Nick Connor

A schematic diagram for the stress-strain curve of low carbon steel at room temperature is shown in the figure. There are several stages showing different behaviors, which suggests different mechanical properties. To clarify, materials can miss one or more stages shown in the figure, or have totally different stages. In this case we have to distinguish between stress-strain characteristics of ductile and brittle materials. The following points describe the different regions of the stress-strain curve and the importance of several specific locations.

• Proportional limit. The proportional limit corresponds to the location of stress at the end of the linear region, so the stress-strain graph is a straight line, and the gradient will be equal to the elastic modulus of the material. For tensile and compressive stress, the slope of the portion of the curve where stress is proportional to strain is referred to as Young’s modulus and Hooke’s Law applies. Between the proportional limit and the yield point the Hooke’s Law becomes questionable between and strain increases more rapidly.
• Yield point. The yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning plastic behavior. Yield strength or yield stress is the material property defined as the stress at which a material begins to deform plastically whereas yield point is the point where nonlinear (elastic + plastic) deformation begins. Prior to the yield point, the material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible. Some steels and other materials exhibit a behaviour termed a yield point phenomenon. Yield strengths vary from 35 MPa for a low-strength aluminum to greater than 1400 MPa for very high-strength steels.
• Ultimate tensile strength. The ultimate tensile strength is the maximum on the engineering stress-strain curve. This corresponds to the maximum stress that can be sustained by a structure in tension. Ultimate tensile strength is often shortened to “tensile strength” or even to “the ultimate.” If this stress is applied and maintained, fracture will result. Often, this value is significantly more than the yield stress (as much as 50 to 60 percent more than the yield for some types of metals). When a ductile material reaches its ultimate strength, it experiences necking where the cross-sectional area reduces locally. The stress-strain curve contains no higher stress than the ultimate strength. Even though deformations can continue to increase, the stress usually decreases after the ultimate strength has been achieved. It is an intensive property; therefore its value does not depend on the size of the test specimen. However, it is dependent on other factors, such as the preparation of the specimen, the presence or otherwise of surface defects, and the temperature of the test environment and material. Ultimate tensile strengths vary from 50 MPa for an aluminum to as high as 3000 MPa for very high-strength steels.
• Fracture point: The fracture point is the point of strain where the material physically separates. At this point, the strain reaches its maximum value and the material actually fractures, even though the corresponding stress may be less than the ultimate strength at this point. Ductile materials have a fracture strength lower than the ultimate tensile strength (UTS), whereas in brittle materials the fracture strength is equivalent to the UTS. If a ductile material reaches its ultimate tensile strength in a load-controlled situation, it will continue to deform, with no additional load application, until it ruptures. However, if the loading is displacement-controlled, the deformation of the material may relieve the load, preventing rupture.

Ductile vs. Brittle – Stress-strain curves

The following figure shows a typical stress-strain curve of a ductile material and a brittle material. A ductile material is a material, where the strength is small, and the plastic region is great. The material will bear more strain (deformation) before fracture. A brittle material is a material where the plastic region is small and the strength of the material is high. The tensile test supplies three descriptive facts about a material. These are the stress at which observable plastic deformation or “yielding” begins; the ultimate tensile strength or maximum intensity of load that can be carried in tension; and the percent elongation or strain (the amount the material will stretch) and the accompanying percent reduction of the cross-sectional area caused by stretching. The rupture or fracture point can also be determined.

