Time to read: 15 min
This article was originally published in February 2017 by Humberto Villasenor. The content has been updated.
Understanding the differences between the mechanical properties of strength vs. stiffness vs. hardness is foundational in mechanical engineering, yet these properties are often confused. These properties are related, but they have important differences:
- Stiffness is an indicator of the tendency for an element to return to its original form after being subjected to a force.
- Strength measures how much stress can be applied to an element before it deforms permanently or fractures.
- Hardness measures a material’s resistance to surface deformation. For some metals, like steel, hardness and tensile strength are roughly proportional (see ASTM A 370-68 Steel Tables).
For this article, we’ll review the fundamentals of each, identify common pitfalls differentiating mechanical strength vs. stiffness vs hardness, examine the technical differences between the three, and discuss their relevance in the selection of materials for product development.
It’s especially easy to confuse strength vs stiffness. If a material is stiff, then it must be strong enough to support a large load, right? So, aren’t strength and stiffness the same? No! A material can be strong and elastic or strong and stiff (See section “Axial Loading on a Straight Member”), but strength and stiffness are two separate qualities — there are many types of material strength, including tensile and yield strength.
Key Definitions
- Yield strength is used to describe materials that exhibit elastic behavior. It’s the maximum tensile stress the material can handle before permanent deformation.
- Ultimate strength refers to the maximum stress before failure occurs.
- Fracture strength is the value corresponding to the stress at which total failure occurs.
- Stiffness is how a component resists elastic deformation when a load is applied.
- Hardness is resistance to localized surface deformation.
Tensile strength can be calculated from hardness and is easy to determine because hardness tests — such as Rockwell — are simple to perform, inexpensive, and non-destructive because only a small penetration is performed on the specimen. For many metals, tensile strength increases as hardness increases.
Young’s Modulus
Young’s Modulus stress-strain curve is a great reference tool for understanding the relationship between stiffness and strength. Young’s Modulus (aka elastic modulus, shear modulus, or bulk modulus) defines a material’s ability to resist elastic deformation while under loading conditions and is the ratio of normal stress to normal strain. In basic terms, this tells us how easily a material can stretch and deform.
Stiffness
Stiffness is a material’s ability to return to its original form after being subjected to a force. Strength is how much stress can be applied to a material before it goes into plastic deformation or fractures. Stiffness and elastic modulus are related: as the elastic modulus goes up, the stiffness of a material also goes up. Since stiffness and strength are related to the elastic modulus of a material, you can look up the elastic modulus in a material properties reference handbook to determine the strength and/or stiffness of a given material.
The stiffness of a material can be quantified by the slope of the stress-strain curve, as illustrated in the graph below. There are many types of stiffness to consider, depending upon your application, including tension/compression stiffness, axial force ratio, axial linear strain (EA), torsional stiffness, bending stiffness, beam stiffness, spring stiffness, and shear stiffness. In general terms, the stiffness of a material is calculated by using the following equation:
stiffness =
Force
displacement
The Young’s modulus stress-strain curve shown above is a good way of graphically demonstrating stiffness. The ratio of stress to strain is the elastic modulus (stiffness), but the way a material responds to stress, and only the stress, defines the strength of the material.
Pro-Tip: Check out How to Design for Part Stiffness Using a Geometric Approach for a deeper dive into stiffness and how it’s related to part geometry.
Strength
Strength measures how much stress a material can handle before permanent deformation or fracture occurs. Both tensile strength and hardness are indicators of a metal’s resistance to plastic deformation. Multiple types of strength are worth considering depending on your application, including ultimate tensile strength vs yield strength. Ultimate tensile strength is the maximum stress a material can withstand before it fails or breaks (which is the failure point in the graph above). Yield strength is the maximum stress a material can withstand before plastic deformation occurs (which is the yield point inthe graph above). Simple stress-strain curves illustrating stiff vs non-stiff behavior. Curves A and B correspond to stiffer materials, whereas curve C represents a non-stiff (ductile) material. (Image source)
Pro-tip: If you want more information on how materials respond to stress and how to determine the strength of materials, check out Strength Theory.
Hardness
Hardness is a measure of a material’s ability to withstand plastic deformation or a material’s resistance to penetration by a pointed tool. This is a critical characteristic to consider in applications with two materials impacting each other — the harder one will scratch or cause plastic deformation on the other material. Hardness is dependent upon ductility, plasticity, strain, strength, toughness, viscosity, and viscoelasticity. It’s an important measure when considering the wear resistance (abrasion or erosion resistance of a part) since harder materials typically have higher wear resistance.
Hardness testing is accomplished by lowering a probe with a hard (typically diamond) tip onto a material at a set force and measuring the amount of indentation that the probe (the indentor) produces (depth of plastic deformation). Hardness testers also operate by measuring the size of the impression left by the indentor.
Understanding Stress and Strain
Stress is an internal force resulting from an applied load; it acts on the cross-section of a mechanical or structural component. Strain is the change in shape or size of a body (deformation) that occurs whenever a force is applied. There are two types of strain that correspond with the two types of stress:
- Normal Strain: deformations that occur perpendicular to the cross-section; normal strain is caused by normal stress
- Shear Strain: deformations that occur parallel to the cross-section; shear strain is caused by shear stress
Top left: axial load causing tension or compression. Top right: shear stresses within a member. Bottom left: torsional stress about a circular cross-section. Bottom right: Bending stress caused by a moment.
Examples: Strength vs. Stiffness
To further understand the difference between strength and stiffness, let’s go back to the basics of how we were or were probably initially taught about strength and stiffness. Utilize the following examples and downloadable calculator as thought exercises to deepen your understanding of the concepts of stiffness vs strength.
Beam Deflection
The image below is a finite element analysis (FEA) rendering of a beam subjected to a load. The beam’s response to the loading is a deflection resulting from internal bending and shear stress. If the internal stresses exceed the yield strength of the beam’s material, then you need a material with a higher Young’s Modulus value — a material with higher stiffness (to resist deformation) and also higher yield strength (to prevent permanent deformation and possible fracture).
Finite Element Analysis of beam deflection.
Area Moment of Inertia Calculator
If you’re looking for a simple way to calculate the Area Moment of Inertia for a round tube, solid tube, or rectangular beam — or to calculate deflection and stiffness for a cantilever beam — you can use our Area Moment of Inertia Calculator. This tool also allows you to play around with geometry to understand how the cross-sectional shape of a part impacts stiffness and deflection.
Download Free Calculator