A new parameter for prediction of creep crack growth rate at high temperature

By analysis based on a series of experimental data obtained by continuous observations using high temperature microscope during the creep test without interruption in vacuum of 10^?5 mm Hg for the purpose of the crack length measurements, a new mathematical equation for prediction of high temperature creep crack growth rate has been proposed in terms of disposable parameters, that is $\text{α}\text{a}{}_{\mathrm{<mtext>eff</mtext>}}\text{σ}{}_{\mathrm{g}}\text{,σ}{}_{\mathrm{g}}$ and temperature for 304 stainless steel within the range of $\text{α}{}_{\mathrm{g}}$ and temperature concerned. It can be seen that it is the best one to fit the experimental data among any other formula proposed hitherto.The new parameter proposed herein

$\text{8.48 × 10}{}^3\text{t}\text{log}{}_{10}\text{α}\text{α}{}_{\mathrm{<mtext>eff</mtext>}}\text{α}{}_{\mathrm{<mtext>g</mtext>}}\text{4.66 × 10}{}^2\text{+ 5.46}\text{log}{}_{10}\text{α}{}_{\mathrm{<mtext>g</mtext>}}$

where

$\text{α = 1.98 +0.36}\text{a}\text{w}\text{? 2.12}\text{a}\text{w}{}^2\text{+ 3.42}\text{a}\text{w}{}^3\text{, a≦0.7w}$

may be used for characterizing the creep crack growth rate just similar as Larson-Miller parameter for the creep life.     

The stress dependence of the crack growth rate during creep

An equation is derived for the crack growth rate under creep conditions. In the model, the propagation of a grain boundary crack is controlled by the plastic growth of cavities located in the grain boundaries ahead of the crack. It is assumed that the cavities grow by power law creep in the elastic crack tip stress field. Hence, the stress dependence of the crack velocity is provided through the elastic stress intensity factor, i.e., dC/dt=BK _I ^p .The cavity spacing, , appears as an important factor in the coefficient,B ^–(p–2)/2. At large values of , corresponding to less severe creep damage in the grain boundaries, the above equation would predict very low values for the crack velocity. Under such conditions, we suggest that another mechanism, whose stress dependence is provided through the net section stress, becomes active, i.e., dC/dt=B _net ^p . Since increases with decreasing applied stress, one should observe the _net correlation at low stresses. The results of recent creep crack growth experiments which tend to support this hypothesis are presented.

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Résumé On dérive une équation décrivant la vitesse de propagation d'une fissure dans les conditions de fluage. Dans ce modèle, la propagation d'une fissure aux frontières de grains est contrôlée par la croissance dans le domaine plastique de cavités situées aux frontières de grains en avant de la fissure.On suppose que les cavités s'étendent dans le champ de contraintes élastiques situées à l'extrémité de la fissure en suivant une loi de fluage parabolique. Dès lors, la dépendance de la vitesse de la fissuration en fonction de la contrainte est fournie par un facteur d'intensité de contrainte élastique, c'est-à-dire dC/dt=BK _I ^p .L'espace entre les cavités, , apparaît être un facteur important dans les coefficientsB. Pour de grandes valeurs de , qui correspondent à un dommage moins sévère par fluage aux frontières des grains, l'équation ci-dessus permettrait de prédire des valeurs très faibles de la vitesse de fissuration.Sous ces conditions, il est suggèré qu'un autre mécanisme, dont la dépendance de la contrainte est fournie par la contrainte agissant sur la section droite, devient plus actif; on a alors dC/dt=B _nette ^p .Comme augmente lorsque la contrainte appliquée diminue, on devrait observer une corrélation de nette à basses contraintes.Les résultats d'essais de croissance de fissure sous des conditions de fluage effectués récemment tendent à supporter cette hypothèse et sont présentés.

     

Configurational force based analysis of creep crack growth

International Journal of Fracture - Based on the concept of configurational forces, the driving force of cracks in elastic–plastic, creeping materials is derived. In a numerical study, the...     

Some observations on creep crack growth

Equations for the steady state motion of a crack in a creeping structure are investigated. Although general solutions of these equations are not attempted, it is shown that under certain circumstances particular solutions described by the stress intensity factorK or the stationary creep parameterC* are valid. The crack velocities for which these particular solutions hold are determined. A simple formula for estimatingC* is given. Experimental evidence is examined for its relevance toK-controlled orC*-controlled crack growth.

