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.

/pdf/a-fracture-resistant-high-entropy-alloy-for-cryogenic-4v6ic2t1x4.pdf

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

A solution is presented for the elastic stress intensity factors at the tip of a slightly curved or kinked two-dimensional crack. The solution is accurate to first order in the deviation of the crack surface from a straight line and is carried out by perturbation procedures analogous to those of Banichuk [1] and Goldstein and Salganik [2, 3]. Comparison with exact solutions for circular arc cracks and straight cracks with kinks indicates that the first order solution is numerically accurate for considerable deviations from straightness. The solution is applied to fromulate an equation for the path of crack growth, on the assumption that the path is characterized by pure Mode I conditions (i.e., K
II=0) at the advancing tip. This method confirms the dependence of the stability, under Mode I loading, of a straight crack path on the sign of the non-singular stress term, representing tensile stress T acting parallel to the crack, in the Irwin-Williams expansion of the crack tip field. The straight path is shown to be stable under Mode I loading for T 0.

Slightly curved or kinked cracks

In a ductile material, the total work of fracture is not a material constant and linear fracture mechanics is inappropriate. The work performed in the end region at the tip of a crack, where the fracture process takes place, is considered the essential work of fracture, and a constant for a particular sheet thickness. It is shown that this essential work can be estimated from deep edge notched tension specimens by extrapolating the straight line relationship between the work of fracture and ligament length to zero ligament length.

The essential work of plane stress ductile fracture

The essential work of fracture concept has been extended to cover ductile tearing of polymeric materials that neck before fracture. It is shown that the plane stress specific essential fracture work (we) can be obtained from deeply edge-notched tension specimens, containing either single or double notches, by extrapolating the straight line relationship between the total specific fracture work (wf) and ligament length (l) to zero ligament. In this way, specific essential fracture works have been obtained for nylon 66 and two polyethylenes. It seems that weis a material property for a given sheet thickness being independent of specimen geometry. The straight line relationship between wfand l breaks down when the ligament length to sheet thickness ratio is less than about three, since the fracture data fall in the plane stress-plane strain transition region. However, a plane strain specific essential fracture work can still be obtained by extrapolating the least squares curve of the data to zero ligament provided the thickness satisfies plane strain condition. If this condition is not satisfied a near plane strain value is obtained which is dependent upon thickness. This method is also appropriate for ductile polymers like the rubber modified polystyrenes that craze rather than neck.

On the essential work of ductile fracture in polymers

An understanding of the mechanics involved in flake formation provides an opportunity for deriving more behavioral information from flake and flake scar morphology. The mechanics of flake formation are directly relevant to the identification of prehistoric flaking techniques and stone tool use. In this paper we provide a model of flake formation that accounts for much of the variation in flake morphology. Flakes can form in a number of ways and despite popular belief they are not all of the conchoidal variety. The bending flake is common in use wear though it is often misidentified as a conchoidal flake. A third major type of flake, the compression flake, is a common product of bipolar impact. To account for the wide variation in flake morphology we follow a tripartite scheme of flake formation comprising initiation, propagation, and termination phases, within which different mechanisms can operate.

The formation of flakes

https://dr.ntu.edu.sg/bitstream/10356/98738/1/71.%20A%20Mechanical%20Assessment%20of%20Flexible%20Optoelectronic%20Devices.pdf

Brian Cotterell

Papers

Slightly curved or kinked cracks

The essential work of plane stress ductile fracture

On the essential work of ductile fracture in polymers

The formation of flakes

A mechanical assessment of flexible optoelectronic devices