Fracture mechanics is the field of
mechanicsMechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....
concerned with the study of the propagation of cracks in materials. It uses methods of analytical
solid mechanicsSolid 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...
to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to
fractureA 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...
.
In modern
materials scienceMaterials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. This scientific field investigates the relationship between the structure of materials at atomic or molecular scales and their macroscopic properties. It incorporates...
, fracture mechanics is an important tool in improving the mechanical performance of materials and components. It applies the
physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
of
stressIn continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...
and
strainIn continuum mechanics, the infinitesimal strain theory, sometimes called small deformation theory, small displacement theory, or small displacement-gradient theory, deals with infinitesimal deformations of a continuum body...
, in particular the theories of
elasticityIn physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....
and
plasticityIn physics and materials science, plasticity describes the deformation of a material undergoing non-reversible changes of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the...
, to the microscopic
crystallographic defectCrystalline solids exhibit a periodic crystal structure. The positions of atoms or molecules occur on repeating fixed distances, determined by the unit cell parameters. However, the arrangement of atom or molecules in most crystalline materials is not perfect...
s found in real materials in order to predict the macroscopic mechanical failure of bodies.
FractographyFractography is the study of fracture surfaces of materials. Fractographic methods are routinely used to determine the cause of failure in engineering structures, especially in product failure and the practice of forensic engineering or failure analysis...
is widely used with fracture mechanics to understand the causes of failures and also verify the theoretical failure predictions with real life failures.
Griffith's criterion
Fracture mechanics was developed during World War I by English aeronautical engineer,
A. A. GriffithAlan Arnold Griffith was an English engineer, who, among many other contributions, is best known for his work on stress and fracture in metals that is now known as metal fatigue, as well as being one of the first to develop a strong theoretical basis for the jet engine.-Early work:A. A...
, to explain the failure of brittle materials. Griffith's work was motivated by two contradictory facts:
- The stress needed to fracture bulk glass
Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...
is around 100 MPa (14,503.8 psi).
- The theoretical stress needed for breaking atomic bonds is approximately 10000 MPa (1,450,377.4 psi).
A theory was needed to reconcile these conflicting observations. Also, experiments on glass fibers that Griffith himself conducted suggested that the fracture stress increases as the fiber diameter decreases. Hence the uniaxial tensile strength, which had been used extensively to predict material failure before Griffith, could not be a specimen-independent material property. Griffith suggested that the low fracture strength observed in experiments, as well as the size-dependence of strength, was due to the presence of microscopic flaws in the bulk material.
To verify the flaw hypothesis, Griffith introduced an artificial flaw in his experimental specimens. The artificial flaw was in the form of a surface crack which was much larger than other flaws in a specimen. The experiments showed that the product of the square root of the flaw length (
a) and the stress at fracture (
σf) was nearly constant, which is expressed by the equation:
An explanation of this relation in terms of linear elasticity theory is problematic. Linear elasticity theory predicts that stress (and hence the strain) at the tip of a sharp flaw in a linear elastic material is infinite. To avoid that problem, Griffith developed a thermodynamic approach to explain the relation that he observed.
The growth of a crack requires the creation of two new surfaces and hence an increase in the
surface energySurface energy quantifies the disruption of intermolecular bonds that occur when a surface is created. In the physics of solids, surfaces must be intrinsically less energetically favorable than the bulk of a material, otherwise there would be a driving force for surfaces to be created, removing...
. Griffith found an expression for the constant
C in terms of the surface energy of the crack by solving the elasticity problem of a finite crack in an elastic plate. Briefly, the approach was:
- Compute the potential energy
In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...
stored in a perfect specimen under an uniaxial tensile load.
- Fix the boundary so that the applied load does no work and then introduce a crack into the specimen. The crack relaxes the stress and hence reduces the elastic energy
Elastic energy is the potential mechanical energy stored in the configuration of a material or physical system as work is performed to distort its volume or shape....
near the crack faces. On the other hand, the crack increases the total surface energy of the specimen.
- Compute the change in the free energy
The thermodynamic free energy is the amount of work that a thermodynamic system can perform. The concept is useful in the thermodynamics of chemical or thermal processes in engineering and science. The free energy is the internal energy of a system less the amount of energy that cannot be used to...
