Christensen Failure Criterion
Encyclopedia
Failure criteria
for isotropic materials has been a long standing problem. Despite many historical attempts, there have not been any successful general forms that span the range from ductile
to brittle materials. A new failure criterion that aims to do so has been recently developed. The isotropic material failure theory
by Christensen has a two property form calibrated by the uniaxial tensile
and compressive strengths T
and C 
. It is based upon a sequence of seven related archive journal papers, the first of which was published in 1997. The website describing it in considerable detail was started in 2007, and it was first utilized by eFunda in 2008.
The overall failure criterion is composed of two separate subcriteria representing competitive failure mechanisms. when expressed in principal stress components, it is given by :
Polynomial Invariants Failure Criterion
For
Coordinated Fracture Criterion
For
The geometric form of is that of a paraboloid in principal stress space. The fracture
criterion (applicable only over the partial range 0 ≤ T/C ≤ 1/2 ) cuts slices off the paraboloid, leaving three flattened elliptical surfaces on it. The fracture cutoff is vanishingly small at T/C=1/2 but it grows progressively larger as T/C diminishes.
The organizing principle underlying the theory is that all isotropic materials admit a distinct classification system based upon their T/C ratio. The comprehensive failure criterion and reduces to the Mises criterion at the ductile
limit, T/C = 1. At the brittle limit, T/C = 0, it reduces to a form that cannot sustain any tensile components of stress.
Many cases of verification have been examined over the complete range of materials from extremely ductile to extremely brittle types. Also, examples of applications have been given. Related criteria distinguishing ductile from brittle failure behaviors have been derived and interpreted.
Applications have been given by Ha to the failure of the isotropic, polymeric matrix phase in fiber composite material
s.
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...
for isotropic materials has been a long standing problem. Despite many historical attempts, there have not been any successful general forms that span the range from ductile
Ductility
In materials science, ductility is a solid material's ability to deform under tensile stress; this is often characterized by the material's ability to be stretched into a wire. Malleability, a similar property, is a material's ability to deform under compressive stress; this is often characterized...
to brittle materials. A new failure criterion that aims to do so has been recently developed. The isotropic material failure theory
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...
by Christensen has a two property form calibrated by the uniaxial tensile
Tensile strength
Ultimate tensile strength , often shortened to tensile strength or ultimate strength, is the maximum stress that a material can withstand while being stretched or pulled before necking, which is when the specimen's cross-section starts to significantly contract...
and compressive strengths T
and C . It is based upon a sequence of seven related archive journal papers, the first of which was published in 1997. The website describing it in considerable detail was started in 2007, and it was first utilized by eFunda in 2008.The overall failure criterion is composed of two separate subcriteria representing competitive failure mechanisms. when expressed in principal stress components, it is given by :
Polynomial Invariants Failure Criterion
For
Coordinated Fracture Criterion
For
The geometric form of is that of a paraboloid in principal stress space. The 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...
criterion (applicable only over the partial range 0 ≤ T/C ≤ 1/2 ) cuts slices off the paraboloid, leaving three flattened elliptical surfaces on it. The fracture cutoff is vanishingly small at T/C=1/2 but it grows progressively larger as T/C diminishes.
The organizing principle underlying the theory is that all isotropic materials admit a distinct classification system based upon their T/C ratio. The comprehensive failure criterion and reduces to the Mises criterion at the ductile
Ductility
In materials science, ductility is a solid material's ability to deform under tensile stress; this is often characterized by the material's ability to be stretched into a wire. Malleability, a similar property, is a material's ability to deform under compressive stress; this is often characterized...
limit, T/C = 1. At the brittle limit, T/C = 0, it reduces to a form that cannot sustain any tensile components of stress.
Many cases of verification have been examined over the complete range of materials from extremely ductile to extremely brittle types. Also, examples of applications have been given. Related criteria distinguishing ductile from brittle failure behaviors have been derived and interpreted.
Applications have been given by Ha to the failure of the isotropic, polymeric matrix phase in fiber composite material
Composite material
Composite materials, often shortened to composites or called composition materials, are engineered or naturally occurring materials made from two or more constituent materials with significantly different physical or chemical properties which remain separate and distinct at the macroscopic or...
s.
See also
- Strength of materialsStrength of materialsIn materials science, the strength of a material is its ability to withstand an applied stress without failure. The applied stress may be tensile, compressive, or shear. Strength of materials is a subject which deals with loads, deformations and the forces acting on a material. A load applied to a...
- Failure theory (material)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...
- Von Mises yield criterion
- Mohr–Coulomb theory