PowerPoint presentation (1.5 MB)

Strength

Strength is the stress at failure and is normally measured in MPa (MegaPascals = GN/m²). Failure may be either a non-reversible change of state (propagation of cracks within the material) or the ultimate stress where the specimen breaks into two or more pieces.   For a unidirectional composite where the fibres have a lower tensile strain to failure than the matrix, the Kelly-Tyson model [1] to predict the ultimate strength assumes that all fibres have identical strength and that both the fibre and the matrix fail at the failure strain of the fibre:

σ_c = σ_fV_f + σ_m*(1-V_f)

σ_c = σ_fV_fsec²θ.

Failure mechanisms

• matrix cracking
• (fibre-matrix) debonding
• debonding is separation of the fibre from the matrix.  The image shows debonded glass fibres:

• delamination
  • delamination is the failure mode in which cracks propagate between the layers (lamina) of the composite.
• fibre fracture
• fibre fracture is failure of the reinforcement and normally occurs across the diameter of the fibre.  The image show a glass fibre with (unusually) a double crack running from the lower edge:

• fibre pullout
• microbuckling
  • the image below show microbuckling failure adjacent to the loading anvil from three-point flexural testing of an 8-ply [-45/90/+45/0]s 1225 gsm quadriaxial stitched non-crimp glass fabric (2 layers) fibreglass/epoxy composite

• kink bands (advanced composites only)
  • The following images [3] were provided by Soraia Pimenta of Imperial College.  The left hand image at low magnification (a) shows the crack propagating from right to left.  In consequence, the other images show (b) initial buckling of the fibres, (c) cracking at the lower edge and (d) the fully developed kink-band.

a:

b:

c:

d:

• cone of fracture (carbon fibre composites)
• in this failure, the impacted face shows little or no sign of damage yet delamination occurs in a cone of increasing diameter until fibres spall from the composite at the back face. This is known in the aerospace industry as BVID (barely visible impact damage) [4] or barely detectable impact damage.  It is normal to encourage reporting of impacts to permit non-destructive evaluation of the extent of damage.  The United States Federal Aviation Regulation FAR section 23.573 (Damage tolerance and fatigue evaluation of structure) requires "that the [composite] structure is capable of carrying ultimate load with damage up to the threshold of detectability (TOD) considering the inspection procedures employed" and "the structure must ... be able to withstand critical limit flight loads, considered as ultimate loads, with the extent of detectable damage consistent with the results of the damage tolerance evaluations".

Imetrum have taken high-speed (25,000 frames per second) video (3 MB MPEG file) of the failure of a "carbon composite material" in tension.

Fractography and microstructural characterisation

The following micrographs of fracture surfaces appear in books:

Lothar Engel et al [5]

• page 226 Figure 420: Glass fibre reinforced polyester sample failed under repeated stress loading. Long sections of glass fibre had been exposed due to vibration stresses, leaving a matrix perforated by tubes and voids. The characteristic features of dynamic fatigue fracture are long bundles of glass fibres protruding from the fracture surfaces. Resin residues adhere to these bundles. This does not occur if an identical sample is fractured by static stress.
• page 114 Figure 196 and page 114 Figure 197: The fracture surface of a glass reinforced polyester specimen was immersed in hydrofluoric acid, which completely dissolved the glass fibres without attacking the resin

Anne Roulin-Moloney [6]

• page 380 Figure 26: Impact damage - fibre breakage as well as interlaminar and transverse cracking in a CFRP plate with a high fracture energy matrix.
• page 515 Figure 20: Stress corrosion fracture surface showing directions of crack propagation
• page 516 Figure 21: Area of stress corrosion fracture surface with crack growth directions deduced from surface markings. A: nucleation areas. B-B: starter notch. C: crack growth perpendicular to overall crack growth direction.
• page 519 Figure 23: Mating areas of stress corrosion fracture surface showing post failure degradation.  A: interface failure. B: fibre splitting. C: loss of fibre end.
• page 45 Figure 1c: A Nomex® honeycomb sandwich core material viewed in the SEM.

