Mechanical Properties Review: Strength, Stiffness, and Hardness Comparisons

Comprehending the distinctions among the mechanical properties of strength, stiffness, and hardness is fundamental in the realm of mechanical engineering, yet these properties frequently encounter misinterpretations. While interrelated, each property holds distinct significance:

Stiffness denotes the propensity of a component to revert to its initial configuration subsequent to encountering an external force.

Strength quantifies the maximum stress that a component can endure before experiencing permanent deformation or structural failure.

Hardness delineates a material’s resistance to surface alteration under applied pressure. Notably, for certain metals such as steel, hardness often correlates with tensile strength, as elucidated in ASTM A 370-68 Steel Tables.

This article aims to elucidate the fundamental aspects of each property, pinpoint common pitfalls in distinguishing mechanical strength from stiffness and hardness, dissect the technical disparities among them, and deliberate on their implications in material selection for product design and development.

Distinguishing between strength and stiffness can pose a particular challenge. It is a common misconception that a material exhibiting high stiffness necessarily boasts adequate strength to support substantial loads. However, this is not always the case. Material properties can manifest as both resilient and stiff or robust and stiff, as elaborated upon in the section “Axial Loading on a Straight Member.” Therefore, it is imperative to recognize that strength and stiffness constitute distinct attributes, with various manifestations of material strength encompassing tensile and yield strength, among others.

Key Definitions

  1. Yield Strength: Yield strength characterizes the elastic behavior of materials, denoting the maximum tensile stress they can sustain before undergoing permanent deformation.
  2. Ultimate Strength: Ultimate strength refers to the maximum stress a material can endure before failure.
  3. Fracture Strength: Fracture strength indicates the stress level at which complete failure of the material occurs.
  4. Stiffness: Stiffness denotes a material’s resistance to elastic deformation when subjected to an applied load.
  5. Hardness: Hardness measures a material’s resistance to localized surface deformation.
  6. Tensile Strength: Tensile strength, derivable from hardness tests such as Rockwell, is relatively easy to ascertain. These tests are simple, cost-effective, and non-destructive, involving minimal penetration into the specimen. In many metals, tensile strength correlates with hardness, increasing as hardness does.

Young’s Modulus: Young’s Modulus stress-strain curve serves as an invaluable tool for understanding the interplay between stiffness and strength. Young’s Modulus, also known as elastic modulus, shear modulus, or bulk modulus, quantifies a material’s ability to resist elastic deformation under load. It represents the ratio of normal stress to normal strain, providing insight into a material’s propensity to stretch and deform under external forces.

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Elastic Modulus and Material Stiffness

Stiffness refers to a material’s capacity to revert to its original shape following the application of an external force, while strength denotes the maximum stress a material can withstand before undergoing plastic deformation or fracturing. These properties are intricately linked to the material’s elastic modulus, which defines its stiffness. Consequently, an increase in elastic modulus corresponds to a rise in material stiffness.

To assess stiffness, one can examine the stress-strain curve, with stiffness quantified by the slope of this curve. Various stiffness parameters exist, tailored to specific applications, such as tension/compression stiffness, axial force ratio, axial linear strain (EA), torsional stiffness, bending stiffness, beam stiffness, spring stiffness, and shear stiffness.

In mathematical terms, stiffness can be calculated using the formula:

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To ascertain the stiffness or strength of a given material, consulting a materials properties handbook for the elastic modulus values is advisable. This approach facilitates the estimation of the material’s stiffness or strength based on its elastic modulus.

The stress-strain curve depicted above represents the Young’s modulus, serving as a valuable tool for illustrating material stiffness. Defined as the ratio of stress to strain within the elastic region, Young’s modulus quantifies a material’s inherent stiffness. However, it is imperative to recognize that a material’s strength is exclusively determined by its response to stress, distinct from its stiffness properties.


Strength is a fundamental property of materials denoting their ability to withstand external forces without undergoing permanent deformation or fracture. It encompasses various aspects such as tensile strength and hardness, which reflect a material’s resistance to plastic deformation. Understanding different types of strength, such as ultimate tensile strength and yield strength, is crucial for assessing the structural integrity and performance of materials in diverse applications. Ultimate tensile strength represents the maximum stress a material can endure before failure, while yield strength indicates the stress threshold beyond which plastic deformation initiates. The interpretation of stress-strain curves aids in distinguishing materials based on their stiffness characteristics, with ductile materials exhibiting distinct behaviors. For a comprehensive understanding of material strength and its implications, delve into Strength Theory.


