Holistic Approach on the Research of Yielding, Creep and Fatigue Crack Growth Rate of Metals Based on Simplified Model of Dislocation Group Dynamics

A Toshimitsu Yokobori

doi:10.3390/met10081048

Abstract

The simplified model of numerical analyses of discrete dislocation motion and emission from a stressed source was applied to predict the yield stress, dislocation creep, and fatigue crack growth rate of metals dominated by dislocation motion. The results obtained by these numerical analyses enabled us to link various dynamical effects on the yield stress, dislocation creep, and fatigue crack growth rate with the experimental results of macroscopic phenomena, as well as to link them with theoretical results obtained by the concept of static, continuously distributed infinitesimal dislocations for the equilibrium state under low strain or stress rate conditions. This will be useful to holistic research approaches with concern for time and space scales, that is, in a time scale ranging from results under high strain rate condition to those under static or low strain rate condition, and in a space scale ranging from meso-scale to macro-scale mechanics. The originality of results obtained by these analyses were found by deriving the analytical formulations of number of dislocation emitted from a stressed source and a local dynamic stress intensity factor at the pile-up site of dislocations as a function of applied stress or stress rate and temperature material constants. This enabled us to develop the predictive law of yield stress, creep deformation rate, and fatigue crack growth rate of metals dominated by dislocation motion. Especially, yielding phenomena such as the stress rate and grain size dependence of yield stress and the delayed time of yielding were clarified as a holistic phenomenon composed of sequential processes of dislocation release from a solute atom, dislocation group moving, and stress concentration by pile-up at the grain boundary.

Highlights

The purpose of the research of dislocation mechanics is considered to have two directionalities, that is, application to the research of materials science and application to the research of the strength of materials such as that of yielding and fatigue crack growth rate. The former closely relates to micro plasticity, such as the conditions of dislocation emission, annihilation, and cross slip, and this research was developed in the manner of the modern dislocation dynamics [1]
The numerical results of the number of moving dislocations emitted from a stressed source and local stress concentration caused by a dislocation pile-up were necessary to be formulated as an analytical function of applied stress or stress rate, temperature, and material constants [2,3]
In our research, the establishment of a predictive theory of strength and fracture of materials was conducted by conducting the simplification of the model of analysis [3] and verification with experimental results [3,6]. Yielding phenomena such as stress rate and grain size dependence of yield stress and delayed time of yielding were especially clarified as a holistic phenomenon composed of sequential processes of dislocation release from a solute atom [7,8], dislocation group moving [6], and stress concentration by a pile-up at the grain boundary [2,3,4]

Summary

Introduction

The purpose of the research of dislocation mechanics is considered to have two directionalities, that is, application to the research of materials science and application to the research of the strength of materials such as that of yielding and fatigue crack growth rate. Pile-up is given by Equation (17) and is shown in Figure 6 for comparison with the dynamic stress intensity factor, Kd (θ). These results showed when the stress application (θ) at the site of pile-up such as grain boundary in nonstress factor rate,The τ,The ordynamic grain size, d, isintensity small, and a static equilibrium solution based on aascontinuous distribution (θ) at the site dynamic stress intensity factor of pile-up such grain boundary in non(θ)/ (θ) is plotted against dimensional form can be obtained using (16).

Basic Equations

Application to Problem of Creep

Findings

Concluding