Reference Stress Method Research Articles

Identification of creep damage properties of coating via a compound miniaturized testing method and an inverse approach

A systematic analytical approach has been developed to comprehensively characterize the creep damage material properties of coatings on thin-layer substrates. This involves conducting creep tests using a compound, two-material, miniaturized thin plate specimen (MTPS) with an inverse approach. For demonstration, independent creep tests were performed on miniature specimens of the substrate (P91 steel) and the coating (CoNiCrAlY) at 650 °C, as well as on compound substrate-coating specimens. The reference stress method, coupled with finite element analysis, was utilized to obtain conversion parameters for strain data from the miniature specimen tests. Analytical solutions for the Kachanov creep damage model specific to the two-material substrate-coating system were adopted for inverse optimization. The MTPS testing method and the associated inverse approach have proven effective in accurately determining the complete three-stage creep constants within the coating-substrate system. Results obtained for the P91–CoNiCrAlY coated system have shown a clear demonstration of the accuracy and capability of the method in identifying the full sets of uniaxial creep damage properties, i.e. A, n, m, B, χ, and φ, provided the feasible experimental data are available.

Interpretation of non-conventional miniaturized creep test: derivation of equivalent gauge length

The objective of this paper is to clarify the nature of the equivalent gauge length of miniaturized creep test methods. A mechanics-based approach was employed to allow conventional uniaxial creep data to be obtained from non-conventional miniaturized creep tests, under steady-state creep. The data interpretation is based on the reference stress method. On this basis, the theoretical derivation of the equivalent gauge lengths for a range of miniature specimen types is presented, including sub-size uniaxial, small punch, impression, small rings, miniature 2 bars, and miniature bending beams and plate. Then the effect of geometry change due to the creep test on the conversion parameters is evaluated. Finally, several theoretical and practical aspects, related to specimen deformation modes, the basis of the correlation methods, the sensitivity of “strain measurements”, the effective volumes, the choice of test methods, etc, are addressed.

Creep lifetime of Al 6061-T6 pressurized rotating friction stir welded tube subjected to internal pressure and rotational velocity: Welding and creep lifetime optimization

Aluminum 6061-T6 alloys have numerous applications in the industry due to their unique properties such as higher corrosion resistance and strength-to-weight ratio. Friction stir welding is also a technique that can be used in aluminum joints because of its numerous advantages. In this paper, optimum friction stir welding parameters that lead to a higher failure load are obtained using tensile test data and analysis of variance technique. According to the analysis of variance results, it is found that the tool rotational speed has a major effect among the welding parameters on the failure load. Then, creep tests are carried out on non-welded and welded specimens to predict their creep behavior. The Norton power law equation is used as a creep constitutive equation to model the creep behavior of the specimens. The model is used to predict the creep lifetime of the welded and non-welded rotating pressurized vessels. The results show that an optimally welded vessel can only sustain up to 0.75 of pressure for the non-welded vessel with the same rotating speed. Since this comparison is not straightforward because of the number of affecting parameters. Hence, the reference stress method is used to produce a set of diagrams that provide design conditions and optimum creep lifetime for the friction stir welded Al 6061-T6 rotating pressurized vessels.

J Predictions for Defective Pipe Elbows Via the Reference Stress Method

Abstract In R6, the J-based failure assessment diagram (FAD) method is used in the fracture assessment and is underpinned by the reference stress J scheme. Therefore, an assessment using the R6 FAD method is equivalent to a J prediction using the reference stress method. In this paper, the effect of global and local limit load solutions for defective elbows on the reference stress and hence the J predictions is investigated using published three-dimensional elastic-plastic finite element (FE) J results, in order to create guidance for users to follow when performing structural integrity assessments of defective elbows using the R6 procedure. The results show that using the global limit load solutions recommended in this paper can lead to good and reasonably conservative J predictions. However, the availability of global limit load solutions is very limited. The results also show that using the local limit load evaluated from the local limit load model recommended in this paper can lead to conservative J predictions for most of the cases considered.