Hardness serves as a key metric characterizing a material’s ability to resist plastic deformation or penetration by external forces, such as pointed tools. It is a pivotal consideration in scenarios involving material interaction, where the relative hardness influences scratching or deformation outcomes. Hardness is contingent upon various factors including ductility, plasticity, strain, strength, toughness, viscosity, and viscoelasticity, collectively shaping a material’s resistance profile. Assessing hardness typically involves employing hardness testing methodologies, wherein a probe with a rigid (often diamond) tip is applied to the material under controlled force to measure the resultant indentation or depth of plastic deformation. This process facilitates the evaluation of wear resistance, as harder materials tend to exhibit superior resistance against abrasion or erosion, making hardness testing an indispensable tool in materials characterization and selection processes.

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Understanding Stress and Strain in Mechanical and Structural Components

Stress is an internal force that arises from an external load applied to a mechanical or structural component, acting on its cross-sectional area. Conversely, strain refers to the deformation, or change in shape or size, that occurs in response to applied forces. There are two principal types of strain corresponding to the types of stress:

  1. Normal Strain: This type of strain manifests as deformations perpendicular to the cross-section and is induced by normal stress.
  2. Shear Strain: Shear strain involves deformations parallel to the cross-section and is caused by shear stress.
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Key Stressors in Structural Analysis

In structural analysis, various stressors are encountered, including axial loads, shear stresses, torsional stress, and bending stress. Each of these stressors influences the behavior and response of the structural elements.

Illustrative Examples: Strength vs. Stiffness To delineate the disparity between strength and stiffness, let us revisit fundamental concepts. The ensuing examples and the accompanying calculator serve as intellectual exercises to enhance comprehension.

Beam Deflection Analysis

A finite element analysis (FEA) visualization of a beam subjected to loading showcases the resultant deflection arising from internal bending and shear stress. If the internal stresses surpass the yield strength of the material composing the beam, a material exhibiting higher Young’s Modulus, thereby possessing elevated stiffness, is requisite to withstand deformation and mitigate the risk of permanent deformation or fracture.

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Tool Utilization

Area Moment of Inertia Calculator For a straightforward determination of the Area Moment of Inertia pertaining to round or solid tubes, as well as rectangular beams, or for assessing deflection and stiffness in a cantilever beam configuration, our Area Moment of Inertia Calculator offers an expedient solution. This tool facilitates exploration of geometric variations to comprehend how the cross-sectional configuration influences stiffness and deflection characteristics.

Modulus of toughness formula

The modulus of toughness is a critical mechanical property that characterizes a material’s ability to absorb energy before fracturing. It is a fundamental parameter in materials science and engineering, providing valuable insights into a material’s resilience and durability under various loading conditions.

The formula for calculating the modulus of toughness involves integrating the stress-strain curve obtained from tensile testing. Mathematically, it is represented as the area under the stress-strain curve up to the point of fracture. This integral encompasses both elastic and plastic deformation regions, reflecting the total energy absorbed by the material before failur

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This formula encapsulates the entire mechanical response of a material, capturing its ability to deform plastically and absorb energy before ultimate failure. Understanding the modulus of toughness is indispensable in materials selection and design optimization, as it informs engineers about a material’s performance under real-world loading conditions. By evaluating this parameter, engineers can make informed decisions to ensure the reliability and safety of engineered structures and components.

Axial Loading Analysis of Straight Members – Focus on Stiffness

To delve deeper into the concept of stiffness, let us examine the behavior of a metal bar under tensile loading, experiencing axial stress. As the material reaches its yield point at 100 lbf, it undergoes a deformation of 1% relative to its original length before fracturing.

Now, let’s contrast this scenario with that of a rod-shaped polymer possessing rubber-like properties, subjected to the same axial load. This polymer deforms by 5% of its original length before failure occurs at 100 lbf. While both materials exhibit equivalent strength, the metal demonstrates superior stiffness compared to the polymer. Stiffness, in this context, refers to the material’s ability to resist deformation under applied loads. This analytical exercise vividly illustrates the principle that as stiffness increases, deformation for a given load diminishes.

what is another term for an arrow’s resistance to bending

Another term for an arrow’s resistance to bending is its stiffness. Stiffness refers to the arrow’s ability to resist bending when subjected to external forces, such as those encountered during flight or upon impact with a target. A stiffer arrow will exhibit minimal bending or deflection, leading to improved accuracy and consistency in trajectory. Therefore, when selecting arrows for archery or other applications, considering their stiffness is crucial to achieving desired performance outcomes.

