Stiffness

What is flexural modulus?
What is the formula of flexural modulus?
What are units of flexural modulus?
Which materials show high stiffness?
What is the importance of flexural modulus?
What are the factors affecting flexural modulus?
What are the test methods to measure flexural modulus?
What are the flexural modulus values of several plastics?

What is flexural modulus?

Flexural modulus denotes the ability of a plastic material to bend. It measures the material's stiffness or its resistance to bend. Stiffness (or rigidity) is one of the most important properties of solid materials.

Other names of flexural modulus include:

bending modulus of elasticity,
elastic modulus, or
simply modulus.

The flexural modulus is represented by the slope of the initial straight-line part of the stress-strain curve. Hence, the ratio of stress to strain is a measure of the flexural modulus.

What is the formula of flexural modulus?

Flexural modulus measures the stiffness of plastics or resistance to bending when force is applied perpendicular to the long edge of a sample. This is known as the three-point bend test.

Three-point bend test of a test bar (gray color)

The flexural modulus is calculated from the following equation:

E = L³F/4bℎ³d

where,

E = Flexural modulus
L = length of test bar
d = distance covered by a load F during flexure, measured from the initial position
F = load applied on the test bar
b = width of test bar (in mm), and
h = height of test bar (in mm)

The higher the Flexural Modulus, the stiffer the material; the lower the Flexural Modulus, the more flexible it is.

What are units of flexural modulus?

The International Standard unit of Flexural Modulus is the pascal (Pa or N/m² or m^-1.kg.s^-2).
The practical units used are megapascals (MPa or N/mm²) or gigapascals (GPa or kN/mm²).
In the US customary units, it is expressed as pounds (force) per square inch (psi).

Stiffness - Mechanical Properties of Plastics

Which materials show high stiffness?

Thermoplastics with High Stiffness – View Product List

TPEs/TPVs with High Stiffness – View Product List

Thermosets with High Stiffness – View Product List

Rubbers with High Stiffness – View Product List

What is the importance of flexural modulus?

Flexural modulus is important because of the following reasons:

It influences composite selection in high-stress situations.
It helps to improve design quality for load-bearing applications.

What are the factors affecting flexural modulus?

Impact of fillers

The addition of fillers increases the stiffness or flexural modulus (mechanical property) of a polymer system, especially polyolefins (PP, TPOs). The selection of filler majorly depends on its:

aspect ratio and
particle size

The higher the aspect ratio, high is the stiffness. For example, talc has a high aspect ratio, i.e., 20:1. It is one of the most efficient minerals for improving flexural modulus.

Impact of blends

elongation at break (Son and co-workers).

What are the test methods to measure flexural modulus?

The most used standards to measure the flexural modulus are ASTM D790 and ISO 178. These methods determine the bending properties of:

reinforced and unreinforced plastics
electrical insulation materials

The values are significantly different from the tensile modulus. This is because the stress pattern in the specimen is a combination of tension and compression. The data is useful for comparing the strength and stiffness of different plastics.

For ASTM D790: The test is stopped when the specimen reaches 5% deflection or the specimen breaks before 5%.
For ISO 178: The test is stopped when the specimen breaks. If the specimen does not break, the test is continued as far as possible and the stress at 3.5% (conventional deflection) is reported.

Check out an interesting video showing method to test elastic modulus
Source: Instron®

What are the flexural modulus values of several plastics?

Polymer Name	Min Value (GPa)	Max Value (GPa)
ABS - Acrylonitrile Butadiene Styrene	1.60	2.40
ABS Flame Retardant	2.00	4.00
ABS High Heat	2.00	3.00
ABS High Impact	1.00	2.50
ABS/PC Blend - Acrylonitrile Butadiene Styrene/Polycarbonate Blend	2.00	2.30
ABS/PC Blend 20% Glass Fiber	5.90	6.10
ABS/PC Flame Retardant	2.50	3.0
Amorphous TPI Blend, Ultra-high heat, Chemical Resistant (High Flow)	3.00	3.00
Amorphous TPI, High Heat, High Flow, Lead-Free Solderable, 30% GF	9.00	9.00
Amorphous TPI, High Heat, High Flow, Transparent, Lead-Free Solderable (High Flow)	0.12	0.12
Amorphous TPI, High Heat, High Flow, Transparent, Lead-Free Solderable (Standard Flow)	2.85	2.85
Amorphous TPI, Highest Heat, Chemical Resistant, 260C UL RTI	3.60	3.60
Amorphous TPI, Moderate Heat, Transparent	3.08	3.08
Amorphous TPI, Moderate Heat, Transparent (Food Contact Approved)	3.08	3.08
Amorphous TPI, Moderate Heat, Transparent (Mold Release grade)	3.07	3.07
Amorphous TPI, Moderate Heat, Transparent (Powder form)	3.08	3.08
ASA - Acrylonitrile Styrene Acrylate	1.50	2.40
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	0.60	2.10
CP - Cellulose Proprionate	0.45	1.40
COC - Cyclic Olefin Copolymer	2.50	3.50
CPVC - Chlorinated Polyvinyl Chloride	2.50	3.20
ETFE - Ethylene Tetrafluoroethylene	0.80	1.40
ECTFE	1.70	1.70
EVA - Ethylene Vinyl Acetate	0.007	0.10
EVOH - Ethylene Vinyl Alcohol	2.80	5.80
FEP - Fluorinated Ethylene Propylene	0.30	0.70
HDPE - High Density Polyethylene	0.75	1.575
HIPS - High Impact Polystyrene	1.50	3.00
HIPS Flame Retardant V0	2.00	2.50
Ionomer (Ethylene-Methyl Acrylate Copolymer)	0.03	0.50
LCP - Liquid Crystal Polymer	10.0	19.0
LCP Carbon Fiber-reinforced	31.0	37.0
LCP Glass Fiber-reinforced	13.0	24.0
LCP Mineral-filled	12.0	20.0
LDPE - Low Density Polyethylene	0.245	0.335
LLDPE - Linear Low Density Polyethylene	0.28	0.735
PA 11 - (Polyamide 11) 30% Glass fiber reinforced	3.00	3.00
PA 11, Conductive	0.58	0.64
PA 11, Flexible	0.29	0.35
PA 11, Rigid	1.00	1.48
PA 12 (Polyamide 12), Conductive	0.740	-
PA 12, Fiber-reinforced	3.00	13.70
PA 12, Flexible	0.36	0.46
PA 12, Glass Filled	1.75	2.00
PA 12, Rigid	1.17	1.48
PA 46 - Polyamide 46	1.00	3.20
PA 46, 30% Glass Fiber	7.80	3.20
PA 6 - Polyamide 6	0.80	2.00
PA 6-10 - Polyamide 6-10	1.00	2.00
PA 66 - Polyamide 6-6	0.80	3.00
PA 66, 30% Glass Fiber	5.00	8.00
PA 66, 30% Mineral filled	3.90	4.10
PA 66, Impact Modified, 15-30% Glass Fiber	3.00	7.00
PA 66, Impact Modified	0.80	1.20
PA 66, Carbon Fiber, Long, 30% Filler by Weight	18.00	18.00
PA 66, Carbon Fiber, Long, 40% Filler by Weight	24.00	24.00
PA 66, Glass Fiber, Long, 40% Filler by Weight	10.50	10.50
PA 66, Glass Fiber, Long, 50% Filler by Weight	13.00	13.00
PA 66, Glass Fiber, Long, 60% Filler by Weight	17.00	17.00
Polyamide semi-aromatic	1.80	2.11
PAI - Polyamide-Imide	4.00	7.00
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	11.00	21.00
PBT - Polybutylene Terephthalate	2.00	4.00
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	1.60	3.90
PC/PBT blend, Glass Filled	2.80	6.90
PCL - Polycaprolactone	0.50	0.60
PCTFE - Polymonochlorotrifluoroethylene	1.20	1.50
PE - Polyethylene 30% Glass Fiber	4.90	5.60
PEEK - Polyetheretherketone	3.70	4.00
PEEK 30% Carbon Fiber-reinforced	13.00	19.00
PEEK 30% Glass Fiber-reinforced	9.00	10.00
PEI - Polyetherimide	3.00	3.40
PEI, 30% Glass Fiber-reinforced	9.00	9.00
PEI, Mineral Filled	5.00	7.00
PEKK (Polyetherketoneketone), Low Crystallinity Grade	3.30	3.40
PESU - Polyethersulfone	2.50	2.70
PESU 10-30% glass fiber	3.80	8.40
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	2.20	2.20
PFA - Perfluoroalkoxy	0.70	0.80
PHB - Polyhydroxybutyrate	3.00	3.20
PI - Polyimide	2.48	4.10
PLA - Polylactide	3.80	3.80
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	0.80	1.50
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	2.00	3.00
POM (Acetal) Mineral Filled	4.00	5.50
PP - Polypropylene 10-20% Glass Fiber	2.50	3.50
PP, 10-40% Mineral Filled	1.40	3.10
PP, 10-40% Talc Filled	1.50	4.00
PP, 30-40% Glass Fiber-reinforced	4.00	7.00
PP (Polypropylene) Copolymer	1.00	1.40
PP (Polypropylene) Homopolymer	1.20	1.60
PP Homopolymer, Long Glass Fiber, 30% Filler by Weight	5.50	5.50
PP Homopolymer, Long Glass Fiber, 40% Filler by Weight	7.00	7.00
PP Homopolymer, Long Glass Fiber, 50% Filler by Weight	9.00	9.00
PP, Impact Modified	0.40	1.00
PPA - Polyphthalamide	2.10	3.70
PPA, 30% Mineral-filled	5.40	5.60
PPA, 33% Glass Fiber-reinforced	11.30	11.50
PPA, 33% Glass Fiber-reinforced – High Flow	10.00	12.00
PPA, 45% Glass Fiber-reinforced	13.70	13.90
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	3.80	4.20
PPS, 20-30% Glass Fiber-reinforced	6.00	12.00
PPS, 40% Glass Fiber-reinforced	12.00	15.00
PPS, Conductive	17.00	19.00
PPS, Glass fiber & Mineral-filled	10.00	17.00
PPSU - Polyphenylene Sulfone	2.38	2.41
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	2.70	3.00
PSU, 30% Glass fiber-reinforced	7.00	8.50
PSU Mineral Filled	4.00	5.00
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	1.80
PVC, Plasticized Filled	0.001	1.000
PVC Rigid	2.10	3.50
PVDC - Polyvinylidene Chloride	0.35	0.60
PVDF - Polyvinylidene Fluoride	1.50	2.00
SAN - Styrene Acrylonitrile	3.50	4.20
SAN, 20% Glass Fiber-reinforced	7.00	9.00
SMA - Styrene Maleic Anhydride	2.30	3.30
SMA, 20% Glass Fiber-reinforced	5.00	6.00
SMA, Flame Retardant V0	1.90	2.00
SMMA - Styrene Methyl Methacrylate	2.00	3.20
SRP - Self-reinforced Polyphenylene	6.20	8.30
TPI-PEEK Blend, Ultra-high heat, Chemical Resistant, High Flow, 240C UL RTI	3.60	3.60
UHMWPE - Ultra High Molecular Weight Polyethylene	0.45	0.60
XLPE - Crosslinked Polyethylene	0.35	3.50

Disclaimer: all data and information obtained via the Polymer Selector including but not limited to material suitability, material properties, performances, characteristics and cost are given for information purpose only. Although the data and information contained in the Polymer Selector are believed to be accurate and correspond to the best of our knowledge, they are provided without implied warranty of any kind. Data and information contained in the Polymer Selector are intended for guidance in a polymer selection process and should not be considered as binding specifications. The determination of the suitability of this information for any particular use is solely the responsibility of the user. Before working with any material, users should contact material suppliers in order to receive specific, complete and detailed information about the material they are considering. Part of the data and information contained in the Polymer Selector are genericised based on commercial literature provided by polymer suppliers and other parts are coming from assessments of our experts.

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