Creep Crack Initiation Time Research Articles

Effect of constraint on creep fracture toughness of a Cr-Mo-V steel

The creep fracture toughness of materials is required for the assessment of defective components at high-temperatures. Existing evidence indicates that creep crack-tip constraint state has a great influence on the fracture behavior of materials. In this work, the effect of constraint on creep fracture toughness was explored by conducting a series of creep crack growth tests on specimens with various thicknesses and loading modes. Results showed that the curves of creep fracture toughness with creep crack initiation time on the logarithmic scale for different groups of specimens were almost parallel with one another. Through the characterization of crack-tip constraint level for different groups of specimens in terms of a load-independent creep fracture constraint parameter, R*, the creep fracture toughness was found to increase with the decrease in the crack-tip constraint level. Moreover, evident effect of specimen geometry on creep fracture toughness was observed. Of all types of specimens, the CCT2 and CT10-SG exhibited the highest and lowest values of Kcmat at the same ti, respectively. In addition, the Kcmat was found to increase following a specimen group order of CT10-SG, CT10, CT5, SENT5, CT2, SENT2 and CCT2 at a given ti. Finally, a constraint-dependent creep fracture toughness equation was established for the Cr-Mo-V steel, which is expected for practical applications to improve accuracy of life assessment methods. Follow-up work on life assessment methods incorporating the constraint parameter R* is still necessary.

Effect of holding time in brazing cooling process on creep life of the solid oxide fuel cell with bonded compliant seal

In present paper, effect of holding time at 600 °C during the brazing cooling process on creep life of solid oxide fuel cell (SOFC) with bonded compliant seal (BCS) is investigated by the finite element method. The research indicates that creep crack initiation time in BCS structure increases significantly with the holding time increasing. Compared with that the traditional cooling method during the brazing process, the creep crack initiation time can be prolonged more than twice by the holding time of 150 h with the operating temperature of 600 °C, it increases from 14,949 h to 31,911 h. When the operating temperature is 800 °C, the creep crack initiation time of SOFC can hardly be affected if the holding time exceeds 10 h. Based on the creep damage analysis and considering the cost of the SOFC manufacturing process, it is recommended that the holding time should not be exceeded 300 h if the operating temperature is below 750 °C. And when the operating temperature is 800 °C, the recommended holding time should not be longer than 10 h. The research of the present paper can provide theoretical guidance for the long life manufacturing and reliability operation of SOFC.

Characterization of creep constraint effects on creep crack growth behavior by Q-type parameters

The effect of creep constraint on creep crack growth behavior and the stress field around the creep crack-tip was studied under different specimen geometry conditions. The correlation between the constraint parameters Q and Qm with the stress triaxiality under creep conditions was investigated. The results showed that the Q and Qm depend linearly on the stress triaxiality. Moreover, based on the existing constraint parameters Q∗ and Qm, a new load-independent constraint parameter Qm∗ was proposed to quantify the creep constraint effect. The Qm∗ was superior to Q∗ in quantifying higher out-of-plane creep constraints induced by specimen width and thickness. Furthermore, the Q∗ and Qm∗ were employed to correlate with the normalized creep crack growth rate and initiation time. Finally, the constraint-dependent creep crack growth prediction model based on constraint parameters Q∗ and Qm∗ had been established.

Prediction of creep crack initiation time based on constraint parameters in specimens with different geometries

Based on two creep constraint parameters (R* and Ac), the constraint-dependent creep crack initiation (CCI) time equations of a Cr–Mo–V steel at 566 °C have been established over a wide range of C* region. The equations are independent on the choice of the reference specimen. Based on the two-parameter (C*-R* and C*-Ac) and the constraint-dependent CCI time equations, the CCI time for the specimens with different geometries and dimensions (with a wide range of constraint levels) has been predicted over a wide range of C* region. The predicted CCI time agrees well with experimental data available and CCI time of finite element simulations based on the creep ductility exhaustion model. The specimen geometry with high constraint strengthens the effect of out-of-plane constraint on the CCI time. The two constraint parameters R* and Ac can give similar CCI time prediction results. The two-parameter approaches with considering constraint effect may be applied in the CCI life assessment of high-temperature components (such as pressure pipes and vessels) under static loads in operating plants.

Analysis of 316H creep crack initiation data at 550 °C using a crack tip constraint parameter

In this paper, 316H creep crack growth data at 550 °C are analysed to investigate the effect of in-plane constraint on creep crack initiation times. A constraint parameter is proposed to quantify the difference between an actual opening stress and the Riedel-Rice opening stress field in plane strain, using experimentally measured C*. Test data analysis shows that creep crack initiation times can be well characterized by the C* integral with the proposed parameter. A modified form of a model due to Nikbin, Smith and Webster is suggested, and scatter in predictions is shown to be reduced from ~40 to ~5.

Effects of dual-cracks on the creep crack growth behaviour of HastelloyC276-BNi2 brazed joints

ABSTRACT In this paper, the effects of dual-cracks on the CCG behaviour of Hastelloy C276-BNi2 brazed joints were investigated. And the effects of inner crack length, inner crack distance and mismatched material coefficients on the creep crack initiation (CCI) time, CCG rate and creep life were also discussed. The results show that the creep crack can across over the inner crack and propagates continuously. The brazing defects can accelerate the CCG rate, thus leading to the decrease in the creep life and CCG length. With the increases in inner crack length and the decreases in inner crack distance, the CCI time, creep life and CCG length decrease. Longer inner crack distance and shorter defect length can suppress creep crack initiation and propagation. Bigger mismatch factor between base metal and filler metal may avoid the weakening effects of brazing defect on creep life.

Analysis of the constraint levels and the creep crack initiation times for pressurized pipes with long surface cracks

Abstract The constraint levels and the creep crack initiation (CCI) times for pressurized pipes with four types of long surface cracks and different geometrical sizes were investigated by using 3D finite element (FE) method. The C*–Q* two-parameter approach was also applied to estimate the CCI times for different conditions. For each type of long surface cracks, it could be found that the larger crack depth (a/t) was associated with the larger constraint and shorter the CCI time. Furthermore, for the same crack depth (a/t) and pressure, the order of constraint levels was axial internal crack > circumferential internal crack > axial external crack > circumferential external crack, while the CCI times were in contrary sequence. Generally, long external surface cracks were less dangerous than long internal surface cracks no matter they were axial or circumferential surface cracks. Additionally, the fitting formulae between CCI times and crack depth ratio a/t and pressure (or stress intensity factor) were developed and verified to be effective. The power law relation between the CCI times and constraint parameter Q* was also established and validated. Finally, the suitability of the transient prediction models in C*–Q* two-parameter approach was verified by comparing results of the two-parameter theoretical analysis and simulation. What's more, it was known that for long internal surface cracks (axial or circumferential), the K-RR solutions were more accurate than the HRR-RR solutions when pressure is below 10 MPa, while the HRR-RR solutions would be better for higher pressure. As to the long external surface cracks, the critical pressure between these two solutions was about 12 MPa.

Engineering application of enhanced C*-Q* two parameter approaches for predicting creep crack initiation times

Enhanced C*-Q* two parameter approaches were developed into engineering application where the creep crack initiation was defined by a critical distance of 0.2 or 0.5 mm. Enhanced C*-Q* approaches coupled the stress-regime creep strain rate and Fermi's function of creep ductility as well as constraint effect was used. Two methods were proposed to evaluate the creep crack initiation (CCI) times based on enhanced C*-Q* approaches. (1) Simple method I, i.e. directly applying engineering critical distance 4d into enhanced C*-Q* two parameter approaches to calculate the CCI times. (2) Four-stages method II, i.e. divide 0.2 mm into 4 stages, in each stage, critical distance d = 0.05 mm could be applied into enhanced C*-Q* approaches to obtain creep time, and then CCI times were total creep times in four stages. The estimation method of initial stress state and selection criterion of prediction model for plane stress and plane strain state was also proposed. By comparing CCI times between the predictions from method I, method II and R5 method, and finite element simulation and experimental data, it was indicated that method I (with average crack length a+1.5d) and method II could be accurate and conservative. Method I was more convenient than method II, while method II was more accurate. Hence, it was recommended to apply these methods according to actual condition or demand.

Prediction models of creep crack initiation for different specimen geometry

In this article, the prediction models of the creep crack initiation for the specimen geometry was quantified by six different types of cracked specimens [including C-ring in tension CS(T), compact tension C(T), single notch tension SEN(T), single notch bend SEN(B), middle tension M(T), and double edge notch bend tension DEN(T)]. Load-independence constraint parameter Q* was introduced to quantify the in-plane constraint. The specimen order of Q* and the creep damage accumulation rate of the different specimen geometries from high to low was C(T), CS(T), SEN(B), SEN(T), DEN(T), and M(T), which generally represented the distinctions of in-plane constraint level in these specimens. For a specific load level, C(T) and CS(T) specimens showed the highest crack damage accumulation rate or the shortest creep crack initiation time, whereas the lowest rates or the longest CCI time existed in M(T). Moreover, the relationship between the CCI times and specimen thickness and crack depths was obtained, and a series of empirical equations were fitted. Finally, the power law relation between the CCI times and constraint parameter Q* was extrapolated.

Enhanced models of creep crack initiation prediction coupled the stress-regime creep properties and constraint effect

In this work, enhanced theoretical analysis and finite-element (FE) simulation were carried out to evaluate the creep crack initiation times by coupling the stress-regime creep strain rate and creep ductility and constraint effect. Firstly, the enhanced theoretical approaches were derivated based on the ductility exhaustion model, 2RN (2 regimes Norton) creep model and the Fermi's fit (between the creep ductility and creep strain rate), and several analytical models of CCI prediction were proposed under the different stress field condition. Then the constraint effect was coupled into the enhanced C*-Q* approaches. The comparison of CCI time predictions between the FE solutions and the enhanced C*-Q* approaches verified the accuracy of the latter. Reasonable and conservative predictions of CCI time could be obtained from the theoretical solutions when the constraint effects were considered in the K-RR and HRR-RR controlled models when compared with FE solutions. The K-RR and solutions were accurate when initial stress intensity factor K was at low and high range, respectively. Finally, the accuracy of the enhanced approaches and the suitability of finite element simulation were validated by the experimental data of 316H steel.

Effects of Inner Defects on Creep Damage and Crack Initiation for a Brazed Joint

AbstractIn the brazing process, some brazing defects like semicircular or straight type are generated due to incomplete filling. In this paper, the creep damage and creep crack initiation (CCI) time of Hastelloy C276-BNi2 brazed joint with defects are investigated by a ductility exhaustion damage model. The effects of defect dimension and filler metal thickness are also discussed. The results show that the different defects have different creep damage distributions and CCI times. The maximum creep damage is located at the defect frontier due to the larger stress concentration. With the increase of semicircular defect radius and straight defect length, the CCI time decreases. The creep fracture is inclined to generate in semicircular defect for the smaller defect area ratio, while it is easy to generate in straight defect for the bigger defect area ratio. As the filler metal thickness increases, the CCI time increases. For the thicker filler metal, the creep crack is easy to initiate in semicircular defect.

A more appropriate FE model to predict the creep crack initiation and growth behavior of brazed joint

In this paper, a more appropriate finite element (FE) model was proposed to predict the creep crack initiation (CCI) and growth (CCG) behavior of HastelloyC276-BNi2 brazed joint at high temperature. The effects of single-material, bi-material and three-material method on CCI and CCG behavior have been discussed fully. The relationships between CCG rate and parameter C∗ for different simulation methods were obtained. The results show that the simulation method has a great influence on CCI and CCG behavior of brazed joint. The brazed residual stress (RS) can accelerate CCI and enhance CCG rate, leading to the reduction of creep life. The CCI time and creep life predicted by single-material method is smaller than those by bi-material and three-material method. The creep life and crack growth morphology predicted by single-material method have a good consistent with the experimental results. The single-material method can accurately predict the CCG behavior of brazed joints. Bigger uniaxial creep strain can prolong the CCI time and reduce the CCG rate. The creep life of brazed joint can be enhanced by increasing uniaxial creep strain.

Analytical and numerical investigations of creep crack initiation considering the load-independent constraint parameter $${{\varvec{Q}}}^{*}$$ Q ∗

The numerical simulation and a new theoretical approach were conducted to investigate the creep crack initiation (CCI) time and the effect of constraints induced by the specimen thickness of P92 steel. The theoretical enhanced $$C^{*}-Q^{*}$$ approach, which considered the load-independent constraint parameter $$Q^{*}$$ , was proposed to predict the CCI time around a sharp crack tip. Moreover, finite element analysis was used to verify the load independence of parameter $$Q^{*}$$ as the value of $${C}^{*}$$ varied. The larger thickness of the compact tension (CT) specimen contributed to a larger constraint parameter $$Q^{*}$$ , and the highly constrained CT specimens with larger thicknesses observably showed lower CCI times. The variation of hydrostatic stresses, triaxiality and multiaxial strain factor considering the constraint was discussed. The suitability of the analytical approach was verified to predict CCI, and the comparison between analytical and simulated results demonstrated that the $$C^{*}-Q^{*}$$ two-parameter prediction approach under stress intensity factor and Riedel–Rice (K-RR) control (initially by K, then by transient creep stress or Riedel–Rice conditions) and Hutchinson–Rice–Rosengren and Riedel–Rice (HRR-RR) control (initially by plastic HRR control, then by RR conditions) could conservatively and effectively characterize the CCI times. The K-RR solutions were more accurate when initial stress intensity factor $${K}<6\,\hbox {MPam}^{1/2}$$ , and the HRR-RR solutions were more appropriate when $${K}>6\,\hbox {MPam}^{1/2}$$ .

Creep crack initiation prediction considering constraint effect for pressurized pipelines with circumferential surface cracks

AbstractTheoretical 2‐parameter C*‐Q* approaches and numerical simulation were conducted to investigate the creep crack initiation (CCI) time and the effect of constraints induced by the geometrical sizes of pipelines with circumferential surface cracks. The theoretical enhancement model of the C*‐Q* approaches under the transient creep condition, which considered the load‐independent constraint parameter Q*, was proposed to predict the CCI time around the crack front. The results revealed that the distribution regulation of Q* along the crack front for circumferential internal surface cracks and external surface cracks was similar. The maximum constraint level occurred near the deepest crack front part for cracks with small a/c (a/c &lt; 0.4), while it occurred near the free surface for cracks with large a/c (a/c &gt; 0.4). The constraint values at the same position (2Φ/π) increased with the increasing of the crack depth when a/c kept constant. In addition, the circumferential internal surface cracks of pipelines were proved more dangerous than the external surface cracks with the same geometrical size. Furthermore, the CCI times were decided by the peak values of constraint, or the CCI firstly occurred at the position where the constraint level was maximum. Additionally, the variation of hydrostatic stresses, triaxiality, and multiaxial strain factor considering the constraint parameter Q* was discussed. The suitability of the analytical C*‐Q* approaches was verified to predict CCI. The comparison of CCI times between the analytical approach and the BS 7910 as well as the finite element results demonstrated that the solutions under stress intensity factor–Riedel‐Rice control (initially by stress intensity factor and then by transient creep stress or Riedel‐Rice conditions)—were more accurate when internal pressure P &lt; 18 MPa, but the solutions under Hutchinson‐Rice‐Rosengren–Riedel‐Rice control (initially by plastic Hutchinson‐Rice‐Rosengren control and then by Riedel‐Rice conditions) were more appropriate when P &gt; 18 MPa. Finally, the accuracy of C*‐Q* 2‐parameter approaches and the suitability of finite element simulation were validated.