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Résumé On étudie des équations décrivant le mouvement quasi statique d'une fissure dans une structure en cours de fluage. Même si l'on ne tente pas d'établir des solutions générales pour ces équations, on peut montrer que, sous certaines circonstances, des solutions particulières décrites par le facteur d'intensité de contrainteK ou par le paramètreC de fluage stationaire sont applicables. Les vitesses de fissuration, pour lesquelles ces solutions particulières conviennent, sont déterminées. On fournit une formule simple pour estimerC. Des observations expérimentales sont analysées en ce qui regarde leur relation avec une propagation de fissure sousK contrôlé on sousC contrôlé.

     

小试样高通量蠕变及蠕变裂纹扩展试验装置设计

对于某些取样受限的结构,如在役构件、薄壁件、焊接接头、功能性梯度结构,无法采用传统试样测试获得高温蠕变及裂纹扩展性能,小试样测试方法使得此类构件的高温力学性能的获取成为可能。但现有小试样蠕变试验装置用途单一且存在试样氧化的问题,无法满足试验要求。本文设计一种基于小试样的材料蠕变及蠕变裂纹扩展性能测试装置,装置配备专用夹具和真空系统,可满足不同种类小试样真空环境下的高温试验,避免试样氧化,并可同时完成6个同类或不同类型小试样的蠕变和蠕变裂纹扩展试验。装置采用马弗炉对试样加热,最高试验温度可达1 200℃。采用光栅位移传感器测量小试样变形量,直流电位法测量裂纹长度,提高了变形测量精度。试验结果表明,该装置可以精确测量小试样位移和裂纹长度,用以研究材料蠕变及裂纹扩展性能。     

A fracture mechanics concept for the accelerated characterization of creep crack growth in PE-HD pipe grades

For the lifetime prediction of pressurized polyethylene (PE) pipes based on methods of the linear elastic fracture mechanics the knowledge of the crack resistance and the kinetics of creep crack growth (CCG) is essential. In the present work a rather brittle nonpipe material was used to develop a methodology for an accelerated measurement of crack kinetics in fatigue tests on cracked round bar (CRB) specimens at ambient temperatures of 23 °C. A material and specimen specific compliance calibration curve was generated to detect the crack kinetics with only one single CRB test. Based on an already proposed concept the kinetics at different R-ratios (minimum/maximum load) was measured and extrapolated to the case of CCG. To demonstrate the transferability of this concept to pipe materials a PE 80 pipe grade was used. Although the necessary testing time increased considerably the concept still has the potential to reduce the overall testing time for new pipe materials to be certified significantly. With the presented procedure a characterization of CCG in modern PE pipe grades at room temperature and without the use of stress cracking liquids is possible within a few months.     

Effect of stress dependent creep ductility on creep crack growth behaviour of steels for wide range of C*

Abstract

In this work, the effect of stress dependent creep ductility on the creep crack growth (CCG) behaviour of steels has been investigated by finite element simulations based on ductility exhaustion damage model. The relationship between the transition region of creep ductility and the transition behaviour of CCG rate on da/dt-C* curves has been examined and the CCG life assessments of components and CCG resistance of materials for a wide range of C* were discussed. The results show that with increasing the transition region size of creep ductility, the transition C* region size on da/dt-C* curves increases. With moving transition region position of creep ductility to high stress region (increasing transition stress levels), the transition C* region on the da/dt-C* curves also moves to high C* region. Decreasing transition stress levels and transition region sizes of creep ductility and increasing the lower shelf and upper shelf creep ductility values can improve the CCG resistance of materials. If the extrapolation CCG rate data from the high C* region or from the transition C* region are used in life assessments of the components at low C* region, the non-conservative or excessive conservative results may be produced. Therefore, the CCG rate data should be obtained for a wide range of C* by long term laboratory tests or numerical predictions using the stress dependent creep ductility and model.     

Load history effects on creep crack growth

In this paper the effects of load history on the high-temperature creep crack growth process are studied through a combined experimental and computational approach. The general features of constitutive response during cyclic creep are reviewed. Next, fracture parameters for creep crack growth are reviewed, with special emphasis on integral parameters. Finally, examples comparing computational predictions of experiments which experience history dependent load histories are presented. This includes displacement time comparisons and fracture parameter comparisons.     

Analysis of crack growth rate based on rotation at the crack tip plastic zone

The crack growth rate of a line crack is obtained from a linear elastic analysis of work required in the formation of a crack tip plastic zone. Equations of crack growth rate are derived from rigid body rotation at the root of Dugdale's plastic zone. The proposed relations are used to study the fracture behaviour of materials in tension tests and the three point bending tests. This revised version was published online in August 2006 with corrections to the Cover Date.     

