Mullins effect
Encyclopedia
The Mullins effect is a particular aspect of the mechanical response in filled rubbers in which the stress-strain curve depends on the maximum loading previously encountered. The phenomenon, named for rubber scientist Leonard Mullins, working at the NRPRA in Hertford
, 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 behavior prevails.
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
are independent of carbon black
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 at least one commercial finite element code.
Hertford
Hertford is the county town of Hertfordshire, England, and is also a civil parish in the East Hertfordshire district of the county. Forming a civil parish, the 2001 census put the population of Hertford at about 24,180. Recent estimates are that it is now around 28,000...
, 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 behavior prevails.
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
Elastomer
An elastomer is a polymer with the property of viscoelasticity , generally having notably low Young's modulus and high yield strain compared with other materials. The term, which is derived from elastic polymer, is often used interchangeably with the term rubber, although the latter is preferred...
are independent of carbon black
Carbon black
Carbon black is a material produced by the incomplete combustion of heavy petroleum products such as FCC tar, coal tar, ethylene cracking tar, and a small amount from vegetable oil. Carbon black is a form of amorphous carbon that has a high surface-area-to-volume ratio, although its...
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
Constitutive equation
In physics, a constitutive equation is a relation between two physical quantities that is specific to a material or substance, and approximates the response of that material to external forces...
have been proposed to describe the effect. For example, the [Ogden-Roxburgh model] is used in at least one commercial finite element code.