Scaling of surface roughness in perfectly plastic disordered media

This paper investigates surface roughness characteristics of localized plastic yield surface in a perfectly plastic disordered material. We model the plastic disordered material using perfectly plastic random spring model. Our results indicate that plasticity in a disordered material evolves in a diffusive manner until macroscopic yielding, which is in contrast to the localized failure observed in brittle fracture of disordered materials. On the other hand, the height-height fluctuations of the plastic yield surfaces generated by the spring model exhibit roughness exponents similar to those obtained in the brittle fracture of disordered materials, albeit anomalous scaling of plastic surface roughness is not observed. The local and global roughness exponents (ζ(loc) and ζ, respectively) are equal to each other, and the two-dimensional crack roughness exponent is estimated to be ζ(loc)=ζ=0.67±0.03. The probability density distribution p[Δh(ℓ)] of the height differences Δh(ℓ)=[h(x+ℓ)-h(x)] of the crack profile follows a Gaussian distribution.