to the full rupture load. The corresponding FE-model (see Figure 28) utilizes all the adopted material and damage properties as determined in WP 3 with 2 different fiber orientations: tension angle (y-axis) oriented fibers and 45 degree rotated fiber orientation. All geometrical and load settings have been adapted to the experimental conditions.
Figure 28: Clamped double punched specimen (left) and FE mesh with boundary condition hints
4.2 Results and discussion
As to see in Figure 29 for fiber orientation 0° and in Figure 31 for fiber orientation 45° for instance, the fiber and matrix failure measures indicate the same failure regions in experiment and FE-simulation. In FE-results SDV1 and SDV2 characterize the degree of damage. They range from 0 (undamaged) to 1 (completely damaged). A closer look onto the simulation results explains – that
1. The fibers are not completely disrupted (SDV1 >1) while
2. The matrix is completely broken within the red zones, the region between the wholes, especially.
3. The damaged zones do not completely follow the fiber orientations (as to see in experiment) which is acceptable a result of the underlying homogenized orthotropic material behaviour.
Figure 29: Damaged sample with 0° fiber orientation – experimentally observed damage pattern (upper picture), fiber failure measure in FEA (lower left picture) and matrix failure measure (lower right picture)
Figure 30: Tension-Shear samples with 0° fiber orientation after testing
The samples show a good reproducibility of the results and good agreement between simulation and reality. It also picture accurately the chronological fracture propagation (outside first, between the holes last) as observed on high speed movies. During experiment, the fracture goes through the fiber bundle on both sample sides, following a straight line whereas in the simulation, a random path is pictured (Figure 29). This could be due that in the model the fiber plies lie next to each other, whereas in reality the fiber bundles are tightly interwoven.
Figure 31: Damaged sample with 45° fiber orientation – experimentally observed damage pattern (upper picture), fiber failure measure in FEA (lower left picture) and matrix failure measure (lower right picture)
Figure 32: Tension-Shear samples for four 45° fiber orientation after testing
The samples show a good reproducibility of the results and a great agreement between simulation and reality even for the chronological appearance of the fractures (middle first outside last).
4.3 Conclusion
The realized procedure of capturing elastic properties as well as failure/damage properties of one-ply and multiply composites is in principal working. First testing samples showing combined loading stress situations in dedicated local areas have been experimentally investigated by simple tensile testing up to the point of complete rupture. Suitable FE-models have been set up and simulated taking into account the captured elastic properties as well as failure/damage properties from previous work packages. The final failure pattern and also the follow up of damage/crack propagation trough the specimens reflected by the simulation results. Whilst these results are in a good agreement with experiments further enhancements are necessary to improve the reliability of all captured parameters – the shear stress related properties especially. Dedicated experiments for shear loading could overcome the current uncertainties regarding this data.
References:
[1] S. Rzepka et al; Accelerated fatigue testing methodology for reliability assessments of fiber reinforced compo-site polymer materials in micro/nano systems; EuroSimE 2011
[2] Miyano, Y., Nakada, M., and Nishigaki, K., “Prediction of long-term fatigue life of quasi-isotropic CFRP laminates for aircraft use”. 3rd International Conference on Fatigue of Composites. International Journal of Fatigue 28, 10 (2006/10), 1217–1225
[3] Li Qing-fen, Qi Gui-ying, Yan Sheng-yuan, Buchholz F.-G. “Computational Fracture Analyses of a Compact Tension Shear (CTS) Specimen with an inclined Crack Plane.” Key engineering materials 385-387 (2008) 741-744
[4] El-Assal, A.M. Khashaba, U.A. “Fatigue analysis of unidirectional GFRP composites under combined bending and torsional loads”, Composite Structures 79 (2007) 599–605
[5] SIMULIA (ABAQUS) Manuals (V. 6.11) Dassault Systemes Simula Corp., Providence, RI, USA, 2011
[6] Mollenhauer D. et al., “Simulation of discrete damage in composite Overheight Compact Tension specimens”. Composites Part A 43 (2012), 1667–1679.
[7] Camanho, P. P., and C. G. Davila, “Mixed-Mode Decohesion Finite Elements for the Simulation of Delamination in Composite Materials,” NASA/TM-2002–211737, pp. 1–37, 2002
[8] Hashin, Z., “Failure Criteria for Unidirectional Fiber Composites,” Journal of Applied Mechanics, vol. 47, pp. 329–334, 1980
[9] Hashin, Z., and A. Rotem, “A Fatigue Criterion for Fiber-Reinforced Materials,” Journal of Composite Materials, vol. 7, pp. 448–464, 1973
[10] Matzenmiller, A., J. Lubliner, and R. L. Taylor, “A Constitutive Model for Anisotropic
Potential Impact:
The main final results comprise on the one hand the in depth understanding of typical failure modes in FRP and on the other hand the quantitative determination of a mechanical failure criterion. This mechanical criterion enables us in further projects to assess the fatigue status of a particular FRP structure and to predict its lifetime under more real loading situations. The acquired knowledge will be used to develop more realistic models, which will allow making more realistic lifetime predictions at a minimum time. The experimental and simulation knowledge gather throughout the project (combine loading test followed with high speed camera and in depth analysis using FEM simulation) are precious assets that will be further developed within our company. Moreover, based on our new experience, further synergies may arise, which will result in customer-specific requests or further R&D contracts. As a result of combining the experience of prior services provided to automotive industry with the technological requirements of energy-efficient sandwich composite structures for aerospace industry, an extension of AMITRONICS’ portfolio will further developed within BMWi project “moZat”.
List of Websites:
The development of a website wasn’t part of the project task. However, for dissemination purposes project results will be published under the beneficiary’s website at http://www.amitronics.de/unternehmensbereiche/Amitronics+Project(se abrirá en una nueva ventana).