Some materials break very sharply, without plastic deformation, in what is called a brittle failure. Others, which are more ductile, including most metals, experience some plastic deformation and possibly necking before fracture. It is possible to distinguish some common characteristics among the stress–strain curves of various groups of materials. On this basis, it is possible to divide materials into two broad categories; namely:

• Ductile Materials. Ductility is the ability of a material to be elongated in tension. Ductile material will deform (elongate) more than brittle material. Ductile materials show large deformation before fracture. In ductile fracture, extensive plastic deformation (necking) takes place before fracture. Ductile fracture (shear fracture) is better than brittle fracture, because there is slow propagation and an absorption of a large amount energy before fracture. Ductility is desirable in the high temperature and high pressure applications in reactor plants because of the added stresses on the metals. High ductility in these applications helps prevent brittle fracture.
• Brittle Materials. Brittle materials, when subjected to stress, break with little elastic deformation and without significant plastic deformation. Brittle materials absorb relatively little energy prior to fracture, even those of high strength. In brittle fracture (transgranular cleavage), no apparent plastic deformation takes place before fracture. Cracks propagate rapidly.

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Stress-strain Curve

The following figure shows a typical stress-strain curve of a ductile material and a brittle material. A ductile material is a material, where the strength is small, and the plastic region is great. The material will bear more strain (deformation) before fracture. A brittle material is a material where the plastic region is small and the strength of the material is high. The tensile test supplies three descriptive facts about a material. These are the stress at which observable plastic deformation or “yielding” begins; the ultimate tensile strength or maximum intensity of load that can be carried in tension; and the percent elongation or strain (the amount the material will stretch) and the accompanying percent reduction of the cross-sectional area caused by stretching. The rupture or fracture point can also be determined.

Some materials break very sharply, without plastic deformation, in what is called a brittle failure. Others, which are more ductile, including most metals, experience some plastic deformation and possibly necking before fracture. It is possible to distinguish some common characteristics among the stress–strain curves of various groups of materials. On this basis, it is possible to divide materials into two broad categories; namely:

• Ductile Materials. Ductility is the ability of a material to be elongated in tension. Ductile material will deform (elongate) more than brittle material. Ductile materials show large deformation before fracture. In ductile fracture, extensive plastic deformation (necking) takes place before fracture. Ductile fracture (shear fracture) is better than brittle fracture, because there is slow propagation and an absorption of a large amount energy before fracture. Ductility is desirable in the high temperature and high pressure applications in reactor plants because of the added stresses on the metals. High ductility in these applications helps prevent brittle fracture.
• Brittle Materials. Brittle materials, when subjected to stress, break with little elastic deformation and without significant plastic deformation. Brittle materials absorb relatively little energy prior to fracture, even those of high strength. In brittle fracture (transgranular cleavage), no apparent plastic deformation takes place before fracture. Cracks propagate rapidly.

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Stress-strain Curve

In materials science, strain is also very important variable, since it defines the deformation of an object. Unlike stress in an object, which you can’t actually see, deformation is a visible and measurable quantity. When you pull on a tension rod, you can see the rod physically increase in length (or elongate). When you bend a beam, you see it curve. Deformations are a direct indicator of strain. The mechanical behavior of solids is usually defined by constitutive stress-strain relations. When a metal is subjected to a load (force), it is distorted or deformed, no matter how strong the metal or light the load. If the load is small, the distortion will probably disappear when the load is removed. Such a proportional dimensional change (intensity or degree of the distortion) is called strain and is measured as the total deformation (elongation) per reference length of material due to some applied stress.

In mechanics of materials, we can define two basic types of strain:

Normal strain

A normal strain results from tensile stress and is a strain computed from relative displacements that are measured perpendicular to two reference planes. Normal strains measure the relative perpendicular movement of one reference plane with respect to another. The symbol for normal strain is usually the lowercase Greek symbol epsilon (ε).

Shear strain

A shear strain results from shear stress and it is a strain computed from relative displacements that are measured parallel to two reference planes. Shear strains measure the relative parallel movement of one reference plane with respect to another. The symbol for shear strain is usually the lowercase Greek symbol gamma (γ ).

 

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Strength

The deformation is a measure of how much an object deforms from its original dimensions or size in a given direction. Depending on which deformation you measure, you can calculate different types of strain.

A deformation is called elastic deformation, if the stress is a linear function of strain. In other words, stress and strain follows Hooke’s law. Beyond the linear region, stress and strain show nonlinear behavior. This inelastic behavior is called plastic deformation.

