Czél, Gergely

Jalalvand, Meisam

Wisnom, Michael R.

Hybridisation is one of the approaches to introduce pseudo-ductility to brittle composite materials. In this approach, two layers with different types of fibre are combined and a new stress-strain response which depends on the material properties of the components and thickness of the constituents is produced. In this paper, an analytical method of predicting the damage progress of UD hybrids is proposed which has an acceptable accuracy and is significantly faster than numerical methods such as FE. A new chart called a "damage mode map" is produced that relates the configuration of a UD hybrid to its predicted damage scenario straightaway. This map has been found to be a very useful tool to find the optimum configuration in designing new hybrid composites.</p

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                          Jalalvand, M., Czél, G., & Wisnom, M. R. (2014). Damage mode maps andparametric study of thin UD hybrid composites. In ECCM16 - 16th EuropeanConference on Composite Materials: Seville, Spain, 22-26 June 2014.European Conference on Composite Materials, ECCM.Peer reviewed versionLink to publication record in Explore Bristol ResearchPDF-documentUniversity of Bristol - Explore Bristol ResearchGeneral rightsThis document is made available in accordance with publisher policies. Please cite only the publishedversion using the reference above. Full terms of use are available:http://www.bristol.ac.uk/pure/about/ebr-terms.htmlTake down policyExplore Bristol Research is a digital archive and the intention is that deposited content should not beremoved. However, if you believe that this version of the work breaches copyright law please contactopen-access@bristol.ac.uk and include the following information in your message:• Your contact details• Bibliographic details for the item, including a URL• An outline of the nature of the complaintOn receipt of your message the Open Access Team will immediately investigate your claim, make aninitial judgement of the validity of the claim and, where appropriate, withdraw the item in questionfrom public view.ECCM16 - 16TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Spain, 22-26 June 2014  1     DAMAGE MODE MAPS AND PARAMETRIC STUDY OF THIN UD HYBRID COMPOSITES    Meisam Jalalvand*, Gergely Czél, Michael R. Wisnom  Advanced Composites Centre for Innovation and Science, University of Bristol, UK  *M.Jalalvand@Bristol.ac.uk  Keywords: Hybrid, Thin-ply, Damage, Analytical method   Abstract  Hybridisation is one of the approaches to introduce pseudo-ductility to brittle composite materials. In this approach, two layers with different types of fibre are combined and a new stress-strain response which depends on the material properties of the components and thickness of the constituents is produced. In this paper, an analytical method of predicting the damage progress of UD hybrids is proposed which has an acceptable accuracy and is significantly faster than numerical methods such as FE. A new chart called a “damage mode map” is produced that relates the configuration of a UD hybrid to its predicted damage scenario straightaway. This map has been found to be a very useful tool to find the optimum configuration in designing new hybrid composites.   1. Introduction   Brittle failure is one of the main problems of fibrous composite materials that obliges designers to use high safety margins and results in reducing the weight saving that potentially could be achieved. The aim of the HiPerDuCT programme is to investigate different approaches of introducing more gradual failure or pseudo-ductility into conventional composite materials and thin ply hybridisation is one of the applied methods.  To determine promising hybrid configurations for obtaining optimal pseudo ductile response, it is necessary to not only understand the damage modes of UD hybrid laminates as the constituents of a hybrid composite structure but also to find a simple method to check the effect of different parameters on the final response. In [1],  a FE-based method was proposed to understand the details of the damage process in different UD hybrids. The proposed approach was in good agreement with the experimental results of [2]. In this paper, a new analytical method is outlined to make the process of finding new optimised UD hybrids easier and faster. In fact, the previously proposed FE-based approach was good for modelling of specific UD hybrid configurations but expensive for extracting general trends and design guidelines for the UD hybrids. Here, a simple analytical method with an acceptable accuracy is presented to comply with this need.   