Abstract

Pure waterjet surface treatment without abrasive particles has a promising application in the biomedical field, because it induces compressive residual stresses on a metal surface and never leaves the tiny hard particles. In this work, the influence of operation pressure, standoff distance and the number of paths of the waterjet on the surface topography as well as the hardness was studied using the Taguchi method. The results showed that the most essential parameter is the operation pressure. By tuning the operation pressure from 100 to 300 MPa, the surface of Ti6Al4V specimens can be smoothed, roughened or damaged; when the surface layer is eroded, the new-born surface exhibits a clear stochastic nature accompanied by microvoids. The standoff distance benefits finer controlling the height parameters, whilst the number of paths affects the waviness. The hardening effect generated by the waterjet impingement extends to a few hundred-micron depth of the specimens, and the peak value of microhardness was found at a depth of 70 μm, which is an increase by greater than 20 %. The roughness parameters of Arithmetical mean height (Sa), Skewness (Ssk), Auto-correlation length (Sal), and Developed interfacial area ratio (Sdr) as a set are recommended to characterize the biomaterial’s surface. The present research results promote the application of waterjet treatment in the field of fine-tuning biomaterial surface morphology.

Introduction

The surface topography of the implant significantly influences the bone response [1,2]. There are two stages (short/long) of biological response after implantation [3]. One is the short-term response that a fibrous soft tissue is formed and capsules around the implant, and another response directly relates to bone-implant contact without the connective tissue layer, known as osseointegration [4]. The surface topography plays an important role in the biomechanical fixation between the implant and the soft fibrous tissue at the early stage of implantation. Meanwhile, the rate and quality of osseointegration that determine the long-term success of the clinic implantation are also affected by the surface topography [5]. The demand for specific surface finishes of biomedical devices [6] drives researchers to develop efficient surface modification methods.

Waterjet technology that places a sample under the waterjet itself and subjects it to the water pressure in the air or underwater is one of the promising methods [7,8]. As one of the fastest-growing technologies, the waterjet can machine (cut, drill and mill, clean, remove) almost any material [9]. Waterjet is used in a variety of fields from automotive and aerospace to medical and the food industries [10]. Particularly, pure waterjet induces compressive residual stress to enhance fatigue strength [11], and never leaves tiny residues (hard particles) on a metal surface compared to the abrasive waterjet, it holds tremendous promise in the medical industry [7,11].

Conclusion

Using the Taguchi method, nine waterjet experimental cases were designed and conducted. The influence of the operation pressure, standoff distance, and the number of paths on the surface topography and the areal roughness parameters as well as the hardness were analyzed and discussed. The main conclusion is drawn as follows:
• Among the three process parameters of waterjet treatment, the most critical one is the operation pressure. The standoff distance is beneficial for finer control of the height parameters, whilst the number of paths affects the waviness.

• By increasing the operation pressure from 100 to 300 MPa, the surface of Ti6Al4V specimens can be smoothed, roughened, or damaged; when the surface layer is eroded, the new-born surface exhibits a clear stochastic nature accompanied by microvoids.

• The hardening effect generated by the impingement of waterjet spans over a few hundred microns width, with the peak microhardness being found at a depth of 70 μm, which increases by over 20 %.

• After a comprehensive analysis of the 5 categories of 14 areal roughness parameters, the parameters of Sa, Ssk, Sal, and Sdr as a set are recommended to characterize the biomaterial’s surface.

