Notch Tip Strain Research Articles

Analysis of Ductile-to-Brittle Transition Characteristics of Reactor Pressure Vessel Steels

Ductile-to-brittle transition (DBT) characteristics of three steels for reactor pressure vessel (RPV) belt line application are analyzed from new parameters based on model functions describing the strength and toughness characteristics of the materials. In order to estimate nil-ductility temperature (NDT) from strength property, a strain rate–compensated temperature parameter based on the thermally activated deformation of materials is adopted. A measure of NDT is determined from tensile strength properties for the first time assuming an estimated notch tip strain rate at the lower shelf. It is estimated to be 110, 42, and 106 K for the Cr-Mo-V-Ni, 20MnMoNi55, and A533B steels, respectively. The measure of ductile-to-brittle transition temperature (DBTT) in steels using 41-J Charpy impact-absorbed energy on the basis of a logistic class of functions is compared and shown to be equivalent with those obtained from fitting the tanh model equation. A bi-logistic function based on the concept of separable parameters representing the fracture of ductile and brittle zones in steels within the DBTT regime was applied to model the Charpy impact energy behavior of the three steels. The bi-logistic function-fitting parameters yielded a new measure of brittleness as a DBT characteristic of steels that correlated well with other measures of transition temperature of the selected RPV steels. The parameters from the hyperbolic and logistic fitting were used to develop a model relationship suitable for the generation of a master curve based on Charpy energy in exponential form that unifies the transition temperature behavior of the selected western and eastern RPV materials. The model relationship is also found to closely predict ~5 K of the reference temperature To determined as per American Society for Testing and Materials standard E1921 of the selected RPV steels.

Hydrogen embrittlement of pearlitic steel in the presence of notches: A kinematic fracture criterion based on the notch tip strain rate

This paper offers a kinematic fracture criterion for hydrogen embrittlement (or hydrogen assisted fracture) of notched samples of high strength pearlitic steel tested at very different loading/straining rates under cathodic electrochemical conditions promoting hydrogen entry and diffusion into the specimens. The local strain rate at the notch tip (notch tip strain rate NTSR) is shown to be the relevant variable governing the hydrogen embrittlement process. To this end, a fracture criterion is kinematically formulated over the hydrogen affected zone: fracture will take place when the equivalent stress reaches a critical value over a critical zone, both being a function of the local strain rate at the notch tip (or notch tip strain rate NTSR). Experimental results show that under certain conditions the results are universal and independent of the specimen geometry, which supports the validity of the present approach and the relevance of the role of local strain rate in the close vicinity of the notch tip.

A comparison of methods for calculating notch tip strains and stresses under multiaxial loading

Selected methods for calculating notch tip strains and stresses in elastic–plastic isotropic bodies subjected to multiaxial monotonic loading were compared. The methods use sets of equations where hypothetical notch tip elastic strains and stresses obtained from FEM calculations serve as an input. The comparison was performed within two separate groups of methods: the first group consists of the methods intended for cases of multiaxial proportional loading and the second group deals with multiaxial non-proportional loading. Originally, the precision of the methods was validated by comparison with results obtained from elastic–plastic FEM analyses. Since computer performance at the time was lower than nowadays, verification of the proposed methods on FEM models with a finer mesh was needed. Such verification was carried out and is presented in this paper. The effect of various formulations of material stress–strain curve was also evaluated. KEYWORDS. Notch stresses; Multiaxial loading; FEM; Neuber’s rule; ESED rule.

Analysis of creep stresses and strains around sharp and blunt V-notches

Geometrical discontinues, such as notches, need careful consideration due to stress concentration appearing in their proximity. Notches become even more dangerous in the case of mechanical and structural components subjected to high temperature and cyclic loading resulting often in localized creep deformations. It appears, based on the current state of art, that needed are numerical or analytical tools enabling the analysis and simulation of creep deformations near notches.The knowledge of notch tip stresses and strains can be used as the input into stress-strain creep models used for strength and fracture evaluations of mechanical and structural components. The method discussed below is based on considerations of the strain energy density variations near notches. Several examples concerning V-notches have been analysed to validate the concept. Finally, the problem associated with the analysis of sharp notches and cracks is discussed in terms of the proposed methodology.

