Strain energy release rate
Encyclopedia
Strain energy release rate (or energy release rate) is the energy
dissipated
during fracture
per unit of newly created fracture surface area. This quantity is central to fracture mechanics
because the energy that must be supplied to a crack
tip for it to grow must be balanced by the amount of energy dissipated due to the formation of new surfaces and other dissipative processes such as plasticity
.
For the purposes of calculation, the energy release rate is defined as
where
is the potential energy available for crack growth and 
is the crack area (crack length for two-dimensional problems). The units of 
are J/m2.
The energy release rate failure criterion
states that a crack will grow when the available energy release rate
is greater than or equal to a critical value 
The quantity
is the fracture energy and is considered to be a material property which is independent of the applied loads and the geometry of the body.
) involving cracks that move in a straight path, the mode I stress intensity factor
(
) is related to the energy release rate (
) by
where
is the Young's modulus
and
for plane stress and 
for plane strain.
Therefore the energy release rate failure criterion may also be expressed as
where
is the mode I fracture toughness
.
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
dissipated
Dissipation
In physics, dissipation embodies the concept of a dynamical system where important mechanical models, such as waves or oscillations, lose energy over time, typically from friction or turbulence. The lost energy converts into heat, which raises the temperature of the system. Such systems are called...
during fracture
Fracture
A fracture is the separation of an object or material into two, or more, pieces under the action of stress.The word fracture is often applied to bones of living creatures , or to crystals or crystalline materials, such as gemstones or metal...
per unit of newly created fracture surface area. This quantity is central to fracture mechanics
Fracture mechanics
Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture.In...
because the energy that must be supplied to a crack
Fracture
A fracture is the separation of an object or material into two, or more, pieces under the action of stress.The word fracture is often applied to bones of living creatures , or to crystals or crystalline materials, such as gemstones or metal...
tip for it to grow must be balanced by the amount of energy dissipated due to the formation of new surfaces and other dissipative processes such as plasticity
Plasticity
Plasticity may refer to:Science* Plasticity , in physics and engineering, plasticity is the propensity of a material to undergo permanent deformation under load...
.
For the purposes of calculation, the energy release rate is defined as
where
is the potential energy available for crack growth and is the crack area (crack length for two-dimensional problems). The units of are J/m2.The energy release rate failure criterion
Failure theory (material)
Failure theory is the science of predicting the conditions under which solid materials fail under the action of external loads. The failure of a material is usually classified into brittle failure or ductile failure . Depending on the conditions most materials can fail in a brittle or ductile...
states that a crack will grow when the available energy release rate
is greater than or equal to a critical value The quantity
is the fracture energy and is considered to be a material property which is independent of the applied loads and the geometry of the body.Relation to fracture toughness
For two-dimensional problems (plane stress, plane strain, antiplane shearAntiplane shear
Antiplane shear or antiplane strain is a special state of strain in a body. This state of strain is achieved when the displacements in the body are zero in the plane of interest but nonzero in the direction perpendicular to the plane...
) involving cracks that move in a straight path, the mode I stress intensity factor
Stress Intensity Factor
The stress intensity factor, K, is used in fracture mechanics to predict the stress state near the tip of a crack caused by a remote load or residual stresses. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion...
(
) is related to the energy release rate () bywhere
is the Young's modulusYoung's modulus
Young's modulus is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. In solid mechanics, the slope of the stress-strain...
and
for plane stress and for plane strain.Therefore the energy release rate failure criterion may also be expressed as
where
is the mode I fracture toughnessFracture toughness
In materials science, fracture toughness is a property which describes the ability of a material containing a crack to resist fracture, and is one of the most important properties of any material for virtually all design applications. The fracture toughness of a material is determined from the...
.
See also
- FractureFractureA fracture is the separation of an object or material into two, or more, pieces under the action of stress.The word fracture is often applied to bones of living creatures , or to crystals or crystalline materials, such as gemstones or metal...
- Fracture mechanicsFracture mechanicsFracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture.In...
- Fracture toughnessFracture toughnessIn materials science, fracture toughness is a property which describes the ability of a material containing a crack to resist fracture, and is one of the most important properties of any material for virtually all design applications. The fracture toughness of a material is determined from the...
- J integralJ integralThe J-integral represents a way to calculate the strain energy release rate, or work per unit fracture surface area, in a material. The theoretical concept of J-integral was developed in 1967 by Cherepanov and in 1968 by Jim Rice independently, who showed that an energetic contour path integral ...
- Stress intensity factorStress Intensity FactorThe stress intensity factor, K, is used in fracture mechanics to predict the stress state near the tip of a crack caused by a remote load or residual stresses. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion...