Effect of dynamic strain aging on isotropic hardening in low cycle fatigue for carbon manganese steel

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Abstract

Carbon–manganese steel A48 (French standard) is used in steam generator pipes of nuclear reactor pressure vessels at high temperatures (about 200 °C). The steel is sensitive to dynamic strain aging in monotonic tensile test and low cycle fatigue test at certain temperature range and strain rate. Its isotropic hardening behavior observed from experiments has a hardening, softening and hardening evolution with the effect of dynamic strain aging. The isotropic hardening model is improved by coupling the dislocation and dynamic strain aging theory to describe the behavior of A48 at 200 °C.

Introduction

In steam generator of PWR plants and feedwater lines connected to the loop pipes have been designed to withstand the internal pressure. In terms of the previous reports [1], these pipes also sustain long time and repeated alternation loads due to intermittent injection of cold water which introduces a stratified water distribution and forms cyclic thermal stress. Fatigue damage in the tubes is caused by the cyclic load. The fatigue life prediction for the notched or welded specimen is investigated by Berto and Lazzarin [2], [3] by using volume based Strain Energy Density (SED) approach which gives a fatigue criteria and is used to correctly describe the fatigue behavior.

For metal materials, under loading (tensile, fatigue, etc), several metallurgical instabilities such as Lüders bands, Portevin le Chatelier bands, Neuman bands, twinning and phase transformation, are related with the spreading of solute atoms over crystal lattice or the crystallographic structure changing [4], [5], [6].

Dynamic Strain Aging (DSA) is a result of the interaction of strong solute atoms pinning and dislocations moving, which influence the mechanical characters of materials. The solute atoms are capable of diffusing over short distance and arrest mobile dislocations in certain strain rate and temperature range. The strain rate sensitivity coefficient becomes negative when DSA happens and the well known localized deformation bands (Portevin-Le Chatelier) appear in the monotonic tensile test [7]. In the case of low cycle fatigue test, serrated yielding is also observed in the strain–stress curve [8].

Insufficiently killed steels are sensitive to DSA and lead to varying mechanical characters such as the increasing of flow stress, ultimate tensile strength (UTS), work hardening coefficient, and the decreasing of ductility and fracture toughness. Some typical characters of DSA in cyclic tests are reported in the literature [9], [10], [11]: inverse dependence of the peak tensile stress with strain rate and an unusual increase in the effect of DSA in the single phased ferrite austenitic stainless steels. Tsuzaki et al. [11] reported that the DSA sensitive temperature is lower in fatigue than in monotonic tensile for austenitic stainless steel. Abdel Raouf et al. [12] observed DSA hardening in the LCF test for low carbon steel.

The effect of DSA with loading speed on LCF behavior strongly depends on the material composition and the heat treatment. The article mainly focuses on the DSA effect on LCF isotropic hardening for the low carbon manganese steel. Double hardening in the peak tensile stress evolution is studied from the test results. In order to describe this behavior, an improved isotropic hardening constitutive model is proposed by considering the DSA effect, the interaction of dislocation movement and the solute atoms diffusion.

Section snippets

Material and experiment

The plates of steel A48 are selected to study. The material composition is shown in Table 1. The steel has been semi-killed by silicon and normalized at 870 °C followed by air cooling, so that the aluminum content of this steel is low (0.004%).

The material is a kind of duplex phase steel. The microstructure shows alternating bands of ferrite and pearlite (Fig. 1) which has segregated minor inter-dendritic elements (mainly manganese). The distance between the bands of pearlite is about 30–40 μm

Internal friction and monotonic tensile experiments

Attenuation of vibration of a solid material is due to the internal friction which is an intrinsic property of the material and can be defined as the capacity of the solid material dissipating thermal energy when it sustains cyclic load in the elastic domain. The specimens for internal friction experiment were machined into 3 mm diameter, 50 mm gauge length in the quarter thickness of transverse direction of the plates. The mechanical spectrometry is obtained by measuring the dissipated energy

Tensile peak stress evolution in LCF

For the C–Mn steel, two kinds of atoms are extremely important: carbon and nitrogen. They are part of the solid solution of insertion into the centered cubic iron network, and their small size enables them to get inserted into the network and form solid solutions, or precipitates in the form of carbides (mainly iron Fe3C), nitrides of aluminum and iron.

The atoms in the solid solution are distributed in 2 locations: the solid solution near the dislocations and the solid solution “free” in the

Predicting the onset cycle of DSA hardening

A total time of dislocations moving between cell walls such as cell shuttling motion is considered as [12]:tt=tw+tfwhere tw is the waiting time at the cell wall and tf is the flight time across the cell structure. The flight time tf might be negligible because it is very short compared with the waiting time which is approximately considered as the same as the total time. The total time can be rewritten as [15]:tttw=w(p)ṗ

If the waiting time is long enough, with the dislocation multiplication

Modeling HSH process

As a preliminarily exploitation, the evolution of back stress is not included in the model. Isotropic hardening coupled with kinematic hardening with the effect of DSA would be studied in the future work. The isotropic hardening is considered and applied to the smooth specimen and the uniaxial stress may be expressed as [19], [20]σ=σy+iX(i)+kR(k)where X(t) is the back stress; σy is the cyclic yield stress; R(k) is the isotropic hardening/softening stress. For A48 at 200 °C, the isotropic

Identification and verification

The paper aims to investigate the isotropic hardening with DSA effect on LCF. The isotropic hardening stress can be obtained by subtracting the back stress (X in Eq.(10)) and cyclic yield stress σy in the hysteresis loops from the maximum cyclic stress of LCF tests results [23]. The cyclic yield stress (σy) could be considered as a constant in the fatigue test. The evolution of isotropic hardening is obtained from the LCF test results and plotted in Fig. 9 with the growth of accumulated plastic

Conclusions

This paper investigates the pronounced double isotropic hardening behavior of A48 steel in LCF. The material presents some special mechanical characteristics caused by DSA effect in monotonic tensile tests and LCF tests. The conclusions are as follows:

  • 1.

    At high temperature, 200 °C, the stress amplitude evolution of the steel (A48) reveal hardening, softening and hardening process before crack initiation. The primary hardening seems to be caused by the cyclic plastic deformation and the dislocation

Acknowledgments

Cooperation with AREVA is gratefully acknowledged, especially the support of Professor T. Palin-Luc in ENSAM Bordeaux for the LCF experiments at high temperature. Financial support by the National Natural Science Research Foundation of China (No. 51101107 and No.11372201) is also gratefully acknowledged.

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