Evaluation of J-integral based on reference stress method

Evaluation of J-integral based on reference stress method

Obtaining optimum creep lifetime of Al 7075-T6 rotating pressurized vessel based on the experimental data, using reference stress method (RSM)

Most of the mechanical components are exposed to environmental attacks and different loading conditions, e.g., internal pressure, high-temperature gradient, and angular velocity. Therefore, investigating their mechanical behavior under operating conditions is necessary to gain higher efficiency and less mechanical failure. Due to the vast industrial applications of Aluminum (Al) alloys, in this paper, the tensile and creep behavior of Al 7075-T6 were studied at elevated temperatures. The Norton-Power Law (NPL) equation was considered as a creep constitutive equation to estimate the creep behavior of Al 7075-T6 alloy. To this aim, experimental uniaxial creep tests were carried out to derive creep constitutive parameters. These parameters were used to predict the creep behavior of different structures, such as Al vessels. The reference stress method (RSM) and developed constitutive model were utilized to plot graphs that provide design conditions and optimum creep lifetime for Al vessel subjected to combined rotation and internal pressure. These graphs can be employed in industrial applications to facilitate the design process of Al vessels.

A new approach to evaluate material creep properties by C-shape ring specimen with fixed constraints

Small specimen test technique is widely used to evaluate material creep properties for those components operated at the elevated temperatures. However, the existing small specimen test techniques cannot be well applied for small miniature tubular components well, such as steam pipe and gas turbine recuperator in aviation, due to the equivalent gauge length, specimen volume, stress analysis method and conversion relationship. In this paper, combing the advantages of three-point bending specimen with fixed constraints and small ring creep specimen, a new C-shape ring specimen with fixed constraints (CRSFC) was proposed. Based on beam bending model, the conversion relationship between CRSFC and uniaxial creep test data was established by using complementary strain energy and reference stress method. Using finite element method, conversion coefficients and stress evolution process were obtained. Then the feasibility and accuracy of the above conversion relationship were verified by carrying out four sets of CRSFC creep tests of 1.25Cr0.5MoSi at 550 °C. It can be seen that creep parameters obtained by CRSFC agree well with those from uniaxial creep test with the maximum error of 22.6%. Finally, the effects of the straight edge length, indenter radius, eccentric load and indenter-specimen surface friction coefficient on the load-point steady-state displacement rate were investigated by finite element method. The results show that the effect of the straight edge length is negligible. In order to minimize the effects of other parameters, the indenter radius 0.6 mm ≤ r ≤ 1.2 mm, eccentric displacements e ≤ 0.2 mm and friction coefficient f ≤ 0.8 are recommended in CRSFC creep test.

Estimation of C∗-Integral for Central Cracked Plate Under Biaxial Loading

The reference stress method (RSM) is a classical method to estimate [Formula: see text]-integral of creep crack. An extended reference stress method (ERSM) is given for the central cracked plate (CCP) under biaxial loading in this paper. The applicability and verification for the proposed ERSM is given. The study finds that the solutions with the proposed ERSM agree better than those of RSM under biaxial loading condition. A theoretical form to predict the relationship of [Formula: see text]-integral between biaxial loading and uniaxial loading is discussed. Relation between [Formula: see text]-integral and creep time under biaxial loading is validated and discussed.

Research on the Conversion Relationship for Three-Point Bending Specimen With Fixed Constraints in the Large Deformation Stage

Abstract In this study, based on the rod tensile model, a conversion relationship between three-point bending specimen with fixed constraints (TPBSF) and uniaxial creep data in the large deformation stage is defined by the reference stress method. Using finite element method, conversion coefficients are determined. Then it is verified by the creep test data of A7N01 at 350 °C (Zhuang, F. K., 2014, “Research on Creep Test Method of Small Specimen Based on Beam Bending Theory,” Ph.D. thesis, East China University of Science and Technology, Shanghai, China). The results show that creep stress exponent n is the same, but creep constant B obtained by rod tensile model is much closer to uniaxial creep than beam bending model. Finally, effects of geometric parameters and friction on conversion coefficients are investigated. On this basis, the specimen cross section aspect ratio greater than 1 and the indenter radius larger than 1 mm are recommended to minimize the influence of TPBSF geometric parameters on conversion coefficients. The influence of friction on conversion coefficients can be negligible.

Limit load solutions for elbows with circumferential through-wall crack under the pressure-induced bending restraint effect

A typical pipe finite element model is made by assuming there is internal pressure with a single crack located in the middle of the pipe where both ends are constraint-free. In reality, however, both ends are constrained by their connections to components such as the pressure vessel or pump. Furthermore, due to the complexity of the pipe system, it also experiences a self-constraint effect. This is called the pressure-induced bending restraint effect, and is known to affect the fracture mechanics parameters at the crack tip. Some studies exist on the pressure-induced bending restraint effect of straight pipes, but none have focused on elbow pipe and junction between straight pipe and elbow.This study suggests limit load solutions for elbow and their jointing regions with circumferential through-wall cracks under the pressure-induced bending restraint effect. The relevant equations can be used to estimate the maximum withstand load evaluation of a highly ductile pipe, and can also be used to estimate the elasto-plastic fracture mechanics parameters using the reference stress method.

Optimizing creep lifetime of friction stir welded PMMA pipes subjected to combined loadings using rheological model

Abstract The most important feature of the polymeric pipes is that they creep even at room temperature. Therefore, investigating the creep behavior of the polymers and their welded joints is a major concern in the mechanical engineering. The aim of this research is to estimate the creep lifetime of the friction stir welded Polymethyl Methacrylate (PMMA) pipes which operate under combined loading. To develop the creep constitutive equations for both weld zone and parent material, creep test samples have been cut from the weld zone and parent material of a PMMA sheet with friction stir butt welded joint. Constant load tests have been carried out at different initial stress and temperature levels. Based on the results of the tests, parameters of the modified Burgers model form of the constitutive equation have been derived. To validate the model, it is introduced to finite element software “ABAQUS” and the simulated creep behavior is compared with the experimental data. Furthermore, the developed constitutive model and the reference stress method (RSM) are used to produce a set of graphs which provide optimum creep lifetime and design conditions for the friction stir welded PMMA pipes that are subjected to combined internal pressure and rotation. The results show that despite using optimum conditions, creep life of the welded pipes is significantly lower than the non-welded pipe.

Creep constitutive equations for as-received 9Cr1Mo steel

9Cr1Mo has a wide application in petrochemical and power generation plants, prediction of its creep behavior is a major concern in these industries. In this paper, the creep behavior and creep lifetime of test samples machined from 15 years of service exposed boiler tubes in an oil refinery plant, are studied using uni-axial creep tests. Tests are carried out according to ASTM E139 at different stress and temperature levels (from 80 MPa to 190 MPa and at 550 °C, 600 °C and 650 °C). Based on the experimental data, the creep constitutive coefficients for three types of creep laws: Norton, Plrandtl and Garofalo are obtained together with Monkman-Grant and Larson Miller parameters. It has been shown that the constitutive equations in the form of Garofalo law predict the creep behavior of the material more accurately. The results show that the creep life relationships obtained based on both Garofalo and Norton power law give acceptable estimation. Also, the results are implemented in reference stress method to produce a set of loci for the optimal geometry of the tubes under combined loadings with maximum creep lifetime.

Reference Stress Approach for Fracture Assessment of Extrados Circumferential Through-Wall Crack at the Interface between Elbow and Pipe Subjected to Internal Pressure

The fracture assessment of a cracked component can provide a technical support for an effective maintenance and a prevention of catastrophic accident. The present study applies the reference stress method to extend the J-integral solution from the finite element analysis for the Ramberg-Osgood stress-strain relationship to other types of stress-strain relationship. The problem in this study is an extrados circumferential through-wall crack at the interface between elbow and pipe subjected to internal pressure. The finite element results from the literature were analyzed to determine the optimized reference pressure. The reference-stress-based failure assessment curve which incorporated with the obtained reference pressure can be used to estimate the finite-element-based failure assessment curve with a sufficient accuracy in fracture assessment. The failure load predicted from the reference-stress-based failure assessment curve deviated from that predicted from the finite-element-based failure assessment curve within the range of -7% to 11%.

