Glossary: What are ‘elastic modulus’ and ‘strength’ in material properties?

Introduction

In product design and CAE analysis, correctly understanding material properties is essential. Among these, the concepts of ‘elastic modulus’ and ‘strength’ are particularly important. While seemingly similar, they are distinct concepts. Designers must appropriately distinguish and handle them to enable product development that excels in safety, reliability, and cost efficiency. This article introduces the definitions of both and points to note when using them in CAE.

1. What is Elastic Modulus?

Definition

Elastic modulus, also known as Young's modulus, is a constant representing the proportional relationship between stress applied to a material and the resulting strain. It is defined as the slope of the straight line segment within the proportional limit on a stress-strain diagram.

Mathematically, it is expressed as follows:

　　　　　　　　　E：elastic modulus（Pa）　σ：stress（Pa）　ε：strain（dimensionless）

Characteristics

Higher values indicate greater rigidity: smaller deformation under the same applied force.

Lower values indicate greater flexibility: larger deformation under the same force.

Examples of typical values

Steel (general structural steel SS400): 200 GPa

Aluminium alloy (A5052): 70 GPa

Resin (Polyethylene): Approximately 1 GPa

Thus, the elastic modulus is a numerical indicator of “hardness/rigidity” and is indispensable for predicting a product's deformation behaviour.

2. What is Strength?

Definition

Strength refers to the maximum stress a material can withstand before failure. There are several types depending on the application; those referenced in design and CAE are as follows:

Tensile Strength: Maximum stress resisted under tension

Yield Strength: Stress at the threshold causing permanent deformation

Compressive Strength: Resistance to crushing forces

Shear Strength: Resistance to sliding forces

Characteristics

Higher values indicate greater resistance to failure: higher limits against external forces.

Directly relevant to material selection: used in design criteria after applying safety factors.

Example Representative Values

Steel (General Structural Steel SS400): Tensile Strength 400–510 MPa

Aluminium Alloy (A5052): Tensile Strength approx. 300 MPa

Resin (Polyethylene): Tensile strength approx. 20 MPa

Thus, strength serves as the criterion for ‘whether something breaks’ and is a crucial value for ensuring product safety.

3. Difference between Young's Modulus and Strength

Although often confused, ‘Young's Modulus’ and ‘Strength’ are fundamentally different.

Young's Modulus: Indicates ease of deformation (rigidity).

Strength: Indicates the limit before failure occurs.

For example, glass has a high elastic modulus and is resistant to deformation, but its tensile strength is low, making it brittle. Conversely, rubber has a low elastic modulus and is soft, yet it can withstand extremely large strains before breaking.

4. Application in CAE

Let us now examine how elastic modulus and strength are utilised in practice using CAE.

The model below represents a dumbbell specimen, commonly used in material testing.

The following two tensile conditions are applied to this model.

Materials:

① Steel (General Structural Steel SS400): Young's modulus: 200 GPa; Tensile strength: 450 MPa

② Aluminium alloy (A5052): Young's modulus: 70 GPa; Tensile strength: 300 MPa

③ Resin (Polyethylene): Young's modulus: 1 GPa, Tensile strength: 20 MPa

The comparison was conducted using these three materials.

Condition ①: A tensile load of 1000 N was applied.

It can be seen that the steel with the highest Young's modulus exhibits the smallest deformation.

It can also be seen that the maximum stress remains unchanged regardless of the material.

During product design, the risk of failure and safety factor are calculated by comparing this maximum stress with the material strength. In the above case, the maximum stress of 73.4 MPa exceeds the tensile strength of the resin (20 MPa), indicating a problem.

Aluminium and steel both exceed 300 MPa, so they can be considered acceptable.

In scenarios involving significant loads, materials with sufficient strength are appropriate.

*Note: This is a linear analysis; non-linear analysis is required if yield stress needs to be considered.

Condition ②: Apply a forced displacement of 2 mm

In this case, the material with the lowest maximum stress is the resin (polyethylene), while the material with the highest maximum stress is steel. Although a higher Young's modulus indicates greater resistance to deformation, under conditions where the amount of deformation (strain) is constant, as in this case, the magnitude of Young's modulus is directly proportional to the stress.

Therefore, materials with a high Young's modulus are unsuitable for locations where significant deformation is anticipated. (Materials with a low Young's modulus, such as rubber, are appropriate.)

★How to determine failure?

In linear analysis, material properties increase in a stress-strain proportional relationship.

As this analysis ignores the material's yield point, predicting failure or damage requires non-linear analysis that considers the material's plastic region. For material property settings in the plastic region, see here

5. Application in Design

Case 1: Design prioritising rigidity

Examples: Automotive bodies, structural components

Requires materials with high elastic modulus

Minimises deflection to ensure usability and safety

Case 2: Design prioritising strength

Examples: Aircraft components, bridges, pressure vessels

Selects high-strength materials

Applies a safety factor to the design strength to prevent failure

Case 3: Balancing flexibility and strength

Example: Resin products, medical device components

Acceptable if strength is ensured even with low elastic modulus

Enables designs that bend without breaking

6. Points for Designers to Note

Introduction of Safety Factors

Strength must be assessed not just theoretically, but with safety factors accounting for environmental and manufacturing tolerances. Example: Typically 2.0–3.0 in mechanical design.

Verification of Material Test Data

CAE input values often depend on actual production batches and molding conditions, not catalogue values. Plastics, in particular, exhibit significant temperature dependence.

Consideration of Stress Concentration

Design strength assumes uniform stress distribution, but stress concentration occurs in reality at ribs, holes, and corners. Verifying localised stresses via CAE analysis is crucial.

7. Summary

The elastic modulus represents “resistance to deformation (stiffness)”.

Strength represents “the limit before failure”.

These are independent metrics, yet are always used together in product design and CAE analysis.

During the design phase, a two-step approach is essential: “verify deformation using the elastic modulus” and “verify failure using strength”.

Appropriate material selection and the introduction of a safety factor enable safe and efficient design.

Elastic modulus and strength are fundamental elements of design. Understanding and correctly applying these enables design optimisation, weight reduction, and enhanced safety through the use of CAE.