Contenido

Dependiendo del tipo de material, tamaño y geometría del objeto, y las fuerzas aplicadas, pueden resultar varios tipos de deformación. La imagen de la derecha muestra el diagrama de esfuerzo de ingeniería frente a deformación para un material dúctil típico como el acero. Pueden ocurrir diferentes modos de deformación bajo diferentes condiciones, como se puede representar usando un gráfico de deformación.

La deformación permanente es irreversible; la deformación permanece incluso después de la eliminación de las fuerzas aplicadas, mientras que la deformación temporal es recuperable, ya que desaparece después de la eliminación de las fuerzas aplicadas.

La deformación temporal también se denomina deformación elástica, mientras que la deformación permanente se denomina deformación plástica.[2]​.

elastic deformation

In civil engineering, the study of temporal or elastic deformation is applied to materials used in construction, such as concrete or steel, which are subjected to very small deformations. The phenomenon can be modeled by the theory of infinitesimal deformations, also known as theory of small deformations, theory of small displacements or theory of small displacement gradients where it is assumed that the deformations and rotations produced by the stresses are small.

For some materials, such as elastomers and polymers, subject to large strains, the engineering definition of strain is not applicable (typically restricted to strains less than 1%),[4] so these materials require other, more complex definitions of strain, such as "stretch", "logarithmic strain", "Green's strain" or "Almansi strain". Elastomers and memory metals "Thermal memory effect (metals)") such as nitinol, exhibit large ranges of elastic deformation, as does rubber. However, elasticity is not linear in these materials.

Common construction metals such as ceramics, metals, concrete and most glass show linear elasticity and a smaller elastic range. For these materials it is common to assume that elastic deformation is linear and governed by Hooke's law:

where is the applied stress, is a material constant called Young's modulus or elastic modulus, and ε is the resulting elongation. This relationship only applies in the elastic range and indicates that the slope of the stress/strain curve can be used to determine the Young's modulus () of a material. Materials laboratories use this calculation based on data obtained in tensile tests.

It should be noted that not all elastic materials undergo linear elastic deformation; some, such as concrete, gray cast iron, and many polymers, respond nonlinearly. For these materials, Hooke's law is not applicable.[5]​.

True stress and strain

Since, in practice, the change of the cross section of the material sample as it is stretched during the above deformation process is not always precisely known, the true stress-strain curve must be refitted. For small strains there is not much difference between any two measurements of stress or strain. In uniaxial tests it is common to measure the so-called engineering stress and strain and subsequently calculate other corrected measurements according to the area or instantaneous lengths of the stretched prism, which are called true stress and strain (for the regime of large strains, many other additional measures are defined that go beyond the previous ones).

To derive the stress-strain curve, we consider a prism of initial section and height and current or final section and height. Engineering deformation is defined as:

Furthermore, for an isotropic elastic material in the regime of small deformations, the change in volume is given by:.

So we have , where is the so-called Poisson's ratio that may undergo some changes throughout the test. .

Then, the true stress or Cauchy stress can be expressed as follows (using Taylor series up to first order):

Furthermore, the true strain ε can be expressed as follows:.

Then, the value is expressed as.

Therefore, we can derive the graph in terms of y as it appears in the figure to the right.

Furthermore, based on the true stress-strain curve, the region where necking begins to occur can be estimated. From the moment a visible narrowing of the section begins to appear, until the final tension is reached (when the maximum force was applied), this situation can be expressed as follows:

which in turn can be expressed as follows:

The plot shows that necking begins to appear where the reduction in area becomes much more significant compared to the change in stress. The tension is then maximized in the specific area where the narrowing appears.

Furthermore, several relationships can be deduced based on the true stress-strain curve.

1. The true stress and strain curve can be expressed by the approximate linear relationship by taking a logarithm of the true stress and strain. The relationship can be expressed as follows:

where is the stress coefficient and is the strain hardening coefficient. Typically, the value of has a range of 0.02 to 0.5 at room temperature. If the value of is 1, then the material is said to be perfectly elastic.[6][7]​.

2. Actually, the stress also depends greatly on the rate of change of strain. Therefore, an empirical equation can be derived based on the variation of the strain rate:

where is a constant related to the flow stress of the material. indicates the derivative of strain with respect to time, which is also known as strain rate. is the sensitivity to strain rate. Furthermore, the value of is related to the throttling resistance. Typically, the value of is in the range of 0-0.1 at room temperature and can be as high as 0.8 when the temperature is increased.

plastic deformation

This type of deformation is not reversed simply by eliminating the applied force; it is therefore a thermodynamically irreversible process. However, an object in the range of plastic deformation will first have undergone elastic deformation (which does disappear when the applied force is removed), so the object will partially return to its original shape. Lightweight thermoplastics have a fairly large plastic deformation range, as do ductile metals such as copper, silver and gold. Steel also exhibits this behavior, but cast iron does not. Hard thermosetting plastics, rubber, glass and ceramics have minimum ranges of plastic deformation. An example of a material with a wide range of plastic deformation is chewing gum once moistened, which can stretch to tens of times its original length.

