FRACTURE:

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

The fracture of a solid almost always occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops in this case perpendicular to the surface of displacement, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially to the surface of displacement, it is called a shear crack, slip band, or dislocation.

The word fracture is often applied to bones of living creatures (that is, a bone fracture), or to crystals or crystalline materials, such as gemstones or metal. Sometimes, in crystalline materials, individual crystals fracture without the body actually separating into two or more pieces. Depending on the substance which is fractured, a fracture reduces strength (most substances) or inhibits transmission of light (optical crystals).

A detailed understanding of how fracture occurs in materials may be assisted by the study of fracture mechanics.

A fracture is also the term used for a particular mask data preparation procedure within the realm of integrated circuit design that involves transposing complex polygons into simpler shapes such as trapezoids and rectangles.

Ductile and Brittle Metal Characteristics

Ductile metals experience observable plastic deformation prior to fracture.  Brittle metals experience little or no plastic deformation prior to fracture.  At times metals behave in a transitional manner – partially ductile/brittle.

Ductile fracture has dimpled, cup and cone fracture appearance.  The dimples can become elongated by a lateral shearing force, or if the crack is in the opening (tearing) mode.

Brittle fracture displays either cleavage (transgranular) or intergranular fracture. This depends upon whether the grain boundaries are stronger or weaker than the grains.

The fracture modes (dimples, cleavage, or intergranular fracture) may be seen on the fracture surface and it is possible all three modes will be present of a given fracture face.

clip_image001

Schematics of typical tensile test fractures are displayed above.

Brittle Fractures

Brittle fracture is characterized by rapid crack propagation with low energy release and without significant plastic deformation.  The  fracture may have a bright granular appearance.  The fractures are generally of the flat type and chevron patterns may be present. 

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Ductile Fractures

Ductile fracture is characterized by tearing of metal and significant plastic deformation.  The ductile fracture may have a gray, fibrous appearance.  Ductile fractures are associated with overload of the structure or large discontinuities.

Fracture strength

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Stress vs. strain curve typical of aluminum
1.
Ultimate tensile strength
2. Yield strength
3. Proportional limit stress
4. Fracture
5. Offset strain (typically 0.2%)

Fracture strength, also known as breaking strength, is the stress at which a specimen fails via fracture. This is usually determined for a given specimen by a tensile test, which charts the stress-strain curve (see image). The final recorded point is the fracture strength.

Ductile materials have fracture strength lower than the ultimate tensile strength (UTS), whereas in brittle materials the fracture strength is equivalent to the UTS. If a ductile material reaches its ultimate tensile strength in a load-controlled situation,[Note 1] it will continue to deform, with no additional load application, until it ruptures. However, if the loading is displacement-controlled, the deformation of the material may relieve the load, preventing rupture.

If the stress-strain curve is plotted in terms of true stress and true strain the curve will always slope upwards and never reverse, as true stress is corrected for the decrease in cross-sectional area. The true stress on the material at the time of rupture is known as the breaking strength. This is the maximum stress on the true stress-strain curve, given by point 1 on curve B.

Types

Brittle fracture

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Brittle fracture in glass.

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Fracture of an aluminum crank arm. Bright: brittle fracture. Dark: fatigue 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)

clip_image007

where: –

clip_image008 is the Young’s modulus of the material,

clip_image009 is the surface energy, and

clip_image010 is the equilibrium distance between atomic centers.

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

image 

(For sharp cracks)

where: –

clip_image012 is the loading stress,

clip_image013 is half the length of the crack, and

clip_image014 is the radius of curvature at the crack tip.

Putting these two equations together, we get

clip_image015

Looking closely, we can see that sharp cracks (small clip_image014[1]) and large defects (large clip_image013[1]) 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.

Ductile fracture:

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Ductile failure of a specimen strained axially.

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Schematic representation of the steps inductile fracture (in pure tension).

In ductile fracture, extensive plastic deformation (necking) takes place before fracture. The termsrupture or ductile rupture describe 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 favorable 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 behavior 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:

image

The three fracture modes.

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

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

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

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.

Griffith’s Theory:

The Griffiths equation describes the relationship between applied nominal stress and crack length at fracture, i.e. when it becomes energetically favorable for a crack to grow.  Griffith was concerned with the energetic of fracture, and considered the energy changes associated with incremental crack extension.

For a loaded brittle body undergoing incremental crack extension, the only contributors to energy changes are the energy of the new fracture surfaces (two surfaces per crack tip) and the change in potential energy in the body.  The surface energy term (S) represents energy absorbed in crack growth, while the some stored strain energy (U) is released as the crack extends (due to unloading of regions adjacent to the new fracture surfaces).  Surface energy has a constant value per unit area (or unit length for a unit thickness of body) and is therefore a linear function of (crack length), while the stored strain energy released in crack growth is a function of (crack length)2, and is hence parabolic.  These changes are indicated in the figure below:

clip_image022

The next step in the development of Griffith’s argument was consideration of the rates of energy change with crack extension, because the critical condition corresponds to the maximum point in the total energy curve, i.e. dW/da = 0, where a = a*.  For crack lengths greater than this value (under a given applied stress), the body is going to a lower energy state, which is favorable, and hence fast fracture occurs.  dW/da = 0 occurs when dS/da = dU/da.  The sketch below shows these energy rates, or differentials with respect to a.

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R is the resistance to crack growth (= dS/da) and G is the strain energy release rate (= dU/da).

When fracture occurs, R = G and we can define Gcrit as the critical value of strain energy release, and equate this to R.  Hence Gcrit represents the fracture toughness of the material.  In plane stress the Griffith equation is:

clip_image024

where, to get the fracture stress in MPa (the standard SI engineering unit), the critical strain energy release rate is in N/m, E is in N/m2, and a is in m.  This provides an answer in N/m2 (Pa), which needs to be divided by 106 to get the standard engineering unit of MPa.  In plane strain:

image

Cleavage Fracture

Cleavage fracture by definition occurs along crystallographic planes in each grain fractured.

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