Effects of creep properties of materials on creep crack-tip constraint parameter R*

Extensive finite element analyses have been conducted to investigate the effect of creep properties of materials on the creep crack-tip constraint parameter R*. The results show that the parameter R* increases with increasing power law creep stress exponent n of materials, and it is sensitive to lower n values and lower in-plane and out-of-plane constraints. In the engineering estimations of the creep constraint parameter R*, only the creep exponent effect needs to be considered for cracked components with lower exponent n and lower constraint, and the Norton’s coefficient A of power law creep materials can be ignored due to its insensitivity to the R*. The R*-n relation formulae have been established for single-edge-notched tension specimen (it has similar constraint level to pressurised pipes) with different in-plane and out-of-plane constraints, and they may be used to estimate the creep crack-tip constraint levels for cracked pipes with lower exponent n and lower constraint.     

Effect of microstructure degradation on creep crack growth

Creep crack growth by grain boundary cavitation is analysed numerically for center cracked and edge cracked panels. Creep acceleration induced by microstructure degradation is incorporated in the material model that describes the nucleation and growth of cavities in the grain boundary, including the effect of diffusion, dislocation creep and grain boundary sliding. It is found that the creep acceleration significantly reduces the notch sensitivity of the material.

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Résumé On analyse par voie numérique la croissance d'une fissure de fluage par cavitations aux joints de grain dans le cas de plaques fissurées en leur centre ou sur leurs bords. Un modèle du matériau, qui incorpore l'accélération du fluage due à sa dégradation, décrit la naissance et la croissance des cavités aux joints de grains, en tenant compte de l'effet de la diffusion, du fluage associé aux dislocations et du glissement des joints de grains.On trouve que l'accélération du fluage réduit de manière significative la sensibilité à l'entaille du matériau.

     

Damage mechanics based predictions of creep crack growth in 316 stainless steel

This paper describes a novel modelling process for creep crack growth prediction of a 316 stainless steel using continuum damage mechanics, in conjunction with finite element (FE) analysis. A damage material behaviour model, proposed by Liu and Murakami [1], was used which is believed to have advantages in modelling components with cracks. The methods used to obtain the material properties in the multiaxial form of the creep damage and creep strain equations are described, based on uniaxial creep and creep crack growth test data obtained at 600 °C. Most of the material constants were obtained from uniaxial creep test data. However, a novel procedure was developed to determine the tri-axial stress state parameter in the damage model by use of creep crack growth data obtained from testing of compact tension (CT) specimens. The full set of material properties derived were then used to model the creep crack growth for a set of thumbnail crack specimen creep tests which were also tested at 600 °C. Excellent predictions have been achieved when comparing the predicted surface profiles to those obtained from experiments. The results obtained clearly show the validity and capability of the continuum damage modelling approach, which has been established, in modelling the creep crack growth for components with complex initial crack shapes.     

Effect of strain rate on stepwise fatigue and creep slow crack growth in high density polyethylene

The effects of frequency and R-ratio (the ratio of minimum to maximum stress in the fatigue loading cycle) on the kinetics of step-wise crack propagation in fatigue and creep of high density polyethylene (HDPE) was characterized. Stepwise crack growth was observed over the entire range of frequency and R-ratio examined. A model relating crack growth rate to stress intensity factor parameters and applied strain rate was proposed by considering the total crack growth rate to consist of contributions from creep and fatigue loading components. The creep contribution in a fatigue test was calculated from the sinusoidal loading curve and the known dependence of creep crack growth on stress intensity factor in polyethylene. At a very low frequency of 0.01 Hz, fatigue crack growth rate was found to be completely controlled by creep processes. Comparison of the frequency and R-ratio tests revealed that the fatigue loading component depended on strain rate. Therefore, crack growth rate could be modeled with a creep contribution that depended only on the stress intensity factor parameters and a fatigue contribution that depended on strain rate.     

