{"id":27817,"date":"2020-11-12T16:11:45","date_gmt":"2020-11-12T16:11:45","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=27817"},"modified":"2023-08-08T09:09:30","modified_gmt":"2023-08-08T09:09:30","slug":"strength","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-engineering\/materials-science\/material-properties\/strength\/","title":{"rendered":"Strength"},"content":{"rendered":"
<\/a>In the mechanics of materials, the strength of a material<\/strong> is its ability to withstand an applied load without failure or plastic deformation. The strength\u00a0of materials<\/strong> considers the relationship between the external loads<\/strong> applied to a material and the resulting deformation<\/strong> or change in material dimensions. In designing structures and machines, it is important to consider these factors so that the material selected will have adequate strength to resist applied loads or forces and retain its original shape. The strength\u00a0of a material<\/strong> is its ability to withstand this applied load without failure or plastic deformation.<\/p>\n However, we must note that the load which will deform a small component will be less than the load to deform a larger component of the same material. Therefore, the load (force) is not a suitable term<\/strong> for strength<\/strong>. Instead, we can use the force (load) per unit of area<\/b> (\u03c3 = F\/A), called stress<\/strong>, which is constant (until deformation occurs) for a given material regardless of the size of the component part. In this concept, strain<\/strong> is also a very important variable since it defines the deformation of an object. In summary, the mechanical behavior of solids is usually defined by constitutive stress-strain relations.<\/b> A deformation is called elastic deformation if the stress is a linear function of strain. In other words, stress and strain follow Hooke\u2019s law<\/strong>. Beyond the linear region, stress and strain show nonlinear behavior. This inelastic behavior is called plastic deformation.<\/p>\n In mechanics and materials science, stress<\/strong> (represented by a lowercase Greek letter sigma – \u03c3<\/strong>) is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other. At the same time, strain is the measure of the deformation of the material, which is not a physical quantity.<\/p>\n 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 (\u03c3)<\/strong> can be equated to the load per unit area or the force (F) applied per cross-sectional area (A) perpendicular to the force as:<\/p>\n <\/a><\/p>\n 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<\/i><\/strong>. A deformation is called elastic deformation<\/strong> if the stress is a linear function of strain. In other words, stress and strain follow Hooke\u2019s law<\/strong>. Beyond the linear region, stress and strain show nonlinear behavior. This inelastic behavior is called plastic deformation<\/strong>.<\/p>\n Stress is the internal resistance, or counterforce, 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.<\/p>\n Stresses occur in any material subject to a load or applied force. There are many types of stress<\/strong>, but they can all be generally classified into one of six categories:<\/p>\n <\/a>From an internal point of view, stress intensity within the body of a component is expressed as one of three basic internal load types: tension, compression, and shear<\/strong>. In engineering practice, many loads are torsional rather than pure shear. Mathematically, there are only two types of an internal load because tensile and compressive stress may be regarded as the positive and negative versions of the same type of normal loading.<\/p>\n In materials science<\/a>, strain<\/strong> is also a very important variable since it defines the deformation<\/strong> of an object. Unlike stress in an object, which you can\u2019t 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.<\/b> 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<\/b>. Due to applied stress, it is measured as the material\u2019s total deformation (elongation) per reference length.<\/p>\n <\/a><\/p>\n In the mechanics of materials, we can define two basic types of strain:<\/p>\n The deformation measures 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.<\/p>\n <\/a><\/p>\n A deformation is called elastic deformation if the stress is a linear function of strain. In other words, stress and strain follow Hooke\u2019s law<\/strong>. Beyond the linear region, stress and strain show nonlinear behavior, and this inelastic behavior is called plastic deformation.<\/p>\n <\/a>The strength of materials<\/strong> considers the relationship between the external loads<\/strong> applied to a material and the resulting deformation<\/strong> or change in material dimensions. In designing structures and machines, it is important to consider these factors so that the material selected will have adequate strength to resist applied loads or forces and retain its original shape. The strength\u00a0of a material<\/strong> is its ability to withstand this applied load without failure or plastic deformation.<\/p>\n However, we must note that the load which will deform a small component will be less than the load to deform a larger component of the same material. Therefore, the load (force) is not a suitable term<\/strong> for strength<\/strong>. Instead, we can use the force (load) per unit of area<\/b> (\u03c3 = F\/A), called stress<\/strong>, which is constant (until deformation occurs) for a given material regardless of the size of the component part. In this concept, strain<\/strong> is also a very important variable since it defines the deformation of an object. In summary, the mechanical behavior of solids is usually defined by constitutive stress-strain relations.