PSI - Issue 2_A

Dong-Jun Kim et al. / Procedia Structural Integrity 2 (2016) 832–839 Dong-Jun Kim et al. / Structural Integrity Procedia 00 (2016) 000–000

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Nomenclature A, B

material constant for plasticity and creep C(t) , C * C -integral for transient and steady state creep conditions E Young’s modulus I m , I n integration constant that depends on m or n J(0) J -integral for initial time (t=0) conditions K I linear elastic stress intensity factor m , n strain hardening exponent, creep exponent r ,  polar coordinate at the crack tip t , t red time, redistribution time  coefficient in the Ramberg-Osgood model  strain  Poison’s ratio  stress

time. Depending on the type of load, it appears different features of the creep behavior. Load types may be divided into primary load and secondary load by Ainsworth, R. A. (1986). In general, the primary load means the mechanical load, such as pressure, and the load by load control condition and affects the plastic collapse. The primary load in the creep environment has a behavior that converges to a constant value after a certain period of time. Secondary load includes thermal loadings, residual stresses and the load by displacement control condition. The secondary load has the self-equilibrating characteristic and disappears over time. In the structure with the discontinuity, such as a crack, the elastic-follow-up behavior can appear and the characteristics that are similar to the primary load can also appear by Robinson, E. L. (1955). The research related the crack-tip creep behavior on the loads has been conducted. Previous studies have the limitations that are applicable only if the plastic exponent, m and creep exponent, n are equal. In this paper existing formulas are modified to improve the limits and this modified equation to predict the crack-tip stress field under creep condition are proposed for each load type. For the single-edge-cracked bend (SEB) specimen finite element analyses is conducted to validate the proposed equation. Section 2 briefly reviews the existing formulas on the characterization of crack-tip stress fields. Section 3 suggests the modified equation and Section 4 describes FE analysis, employed in the present study. And the results are presented in Section 4. Section 5 concludes the present work. 2. Characterization of crack-tip stress fields 2.1. Elastic-plastic region In elastic-plastic deformation, the strain can be defined as the sum of the elastic strain and plastic strain. This relationship is expressed as: 0.002 with and m e p o o o o o E E E                        where e  and p  is elastic and plastic strain, respectively; A and m are material constants. For an elastic-plastic material, the fracture mechanics parameter, J -integral, may be used to describe the stress fields around the crack tip. The relationship between the J -integral and the stress fields is known as the HRR fields by Huchinson, J. W. (1968) and Rice, J. R. et al. (1968). As part of the relative loading magnitude, the reference stress is used. The reference stress may indicate the rate of plasticity in a specimen. The reference stress is defined by limit load solutions and can be expressed as: m A E     (1)