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Stress vs Strain explained: The essential Guide

In 3D printing, understanding stress and strain is key to designing strong, reliable parts. Whether you’re printing a cross brace, a tensile rod, or a load-bearing figure, these principles help predict how a printed object will react to applied force. This guide explores the core differences between stress and strain and how they influence material behavior in 3D printing applications. 

Key Takeaways

  • Stress refers to the internal forces within a material, expressed as force per unit area
  • Strain measures the deformation of a material under those forces, expressed as a dimensionless ratio
  • The stress-strain curve is a graphical representation that highlights a material’s response to stress, revealing its elastic and plastic behavior
  • Understanding the interplay between stress and strain is crucial for safe and efficient engineering design
  • Different materials behave uniquely under stress, with properties like ductility and brittleness shaping their responses

What is Stress? Understanding internal forces in materials

Stress is a term you’ll encounter frequently in engineering and material science, and it’s all about how internal forces develop within a material. When you apply a load to a material, it doesn’t just sit there passively. Instead, it reacts, and this reaction is what we call stress. Understanding stress is crucial because it helps engineers determine how materials will respond to various external loads, whether it’s the weight of a building or the tension in a cable.

Stress is defined as the force applied per unit area within materials. Imagine pressing down on a block of rubber. The force you exert is distributed across the surface area of the rubber, and this distribution is what creates stress. There are several types of stress. 

Stress can be:

  • Normal stress : Acts perpendicular to the surface or cross-section.
  • Shear stress : Acts parallel to the surface, common in layer delamination.
  • Bulk stress : Involves volume change under uniform pressure.
  • Tensile stress : Pulls the object, causing elongation.
  • Compressive stress : Pushes inward, reducing object length.

Stress is about recognizing how these internal forces influence material strength. For instance, a bridge designed without accounting for stress might buckle under pressure, leading to catastrophic failure. Therefore, measuring stress accurately and understanding its implications on material behavior are paramount. Terms like elastic modulus and yield strength come into play here, helping predict how close a material is to permanent deformation.

Stress is expressed in units of pressure, such as Pascals (Pa), and is a pivotal factor in determining the ultimate tensile strength of materials. 

stress formula
Stress Formula

σ is stress, measured in N/m² or Pa

F is the applied force, measured in Newtons (N)

A is the cross-sectional area to which the force is applied, measured in m²

What is Strain? Measuring material deformation

While stress deals with internal forces, strain is all about what those forces do to a material. Strain measures how much a material deforms when subjected to stress. It’s an indicator of the material’s response to how far it stretches, compresses, or twists under a given force. 

To calculate strain, engineers look at the change in length of a material divided by its original length. This gives us a dimensionless ratio, making strain a pure measure of deformation. Think of it as the percentage change in an object’s shape. 

strain formula
Strain Formula

Strain (ε) is the fractional or percentage change in length or another dimension.

L is the length of the material after an external load is applied.

L0 is its original length measured in the same units as “L”.

There are different types of strain, each type provides insights into how materials react under specific conditions.

Types include:

  • Tensile strain: Object stretches.
  • Compressive strain: Object shortens.
  • Shear strain: Object skews or twists.

A material with a high tensile strain might elongate significantly before breaking, while a material with low compressive strain might resist squishing until it shatters. Understanding these properties helps engineers select the right materials for specific applications, ensuring safety and reliability.

While strain is dimensionless, its implications are profound. It highlights whether a material will undergo elastic deformation returning to its original shape after stress is removed or plastic deformation, where changes are permanent. By plotting strain against stress on a graph, engineers can visualize the material’s behavior, leading to the next crucial concept: the strain curve.

The fundamental relationship: How Stress causes Strain

Now that we’ve explored stress and strain individually, it’s time to connect the dots. Stress and strain have a symbiotic relationship, where stress directly causes strain in materials. When stress is applied, the material deforms, and this deformation is what we measure as strain. The interplay between these two concepts is fundamental for understanding material behavior under load. 

The relationship between stress and strain isn’t uniform across all materials. Elastic materials, like rubber bands, demonstrate a linear relationship where they return to their original shape after the stress is removed. This is due to their elastic modulus, a measure of a material’s ability to resist deformation. On the other hand, some materials experience plastic deformation, where they don’t fully recover their original shape, like a bent piece of metal.

Stress strain curve
Stress-strain curve

The stress-strain curve is a fundamental tool in materials science and mechanical engineering for analyzing how a material behaves under tensile force. It plots stress (σ) on the vertical axis against strain (ε) on the horizontal axis. In the initial elastic region, the material deforms linearly, and it returns to its original shape when the force is removed. The slope of this linear part represents the Young’s modulus, a measure of material stiffness, calculated as:

Young's Module Formula

E is Young’s modulus, a measure of stiffness, expressed in pascals (Pa or N/m²)

σ is stress, measured in newtons per square meter (N/m²) or pascals (Pa)

ε is strain, a dimensionless quantity (no units)

As stress increases beyond the yield strength, the material enters the plastic region, where permanent deformation occurs. During strain hardening, the material strengthens until reaching its ultimate strength, the maximum stress it can endure. After this, necking begins, a localized decrease in cross-sectional area, eventually leading to fracture.