1- Introduction

2- Theories and methodology

3- Results and discussion

4- Conclusions

References

Abstract

In order to account for rigid-flexible coupling effects of floating offshore wind turbines, a nonlinear rigid-flexible coupled dynamic model is proposed in this paper. The proposed nonlinear coupled model takes the higher-order axial displacements into account, which are usually neglected in the conventional linear dynamic model. Subsequently, investigations on the dynamic differences between the proposed nonlinear dynamic model and the linear one are conducted. The results demonstrate that the stiffness of the turbine blades in the proposed nonlinear dynamic model increases with larger overall motions but that in the linear dynamic model declines with larger overall motions. Deformation of the blades in the nonlinear dynamic model is more reasonable than that in the linear model as well. Additionally, more distinct coupling effects are observed in the proposed nonlinear model than those in the linear model. Finally, it shows that the aerodynamic loads, the structural loads and global dynamic responses of floating offshore wind turbines using the nonlinear dynamic model are slightly smaller than those using the linear dynamic model. In summary, compared with the conventional linear dynamic model, the proposed nonlinear coupling dynamic model is a higher-order dynamic model in consideration of the rigid-flexible coupling effects of floating offshore wind turbines, and accord more perfectly with the engineering facts.

Introduction

In recent years, floating offshore wind turbines (FOWTs) have been receiving increasing attention due to their prominent advantages, such as steadier and stronger wind available resources, lower operational noise, reduced visual pollution and fewer space limitations (Karimirad et al., 2011; Bachynski and Moan, 2012; Pérez-Collazo et al., 2015; Ma et al., 2015). FOWTs are complex rigid-flexible coupled multi-body systems (Namik and Stol, 2010; Wang and Sweetman, 2013; Nejad et al., 2015). Moreover, because the slender blades of an FOWT system typically work at a high rotational speed and are influenced by the motions of the floating platform, rigid-flexible coupled dynamic responses of FOWT systems are more complicated than those of the fixed bottom wind turbines. Rigid-flexible coupled multi-body dynamics have received considerable attentions during the development of modern high-speed airplanes (Shabana, 1997; Bauchau, 2011). In the 1970s, Winfrey (1971) proposed the “kinetoelastodynamics” (KED) method to model the dynamic behaviour of rigid-flexible coupled multi-body systems. In this method, the system is first modelled as a rigid multi-body system to calculate the motion and inertia forces on the system.

1. Introduction

2. Experimental fatigue tests on scotch yokes

3. Fatigue test results

4. FE stress analyses

5. Methodologies for fatigue strength assessment of scotch yokes

6. Conclusions

7. Acknowledgments

8. References

Aim of this work is the fatigue assessment of a main component, termed scotch yoke, of a valve actuator used for oil & gas, power and chemical industries, in order to comply with its heavy-duty applications. To do this, full-scale specimens of the scotch yoke made of structural steel have been fatigue tested under nominal axial loading. All specimens have been tested under stress-relieved conditions by adopting a nominal load ratio R=-1. After experimental tests, the fatigue crack paths have been analysed by means of liquid penetrant inspections. The fatigue strength class of the considered scotch yoke has been determined by statistically re-analysing the experimental results, expressed in terms of range of the nominal applied load, and it has been compared with the design condition required by the relevant European Standard, EN 15714-3/4. Finally, two methodologies for fatigue strength assessment of the considered scotch yokes have been proposed, which are based on experimental fatigue data derived from smooth or sharp V-notched specimens, respectively, made of the same yoke material. The assessment capability of the proposed methodologies has been evaluated and discussed by comparing theoretical estimations with the experimental fatigue results of the scotch yokes.

Introduction

Pneumatic scotch yoke valve actuators are commonly used in many industrial sectors for different applications. High-cycle applications are among the most challenging scenarios for heavy-duty actuation, which impose high frequency of operation often at relatively high operating speed. The LPS actuator series, see an example in Fig. 1, are mainly adopted in the Oil&Gas field and are able to provide a very high torque output. They are currently designed by FLOWSERVE – Limitorque according to the relevant European Standard, i.e. EN 15714-3/4 [1], which requires actuators to operate for a minimum number of cycles as a function of the nominal output torque. The required minimum number of cycle could be very different, even by some orders of magnitude. As an example, dealing with the Limitorque actuator model LPS-15, which is designed for a nominal output torque of 6000 Nm, the minimum number of cycles required by the Standard [1] is equal to 105 . However, in high-cycle applications sometimes required also from chemical sector, customers frequently ask for actuators operating at least for 2 million cycles. Accordingly, the adoption of standard actuator series for a wide range of applications inevitably leads to an oversize and an increase of the cost of the project, which corresponds to a decrease of the competitiveness on the global market. This issue can be addressed by adopting a validated design and by optimizing the actuator construction features, in order to guarantee the number of cycles required by Standards while avoiding an oversizing of the actuator.

1- Introduction

2- Triple tube exchanger advancements

3- Conclusions

References

Abstract

In the past decades have faced the challenges in meeting out the cooling demand due to the technological developments. More works are being carried out for optimum heat transfer in concentric heat exchangers, one among the double tube heat exchangers investigation is the triple tube heat exchangers (TTHE). Reported that the triple tube heat exchangers are more effective than double tube heat exchangers. In this paper, investigations carried out on triple tube heat exchangers are reviewed and the reports published by different researchers are critically analyzed in order to carry out the advanced research work on triple tube heat exchangers.

Introduction

The basic type of heat exchanger used in a wide range of applications is a double tube heat exchanger. Its working phenomenon is based on heat transfer between two pipes with cold and hot fluids. It has its significance in freezing, boiling drying, dairy, and pharmaceutical, food, pasteurization and chemical industries. In order to manage high-temperature differences, the heat exchange area should be increased, which could be possible only by increasing the heat exchanger’s length. TTHE solves this problem, by increasing the heat transfer area for the same length of the double tube heat exchanger. It has three concentric tubes specifically three compartments which are mentioned to be inner tube, inner annulus and outer annulus. It is needed to flow the target fluid whose temperature variations are of main concern for application fulfillment within the inner annulus for taking better advantage of the heat exchanger. The inner annulus has 2 heat exchange surfaces (inner tube outer surface and outer tube inner surface) that will increase the heat exchange area of heat exchanger marginally compared to double tube device (has just one heat exchange surface) which will increase the speed of heat exchange. It conjointly in terms will increase the potency of heat exchanger.

18-1- Atomic Magnetic Dipole Moment

18-2- Magnetization 18.3. Magnetic Induction

18-4- Potential Energy of Magnetic Dipole Moment

18-5- Larmor Precession

18-6- Quantum Theory of Diamagnetism

18-7- Paramagnetism

18-8- Hund’s Rule

18-9- Crystal Field Splitting

Suggested Reading

Abstract

The next four chapters are devoted exclusively to magnetism, a very important property of solids from the technological point of view. This chapter begins with an estimation of the atomic magnetic dipole moments responsible for the existence of magnetism in solids. The matrix representation of magnetization, magnetic susceptibility, and magnetic induction in magnetic solids has been presented. Classical and quantum theories of diamagnetism and paramagnetism have been described in reasonable detail. The magnetic susceptibility of paramagnetic solids obeys the Curie law at high temperatures. The chapter concludes with a statement of Hund’s rule, which is applied to evaluate the effective atomic magnetic moments in transition and rare-earth elements. It was noted that quenching of the orbital magnetic moment takes place due to the presence of an inhomogeneous crystal field.

ATOMIC MAGNETIC DIPOLE MOMENT

In an atom, electrons revolve around the nucleus and the nucleus contains protons and neutrons. An atom as a whole is electrically neutral, but it consists of moving charged particles that may behave as magnetic dipoles. An electron in an atom has two motions: orbital and spin. Similarly, protons and neutrons also possess orbital and spin motions inside the nucleus. Therefore, the magnetic moment of an electron has two principal contributions, which are the orbital and spin magnetic moments. There is also a third contribution to the magnetic moment arising from the spin-orbit interaction. If the spin and orbital motions are assumed to be independent of each other, then the spin-orbit contribution vanishes and the total magnetic moment of the ith electron m ! ei is the vector sum of its orbital and spin contributions, i.e.,

1- Introduction

2- Mathematical modeling

3- Data reduction

4- Results and discussion

5- Conclusions

References

Abstract

In this paper, an optimization method is proposed to improve the performance of a novel heat exchanger with latent heat thermal energy storage. Paraffin/expanded graphite composites were used as phase change material filled in annular tube, maintained contact with the shell and tube flow channels simultaneously. The heat transfer and flow characteristics of this novel heat exchanger were investigated in a previous study, which indicated that further research was required to enhance thermal transfer rates. Therefore, in this work, the thermal property of the material and geometric parameters of the heat exchanger, including compression density, tube diameter, and fins and baffle configuration, were studied numerically to improve the thermal behavior of the system. It was found that a composite with density of 600 kg/m3, a tube diameter of 19 mm, and an extended surface and baffle space of 100 mm, can be used for the final optimization result. The results show that, after optimization, the thermal conductivity of the phase change material can reach 5.16 W/m K and the latent thermal energy stored in system could be twice that previously obtained. The solidification rate can increase to a maximum of 50% while the shell side Nu/Pr1/3 can reach 29.98. The improved heat exchanger shows better energy storage capacity and working power.

Introduction

Currently, thermal energy storage (TES) plays an important role in overcoming the lack of balance between energy supply and demand. TES can be divided into three technologies: sensible, latent, and thermochemical. Latent heat thermal energy storage (LHTES) based on a phase change material (PCM) is considered to be a promising technique, because it has high energy storage density and low-fluctuation operating temperature [1]. Owing to the superior performance of the LHTES unit, it is employed in many fields, such as industrial waste heat recovery [2], solar energy utilization [3], thermal management of electron device [4], and building energy conservation [5]. A heat exchanger based on latent heat storage is the key of the LHTES unit. A cylindrical shell-and-tube heat exchanger is commonly used for heat storage system owing to its robust structure, easy maintenance, and high heat transfer rate [6]. Cano et al. [7] studied four types of PCMs filled in the shell side of the heat exchanger and the influence of the heat transfer flow rate, and different operation modes (watertight and countercurrent PCM flow) were evaluated. It was found that the shell-side PCM countercurrent flow system showed the best energy transfer performance. Hosseini et al. [8] investigated the melting and solidification performance of paraffin RT50 in the shell side of a shell-and-tube heat exchanger and found that by increasing the inlet water temperature from 70 C to 80 C, the charging and discharging efficiency of the heat exchanger rose from 81.1% to 88.4% and 79.7% to 81.4%, respectively. Kibria et al. [9] experimentally and numerically studied the latent heat storage system with shell and tube arrangement, where the PCM was filled in the shell and water passed through the tube. It was found that the influence of inlet temperature of the fluid on the solidification and melting of the PCM is considerable, whereas that of the mass flow rate is negligible. In spite of the great potential of the LHTES system, the low thermal conductivity of the PCM still limits its practical feasibility.

