Composites reinforced with cellulose based fibres

Publisher Summary This chapter describes the mixed mode cracking in layered materials. There is ample experimental evidence that cracks in brittle, isotropic, homogeneous materials propagate such that pure mode I conditions are maintained at the crack tip. An unloaded crack subsequently subject to a combination of modes I and II will initiate growth by kinking in such a direction that the advancing tip is in mode I. The chapter also elaborates some of the basic results on the characterization of crack tip fields and on the specification of interface toughness. The competition between crack advance within the interface and kinking out of the interface depends on the relative toughness of the interface to that of the adjoining material. The interface stress intensity factors play precisely the same role as their counterparts in elastic fracture mechanics for homogeneous, isotropic solids. When an interface between a bimaterial system is actually a very thin layer of a third phase, the details of the cracking morphology in the thin interface layer can also play a role in determining the mixed mode toughness. The elasticity solutions for cracks in multilayers are also elaborated.

Mixed mode cracking in layered materials

High-entropy alloys are equiatomic, multi-element systems that can crystallize as a single phase, despite containing multiple elements with different crystal structures. A rationale for this is that the configurational entropy contribution to the total free energy in alloys with five or more major elements may stabilize the solid-solution state relative to multiphase microstructures. We examined a five-element high-entropy alloy, CrMnFeCoNi, which forms a single-phase face-centered cubic solid solution, and found it to have exceptional damage tolerance with tensile strengths above 1 GPa and fracture toughness values exceeding 200 MPa·m(1/2). Furthermore, its mechanical properties actually improve at cryogenic temperatures; we attribute this to a transition from planar-slip dislocation activity at room temperature to deformation by mechanical nanotwinning with decreasing temperature, which results in continuous steady strain hardening.

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A fracture-resistant high-entropy alloy for cryogenic applications

Graphene based materials: Past, present and future

This paper deals with the general problem of crack extension in a combined stress field where a crack can grow in any arbitrary direction with reference to its original position. In a situation, when both of the stress-intensity factors,k
1,k
2 are present along the crack front, the crack may spread in any direction in a plane normal to the crack edge depending on the loading conditions. Preliminary results indicate that the direction of crack growth and fracture toughness for the mixed problem of Mode I and Mode II are governed by the critical value of the strain-energy-density factor,S
cr. The basic assumption is that crack initiation occurs when the interior minimum ofS reaches a critical value designatedS
cr. The strain-energy-density factorS represents the strength of the elastic energy field in the vicinity of the crack tip which is singular of the order of 1/r where the radial distancer is measured from the crack front. In the special case of Mode I crack extensionS
cr is related tok
1c alone asS
cr = (κ − 1)k

 1
 2
 /8μ. In general,S takes the quadratic forma
1 1
k
1 + 2a
1 2
k
1
k
2 +a
2 2
k
2 whose critical value is assumed to be a material constant. The analytical predictions are in good agreement with experimental data on the problem of an inclined crack in plexiglass and aluminum alloy specimens. The result of this investigation provides a convenient procedure for determining the critical crack size that a structure will tolerate under mixed mode conditions for a given applied stress.

Strain-energy-density factor applied to mixed mode crack problems

Plastic rotation factors (rp) for three-point bend and compact tension specimens were obtained for a range of normalized crack depths (a/W) from 0.25 to 0.88 and power law hardening materials. The theoretical slip-line field solutions were used for non-strain hardening materials (i.e., n = ∞) and the Kumar-German-Shih finite element plastic displacement solutions for strain hardening materials (i.e., n 5 and are in reasonable agreement with those values recommended by ASTM Subcommittee E24.08 for calculation of crack tip opening displacements in these two types of specimens. For n ≤ 5 the error in rp becomes appreciably large.

Plastic Rotation Factors of Three-Point Bend and Compact Tension Specimens

The effect of hydrostatic stress on the growth of voids from inclusions located near the tips of deep and shallow notches in three-point bend specimens is analysed using slip-line field theory and the Rice-Tracey void growth model. The analysis explains qualitatively the observed dependence of the crack tip opening displacement δi at the initiation of a ductile tear in low carbon steel on the hydrostatic stress. Although a plot of the experimental values of δi normalised by the inclusion spacing against the inclusion spacing/size ratio do not agree well with the theory, the plot is a promising means of determining experimentally the dependence of δi on hydrostatic stress for any particular steel.

On the relationship between crack tip opening displacement at the initiation of a ductile tear in low carbon steel, hydrostatic stress, and void growth

In this paper, energy dissipation rate D vs. Δa curves in ductile fracture are predicted using a ‘conversion’ between loads, load-point displacements and crack lengths predicted by NLEFM and those found in real ELPL propagation. The NLEFM/ELPL link was recently discovered for the DCB testpiece, and we believe it applies to other cracked geometries. The predictions for D agree with experimental results. The model permits a crack tip toughness R(Δa) which rises from Jc and saturates out when (if) steady state propagation is reached after a transient stage in which all tunnelling, crack tip necking and shear lip formation is established. JR is always greater than the crack tip R(Δa) and continues to rise even after R(Δa) levels off.



The analysis is capable of predicting the usual D vs. Δa curves in the literature which have high initial values and fall monotonically to a plateau at large Δa. It also predicts that D curves for CCT testpieces should be higher than those for SENB/CT, as found in practice. The possibility that D curves at some intermediate Δa may dip to a minimum below the levelled-off value at large Δa is predicted and confirmed by experiment. Recently reported D curves that have smaller initial D than the D-values after extensive propagation can also be predicted. The testpiece geometry and crack tip R(Δa) conditions required to produce these different-shaped D vs. Δa curves are established and confirmed by comparison with experiment.



The energy dissipation rate D vs. Δa is not a transferable property as it depends on geometry. The material characteristic R(Δa) may be the ‘transferable property’ for scaling problems in ELPL fracture. How it can be deduced from D vs. Δa curves (and by implication, JR vs. Δa curves) is established.

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Prediction of the energy dissipation rate in ductile crack propagation

Analysis of fatigue crack growth in a rubber-toughened epoxy resin: effect of temperature and stress ratio

Measurements of the plane strain fracture toughness KIc of sintered steels have frequently been invalid because the requirement that Pmax/PQ<1.1 (where Pmax = maximum load and PQ=load used to calculate KIc) has not been met. We show that the reason for the criterion not being met is that sintered steels have a considerable crack growth resistance KR. Values obtained in the past for KIc probably have been over-estimates of the initiation value of the crack growth resistance Ki and under-estimates of the maximum crack growth resistance K∞. The important point is that the assessment of the toughness of sintered steels by a single parameter is not appropriate. Test methods to determine the crack growth resistance of sintered steels are discussed. Crack growth, which is difficult to detect by visual observation, can be determined by compliance techniques. Because of the porous nature of sintered steel, fatigue cracks are unnecessary at the tip of the notch and indeed are undesirable as they can easily cause errors in toughness measurements through inadvertent overloading. The thickness requirement for plane strain measurements can also be relaxed.

Brian Cotterell

Papers

Plastic Rotation Factors of Three-Point Bend and Compact Tension Specimens

On the relationship between crack tip opening displacement at the initiation of a ductile tear in low carbon steel, hydrostatic stress, and void growth

Prediction of the energy dissipation rate in ductile crack propagation

Analysis of fatigue crack growth in a rubber-toughened epoxy resin: effect of temperature and stress ratio

Fracture parameters for sintered steels