This curve is essential for understanding material performance in 3D printing, particularly when evaluating tensile strength, yield point, elastic modulus, and deformation behavior of printed objects. By studying this curve, engineers can select the right material and orientation for force-bearing parts, ensuring structural reliability.

Stress vs. Strain: Key differences summarized

Aspect Stress Strain
Definition Internal resistance offered by a material per unit area when force is applied The deformation or elongation of a material in response to applied stress
Symbol σ (sigma) ε (epsilon)
Formula σ = F / A (F = Force, A = Cross-sectional area) ε = ΔL / L₀ (ΔL = Change in length, L₀ = Original length)
Units Pascals (Pa) or N/m² Dimensionless (no units)
What it measures Force intensity acting on the material's surface Relative change in shape or size of the material
Depends on Applied force and cross-sectional area Change in length and original length
Type of quantity External mechanical property Geometric (dimensionless) property
Use in 3D Printing Determines how much load a printed part can handle Indicates how much a part elongates or compresses under load
Sculpteo material case Ultrasint® PA11 CF: resists high mechanical stress, great for functional parts Standard SLA resin: shows higher strain, suitable for visual or conceptual models

Why Direction, Area, and Volume matter

In 3D printing, print direction, cross-sectional area, and object volume are key factors that affect how a part handles applied force.

Print orientation decides how the layers are stacked. If a part is printed vertically (along the Z-axis), the layers are stacked one on top of the other. This might make it weaker (depending on the material) in tensile strength because the layers can pull apart more easily. On the other hand, printing along the X-Y plane aligns the layers with the direction of the force, making the part stronger.

Cross-sectional area also matters. Using the formula for stress (σ = F / A), we see that if the area (A) is bigger, the stress (σ) will be lower for the same force (F). For example, a rod with a larger diameter spreads the force over more material, so it’s less likely to break.

Volume affects how much a part resists deformation. A part with more bulk can handle more compressive or shear force without changing shape. This is important for functional parts that need to stay strong under load.

Finally, the surface geometry like adding fillets, ribs, or smooth curves helps spread out the force more evenly. This avoids high stress points that can cause cracks or failure.

By considering direction, area, volume, and geometry, you can design printed parts that are stronger, lighter, and more efficient.

Yield Point and Failure in 3D Printing

The yield point is an important moment in 3D printing design. When a printed part reaches this point under force, it starts to deform permanently it won’t go back to its original shape even if the force is removed. This is a big concern for load-bearing parts, where even a small change in shape can lead to mechanical failure.

Different materials have different tensile and compressive yield strengths. For example, PLA may reach its yield point under a lower stress than nylon, meaning it bends or breaks more easily under load. But PLA might still keep its shape better when used in low-stress situations, thanks to its good dimensional stability.

To avoid unwanted failures, designers need to think about the yield point, the part’s surface quality, and the material’s modulus (how stiff it is). Choosing the right material and design helps make printed parts safe and reliable.

Sculpteo materials comparison

Material Technology Young’s Modulus (MPa) Tensile Strength (MPa) Elongation at Break (%)
PA12 SLS / MJF 1700 ± 150 MPa 45 ± 3 MPa 20 ± 5 %
PA11 CF SLS XY: 5900 MPa Z: 2500 MPa (dry) XY: 82 MPa Z: 55 MPa (dry) XY: 7% Z: 11% (dry)
PA12 Grey GF SLS 3200 MPa 51 MPa 9%
PA2210 FR SLS 2500 (dry) MPa 2400 (cond) MPa 46 (dry) MPa 43 (cond) MPa 4% (dry) 7% (cond)
Ultrasint® PA11 SLS / MJF XY: 1750 MPa Z: 1800 MPa (dry) XY: 52 MPa Z: 54 MPa (dry) XY: 28% Z: 24% (dry, 23°C)
PA11 ESD SLS XY: 3150 MPa Z: 2150 MPa (dry) XY: 65 MPa Z: 55 MPa (dry) XY: 20% Z: 23% (dry, 23°C)
TPU 88A SLS 75 MPa 8 MPa X: 270% Z: 130%

Conclusion: Mastering Stress and Strain for 3D Printing success

To optimize 3D printed parts, engineers must deeply understand how force, stress, strain, and deformation interact. Choosing the right material with suitable modulus values (Young, shear, bulk), optimizing cross-sectional area, and predicting behavior at each stress-strain point leads to reliable prints. Whether you’re designing a cross support, tensile rod, or structural figure, knowing how to control force direction, deformation, and strain ensures the success of your project.

Frequently Asked Questions

What is the difference between stress and strain?

What are the different types of stress?

How do engineers and scientists use stress and strain in their work?

What are some real-world applications of stress and strain analysis?

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