CHEM-E2105. Wood and Wood Products

Transcription

1 CHEM-E2105 Wood and Wood Products Mechanical properties II: The fracture & toughness of wood Mark Hughes 24 th February 2016

2 Toughness The worst sin in an engineering material is not lack of strength or lack of stiffness, desirable as these properties are, but lack of toughness, that is to say, lack of resistance to the propagation of cracks J.E. Gordon, The New Science of Strong Materials

3 Tension vs compression In most structures there is the need to carry tensile as well as compressive loads Brittle materials are okay in compression (mainly) as cracks are not opened Think of how, for example, masonry (brick, stone) is used in construction Tension: The Menai suspension bridge, Wales Compression: A Roman arch

4 Is toughness important? Catastrophic failure! WW II Liberty ship

5 Are tough materials always tough and vice versa? Lower the temperature and certain steels can become brittle and in some cases can lead to catastrophic failure (as in the case of the Liberty ships the failure changed from ductile to brittle when the temperature dropped in winter) Brittle materials such as glass, ceramics and certain polymers are intrinsically brittle but can be tough if combined together

6 Properties of cracks

7 Crack opening modes Opening Forward shear Anti-planar shear

8 Cracks and crack-like defects All real materials contain cracks or crack-like defects at some scale These could be macroscopic cracks or stress concentrators or stress risers such a holes or sharp changes in section The failure of the Liberty ships initiated at the corners of hatches (openings in the decks) Or they could be microscopic cracks There will be some kind of cracks or discontinuities (changes in section or in material properties) in all forms of material. Here cracks can initiate and propagate In effect cracks weaken materials. One of the best examples is the effect of fibre diameter on the strength of glass fibre. As the diameter reduces the probability of cracks on the surface diminishes and so the strength increases

9 What is the effect of a crack? These cracks result in localised stress concentrations, the magnitude of which depend upon the size and shape of the crack

10 What is the effect of a crack? If the stress concentrations are high enough, the material near the crack-tip may fail. Under certain conditions a crack may propagate catastrophically, leading to sudden failure of the material The crack-tip may, therefore, be viewed as a mechanism whereby local stresses in the material are raised sufficiently for fracture to occur

11 Cracks Stress concentration is dependent upon the shape of the crack Can be modelled as an ellipse As the crack tip radius approaches zero (i.e. very sharp ratio of major to minor axis is high) then the theoretical stress concentration approaches infinity (Source: Piggott, 1980) max 1 2 a b

12 Properties of heterogeneous materials: crack-blunting and crackdeflection

13 More about cracks (Source: Piggott, 1980) (Cook & Gordon 1964)

14 Interface Crack-stopping mechanisms Wood contains multiple interfaces at several hierarchical levels!

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16 Multiple interfaces

17 Fracture and energy

18 Toughness of materials (Source Hull and Clyne 1996)

19 Energy & fracture To break a material you need to do work on it! In other words you need to supply energy When a material is placed under load it is deformed The stored strain energy is available to propagate a crack think of a longbow the string is pulled back with the arrow and bends the bow. As the string is released the stored strain energy in the bow is converted to kinetic energy in the arrow If you need to do a lot of work to propagate a crack then the material is tough (Image:

20 Energy & fracture Another way of looking at it is that if the material can absorb large amounts of energy when fracturing then it is likely to be tough If the material can absorb more energy when a crack advances than can be supplied by the stored strain energy (change in potential), then the crack will stop advancing Measuring energy absorption during fracture is a convenient method of measuring the toughness of a material. This is why impact tests such as the Charpy test are so popular

21 Measurement of toughness Charpy or Izod tests provide a measure to toughness under impact conditions Work of fracture measured by loss of energy of a swinging pendulum Impact strength expressed as energy absorbed by specimen over fracture surface area The Charpy impact test

22 Stress concentrations and energy So, cracks create stress concentrations in a material that can raise the local stress sufficiently to cause failure However, energy is needed to drive the crack So, both stress and energy are important in fracture In 1920 A.A. Griffiths proposed a thermodynamic explanation for fracture and started the science of fracture mechanics

