# Engineering Fundamentals Refresh: Strength vs Stiffness vs Hardness

Understanding the mechanical properties of strength vs stiffness vs hardness is foundational in mechanical engineering, yet these properties can often be confused. These properties are related, but there are very important differences between them:

• 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 Hardware Guide article, we're doing a refresh of the fundamentals, looking at some common pitfalls in identifying between mechanical strength vs. stiffness vs hardness, the technical differences between the three, and their relevance in the selection of materials for product development.

## Common Pitfalls: Strength vs Stiffness vs Hardness

It can be especially easy to confuse the difference between strength and stiffness. If a material is stiff, then it must be strong enough to support a large load, right? Therefore, aren’t strength and stiffness the same? The answer is a resounding 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.

Let's break it down.

Since stiffness and strength are both related to the elastic modulus of a material (Young’s Modulus), it’s easy to look up the value in a material properties reference handbook and determine the strength and/or stiffness of given material. The elastic modulus measures the stiffness in a material, but strength is a function of the modulus. Both tensile strength and hardness are indicators of a metal’s resistance to plastic deformation.

The stress-strain curve (Figure 1) above is a good way of graphically demonstrating this. The ratio of stress to strain is the elastic modulus—stiffness, but the stress, and only the stress, defines the strength of the material. Remember, strength measures how much stress the material can handle before permanent deformation or fracture occurs, whereas the stiffness measures the resistance to elastic deformation.

## Understanding the Concepts of 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 that occurs whenever a force is applied.

## Important Definitions for Strength, Stiffness, and Hardness

Here are a few important definitions to keep top of mind:

• Yield strength is used in materials that exhibit an elastic behavior. It’s the maximum tensile stress the material can handle before permanent deformation occurs.
• 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.

The strength of a material can refer to yield strength, ultimate strength, or fracture strength. Tensile strength can be calculated from hardness and is convenient because hardness tests—such as Rockwell—are usually simple to do, inexpensive, and nondestructive. Only a small penetration is performed on the specimen. For many metals, tensile strength increases as hardness increases.*

## Retrieving Mechanical Property Data

Mechanical, thermal, or electrical property data may be obtained for specific material types from the American Society for Testing Materials (ASTM), or consult the manufacturer’s website from which you’re planning to purchase materials.

*This is NOT the case for all materials, but for many metallic materials, hardness correlates very well to tensile strength. For details, see ASTM A 370-68 Tables.

A reliable online source is www.MatWeb.com, where accurate data can be obtained quickly.

## Examples: Strength vs. Stiffness

### Beam deflection

The image below is a finite element analysis (FEA) of a beam subjected to a loading. 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’d want a material with a higher Young’s modulus value—in other words, a stiffer material to resist the deformation and also higher yield strength to prevent permanent deformation and possible fracture.

Imagine a metal bar in tension, subjected to an axial load of some value. The internal stresses cause a deformation of 1% the metal’s original length when it breaks at 100 lbf. Next, consider some rubber-like rod-shaped polymer that’s subjected to the same force but deforms 5% its original length and breaks at 100 lbf. Key point: Both materials are equally strong, but the metal is stiffer than the polymer.

## Thermal stress

Thermal stress also affects the deformation response of a component who’s already subject to some force. In this case, due to a temperature gradient within the member, the thermal stress induces additional strain to the strain already imposed by forces acting on it. Thermal stress has effects on the strength of materials. Computing thermal stress provides insight to select what values of stiffness and strength are appropriate for your design, assuming the temperature difference is not large enough that it will change the microscopic properties of the material!

## 4 Best Practices in Designing for Strength and Stiffness

Here are 3 best practices to keep in mind throughout the design process:

### 1. Identify important components in the early stages of your design

In the early stages of your design, such as when constructing the CAD model, determine which components will be critical to your design. Determine which ones will be subjected to impact loadings, uniform loadings, concentrated loads, constant loads, etc., so you get an idea of the stiffness or strength you need for your components. If needed, develop graphical representations of complex dynamical systems using bond graph or block-diagram modeling, and utilize software to model sophisticated systems.

### 2. Determine applied forces to each component

Calculate the expected stresses on mechanical components to find out where problems may arise or where forces may seem large. Measure how the design responds to various inputs using instrumentation techniques and perform data analysis to predict your model’s behavior. Consider creep and fatigue variables in subsystems and associated with the environment to which your system will be exposed.

### 3. Best practices for material selection

Metals, ceramics, polymers, and composites are material types with specific mechanical properties. Ceramics are usually brittle, meaning that there’s hardly any deformation before fracture; cracks may spread extremely rapidly, with very little accompanying plastic deformation. Metals exhibit two modes: ductile or brittle. A ductile material is accompanied by plastic deformation before fracture, while brittle materials are not.

The fracture process for ductile metals normally occurs in several stages—ductile or brittle behavior in polymers depends on temperature. For raw materials, determine which manufacturing processes will provide you with the desired material properties. Testing of materials must conform to ASTM standards; consult engineering handbooks to obtain reliable material data.

### 4. Verify your designs before prototyping

Perform design studies using CAD software to assess and optimize the geometry of your design. Use FEA analysis, numerical analysis; and when feasible, perform hand calculations ensuring results are in agreement before you begin prototyping to save time and money. Consult with other engineers for review.

## Main Takeaways

The proper use and implementation of stiffness, strength, and other mechanical properties throughout your design process will contribute to higher-quality products, since these properties characterize how a material will respond to applied loads. A clear understanding of the intended use of a product is key for choosing appropriate material properties that will promote a cost-effective design while maintaining safety standards, structural integrity, and achieving desired performance.