At the atomic and molecular level, the modulus of elasticity is related to the forces between atoms or molecules in a material. In a crystalline material, for example, the atoms are arranged in a regular lattice. When a force is applied, the atoms are displaced from their equilibrium positions. The bonds between the atoms act like springs, and the Young’s modulus is related to the stiffness of these “springs.” The stronger the bonds between the atoms, the higher the Young’s modulus of the material.
In amorphous materials, such as glasses and some polymers, the modulus is determined by the intermolecular forces and the entanglement of polymer chains (in the case of polymers). The ability of these materials to resist deformation depends on the nature and strength of these interactions.
The modulus of elasticity is a fundamental property in the field of materials science and engineering. It provides crucial information about a material’s ability to deform under an applied force and then return to its original shape once the force is removed. Understanding this property is essential for designing structures, selecting appropriate materials for various applications, and predicting the behavior of materials under different loading conditions.
What Is Young’s Modulus?
Young’s modulus, also known as the tensile modulus, is a measure of the stiffness of a solid material. It is defined as the ratio of the tensile stress (force per unit area) to the tensile strain (proportional deformation) in the linear elastic region of a material. In simpler terms, it tells us how much a material will stretch or compress when a force is applied along a particular axis.
Young’s Modulus Formula
Young’s Modulus Formula From Other Quantities
Notations Used In The Young’s Modulus Formula
- E is Young’s modulus in Pa
- 𝞂 is the uniaxial stress in Pa
- ε is the strain or proportional deformation
- F is the force exerted by the object under tension
- A is the actual cross-sectional area
- ΔL is the change in the length
- L0 is the actual length
What Are the Units of Young’s Modulus?
The SI unit of Young’s modulus is the pascal (Pa), which is equal to 1 newton per square meter ( N/m²). In practice, because the values of Young’s modulus can be quite large, it is often expressed in gigapascals (GPa),
The Physics Behind Young’s Modulus
At the atomic and molecular level, the modulus of elasticity is related to the forces between atoms or molecules in a material. In a crystalline material, for example, the atoms are arranged in a regular lattice. When a force is applied, the atoms are displaced from their equilibrium positions. The bonds between the atoms act like springs, and the Young’s modulus is related to the stiffness of these “springs.” The stronger the bonds between the atoms, the higher the Young’s modulus of the material.
In amorphous materials, such as glasses and some polymers, the modulus is determined by the intermolecular forces and the entanglement of polymer chains (in the case of polymers). The ability of these materials to resist deformation depends on the nature and strength of these interactions.
What Are the Factors Affecting Young’s Modulus?
Material Composition: Different elements and their arrangements in a material have a significant impact. For example, in alloys, the addition of different metals can change the modulus. In a steel – carbon alloy, increasing the carbon content can increase the Young’s modulus up to a certain point.
Temperature: As the temperature of a material increases, the thermal energy causes the atoms or molecules to vibrate more vigorously. This can lead to a decrease in the modulus of elasticity. For most materials, there is a negative correlation between temperature and Young’s modulus. However, some materials, like certain shape – memory alloys, can exhibit more complex behavior.
Microstructure: The presence of defects such as voids, dislocations, and grain boundaries in a material can affect its modulus. For instance, materials with a fine – grained microstructure tend to have a higher modulus compared to those with a coarse – grained structure, as the grain boundaries can impede the movement of dislocations and thus enhance the material’s stiffness.
Which Instrument Is Used to Determine Young’s Modulus?
Tensile Testing Machine: This is the most common instrument used. A sample of the material with a known cross – sectional area and length is clamped at both ends. A gradually increasing tensile force is applied axially, and the corresponding elongation of the sample is measured. By recording the force – displacement data, the stress – strain curve can be plotted, and Young’s modulus can be calculated from the linear part of the curve.
Ultrasonic Testing Equipment: Ultrasonic waves can also be used to measure the elastic modulus. The speed of sound in a material is related to its elastic properties. By measuring the speed of ultrasonic waves through a material sample, the Young’s modulus can be determined using appropriate relationships that link the wave speed, density, and elastic modulus of the material.
How to Calculate Young’s Modulus?
