Modulus of Elasticity

1. What are stress and strain?
2. What is Young’s modulus?
3. What are the units of Young’s modulus?
4. What are the factors affecting Young’s modulus?
5. Which plastics have high or low modulus?
6. What is the modulus value of plastics vs. others?
7. What are the applications of Young’s modulus?
8. What are the test methods to calculate Young’s modulus?
9. Which instrument is used to determine Young’s modulus?
10. What are the Young’s modulus values of several plastics?

What are stress and strain?

Definition of stress

Stress is defined as the force per unit area of plastic. The units of stress are N/m² or Pa.

where,

• σ is the stress (in Newtons per square meter or, equivalently, Pascals),
• F is the force (in Newtons, commonly abbreviated N), and
• A is the cross-sectional area of the sample.

Definition of strain

Strain is defined as extension per unit length. And, since it is a ratio of lengths, the strain has no units.

ε = ΔL/L0; ΔL = L-L0

where,

• ε is the strain
• L0 is the original length of a bar being stretched,
• L is its length after it has been stretched, and
• ΔL is the extension of the bar, the difference between these two lengths.

What is Young’s modulus?

Young’s modulus is the ratio of stress to the strain applied to the material. The force is applied along the longitudinal axis of the specimen tested. It is the measure of the stiffness of an elastic material.

The formula of Young's modulus is:
where,

• E is the Young’s modulus
• σ is the stress and
• ε is the strain

Other names include tensile modulus, elastic modulus, or modulus of elasticity.

The physics behind young's modulus

When a stretching force (tensile force) is applied to an object, it extends. Its behavior can be obtained using stress-strain curve in the elastic deformation region. This is known as Hooke’s Law. The extension that a force produces depends upon the:

• material
• dimensions of the object (e.g., length, thickness, etc.)

What are the units of Young’s modulus?

SI unit of Young modulus is Pascal (Pa). It is also equal to newton per square meter (N/m²).

The practical units used in plastics are:

• Megapascals (MPa or N/mm²)
• Gigapascals (GPa or kN/mm²)

In the United States customary units, it is often expressed as pounds (force) per square inch (psi).

What are the factors affecting Young’s modulus?

The modulus is closely related to the binding energies of the atoms. Binding forces and modulus of elasticity are higher for high melting point materials. Young’s modulus depends on the orientation of a single crystal material.

The higher temperature in the material increases atomic vibration. This in turn decreases the necessary energy to separate the atoms from one another. This generally decreases the stress needed to produce a given strain.


Relation between tensile properties and temperature (Source: Engineering Archives)


Presence of impurity atoms, alloying atoms, non-metallic inclusions, secondary phase particles, dislocations (shifts or mismatches in the lattice structure), and defects (cracks, grain boundaries, etc.). All of these things can serve to either weaken or strengthen a material.

• Anything that impedes the motion of dislocations through the lattice tends to increase the modulus. This will thus the yield strength.
• Anything that facilitates dislocation movement or localized stress will decrease strength. An increase in temperature eases dislocation movement. Cracks and inclusions rise localized stress. For example, promoting early onset of failure.

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Which plastics have high or low modulus?

• Polymers with High Modulus ‐ View Product List
• Polymers with Low Modulus ‐ View Product List

What is the modulus values of plastics vs. others?

The modulus of elasticity of plastics is much smaller than that for metals, ceramics, and glasses. For example:

• The modulus of elasticity of nylon is 2.7 GPa (0.4 x 106 psi)
• The modulus of glass fibers is 72 GPa (10.5 x 106 psi)
• The Young’s modulus of composites such as glass fiber-reinforced composites (GFRC) or carbon fiber-reinforced composites (CFRC) lies between the values for the matrix polymer and the fiber phase (carbon or glass fibers) and depends upon their relative volume fractions.

What are the applications of Young’s modulus?

Elastic modulus is an important mechanical property for:

1. Material selection for various purposes. This depends upon how the polymer reacts under different types of forces. For example, high-stiffness materials should have a higher Young's modulus.
2. Product design for specific industries. Used in several engineering as well as medical applications.
3. Performance analysis determines the batch quality and consistency in the manufacture. This in turn reduces material costs.

What are the test methods to calculate Young’s modulus?

In general, “tensile test methods” measure the modulus of elasticity of materials. The common methods used are:

• ASTM D638 - Standard Test Method for Tensile Properties of Plastics
• ISO 527-1:2012 - Determination of tensile properties. General principles

These methods determine the tensile properties of plastics and plastic composites. This is done under defined conditions that can range from:

• pretreatment,
• temperature,
• humidity, and
• machine speed

The test specimens are in the form of a standard dumbbell shaped.

For ASTM D638, the test speed is determined by the material specification. For ISO 527, the test speed is typically 5 or 50 mm/min for measuring strength and elongation, and 1 mm/min for measuring modulus.

Apart from Young's modulus, the tensile test results can also calculate:

• Tensile strength (at yield and at break)
• Tensile modulus
• Strain
• Elongation and percent elongation at yield
• Elongation and percent elongation at break

Which instrument is used to determine Young’s modulus?

An extensometer determines the elongation and tensile modulus. It is a device that measures the changes in the length of an object. It evaluates the stress-strain curve values.

The two main types of extensometers are contact and non-contact.

1. Contact extensometers are further divided into two types:
   
   
   • Clip-on extensometer: They can measure displacements from very small to relatively large. That is from less than 1 mm to over 100 mm. Used for applications requiring high-precision strain measurement (most ASTM-based tests). Major advantages include:
     
     
     • Low cost
     • Easy to use
   
   
   • Automated testing clip-ons: They replace digital "sensor arm" extensometers. They can be applied to the specimen automatically by a motorized system. They produce much more repeatable results than traditional clip-on devices. They measure very high extensions (up to 1000 mm) without losing any accuracy. Major advantages include:
     
     
     • Better linearity,
     • reduced signal noise, and
     • synchronization with the corresponding force data.


2. Non-contact extensometers: These devices are beginning to bring advantages for certain applications. Especially, in industries where it is impractical to use contact extensometers.

What are Young's modulus values of several plastics?

Click to find polymer you are looking for:

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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 - Acrylonitrile Butadiene Styrene/Polycarbonate 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, Ultra-high heat, Chemical Resistant (High Flow)	3.50	3.50
Amorphous TPI, High Heat, High Flow, Lead-Free Solderable, 30% GF	10.53	10.53
Amorphous TPI, High Heat, High Flow, Transparent, Lead-Free Solderable (High Flow)	3.10	3.10
Amorphous TPI, High Heat, High Flow, Transparent, Lead-Free Solderable (Standard Flow)	3.16	3.16
Amorphous TPI, Highest Heat, Chemical Resistant, 260°C UL RTI	3.90	3.90
Amorphous TPI, Moderate Heat, Transparent	3.11	3.11
Amorphous TPI, Moderate Heat, Transparent (Food Contact Approved)	3.11	3.10
Amorphous TPI, Moderate Heat, Transparent (Mold Release grade)	3.12	3.12
Amorphous TPI, Moderate Heat, Transparent (Powder form)	3.11	3.11
ASA - Acrylonitrile Styrene Acrylate	2.00	2.60
ASA/PC Blend - Acrylonitrile Styrene Acrylate/Polycarbonate Blend	2.00	2.60
ASA/PC Flame Retardant	2.50	2.50
ASA/PVC Blend - Acrylonitrile Styrene Acrylate/Polyvinyl Chloride Blend	2.00	2.20
CA - Cellulose Acetate	0.60	2.80
CAB - Cellulose Acetate Butyrate	0.40	1.70
Cellulose Diacetate-Pearlescent Films	2.00	2.50
Cellulose Diacetate-Gloss Film	2.00	2.50
Cellulose Diacetate-Integuard Films	2.50	2.90
Cellulose Diacetate-Matt Film	2.00	2.90
Cellulose Diacetate-Window Patch Film (Food Grade)	2.00	2.50
Cellulose Diacetate-Clareflect metallized film	2.10	2.60
Cellulose Diacetate-Colored Films	2.00	2.50
Cellulose Diacetate-Flame retardant Film	2.00	2.50
Cellulose Diacetate-High Slip Film	2.30	2.80
Cellulose Diacetate-Semitone Films	2.00	2.50
CP - Cellulose Proprionate	0.45	1.40
COC - Cyclic Olefin Copolymer	2.60	3.20
CPVC - Chlorinated Polyvinyl Chloride	2.50	3.20
ECTFE	1.70	1.70
ETFE - Ethylene Tetrafluoroethylene	0.80	0.80
EVA - Ethylene Vinyl Acetate	0.01	0.20
EVOH - Ethylene Vinyl Alcohol	1.90	3.50
FEP - Fluorinated Ethylene Propylene	0.30	0.70
HDPE - High Density Polyethylene	0.50	1.10
HIPS - High Impact Polystyrene	1.50	3.00
HIPS Flame Retardant V0	2.00	2.50
Ionomer (Ethylene-Methyl Acrylate Copolymer)	0.80	0.40
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
MABS - Transparent Acrylonitrile Butadiene Styrene	1.90	2.00
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% Glass Fiber	5.00	8.00
PA 66, 30% Mineral filled	1.40	5.50
PA 66, Impact Modified, 15-30% Glass Fiber	2.00	11.00
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
PAN - Polyacrylonitrile	3.10	3.80
PAR - Polyarylate	2.00	2.30
PARA (Polyarylamide), 30-60% glass fiber	11.50	24.00
PBT - Polybutylene Terephthalate	2.00	3.00
PBT, 30% Glass Fiber	9.00	11.50
PC (Polycarbonate) 20-40% Glass Fiber	6.00	10.00
PC (Polycarbonate) 20-40% Glass Fiber Flame Retardant	7.00	8.00
PC - Polycarbonate, high heat	2.20	2.50
PC/PBT Blend - Polycarbonate/Polybutylene Terephthalate Blend	1.80	2.30
PC/PBT blend, Glass Filled	4.50	5.10
PCL - Polycaprolactone	0.38	0.43
PCTFE - Polymonochlorotrifluoroethylene	1.20	1.50
PE - Polyethylene 30% Glass Fiber	4.90	6.30
PE/TPS Blend - Polyethylene/Thermoplastic Starch	0.19	0.30
PEEK - Polyetheretherketone	3.50	3.90
PEEK 30% Carbon Fiber-reinforced	13.00	22.30
PEEK 30% Glass Fiber-reinforced	9.00	11.40
PEI - Polyetherimide	3.00	3.00
PEI, 30% Glass Fiber-reinforced	9.00	9.00
PEI, Mineral Filled	5.00	7.00
PEKK (Polyetherketoneketone), Low Crystallinity Grade	3.40	3.50
PESU - Polyethersulfone	2.30	2.80
PESU 10-30% glass fiber	3.50	8.50
PET - Polyethylene Terephthalate	2.80	3.50
PET, 30% Glass Fiber-reinforced	9.00	12.00
PET, 30/35% Glass Fiber-reinforced, Impact Modified	7.00	9.00
PETG - Polyethylene Terephthalate Glycol	1.90	2.00
PFA - Perfluoroalkoxy	0.70	0.80
PGA - Polyglycolides	6.50	6.90
PHB - Polyhydroxybutyrate	3.10	3.30
PI - Polyimide	1.30	4.00
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
PMP - Polymethylpentene	0.50	1.60
PMP 30% Glass Fiber-reinforced	5.00	6.00
PMP Mineral Filled	1.70	2.00
POM - Polyoxymethylene (Acetal)	2.80	3.70
POM (Acetal) Impact Modified	1.40	2.30
POM (Acetal) Low Friction	1.80	3.00
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 Homopolymer, Long Glass Fiber, 30% Filler by Weight	7.00	7.00
PP Homopolymer, Long Glass Fiber, 40% Filler by Weight	9.00	9.00
PP Homopolymer, Long Glass Fiber, 50% Filler by Weight	12.00	13.50
PP, Impact Modified	0.40	1.00
PPA - Polyphthalamide	3.70	3.70
PPA, 33% Glass Fiber-reinforced – High Flow	13.00	13.20
PPA, 45% Glass Fiber-reinforced	17.10	17.30
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
PPSU - Polyphenylene Sulfone	2.34	2.34
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 (Polyvinyl Chloride), 20% Glass Fiber-reinforced	4.50	7.00
PVC, Plasticized	0.001	1.800
PVC, Plasticized Filled	0.001	1.00
PVC Rigid	2.40	4.00
PVDC - Polyvinylidene Chloride	0.35	0.50
PVDF - Polyvinylidene Fluoride	1.50	2.00
SAN - Styrene Acrylonitrile	2.80	4.00
SAN, 20% Glass Fiber-reinforced	8.00	11.00
SMA - Styrene Maleic Anhydride	2.40	3.00
SMA, 20% Glass Fiber-reinforced	5.00	6.00
SMA, Flame Retardant V0	1.80	2.00
SMMA - Styrene Methyl Methacrylate	2.10	3.40
SRP - Self-reinforced Polyphenylene	5.90	8.30
TPI-PEEK Blend, Ultra-high heat, Chemical Resistant, High Flow, 240C UL RTI	4.20	4.20
TPS, Injection General Purpose	0.80	3.00
TPS, Injection Water Resistant	0.63	0.72
UHMWPE - Ultra High Molecular Weight Polyethylene	0.30	0.60
XLPE - Crosslinked Polyethylene	0.35	3.50