Elastic Deformation

Elastic deformation and elastic strain is a transitory dimensional change that exists only while the initiating stress is applied and disappears immediately upon removal of the stress. When a metal is subjected to a load (force), it is distorted or deformed, no matter how strong the metal or light the load. This deformation may or may not be permanent. Up to a limiting stress, a body will be able to recover its dimensions on removal of the load. The applied stresses cause the atoms in a crystal to move from their equilibrium position. All the atoms are displaced the same amount and still maintain their relative geometry. When the stresses are removed, all the atoms return to their original positions and no permanent deformation occurs.

Plastic Deformation

Plastic deformation and plastic strain is a dimensional change that does not disappear when the initiating stress is removed. It occurs, if the limiting load is exceeded then the body will experience some permanent deformation on removal of the load. Plastic deformation occurs in material bodies after stresses have attained a certain threshold value known as the elastic limit or yield stress, and are the result of slip, or dislocation mechanisms at the atomic level.

 

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Strength

In materials science, strain is also very important variable, since it defines the deformation of an object. Unlike stress in an object, which you can’t actually see, deformation is a visible and measurable quantity. When you pull on a tension rod, you can see the rod physically increase in length (or elongate). When you bend a beam, you see it curve. Deformations are a direct indicator of strain. The mechanical behavior of solids is usually defined by constitutive stress-strain relations. When a metal is subjected to a load (force), it is distorted or deformed, no matter how strong the metal or light the load. If the load is small, the distortion will probably disappear when the load is removed. Such a proportional dimensional change (intensity or degree of the distortion) is called strain and is measured as the total deformation (elongation) per reference length of material due to some applied stress.

In mechanics of materials, we can define two basic types of strain:

• Normal strains. A normal strain results from tensile stress and is a strain computed from relative displacements that are measured perpendicular to two reference planes. Normal strains measure the relative perpendicular movement of one reference plane with respect to another. The symbol for normal strain is usually the lowercase Greek symbol epsilon (ε).
• Shear strains. A shear strain results from shear stress and it is a strain computed from relative displacements that are measured parallel to two reference planes. Shear strains measure the relative parallel movement of one reference plane with respect to another. The symbol for shear strain is usually the lowercase Greek symbol gamma (γ ).

Deformation

The deformation is a measure of how much an object deforms from its original dimensions or size in a given direction. Depending on which deformation you measure, you can calculate different types of strain.

A deformation is called elastic deformation, if the stress is a linear function of strain. In other words, stress and strain follows Hooke’s law. Beyond the linear region, stress and strain show nonlinear behavior. This inelastic behavior is called plastic deformation.

• Elastic Deformation. Elastic deformation and elastic strain is a transitory dimensional change that exists only while the initiating stress is applied and disappears immediately upon removal of the stress. When a metal is subjected to a load (force), it is distorted or deformed, no matter how strong the metal or light the load. This deformation may or may not be permanent. Up to a limiting stress, a body will be able to recover its dimensions on removal of the load. The applied stresses cause the atoms in a crystal to move from their equilibrium position. All the atoms are displaced the same amount and still maintain their relative geometry. When the stresses are removed, all the atoms return to their original positions and no permanent deformation occurs.
• Plastic Deformation. Plastic deformation and plastic strain is a dimensional change that does not disappear when the initiating stress is removed. It occurs, if the limiting load is exceeded then the body will experience some permanent deformation on removal of the load. Plastic deformation occurs in material bodies after stresses have attained a certain threshold value known as the elastic limit or yield stress, and are the result of slip, or dislocation mechanisms at the atomic level.

See above:

Strength

Stress

In mechanics and materials science, stress (represented by a lowercase Greek letter sigma – σ) is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material which is not a physical quantity.