Any hybrid composite includes at least two different types of fibre. The material which has a lower failure strain (e.g. carbon in a glass/carbon hybrid) will be called the low strain material (LSM) and the one with higher failure strain (e.g. glass in the glass/carbon hybrid) will be called the high strain material (HSM). ECCM16 - 16TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Spain, 22-26 June 2014  2   2. Damage modes  The possible damage modes of UD hybrid composites are known to be one or a combination of (i) fragmentation (multiple fracture) of the low strain material, (ii) delamination and (iii) failure of the high strain material. The first damage mode in a sandwich hybrid composite under uniform tension is a crack in the low strain material and it happens at the failure strain of the low strain material since there is no stress variation along the length before that. However, the subsequent damage modes depend on the configuration and material properties of the constituents and the interface. Each damage mode requires a certain stress level which can be found based on mechanics of materials and fracture mechanics. The winning damage mode is the one which needs the lowest stress level to occur.   1.1. First fracture in and fragmentation of the low strain material  Before the first failure in the low strain material, there is no strain variation along the specimen so the stress in the laminate at first fracture of the low strain material, LF@ , can be related to the strength of the low strain material, LS   as below:  LHLLHHLL@LFtttEtESE  (1)  where HE and LE are the fibre direction modulus of the high and low strain materials. Ht and Lt  are also the thickness of the high and low strain material as shown in Figure 1. This figure indicates a hybrid with a crack in the low strain material and the stress variation along the length in each component. Within a lc/2 distance from the crack, the stress in the low strain material is lower than the far field stress and therefore, it is not expected to have a new crack. Since new cracks occur in areas with no stress variation along the length, the fragmentation stress level at which multiple cracks take place within the low strain material can be found using equation 1, provided the strength of the material is uniformly constant along the length.   Figure 1- Schematic of low strain material with a crack and stress variation in high and low strain matrials    LSL 2tL x HSLtL/tH x SLEH/EL lc F,  tH ECCM16 - 16TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Spain, 22-26 June 2014  3   1.2. Delamination  Figure 2 indicates a quarter of a 2L length of the hybrid specimen where the low strain material in the middle has already fragmented and there is also an interlaminar crack. Since the delaminated part of the low strain material does not contribute to load transfer, it is not shown. The length of the delaminated and un-delaminated parts is L1 and L2 respectively and tH and tL are half of the total thickness of the high and low strain material. In the present paper, a uniform distribution of damage is assumed over the length of the specimen so the shown part of the hybrid in Figure 2 can be treated as a Representative Volume Element (RVE) of the whole specimen.    Figure 2- A quarter of a representative volume element of the hybrid with a L1 length delamination  The stiffness of the RVE, Ktot, depends on the length of the delamination and the stiffness of the delaminated and un-delaminated parts.  The relationship between the stiffness of these parts and the elastic modulus of the high and low strain material (EH and EL) and their thickness (tH and tL), can be written as follows:  122121totLDLDDDK  (2)  Where HH1 tED  and LLHH2 tEtED  . The total strain energy of the RVE can be found from equation (2) and differentiating with respect to crack length (L1) gives the energy release rate at the stress level, del , where delamination propagates. Delamination propagates when the strain energy release rate is equal to GIIc since the crack propagates due to shear loading. Equation (3) indicates the stress level in the laminate at which delamination propagates.   1221IIcLHdelDDD DGtt 21  (3)  1.3. Failure of the high strain material   The RVE shown in Figure 2 can also be used for failure analysis of the high strain material. The simplest failure criterion is to check the largest value of stress in the high strain material and compare it with its strength, SH. Since the low strain material is not contributing to load transfer, the stress in part 1 of the high stress material is higher than in part 2. If a stress concentration factor of Kt is assumed around the crack tip, the maximum/critical value of longitudinal stress in the high strain material, max_H , becomes as follows, where  is the average stress in the laminate.  