Under tensile stress, plastic deformation is characterized by the appearance of a region of strain hardening and a region of necking&action=edit&redlink=1 "Narrowing (engineering) (not yet written)") and finally, by a state of fracture (also called failure). During strain hardening, the material becomes stronger due to the formation of atomic dislocations "Dislocation (crystal defect)"). The phase of formation of a neck neck is characterized by a reduction in the cross-sectional area of ​​the sample. The phenomenon occurs after the maximum voltage is reached. During necking, the material can no longer withstand the maximum stress, and localized stresses in the sample increase rapidly. Plastic deformation ends with the fracture of the material.

Another deformation mechanism is material fatigue, which occurs mainly in ductile metals. It was initially thought that a material deformed exclusively within the elastic range would completely return to its original state once the applied forces were removed. However, failures occur at the molecular level with each deformation. After many cycles of loading and unloading, cracks will begin to appear, followed shortly by fracture, with no apparent plastic deformation involved. Depending on the material, the shape, and how close to the elastic limit it is deformed, thousands, millions, billions, or trillions of strains may be required for material failure to occur.

Metal fatigue has been a major cause of aircraft failure, especially before the process was well understood (see, for example, the De Havilland Comet accidents). There are two ways to determine when a part is in danger of fatigue problems: predict when failure will occur based on the combination of material/strength/shape/iterations, and replace vulnerable materials before this occurs, or perform microscopic inspections for early cracks, replacing affected parts once they appear. Selecting materials that are unlikely to suffer metal fatigue over the life of the product is the best solution, but it is not always possible. Avoiding shapes with sharp corners limits metal fatigue by reducing stress concentrations, but does not eliminate it.

Fracture

This type of deformation is also irreversible. Failure occurs after the material has reached the end of the elastic and then plastic deformation ranges. At this point, forces build up until they are sufficient to cause a fracture. All materials will eventually fracture if sufficient forces are applied.

A common misconception is that all materials that bend are "weak" and those that do not are "strong." In reality, many materials that undergo large elastic and plastic deformations, such as steel, are capable of absorbing stresses that would cause the breakage of brittle or fragile materials, such as glass, which has low ductility with minimal margins of plastic deformation.[10]​.

Contenido

Dependiendo del tipo de material, tamaño y geometría del objeto, y las fuerzas aplicadas, pueden resultar varios tipos de deformación. La imagen de la derecha muestra el diagrama de esfuerzo de ingeniería frente a deformación para un material dúctil típico como el acero. Pueden ocurrir diferentes modos de deformación bajo diferentes condiciones, como se puede representar usando un gráfico de deformación.

La deformación permanente es irreversible; la deformación permanece incluso después de la eliminación de las fuerzas aplicadas, mientras que la deformación temporal es recuperable, ya que desaparece después de la eliminación de las fuerzas aplicadas.

La deformación temporal también se denomina deformación elástica, mientras que la deformación permanente se denomina deformación plástica.[2]​.

elastic deformation

In civil engineering, the study of temporal or elastic deformation is applied to materials used in construction, such as concrete or steel, which are subjected to very small deformations. The phenomenon can be modeled by the theory of infinitesimal deformations, also known as theory of small deformations, theory of small displacements or theory of small displacement gradients where it is assumed that the deformations and rotations produced by the stresses are small.

For some materials, such as elastomers and polymers, subject to large strains, the engineering definition of strain is not applicable (typically restricted to strains less than 1%),[4] so these materials require other, more complex definitions of strain, such as "stretch", "logarithmic strain", "Green's strain" or "Almansi strain". Elastomers and memory metals "Thermal memory effect (metals)") such as nitinol, exhibit large ranges of elastic deformation, as does rubber. However, elasticity is not linear in these materials.

Common construction metals such as ceramics, metals, concrete and most glass show linear elasticity and a smaller elastic range. For these materials it is common to assume that elastic deformation is linear and governed by Hooke's law:

where is the applied stress, is a material constant called Young's modulus or elastic modulus, and ε is the resulting elongation. This relationship only applies in the elastic range and indicates that the slope of the stress/strain curve can be used to determine the Young's modulus () of a material. Materials laboratories use this calculation based on data obtained in tensile tests.

It should be noted that not all elastic materials undergo linear elastic deformation; some, such as concrete, gray cast iron, and many polymers, respond nonlinearly. For these materials, Hooke's law is not applicable.[5]​.

