Contenido

La mayoría de los materiales usados en ingeniería muestran un comportamiento no lineal e inelástico en condiciones de funcionamiento que implican grandes cargas. En dichos materiales, las suposiciones que se hacen en la mecánica de la fractura lineal elástica pueden no cumplirse, es decir:.

Por lo tanto se necesita utilizar una teoría más general de crecimiento de la grieta en materiales con comportamiento elastoplástico que pueda tener en cuenta:.

R curve

A first approach in the direction of elasto-plastic fracture mechanics was Irwin's explanation called crack extension resistance curve or R curve. This curve represents the fact that fracture resistance increases with crack size in elasto-plastic materials. The R curve is a graph of the rate of total energy dissipation as a function of crack size and can be used to examine the slow growth processes of stable cracks and fracture. unstable. However, the R curve was not widely used in applications until the 1970s. The main reasons appear to be that the R curve depends on the geometry of the sample, and that the applied breaking force can be difficult to calculate.[2]​.

Integral J

In the mid-1960s J. R. Rice") (then at Brown University) and G.P. Cherepanov independently developed a new measure of hardness to describe the case in which there is sufficient deformation at the fracture tip so that the piece no longer obeys the linear-elastic approximation. Rice's analysis that assumes nonlinear elastic deformation (or monotonic plastic strain) is designated J integral") crack. This analysis is limited to situations in which the plastic deformation at the crack tip does not extend to the far edge of the loading part. It also requires that the assumed nonlinear elastic behavior of the material is a reasonable approximation to the shape and magnitude of the actual material loading response. The elastic-plastic failure parameter is designated J and is conventionally converted to K by equation (3.1) in the Appendix of this article. for linear-elastic behavior.

If the alloy is so hard that the region produced in front of the crack extends to the edge of the specimen before fracture, the crack no longer acts as an effective stress concentrator. Instead, the presence of the crack only serves to reduce the effective area where the load is distributed. In this regime the failure stress is conventionally assumed to be the average of the yields and fracture strength of the alloy.

Knowledge in Fracture Mechanics is necessary to predict the following problems:

Generally not all information is available and conservative hypotheses are not realistic in many cases.

Sometimes a post-mortem analysis can be performed. In the absence of overload, one can look for insufficient toughness in the material (K) or an excessive crack not detected during the inspection.

Currently, new production methods have given rise to research into superficial and internal fractures, especially in metals. Not all fractures are unstable under certain service conditions. Fracture mechanics is the analysis that attempts to discover which of these faults are safe (that is, they will not grow) and what is the maximum level of service that we can demand of the structure. The study of fractures is a relatively new science, compared to other sciences, but it is in high demand by engineers who seek to ensure that there are no failures due to breakage, which are usually the most striking for the general public.

Griffith's Fracture Theory: Storage Energy Coefficient G

For the simple case of a rectangular plate with a perpendicular crack loaded, Griffith's theory tells us that:

where is the stored energy coefficient, is the applied stress, is half the crack length, and is Young's Modulus. The storage energy coefficient can be understood as: the ratio of the energy that is absorbed for the development of the crack..

However we may also have to ES:.

If ≥ , then the crack will begin to propagate.

Griffith's theory modified by Irwin: fracture toughness

Thus a new modification to Griffith's theory of solids appeared, with a term called stress intensity appearing that replaced the energy release rate and fracture toughness replaced the surface rupture energy. Both terms simplified the energy terms used by Griffith:.

where K is the stress intensity, K is the fracture toughness that would be the maximum to be reached to reach failure, and is the Poisson ratio. It is important to note that K has different values ​​depending on whether we are measuring plane stress and plane strain. If we have a cracked plate, the plane stress will occur on the surface of the plate where the crack is located, while in the center of the thickness we will have plane strain if the thickness is large enough.

The fracture occurs when. For the special case of plane strain, it becomes and is considered a property of the material. The subscript "I" arises from the fact that there are different modes of fracture in addition to I, these are:

We must realize that the expression of equation 2.1 will be different depending on the geometry. For this reason, it is necessary to introduce a dimensionless coefficient, called Y, which will characterize the geometry of the piece under study. Thus we would have:

where Y is a function that depends on the length and width of the fracture in a sheet given by:.

for a sheet of finite thickness W (W for width in English, width) containing a crack of length 2a, or.

for a sheet of finite thickness W containing a crack of length a.

Elasto-plastic fracture mechanics theory

Since engineers began using K to characterize fracture toughness, a relationship has been used to reduce J to this:.

The way to obtain the formula is not included here, so it is recommended to look for it on external pages.

