The Mullins effect is a particular aspect of the mechanical response in filled

rubbers Rubber, also called India rubber, latex, Amazonian rubber, ''caucho'', or ''caoutchouc'', as initially produced, consists of polymers of the organic compound isoprene, with minor impurities of other organic compounds. Thailand, Malaysia, and ...

, in which the stress–strain curve depends on the maximum loading previously encountered. The phenomenon, named for rubber scientist

Leonard Mullins Leonard Mullins (1918 – 19 September 1997) was a scientist and long-time Research Director at the former Malaysian Rubber Producers' Research Association. He is known for his work on the stress-softening behavior of rubber, a phenomenon now kno ...

, working at the

Tun Abdul Razak Research Centre The Tun Abdul Razak Research Centre, originally known as the British Rubber Producers' Research Association, carries out research into rubber and is funded by the Malaysian government. Early years: as the British Rubber Producers Research Associa ...

Hertford Hertford ( ) is the county town of Hertfordshire, England, and is also a civil parish in the East Hertfordshire district of the county. The parish had a population of 26,783 at the 2011 census. The town grew around a ford on the River Lea, ne ...

, can be idealized for many purposes as an instantaneous and irreversible softening of the stress–strain curve that occurs whenever the load increases beyond its prior all-time maximum value. At times, when the load is less than a prior maximum, nonlinear

elastic Elastic is a word often used to describe or identify certain types of elastomer, elastic used in garments or stretchable fabrics. Elastic may also refer to: Alternative name * Rubber band, ring-shaped band of rubber used to hold objects togeth ...

behavior prevails. The effect should not be confused with the

Payne effect The Payne effect is a particular feature of the stress–strain behaviour of rubber, especially rubber compounds containing Filler (materials), fillers such as carbon black. It is named after the British rubber scientist A. R. Payne, who made exte ...

. Although the term "Mullins effect" is commonly applied to stress softening in filled rubbers, the phenomenon is common to all rubbers, including "gums" (rubber lacking filler). As first shown by Mullins and coworkers, the retraction stresses of an

elastomer An elastomer is a polymer with viscoelasticity (i.e. both viscosity and elasticity) and with weak intermolecular forces, generally low Young's modulus and high failure strain compared with other materials. The term, a portmanteau of ''elastic p ...

are independent of

carbon black Carbon black (subtypes are acetylene black, channel black, furnace black, lamp black and thermal black) is a material produced by the incomplete combustion of coal and coal tar, vegetable matter, or petroleum products, including fuel oil, fluid ...

when the stress at the maximum strain is constant. Mullins softening is a viscoelastic effect, although in filled rubber there can be additional contributions to the mechanical hysteresis from filler particles debonding from each other or from the polymer chains. A number of constitutive models have been proposed to describe the effect. For example, the Ogden-Roxburgh model is used in several commercial

finite element The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat t ...

codes.

References

L. Mullins,

Rubber Chemistry and Technology ''Rubber Chemistry and Technology'' is a quarterly peer-reviewed scientific journal covering fundamental research and technical developments relating to chemistry, materials science, and engineering of rubber, elastomers, and related materials. ...

, 42, 339 (1969). J.A.C. Harwood and A.R. Payne, J. Appl. Polym Sci. 10, 315 (1966). W. V. Mars, Evaluation of a pseudo-elastic model for the Mullins effect. Tire Science and Technology, 32(3), 120–145 (2004). {{refend Rubber properties

See also

References