Statistical considerations

The failure characteristics of most materials have statistical variability which is normally better modelled using Weibull statistics [7, 8] instead of normal distributions.  The use of A-Basis and B-Basis allowables to reduce risk in the structural design of composite materials and components has two statistically based tolerance bounds:

• A-Basis or T99: At least 99% of the population of material values is expected to equal or exceed this tolerance bound [9, 10] with 95% confidence (single point catastrophic failure with no-load redistribution),
• B-Basis or T90: At least 90% of the population of material values is expected to equal or exceed this tolerance bound with 95% confidence (redundant load path with load redistribution).

Multi-scale analysis on a hierarchical basis may combine micro-mechanics and macro-mechanics with finite element analysis, damage tracking, fracture and material degradation capability to analyse structures in depth [11].

Failure criteria

See Hinton et al [12] and Christensen [13].

Fracture mechanics (for homogeneous isotropic materials)

In the following analysis, a is the half-crack length, W is the component width and Y is a dimensionless parameter or function that depends on both the crack and specimen sizes and geometries, as well as the manner of load application [14].

• direction I is in the plane of the materials with direct stress normal to the crack faces,
• direction II is in the plane of the material with shear stress parallel to the crack
  
• direction III is out of the plane of the material with shear stress parallel to the crack faces

BE CAREFUL to ensure that the stress axes and the material axes are accurately specified for composite materials.  Also consider whether the failure mode is relevant to the analysis (has the crack turned to run along a fibre/matrix of interlaminar interface)?

For a more detailed description, see [15, 16].  For an excellent review of the subject in the context of composites see the paper by Williams [17].

References

1. A Kelly and WR Tyson, Tensile properties of fibre-reinforced metals: copper/tungsten and copper/molybdenum, Journal of the Mechanics and Physics of Solids, 1965, 13, 329-350.
2. RT Potter, Strength of composites, In A Kelly (editor): Concise Encyclopedia of Composite Materials, Pergamon, Oxford, 1989. ISBN 0-08-034718-5.
3. R Gutkin, ST Pinho, P Robinson, PT Curtis, Physical mechanisms associated with initiation and propagation of kink-bands, 13th European Conference on Composite Materials (ECCM13), Stockholm, 2 June 2008.
4. KB Armstrong and RT Barrett, Care and Repair of Advanced Composites, SAE International, Warrendale PA, 1998.  ISBN 0-7680-0047-5.
5. Lothar Engel, Hermann Klingele, Gottfried W Ehrenstein and Helmut Schaper (translated by MS Welling), An Atlas of Polymer Damage: Surface Examination by Scanning Electron Microscope, Wolfe Science Books, London, 1981.  ISBN 0-7234-0751-7. UOP Library
6. Anne C Roulin-Moloney, Fractography and Failure Mechanisms of Polymers and Composites, Chapman & Hall (originally Elsevier Applied Science), London, 1988.  ISBN 1-85166-296-0. UoP Library shelfmark 620.1920426 FRA.  UOP Library
7. S van der Zwaag, The concept of filament strength and the Weibull modulus, Journal of Testing and Evaluation, September 1989, 17(5), 292-298.
8. P Kittl and G Diaz, Weibull's fracture statistics, or probabilistic strength of materials: state of the art, Res Mechanica, 1988, 24(2), 99-207.
9. R Rice, R Randall, J Bakuckas and S Thompson, Development of MMPDS Handbook Aircraft Design Allowables, 7th Joint DOD/FAA/NASA Conference on Aging Aircraft, New Orleans LA, 8-11 September 2003.
10. DOT/FAA/AR-03/19, Final Report: Material Qualification and Equivalency for Polymer Matrix Composite Material System: Updated Procedure, US Department of Transportation Federal Aviation Administration - Office of Aviation Research, Washington DC, September, 2003.
11. MR Talagani, Z Gurdal, F Abdi and S Verhoef, Obtaining A-Basis and B-Basis Allowable Values for Open-Hole Specimens Using Virtual Testing, AIAAC-2007-127, 4. International Aerospace Conference, Ankara, 10-12 September 2007
12. MJ Hinton, AS Kaddour and PD Soden, Failure criteria in fibre reinforced polymer composites: the world-wide failure exercise, Elsevier, Amsterdam, 2004. ISBN 0-08-044475-x.  UOP Library
13. Richard M Christensen, Stress Based Failure Criteria for Materials Science and Engineering, 2008,
    and specifically III: Failure Criteria for Anisotropic Fiber Composite Materials.
14. WD Callister, Materials Science and Engineering - An Introduction - fifth edition, John Wiley & Sons, New York, 2000.  ISBN 0-471-32013-7.
15. Chapter 9: Analysis of Fracture, in RF Gibson, Principles of composite material mechanics, McGraw-Hill, 1994, pages 338-373. ISBN 0-07-023451-5. UOP Library
16. RJ Sanford, Principles of Fracture Mechanics, Prentice Hall, New Jersey, 2003. ISBN 0-13-092992-1.
17. JG Williams, Fracture mechanics of composite failure, Proc IMechE Part C: Journal of Mechanical Engineering Science, 1990, 204(4), 209-218.

