A strain hardening failure assessment diagram derived from carbon-manganese steel compact tension specimens

A failure assessment diagram is derived from carbon-manganese steel compact tension specimens. The diagram has been determined from an elastic-plastic finite element analysis of a compact tension specimen geometry. The diagram has been validated by using experimental fracture toughness data obtained on the same steel and specimen geometry modelled in the finite element analysis. The plastic collapse load has been determined empirically for this geometry.It is shown that a non-work-hardening failure assessment diagram is not a good representation of the experimental data and that the computed failure assessment diagram is more appropriate for describing the behaviour of the carbon-manganese steel specimens.     

Use of the failure assessment diagram to deduce ductile fracture toughness of the RAFM steel EUROFER97

In the current work we use the failure assessment diagram (R6) to deduce ductile fracture toughness for the reduced activation ferritic/martensitic steel EUROFER97 by applying Small Specimen Testing Technology. Fracture parameters have been determined in quasi-static three-point-bend experiments. The fracture toughness results obtained with option 1 curve of R6 are sensibly independent of specimen geometry, constraint state and initial crack length and agree well with the results obtained by the analysis of crack resistance curves. Application of option 2 curve of R6 results into less conservative fracture toughness values.     

Prediction of slant ductile fracture using damage plasticity theory

Slant ductile rupture is one of the common failure modes in the pressure vessel and piping industry. Such failure in tubing and casing can be the result of excessive internal pressure and/or axial loading. The underlying physics of ductile rupture is essential in predicting the fracture modes and the crack propagation path for ductile metals. The slant fracture phenomenon is studied numerically by adopting a recently developed damage plasticity theory. The damage plasticity theory incorporates all three stress invariants in a nonlinear damaging process of the material. The numerical integration algorithm for the new model is presented for small strain case. Three applications of different loading conditions are shown to illustrate its effectiveness in predicting ductile fracture. Emphasis is given to the influencing factors to slant fracture and the shear nature of the crack pattern in these applications. These numerical solutions are in good agreement with the experimental observations.     

On the probabilistic failure assessment diagram

Reliability analysis of structures containing defects carried out directly by practising engineers is quite complex and costly. Therefore, a simple and convenient reliability analysis method should be investigated and established. In this paper, the principle and building procedure of a reliability analysis method are described and the feasibility of the method are also explicitly clarified. Based on the assumptions that: (1) the load is a deterministic variable; (2) the yield strength and fracture toughness satisfy normal distribution and their variational coefficients are constant; (3) the initial crack length remains unchangeable, a set of probabilistic failure assessment diagrams (PFAD) called elementary reliability assessment method are established under the simplified option 1 curve of the 3rd version of CEGB R6. The investigation shows that the distribution of random safety factor and failure probability of a structure only depend on the coordinates of the expectation of P(L_r,K_r) in the failure assessment diagram of the simplified option 1 curve and is not influenced by the other factors. The investigation further shows that the failure probability will decrease with the increase of the initial crack length if the expectation of P(L_r,K_r) keeps unchanged. A conservative result will be given when using the PFAD as an elementary reliability analysis method to assess the integrity of a structure and only a simple procedure is required like the deterministic assessment method given in CEGB R6. When the secondary stress exists, the conservativeness of the result assessed will increase with the increase of parameter ρ although the PFAD is only established based on considering primary stress.     

A new approach to ductile tearing assessment of pipelines under large-scale yielding

In this paper we focus on the issue of ductile tearing assessment for cases with global plasticity, relevant for example to strain-based design of pipelines. A proposal for a set of simplified strain-based driving force equations is used as a basis for calculation of ductile tearing. We compare the traditional approach using the tangency criterion to predict unstable tearing, with a new alternative approach for ductile tearing calculations. A criterion to determine the CTOD at maximum load carrying capacity in the crack ligament is proposed, and used as the failure criterion in the new approach. Compared to numerical reference simulations, the tangency criterion predicts conservative results with regard to the strain capacity. The new approach yields results in better agreement with the reference numerical simulations.     

Evaluation of fracture mechanics parameters for bimaterial compact tension specimens

Abstract

The elastic–plastic fracture mechanics parameter J and its analogous creep fracture parameter C* are widely used to measure the fracture resistance of a material. The non-linear component of the J and C* parameters can be evaluated experimentally using the η factor. For weldments, the η factor is dependent on the relative properties of the base (parent) and weld materials, particularly the mismatch in their yield strengths. In this work, the η factor has been evaluated using non-linear finite element analyses in a standard compact tension C(T) specimen for a power law material. A range of mismatches in base/weld material properties have been considered. A through thickness strip of weld material, of height 2h, has been modelled, which was positioned at the mid height of the specimen. The η factor has been evaluated for a range of crack lengths and power law hardening exponents under both plane stress and plane strain conditions and the results compared with literature where available. For a given crack length and weld width, the η solutions of the undermatched and overmatched conditions examined show a maximum variation of 12% from the mean value. A relationship has been proposed with respect to crack length for the C(T) specimen to describe the decrease in the η factor with an increase in mismatch ratio.     

