Tensile Stress Explained: Definition, Formula, Units, and Practical Examples

Tensile stress is an essential concept in understanding the strength of materials and their capability to endure loads in the real world. It is the ratio of a stretching force to the cross-sectional area of a material. This article will discuss the tensile stress definition, formula, and unit of measurement when calculated.

What Is Tensile Stress?

Tensile stress is the ratio of a stretching force acting on a material to the cross-sectional area of that material. It is the force per unit area that is putting an object in tension. Tensile stress is measured in standardized material tests to indicate tensile strength—the maximum stress that a material can withstand before breaking. It is a key parameter in the selection of materials and occurs when a stretching force acts on a material, or in other words, when an object is under "tension."

When Does Tensile Stress Occur?

Tensile stress occurs when a stretching force acts on a material, or in other words when an object is under tension.

What Can Be Calculated When Tensile Stress Acts on a Material?

When tensile stress acts on a material, there are a number of essential properties that can be calculated as a result, including:

1. Modulus of Resilience

The modulus of resilience is the amount of energy elastically stored in a material per unit volume. The resilience is calculated as the area under the curve of the tensile stress-strain curve, before the elastic limit (before the material starts to deform plastically). Resilience indicates the energy stored in a material that is under stress, as energy can be calculated as the product of force (stress) and distance (strain). The modulus of resilience is specifically per unit volume.

2. Elastic Modulus

The elastic modulus also referred to as the modulus of elasticity or Young’s modulus, can be calculated by applying tensile stress to a material. The elastic modulus is the ratio between tensile stress and longitudinal strain (stretching). It is calculated as the gradient of the tensile stress curve in the elastic section. The elastic modulus infers how much strain a material will experience when subjected to a specific tensile stress.

3. Fracture Stress

Fracture stress is the tensile stress at which the material breaks (fractures). In a tensile stress test, fracture stress is the stress recorded at the end of the trial when rupture occurs. For ductile materials, the stress at fracture will be lower than the ultimate tensile stress, as necking occurs in the material sample.

4. Ultimate Tensile Stress

Ultimate tensile stress is the maximum tensile stress that a material is able to withstand before fracture. During testing (according to Hooke’s law), the stress is proportional to the strain (stretching) of a material in the elastic deformation region. As strain increases, the material begins to deform plastically (irreversibly). Maximum tensile stress will occur in the material at a point in the plastic deformation—this is the ultimate tensile stress. As strain increases past this point, the tensile stress drops until fracture.

The Formula for Tensile Stress

The formula for tensile stress is simply force over area, written as:

σ = F/A

Tensile stress is the ratio of the stretching force applied to the cross-sectional area of the material experiencing the tension.

What Is the Unit of Tensile Stress?

The unit of tensile stress is the pascal (Pa). This is force over area, similar to pressure; thus, tensile stress shares units with pressure. The units can therefore also be stated as N/m2, or else as psi. Due to the magnitude of tensile strengths of common materials, the unit most commonly used is MPa (1 x 106 Pa).

What Is the Tensile Stress Symbol?

The symbol for tensile stress is the Greek lowercase letter sigma σ.

How To Calculate Tensile Stress?

To calculate tensile stress, first begin with the formula:

σ = F/A

Tensile stress is calculated as the tensile force applied, divided by the cross-sectional area. The second step then is to establish the force acting on the material, in newtons or pounds-force. The third step is to calculate the cross-sectional area that the force is acting on. This is specifically the area perpendicular to the direction of the tensile stress. It is essential to consider the possible deformation of the object due to the tensile stress acting on it. The tension causes the material to stretch, which thins the material and reduces its cross-sectional area. This should therefore ideally be measured when under stress. Finally, the tensile stress is calculated by dividing the force by the cross-sectional area.

How To Understand the Tensile Stress Curve?

To understand the tensile stress curve, it is important for you to first learn how the curve is created. The material to be tested, in a dumbbell (or dogbone) shape, is placed into a machine that grips each end. The grips then move apart slowly, increasing the strain (displacement) of the material, and inducing stress. The strain is increased until the material breaks, and the stress is measured throughout. The relationship between stress and strain is plotted, with the constantly increasing strain on the X-axis, and the resulting stress on the Y-axis.

Second, there are key points to be identified on the tensile stress curve—refer to Figure 1 below: