English
中文Introduction
The marvel of band configuration in ferritic steels was initially documented by Piobert et al., in 1842 and later by Luders in 1860. Therefore, it is recognised as Piober-Luders band configuration (Tsukahara, & Thierry, 1998). Investigations revealed that yield drop recorded in moderate steel was due to interstitial carbon atoms joining dislocation cores. These interstitial carbon atoms known as Cottrell atmospheres get collected below at the border dislocation for decreasing the total lattice strain (Cottrell & Bilby, 1949). Cottrell and Bilby further added that the stress needed to slit away a dislocation from the settings depended upon the higher yield position. There are several professors (Yoshida, 2000; Yoshida et al., 2008) who after the dislocation have stirred away from the pinning carbon atoms and have believed that smooth movement on the slither plane becomes comfortable and therefore the stress for moving the dislocation decrease towards lower yield stress. There are various approaches for measuring stress and evaluating its efficiency and finite element (FE) modelling of Lüders band behaviour (Henri, & Iung, 1997). Different experts worked on Cottrell situation pinning along with multiplication models for dynamic strain maturity (Yoshida, 2003; Yoshida, et al, 2008).
Johnston and Gilman approach is helpful in finite element stimulations. The constitutive plastic models were formed especially for testing with dynamic strain ageing (DSA) and are being employed for rebuilding the yield drop attitude evident in the ferritic steels (Graff, et al., 2004). Many experts have opted for Zhang model (Wenman, & Plant, 2006; Ballarian et al., 2009; Zhang, 2008) for placing the yeild drop in the plastic strain data assigned to a finite element code in the shape of stress-plastic strain table. Few others have measured stress with the help of other techniques like FE and X-ray synchrotron measurement approaches (Steuwer, et al., 2004; Steuwer, et al., 2006 Turski, et al., 2008; Wenman, et al., 2009; Withers, et al., 2008). Development of the residual stress measurement systems has been quite helpful in authenticating different modeling methods and their capability (Withers et al., 2008). Few years ago, Yoshida has projected a viscoplastic constitutive model that can precisely explain the yield point incident and the parallel cyclic plasticity attitude (Sun, et al., 2003). Another finite element method utilising a viscoplastic constitutive model was proposed by Yoshida (2000) and was used to replicate the transmission of Lüders band for annealed low-carbon steel band in uniaxial tension examination.
Finite Element Modelling
Johnston and Gilman approach is helpful in finite element stimulations. Initial finite element modelling, formed in ABAQUS CAE v 6.8 software focused upon harmonising the tensile results at various strain rates and the paradigms of the tensile specimen along with the grips employed. This model comprised of a systematic firm object with a central reference point at the tip for the upper grip while the lower end was preset in all points of autonomy.
It was noted that mass scaling of around 50,000 times was needed to decrease run times for this division of the modelling as it efficiently enhances the loading speed of the test in accordance with the square root of the mass scaling value utilised. This consequently leads to an improvement in the higher yield positions that are quite responsive to the strain rate. But, this was believed to be a practical submission for run time as studied by enhancing the mass scaling on the tensile model.
Constitutive plastic models that have been formed especially for testing with dynamic strain ageing (DSA) have proved to be effective and therefore are being employed for rebuilding the yield drop attitude evident in the ferritic steels (Graff, et al., 2004). Assessment of DSA influences at V-notches and splits in CT specimens has been performed for Al-Cu and Al-Li alloys which revealed that Zhang’s model can create strain localisation bands in the plastic zone which are not evident in the absence of DSA integrated models.
The constitutive model and four standard elastic-plastic isotropic multi-linear hardening models (also referred as standard hardening models) were utilised for the purpose of comparison (Zhang, 2001). The plastic hardening curves employed for the standard hardening models have been clearly indicated in a research along with the sole element reaction and a complete stress-strain curve formed by the Zhang model of a tensile study at a rate of 0.01s-1. Many experts has opted for Zhang model (Wenman, & Plant, 2006; Ballarian et al., 2009; Zhang, 2008) for placing the yeild drop in the plastic strain data assigned to a finite element code in the shape of stress-plastic strain table which acts for the uniaxial tensile project yet it does not thoroughly handle the triaxial stress and differential stress conditions under complicated loading circumstances.
Complex loading signifies triaxial stress function of various magnitudes and signals besides making each of the elements feel a distinctive strain rate will be different at different time. For instance, an element placed at the marked root may feel a strain rate which might be higher than felt by an element placed in the plastic zone that is yielded, yet at some distanced from the notch root. It is therefore expected that the model should be effective to perform properly under such conditions. In the plastic zone for these present models at the notch root, strain rates were approximately five times more powerful as compared to the strain rate at other locations. This consequently results in the yield drop with variations in the lower and upper yield stresses in the peculiar components.
For the purpose of investigations, four instances of standard elastic-plastic hardening were compared to constitutive yield drop model. In case of the initial two instances, it was decided to concentrate upon the work hardening attitude from the lesser yield position whereas Luder’s strain and yield point were completely overlooked. The results of the tests were recorded and the information for the plastic curves was also acquired by performing two tensile examinations at various strain levels. However, 0.01 and 0.001s-1 were selected. The remaining two instances were less standard with the exclusion of the yield point but inclusive of Luders strain.
The CT specimens comprised of depressions on its exterior border permitting preloading of the CT specimen under compression. Recently, the complicated loading geometry has been selected for testing is CT specimen laden with in-plane compression that have been developed (Cotton, 1997 and Sherry, et al., 2002) for introducing prominent residual stresses through mechanical curve to evaluate the effect of residual stress on the hardened split of the material. Many experts have measured stress with the help of other techniques like FE and X-ray synchrotron measurement approaches (Steuwer, et al., 2004; Steuwer, et al., 2006 Turski, et al., 2008; Wenman, et al., 2009; Withers, et al., 2008). But, these experts feel that FE approach of these residual stresses ignored the yield drop phenomenon in the plasticity model. Hence, they believe that it might be inappropriate to explain the genuine residual stress area in ferritic steels.
Residual Stress Management
Modeling residual stress fields in the finite element analysis is a section which is drawing interest of the experts in UK. Development of the residual stress measurement systems has been quite helpful in authenticating different modeling methods and their capability (Withers et al., 2008).
Steuwer et al. (2004) have revealed the probability of plotting residual strains in the areas of split end points in the steel equipments that are around 25 mm in breadth at rational strain resolution (10_4) and counting period with the help of elevated power white beam SXRD at ID15A in the European Synchrotron Radiation Facility (ESRF). CT specimens prepared out of 316L stainless steel and laden in in-plane compression were broken with fatigue and plotted with the help of a 0.4 by 0.4 mm beam dimension. A parallel method and system was developed later using ferritic instead of austenitic steel. Ferritic has better grain composition (as austenitic steel only) therefore little diffraction gauge dimension is to be involved. As big slit dimensions add to volume but reduces resolution in elevated stress inclined areas. Also a big slit dimension may lead to few difficulties related to the dispersion of the solid-status detectors because of enhanced flux intensity (Turski, Bouchard, & Withers, 2007). It was possible to decrease the gauge dimension in this case as the grain size was below 10 µm. the investigation also purposed to clarify the effect of plasticity activities on the residual stress.
Finite element analysis of the residual stress field in a CT specimen
The assessment of the finite element model of the residual stress field in a CT specimen can be conducted with the help of viable FE evaluation software ABAQUS v 6.6. The modeling process comprises of two major steps which include reformation of the residual stress field introduced and reformation of a fatigue split and redeployment of the residual stress field (Withers, & Bhadeshia, 2000; Fonseca, Goldthorpe, & Sherry, 2005).
Mathematical conclusion have exposed that the peak stress in the forecasted residual stress allocation in the unsplit body is affected by the plasticity model applied for explaining the resources post yield attitude. A highest tensile residual stress within the isotropic version is created which is absent in a kinematic model. The kinematic model strongly corresponds to the rate calculated by X-ray synchrotron.
The material toughening attitude can be broadly segregated into kinematic and isotropic. The right toughening model will affect the residual stress stimulated by the pre-loading procedure to a great extent. An investigation involving bilinear kinematic model and multi-linear isotropic model accessible in ABAQUS Standard was carried out for obtaining plasticity data from the tensile tests. The Poisson’s ratio was fixed at 0.3 while the Young’s modulus was fixed at 220 GPa.
Few years ago, Yoshida has projected a viscoplastic constitutive model that can precisely explain the yield point incident and the parallel cyclic plasticity attitude (Sun, et al., 2003). Most of the above explained approaches have proved quite satisfactory in their performance, yet there has been some data confirming that through the beam width of 150 mm only, the spilt end strain measurements were put under a little volume averaging. It is highly possible that in the coming years, a minor ray volume would be effective provided the additional factors like grain size permit this. The work in upcoming years should apply a joint isotropic/kinematic approach with information acquired through the single-cycle analysis. This is likely to result in an enhanced sign of residual stresses before the introduction of a fatigue spilt.
Another finite element method utilising a viscoplastic constitutive model was proposed by Yoshida (2000) and was used to replicate the transmission of Lüders band for annealed low-carbon steel band in uniaxial tension examination. By decreasing the width of parallel factors, extra stress concentration was initiated into the FEM model. The results uncovered the fact that the pattern and propagation of Lüders band are influenced by the intensity of stress present at the terminals of the sample.
Importance to Nuclear Industry
During the previous years, weld-stimulated residual stresses harmed number of power plant elements, components and techniques (McDonald, Hallam, & Flewitt, 2005). Some of the experts believe that in BWR nuclear power plants, there could be a similar situation due to the mechanism of intergranular stress rust splitting in austenitic pipes or the primary cover in the reactor pressure vessel (Wenman & Chard-Trukey, 2000). This stress they believe is likely to get aggravated due to weld-induced residual stresses. It has been suggested that this can possibly be answered with the application of weld maximisation testing with other experimental approaches of residual stresses (Bouchard, et al., 2005; Elcoate, et al., 2005). The experimental evaluation including all the pertinent factors is not a simple task indeed. Mathematical simulation with the use of FE method complements this approach and is a similar convincing option. There is another computer programme known as (finite element residual stress analysis) which is available in ABAQUS code and which can also be applied as a 2-D or 3-D FEM analysis. A 3D version assists in the inspection of the in-breadth residual stress allocation (Dong, & Hong, 2005). The selection of the model usually depends upon the job description and can then offer a preliminary point ensuring a fracture mechanics safety scrutiny and satisfactory processing periods.
With various destructive and nondestructive methods for measuring stress in nuclear power production plants are available (Prime, 2001). In the table above three of the techniques have been discussed and compared for assessing the development of residual stress.
Magnetic stress calculations are beneficial as they are fast, economical, convenient and perfect for performing calculations on the nuclear plants at the time of maintenance shut down. Also, they are considerably effective in recognising the chief stress information. As far as destructive methods are concerned the contour model appears to be quite capable than the other available methods.
Conclusion
There are various approaches for measuring stress and evaluating its efficiency and finite element (FE) modelling of Lüders band behaviour. Johnston and Gilman approach is helpful in finite element stimulations. Initial finite element modelling, formed in ABAQUS CAE v 6.8 software focused upon harmonising the tensile results at various strain rates and the paradigms of the tensile specimen along with the grips employed. But, these experts feel that FE approach of these residual stresses ignored the yield drop phenomenon in the plasticity model. Hence, they believe that it might be inappropriate to explain the genuine residual stress area in ferritic steels. Magnetic stress calculations are beneficial as they are fast, economical, convenient and perfect for performing calculations on the nuclear plants at the time of maintenance shut down.