L tH tL L2 L1 F δ ECCM16 - 16TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Spain, 22-26 June 2014  4  HLHtHtttKmax_  (4)  To consider the size effect in the prediction procedure, Weibull random distribution theory, used in [3], can be applied  by simply replacing the stress distribution with the right hand side of equation (4). This results in the following equation for predicting high strain material failure  )(@LHmHtHHFttVtKS   (5) where m is the Weibull distribution modulus and V is the volume of the high strain material.   3. Damage mode map   As described in section 2, the first damage in a sandwich hybrid is a crack in the low strain material, regardless of the material properties and configurations. However, the following damage modes are different. Since the first damage is essentially similar in all of the hybrids and can be found via equation (1), the difference between the various damage processes is related to the following damage modes and the first damage mode is not discussed hereafter.   For any hybrid configuration, it is possible to calculate the values of stress for fragmentation in the low strain material ( LF@ ), delamination ( del ) and also failure in the high strain material ( HF@ ) as presented earlier. The six possible permutations of the damage process are listed in the first column of Table 1.  Based on the order of the damage modes, it is possible to predict the expected damage process.   The obtained values and associated order of damage modes rely on the assumed constraints shown in Figure 2. If failure in the HSM occurs at any stage, the calculated values of stress for the other types of damage are not valid afterwards and the damage process cannot progress to other types of damage. Furthermore, if the delamination stress is lower than the LSM fragmentation stress, there is no chance for fragmentation to develop, but the predicted failure stress for the HSM stays valid.  The expected damage process for each of the permutations is also shown in Table 1. If delamination happens after fragmentation of the LSM, interlaminar cracks initiate from the tips of the cracks in the LSM in a dispersed manner. This kind of delamination is called dispersed delamination.  ECCM16 - 16TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Spain, 22-26 June 2014  5   No. Order of required stress for damage modes Expected damage process after the initial crack in the LSM 1 HFdelLF @@    Fragmentation in LSM Dispersed delamination Failure of HSM 2 delHFLF   @@  Fragmentation of LSM Failure in HSM  3a HFLFdel @@    Single delamination Failure in HSM  3b LFHFdel @@    Single delamination Failure in HSM  4a delLFHF   @@  Failure in HSM   4b LFdelHF @@    Failure in HSM   Table 1- Summary of the expected damage modes for different stress conditions after the initial crack in the LSM  The expected damage processes in Table 1 can be categorised into four groups: (1) fragmentation in the LSM, dispersed delamination and failure in the HSM, (2) fragmentation in the LSM and failure of the HSM, (3) single delamination and failure of the HSM, and (4) premature failure of the HSM. Plotting these four regions for different configurations produces a damage-mode map. This map will be drawn in the example below.  3.1 Damage mode map of SkyFlex carbon/E-glass hybrid  To demonstrate the application of the proposed analytical approach, the combination of ultra-thin SkyFlex carbon/E-glass is selected as a case study. This UD hybrid has been extensively studied experimentally and numerically in [1], [2]. The material properties of the carbon and glass layers as well as the interface are given in Table 2. The value of stress concentration factor, Kt, was assumed equal to one for the following results. The length of the specimen was taken as L=160mm.   Hexcel 913/E-Glass[4] SkyFlex USN020A Carbon[5] Interface EH (GPa) SH (MPa) Layer thickness (mm) Weibull Modulus EL (GPa) SL (MPa) Layer thickness (mm) GIIC (N/mm) 38.7* 1350 0.144 29.3 101.7 1962 0.03 1.0 * modified value for the measured thickness of glass layer Table 2- Elastic material properties of Hexcel 913/E-glass and SkyFlex USN020A carbon prepreg   For any hybrid configuration, it is possible to find the required stress for each damage mode using equations (1), (3) and (5). When the values of required stress for all possible damage modes are found, the expected damage process of the configuration can easily be seen according to Table 1. Grouping all of the configurations with the same damage process leads to the damage mode map. For given values of relative and absolute carbon thickness, it is possible to uniquely determine any hybrid configuration. Figure 3 shows the six cases summarised in Table 1 on the damage mode map with the relative and absolute carbon thickness as the horizontal and vertical axes. The expected damage processes are schematically shown and numbered on each region of the map.   