Tensile strength vs yield strength

Tensile strength and yield strength are both critical mechanical properties used to evaluate the performance and suitability of materials for various applications. Tensile strength refers to the maximum stress a material can withstand before fracturing under tensile loading conditions. It essentially represents the ultimate capacity of a material to resist breaking when subjected to pulling forces.

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On the other hand, yield strength denotes the stress level at which a material begins to deform plastically, exhibiting permanent deformation without undergoing fracture. It signifies the onset of yielding or plastic behavior in the material. Unlike tensile strength, which indicates the maximum stress endured before fracture, yield strength reflects the stress point at which a material transitions from elastic to plastic deformation.

In practical terms, yield strength is a crucial parameter in engineering design as it defines the limit within which a material can be loaded without undergoing permanent deformation. Understanding both tensile and yield strengths is essential for ensuring the structural integrity and safety of components subjected to mechanical loads, guiding material selection and design optimization processes accordingly.

Consideration of Tensile Strength

In the context of material testing, the tensile strength test serves as a pivotal assessment method for quantifying a material’s resistance to breaking under tension.

Analyzing Thermal Stress Effects

Furthermore, thermal stress represents a crucial factor influencing the deformation characteristics of a component already subjected to mechanical loading. Thermal stress arises due to temperature differentials within the member, exacerbating existing strain conditions. For instance, when a metal bar experiences temperature fluctuations, leading to expansion or contraction, it undergoes additional stress. When this thermal stress combines with external mechanical loads, the material’s susceptibility to failure increases. The calculation of thermal stress involves intricate methodologies tailored to the specific thermal and mechanical properties of the material under consideration.



𝜎 = thermal stress 

Where α = coefficient of thermal expansion 

ΔT = difference in initial temperature and final temperature 

E = Young’s Modulus 

The depicted equation elucidates the relationship between thermal stress and Young’s Modulus, a fundamental measure of material stiffness. Analyzing thermal stress facilitates informed decisions regarding the selection of stiffness and strength parameters conducive to the desired design outcome, under the assumption that the temperature differential does not induce significant alterations in the material’s microstructural properties.

Toughness vs hardness

Toughness and hardness are two fundamental mechanical properties that play crucial roles in material selection and design optimization. While they are related concepts, they address different aspects of a material’s behavior under stress.

Hardness refers to a material’s resistance to surface indentation or abrasion, often measured using standardized tests like the Rockwell or Vickers hardness tests. It indicates how well a material can withstand localized forces without undergoing plastic deformation or damage. Materials with high hardness values are typically more resistant to wear and scratching, making them suitable for applications exposed to abrasive environments or mechanical loading.

On the other hand, toughness characterizes a material’s ability to absorb energy and deform plastically before fracturing. It reflects the amount of energy a material can absorb before failure and is crucial in applications where impact or sudden loading occurs. Toughness is influenced by factors such as material composition, microstructure, and processing techniques. Ductile materials, such as certain metals and polymers, tend to exhibit higher toughness due to their ability to deform and redistribute stress before ultimate failure.

In engineering applications, the balance between hardness and toughness is often sought to achieve optimal performance. While hard materials offer superior resistance to surface damage, excessively hard materials may lack the ability to deform and absorb energy, leading to brittle failure. Conversely, excessively tough materials may be prone to deformation or excessive plasticity, compromising dimensional stability and precision.

Therefore, a comprehensive understanding of both hardness and toughness is essential in material selection and design optimization to ensure that the chosen material exhibits the desired combination of properties for the specific application requirements.

Mechanical Property Data Acquisition

In the pursuit of obtaining mechanical (or thermal, or electrical) property data for specific materials, professionals often turn to authoritative sources such as the American Society for Testing Materials (ASTM) or the official websites of material manufacturers. These repositories typically offer a comprehensive array of data points encompassing material stiffness, mechanical strength, hardness, and tensile strength. Notably, MatWeb stands out as a reliable and expedient resource renowned for its accurate data compilation.

