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Stress-Strain Behavior of Polymeric Elastomers

JHUS tress- strain Behavior of Polymeric ElastomersA Polymeric elastomer is defined by the American Society for Testing and Materials (ASTM)as a material that, at room temperature, can be stretched repeatedly to at least twice its originallength, and, upon immediate release of the stretch, will return with force to its approximateoriginal length . First developed in Germany in 1937, production of (polyurethane) elastomericfibers has increased in demand over the last forty years, primarily due to the development offibers that can move with and physically support the human Elastomers chemically con-Figure 1: Virtual crosslinks formed by attractionsbetween hard blocks in a Polymeric of long, randomly coiled domains ofaliphatic polyethers or polyesters, joinedby stiff regions of urethane linkages. To-gether, these two groups form blocks orsegments on the polymer, which are softor spring-like in the former case and hardin the latter.

J H U Stress-Strain Behavior of Polymeric Elastomers A polymeric elastomer is defined by the American Society for Testing and Materials (ASTM) as “a material that, at room temperature, can be stretched repeatedly to at least twice its original

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Transcription of Stress-Strain Behavior of Polymeric Elastomers

1 JHUS tress- strain Behavior of Polymeric ElastomersA Polymeric elastomer is defined by the American Society for Testing and Materials (ASTM)as a material that, at room temperature, can be stretched repeatedly to at least twice its originallength, and, upon immediate release of the stretch, will return with force to its approximateoriginal length . First developed in Germany in 1937, production of (polyurethane) elastomericfibers has increased in demand over the last forty years, primarily due to the development offibers that can move with and physically support the human Elastomers chemically con-Figure 1: Virtual crosslinks formed by attractionsbetween hard blocks in a Polymeric of long, randomly coiled domains ofaliphatic polyethers or polyesters, joinedby stiff regions of urethane linkages. To-gether, these two groups form blocks orsegments on the polymer, which are softor spring-like in the former case and hardin the latter.

2 The soft blocks usually makeup 65-90% of the molecular weight of thepolymer, and are essentially unoriented ina relaxed fiber. The hard blocks providelong range molecular attractions by shar-ing electrons2; this results in the forma-tion of what are known as virtual crosslinks. There is some experimental evidence from bothx-ray diffraction techniques and differential scanning calorimetry for the formation of theseclusters. A schematic of these virtual crosslinks is illustrated in Figure makes Polymeric Elastomers so usefulStrain (%) stress (psi)070006000 stress (psi)070006000 Figure 2: The unusual Stress-Strain behaviorof Polymeric their unusual Stress-Strain Behavior , which isshown in Figure 2. Upon stretching, it is imme-diately noted that there is a large flat region inthe Stress-Strain curve. This essentially meansthat after an initial elongation, there is a regionof stretching which occurs without increasingstrain.

3 The purpose of this project is to pro-duce a model of the Elastomers that can dupli-cate this Behavior . There are two different as-pects to this project. First, it is desired to pro-duce a model that can represent an elastomerfiber immediately after production, before everbeing stretched for the first time. Secondly, af-ter formation, the polymer network will ripen or continue to develop while still in the production tanks. It is expected that the stress -strainbehavior of a fiber after this ripening period will be different than that of a fiber immediatelyafter formation. The model should be capable of duplicating these model used in this study consists of a lattice upon which molecules are laid down one atProfessor Marc DonohueDepartment of Chemical EngineeringJohns Hopkins UniversityJHUa time. The model polymers consist of two hard blocks, connected by a soft block of a specifiedlength.

4 Lattice sites are allowed to have multiple hard blocks on them. After randomly layingdown all of the segments, the lattice is checked for percolation, which is a condition in whichthere is an unbroken path that connects the top and the bottom of the lattice. By an unbrokenpath, we mean a continuous path that is made up of polymer segments that have overlappinghard blocks. Percolation insures that if the fiber is stretched, there will be a resistance. If thesystem is percolated, the Stress-Strain Behavior is calculated by replacing each polymer witha combination of circuit elements. Specifically, the voltage across the system is ramped to aspecified value and the current through the network is capture the time dependant Behavior of the fiber, the system is allowed to ripen in thefollowing manner. Hard blocks are given an attractive potential. A hard block on the lattice isselected at random. The algorithm then attempts to move that hard block to a second, randomlyselected site that is within a radius from the other end of the chain specified by the length of thesoft block.

5 System energies for each location are calculated, and the proposed move is acceptedor rejected according to the Metropolis algorithm. After a specified number of attempted moves,the system is again checked for percolation, and if it is, the Stress-Strain properties are obtainedas described above. In this manner, the change in the Stress-Strain Behavior can be obtained asa function of , Elastomers , 2nd ed.; Elsevier Science Publishers: New York, , M. InHandbook of Fiber Science and Technology; Lewin, M., Sello, S. B. Eds.; Marcel Dekker: NewYork, Marc DonohueDepartment of Chemical EngineeringJohns Hopkins University


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