ECCM16 - 16TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Spain, 22-26 June 2014  6   Figure 3- Damage mode map for SkyFlex/E-glass hybrid  To avoid brittle failure, it is necessary to have the UD hybrid configuration away from either region 3 or 4. In region 4, the high strain material will fail straightaway after the first crack in the low strain material and in region 3, the integrity of the whole laminate is lost due to the long interlaminar cracks. However, the damage process in region 1 and 2 is gradual and pseudo-ductile. If the hybrid configuration is located in region 2, fragmentation in the low strain material occurs before HSM final failure. The hybrid configurations within region 1 have another extra damage mode, dispersed delamination, before HSM final failure which adds to the produced pseudo-ductility. Figure 4 indicates the distribution of the required stress level for each of the fragmentation, delamination and HSM final failure modes in regions 1 and 2. The value of required stress for LSM fragmentation in these two regions is lower than the other two damage modes and therefore, it is the first damage mode. The required stress level for delamination is also lower than HSM failure in region 2 so it occurs before HSM failure.    Figure 4- Damage mode map of SkyFlex carbon/E-glass hybrid including the required stress for each damage mode of UD hybrids (fragmentation, delamination and failure of HSM) 4b 4a 3b 1 2 3a ECCM16 - 16TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Spain, 22-26 June 2014  7  Figure 5 is the damage mode map of the same hybrid combination (Figure 3) with the tested specimens from [1], [2]. The specimens with similar damage mode are shown with similar markers defined on the picture. The observed damage modes [1], [2] are in good agreement with the damage mode map.   Figure 5- Comparison between the predicted damage modes using the proposed analytical method for SkyFlex carbon/E-glass hybrid and the experimental specimens[1], [2]   4. Conclusion  In this paper, an analytical method for predicting the damage process of UD hybrids was presented. Three stress criteria for the three possible damage modes in hybrids were derived and used for predicting the damage process of the UH hybrid composite. To have an overall picture of the behaviour of a material combination, the required stress for each of the possible damage modes in a hybrid have been plotted. Different regions of damage process have been shown on a damage mode map, which can give a quick overview of the optimum configurations for a certain hybrid material configuration. There was a good agreement between the damage mode map of SkyFlex carbon/E-glass hybrid and the experimental results. Such a method is useful to find the desired damage process of a specific material set quickly and therefore can be used in the design procedure for new hybrid composites.    Acknowledgement This work was funded under the EPSRC Programme Grant EP/I02946X/1 on High Performance Ductile Composite Technology in collaboration with Imperial College, London.     ECCM16 - 16TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Spain, 22-26 June 2014  8   References [1] M. Jalalvand, G. Czél, and M. R. Wisnom, “Numerical modelling of the damage modes in UD thin carbon/glass hybrid laminates,” Compos. Sci. Technol., vol. 94, pp. 39–47, Jan. 2014. [2] G. Czél and M. R. Wisnom, “Demonstration of pseudo-ductility in high performance glass-epoxy composites by hybridisation with thin-ply carbon prepreg,” Compos. Part A Appl. Sci. Manuf., vol. 52, pp. 23–30, Apr. 2013. [3] M. R. Wisnom and J. W. Atkinson, “Reduction in tensile and flexural strength of unidirectional glass fibre-epoxy with increasing specimen size,” Compos. Struct., vol. 38, no. 1–4, pp. 405–411, May 1997. [4] S. R. Hallett, “Numerical Investigation of Progressive Damage and the Effect of Layup in Notched Tensile Tests,” J. Compos. Mater., vol. 40, no. 14, pp. 1229–1245, Sep. 2005. [5] J. Fuller and M. R. Wisnom, “Damage suppression in thin ply angle-ply carbon/epoxy laminates,” in The 19th International Conference on Composite Materials, 2013.    

Damage mode maps and parametric study of thin UD hybrid composites

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Damage mode maps and parametric study of thin UD hybrid composites

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