Contenido

La mayoría de los materiales usados en ingeniería muestran un comportamiento no lineal e inelástico en condiciones de funcionamiento que implican grandes cargas. En dichos materiales, las suposiciones que se hacen en la mecánica de la fractura lineal elástica pueden no cumplirse, es decir:.

Por lo tanto se necesita utilizar una teoría más general de crecimiento de la grieta en materiales con comportamiento elastoplástico que pueda tener en cuenta:.

R curve

A first approach in the direction of elasto-plastic fracture mechanics was Irwin's explanation called crack extension resistance curve or R curve. This curve represents the fact that fracture resistance increases with crack size in elasto-plastic materials. The R curve is a graph of the rate of total energy dissipation as a function of crack size and can be used to examine the slow growth processes of stable cracks and fracture. unstable. However, the R curve was not widely used in applications until the 1970s. The main reasons appear to be that the R curve depends on the geometry of the sample, and that the applied breaking force can be difficult to calculate.[2]​.

Integral J

In the mid-1960s J. R. Rice") (then at Brown University) and G.P. Cherepanov independently developed a new measure of hardness to describe the case in which there is sufficient deformation at the fracture tip so that the piece no longer obeys the linear-elastic approximation. Rice's analysis that assumes nonlinear elastic deformation (or monotonic plastic strain) is designated J integral") crack. This analysis is limited to situations in which the plastic deformation at the crack tip does not extend to the far edge of the loading part. It also requires that the assumed nonlinear elastic behavior of the material is a reasonable approximation to the shape and magnitude of the actual material loading response. The elastic-plastic failure parameter is designated J and is conventionally converted to K by equation (3.1) in the Appendix of this article. for linear-elastic behavior.

If the alloy is so hard that the region produced in front of the crack extends to the edge of the specimen before fracture, the crack no longer acts as an effective stress concentrator. Instead, the presence of the crack only serves to reduce the effective area where the load is distributed. In this regime the failure stress is conventionally assumed to be the average of the yields and fracture strength of the alloy.

Knowledge in Fracture Mechanics is necessary to predict the following problems:

Generally not all information is available and conservative hypotheses are not realistic in many cases.

Sometimes a post-mortem analysis can be performed. In the absence of overload, one can look for insufficient toughness in the material (K) or an excessive crack not detected during the inspection.

Currently, new production methods have given rise to research into superficial and internal fractures, especially in metals. Not all fractures are unstable under certain service conditions. Fracture mechanics is the analysis that attempts to discover which of these faults are safe (that is, they will not grow) and what is the maximum level of service that we can demand of the structure. The study of fractures is a relatively new science, compared to other sciences, but it is in high demand by engineers who seek to ensure that there are no failures due to breakage, which are usually the most striking for the general public.

Griffith's Fracture Theory: Storage Energy Coefficient G

For the simple case of a rectangular plate with a perpendicular crack loaded, Griffith's theory tells us that:

where is the stored energy coefficient, is the applied stress, is half the crack length, and is Young's Modulus. The storage energy coefficient can be understood as: the ratio of the energy that is absorbed for the development of the crack..

However we may also have to ES:.

If ≥ , then the crack will begin to propagate.

Griffith's theory modified by Irwin: fracture toughness

Thus a new modification to Griffith's theory of solids appeared, with a term called stress intensity appearing that replaced the energy release rate and fracture toughness replaced the surface rupture energy. Both terms simplified the energy terms used by Griffith:.

where K is the stress intensity, K is the fracture toughness that would be the maximum to be reached to reach failure, and is the Poisson ratio. It is important to note that K has different values ​​depending on whether we are measuring plane stress and plane strain. If we have a cracked plate, the plane stress will occur on the surface of the plate where the crack is located, while in the center of the thickness we will have plane strain if the thickness is large enough.

The fracture occurs when. For the special case of plane strain, it becomes and is considered a property of the material. The subscript "I" arises from the fact that there are different modes of fracture in addition to I, these are:

We must realize that the expression of equation 2.1 will be different depending on the geometry. For this reason, it is necessary to introduce a dimensionless coefficient, called Y, which will characterize the geometry of the piece under study. Thus we would have:

where Y is a function that depends on the length and width of the fracture in a sheet given by:.

for a sheet of finite thickness W (W for width in English, width) containing a crack of length 2a, or.

for a sheet of finite thickness W containing a crack of length a.

Elasto-plastic fracture mechanics theory

Since engineers began using K to characterize fracture toughness, a relationship has been used to reduce J to this:.

The way to obtain the formula is not included here, so it is recommended to look for it on external pages.