(surface energy − elastic energy) as a function of the crack length. Failure occurs when the free energy attains a peak value at a critical crack length, beyond which the free energy decreases by increasing the crack length, i.e. by causing fracture. Using this procedure, Griffith found that
where
E is the Young's modulus of the material and
γ is the surface energy density of the material. Assuming
E = 62 GPa and
γ = 1 J/m
2 gives excellent agreement of Griffith's predicted fracture stress with experimental results for glass.
Irwin's modification
Griffith's work was largely ignored by the engineering community until the early 1950s. The reasons for this appear to be (a) in the actual structural materials the level of energy needed to cause fracture is orders of magnitude higher than the corresponding surface energy, and (b) in structural materials there are always some inelastic deformations around the crack front that would make the assumption of linear elastic medium with infinite stresses at the crack tip highly unrealistic. F. Erdogan (2000)
Griffith's theory provides excellent agreement with experimental data for
brittleA material is brittle if, when subjected to stress, it breaks without significant deformation . Brittle materials absorb relatively little energy prior to fracture, even those of high strength. Breaking is often accompanied by a snapping sound. Brittle materials include most ceramics and glasses ...
materials such as glass. For ductile materials such as
steelSteel is an alloy that consists mostly of iron and has a carbon content between 0.2% and 2.1% by weight, depending on the grade. Carbon is the most common alloying material for iron, but various other alloying elements are used, such as manganese, chromium, vanadium, and tungsten...
, though the relation
still holds, the surface energy (
γ) predicted by Griffith's theory is usually unrealistically high. A group working under G. R. Irwin at the U.S. Naval Research Laboratory (NRL) during World War II realized that plasticity must play a significant role in the fracture of ductile materials.
In ductile materials (and even in materials that appear to be brittle), a
plasticA plastic material is any of a wide range of synthetic or semi-synthetic organic solids used in the manufacture of industrial products. Plastics are typically polymers of high molecular mass, and may contain other substances to improve performance and/or reduce production costs...
zone develops at the tip of the crack. As the applied
loadStructural loads or actions are forces, deformations or accelerations applied to a structure or its components.Loads cause stresses, deformations and displacements in structures. Assessment of their effects is carried out by the methods of structural analysis...
increases, the plastic zone increases in size until the crack grows and the material behind the crack tip unloads. The plastic loading and unloading cycle near the crack tip leads to the
dissipationIn 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...
of
energyIn 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...
as
heatIn physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...
. Hence, a dissipative term has to be added to the energy balance relation devised by Griffith for brittle materials. In physical terms, additional energy is needed for crack growth in ductile materials when compared to brittle materials.
Irwin's strategy was to partition the energy into two parts:
- the stored elastic strain energy which is released as a crack grows. This is the thermodynamic driving force for fracture.
- the dissipated energy which includes plastic dissipation and the surface energy (and any other dissipative forces that may be at work). The dissipated energy provides the thermodynamic resistance to fracture. Then the total energy dissipated is
where
γ is the surface energy and
Gp is the plastic dissipation (and dissipation from other sources) per unit area of crack growth.
The modified version of Griffith's energy criterion can then be written as
For brittle materials such as glass, the surface energy term dominates and
. For ductile materials such as steel, the plastic dissipation term dominates and
. For polymers close to the
glass transitionThe liquid-glass transition is the reversible transition in amorphous materials from a hard and relatively brittle state into a molten or rubber-like state. An amorphous solid that exhibits a glass transition is called a glass...
temperature, we have intermediate values of
.
Stress intensity factor
Another significant achievement of Irwin and his colleagues was to find a method of calculating the amount of energy available for fracture in terms of the asymptotic stress and displacement fields around a crack front in a linear elastic solid. This asymptotic expression for the stress field around a crack tip is
where
σij are the Cauchy stresses,
r is the distance from the crack tip,
θ is the angle with respect to the plane of the crack, and
fij are functions that are independent of the crack geometry and loading conditions. Irwin called the quantity
K the
stress 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...
. Since the quantity
fij is dimensionless, the stress intensity factor can be expressed in units of
.
When a
rigid line inclusionA rigid line inclusion, also called stiffener, is a mathematical model used in solid mechanics to describe a narrow hard phase, dispersed within a matrix material...
is considered, a similar asymptotic expression for the stress fields is obtained.
