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Understanding the differences amongst 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 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

Strength vs. Stiffness vs. Hardness

It can be especially easy to confuse the difference between strength vs 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. There are many types of material strength, including tensile and yield strength. 

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. 

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 increases1

Young’s Modulus, Strength, and Stiffness 

The Young’s Modulus stress strain curve is a great material tool to reference in order to understand the relationship amongst stiffness and strength. Young’s Modulus, or the elastic modulus, of a material defines a material’s ability to resist elastic deformation while under loading conditions. 

Young’s Modulus =

𝐸=

𝑡𝑒𝑛𝑠𝑖𝑙𝑒𝑠𝑡𝑟𝑒𝑠𝑠

𝑡𝑒𝑛𝑠𝑖𝑙𝑒𝑠𝑡𝑟𝑎𝑖𝑛

E=tensile stresstensile strain

stress-strain curve showing the relationship between stiffness and yield strength

 

Remember that stiffness is a material’s ability to return to its original forma after being subjected to a force and strength is how much stress can be applied to a material before it goes into plastic deformation or fractures. 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. From the diagram below, see that stiffness of a material can be quantified by the slope of the stress-strain curve. 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.

stress-strain showing nonelastic region

The Young’s modulus 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 way a material responds to 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. More information on how material responds to stress and the strength of materials can be found by researching the Strength Theory

stress-strain curves illustrating stiff vs non-stiff behaviorFigure 2. 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 material. (Image source)

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 (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

axial load, shear stresses, torsional stress, and bending stress

Figure 3. 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.

 

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 by consulting the manufacturer’s website from which you’re planning to purchase materials. Values you may obtain could range from material stiffness to mechanical strength to hardness to tensile strength. 

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) rendering 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 to choose a material with a higher Young’s Modulus value—in other words, a material with a higher stiffness to resist the deformation and also higher yield strength to prevent permanent deformation and possible fracture.

FEA analysis of beam deflection.

Figure 5. FEA analysis of beam deflection.

Axial loading on a straight member 

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, which means that it deflects less for the same given loading condition. 

tensile strength test

Figure 6. Tensile strength test.

Thermal stress 

Thermal stress also affects the deformation response of a component that is 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. For example, metals tend to expand when heated and contract when cooled. This causes the metal to be stressed and coupled with any externally applied stress from loading, can propagate and cause more rapid material failure.  

𝜎=𝐸𝛼Δ𝑇 

𝜎=E𝛼ΔT 

𝜎 = thermal stress 

Where α = coefficient of thermal expansion 

ΔT = difference in initial temperature and final temperature 

E = Young’s Modulus 

From the equation above, thermal stress is dependent on Young’s Modulus, or the stiffness of a material. 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! 

Best Practices in Designing for Strength, Stiffness, and Hardness 

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

One: 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 and calculate stress 

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. For a refresher on calculating stresses that designed components are subjected to, refer to my favorite Mechanical Engineering Design book here

3. Best practices for material selection 

As previously discussed, each material type has its own set of mechanical, thermal and electrical properties. Different materials are optimal for different applications. 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 in response to applied stress: ductile or brittle. A ductile material is accompanied by plastic deformation before fracture, while brittle materials are not.

Ductile vs. Brittle

Figure 7. Ductile vs. Brittle

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. 

In addition, material should be selected based off environmental conditions the components will be exposed to. The chemical composition of a material determines its ability to withstand environmental conditions such as water, salt solutions or even chemical attack. Stainless steel, aluminum, and titanium are good material choices when environmental resistance is necessary for the application. The material’s hardness plays a role in determining whether or not it can withstand abrasive environments such as desert conditions. As a rule of thumb, your material should have a higher hardness than the abrasive materials it may come into contact with to prevent material loss.  

 4. Verify your designs before prototyping 

Design optimization and verification should be performed prior to prototyping a design. 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. 

You should also consider Design for Manufacturability when optimizing a design prior to production. Even the most intelligent designs will fail if they are not designed, with the manufacturing methods in mind. To assist with this, Fictiv offers instant DFM feedback with our intelligent platform. Simply upload a model and receive instant optimization tips.   

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. 

Quick Facts 

  • Mechanical strength measures how much stress can be applied to an element before it deforms permanently or fractures. 
  • Stiffness in mechanical engineering is an indicator of the tendency for an element to return to its original form after being subjected to a force. 
  • Hardness measures a material’s resistance to surface deformation. 
  • Young’s Modulus is a quantifier of how much a material is able to resist elastic deformation under loading conditions. A stiff material has a high Young’s Modulus and is able to hold its shape minimally when subjected to elastic loads.  
  • Ultimate Tensile Strength, or referred to as Tensile Strength, is the maximum tensile load a material can withstand prior to fracturing.