<\/b> A deformation is called elastic deformation if the stress is a linear function of strain. In other words, stress and strain follow Hooke\u2019s law<\/strong>. Beyond the linear region, stress and strain show nonlinear behavior. This inelastic behavior is called plastic deformation.<\/p>\n A schematic diagram for the stress-strain curve<\/strong> of low carbon steel at room temperature is shown in the figure. Several stages show different behaviors, which suggests different mechanical properties. Materials can miss one or more stages shown in the figure or have different stages to clarify. In this case, we have to distinguish between stress-strain characteristics of ductile<\/strong> and brittle<\/strong> materials. The following points describe the different regions of the stress-strain curve and the importance of several specific locations.<\/p>\n In many situations, the yield strength is used to identify the allowable stress to which a material can be subjected. This criterion is not adequate for components that have to withstand high pressures, such as those used in pressurized water reactors (PWRs). The maximum shear stress theory<\/b> of failure has been incorporated into the ASME (The American Society of Mechanical Engineers) Boiler and Pressure Vessel Code, Section III, Rules for Construction of Nuclear Pressure Vessels to cover these situations. This theory states that failure of a piping component occurs when the maximum shear stress exceeds the shear stress at the yield point in a tensile test.<\/p>\n Some materials break very sharply, without plastic deformation, in 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:<\/p>\n <\/a>The following figure shows a typical stress-strain curve of ductile and brittle materials. Ductile material is a material with a small strength, 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 \u201cyielding\u201d 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.<\/p>\n One of the stages in the stress-strain curve<\/strong> is the strain hardening region<\/strong>. This region starts as the strain goes beyond the yield point<\/strong> and ends at the ultimate strength point, the maximal stress shown in the stress-strain curve. In this region, the stress mainly increases as the material elongates, except that there is a nearly flat region at the beginning. Strain hardening<\/strong> is also called work-hardening<\/strong> or cold-working<\/strong>. It is called cold-working because the plastic deformation must occur at a temperature low enough that atoms cannot rearrange themselves. It is a process of making a metal harder and stronger through plastic deformation. When a metal is plastically deformed, dislocations<\/a> move, and additional dislocations are generated. Dislocations can move if the atoms from one of the surrounding planes break their bonds and rebond with the atoms at the terminating edge. The dislocation density in a metal increases with deformation or cold work because of dislocation multiplication or the formation of new dislocations. The more dislocations within a material, the more they interact and become pinned or tangled. This will result in a decrease in the mobility of the dislocations and a strengthening of the material.<\/p>\n <\/a>Most polycrystalline materials have an almost constant relationship between stress and strain within their elastic range. In 1678 an English scientist named Robert Hooke<\/strong> ran experiments that provided data showing that strain is proportional to stress in the elastic range of material. Robert Hooke concluded that the force F in any spring is proportional to the extension (the deformation from the relaxed state) x as follows:<\/p>\n F = k \u00b7 x<\/strong><\/p>\n where the term k<\/strong> is the stiffness<\/strong> of the spring and x is small compared to the total possible deformation of the spring. It must eventually fail once the forces exceed some limit since no material can be compressed beyond a certain minimum size or stretched beyond a maximum size without some permanent deformation or change of state.<\/p>\n In the case of tensional stress of a uniform bar (stress-strain curve), Hooke\u2019s law<\/b> describes the behavior of a bar in the elastic region. In this region, the elongation of the bar is directly proportional to the tensile force and the length of the bar and inversely proportional to the cross-sectional area and the modulus of elasticity<\/b>. Up to limiting stress, a body will be able to recover its dimensions on the removal of the load. The applied stresses cause the atoms in a crystal to move from their equilibrium position, and 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. According to Hooke\u2019s law, <\/b>\u00a0the stress is proportional to the strain (in the elastic region), and the slope is Young\u2019s modulus<\/b>.<\/p>\n <\/a>We can extend the same idea of relating stress to strain to shear applications in the linear region, relating shear stress to shear strain to create Hooke\u2019s law for shear stress<\/b>:<\/p>\n <\/a><\/p>\n For isotropic materials within the elastic region, you can relate Poisson\u2019s ratio (\u03bd), Young\u2019s modulus of elasticity (E), and the shear modulus of elasticity (G):<\/p>\n <\/a><\/p>\n The elastic moduli relevant to polycrystalline materials:<\/p>\nStress<\/h2>\n
Types of Stress<\/h3>\n
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Applied Stress<\/h3>\n
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Strain<\/h2>\n
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Deformation<\/h3>\n
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Stress-Strain Curve
\n<\/b><\/h2>\n\n
Ductile vs. Brittle \u2013 Stress-strain curves<\/h3>\n<\/p>
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Strain Hardening<\/h2>\n
Hooke\u2019s law
\n<\/b><\/h2>\n