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Resources3D Printing DesignTensile Stress: Definition, Formula, Unit, Calculation, and Examples # Tensile Stress: Definition, Formula, Unit, Calculation, and Examples By Team Xometry
March 30, 2023
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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.

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. Tensile strength is a key parameter in the selection of materials.

### 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.

## What Is 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 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:

Slide 1 of 1   Tensile stress curve.

Image Credit: https://omnexus.specialchem.com/

The first point is the yield strength, where the material stops deforming elastically (reversibly) and starts to deform plastically (irreversibly). The gradient of the line before this point gives Young’s modulus or the modulus of elasticity. Another key point is the ultimate tensile strength, which is the highest stress recorded during the test. Then the strength at break is the measured tensile stress when the material sample finally breaks. Further, the elongation of the material can be read from the graph and can indicate whether a material is ductile or brittle.

Third, it is necessary to understand the implications of these points on a material’s practical application. The tensile stress applied to a material should never exceed its tensile strength, or else it will break. However, for most practical applications, it is preferable not to have the material deform plastically either. So generally, materials should not experience stress above their yield strength. Further, depending on the rigidity that is needed in an application, the elongation of material and stress also need to be considered—a high deformation (even elastic) may be unacceptable in many applications.

## How Does Tensile Stress Relate to 3D Printing?

Tensile stress relates to 3D printing by causing design decisions to be made during printing that determines the tensile strength of the printed parts. The ultimate tensile strength of a 3D-printed part refers to the maximum tensile stress that the item can withstand. Depending on the intended application for a part, and its desired tensile strength, different decisions will be made while printing.

Some materials used for 3D printing have a higher tensile strength. The need for the part to withstand load may dictate which material is used for printing. Other parameters that can increase the tensile strength of a 3D-printed part include a higher percentage of infill and thicker layers.

### Is Tensile Stress Important in 3D Printing?

Yes, tensile stress is important in 3D printing. This is particularly true for 3D-printed parts that need to withstand loads and stresses during use. Plastic parts that are manufactured with additive techniques are typically more fragile than a similar part that has been injection molded. If a 3D printed part is expected to withstand a meaningful tensile stress (have a reasonable tensile strength), then there are a number of decisions that need to be taken during printing to enable that, including: the 3D printing technology used, the degree of infill, layer thickness, and the axis where the stress is applied. A 3D-printed part is typically weakest in the Z direction—the direction in which layers are added. Higher strength is exhibited when stress is applied in the direction of the layers—the X-Y plane.

## What Are Examples of Tensile Stress?

There are examples of tensile strength in everyday life including stretching a rubber band. The elongation of the rubber band is immediately seen, as well as the thinning of the cross-sectional area. If you are able to pull hard enough, you will apply a tensile stress that is greater than the ultimate tensile strength of the rubber band and it will break.

A tuned guitar string is another example of tensile stress applied to an object. Applying the correct tension to each guitar string is necessary to achieve the correct note from the vibrations of the string. Tuning a guitar adjusts the tension on each string to ensure that it produces the correct note when plucked. If the tension (tensile stress) applied is too great, the string will snap.

An engineering example of tensile stress is the thick wire cables that are used in suspension bridges. Suspension bridges specifically rely on the tensile strength of metal cables to support the load of the vehicles crossing the bridge (and the load of the bridge deck itself).

### How Often Does Tensile Stress Failure Happen?

Tensile stress failure should not happen often, but it depends on how critical the application is. For instance, if a fishing line fails under tensile stress, it is frustrating and inconvenient, but there is very little consequence. However, if a suspension bridge fails due to excessive tensile stress in the cables, that could be a catastrophic failure.

Tensile stress failures are consciously avoided by selecting materials with tensile strengths higher than the stresses that will be experienced in that application. The engineering estimation of the stress to be resisted, and the selection of the material (together with some safety factor) aims to prevent a tensile stress failure.

#### What Is the Difference Between Tensile Stress and Tensile Strength?

Tensile stress is simply the force per unit area acting on the material in an outward normal direction (pulling). Tensile strength, however, is the maximum tensile stress that a material can withstand before breaking. Tensile stress is any force that is stretching or placing tension on a material, but the tensile strength is a specific tensile stress—the highest measured tensile stress in a breakage test.

#### What Is the Difference Between Tensile Stress and Compressive Stress?

The difference between tensile stress and compressive stress is the direction in which the external force is acting. With tensile stress, the force is pulling outwards, stretching the material and causing it to elongate. With compressive stress, the force is pushing inwards, squashing the material. Although the force is in the same plane, the direction is the key difference. Many materials have different compressive strengths compared to tensile strengths—for example, concrete is much stronger in compression than in tension.

## Summary 