The shear modulus of aluminum, also known as the modulus of rigidity (G), is a measure of a material’s resistance to shear deformation.
Aluminum has a shear modulus of approximately 26 GPa (3.8 × 10⁶ psi), but the exact value varies slightly depending on the alloy, temper, and processing method.
For example, common alloys like 6061-T6 have a shear modulus of about 26 GPa, while 7075-T6 is slightly higher at about 26.9 GPa. High-strength 2024-T3 aluminum can reach around 28 GPa.
This article introduces the shear modulus of aluminum, typical values for common aluminum alloys, influencing factors, testing methods, and comparisons with other metals.
Definition of Shear Modulus
Shear modulus defines the linear relationship between shear stress and shear strain in the elastic region:
G = τ / γ
Where:
- G = shear modulus, or modulus of rigidity
- τ = shear stress
- γ = shear strain
Shear modulus describes how strongly a material resists shape change when forces act parallel to its cross section.
A higher shear modulus means the material is more resistant to angular deformation. A lower shear modulus means the material is easier to twist, bend, or distort under shear loading.
For isotropic materials, shear modulus is related to Young’s modulus and Poisson’s ratio:
G = E / [2(1 + ν)]
Where:
- E = Young’s modulus
- ν = Poisson’s ratio
- G = shear modulus
Since aluminum has a Young’s modulus of about 69–70 GPa and a Poisson’s ratio around 0.33, its shear modulus is usually close to 26 GPa.
Shear modulus should not be confused with shear strength. Shear modulus measures elastic stiffness under shear. Shear strength measures the stress level at which the material begins to fail or permanently deform in shear.
Shear Modulus of Pure Aluminum
Pure aluminum typically has a shear modulus of about 25–26 GPa.
Key characteristics include:
- Clear linear-elastic behavior under small shear loads
- Lower shear stiffness than steel, copper, and titanium
- Higher shear stiffness than magnesium
- Good stiffness-to-weight performance due to low density
- Slight variation depending on purity, processing, and test method
Pure aluminum is soft and highly ductile. Its shear strength is much lower than many aluminum alloys, but its shear modulus remains close to most commercial aluminum grades.
This is because alloying and heat treatment change strength much more than they change elastic modulus.
Shear Modulus of Aluminum Alloys
Most aluminum alloys have a shear modulus between 25 and 28 GPa. The difference between common alloys is usually small.
The following table lists typical values for frequently used aluminum alloys.
The table shows that 2024 and 7075 have slightly higher shear modulus values than 6061 and 6063.
However, the difference is not dramatic. In many practical applications, the geometry of the part has a larger effect on torsional rigidity than the small difference in shear modulus between aluminum alloys.
Heat treatment has limited influence on shear modulus. It significantly affects yield strength, tensile strength, hardness, and shear strength, but the elastic stiffness remains relatively stable.
Shear Modulus Comparison: Aluminum vs Other Metals
Aluminum has a lower shear modulus than most structural metals. This means it deforms more under the same shear stress.
However, aluminum is also much lighter than steel, copper, and titanium. Its low density allows designers to use larger sections while still keeping the component lightweight.
The following table compares aluminum with several common engineering metals.
Compared with carbon steel, aluminum has about one-third of the shear modulus. This means an aluminum shaft, tube, or structural member will twist more than a steel one with the same shape and load.
But the weight difference is also important. Aluminum’s density is about one-third that of steel. This makes aluminum suitable for lightweight structures where weight reduction matters.
Factors Affecting Shear Modulus
Several factors may influence the measured shear modulus of aluminum:
- Alloy composition: Elements such as magnesium, silicon, copper, zinc, and manganese can slightly change elastic properties.
- Temper condition: Heat treatment has a small effect on shear modulus but a large effect on strength.
- Temperature: Higher temperature generally reduces stiffness.
- Manufacturing process: Extrusion, rolling, forging, or casting may create slight anisotropy.
- Porosity and defects: Casting pores, cracks, weld defects, and inclusions may reduce the effective stiffness of a part.
- Test direction: Rolled or extruded products may show small differences between longitudinal and transverse directions.
For most standard engineering calculations, aluminum alloys are treated as having a shear modulus close to 26 GPa.