Crack propagation speed in ultra high performance concrete (UHPC)

This paper investigates crack speed in ultra-high performance concrete (UHPC) using pre-notched three-point bending specimens. The experimental parameters are fiber volume fraction and rate of loading. A hydraulic servo-controlled testing machine is used to apply lower notch tip strain rates, in the range of 0.025–1.01/s, while a newly developed impact testing system is used to achieve higher notch tip strain rates, ranging from 6.8 to 41.11/s. A high-speed camera is used to record images of the UHPC specimens during testing. Notch tip strain and crack speed are computed from the images, which show that crack speed increases asymptotically as the crack initiation strain rate increases. Crack speeds of up to 514m/s were achieved at the lower notch tip strain rates and up to 1454m/s for the higher notch tip strain rates. The achieved relationships are incorporated into a recently proposed crack-velocity dependent dynamic fracture model. The model is validated using published experimental data and used to show that, like conventional concrete, the strain rate sensitivity of UHPC is strongly associated with the characteristics of dynamic crack growth.

Mode III Loading of Composite Panels

Efficient design of modern aircraft requires an understanding of the mechanical behavior of carbon fiber panels under both in-plane and out-of-plane loading conditions. Currently, relatively little published literature exists for out-of-plane shear (mode III) loading. This paper presents both experimental and computational results for strain fields showing damage initiation, and propagation of notched carbon fiber panels under mode III loading. Experimentally, strain fields were measured using digital image correlation. Computationally, the commercial finite element package Abaqus, using typical composite analysis techniques, was used to calculate strain fields. Comparisons were made between measured and calculated values. Experimental results indicated that areas of both tensile and compressive strain concentrations existed at the notch tip. Damage initiation occurred in these areas, typically only in one or the other. Subsequent damage propagation occurred both in areas of elevated tensile strain and in areas of elevated compressive strain. Computational results showed differences of typically to as compared with experimental results for notch tip strain concentrations before damage and with larger differences after damage had occurred. Overall, these results provide information on how notched carbon fiber panels behave under mode III loading and the effectiveness of a commonly used computational approach in predicating this behavior.

Recent Trends in Elastic-Plastic Analysis Using Elastic Solutions

Methodologiesfor predicting elastic-plastic stresses and strains under various loadings are discussed and reviewed. An overview of various approaches for predicting notch tip elastic-plastic stresses and strains are presented. The need for computing elastic-plastic stress strain history and methods evolved during time from simplest models under uniaxial loading to models for addressing multiaxial proportional and non-proportional loadings are discussed and summarized. Analytical approximation methods which use elastic solutions to estimate elastic-plastic behaviour at geometric discontinuities are mainly focused. Methodologies for elastic-plastic stresses and strains under uniaxial loading with plane stress and plane cases are discussed and analyzed. Methodologies for non-proportional loading based on incremental plasticity theories and total deformation theory are thoroughly studied. The research efforts on this topic have been increased, emphasizing the development of more generalized approaches for simulating elastic plastic cyclic stress strain behaviour under complex loading conditions.

Crack-tip strain fields in collagen biomaterials for skin tissue engineering

Abstract The objective of this investigation was to determine the notch-tip strain fields in Type-I collagen biomaterials. Experiments were performed in-situ in a fixture mounted on the stage of an optical stereozoom microscope with edge-notched Type-I collagen tensile specimens. Image markers were added around the notch, and a tensile strain was applied. High-resolution images were collected at different levels of far-field strain. Image analysis was performed to measure the displacements of individual surface markers. The resultant displacement fields were analyzed to yield in-plane surface strain profiles along trajectories perpendicular to the crack plane. The results revealed significant local strain amplifications near the notch tip of nearly twenty times. These results are discussed in light of existing constitutive models for crack-tip strain fields.

OS01W0308 Evaluation of notch tip strains using whole field optical measurement techniques

Structural components subjected to notched geometry often show localized yielding upon heavily imposed external loading. Accurate inelastic notch tip strains, required for reliable fatigue design and to prevent catastrophic failure, are frequently calculated by Neuber and Glinka approximations. It is well known that they are extremely efficient, in terms of reduced computational demands, but give poor accuracy because the approaches rely on simple implicit deformation plasticity. In this study, whole field optical measurement techniques, such as reflective moire interferometry and electronic speckle pattern interferometry (ESPI), are applied and compared with the notch-tip strain predictions proposed by Neuber and Glinka. Included are also results obtained by FEM analysis.

