Stress (physics) Guide, Meaning , Facts, Information and Description
In physics, stress is the internal distribution of forces within a body that balance and react to the loads applied to it. Stress is a nine-dimension tensor that can be fully described with six dimensions. Simplifying assumptions are often used to represent stress as a vector for engineering calculations.
A simplified definition for stress is force divided by area (see also pressure (physics)). Force normal to the area causes normal stress (usually denoted by ), and force parallel to the area causes shear stress (usually denoted by ).
Stress can occure in solids, liquids and gases. Liquids and gasses supprty normal stress (pressure), but flow under shear stress (see viscosity). Solids support both shear and normal stress, with brittle materials failing under normal stress and plastic or ductile materials failing under shear stress.
| Table of contents |
|
2 Cauchy's principle 3 Plane stress 4 Stress in three dimensions 5 Stress tensor 6 Stress measurement 7 Units 8 Residual stress 9 See also 10 Books |
Stress in one dimension
The idea of stress originates in two simple, but important, observations of the loading (in tension) of a one-dimensional body, for example, a steel wire.
- For small loads, the deformation (strain) of the wire is proportional to the applied load divided by the cross-sectional area of the wire: σ = F / A.
- Failure occurs when the load exceeds a critical value for the material (the tensile strength) multiplied by the cross-sectional area of the wire: Fc = σt x A
For instance, a steel bolt of diameter 5 mm, has a cross-sectional area of 19.63 mm2. A load of 50 N induces a stress (force distributed across the cross-section) of σ = 50/19.63 = 2.55 N/mm2 (MPa). This can be thought of as each m2 of bolt supporting 2.55 MN of the total load. In another bolt with half the diameter, and hence a quarter the cross-sectional area, carrying the same 50 N load, the stress will be quadrupled (10.2 MPa).
The ultimate tensile strength is a property of a material and, for any particular geometry, it allows the calculation of the load that would cause fracture. The compressive strength is a similar property for compressive loads. The yield tensile strength is the value of stress causing plastic deformation. These values are determined experimentally using the measurement procedure known as the tensile test.
Cauchy's principle
Augustin Louis Cauchy enunciated the principle that, within a body, the forces that an enclosed volume imposes on the remainder of the material must be in equilibrium with the forces upon it from the rest of the body.
This intuition provides a route to characterizing and calculating complicated patterns of stress. To be exact, the stress at a point may be determined by taking the limit of the load being carried by a particular cross section, divided by that cross section, as the area of the cross section approaches zero. In general the stress may vary from point to point, but for simple cases, such as circular cylinders with pure axial loading, the stress is constant and equal to the cross-sectional area divided by the applied load.We can consider a small element of the body that has an area ΔA, over which a force ΔP acts. By making the element indefinitely small and taking the limit:
Plane stress is a two-dimensional state of stress in a body. This is a good model when a flat thin body is loaded in the plane of the body. A small volume element in equilibrium experiences forces in balance (Figure 1).
By specifying some co-ordinates, the forces P and Q can be resolved normal and perpendicular to the faces of the volume element (Figure 2).
The stresses on the element are (Figure 3):
A graphical method for analyzing plane stress was proposed by Otto Mohr in 1882.
1. Construct an orthogonal pair of axes where the horizontal represents normal stress and the vertical, shear stress (clockwise shears are represented as positive).
2. For any pair of normal stresses (σx, σy) measured orthogonally, mark their magnitudes on the horizontal axes.
3. Mark the mid-point of the two normal stresses, O. (Figure 4)
4. Draw a perpendicular from each marked normal stress with magnitude equal to the corresponding shear stress (τxy) measured in the same co-ordinate system and call its end-point A (Figure 5)
5. Draw a circle with radius OA, centered at O.
6. The points where the circle crosses the horizontal axis represent the magnitudes of the principal stresses. (Figure 6)
Mohrs circle may also be applied to three-dimension stress. In this case the diagram has three circles, two within a third.
Engineers use Mohrs circle to fully examine the state of stress in a loaded structural element. For example, if the material is Brittle the engineer might use Mohrs circle to find the maximum component of normal stress (tension or compression), and for Ductile materials the engineer might look for the maximum shear component of stress.
The considerations above can be generalized to three dimensions. However, this is very complicated, since each shear loading produces shear stresses in one orientation and normal stresses in other orientation, and vice versa. Often, only certain components of stress will be important, depending on the material in question.
Von Mises stress is derived from the distortion energy theory and is a simple way to combine stresses in three dimensions to calculate failure criteria of ductile materials. In this way, the strength of material in a 3D state of stress can be compared to a test sample that was loaded in one dimension.
As with force, stress cannot be measured directly but is usually inferred from measurements of strain and knowledge of elastic properties of the material.
The SI unit for stress is the pascal (symbol Pa); in US Customary units, stress is expressed in pounds per square inch (PSI). See also: Pressure (physics)
Residual stress occures in un-loaded structurs for a variety of reasons. Heat from welding may cause localized expansion, which is taken up during welding by either the molten metal or the placement of parts being welded. When the finished weldment cools, some areas cool and contract more than others, leaving residual stresses. Another example are certian types of gun barrles, which are made with two tubes forced together. The inner tube is compressed and the outer tube streched. This has the effect of better stress distribution when the gun is fired.
Another example are press fits. Automotive wheel studs, for example are pressed into holes on the wheel hub. The holes are smaller than the studs, requiring force to drive the studs into place. The residual stresses fasten the parts together. Nails are another example of a fastener that rely on residual stress.
This is an Article on Stress (physics). Page Contains Information, Facts Details or Explanation Guide About Stress (physics) Plane stress
Principal stresses
Cauchy was the first to demonstrate that it is always possible to transform the co-ordinates on the body into a set in which the shear stress vanishes. The remaining normal stresses are called the principal stresses.Mohr's circle
Stress in three dimensions
Stress tensor
Because the behavior of a body does not depend on the coordinates used to measure it, stress can be described by a tensor. The stress tensor is symmetric and can always be resolved into the sum of two symmetric tensors:
In the case of a fluid, Pascal's Law shows that the hydrostatic stress is the same in all directions, at least to a first approximation, so can be captured by the scalar quantity pressure.Stress measurement
Units
Residual stress
See also
Books