True stress and strain

Since, in practice, the change of the cross section of the material sample as it is stretched during the above deformation process is not always precisely known, the true stress-strain curve must be refitted. For small strains there is not much difference between any two measurements of stress or strain. In uniaxial tests it is common to measure the so-called engineering stress and strain and subsequently calculate other corrected measurements according to the area or instantaneous lengths of the stretched prism, which are called true stress and strain (for the regime of large strains, many other additional measures are defined that go beyond the previous ones).

To derive the stress-strain curve, we consider a prism of initial section and height and current or final section and height. Engineering deformation is defined as:

Furthermore, for an isotropic elastic material in the regime of small deformations, the change in volume is given by:.

So we have , where is the so-called Poisson's ratio that may undergo some changes throughout the test. .

Then, the true stress or Cauchy stress can be expressed as follows (using Taylor series up to first order):

Furthermore, the true strain ε can be expressed as follows:.

Then, the value is expressed as.

Therefore, we can derive the graph in terms of y as it appears in the figure to the right.

Furthermore, based on the true stress-strain curve, the region where necking begins to occur can be estimated. From the moment a visible narrowing of the section begins to appear, until the final tension is reached (when the maximum force was applied), this situation can be expressed as follows:

which in turn can be expressed as follows:

The plot shows that necking begins to appear where the reduction in area becomes much more significant compared to the change in stress. The tension is then maximized in the specific area where the narrowing appears.

Furthermore, several relationships can be deduced based on the true stress-strain curve.

1. The true stress and strain curve can be expressed by the approximate linear relationship by taking a logarithm of the true stress and strain. The relationship can be expressed as follows:

where is the stress coefficient and is the strain hardening coefficient. Typically, the value of has a range of 0.02 to 0.5 at room temperature. If the value of is 1, then the material is said to be perfectly elastic.[6][7]​.

2. Actually, the stress also depends greatly on the rate of change of strain. Therefore, an empirical equation can be derived based on the variation of the strain rate:

where is a constant related to the flow stress of the material. indicates the derivative of strain with respect to time, which is also known as strain rate. is the sensitivity to strain rate. Furthermore, the value of is related to the throttling resistance. Typically, the value of is in the range of 0-0.1 at room temperature and can be as high as 0.8 when the temperature is increased.

plastic deformation

This type of deformation is not reversed simply by eliminating the applied force; it is therefore a thermodynamically irreversible process. However, an object in the range of plastic deformation will first have undergone elastic deformation (which does disappear when the applied force is removed), so the object will partially return to its original shape. Lightweight thermoplastics have a fairly large plastic deformation range, as do ductile metals such as copper, silver and gold. Steel also exhibits this behavior, but cast iron does not. Hard thermosetting plastics, rubber, glass and ceramics have minimum ranges of plastic deformation. An example of a material with a wide range of plastic deformation is chewing gum once moistened, which can stretch to tens of times its original length.

Under tensile stress, plastic deformation is characterized by the appearance of a region of strain hardening and a region of necking&action=edit&redlink=1 "Narrowing (engineering) (not yet written)") and finally, by a state of fracture (also called failure). During strain hardening, the material becomes stronger due to the formation of atomic dislocations "Dislocation (crystal defect)"). The phase of formation of a neck neck is characterized by a reduction in the cross-sectional area of ​​the sample. The phenomenon occurs after the maximum voltage is reached. During necking, the material can no longer withstand the maximum stress, and localized stresses in the sample increase rapidly. Plastic deformation ends with the fracture of the material.

Another deformation mechanism is material fatigue, which occurs mainly in ductile metals. It was initially thought that a material deformed exclusively within the elastic range would completely return to its original state once the applied forces were removed. However, failures occur at the molecular level with each deformation. After many cycles of loading and unloading, cracks will begin to appear, followed shortly by fracture, with no apparent plastic deformation involved. Depending on the material, the shape, and how close to the elastic limit it is deformed, thousands, millions, billions, or trillions of strains may be required for material failure to occur.

Metal fatigue has been a major cause of aircraft failure, especially before the process was well understood (see, for example, the De Havilland Comet accidents). There are two ways to determine when a part is in danger of fatigue problems: predict when failure will occur based on the combination of material/strength/shape/iterations, and replace vulnerable materials before this occurs, or perform microscopic inspections for early cracks, replacing affected parts once they appear. Selecting materials that are unlikely to suffer metal fatigue over the life of the product is the best solution, but it is not always possible. Avoiding shapes with sharp corners limits metal fatigue by reducing stress concentrations, but does not eliminate it.

Fracture

This type of deformation is also irreversible. Failure occurs after the material has reached the end of the elastic and then plastic deformation ranges. At this point, forces build up until they are sufficient to cause a fracture. All materials will eventually fracture if sufficient forces are applied.

A common misconception is that all materials that bend are "weak" and those that do not are "strong." In reality, many materials that undergo large elastic and plastic deformations, such as steel, are capable of absorbing stresses that would cause the breakage of brittle or fragile materials, such as glass, which has low ductility with minimal margins of plastic deformation.[10]​.