Conduct a tensile test and measure the force (F ) applied to the sample and the corresponding elongation (△L).
Calculate the stress (σ) using the formula σ = F/A , where A is the cross – sectional area of the sample.
Calculate the strain (ε) using the formula ε = △L/L, where is the original length of the sample.
Then, calculate Young’s modulus (E) using the formula E = σ/ε
What Are Young's Modulus Values of Several Plastics?
| Polymer Name | Min Value (GPa) | Max Value (GPa) |
| ABS - Acrylonitrile Butadiene Styrene | 1.79 | 3.20 |
| ABS Flame Retardant | 2.00 | 3.00 |
| ABS High Heat | 1.50 | 3.00 |
| ABS High Impact | 1.00 | 2.50 |
| ABS/PC Blend | 2.00 | 2.20 |
| ABS/PC Blend 20% Glass Fiber | 6.00 | 6.00 |
| ABS/PC Flame Retardant | 2.60 | 3.00 |
| Amorphous TPI Blend | 3.50 | 3.50 |
| HDPE - High Density Polyethylene | 0.50 | 1.10 |
| HIPS - High Impact Polystyrene | 1.50 | 3.00 |
| HIPS Flame Retardant V0 | 2.00 | 2.50 |
| LCP - Liquid Crystal Polymer | 10.00 | 19.00 |
| LCP Carbon Fiber-reinforced | 31.00 | 37.00 |
| LCP Glass Fiber-reinforced | 13.00 | 24.00 |
| LCP Mineral-filled | 12.00 | 22.00 |
| LDPE - Low Density Polyethylene | 0.13 | 0.30 |
| LLDPE - Linear Low Density Polyethylene | 0.266 | 0.525 |
| PA 11 - (Polyamide 11) 30% Glass fiber reinforced | 3.80 | 5.20 |
| PA 46 - Polyamide 46 | 1.00 | 3.30 |
| PA 46, 30% Glass Fiber | 7.80 | 8.20 |
| PA 6 - Polyamide 6 | 0.80 | 2.00 |
| PA 6-10 - Polyamide 6-10 | 1.00 | 2.00 |
| PA 66 - Polyamide 6-6 | 1.00 | 3.50 |
| PA 66, 30% Mineral filled | 1.40 | 5.50 |
| PA 66, Impact Modified | 0.80 | 1.20 |
| Polyamide semi-aromatic | 2.07 | 2.23 |
| PAI - Polyamide-Imide | 4.00 | 5.00 |
| PAI, 30% Glass Fiber | 11.00 | 15.00 |
| PAI, Low Friction | 5.00 | 7.00 |
| PBT - Polybutylene Terephthalate | 2.00 | 3.00 |
| PBT, 30% Glass Fiber | 9.00 | 9.00 |
| PC (Polycarbonate) 20-40% Glass Fiber | 6.00 | 10.00 |
| PC - Polycarbonate, high heat | 2.20 | 2.50 |
| PC/PBT blend, Glass Filled | 4.50 | 5.10 |
| PE - Polyethylene 30% Glass Fiber | 4.90 | 6.30 |
| PEEK - Polyetheretherketone | 3.50 | 3.90 |
| PEEK 30% Carbon Fiber-reinforced | 13.00 | 22.30 |
| PEI - Polyetherimide | 3.00 | 3.00 |
| PEI, 30% Glass Fiber-reinforced | 9.00 | 9.00 |
| PEI, Mineral Filled | 5.00 | 7.00 |
| PET - Polyethylene Terephthalate | 2.80 | 3.50 |
| PET, 30% Glass Fiber-reinforced | 9.00 | 12.00 |
| PLA - Polylactide | 3.40 | 3.60 |
| PLA, High Heat Films | 3.30 | 3.50 |
| PLA, Injection molding | 3.50 | 3.60 |
| PMMA - Polymethylmethacrylate/Acrylic | 2.50 | 3.50 |