1. Introduction

2. Experimental method and materials

3. Results and discussion

4. Conclusions and perspectives

Appendix A. Uniaxial tension results

References

1. Introduction

2. Vibration, Dynamics, and FE simulation

3. Important factors in fatigue analysis

4. Experimental modal analysis

5. Improving Fatigue Analysis through Experimental and CAE Correlation

6. Case study

7. Conclusions

References

The durability assessment of a component or structure is often assessed using Finite Element Analysis (FEA)-based structural simulations. Fatigue is a progressive failure mode that is related to the stress cycle’s range in a power law such that the fatigue damage increases exponentially as the stress range increases. When the frequency content of the loading gets closer to the natural frequencies of the structure, resonance effects are activated. In this case, the dynamic properties of the structure must be included in the analysis in order to better account for the increased stress response. A dynamic FEA produces therefore more realistic results compared to a static analysis, but requires knowledge of additional characteristics such as mass and damping. In a dynamic FEA, whether transient or steady state frequency response, the damping property governs indeed the magnitude of the dynamic stress response and hence the durability of the component. Unfortunately a default damping value is sometimes erroneously assumed for all modes leading to errors in the stress response, which in turn leads to significant errors in the fatigue life estimates. The modal parameters – including damping ratios – for the structure’s modes of vibration can be extracted using experimental modal analysis techniques. The purpose of this article is first, to explain the critical role that damping plays in fatigue damage; and second, to recommend best practices for determining modal damping experimentally. A simple example of an automotive component will be used to illustrate the importance of using experimental modal analysis to adjust the properties of a FE-based dynamic structural analysis. An experimental modal test followed by a modal analysis will be described. The mode shapes obtained experimentally and analytically will be compared to validate the mass, stiffness and boundary conditions used in the modelling. Then, it will be shown that using realistic values for the damping ratios will help to obtain stress results that correlate with the measured stress. Finally, this example will illustrate the very high sensitivity of the fatigue life estimate to the damping ratios.

Introduction

Fatigue is a progressive failure mode caused by stress cycles. These stress cycles can be driven by dynamics and resonance under some conditions, so prediction of fatigue life requires an understanding of resonance. FEA is often used for the prediction of product durability and can account for dynamics. However, these analytical stress results need to be correlated to real structural behaviour in order to accurately predict fatigue life. Often a damping ratio is assumed when performing the FE structural analysis. This can lead to errors in the fatigue life estimation. Experimental techniques can be used to properly quantify the damping and therefore improve the accuracy of the durability analysis. This paper recommends best practices for improving FEA-based stress and durability analysis via experimental techniques for determining modal damping and correlating analytical results with the real world.

1. Introduction

2. Experimental

3. Conclusion

Acknowledgements

References

The fatigue performance of laminated glass fiber reinforced polyamide composites was investigated in this study. Fatigue tests were conducted on both unidirectional and cross-ply specimens at room temperature. The S-N diagram of [0]8 followed a bilinear curve, however, the [90]8 laminates presented a linear S-N diagram. Compared to the same lamination of glass/epoxy, [0]8 and [90]8 glass/polyamide laminates presented a lower fatigue resistance, while [02/902]s laminates exhibited a superior fatigue resistance. In addition, stiffness degradation was investigated for the laminates and was compared with that of glass/epoxy with the same lamination. Glass/polyamide composites had lower stiffness reduction compared to glass/epoxy. During fatigue tests, an infrared (IR) camera was also used to monitor the temperature rise in [02/902]s and [04/904]s laminates resulting from mechanical cyclic loading, and to capture the temperature profile associated with the failure area in the specimens. The maximum temperature in [04/904]s laminates was comparable to that of [02/902]s laminates and the final temperature in some of the cross-ply specimens reached 50 °C, which was near the glass transition temperature of the polyamide matrix.

Introduction

Composite materials have gained much interest in different sections of industry due to a lot of advantages that they exhibit e.g. light weight, high stiffness and strength and damage tolerance. These materials are divided into two main groups namely thermoset and thermoplastic composites. In addition to recyclability, thermoplastic composites are tougher and more damage resistance than thermoset composites, so their application for structures under different static and cyclic fatigue loadings are preferred. In this regard, fatigue loading is more critical since it is expressed to be the reason of 80% of service failures [1]. There are some studies on fatigue behavior of thermoplastic composites but are limited to some high performance and engineering thermoplastic composites e.g. PEEK, PPS and PP-based composites. Some of the main research studies on the fatigue behaviour of these composites are as described here. Dickson et al. [2] studied the fatigue behavior of cross ply 0/90 and ±45 carbon/PEEK and carbon/epoxy. They found that 0/90 lay-up for both materials had comparable fatigue resistance while ±45 carbon/PEEK laminates had better fatigue resistance than carbon/epoxy laminates. Aymerich and Found [3] studied the fatigue behaviour of notched and unnotched quasi-isotropic carbon/PEEK and carbon/epoxy composites and evaluated fatigue damage mechanisms through X-radiography and C-scan.

1. Introduction

2. Description of the quarter-turn heavy-duty actuator

3. Fundamental of the adopted criteria for fatigue life assessment

4. Numerical analysis

5. Results and comparison

6. Conclusions and research developments

7. Acknowledgments

8. References

Fatigue design of structural components under multiaxial loading often relies on fatigue life calculations based on a post-processing of the full-field elastic stress/strain maps obtained from finite element (FE) analysis. In the present article, a post-processing tool is adopted to compute the fatigue life of a structural component, and multiaxial fatigue assessment is carried out by considering different criteria such as that of Smith-Watson-Topper and of Fatemi-Socie. The present paper focuses on a specific structural component related to a quarter-turn heavy-duty valve actuator, called scotch yoke, commonly used in many application sectors such as oil & gas, power and chemical industries. The fatigue assessment of the component is carried out by employing a full-model FE analysis, considering fillet-welded joints exposed to in-phase constant amplitude cyclic bending-torsion fatigue load with load ratio R=-1, with applied maximum load according to EN 15714-3, which is the standard in the valve actuator sector. The elastic stress/strain field extracted from the FE model is used to perform the fatigue assessment of the fillet-welded joints, where the potential fatigue crack initiation points (weld toe and weld root) are described by adopting an effective radius at the weld notches.

Introduction

Pneumatic or hydraulic scotch yoke valve actuators are commonly used in many industrial sectors and have many different applications. Among the most challenging scenarios for heavy-duty actuation are high-cycle applications, which impose high frequency of operation often at relatively high operating speed. In order to improve the performance of FLOWSERVE – Limitorque LPS/LHS heavy-duty actuator series, a fatigue assessment is carried out using numerical analysis supported by experimental evidence, to evaluate the high cycle application behavior of one of the main component of the actuator center body, the scotch yoke. The LPS/LHS actuator series, developed by FLOWSERVE – Limitorque in Italy is currently in accordance with the European norm [1], which imposes a minimum number of cycles for a specific loading condition. However, the number of cycles required by high-cycles applications can be very different, sometimes by orders of magnitude. For example, for an actuator like Limitorque model LPS-15, with a design output torque of 6000Nm, the minimum number of cycles required by the norm is with a stroking time of 30s, while in high-cycles applications, a minimum of cycles are frequently requested. The use of standard actuator series inevitably involves some uncertainties and oversizing, decreasing the competitiveness on the global market and increasing the cost of the machine.

1. Introduction

2. Bending stress and H/w parameter

3. Materials and experimental procedure

4. Results, analysis and discussions

5. Conclusions

Acknowledgements

References

The objective of this work is to conduct an experimental campaign to evaluate the effects of the catenary parameter (H/w) on the fatigue life of overhead conductors, being H the horizontal tensile load of the power line and w the weight per unit length of the conductor. A battery of twenty seven (27) fatigue tests was carried out on three types of conductors, an AAAC 900 MCM, an AAC Orchid and an ACSR Tern. For this study, all tests were conducted using the value of H/w = 2144 m. Fatigue damage, one of the major problems affecting power line conductors around the world, is caused by Aeolian vibration, characterised by high frequency and low amplitude movements. Based on field observations, the H/w parameter has recently been proposed as a fatigue design criterion for different families of cables. However, there is little experimental data available in the literature to assess the impacts of this hypothesis. Comparison between the generated S-N curves proved that an ACSR Tern conductor could sustain a significantly higher number of cycles before fatigue failure than the AAAC 900 MCM for this level of H/w. Meanwhile, the AAC Orchid presents a fatigue life situated between the AAAC 900 MCM and the ACSR Tern conductors. Failure analysis of the broken samples revealed not only that cracks initiated in the fretted areas of the aluminium wires but also that their morphology presented clear evidence of fatigue failure, such as observable beach marks and secondary cracks. Additionally, a failure map has been raised to determine the precise layer and the position from the clamp mouth where the wires broke. Furthermore, the provided information could be helpful for planning the maintenance of power lines.