Influence of the crack morphology on the fatigue crack growth rate: A continuously-kinked crack model based on fractals

Threshold condition and rate of fatigue crack growth appear to be significantly affected by the degree of deflection of cracks. In the present paper, the reduction of the fatigue crack growth rate for a so-called ‘periodically-kinked crack’ as compared to that for a straight counterpart is quantified via the Paris–Erdogan law modified according to some simple theoretical arguments. It is shown that such a reduction increases as the value of the kinking angle increases. Then, a so-called ‘continuously-kinked crack’ (the kink length tends to zero) is considered and modelled as a self-similar invasive fractal curve. The sequence of kinking angles in the crack is such that the fatigue crack path is ‘on average’ straight. Using the Richardson’s expression for self-similar fractals, the fractal dimension of the crack is expressed as a function of the kinking angle. It is shown that the fatigue crack growth rate in the Paris range depends not only on the above fractal dimension and in turn on the kinking angle, but also, in an explicit fashion, on the crack length. Some experimental results related to concrete and showing a crack size effect on the fatigue crack growth rate are analysed.     

Mismatch effect in creep properties on creep crack growth behavior in welded joints

The finite element method based on ductility exhaustion model was used to systematically investigate the mismatch effect in creep properties on creep crack growth (CCG) behavior in welded joints. The crack-tip damage, stress states, CCG paths, CCG rate and rupture life were calculated for different configurations of creep properties between weldment constituents under the same load level, and the creep life assessment and design for welded joints were discussed. The results show that when the zone containing the crack is softer than at least one of the other two surrounding materials or both, the creep crack propagates straight along the initial crack plane. Otherwise, it will form a second crack in the soft material near interface. These simulation results were confirmed by the experimental observations in the literature, and the mechanism was analyzed. The harder surrounding materials can lead to higher CCG rate and shorter rupture life due to the higher constraint given from them. The early initiation and propagation of the second cracks increase CCG rate and reduce rupture life, and the incubation time of the second cracks in soft materials near interfaces should be accurately determined in the creep life assessment and design for the welded joints. A proper mismatch design with harder material containing crack and softer surrounding material can improve CCG properties of welded joints (decreasing CCG rate and prolong rupture life).     

Creep crack growth rate predictions in 316H steel using stress dependent creep ductility

Abstract

Short and long term trends in creep crack growth (CCG) rate data over test times of 500–30?000 h are available for Austenitic Type 316H stainless steel at 550°C using compact tension, C(T), specimens. The relationship between CCG rate and its dependence on creep ductility, strain rate and plastic strain levels has been examined. Uniaxial creep data from a number of batches of 316H stainless steel, over the temperature range 550–750°C, have been collected and analysed. Power-law correlations have been determined between the creep ductility, creep rupture times and average creep strain rate data with stress σ normalised by flow stress σ_0·2 over the range 0·2<σ/σ_0·2<3 for uniaxial creep tests times between 100 and 100?000 h. Creep ductility exhibits upper shelf and lower shelf values which are joined by a stress dependent transition region. The creep strain rate and creep rupture exponents have been correlated with stress using a two-stage power-law fit over the stress range 0·2<σ/σ_0·2<3 for temperatures between 550 and 750°C, where it is known that power-law creep dominates. For temperature and stress ranges where no data are currently available, the data trend lines have been extrapolated to provide predictions over the full stress range. A stress dependent creep ductility and strain rate model has been implemented in a ductility exhaustion constraint based damage model using finite element (FE) analysis to predict CCG rates in 316H stainless steel at 550°C. The predicted CCG results are compared to analytical constant creep ductility CCG models (termed NSW models), assuming both plane stress and plane strain conditions, and validated against long and short term CCG test data at 550°C. Good agreement has been found between the FE predicted CCG trends and the available experimental data over a wide stress range although it has been shown that upper-bound NSW plane strain predictions for long term tests are overly conservative.     

Prediction of mode I crack growth resistance based on a comparative investigation of J-integral and energy dissipation rate concept

An energy dissipation rate concept is employed in conjunction with the J-integral to calculate crack growth resistance of elastic-plastic fracture. Different from Rice’s J-integral, the free energy density is employed in place of the stress working density to define an energy-momentum tensor, which yields that the slightly changed J-integral is path dependent regardless of incremental plasticity and deformational plasticity. The J-integral over the remote contour is split into the plastic influence term and the J _FPZ-integral over the fracture process zone which is an appropriate estimate of the separation work of fracture. Finite element simulations are carried out to predict the plane strain mode I crack growth behavior by an embedded fracture process zone. It can be concluded that J-integral characterization is in essence a stress intensity-based fracture resistance similar to the K criterion of linear elastic fracture, and energy dissipation rate fracture resistance can be taken as an extension of the Griffith criterion to the elastic-plastic fracture.