# What is Stress in Materials Science

In mechanics and materials science, stress (represented by a lowercase Greek letter sigma – σ) 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.

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 follow 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 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.

### Types of Stress

Stresses occur in any material subject to a load or applied force. There are many types of stress, but they can all be generally classified into one of six categories:

• Structural stresses are stresses produced in structural members because of the weights they support. The weights provide the loadings. These stresses are found in building foundations and frameworks, as well as in machinery parts.
• Residual stresses are stresses caused by manufacturing processes. This type of stress remains in a solid material after the original cause of the stress has been removed. For example, welding leaves residual stresses in the metals welded. The heat from welding may cause localized expansion, which is taken up during welding by either the molten metal or the placement of welded parts.
• Pressure stresses are stresses induced in vessels containing pressurized materials. The loading is provided by the same force producing the pressure. The reactor vessel is a prime example of a pressure vessel in a reactor facility. 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.
• Thermal stresses exist whenever temperature gradients are present in a material, and different temperatures produce different expansions and subject materials to internal stress. This type of stress is particularly noticeable in mechanisms operating at high temperatures cooled by a cold fluid. 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.
• Flow stresses occur when a mass of flowing fluid induces dynamic pressure on a conduit wall. The force of the fluid striking the wall acts as the load. This type of stress may be applied in an unsteady fashion when flow rates fluctuate. Water hammer is an example of transient flow stress. A Water hammer in a pipe or tube is a pressure spike caused by a sudden flow rate variation. And velocity energy is converted to pressure energy.
• Fatigue stresses. Fatigue 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 been initiated, each loading cycle will grow the crack a small amount. The stresses could be due to vibration or thermal cycling.

### Applied Stress

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. 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.

• Tensile stress. 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 a material can withstand while being stretched or pulled before breaking. In the study of the 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.
• Compressive stress. 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 similarly to tensile stress but has negative values 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 behavior or with a fracture in the 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.
• Shear stress. Shear stress exists when two parts of 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. Shear stress is also of great importance in nature, intimately related to the downslope movement of earth materials (as in the case of avalanches).
References:
Materials Science:
1. U.S. Department of Energy, Material Science. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
2. U.S. Department of Energy, Material Science. DOE Fundamentals Handbook, Volume 2 and 2. January 1993.
3. William D. Callister, David G. Rethwisch. Materials Science and Engineering: An Introduction 9th Edition, Wiley; 9 edition (December 4, 2013), ISBN-13: 978-1118324578.
4. Eberhart, Mark (2003). Why Things Break: Understanding the World by the Way It Comes Apart. Harmony. ISBN 978-1-4000-4760-4.
5. Gaskell, David R. (1995). Introduction to the Thermodynamics of Materials (4th ed.). Taylor and Francis Publishing. ISBN 978-1-56032-992-3.
6. González-Viñas, W. & Mancini, H.L. (2004). An Introduction to Materials Science. Princeton University Press. ISBN 978-0-691-07097-1.
7. Ashby, Michael; Hugh Shercliff; David Cebon (2007). Materials: engineering, science, processing, and design (1st ed.). Butterworth-Heinemann. ISBN 978-0-7506-8391-3.
8. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.

Strength