EngineeringC*‐integral and COD estimates for nonidealized circumferential through‐wall cracked pipes at elevated temperature

AbstractIn this study, creep fracture mechanics parameters,C*‐integral and crack opening displacement (COD) rate, are estimated for a nonidealized circumferential through‐wall crack (TWC) in pipes. The GE/EPRI and enhanced reference stress (ERS) methods are employed. As for creep condition, the Norton and RCC‐MRx creep models are considered for secondary and primary‐secondary creep strain, respectively. The bending moment, axial tension, and internal pressure are applied to a pipe with a nonidealized circumferential TWC, as individual loads. Three‐dimensional elastic‐creep finite element (FE) analyses are performed, and the predictions from the GE/EPRI and ERS methods are compared with FE results. For the Norton creep model, both methods show good agreement with the FE results. For the RCC‐MRx creep model, only the ERS method can be used, and it provides accurate predictions comparing with FE results. Based on the comparison results, the use of the present engineeringC*‐integral and COD estimation methods for nonidealized circumferential TWC is validated.

Reference stress solutions for plates with embedded off-set elliptical cracks under combined biaxial forces and cross-thickness bending

The reference stress solutions for plates with embedded off-set elliptical cracks under combined biaxial forces and cross-thickness bending are derived based on the Mises yield criterion and net-section collapse principle. The newly developed reference stress solutions are compared with the reference stresses of plates with embedded rectangular cracks evaluated using the available limit load solutions. The developed reference stress solutions have been used to predict J via the reference stress J scheme. Elastic-plastic 3-D finite element (FE) analyses are used to calculate J values along the crack front and the results are compared with the reference stress predictions. The results show that the estimated J values based on the reference stress method with the reference stress solutions developed in this paper are very close to the FE J values, but the predictions may be non-conservative. However, the non-conservatism could be removed by simply applying a constant factor less than 1 to the reference stress solutions when they are used in the reference stress J scheme.

Analytical approaches of creep crack initiation prediction coupled with the residual stress and constraint effect

Abstract In this work, the coupled effects of residual stress and constraint on creep damage and creep crack initiation time (CCI) were analyzed by the analytical approaches based on the ductility exhaustion model. The elastic follow-up factor, Z, as well as the reference stress method and constraint parameter Q* , were considered as part of the analytical method. The variation of hydrostatic stresses, triaxiality and multiaxial strain factor considering the constraint was discussed. The suitability of the analytical method to the conditions that coupled secondary stress and the constraint effects was then investigated. Reasonable and conservative predictions of CCI time could be obtained from the theoretical solutions when the coupled effects were taken into account within the Hutchinson-Rice-Rosengren--Riedel-Rice (HRR-RR) (initiation initially under the elastic-plastic Hutchinson-Rice-Rosengren (HRR) field and then under transient creep stress conditions, the Riedel-Rice (RR) controlled stress field) and stress intensity factor—Riedel–Rice (K-RR) control (initially by K, then by transient creep stress or Riedel–Rice conditions) controlled model when compared with finite element (FE) solutions. The K-RR solutions were more accurate when primary initial stress intensity factor K P I 1/2 , and the HRR-RR solutions were more appropriate when K P I >6 MPam 1/2 .