Recommended further reading

• Lothar Engel and H Klingele, An atlas of metal damage: surface examination by scanning electron microscope. Wolfe, London, 1981. ISBN 0-7234-0750-9.
• Lothar Engel, H Klingele, GW Ehrenstein and H Schaper (translated by MS Welling), An atlas of polymer damage: surface examination by scanning electron microscope, Wolfe Science/Hanser, Munich, 1981. ISBN 0-7234-0751-7.
• AJ Kinloch and RJ Young, Fracture Behaviour of Polymers, Chapman & Hall (originally Elsevier Applied Science), London, 1983.  ISBN 0-85334-186-9. UOP Library
• JG Williams, Fracture Mechanics of Polymers, Ellis Horwood Series in Engineering Science, Chichester, 1984.  ISBN 0-85312-685-2.   UOP Library
• AC Garg and Yiu-Wing Mai, Failure mechanisms in toughened epoxy resins: a review, Composites Science and Technology, 1988, 31(3), 179-223.
• AC Roulin-Moloney - Fractography and failure mechanisms of polymers and composites, Elsevier, London & New York, 1990. ISBN 1-85166-296-0.  UOP Library
• WD Bascom and SY Gweon, Fractography and failure mechanisms of carbon fibre-reinforced composite materials, Chapter 9 in AC Roulin-Moloney (see above).
• Kimberley Dransfield, Caroline Baillie and Yiu-Wing Mai, Improving the delamination resistance of CFRP by stitching—a review, Composites Science and Technology, 1994, 50(3), 305-317.
• MR Piggott - The effect of fibre waviness on the mechanical properties of unidirectional fibre composites: a review, Composites Science and Technology, 1995, 53(2), 201-205.
• Myer Ezrin, Plastics Failure Guide: Causes and Prevention, Hanser-Gardner Publications, Cincinnati, 1996. ISBN 1-569-90184-8.  Carl Hanser Verlag, München - Germany, 1996.  ISBN 3-446-15715-8. UOP Library
• GJ Simitses - Buckling of moderately thick laminated cylindrical shells: a review, Composites Part B: Engineering, 1996, 27(6), 581-587.
• J Summerscales, Microstructural Characterisation of Fibre-Reinforced Composites, Woodhead Publishing, Cambridge, July 1998. ISBN 1-85573-240-8.   UOP Library
• Holger Thom - A review of the biaxial strength of fibre-reinforced plastics, Composites Part A: Applied Science and Manufacturing, 1998, 29(8), 869-886.
• T Kant and K Swaminathan - Estimation of transverse/interlaminar stresses in laminated composites: a selective review and survey of current developments, Composite Structures, 2000, 49(1), 65-75.
• LN McCartney - Physically based damage models for laminated composites, Proceedings of the Institution of Mechanical Engineers - Part L: Journal of Materials: Design & Applications, 2003, 217(3), 163-199.
• AO Addin, SM Sapuan, E Mahdi and M Othman - Prediction and detection of failures in laminated composite materials using neural networks - a review, Polymers and Polymer Composites, 2006, 14(4), 433-441.
• S Sridharan, Delamination behaviour of composites, Woodhead Publishing, Cambridge, 2008. ISBN-13: 978 1 84569 244 5.
• ES Greenhalgh, Failure analysis and fractography of polymer composites, Woodhead Publishing, Cambridge, 2009.  ISBN 978-1-84569-217-9.