23 When strain energy is released at a faster rate that it is absorbed, the crack becomes unstable

24 Griffiths and fracture mechanics Griffiths (1920) linked the failure stress ( F ) of a material with the energy required to create new crack surfaces (surface energy for truly brittle material) and, a c, the critical crack length (1) This was later extended to include tougher materials. In these, the surface energy term ( S ) is supplemented by other energy absorption mechanisms (see later) The energy release rate, G, is derived from the Griffith s equation (2) The fracture energy (G c ) analogous to in the Griffith s equation (3) S F 2 S E ac E is Young s modulus S 1/ 2 2 is the work of fracture ( is the surface energy) S G F 2. a E GC E a 1/ 2 (1) (2) (3)

25 Stress intensity The stress state ( intensity ) at the crack-tip can be described by mathematical function of the form K app l Y app Where is the nominal applied stress, l the crack length and Y is a dimensionless constant, known as the K- calibration. The K-calibration depends upon the ratio of crack length to specimen thickness, b. K-calibrations usually take the form of a polynomial: 2 3 Y c c c c Where: l b

26 Equivalence of stress based and energy based fracture criteria A constant K, the stress intensity factor (units of MN m -3/2 ) characterises the crack-tip stress-strain conditions: G K E G K v E (in plane stress) (in plane strain) Where: v is Poisson s ratio

27 Fracture in wood Stefan Winter

28 Crack propagation directions

29 Beware! Assumptions are based on linear elastic material behaviour linear elastic fracture mechanics Does this apply to wood? Wood is orthotropic Highly heterogeneous

30 Dependence of fracture toughness on crack propagation direction (Source: Ashby et al, 1980)

31 Energy absorption mechanisms There are several mechanisms implicated in energy absorption during fracture the fracture of composites. These are: Matrix deformation and fracture Fibre fracture Interfacial debonding Frictional sliding and fibre pull-out The contribution that each of the energy absorbing mechanisms makes to the overall toughness of the composite varies, depending upon the composite system involved and the properties of the phases This is similarly true with wood

32 Work of fracture of wood The work of fracture of wood is ~ kj m -2, however: The intrinsic toughness of cell wall material across the cell wall is approx kj m -2 The intrinsic toughness of cell wall material along the cell wall approx kj m -2 These are much lower than wood itself The difference is due to energy absorbing mechanisms such as fibre pull-out (approx. 1.6 kj m -2 ) and Pseudo plastic buckling of cell wall which can account for 90% of overall work of fracture

33 Pseudo-plastic buckling of the cell wall Observations that wood pulp fibre collapsed inwards during tensile testing, showing a distinct yield point, with post yield extension being significant, indicating large energy absorption Hypothesis was tested by making glass and carbon fibre analogues of wood and testing these Showed the dependence of work of fracture of the winding angle

34 Dependence of work of fracture on microfibril angle (Source: Reiterer et al, 2001)

35 (Source: Reiterer et al, 2001)

36 (Source: Reiterer et al, 2001)

37 Fractured hemp fibre

38 Measuring fracture toughness in wood (Source: Ashby et al, 1980)

39 References and further reading A. REITERER, H. LICHTENEGGER, P. FRATZL, S. E. STANZL-TSCHEGG, Deformation and energy absorption of wood cell walls with different nanostructure under tensile loading, JOURNAL OF MATERIALS SCIENCE 36 (2001) Ashby, M.F., Easterling, K.E., Harrysson, R. and Maiti, S.K. (1985). The Fracture Toughness of Woods. Proc. R. Soc. Lond. A, 398: Jeronimidis, G., (1980). The Fracture Behaviour of Wood and the Relations Between Toughness and Morphology. Proc. R. Soc. Lond. B, 208: Piggott, M.R. (1980). Load-Bearing Fibre Composites. Pergamon, Oxford Cook, J. and Gordon, J.E. (1964). A Mechanism for the Control of Crack Propagation in All-Brittle Systems. Proc. Roy. Soc. Lond. A, 282: Hull, D. and Clyne, T.W. (1996). An Introduction to Composite Materials. Cambridge University Press, Cambridge, UK. Griffith, A.A. (1920). The Phenomenon of Rupture and Flow in Solids. Phil. Trans. R. Soc. Lond. A, 221: J.M. Dinwoodie (2000). Timber: its nature and behaviour