Fatigue life prediction using 2‐scale temporal asymptotic homogenization

Abstract

SUMMARYIn this manuscript, fatigue of structures is modelled as a multiscale phenomenon in time domain. Multiple temporal scales are introduced due to the fact that the load period is orders of magnitude smaller than the useful life span of a structural component. The problem of fatigue life prediction is studied within the framework of mathematical homogenization with two temporal co-ordinates. By this approach the original initial boundary value problem is decomposed into coupled micro-chronological (fast time-scale) and macro-chronological (slow time-scale) problems. The life prediction methodology has been implemented in ABAQUS and validated against direct cycle-by-cycle simulations.

Accelerated molecular dynamics and equation-free methods for simulating diffusion in solids.

“…EFPI is related to, and in some cases a generalization of, temporal multiscale methods that have been developed for specific applications, such as the method of homogenization. For example, Oskay and Fish [36] have developed a time integration scheme for structural fatigue simulations using multiple time scales, in which the slow ("macro-chronological") solution is updated over long times based on the dynamics of the fast ("micro-chronological") solution over short times. One difference between EFPI and other techniques is the lack of any assumptions about the macroscale governing equation in EFPI; coarse scale evolution is driven solely by the fine scale dynamics.…”

A Nonlocal Multiscale Fatigue Model

“…The equivalent plastic strain rate is related to the matrix flow strengtḣ (33) in which E is the Young's modulus; and E t is the tangent to the uniaxial stress-strain diagram at a given stress level. The evolution equation for the center of the yield surface is:…”

“…Verification studies of the local multiscale fatigue model against cycle-by-cycle simulations were conducted in [33] for brittle materials and in [34] for ductile materials. In the present manuscript attention is restricted to calibration and experimental validation of the nonlocal multiscale model for ductile metals.…”

“…To the best of the authors' knowledge, the present study is the first attempt to assess the performance of the nonlocal GTN model under the conditions of cyclic loading. In this manuscript, we focus on the development, calibration and validation of the nonlocal multiscale model of fatigue based on the integral version of the nonlocal GTN model, which is an extension of the local fatigue model developed in [33,34].…”

A simple numerical method of cycle jumps for cyclically loaded structures

“…Even though the theory behind the ''LATIN method'' is interest ing, the implementation into commercial FEA software tends to be too cumbersome in its current form to be of practical interest. Fish and coworkers [15,16] have devel oped an alternative method for cycle jumps where the time is decomposed into two time scales: one micro-chronolog ical (fast time scale) and one macro-chronological (slow time scale). Thus, the micro-chronological time corre sponds to the cyclic behavior, and the macro-chronological to the overall trend of the structure.…”