Mechanical Stress

Johann Maier, winter semester 2015/16

The term stress is a physical quantity used in continuum mechanics and expresses the loading in terms of force applied to a certain cross-sectional area of an object. ^[1] The stress causes a strain, which is the measure of the deformation of the body. ^[2] From the perspective of what is happening within a material, stress is the internal distribution of forces within a body that balance and react to the loads applied to it. The stress distribution may or may not be uniform, depending on the nature of the loading condition. For example, a bar loaded in pure tension will essentially have a uniform tensile stress distribution. However, a bar loaded in bending will have a stress distribution that changes with distance perpendicular to the normal axis. ^[1]

Introduction and Basics

Simplifying assumptions are often used to represent stress as a vector quantity for many engineering calculations and for material property determination. […] For example, the stress in an axially loaded bar is simply equal to the applied force divided by the bar's cross-sectional area. ^[1]

$//<![CDATA[ \begin{array}{l}Stress, \sigma = \frac{Force}{Cross-Sectional Area} = \frac{F}{A_0}\end{array} //]]>$

It must be noted that the stresses in most 2-D or 3-D solids are actually more complex and need be defined more methodically. ^[1]

Some common measurements of stress are:

• $//<![CDATA[ \begin{array}{l}Pa = \frac{N}{m^2}\end{array} //]]>$ (Pascals or Newtons per square meter)

• $//<![CDATA[ \begin{array}{l}MPa = \frac{N}{mm^2} = Megapascals\end{array} //]]>$ (one Newton per square millimeter)
• $//<![CDATA[ \begin{array}{l}GPa = Gigapascals\end{array} //]]>$ (one thousand Megaspascals)

^[1]

Common in anglosaxon region:

• $//<![CDATA[ \begin{array}{l}Psi = \frac{lbs}{in^2}\end{array} //]]>$ (pounds per square inch)

• $//<![CDATA[ \begin{array}{l}ksi\end{array} //]]>$ or $//<![CDATA[ \begin{array}{l}kpsi = \frac{kilopounds}{in^2}\end{array} //]]>$ (one thousand or 10³ pounds per square inch)

^[1]

Residual stresses

Residual stresses are stresses that remain in a solid material after the original cause of the stresses has been removed. […] Residual stresses can occur through a variety of mechanisms including inelastic (plastic) deformations, temperature gradients (during thermal cycle) or structural changes (phase transformation). ^[3]

Measurement techniques

There are many techniques used to measure residual stresses, which are roughly categorized into destructive, semi-destructive and non-destructive techniques. ^[3]

The selection of the technique depends on the information required and the nature of the measurement specimen. Factors include the depth/penetration of the measurement (surface or through-thickness), the length scale to be measured over (macroscopic, mesoscopic or microscopic), the resolution of the information required, and also the composition geometry and location of the specimen. ^[3]

Destructive Techniques

The destructive techniques is such that they result in a large and irreparable structural change to the specimen, meaning that either the specimen cannot not returned to service or a mock-up or spare must be used. ^[3]

Destructive techniques include:

• Contour Method
• Slitting (Crack Compliance)
• Block Removal/Splitting/Layering
• Sach's Boring

^[3]

Semi-destructive Techniques

However these techniques remove only a small amount of material, leaving the overall integrity of the structure intact. ^[3] They include:

• Deep Hole Drilling
• Centre Hole Drilling
• Ring Core

^[3]

Non-destructive Techniques

The non-destructive techniques measure the effects of relationships between the residual stresses and their action of crystallographic properties of the measured material. Some of these work by measuring the diffraction of high frequency electromagnetic radiation through the atomic lattice spacing (which has been deformed due to the stress) relative to a stress-free sample. The Ultrasonic and Magnetic techniques exploit the acoustic and ferromagnetic properties of materials to perform relative measurements of residual stress. Non-destructive techniques include:

• Neutron Diffraction
• Synchrotron Diffraction
• X-Ray Diffraction
• Ultrasonic
• Magnetic

^[3]

Literature

1. Stress and Strain. January 7th, 2016.
2. Stress (mechanics). Wikipedia. January 27th, 2016.
3. Residual stress. January 27th, 2016.