Strain energy release
Irwin was the first to observe that if the size of the plastic zone around a crack is small compared to the size of the crack, the energy required to grow the crack will not be critically dependent on the state of stress at the crack tip. In other words, a purely elastic solution may be used to calculate the amount of energy available for fracture.
The energy release rate for crack growth or
strain energy release rate may then be calculated as the change in elastic strain energy per unit area of crack growth, i.e.,
where
U is the elastic energy of the system and
a is the crack length. Either the load
P or the displacement
u can be kept fixed while evaluating the above expressions.
Irwin showed that for a mode I crack (opening mode) the strain energy release rate and the stress intensity factor are related by:
where
E is the
Young's modulusYoung'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...
,
ν is
Poisson's ratioPoisson's ratio , named after Siméon Poisson, is the ratio, when a sample object is stretched, of the contraction or transverse strain , to the extension or axial strain ....
, and
KI is the
stress 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...
in mode I. Irwin also showed that the strain energy release rate of a planar crack in a linear elastic body can be expressed in terms of the mode I, mode II (sliding mode), and mode III (tearing mode) stress intensity factors for the most general loading conditions.
Next, Irwin adopted the additional assumption that the size and shape of the energy dissipation zone remains approximately constant during brittle fracture. This assumption suggests that the energy needed to create a unit fracture surface is a constant that depends only on the material. This new material property was given the name
fracture 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...
and designated
GIc. Today, it is the critical stress intensity factor
KIc which is accepted as the defining property in linear elastic fracture mechanics.
Limitations
But a problem arose for the NRL researchers because naval materials, e.g., ship-plate steel, are not perfectly elastic but undergo significant plastic deformation at the tip of a crack. One basic assumption in Irwin's linear elastic fracture mechanics is that the size of the plastic zone is small compared to the crack length. However, this assumption is quite restrictive for certain types of failure in structural steels though such steels can be prone to brittle fracture, which has led to a number of catastrophic failures.
Linear-elastic fracture mechanics is of limited practical use for structural steels for another more practical reason. Fracture toughness testing is very expensive and engineers believe that sufficient information for selection of steels can be obtained from the simpler and cheaper
Charpy impact testThe Charpy impact test, also known as the Charpy v-notch test, is a standardized high strain-rate test which determines the amount of energy absorbed by a material during fracture. This absorbed energy is a measure of a given material's toughness and acts as a tool to study temperature-dependent...
.
Elastic–plastic fracture mechanics
Most engineering materials show some nonlinear elastic and inelastic behavior under operating conditions that involve large loads. In such materials the assumptions of linear elastic fracture mechanics may not hold, that is,
- the plastic zone at a crack tip may have a size of the same order of magnitude as the crack size
- the size and shape of the plastic zone may change as the applied load is increased and also as the crack length increases.
Therefore a more general theory of crack growth is needed for elastic-plastic materials that can account for:
- the local conditions for initial crack growth which include the nucleation, growth, and coalescence of voids or decohesion at a crack tip.
- a global energy balance criterion for further crack growth and unstable fracture.
R-curve
An early attempt in the direction of elastic-plastic fracture mechanics was Irwin's
crack extension resistance curve or
R-curve. This curve acknowledges the fact that the resistance to fracture increases with growing crack size in elastic-plastic materials. The R-curve is a plot of the total energy dissipation rate as a function of the crack size and can be used to examine the processes of slow stable crack growth and unstable fracture. However, the R-curve was not widely used in applications until the early 1970s. The main reasons appear to be that the R-curve depends on the geometry of the specimen and the crack driving force may be difficult to calculate.
J-integral
In the mid-1960s
James R. RiceJames Robert Rice is a mechanician who has made fundamental contributions to various aspects of solid mechanics. Two of his early contributions are the concept of the J-integral and an explanation of how plastic deformations localize in a narrow band. In recent years, Rice has focused on the...
(then at
Brown UniversityBrown University is a private, Ivy League university located in Providence, Rhode Island, United States. Founded in 1764 prior to American independence from the British Empire as the College in the English Colony of Rhode Island and Providence Plantations early in the reign of King George III ,...
