Micromechanical modeling of crack-tip rubber particle cavitational process in polymer toughening
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A simple micromechanical modeling of the rubber particle cavitatlonal process at the crack tip was conducted using the combination of Irwin's crack tip stress intensity factor analysis, slip-line field theory, and Dewey's closed-form elastic solution. This unique micromechanical modeling provides fruitful insights concerning the possible role(s) the rubber particles play in front of a constrained (plane-strain) crack tip. The cavitation of the rubber particles at the tip of the crack causes the redistribution of the stress and strain fields around the cavitated rubber particles. This, in turn, alters the stress state the surrounding matrix experiences. Consequently, the fracture process is affected by the rubber particle cavitational event. The results of the micromechanical analyses suggest that both the preexisting holes and the occurrence of cavitation in the rubber particles in front of the crack serve (i) to relieve the plane-strain constraint, (ii) to promote shear yielding of the matrix, and (iii) as stress concentrators. The major difference between the preexisting holes and the rubber particle cavitational event lies on the sudden buildup of the octahedral stress component upon the cavitation of rubber particles in the crack tip region. Experimental observations of toughening mechanisms of various rubber-modified polymers support this micromechanical analyses.
