# What is Shear Strength?

The strength of a material, in general, is the value by which yielding, fracture or excessive deformation occurs in a load-carrying member. Shear strength is a material property that describes a material’s resistance against a shear load before the component fails in shear. The shear action or sliding failure described by shear strength occurs parallel to the direction of the force acting on a plane.

In construction, automotive, aerospace and other engineering industries, knowing the shear strength of materials is vital for the design of mechanical and structural devices as well as the selection of materials to be used for an application. It is also a major consideration in sizing components or parts [1].

• The difference between shear strength and shear stress
• The several theories of failure in materials
• The theory of maximum shear stress
• How shear strength is tested
• The common materials that undergo shear strength testing

## Shear strength and shear stress

Shear strength and shear stress are often used interchangeably, but there is a technical distinction between the two. Shear stress is relative and it changes in relation to the amount of shear load applied to a material per unit area. On the other hand, shear strength is a fixed and definite value in the general nature of a material [1, 2].

## Theories of failure

In order to understand shear strength, understanding different theories of failure are important.

Generally for brittle materials, the cause of failure is due to a force in tension

For ductile materials, the cause of failure is often due to shearing forces.

The stress-strain curve for these two types of material is different. Typically, material strength parameters are identified by conducting uniaxial tests. But in reality, situations produce multi-dimensional and combined stresses that act at a point or throughout a member, and for which it would be impractical to measure each of the stresses and its effect.

Failure theories are necessary in order to predict a material’s performance in relation to its tensile strength and to establish a relationship of each stress source induced.

For brittle materials, the failure by shear is caused by the sliding of the material’s atoms brought on by shear stresses and distortion. Therefore, for design purposes, the yield strength in shear is the strength parameter to be used [2, 3, 4].

## Maximum shear stress theory

This theory states that material failure will take place when the maximum shear stress brought on by combined stresses will equal or be greater than the obtained shear stress value at yield in a uniaxial tensile test [2-4].

Suppose in a uniaxial test, the principal stresses are:

sigma _{1} = S_{y}

sigma _{2} = 0

sigma _{3} = 0

where σ1, σ2, σ3 = maximum normal stress a body can withstand at a certain point; Sy = yield strength.

The shear strength at yielding is:

S_{sy}=\frac{(\sigma _{1}-\sigma_{2})}{2}=\frac{S_{y}}{2}

or

S_{sy}=\frac{(\sigma _{1}-\sigma_{3})}{2}=\frac{S_{y}}{2}

For a homogenous, isotropic, ductile material with two or three-dimensional static stress, to identify and compute for σ1, σ2, σ3 and the maximum shear stress, 𝜏max:

tau_{max}=\frac{(\sigma _{1}-\sigma_{2})}{2}

According to the maximum shear stress theory, we can then compare the maximum shear stress to the failure criterion:

tau _{max}\leq S_{sy}

And therefore, the factor of safety can be given by:

N=\frac{S_{sy}}{\tau _{max}}

## Shear strength tests

Shear strength is one of the key considerations in designing many parts, including fasteners such as pins, bolts and screws. Shear tests can be conducted in two ways in order to determine the maximum shear stress.

1. The first method is performed in a way such that a sample is anchored at both ends so the material may experience a double shear until failure, removing its midsection.
2. The second method is achieved by placing the material’s tapered ends in a fixture that is offset from the vertical axis and then applying a pulling force.

## Materials for shear strength testing

Many materials are tested for their shear strength to be known, but they can be categorised into three groups: rigid substrates, layered composites and adhesives. Shear strength testing helps categorise an adhesive according to shear strength when pulled from the material to which it adheres. Metals, wood and plastics fall under the rigid materials category. Layered composites’ shear strength is determined by testing the limits of its laminates, layers and fibres [5].

Here are the shear strength values of some interesting materials with their relative applications.

 Material Shear Strength (MPa) Applications AMPCOLOY® 83 Rolled material 620 Flash butt welding, parts for electrical components AMPCO® M4 Extrusions 538 Aircraft landing gear bearings, bending dies, gear wheels AMPCO® 45 Extruded and drawn rods 448-483 Aircraft bearings, pump and marine shafts and wear rings AMPCO® 21 Continuous cast 414 Die rings, inserts, forming rolls Phosphor Bronze 250-430 Springs, clips, gauzes, architectural applications Aluminium 5083 H321 185 Fluid Systems, Fluid Storage, Automotive Aluminium 5083 ‘F’ Extrusions 175 Fluid Systems, pressure vessels, commercial vehicles

## Sources

[1] G.N. Frantziskonis, Essentials of the Mechanics of Materials, PA: DEStech Publications, Inc., 2013.

[2] "Theories of Failure", n.d. [Online] Available at: https://www.engr.mun.ca/~katna/5931/Theories%20of%20Failure2.pdf  [Accessed on: 29.11.2019]

[3] "Theories of Failure", n.d. [Online] Available at: http://thegateacademy.com/files/wppdf/Theories-of-failure.pdf [Accessed on: 29.11.2019]

[4] "The second graph is of only the plastic region beyond the strain hardening", n.d. [Online] Available at: https://www.coursehero.com/file/p60393o/The-second-graph-is-of-only-the-plastic-region-beyond-the-strain-hardening-This/ [Accessed on: 29.11.2019]

[5] "Shear Test", n.d. [Online] Available at: https://www.testresources.net/applications/test-types/shear-test/ [Accessed on: 29.11.2019]