) and G. P. Cherepanov independently developed a new toughness measure to describe the case where there is sufficient crack-tip deformation that the part no longer obeys the linear-elastic approximation. Rice's analysis, which assumes non-linear elastic (or monotonic
deformation theoryIn mathematics, deformation theory is the study of infinitesimal conditions associated with varying a solution P of a problem to slightly different solutions Pε, where ε is a small number, or vector of small quantities. The infinitesimal conditions are therefore the result of applying the approach...
plasticA plastic material is any of a wide range of synthetic or semi-synthetic organic solids used in the manufacture of industrial products. Plastics are typically polymers of high molecular mass, and may contain other substances to improve performance and/or reduce production costs...
) deformation ahead of the crack tip, is designated the
J 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 ...
. This analysis is limited to situations where plastic deformation at the crack tip does not extend to the furthest edge of the loaded part. It also demands that the assumed non-linear elastic behavior of the material is a reasonable approximation in shape and magnitude to the real material's load response. The elastic-plastic failure parameter is designated J
Ic and is conventionally converted to K
Ic using Equation (3.1) of the Appendix to this article. Also note that the J integral approach reduces to the Griffith theory for linear-elastic behavior.
Cohesive zone models
When a significant region around a crack tip has undergone plastic deformation, other approaches can be used to determine the possibility of further crack extension and the direction of crack growth and branching. A simple technique that is easily incorporated into numerical calculations is the cohesive zone model method which is based on concepts proposed independently by Barenblatt and
DugdaleDugdale is a surname, and may refer to:*Adam Dugdale , English footballer*Alan Dugdale , English footballer*Dan Dugdale , American baseball player*Edgar Dugdale Dugdale is a surname, and may refer to:*Adam Dugdale (born 1987), English footballer*Alan Dugdale (born 1952), English footballer*Dan...
in the early 1960s. The relationship between the Dugale-Barenblatt models and Griffith's theory was first discussed by Willis in 1967. The equivalence of the two approaches in the context of brittle fracture was shown by
RiceJames Robert Rice is a mechanician who has made fundamental contributions to various aspects of solid mechanics. Two of his early contributions are the concept of the J-integral and an explanation of how plastic deformations localize in a narrow band. In recent years, Rice has focused on the...
in 1968. Interest in cohesive zone modeling of fracture has been reignited since 2000 following the pioneering work on dynamic fracture by Xu and
NeedlemanAlan Needleman was born in 1944 in Philadelphia, PA and is currently the Florence Pirce Grant University Professor of Mechanics of Solids and Structures at Brown University in Providence, RI. Professor Needleman received his B.S. from the University of Pennsylvania in 1966, a M.S. and Ph.D. from...
, and Camacho and Ortiz.
Fully plastic failure
If the material is so tough that the yielded region ahead of the crack extends to the far edge of the specimen before fracture, the crack is no longer an
effective stressKarl von Terzaghi first proposed the relationship for effective stress in 1936. For him, the term ‘effective’ meant the calculated stress that was effective in moving soil, or causing displacements...
concentrator. Instead, the presence of the crack merely serves to reduce the load-bearing area. In this regime the failure stress is conventionally assumed to be the average of the yield and ultimate strengths of the material.
Engineering applications
The following information is needed for a fracture mechanics prediction of failure:
- Applied load
- Residual stress
- Size and shape of the part
- Size, shape, location, and orientation of the crack
Usually not all of this information is available and conservative assumptions have to be made.
Occasionally post-mortem fracture-mechanics analyses are carried out. In the absence of an extreme overload, the causes are either insufficient toughness (K
Ic) or an excessively large crack that was not detected during routine inspection.
Short summary
Arising from the manufacturing process, interior and surface flaws are found in all metal structures. Not all such flaws are unstable under service conditions. Fracture mechanics is the analysis of flaws to discover those that are safe (that is, do not grow) and those that are liable to propagate as cracks and so cause
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...
of the flawed structure. Ensuring safe operation of structure despite these inherent flaws is achieved through
damage toleranceDamage tolerance is a property of a structure relating to its ability to sustain defects safely until repair can be effected. The approach to engineering design to account for damage tolerance is based on the assumption that flaws can exist in any structure and such flaws propagate with usage...
analysis. Fracture mechanics as a subject for critical study has barely been around for a century and thus is relatively new. There is a high demand for engineers with fracture mechanics expertise—particularly in this day and age where engineering failure is considered 'shocking' amongst the general public.