| PMMA (Acrylic) High Heat | 2.50 | 4.30 |
| PMMA (Acrylic) Impact Modified | 1.50 | 3.50 |
| POM - Polyoxymethylene (Acetal) | 2.80 | 3.70 |
| POM (Acetal) Impact Modified | 1.40 | 2.30 |
| POM (Acetal) Mineral Filled | 4.00 | 5.50 |
| PP - Polypropylene 10-20% Glass Fiber | 2.80 | 4.00 |
| PP, 10-40% Mineral Filled | 1.00 | 3.50 |
| PP, 10-40% Talc Filled | 1.50 | 3.50 |
| PP, 30-40% Glass Fiber-reinforced | 4.00 | 10.00 |
| PP (Polypropylene) Copolymer | 1.00 | 1.20 |
| PP (Polypropylene) Homopolymer | 1.10 | 1.60 |
| PP, Impact Modified | 0.40 | 1.00 |
| PPA - Polyphthalamide | 3.70 | 3.70 |
| PPE - Polyphenylene Ether | 2.10 | 2.80 |
| PPE, 30% Glass Fiber-reinforced | 7.00 | 9.00 |
| PPE, Flame Retardant | 2.40 | 2.50 |
| PPE, Impact Modified | 2.10 | 2.80 |
| PPE, Mineral Filled | 2.90 | 3.50 |
| PPS - Polyphenylene Sulfide | 3.30 | 4.00 |
| PPS, 20-30% Glass Fiber-reinforced | 6.00 | 11.00 |
| PPS, 40% Glass Fiber-reinforced | 8.00 | 14.00 |
| PPS, Conductive | 13.00 | 19.00 |
| PPS, Glass fiber & Mineral-filled | 10.00 | 17.00 |
| PS (Polystyrene) 30% glass fiber | 10.00 | 10.00 |
| PS (Polystyrene) Crystal | 2.50 | 3.50 |
| PS, High Heat | 3.00 | 3.50 |
| PSU - Polysulfone | 2.50 | 2.70 |
| PSU, 30% Glass fiber-reinforced | 7.60 | 10.00 |
| PSU Mineral Filled | 3.80 | 4.50 |
| PTFE - Polytetrafluoroethylene | 0.40 | 0.80 |
| PTFE, 25% Glass Fiber-reinforced | 1.40 | 1.70 |
| PVC, Plasticized | 0.001 | 1.800 |
| PVC, Plasticized Filled | 0.001 | 1.00 |
| PVC Rigid | 2.40 | 4.00 |
| Polymer Name | Min Value (GPa) | Max Value (GPa) |
| ABS - Acrylonitrile Butadiene Styrene | 1.79 | 3.20 |
| ABS Flame Retardant | 2.00 | 3.00 |
| ABS High Heat | 1.50 | 3.00 |
| ABS High Impact | 1.00 | 2.50 |
| ABS/PC Blend | 2.00 | 2.20 |
| ABS/PC Blend 20% Glass Fiber | 6.00 | 6.00 |
| ABS/PC Flame Retardant | 2.60 | 3.00 |
| Amorphous TPI Blend | 3.50 | 3.50 |
| HDPE - High Density Polyethylene | 0.50 | 1.10 |
| HIPS - High Impact Polystyrene | 1.50 | 3.00 |
| HIPS Flame Retardant V0 | 2.00 | 2.50 |
| LCP - Liquid Crystal Polymer | 10.00 | 19.00 |
| LCP Carbon Fiber-reinforced | 31.00 | 37.00 |
| LCP Glass Fiber-reinforced | 13.00 | 24.00 |
| LCP Mineral-filled | 12.00 | 22.00 |
| LDPE - Low Density Polyethylene | 0.13 | 0.30 |
| LLDPE - Linear Low Density Polyethylene | 0.266 | 0.525 |
| PA 11 - (Polyamide 11) 30% Glass fiber reinforced | 3.80 | 5.20 |
| PA 46 - Polyamide 46 | 1.00 | 3.30 |
| PA 46, 30% Glass Fiber | 7.80 | 8.20 |
| PA 6 - Polyamide 6 | 0.80 | 2.00 |
| PA 6-10 - Polyamide 6-10 | 1.00 | 2.00 |
| PA 66 - Polyamide 6-6 | 1.00 | 3.50 |