On the Glinka and Neuber methods for calculating notch tip strains under cyclic load spectra

To maintain the continued airworthiness of civil and military aircraft it is essential that the fatigue behaviour of components subjected to complex multiaxial stress conditions be both understood and predicted. This topic is extremely complex and numerous criteria ranging from the purely empirical to the theoretical have been proposed. To this end it is necessary to know the localised stress–strain history. Whilst a detailed finite element analysis can be performed it is often very time consuming. Consequently, the present paper focuses on the development of a simple method which combines modern constitutive theory with either Neuber's, or Glinka's, approach to calculate the localised notch strains. Here particular attention is paid to the effects of cyclic loading, mean stress relaxation and its effect of fatigue damage.

Elastic-plastic stress-strain analysis of notches under non-proportional loading paths

An analytical method for calculating notch tip stresses and strains in elastic-plastic bodies subjected to non-proportional loading sequences is discussed in the paper. The method is based on the incremental formulation relating the hypothetical linear elastic and elastic-plastic strain energy densities at the notch tip, and the material stress-strain behavior simulated according to the Mroz-Garud cyclic plasticity model. Two formulations involving the strain energy density and the complimentary strain density are discussed in the paper, and they appear to give the lower and the upper bound estimations for the elastic-plastic notch tip strains. Each formulation consists of a set of incremental algebraic equations that can easily be solved for elastic-plastic stress and strain increments, knowing the increments of the hypothetical elastic notch tip stress history and the material stress-strain curve. The validation of the proposed model against finite element data obtained for non-proportional loading is also presented. The method is particularly suitable for fatigue life analysis of notched bodies subjected to multiaxial cyclic loading paths.

Higher order asymptotic solutions of V-notch tip fields for damaged nonlinear materials under antiplane shear loading

The higher order solutions of stress and deformation fields near the tip of a sharp V-notch in a power-law hardening material with continuous damage formation are analytically investigated under antiplane shear loading condition. The interaction between a macroscopic sharp notch and distributed microscopic damage is considered by describing the effect of damage in terms of a damage variable in the framework of damage mechanics. A deformation plasticity theory coupled with damage and a damage evolution law are formulated. A hodograph transformation is employed to determine the solution of damaged nonlinear notch problem in the stress plane. Then, inversion of the stress plane solution to the physical plane is performed. Consequently, higher order terms in the asymptotic solutions of the notch tip fields are obtained. Analytical expressions of the dominant and second order singularity exponents and associated angular distribution functions of notch tip stress and strain are presented. Effects of damage and strain hardening exponents and notch angle on the singular behavior of the notch tip quantities are discussed detailly. It is found that damage can lead to a weaker singularity of the dominant term of stress on one hand, but to stronger singularities of the second order term of stress and the dominant and second order terms of strain compared to that for undamaged case on the other. Also, both hardening exponent and notch angle have important effects on the notch tip quantities. Moreover, reduction of the notch tip solutions to a damaged nonlinear crack problem is carried out, and higher order solutions of the crack tip fields are obtained. Effects of damage and hardening exponents on the dominant and second order terms in the crack tip solutions are detailly discussed. Discussions on some other special cases are also presented, which shows that if damage exponent equals to zero, then the present solutions can be easily reduced to the solutions for undamaged cases.

Material factors influencing notch tip strain rate

AbstractWhen precracked or notched specimens are used in slow strain rate stress corrosion testing, it is the local strain rate at the crack or notch tip and not the global strain rate or externally applied testing displacement rate that governs the process. This paper presents computational results from an elastic-plastic finite element analysis of notched specimens, demonstrating that the relationship between local and global strain rates depends not only on the specimen geometry but also on the stress-strain curve of the material and on the load applied on the specimen (the latter two factors controlling the plastic strain distribution in the overall geometry, particularly in the vicinity of the notch tip), which implies that local strain rate changes with time, even for a constant global strain rate externally applied, as in the case of slow strain rate tests. It is shown that the evolution (or variation with time) of the notch tip strain rate depends on the spreading of the plastic zone and thus on t...