Theoretical and numerical analysis of the creep crack initiation time considering the constraint effects for pressurized pipelines with axial surface cracks

A theoretical approach and numerical simulation were conducted to investigate the creep crack initiation (CCI) time and the effect of constraints induced by the geometrical sizes of pipelines with axial surface cracks. The theoretical enhancement model of the C*–Q* approach under the transient creep condition, which considers the load-independent constraint parameter Q*, was proposed to predict the CCI time around the crack front. The results revealed that the distribution regulation of Q* along the crack front for circumferential internal surface cracks and external surface cracks was similar. The maximum constraint level occurred near the deepest crack front part for cracks with small a/c (a/c < 0.4), while it occurred near the free surface for cracks with large a/c (a/c > 0.4). The constraint values at the same position (2Φ/π) increased with the increasing of the crack depth when a/c kept constant. In addition, the axial internal surface cracks of pipelines were proved more dangerous than the external surface cracks with the same geometrical size. Furthermore, the CCI times were decided by the peak values of constraint, or the CCI firstly occurred at the position where the constraint level was maximum. Additionally, the variation of hydrostatic stresses and triaxiality considering the constraint was discussed. The suitability of the analytical C*–Q* approach was verified to predict CCI. The comparison of CCI times between the analytical approach and the BS 7910 as well as the FE results demonstrated that the solutions under stress intensity factor—Riedel–Rice (K-RR) control (initially by K, then by transient creep stress or Riedel–Rice conditions) were more accurate when internal pressure P < 15 MPa, but the solutions under Hutchinson–Rice–Rosengren—Riedel–Rice (HRR-RR) control (initially by plastic HRR control, then by RR conditions) were more appropriate when P > 15 MPa.

Two-parameter approach of creep crack initiation times considering the constraint effect induced by specimen geometry

In this paper, a two-parameter approach and finite element method were conducted to investigate the constraint effect of six different types of cracked specimen geometries on the creep crack initiation (CCI) time. The theoretical enhanced model of the C∗–Q∗ approach, which considers the load-independent constraint parameter Q∗, was proposed to predict the CCI time around a sharp crack tip. The order of Q∗ values and the creep damage accumulation rate for the different specimen geometries was C(T) > CS(T), SEN(B) > SEN(T) > DEN(T) > M(T). Whereas the CCI times were ordered conversely. The influence of the constraint on hydrostatic stresses, triaxiality and multiaxial strain factor was discussed. The suitability of the two-parameter approach was verified due to the comparison of CCI times between theoretical and simulated results, which demonstrated that the C∗–Q∗ two-parameter prediction approach under stress intensity factor—Riedel–Rice (K-RR) control (initially by K, then by transient creep stress or Riedel–Rice conditions) and Hutchinson–Rice–Rosengren—Riedel–Rice (HRR-RR) control (initially by plastic HRR control, then by RR conditions) could conservatively and effectively predict the CCI times. The K-RR solutions were more accurate when initial stress intensity factor K < 6 MPa m1/2, while the HRR-RR solutions were more appropriate when K > 6 MPa m1/2.

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.

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.

Investigation on creep crack initiation prediction considering constraint effect using constraint parameter Q

The creep crack initiation (CCI) time considering the constraint effects induced by the crack depth of P92 steel was investigated via a two-parameter theoretical approach and computational study. Finite element method (FEM) analysis was conducted on different crack-depth compact tension specimens. It indicated that the high constraint with deep cracked depth did accelerate the damage accumulation process and reduce the creep crack initiation time. Further, the variation of the constraint parameter Q under the different crack depth was rather obtained. Moreover, the constraint parameter Q was taken into account in an analytical enhancement model, i.e. the C∗-Q approach was presented to predict the CCI time from a sharp crack tip. Finally, the comparison of the CCI between the analytical slutions and FEM results was employed to verify the accuracy of the analytical approach. It could be concluded that under K-RR–controlled field (initiation initially under the elastic stress intensity factor K-controlled field and then under the transient creep stress or Riedel-Rice (RR) controlled field condition) and HRR-RR–controlled field (initiation initially under the plastic Hutchinson-Rice-Rosengren (HRR) controlled field and then under the transient creep stress condition) could conservatively and effectively characterize the CCI time. The K-RR approach was more appropriate when initial stress intensity factor K was lower than 6 MPa m1/2, and the HRR-RR approach was more accurate when K was greater than 6 MPa m1/2.