Introduction

The overhead conductor is the only part carrying electricity, so its contribution has been estimated as carrying up to 40% of all power line transmission costs. However, this transmission line is susceptible to wind, snow, earthquakes and other weather conditions [1]. Aeolian vibration is the main cause of conductor fatigue failure, especially at devices which restrain its movements [2-4]. Frequently, the observed fatigue failure on overhead conductors occurs near or inside the suspension clamp, or devices attached to the conductor. That fatigue is characterized as the fretting fatigue of conductor strand during its aeolian vibration due to the fixation torque of the device on the conductor and also due to the microslip motion between wires and between the conductor and the device. A suspension clamp is one of the critical devices in term of fretting fatigue of conductor strand as there are many loads acting on the assembly conductor/clamp [5,6]. Among the loads, there are the tensile load of the conductor, the bending displacement due to the Aeolian vibration and the clamping torque. The control of the stretching tension of conductors at the design stage has been a concern for many years [1]. One of the reasons is that the tension of conductors during the most severe climate period does not exceed the allowable tension of the conductor. On the other hand, the stretching tension must be controlled in order to restrict the violation of the line clearance and also to protect the conductor against the harmful Aeolian vibration. It is well-known that a conductor becomes more vulnerable to Aeolian vibration when its tensile tension increases.

1- Introduction

2- Estimation method of C∗

3- Finite element analysis

4- Accuracy of the modified methods and discussion

5- Conclusions

References

Abstract

In some alloys such as 9%Cr heat resistant steels and magnesium alloys, the creep constitutive equation of the power-law requires a term of threshold stress due to the presence of second phase particles. It is necessary to establish an estimation method of C∗ for such alloys to predict the life of their components. In this paper, the General Electric/Electric Power Research Institute (GE/EPRI) method and the reference stress method were modified to estimate C∗ for power-law creep materials with threshold stress. The finite element method was used to verify the accuracy of the modified methods. The accuracy of the calculation equation of C∗ in the American Society for Testing Materials (ASTM) E 1457 was also assessed. The results indicated that the modified GE/EPRI method was sufficiently exact as an engineering method. h1 was slightly affected by the applied load and significantly affected by the threshold stress. The accuracy of the modified reference stress method increased with increased applied load and was within ±40%. The accuracy of the calculation equation of C∗ in ASTM E 1457 was not affected by the threshold stress and the equation could be directly used for power-law creep materials with threshold stress.

Introduction

C∗ is one of the parameters used for characterizing the creep crack growth and the stress field at the crack tip region. Accurate estimation of C⁄ plays an important role in the analysis of fracture mechanics and lifetime prediction for structures at elevated temperatures. Many studies have been conducted to research estimation methods of C⁄ . The General Electric/ Electric Power Research Institute (GE/EPRI) method is widely used to estimate C⁄ for homogeneous materials [1,2]. The reference stress method is another widely used method for estimating C⁄ [3,4]. Based on the reference stress method, Xuan [5] proposed a method to estimate C⁄ for mismatched weld creep cracks and Kim [6,7] proposed an enhanced reference stress method to estimate C⁄ . Other methods have also been proposed to estimate C⁄ for mismatched weld creep cracks [8,9] in addition to cracks in thin T-sections [10] and annular discs [11]. Further, the calculation equation of C⁄ in the American Society for Testing Materials (ASTM) E 1457 was modified for mismatched weld creep cracks by Xuan [12]. However, there has been no research on the estimation of C⁄ for materials with power-law creep constitutive equations that include a term of threshold stress. Since threshold stress exists in some alloys due to the presence of second-phase or nanometer-sized particles, such as dispersion hardened alloys [13–16] and nanocomposites [17,18], it is necessary to establish estimation methods of C⁄ with the effect of threshold stress included.