Comparison of fracture strain based ductile failure simulation with experimental results

This paper provides experimental validation of the approach for simulating ductile failure using finite element methods, recently proposed by the authors. The proposed method is based on a phenomenological stress-modified fracture strain model. Incremental damage is defined by the ratio of the plastic strain increment to the fracture strain, and total damage is calculated using linear summation. When the accumulated damage becomes unity, all stress components at the finite element gauss point are reduced to a small value to simulate progressive failure. The proposed method is validated against four experimental data sets of cracked specimens made of three different materials. Despite the simplicity of the proposed method, the simulated results agree well with experimental data for all cases considered, providing sufficient confidence in the use of the proposed method to simulate ductile failure.     

An assessment of failure probability in elastic-plastic conditions where stable tearing has occurred

An analysis is presented for calculating the failure probability of a structure subject to general elastic-plastic loading and where the fracture mode is ductile. The main statistical variables considered are fracture toughness, flow stress and defect size.The analysis is based on a development of the R6 methodology of defect assessment. The concept of a maximum load locus is developed from the failure assessment line. The maximum load locus is used to predict those combinations of materials properties and defect size that might combine to predict structural failure after some stable crack growth. The method of determining the maximum load locus is described and some examples presented.The maximum load locus is used to estimate the failure probability on the first loading of a structure. It is also shown that the maximum load locus can be used to estimate the failure probability of a proof loaded structure where, in general, there may be a change in the dominant failure mode between proof and fault loadings. Detailed examples are presented to illustrate the analysis.     

Loading rate effect on ductile crack resistance of steels using precracked Charpy specimens

While loading rate effects were extensively investigated in the transition regime where fracture occurs in a brittle manner, they are comparatively much less studied in the ductile regime. The main objective of this paper is to provide experimental data on the effect of loading rate on the ductile fracture behavior and examine the relation that might exist between the various material properties. In particular, the crack resistance behavior of two ferritic steels, A533B plate and 20MnMoNi55 forging, at quasi-static and dynamic (impact) loading rates was examined.     

An investigation of the effect of hydrogen on ductile fracture using a unit cell model

The effect of hydrogen on the ductility of metals is studied by incorporating the hydrogen diffusion process and the hydrogen enhanced localized plasticity (HELP) into a finite element program. A series of unit cell analyses are conducted under various stress states and the loading speed resulting in a steady state hydrogen distribution is determined. The evolution of the local stress and deformation states results in hydrogen redistribution in the material, which in turn changes the material's flow property due to the HELP effect. It is found that localized plastic deformation plays a major role in increasing the hydrogen concentration due to the newly generated trapping sites. The HELP effect promotes material failure by accelerating void growth, which is affected by the macroscopic stress state subjected by the material unit characterized by the stress triaxiality and the Lode parameter. For a constant Lode parameter, the effect of HELP on void growth and failure strain reduction increases with the stress triaxiality. For a constant stress triaxiality, the effect of HELP is highest when the Lode parameter is near 0. As the Lode parameter increases towards 1 or decreases towards −1, the HELP effect gradually diminishes.     

Evaluation of ductile vessel rupture by R-curve analysis using CT specimens and wide plate tests

A large volume, thin-walled vessel was weakened by the introduction of a longitudinal slit sealed from the inside. With the help of compact-tension specimens and wide plates, attempts were made to analyse the failure by means of elastic-plastic fracture mechanics, taking into account the bulging of the vessel by the use of the so-called ‘Folias factor’. With J_R curves obtained from wide plate tensile tests, the crack driving force curves provide stresses at crack initiation and instability which are approximately 20–30% below the corresponding values of the internal pressure test. With regard to stable crack growth, very good agreement was achieved.     

A study on ductile fracture initiation in the PHT piping material of an Indian PHWR using local approach