Theoretical and numerical analysis of creep crack initiation combined with primary and secondary stresses

In this work, the creep crack initiation time (CCI) considering the residual stress effects were investigated by numerical simulation and theoretical approaches based on the ductility exhaustion model. The redistribution of stress under the combined loading condition (i.e. the tensile residual stress generated by the pre-compressed loads and primary loads) was taken into account. The elastic follow-up factor, Z, as well as the reference stress method, was considered as part of the theoretical method. The suitability of the theoretical method to the conditions that included combined primary and secondary stresses was then investigated. Reasonable and conservative predictions of CCI time could be obtained from the theoretical solutions when the elastic follow-up factor, Z, was taken into account within the K-Riedel-Rice (K-RR) controlled model (initiation initially under the elastic K field and then under transient creep stress conditions, the Riedel-Rice (RR)) and the Hutchinson-Rice-Rosengren-Riedel-Rice (HRR-RR) controlled model (initiation initially under the elastic-plastic Hutchinson-Rice-Rosengren (HRR) field and then under RR controlled stress field) compared with finite element (FE) solutions. K-RR was more suitable when the primary stress intensity factor KIP was below 15 MPa m1/2, and HRR-RR was more accurate when KIP was beyond 15 MPa m1/2. However, RRss (initiation under the steady state creep) values were much higher than the FE solutions, but K (initiation under the elastic stress intensity factor K-controlled stress field) controlled values seriously underestimated the initiation times. HRR (initiation under the elastic-plastic HRR-controlled stress field) values underestimated the initiation time when load level KIP was less than 27 MPa m1/2, but slightly overestimated when KIP was larger than 27 MPa m1/2. The HRR-RR and HRR solutions were much close and may be a little unconservative at the high load levels (KIP > 27 MPa m1/2). The CCI time including the elastic follow-up factor Z was much more accurate than when ignoring the residual stress.

Estimation of C∗ including the effect of threshold stress

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.

Prediction of creep crack initiation behavior considering constraint effects for cracked pipes

The creep crack initiation (CCI) location and time of axial surface cracks with different sizes in cracked pipes have been comparatively predicted by finite element calculations based on creep ductility exhaustion model and creep fracture mechanics considering constraint effects by using two new creep constraint parameters (R∗ and Ac). The effects of calculation methods of the parameters C∗, R∗ and Ac along the crack fronts on the prediction accuracy of CCI time have been analyzed. It has been found that with decreasing crack length, the CCI location changes from the deepest part to near surface part along the crack front, and the composite parameters composed of C∗ and constraint parameters can predict the CCI location. The CCI time of pipe cracks increases with decreasing crack depth and length due to the decrease of crack-tip constraint level. The excessive conservatism in conventional CCI life assessments using single parameter C∗ can be significantly reduced by using the two-parameter concept (C∗-R∗ and C∗-Ac) considering constraint effects. When the average values of C∗, R∗ and Ac along the crack fronts (instead of the values at the deepest locations of crack fronts) are calculated and used in CCI life predictions of cracked pipes, the prediction accuracy with respect to the finite element calculations based on creep ductility exhaustion model can be significantly improved. The C∗ values calculated by reference stress method can lead to extra conservatism in CCI life predictions.

Using developed creep constitutive model for optimum design of HDPE pipes

Unlike metal pipes, high density polyethylene (HDPE) pipes are not susceptible to erosion and corrosion. However, the most important mechanical feature of the HDPE pipes is that this material creeps even at room temperature. Therefore, it is essential to study the creep behavior of this material in order to develop a model. In this paper, creep behavior of HDPE at different temperature and stress levels has been experimentally studied to obtain the creep constitutive parameters of the material. These parameters are used to predict the creep behavior of different structures such as HDPE pipes. For this purpose, a number of specimens have been machined from industrial manufactured pipe walls. Uniaxial creep tests have been carried out and creep strain curves with time for each test were recorded. Then, a constitutive model is proposed for HDPE based on the experimental data and optimization methods. The results of this model have been compared with the test data and good agreement is observed. The developed constitutive model and reference stress method (RSM) were used to produce graphs which provide optimum creep lifetime and design conditions for HDPE pipes that are subjected to combined internal pressure and rotation. These graphs can facilitate the design process of HDPE pipes.