Browsing by Author "Scher, H."

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    Time-dependent damage evolution and failure in materials. I. Theory
    Curtin, William A. Jr.; Scher, H. (American Physical Society, 1997-05-01)
    Damage evolution and time-to-failure are investigated for a model material in which damage formation is a stochastic event. Specifically, the probability of failure at any site at time t is proportional to sigma(i)(t)(eta), where sigma(i)(t) is the local stress at site i at time t and differs from the applied stress because of the stress redistribution from prior damage. An analytic model of the damage process predicts two regimes of failure: percolationlike failure for eta less than or equal to 2 and ''avalanche'' failure for eta > 2. In the percolationlike regime, failure occurs by gradual global accumulation of damage culminating in a connected cluster which spans the system. In the avalanche regime, failure occurs by rapid growth of a single crack after a transient period during which the critical crack developed. The scalings of the transient period, the subsequent crack dynamics, and the time-dependent probability distribution for failure are determined analytically as functions of the system size and the exponent eta. Specific predictions are that failure is more abrupt with increasing eta, failure times scale inversely with a power of the logarithm of system size, and the distribution of failure times is a double exponential and broadens with increasing eta, so that the failure becomes less predictable as it is becoming more abrupt. The conditions for the transition to the rapid growth regime are identified, offering the possibility of early detection of impending failure. In a companion paper, numerical simulations of this failure process in two-dimensional lattices are compared in detail to the analytical predictions.
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    Time-dependent damage evolution and failure in materials. II. Simulations
    Curtin, William A. Jr.; Pamel, M.; Scher, H. (American Physical Society, 1997-05-01)
    A two-dimensional triangular spring network model is used to investigate the time-dependent damage evolution and failure of model materials in which the damage formation is a nucleated event. The probability of damage formation r(i)(t) at site i at time t is taken to be proportional to the local stress at site i raised to a power: r(i)(t) = A sigma(i)(t)(eta). As damage evolves in the material, the stress state becomes heterogeneous and drives preferential damage evolution in regions of high stress. As predicted by an analytical model and observed in previous electrical fuse network simulations, there is a transition in the failure behavior at eta = 2: for eta less than or equal to 2, the failure time and damage density are independent of the system size; for eta > 2, the failure time and damage decrease with increasing time and failure occurs by the formation of a finite Critical damage region which rapidly propagates across the remainder of the material. The stress distribution prior to failure exhibits no abrupt changes or scalings that indicate imminent failure. The scalings of the failure time and the failure time distribution are investigated, and compared with analytic predictions. The failure time scales as a power law in In N-T, where N-T is the system size, but the exponent is not the predicted value of 1 - eta/2; this is attributed to a difference in the stress concentration factors (scf) between the discrete lattice and a continuum model. Using the scf values for the lattice lead to predicted scalings consistent with the simulations. Predicted absolute failure times versus size are generally in good agreement with simulation results at larger eta values. The coefficient of variation of the failure time distribution is observed to be nearly constant, in slight contrast to the predicted scaling of (InNT)(-1). Overall, the simulation results quantitatively and qualitatively validate many of the critical predictions of the analytic model.