Although it is impossible to measure the intensity of this stress, the external load and the area to which it is applied can be measured. Stress (σ) can be equated to the load per unit area or the force (F) applied per cross-sectional area (A) perpendicular to the force as:

When a metal is subjected to a load (force), it is distorted or deformed, no matter how strong the metal or light the load. If the load is small, the distortion will probably disappear when the load is removed. The intensity, or degree, of distortion is known as strain. A deformation is called elastic deformation, if the stress is a linear function of strain. In other words, stress and strain follows Hooke’s law. Beyond the linear region, stress and strain show nonlinear behavior. This inelastic behavior is called plastic deformation.

Stress is the internal resistance, or counterfource, of a material to the distorting effects of an external force or load. These counterforces tend to return the atoms to their normal positions. The total resistance developed is equal to the external load.

Shear Stress

From internal point of view, stress intensity within the body of a component is expressed as one of three basic types of internal load, namely, tension, compression, and shear. In engineering practice many loads are torsional rather than pure shear. Mathematically, there are only two types of internal load because tensile and compressive stress may be regarded as the positive and negative versions of the same type of normal loading.

Shear stress exists when two parts of a material tend to slide across each other in any typical plane of shear upon application of force parallel to that plane. Torsion is a variation of pure shear in which a structural member is twisted. Torsional forces produce a rotational motion about the longitudinal axis of one end of the member relative to the other end. Shear stress is also of great importance in nature, being intimately related to the downslope movement of earth materials (as in case of avalanches).

See above:

Strength

Stress

In mechanics and materials science, stress (represented by a lowercase Greek letter sigma – σ) is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material which is not a physical quantity.

Although it is impossible to measure the intensity of this stress, the external load and the area to which it is applied can be measured. Stress (σ) can be equated to the load per unit area or the force (F) applied per cross-sectional area (A) perpendicular to the force as:

When a metal is subjected to a load (force), it is distorted or deformed, no matter how strong the metal or light the load. If the load is small, the distortion will probably disappear when the load is removed. The intensity, or degree, of distortion is known as strain. A deformation is called elastic deformation, if the stress is a linear function of strain. In other words, stress and strain follows Hooke’s law. Beyond the linear region, stress and strain show nonlinear behavior. This inelastic behavior is called plastic deformation.

Stress is the internal resistance, or counterfource, of a material to the distorting effects of an external force or load. These counterforces tend to return the atoms to their normal positions. The total resistance developed is equal to the external load.

Compressive Stress

From internal point of view, stress intensity within the body of a component is expressed as one of three basic types of internal load, namely, tension, compression, and shear. In engineering practice many loads are torsional rather than pure shear. Mathematically, there are only two types of internal load because tensile and compressive stress may be regarded as the positive and negative versions of the same type of normal loading.

Compressive stress is the reverse of tensile stress. Adjacent parts of the material tend to press against each other through a typical stress plane. Compressive stress to bars, columns, etc. leads to shortening. Compressive stress is defined in the same way as the tensile stress but it has negative values so as to express the compression since delta L has the opposite direction. One can increase the compressive stress until compressive strength is reached. Then materials will react with ductile behaviour or with fracture in case of brittle materials. Because tensile and compressive loads produce stresses that act across a plane, in a direction perpendicular (normal) to the plane, tensile and compressive stresses are called normal stresses. The ability of a material to react to compressive stress or pressure is called compressibility.

See above:

Strength

Stress

In mechanics and materials science, stress (represented by a lowercase Greek letter sigma – σ) is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material which is not a physical quantity.

Although it is impossible to measure the intensity of this stress, the external load and the area to which it is applied can be measured. Stress (σ) can be equated to the load per unit area or the force (F) applied per cross-sectional area (A) perpendicular to the force as:

When a metal is subjected to a load (force), it is distorted or deformed, no matter how strong the metal or light the load. If the load is small, the distortion will probably disappear when the load is removed. The intensity, or degree, of distortion is known as strain. A deformation is called elastic deformation, if the stress is a linear function of strain. In other words, stress and strain follows Hooke’s law. Beyond the linear region, stress and strain show nonlinear behavior. This inelastic behavior is called plastic deformation.