| PA 66, 30% Mineral filled | 1.40 | 5.50 |
| PA 66, Impact Modified | 0.80 | 1.20 |
| Polyamide semi-aromatic | 2.07 | 2.23 |
| PAI - Polyamide-Imide | 4.00 | 5.00 |
| PAI, 30% Glass Fiber | 11.00 | 15.00 |
| PAI, Low Friction | 5.00 | 7.00 |
| PBT - Polybutylene Terephthalate | 2.00 | 3.00 |
| PBT, 30% Glass Fiber | 9.00 | 9.00 |
| PC (Polycarbonate) 20-40% Glass Fiber | 6.00 | 10.00 |
| PC - Polycarbonate, high heat | 2.20 | 2.50 |
| PC/PBT blend, Glass Filled | 4.50 | 5.10 |
| PE - Polyethylene 30% Glass Fiber | 4.90 | 6.30 |
| PEEK - Polyetheretherketone | 3.50 | 3.90 |
| PEEK 30% Carbon Fiber-reinforced | 13.00 | 22.30 |
| PEI - Polyetherimide | 3.00 | 3.00 |
| PEI, 30% Glass Fiber-reinforced | 9.00 | 9.00 |
| PEI, Mineral Filled | 5.00 | 7.00 |
| PET - Polyethylene Terephthalate | 2.80 | 3.50 |
| PET, 30% Glass Fiber-reinforced | 9.00 | 12.00 |
| PLA - Polylactide | 3.40 | 3.60 |
| PLA, High Heat Films | 3.30 | 3.50 |
| PLA, Injection molding | 3.50 | 3.60 |
| PMMA - Polymethylmethacrylate/Acrylic | 2.50 | 3.50 |
| PMMA (Acrylic) High Heat | 2.50 | 4.30 |
| PMMA (Acrylic) Impact Modified | 1.50 | 3.50 |
| POM - Polyoxymethylene (Acetal) | 2.80 | 3.70 |
| POM (Acetal) Impact Modified | 1.40 | 2.30 |
| POM (Acetal) Mineral Filled | 4.00 | 5.50 |
| PP - Polypropylene 10-20% Glass Fiber | 2.80 | 4.00 |
| PP, 10-40% Mineral Filled | 1.00 | 3.50 |
| PP, 10-40% Talc Filled | 1.50 | 3.50 |
| PP, 30-40% Glass Fiber-reinforced | 4.00 | 10.00 |
| PP (Polypropylene) Copolymer | 1.00 | 1.20 |
| PP (Polypropylene) Homopolymer | 1.10 | 1.60 |
| PP, Impact Modified | 0.40 | 1.00 |
| PPA - Polyphthalamide | 3.70 | 3.70 |
| PPE - Polyphenylene Ether | 2.10 | 2.80 |
| PPE, 30% Glass Fiber-reinforced | 7.00 | 9.00 |
| PPE, Flame Retardant | 2.40 | 2.50 |
| PPE, Impact Modified | 2.10 | 2.80 |
| PPE, Mineral Filled | 2.90 | 3.50 |
| PPS - Polyphenylene Sulfide | 3.30 | 4.00 |
| PPS, 20-30% Glass Fiber-reinforced | 6.00 | 11.00 |
| PPS, 40% Glass Fiber-reinforced | 8.00 | 14.00 |
| PPS, Conductive | 13.00 | 19.00 |
| PPS, Glass fiber & Mineral-filled | 10.00 | 17.00 |
| PS (Polystyrene) 30% glass fiber | 10.00 | 10.00 |
| PS (Polystyrene) Crystal | 2.50 | 3.50 |
| PS, High Heat | 3.00 | 3.50 |
| PSU - Polysulfone | 2.50 | 2.70 |
| PSU, 30% Glass fiber-reinforced | 7.60 | 10.00 |
| PSU Mineral Filled | 3.80 | 4.50 |
| PTFE - Polytetrafluoroethylene | 0.40 | 0.80 |
| PTFE, 25% Glass Fiber-reinforced | 1.40 | 1.70 |
| PVC, Plasticized | 0.001 | 1.800 |
| PVC, Plasticized Filled | 0.001 | 1.00 |
| PVC Rigid | 2.40 | 4.00 |