Study of hardening and cyclic plastic behaviour around the crack tip of C(T) specimen made by as‐received and annealed copper

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For many materials, plastic deformations under cyclic loadings differ from monotonic loading. Cyclic plastic zone with considering the strain hardening effects becomes complicated during unloading step. In this research, the effects of nonlinear kinematic and isotropic hardening behaviours on the cyclic plastic reaction around the crack tip for different conditions are investigated. For study of various hardening characteristics, as-received and annealed copper are tested under same symmetric cyclic loadings. The results indicate considerable isotropic hardening behaviour in annealed material. A Chaboche nonlinear hardening model was used to determine the hardening parameters. The cyclic plastic zone around the crack tip in C(T) specimen was measured by back stresses. The cyclic plastic zones are specified via variations of the back stresses in a cycle. The cyclic plastic zones predicted by Chaboche model are smaller than those for Irwin model because of the hardening effects. Also, Irwin model for prediction of the cyclic plastic zone size is modified with considering the cyclic plastic effects. According to the results, the cyclic plastic zone around the crack tip is almost constant in the same load range, and load ratio (R) has a slight effect on this zone. Whereas, for constant load range, cyclic J-integral (ΔJ) is different for various R values. For studying of the fatigue crack growth, two parameters of ΔJ and cyclic plastic zone area were evaluated. These parameters can apply in fracture mechanics especially in elastic-plastic conditions with considering the cyclic plastic responses.

Section: Materials Model Detailsmentioning

confidence: 99%

“…The values of C 2 and D 2 are estimated by trial and error to satisfying the following equation:

\frac{C_{1}}{D_{1}} + \frac{C_{2}}{D_{2}} + σ_{0} = σ - \frac{C_{3}}{2} ({}, ε^{P} - ((), - ε_{yc}^{P})),

where

ε_{yc}^{P}

Section: Materials Model Detailsmentioning

confidence: 99%

“…The isotropic hardening characterization is specified by three parameters using the exponential law described in Equation 10 37 :

σ^{0} = σ_{0} + Q_{\infty} ([], 1 - italicexp ((), - b {\overset{false¯}{ε}}^{pl})),

where

{\overset{false¯}{ε}}^{pl}

Section: Materials Model Detailsmentioning

confidence: 99%

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Fatigue crack growth determination based on cyclic plastic zone and cyclic J‐integral in kinematic–isotropic hardening materials with considering Chaboche model

Hosseini

Seifi

2020

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“…Simulation of cyclic‐plastic behaviour of materials is typically done by using the combined isotropic‐kinematic hardening models . The growth (or shrinkage) of the yield surface due to cyclic hardening (or softening) phenomenon is generally simulated using isotropic hardening (IH) models, while the accumulation of plastic strains with cycle or ratcheting phenomenon is modeled by considering kinematic hardening (KH) models, related to the shift of the yield surface.…”

Section: Introductionmentioning

confidence: 99%

Prediction of asymmetric cyclic‐plastic behaviour for cyclically stable non‐ferrous materials

Nath

Barai

Ray

2019

Investigation on asymmetric cyclic‐plastic or ratcheting behaviour of non‐ferrous materials has received relatively little attention compared with ferrous materials. Ratcheting behaviour of materials is generally simulated using isotropic‐kinematic hardening models; however, for materials showing cyclically stable response, isotropic hardening is often not accounted for the constitutive modelling. A methodology based on Chaboche's isotropic‐kinematic hardening (CIKH) model with the consideration of genetic algorithm for optimization of initial estimates of the CIKH parameters is used in this study. The investigated plastic responses incorporate both symmetric strain‐controlled hysteresis loops and ratcheting behaviour. The suggested approach satisfactorily predicts the reported plastic response of cyclically stable non‐ferrous alloys based on aluminum, zirconium, and titanium.

“…Converged mesh for finite element model of (A) 3D 7-wire for steel and copper wires, validated against Judge et al29 ; (B) 3D crossed cylinders; (C) 2D cylinder-on-flat fretting geometry; (D) 2D cylinder-on-flat fretting-fatigue geometry with localized mesh refinement in contact regions for the Class 2 cable (; = 2.5 mm) for pure copper T A B L E 1 Geometrical and mechanical parameters of global 7-wire models for steel29 and copper30 …”

mentioning

confidence: 99%

Global and local modeling for inter‐wire fretting in multi‐wire copper conductors

Poon

Barrett

Leen

2022

Submarine power cables (SPC) are vulnerable to fretting, wear, and fatigue due to the dynamic environment, particularly at end connectors and junctions or other discontinuities, such as seabed features. This paper presents a finite element methodology for global and local analysis of fretting between copper conductors in multi‐strand cables. The salient inter‐wire fretting variables, such as relative slip and contact pressure, almost impossible to measure experimentally, are identified here via the three‐dimensional, global multi‐wire model, which includes frictional contact and large deformation effects. Local 2D and 3D representative models, typical of laboratory‐scale fretting test configurations, are adopted, with fretting boundary conditions derived from the global model fretting variables, for detailed micro‐scale resolution of fretting contact. A critical‐plane, multiaxial fretting‐fatigue life methodology is implemented to quantify fretting‐fatigue life. The effects of lay angle, contact size, wire diameter, friction, and slip are investigated. It is shown that, in general, increasing lay angle, contact size, wire diameter, and friction lead to reduced life. A key novel contribution of the paper is identification of the fretting fatigue relationships between representative local 2D (Hertzian) and 3D (crossed cylinder) modeling, via matching contact pressure, and global multi‐wire contacts. A rationalization of the relative contact size effects associated with transverse‐ and longitudinal‐type contacts in such applications is also presented.