The ductile fracture phenomenon is a local mechanism, which consists of nucleation, growth and coalescence of microscopic voids. These microscopic voids are generally formed around the second phase particles because of the debonding of these particles from the parent matrix or the cracking of these particles themselves. In the present work, the ductile fracture of primary heat transport (PHT) system piping material of an Indian pressurised heavy water reactor (PHWR) was analysed using different models of local approach. Such local approaches use micromechanical models to predict crack initiation and stable crack growth. Two different types of models are used. The first one is based on the critical cavity growth (Rice and Tracey's cavity growth model and Budiansky and coworker's model). The other model is based on the combined effect of damage and yielding (Tai and Yang's and modified Tai and Yang's model). An in-house Elasto-Plastic finite element code thesis was modified and used for the analysis of the notched tensile specimens. In addition, the notched round tensile specimens were used to determine the true stress–strain curve. The fracture strains of the different specimens were determined from the experiment with some modifications. By integrating the cavity growth equations of the respective models up to the fracture strain, the critical values of the parameters were determined. The effect of hydrostatic stress on the critical parameters was studied by varying the notch root radius of the specimens. It was observed that the critical value of Rice and Tracey's parameter is a weak function of stress triaxiality whereas critical parameters of other models showed more dependency on the level of triaxiality. Especially Budiansky and coworker's model showed maximum variation of the parameter with respect to the notch root radius.     

A procedure for the determination of the fracture resistance of ductile steels

This paper describes a procedure for determining the fracture resistance of ductile ferritic steels. The procedure incorporates both single and multiple specimen methods using conventional fracture toughness test specimens. Validity limits to the fracture resistance data are given together with a method of characterising the data in terms of parameters which can be used to assess the structural integrity of components.     

Effects of crack depth and specimen size on ductile crack growth of SENT and SENB specimens for fracture mechanics evaluation of pipeline steels

A strong geometry dependence of ductile crack growth resistance emerges under large scale yielding. The geometry dependence is associated with different levels of crack tip constraint conditions. However, in a recent attempt to identify appropriate fracture mechanics specimens for pipeline steels, an “independent” relationship between the crack growth resistance curves and crack depths for SENT specimens has been observed experimentally. In this paper, we use the complete Gurson model to study the effects of crack depth and specimen size on ductile crack growth behavior. Crack growth resistance curves for plane strain, mode I crack growth under large scale yielding conditions have been computed. SENB and SENT specimens with three different specimen sizes, each specimen size with three different crack depths, have been selected. It has been found that crack tip constraint (Q-parameter) has a weak dependence on the crack depth for specimens in the low constraint regime.     

Application of Edgeworth''s series to the assessment of the fracture failure probability of a spherical tank

This paper presents a method to assess the fracture failure probability of a spherical tank. The method derives the general formulae to calculate the first n moments of the crack on the fatigue growth occasion by use of power series. Then the paper derives the first n moments of the crack tip opening displacement using the Japanese code WES2805, and calculates the first n moments of δ_c − δ by the use of the following formulae:

Lastly, Edgeworth's series is employed to be composed of the first n moments of δ_c − δ to approach the probability distribution function of δ_c − δ, and at the same time easily obtain the fracture failure probability of a spherical tank. Examples given in the paper prove that the presented method is feasible and can save experimental time.     

The study on ductile fracture of the over-matched weldment with mechanical heterogeneity

The ductile fracture of structural steel including weldment can be described as a progressive process with void nucleation, growth and coalescence. The effects of mechanical heterogeneity of the weldment were investigated experimentally on the ductile fracture behaviors of the base metal and the weld metal using round-bar tensile notched bars. The results show that the mechanical heterogeneity of weldment has certain effects on fracture strain, stress triaxiality at fracture, critical void growth and the material constant C. The smaller the distance between the notch root and the fusion line, the larger the fracture stain, the smaller the stress triaxiality and the larger the critical void growth rate.     

Prediction of boiling heat transfer duty in a compact plate-fin heat exchanger using the improved local assumption

A previous study presented a design method for compact plate-fin heat exchangers having flow passages with frequent interruptions. The local assumption was applied whereby the local boiling heat transfer coefficient was assumed to be fixed by the local metal-to-liquid ΔT. The present study extends the local assumption to include the effect of velocity on the local heat transfer coefficient. Confirmation of the new method is provided by a comparison of prediction and data for Freon-113 in an actual heat exchanger.     

Prediction of cleavage fracture from non-sharp defects using the Weibull stress based toughness scaling model

The structural integrity assessment of engineering plant is based on the principles of fracture mechanics that assume defects to be sharp cracks. Whilst conservative, this assumption may be overly conservative in some situations, e.g. for defects that are non-sharp. This paper describes the prediction of cleavage fracture initiation from blunt notches of varying root radii using the Weibull stress based toughness scaling model. Failure predictions are compared with the results of experiments performed on single edge notch bend SE(B) specimens containing both cracks and notches of varying notch root radii. Cleavage initiation sites were located close to the peak tensile stress ahead of the notch, implying that a tensile stress criterion is the main controlling factor for cleavage fracture. The cleavage fracture predictions from the toughness scaling model correlate well with the experimental data; but care needs to be taken to ensure that calibration of the Weibull parameters references fracture toughness data from constraint levels that span that of the defect of interest. This ensures the model interpolates between the constraint states used for calibration, rather than extrapolating outside the range of applicability.