For precision structures, aerospace parts, and finite element analysis, alloy-specific and temper-specific data should be used.
Testing Methods for Shear Modulus
Shear modulus can be measured or estimated by several methods.
Torsion Test
A specimen is twisted under controlled torque. The shear modulus is calculated from the relationship between torque, angle of twist, length, and polar moment of inertia.
This is one of the most direct methods for measuring shear stiffness.
Shear Test
A sample is loaded in shear until deformation occurs. In the elastic region, shear modulus can be calculated from the slope of the shear stress–strain curve.
This method is commonly used for material characterization.
Ultrasonic Testing
Ultrasonic wave velocity can be used to calculate elastic constants, including shear modulus. This method is non-destructive and useful for quality control and research.
Calculation from Young’s Modulus and Poisson’s Ratio
For isotropic materials, shear modulus can be calculated using:
G = E / [2(1 + ν)]
For aluminum, using E = 69 GPa and ν = 0.33:
G ≈ 69 / [2(1 + 0.33)]
G ≈ 25.9 GPa
This is why most aluminum alloys are listed with a shear modulus close to 26 GPa.
Applications Where Shear Modulus Matters
Shear modulus is important when aluminum parts are exposed to torsion, twisting, or shear loading.
Typical applications include:
- Shafts and rotating components
- Aluminum tubes and hollow profiles
- Structural frames
- Brackets and connectors
- Aerospace and automotive parts
- CNC machined aluminum components
- Extruded aluminum profiles
- Fixtures, supports, and mechanical housings
In these applications, shear modulus helps estimate elastic twisting and shear deformation.
For most aluminum parts, shear modulus is only one part of the design. Engineers also consider yield strength, fatigue strength, wall thickness, cross-section shape, load direction, and connection design.
Shear Modulus vs Young’s Modulus of Aluminum
Young’s modulus and shear modulus both describe elastic stiffness, but they apply to different types of loading.
Young’s modulus measures resistance to tensile or compressive deformation.
Shear modulus measures resistance to shear deformation.
For aluminum:
- Young’s modulus: about 69–70 GPa
- Shear modulus: about 25–27 GPa
- Poisson’s ratio: about 0.33
The two values are related, but they are not interchangeable.
If a component is stretched or compressed, Young’s modulus is usually used. If it is twisted or loaded in shear, shear modulus is more relevant.
Summary
Aluminum has a shear modulus of approximately 26 GPa, or 3.8 × 10⁶ psi.
Compared with steel, aluminum has a much lower shear modulus. This means it twists and deforms more under the same shear load.
However, aluminum’s low density gives it strong stiffness-to-weight performance. This is why it remains widely used in lightweight structures, extrusion profiles, CNC machined parts, automotive components, and aerospace applications.
When selecting aluminum for shear or torsional loading, shear modulus should be considered together with strength, geometry, wall thickness, temperature, and manufacturing process.
FAQ
What is the shear modulus of aluminum?
The shear modulus of aluminum is about 26 GPa, or 3.8 × 10⁶ psi. The exact value depends on alloy, temper, and processing method.
What is the shear modulus of 6061-T6 aluminum?
6061-T6 aluminum has a shear modulus(G) of about 26 GPa, or 3.77 × 10⁶ psi.
What is the shear modulus of 6063-T6 aluminum?
6063-T6 aluminum has a shear modulus(G) of about 25.8 GPa, or 3.74 × 10⁶ psi.
What is the shear modulus of 7075 aluminum?
7075-T6 aluminum has a shear modulus(G) of about 26.9 GPa, or 3.90 × 10⁶ psi.
What is the shear modulus of 2024 aluminum?
2024-T3 and 2024-T4 aluminum typically have a shear modulus(G) of about 28 GPa, or 4.06 × 10⁶ psi.
Is shear modulus the same as shear strength?
No. Shear modulus measures elastic resistance to shear deformation. Shear strength measures the maximum shear stress a material can withstand before yielding or failure.
What is the relationship between E and G for aluminum?
For isotropic materials, G = E / [2(1 + ν)]. For aluminum, E is about 69 GPa and Poisson’s ratio is about 0.33, so G is about 26 GPa.
Technical References
[1] MatWeb and ASM material property datasheets
