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Metallurgical Engineering

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Fracture

A fracture is the (local) separation of an object or material into two, or more, pieces under the action of stress.

Types

(i) Brittle fracture

In brittle fracture, no apparent plastic deformation takes place before fracture. In brittle crystalline materials, fracture can occur by cleavage as the result of tensile stress acting normal to crystallographic planes with low bonding (cleavage planes). In amorphous solids, by contrast, the lack of a crystalline structure results in a conchoidal fracture, with cracks proceeding normal to the applied tension.

The theoretical strength of a crystalline material is (roughly)

where: -

E is the Young's modulus of the material,

is the surface energy, and

is the equilibrium distance between atomic centres.

On the other hand, a crack introduces a stress concentration modelled by

(For sharp cracks)

where: -

is the loading stress,

a is half the length of the crack, and

is the radius of curvature at the crack tip.

Putting these two equations together, we get

Looking closely, we can see that sharp cracks (small ) and large defects (large ) both lower the fracture strength of the material.

Recently, scientists have discovered supersonic fracture, the phenomenon of crack motion faster than the speed of sound in a material. This phenomenon was recently also verified by experiment of fracture in rubber-like materials.

(ii) Ductile fracture

In ductile fracture, extensive plastic deformation (necking) takes place before fracture. The terms rupture or ductile rupture describes the ultimate failure of tough ductile materials loaded in tension. Rather than cracking, the material "pulls apart," generally leaving a rough surface. In this case there is slow propagation and an absorption of a large amount energy before fracture.

Many ductile metals, especially materials with high purity, can sustain very large deformation of 50–100% or more strain before fracture under favourable loading condition and environmental condition. The strain at which the fracture happens is controlled by the purity of the materials. At room temperature, pure iron can undergo deformation up to 100% strain before breaking, while cast iron or high-carbon steels can barely sustain 3% of strain.

Because ductile rupture involves a high degree of plastic deformation, the fracture behaviour of a propagating crack as modelled above changes fundamentally. Some of the energy from stress concentrations at the crack tips is dissipated by plastic deformation before the crack actually propagates.

The basic steps are: void formation, void coalescence (also known as crack formation), crack propagation, and failure, often resulting in a cup-and-cone shaped failure surface.

Crack separation modes

There are three ways of applying a force to enable a crack to propagate:

i. Mode I crack – Opening mode (a tensile stress normal to the plane of the crack)

ii. Mode II crack – Sliding mode (a shear stress acting parallel to the plane of the crack and perpendicular to the crack front)

iii. Mode III crack – Tearing mode (a shear stress acting parallel to the plane of the crack and parallel to the crack front)

Crack initiation and propagation accompany fracture. The manner through which the crack propagates through the material gives great insight into the mode of fracture. In ductile materials (ductile fracture), the crack moves slowly and is accompanied by a large amount of plastic deformation. The crack will usually not extend unless an increased stress is applied. On the other hand, in dealing with brittle fracture, cracks spread very rapidly with little or no plastic deformation. The cracks that propagate in a brittle material will continue to grow and increase in magnitude once they are initiated. Another important mannerism of crack propagation is the way in which the advancing crack travels through the material. A crack that passes through the grains within the material is undergoing transgranular fracture. However, a crack that propagates along the grain boundaries is termed an intergranular fracture.