# Experimental Stress Analysis (ESA) using Strain Gauges

## Defining Stress

Stress is defined as the physical response (deformation) in materials caused by force. It usually occurs as a result of an **applied force** **(mechanical stress)**, which causes the material to deform, but is also often due to the **effects of force within a material** **or larger system**.

Stresses are subdivided as follows:

- Type: normal stresses and shear stresses
- Origin: tension, compression, bending, torsion, residual and thermal stresses
- State: uniaxial, biaxial, triaxial or spatial.

The stresses under Origin are categorized as normal and shear stresses (when considering the strength of materials, the type of stress is of interest irrespective of its cause). In addition, stresses can be subdivided according to the states described above.

## Defining Stress according to Type and Origin

Unlike other stresses named after their origin –e.g. **bending stress, torsion stress **– **tensile stress** (positive) and **compressive stress** (negative) occur without any external forces being involved. These comprise **normal and shear stresses**.

**Residual stress **(or inherent stress) can be produced due to the** internal effects of force**, e.g.:

- from non-uniform changes in volume in heat-treated parts during the hardening of steel,
- by non-uniform cooling of cast or injection molded metal or plastic objects,
- with welded or forged parts, through mechanical processing,
- with larger objects, simply from the effect of their own weight.

**Thermal stress **is a type of residual stress. It occurs in systems, in which parts with different thermal expansions are joined together such that free thermal expansion is prevented. It can also occur as a result of non-uniform heating.

**Residual and thermal stresses** affect the material similarly to loading stresses. They reduce the load-bearing capacity of the material by externally applied forces. Questions regarding the operational safety of structural parts can therefore only be answered adequately if the residual stresses are known quantitatively and qualitatively. The determination of these stresses is only possible with normal practical methods when they are “released” and the degree of resilient relaxation exhibited by the material in the non-stressed state is measured. The release of these stresses can take place in different ways, like the hole drilling method or ring core method.

## Defining Stress according to State

Stress states are subdivided as follows:

**1. Uniaxial **stress state: occurs in tension and compression bars only.

**2. Biaxial or planar **stress condition: occurs if the forces producing the stresses occur on two axes that are perpendicular to one another. Resolving of the effective directions of the forces into two main axes at 90° to one another is made on theoretical grounds. The effective directions of different forces acting in the same plane, but at different angles, can be very different. However, they can always be resolved into the two main directions.

**3. Triaxial or three-dimensional **stress state: present if the forces can act in any direction. Similar to the planar stress state, three main axes are defined which are all situated perpendicular to one another.

Strain measurements are restricted by necessity to the accessible surfaces of the structural parts and consequently they can only give information on the stress state at the component's surface.

Whereas **uniaxial and planar stress states** can be analyzed relatively simply with strain measurement techniques, in particular using strain gauges, **three-dimensional stress states** present problems since the required measurements along the third axis, i.e. inside the object, are usually not possible. However, in a three dimensional body, which is stressed by external forces, the maximum stresses occur at the surface! (Exception: Hertz effect problems).

For the designer, who is usually only interested in the maximum stresses, the determination of the stresses at the surface is sufficient. The internal processes are of lesser importance.

**Three-dimensional stress states** can only be analyzed from strain measurements if the strain can be measured along the third axis, i.e. in the object's depth. This is found for example in model measuring techniques where strain gauges can be cast into plastic models. This is also possible in civil engineering where strain measuring equipment can be embedded in concrete during pouring.

## Determining Stress from Measured Strains

**Mechanical stresses** are not accessible for direct measurement. X-ray techniques form an exception to this where the material stresses in the microscopic range can be determined from distortions in the crystal lattice structure, i.e. from the relative changes in the interatomic separation. The process is restricted to layers near the surface of about 5 to 15 μm depth.

**Stresses are calculated either according to the theory of the strength of materials or from strain gauge measurements**. **The latter method is based on** **Hooke's Law**.

The mechanical stress is expressed by the quotient of the force F and the cross-sectional area A of the stressed material:

Learn more on **Hooke's Law here**.