Project Highlights

Simulations Shed More Light on Laws Governing Materials Fracture

The statistical properties of fracture in disordered media are interesting not only in view of practical applications but also for purely theoretical reasons. From a practical point of view, the main issue associated with the fracture of quasi-brittle materials (such as concrete and ceramics) is the scaling of material strength – how properties like strength scales with sample size, also known as the size-effect. In addition to size-effect, understanding the acoustic emission signatures associated with the crackling noise of fracture experiments serves as a methodology for forecasting impending structural failure.

The main theoretical challenge, however, lies in understanding the generic laws that govern fracture of materials. Despite considerable progress, many controversial issues exist between theoretically estimated results and experimentally measured values. For example, the origin of both the scaling and universality of the fracture surface roughness exponent lies at the heart of the controversy.

Despite the recent algorithmic advances, the largest three-dimensional (3-D) lattice system fracture simulation has been limited to system sizes up to 643 since the CPU time required to analyze the fracture simulation of a 3-D disordered lattice system increases as O(L6.5), where L is the linear dimension of the 3-D lattice system. Simulations of much larger systems are required for obtaining accurate scaling laws in 3-D. Researchers at Oak Ridge National Laboratory have pursued the largest ever 3-D disordered lattice systems of size 1283 through their INCITE award to obtain the scaling laws of fracture surfaces (see figures) – requiring over 90 times the computation effort of 643.

For the first time, these simulations show that the crack surface roughness exhibits anomalous scaling as observed in recent experiments on granite and wood samples. In particular, these large-scale simulations result in a local roughness exponent of zloc = 0.4, which is slightly different from the global roughness exponent z = 0.52. A similar difference between local and global exponents was also found in two-dimensional simulations for both triangular and diamond lattices, suggesting that anomalous scaling is a generic feature of the fracture of disordered media as found in fracture experiments. In addition, the numerical results indicate that apparent multiscaling of crack surface roughness observed at small scales is due to the removal of overhangs of the fracture surfaces and that the roughness crosses over to self-affine scaling at large scales.

Contact

Phani Nukala
Oak Ridge National Laboratory