Material factors influencing notch tip strain rate

Material factors influencing notch tip strain rate

Crack propagation under mixed mode (I+III) loading : Yates, J.R. and Mohammed, R.A. Prof. 4th Int. Conf. on Biaxial/Multiaxial Fatigue II, St. Germain en Laye, France, 31 May–3 June 1994, pp. 99–106

The blunt notch fracture toughness of four types of carbon-manganese steel (ASTM A516 grade 70) has been determined by J-integral tests on Charpy-V type samples with different values of notch root radius, ρ. J-ρ plots, determined using specimens with a notch depth to width ratio, a/w, equal to 0.5, have shown the existence of a limiting ρ value (ρeff) below which applied J-intergral values at fracture initiation are constant. These ρeff values have been seen to depend only on second-phase particle distribution and not on their volume fraction or on the steel ferritic grain size. The procedure for deriving J-integral values at the onset of stable crack growth from J resistance curves in the case of notches has also been discussed. Experiments with Charpy specimens with a/w = 0.2 do not allow the derivation of meaningful J-ρ plots. In all cases, a ductile fracture criterion based on the constancy of the notch tip strain at rupture initiation has been proved when ρ >ρeff.

Elastic-plastic stress-strain calculation in notched bodies subjected to non-proportional loading

An analytical method for calculating notch tip stresses and strains in elastic-plastic isotropic bodies subjected to non-proportional loading sequences is presented. The key elements of the two proposed models are generalized relationships between elastic and elastic-plastic strain energy densities, and the material constitutive relations. These two models form the lower and the upper limits of the actual energy densities at the notch tip. Each method consists of a set of seven linear algebraic relations that can easily be solved for elastic-plastic strain and stress increments, knowing the hypothetical notch tip elastic stress history and the material stress-strain curve. Results of the validation show that the proposed methods compare well with finite element data and each solution set forms the limits of a band within which actual notch tip strains fall.

Calculation of elastic-plastic strains and stresses in notches under torsion load

An application of the equivalent strain energy density method for calculation of elastic-plastic notch-tip strains in circumferential notches under torsion is presented. The mathematical formulation of the method is presented together with its numerical interpretations. Finally, the calculated notch-tip strains are compared with the finite element data obtained for several materials and notches. Included are also results obtained from Neuber's rule. Good notch-tip strain predictions based on the equivalent strain energy density concept were achieved for sharp and blunt notches.

Calculation of elasto-plastic strains and stresses in notches under multiaxial loading

A method for calculating elasto-plastic notch tip strains and stresses in bodies subjected to multiaxial loading has been presented. The method has been formulated in terms of strain energy density relationships. Two approximate formulae are derived based on the analysis of strain energy density in the notch tip region. The two formulae represent the lower and upper limits of the band within which the actual elasto-plastic notch tip strains can be found. All necessary relationships are derived for a general multiaxial stress state. The calculated notch tip strain and stress components are compared with experimental and finite element data obtained for a variety of loading conditions and materials. This method may be particularly useful for stress/strain analysis of notched components subjected to lengthy multiaxial cyclic loading histories.

KIC Modelling for a critical strain criterion involving the stress triaxiality effect

An analytical model for predicting fracture toughness K IC is proposed based on a stress-modified critical strain criterion, that reflects the effect of stress triaxiality on ductile fracture. For K IC modelling, the notch-tip strain and stress state are given by introducing asingular field for the case of power-law-hardening materials. Notch fracture toughness is interpreted in terms of the notch-root radius (ϱ): K IC is predicted to increase with increasing ϱ, but has a minimum at a small ϱ. The microstructuralls characteristics distance and the reference critical strain can be estimated by fitting the K IC vs ϱ data on the model equation. Finally, previous notch fracture-toughness data are re-analyzed with the proposed model: the current analysis explains well the interaction effect between the notch-tip strain field and the local-fracture-controlling microstructure even in the small ϱ range.

Improved energy density method for inelastic notch tip strain calculation and its application for pressure vessel and piping design: Tashkinov, A.V. and Filatov, V.M. Int. J. Pressure Vessels and Piping (1993) 53, (2), 183–194

Improved energy density method for inelastic notch tip strain calculation and its application for pressure vessel and piping design: Tashkinov, A.V. and Filatov, V.M. Int. J. Pressure Vessels and Piping (1993) 53, (2), 183–194