Griffith's criterion
For the simple case of a thin rectangular plate with a crack perpendicular to the load Griffith’s theory becomes:
(1.1)
where
is the strain energy release rate,
is the applied stress,
is half the crack length, and
is the Young’s modulus. The strain energy release rate can otherwise be understood as:
the rate at which energy is absorbed by growth of the crack.
However, we also have that:
(1.2)
If
≥
, this is the criterion for which the crack will begin to propagate.
Irwin's modifications
Eventually a modification of Griffith’s solids theory emerged from this work; a term called
stress intensityStress intensity can refer to:* Stress intensity factor in fracture mechanics* Tresca effective stress in material yielding...
replaced strain energy release rate and a term called
fracture 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...
replaced surface weakness energy. Both of these terms are simply related to the energy terms that Griffith used:
(2.1)
and
(for plane stress) (2.2)
(for plane strain) (2.3)
where
KI is the
stress intensityStress intensity can refer to:* Stress intensity factor in fracture mechanics* Tresca effective stress in material yielding...
,
Kc the fracture toughness, and
is Poisson’s ratio. It is important to recognize the fact that fracture parameter
Kc has different values when measured under plane stress and plane strain
Fracture occurs when
. For the special case of plane strain deformation,
becomes
and is considered a material property. The subscript I arises because of the different ways of loading a material to enable a crack to propagate. It refers to so-called "mode I" loading as opposed to mode II or III:
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
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...
acting parallel to the plane of the crack and perpendicular to the crack front)
- Mode III crack – Tearing mode (a shear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...
acting parallel to the plane of the crack and parallel to the crack front)
We must note that the expression for
in equation 2.1 will be different for geometries other than the center-cracked infinite plate, as discussed in the article on the
stress 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...
. Consequently, it is necessary to introduce a dimensionless correction factor,
Y, in order to characterize the geometry. We thus have:
(2.4)
where
Y is a function of the crack length and width of sheet given by:
(2.5)
for a sheet of finite width
W containing a through-thickness crack of length 2
a, or
(2.6)
for a sheet of finite width
W containing a through-thickness edge crack of length
a
Elasticity and plasticity
Since engineers became accustomed to using
KIc to characterise fracture toughness, a relation has been used to reduce
JIc to it:
where
for plane stress and
for plane strain (3.1)
The remainder of the mathematics employed in this approach is interesting, but is probably better summarised in external pages due to its complex nature.
See also
- AFGROW
AFGROW is the Air Force Growth crack life prediction software tool that allows users to analyze crack initiation, fatigue crack growth, fracture, and assess the life of metallic structures. AFGROW is one of the fastest, most efficient, and user-friendly crack life prediction tools available today...
- Fracture mechanics and fatigue crack growth analysis software
- 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...
- Fatigue
'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...
- Peridynamics
Peridynamics is a formulation of continuum mechanics that is oriented toward deformations with discontinuities, especially fractures.-Purpose of peridynamics:...
(a numerical method to solve fracture mechanics problems)
- Shock (mechanics)
A mechanical or physical shock is a sudden acceleration or deceleration caused, for example, by impact, drop, kick, earthquake, or explosion. Shock is a transient physical excitation....
- Strength of glass
- Strength of materials
In 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...
- Stress corrosion cracking
Stress corrosion cracking is the unexpected sudden failure of normally ductile metals subjected to a tensile stress in a corrosive environment, especially at elevated temperature in the case of metals. SCC is highly chemically specific in that certain alloys are likely to undergo SCC only when...
- 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...
- Strain energy release rate
Strain 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...
- Structural fracture mechanics
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...
Further reading
- Davidge, R.W., Mechanical Behavior of Ceramics, Cambridge Solid State Science Series, (1979)
- Green, D., An Introduction to the Mechanical Properties of Ceramics, Cambridge Solid State Science Series, Eds. Clarke, D.R., Suresh, S., Ward, I.M. (1998)
- Lawn, B.R., Fracture of Brittle Solids, Cambridge Solid State Science Series, 2nd Edn. (1993)
- Farahmand, B., Bockrath, G.
George Eugene Bockrath was an aeronautical engineer and early researcher in fracture mechanics. He earned a BS in aeronautical engineering from the University of Michigan and began his research career as an assistant professor at The Catholic University of America in 1936...
, and Glassco, J. (1997) Fatigue and Fracture Mechanics of High-Risk Parts, Chapman & Hall.
External links