Stress is the internal resistance, or counterfource, of a material to the distorting effects of an external force or load. These counterforces tend to return the atoms to their normal positions. The total resistance developed is equal to the external load.

Fatigue Stress

Fatique is the weakening of a material caused by cyclic loading that results in progressive and localized structural damage and the growth of cracks. Once a crack has initiated, each loading cycle will grow the crack a small amount, The stresses could be due to vibration or thermal cycling.

See above:

Strength

Stress

In mechanics and materials science, stress (represented by a lowercase Greek letter sigma – σ) is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material which is not a physical quantity.

Although it is impossible to measure the intensity of this stress, the external load and the area to which it is applied can be measured. Stress (σ) can be equated to the load per unit area or the force (F) applied per cross-sectional area (A) perpendicular to the force as:

When a metal is subjected to a load (force), it is distorted or deformed, no matter how strong the metal or light the load. If the load is small, the distortion will probably disappear when the load is removed. The intensity, or degree, of distortion is known as strain. A deformation is called elastic deformation, if the stress is a linear function of strain. In other words, stress and strain follows Hooke’s law. Beyond the linear region, stress and strain show nonlinear behavior. This inelastic behavior is called plastic deformation.

Stress is the internal resistance, or counterfource, of a material to the distorting effects of an external force or load. These counterforces tend to return the atoms to their normal positions. The total resistance developed is equal to the external load.

Tensile Stress

From internal point of view, stress intensity within the body of a component is expressed as one of three basic types of internal load, namely, tension, compression, and shear. In engineering practice many loads are torsional rather than pure shear. Mathematically, there are only two types of internal load because tensile and compressive stress may be regarded as the positive and negative versions of the same type of normal loading.

One of the most common mechanical stress–strain tests is performed in tension. Tensile stress is that type of stress in which the two sections of material on either side of a stress plane tend to pull apart or elongate. The capacity of a material or structure to withstand loads tending to elongate is known as ultimate tensile strength (UTS). Ultimate tensile strength is measured by the maximum stress that a material can withstand while being stretched or pulled before breaking. In the study of strength of materials, tensile strength, compressive strength, and shear strength can be analyzed independently. Because tensile and compressive loads produce stresses that act across a plane, in a direction perpendicular (normal) to the plane, tensile and compressive stresses are called normal stresses.

See above:

Strength

Stress

In mechanics and materials science, stress (represented by a lowercase Greek letter sigma – σ) is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material which is not a physical quantity.

Although it is impossible to measure the intensity of this stress, the external load and the area to which it is applied can be measured. Stress (σ) can be equated to the load per unit area or the force (F) applied per cross-sectional area (A) perpendicular to the force as:

When a metal is subjected to a load (force), it is distorted or deformed, no matter how strong the metal or light the load. If the load is small, the distortion will probably disappear when the load is removed. The intensity, or degree, of distortion is known as strain. A deformation is called elastic deformation, if the stress is a linear function of strain. In other words, stress and strain follows Hooke’s law. Beyond the linear region, stress and strain show nonlinear behavior. This inelastic behavior is called plastic deformation.

Stress is the internal resistance, or counterfource, of a material to the distorting effects of an external force or load. These counterforces tend to return the atoms to their normal positions. The total resistance developed is equal to the external load.

Pressure Stress

Pressure stresses are stresses induced in vessels containing pressurized materials. The loading is provided by the same force producing the thermodynamics/thermodynamic-properties/what-is-pressure-physics/”>pressure. In a reactor facility, the reactor vessel is a prime example of a pressure vessel. One safety issue that is a long-term problem brought on by the aging of nuclear facilities is pressurized thermal shock (PTS). PTS is the shock experienced by a thick-walled vessel due to the combined stresses from a rapid temperature and/or pressure change.

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Strength