For those unfamiliar with interpreting material data sheets to extract mechanical property data effectively, a valuable resource is available: “How to Read Material Data Sheets.

Throughout the design phase, adherence to best practices is paramount:

  1. Identification of Critical Components: During the initial stages, such as CAD modeling, meticulous identification of critical components is imperative. This involves discerning which components will be subjected to various load types, including impact, uniform, concentrated, or constant loads. Utilizing graphical representations such as bond graph or block-diagram modeling aids in conceptualizing complex dynamical systems. Additionally, sophisticated software facilitates modeling intricate systems with precision.
  2. Analysis of Applied Forces and Stress Calculation: Subsequent to component identification, it is essential to calculate the anticipated stresses on mechanical elements. This process illuminates potential areas of concern and reveals areas of significant force concentration. Employing instrumentation techniques to gauge the design’s response to diverse inputs, coupled with meticulous data analysis, enables accurate prediction of the model’s behavior. Consideration of variables such as creep and fatigue, both within subsystems and in the environmental context, is crucial. A comprehensive mechanical engineering design manual serves as a valuable reference for stress calculation methodologies.
  3. Material Selection Strategies: Each material category possesses distinct mechanical, thermal, and electrical properties, making prudent material selection imperative. Optimal material choice hinges upon the specific application requirements. For instance, ceramics typically exhibit brittleness, characterized by minimal deformation before fracture, leading to rapid crack propagation. Conversely, metals demonstrate varying responses to stress, manifesting as either ductility or brittleness. Ductile materials undergo plastic deformation before fracture, while brittle materials lack this property.

The fracture process in ductile metals typically progresses through multiple stages, with the ductility and brittleness of polymers contingent upon temperature variations. When selecting raw materials, it is imperative to identify manufacturing processes that yield desired material properties. Material testing should adhere to ASTM standards, necessitating consultation of engineering handbooks for reliable material data.

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Moreover, material selection should consider environmental exposure conditions. The chemical composition of a material dictates its resistance to environmental factors such as water, salt solutions, or chemical corrosion. Stainless steel, aluminum, and titanium emerge as favorable choices for their resilience to environmental degradation. Notably, a material’s hardness is pivotal in determining its suitability for abrasive environments like desert conditions, with a general guideline suggesting a higher hardness than encountered abrasive materials to mitigate material loss.

  1. Validate Designs Pre-Prototype

Prior to prototyping, design optimization and validation are imperative, with CAD software facilitating geometry assessment and optimization. Employing FEA and numerical analysis is advisable, supplemented by hand calculations for validation to economize time and resources. Collaborating with other engineers for peer review is also beneficial.

Additionally, designing for manufacturability (DFM) is crucial in optimizing designs for production, considering the constraints imposed by manufacturing methods. Fictiv offers instant DFM feedback for every design uploaded to their platform, ensuring compatibility with manufacturing processes.

Key Insights

A thorough comprehension and integration of stiffness, strength, and other mechanical properties in the design process are essential for developing high-quality products. A clear understanding of the product’s intended application is pivotal in selecting cost-effective, safe materials with requisite structural integrity to meet performance objectives. Key considerations when making material selections include:

  • Mechanical strength, measuring a material’s resistance to deformation or fracture under stress.
  • Stiffness, indicating the propensity of an element to revert to its original shape post-force application.
  • Hardness, denoting a material’s resistance to surface deformation.
  • Young’s Modulus, quantifying a material’s ability to resist elastic deformation.
  • Ultimate Tensile Strength, representing the maximum tensile load a material can endure before fracturing.

Streamlining Procurement

In the pursuit of sourcing materials tailored to meet stringent criteria such as strength, stiffness, and hardness for your upcoming project, BOYI stands ready to assist. Whether your requirements call for CNC machining, injection molding, 3D printing, or urethane casting, BOYI serves as your comprehensive solution for bespoke mechanical components. Our team of engineering professionals is adept at material selection aligned with your specific application needs, providing invaluable guidance throughout the manufacturing journey to ensure optimal outcomes.

Embark on your journey by establishing an account and uploading your design today to experience firsthand the efficacy of our instant quoting system, Design for Manufacturability (DFM) insights, and the intuitive BOYI platform. Witness how we seamlessly deliver intricate components with unparalleled efficiency!

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