Structural Fracture Mechanics
Encyclopedia
Structural Fracture Mechanics is the field of structural engineering
concerned with the study of load-carrying structures that includes one or several failed or damaged components. It uses methods of analytical solid mechanics
, structural engineering, safety engineering
, probability theory
, and catastrophe theory
to calculate the load and stress in the structural components and analyze the safety of a damaged structure.
There is a direct analogy between Fracture Mechanics
of solid and Structural Fracture Mechanics:
There are different causes of the first component failure:
1) mechanical overload
, fatigue (material)
, unpredicted scenario, etc.
2) “human intervention” like unprofessional behavior or a terrorist attack.
There are two typical scenarios:
A. A localized failure does NOT cause immediate collapse of the entire structure.
B. The entire structure fails immediately after one of its components fails.
If the structure does not collapse immediately there is a limited period of time until the catastrophic structural failure
of the entire structure. There is a critical number of structural elements that defines whether the system has reserve ability or not.
Safety engineers use the failure of the first component as an indicator and try to intervene during the given period of time to avoid the catastrophe of the entire structure. For example, “Leak-Before-Break” methodology means that a leak will be discovered prior to a catastrophic failure of the entire piping system occurring in service. It has been applied to pressure vessels, nuclear piping, gas and oil pipelines, etc.
The methods of Structural Fracture Mechanics are used as checking calculations to estimate sensitivity of a structure to its component failure.
The failure of a complex system with parallel redundancy can be estimated based on probabilistic properties of the system elements. The model supposes that failure of several elements causes neighboring elements overloading. The model equation (1) shows the relationship between local and external stresses. The equation (1) is similar to the cusp catastrophe behavior. The theory predicts reserve ability of the complex system and the critical external stress.
Structural engineering
Structural engineering is a field of engineering dealing with the analysis and design of structures that support or resist loads. Structural engineering is usually considered a specialty within civil engineering, but it can also be studied in its own right....
concerned with the study of load-carrying structures that includes one or several failed or damaged components. It uses methods of analytical solid mechanics
Solid mechanics
Solid mechanics is the branch of mechanics, physics, and mathematics that concerns the behavior of solid matter under external actions . It is part of a broader study known as continuum mechanics. One of the most common practical applications of solid mechanics is the Euler-Bernoulli beam equation...
, structural engineering, safety engineering
Safety engineering
Safety engineering is an applied science strongly related to systems engineering / industrial engineering and the subset System Safety Engineering...
, probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, and catastrophe theory
Catastrophe theory
In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry....
to calculate the load and stress in the structural components and analyze the safety of a damaged structure.
There is a direct analogy between 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...
of solid and Structural Fracture Mechanics:
| Fracture Mechanics | Structural Fracture Mechanics | |
|---|---|---|
| Model | Solid with a crack | Multi-component structure with a failed component |
| Defect driving force | 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... |
Overload stress |
| System property | Fracture toughness Fracture 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... |
Reserve ability / Structural robustness |
There are different causes of the first component failure:
1) mechanical overload
Mechanical overload
The failure or fracture of a product or component in a single event is known as mechanical overload. It is a common failure mode, and may be contrasted with fatigue, creep, rupture, or stress relaxation. The terms are used in forensic engineering and structural engineering when analysing product...
, fatigue (material)
Fatigue (material)
'In materials science, fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. The nominal maximum stress values are less than the ultimate tensile stress limit, and may be below the yield stress limit of the material.Fatigue occurs...
, unpredicted scenario, etc.
2) “human intervention” like unprofessional behavior or a terrorist attack.
There are two typical scenarios:
A. A localized failure does NOT cause immediate collapse of the entire structure.
B. The entire structure fails immediately after one of its components fails.
If the structure does not collapse immediately there is a limited period of time until the catastrophic structural failure
Structural failure
Structural failure refers to loss of the load-carrying capacity of a component or member within a structure or of the structure itself. Structural failure is initiated when the material is stressed to its strength limit, thus causing fracture or excessive deformations...
of the entire structure. There is a critical number of structural elements that defines whether the system has reserve ability or not.
Safety engineers use the failure of the first component as an indicator and try to intervene during the given period of time to avoid the catastrophe of the entire structure. For example, “Leak-Before-Break” methodology means that a leak will be discovered prior to a catastrophic failure of the entire piping system occurring in service. It has been applied to pressure vessels, nuclear piping, gas and oil pipelines, etc.
The methods of Structural Fracture Mechanics are used as checking calculations to estimate sensitivity of a structure to its component failure.
The failure of a complex system with parallel redundancy can be estimated based on probabilistic properties of the system elements. The model supposes that failure of several elements causes neighboring elements overloading. The model equation (1) shows the relationship between local and external stresses. The equation (1) is similar to the cusp catastrophe behavior. The theory predicts reserve ability of the complex system and the critical external stress.
See also
- Catastrophic failureCatastrophic failureA catastrophic failure is a sudden and total failure of some system from which recovery is impossible. Catastrophic failures often lead to cascading systems failure....
- Catastrophe theoryCatastrophe theoryIn mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry....
- 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...
- Nuclear safetyNuclear safetyNuclear safety covers the actions taken to prevent nuclear and radiation accidents or to limit their consequences. This covers nuclear power plants as well as all other nuclear facilities, the transportation of nuclear materials, and the use and storage of nuclear materials for medical, power,...
- Progressive collapseProgressive collapseA building undergoes progressive collapse when a primary structural element fails, resulting in the failure of adjoining structural elements, which in turn causes further structural failure, similar to a house of cards....
- Safety engineeringSafety engineeringSafety engineering is an applied science strongly related to systems engineering / industrial engineering and the subset System Safety Engineering...
- Structural failureStructural failureStructural failure refers to loss of the load-carrying capacity of a component or member within a structure or of the structure itself. Structural failure is initiated when the material is stressed to its strength limit, thus causing fracture or excessive deformations...