Fracture toughness diagrams of a notched body

To describe fracture toughness diagrams of notched bodies, a model of the cohesion zone near the notch root and an averaging criterion of stresses in this zone were employed. The geometric stress concentration factor and biaxiality coefficient affect greatly the shape of fracture toughness diagram. The notch root critical stress intensity factor is a decreasing function of geometric stress concentration factor. __________ Translated from Problemy Prochnosti, No. 5, pp. 142–148, September–October, 2006. Report on International Conference “Dynamics, Strength, and Life of Machines and Structures” (1–4 November 2006, Kiev, Ukraine).     

Cleavag Fracture Criterion of Low Alloy Steal and Weld Metal in Notched Specimens

The cleavage fracture criterion of low alloy steel and weld metal in notched specimens is investigated in detail based on a great number of experimental data. It has been found that the most cleavage fractures initiate at a distance shorter (left side) than that of the peak stress location below a notch root, and the cleavage fracture in notched specimens must satisfy a dual criterion, i.e., a critical plastic strain (ε_p ≥ ε_pc) for initiating a crack nucleus, and a critical tensile stress (σ_yy ≥ σ_f) for its propagation. According to the dual criterion model, the great number of experimental data of 4PB (four-point bending) tests for the low alloy steel and weld metal and their statistical distribution are explained. The effects of temperature , the local fracture stress σ_f and the critical plastic strain ε_pc on the locations of cleavage initiation sites and the controlling steps of cleavage fracture process are discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Failure assessment on central-sharp notched carbon/epoxy laminates

Fracture models to predict the strength of laminated composites having sharp notches demand the un-notched strength and the critical damage size ahead of the notch. The critical damage size, in general, depends on the material, geometry of the specimen and size of the sharp notch. The extraordinary success of a fracture model lies in its ability to combine a theoretical framework with experimentally measured quantities. Modifications are made in one of the stress-fracture criteria known as the point stress criterion for accurate prediction of notched tensile strength of composite laminates containing sharp notches. To examine the adequacy of these modifications, fracture data of central-sharp notched carbon/epoxy composite laminates with various lay-ups are considered. The notched strength estimates are found to be close to the test results. The modified point stress criterion is very simple and accurate in predicting the notched tensile strength of laminated composites.     

Fracture analysis of V‐notched rubbers: An experimental and theoretical study

In this study, the rupture load in rubbers weakened by sharp V‐notch is investigated under mode I loading. To this end, first, mode I fracture tests are performed on V‐notched samples made of styrene‐butadiene rubbers and the corresponding rupture loads are obtained. Then, the effective stretch (ES) criterion, which was recently developed by the present authors for rupture assessment of cracked rubber parts, is extended and used for the V‐notched rubbers. It is shown that similar to cracked rubbers, the state of stress near the notch tip is also nearly uniaxial. By employing the ES criterion, the critical displacements corresponding to the rupture in the tested samples are calculated. Finally, the predictions of the criterion are compared with the corresponding experimental values, and good consistency is shown to exist.     

Fatigue life prediction of small notched Ti-6Al-4V specimens using critical distance

This study investigated the method of estimating the fatigue strength of small notched Ti-6Al-4V specimen using the theory of critical distance that employs the stress distribution in the vicinity of the notch root. Circumferential-notched round-bar fatigue tests were conducted to quantify the effects of notch radius and notch depth on fatigue strength. The fatigue tests show that the larger notch radius increases the fatigue strength and the greater notch depth decreases the fatigue strength. The theory of critical distance assumes that fatigue damage can be correctly estimated only if the entire stress field damaging the fatigue fracture process zone is taken into account. Critical distance stress is defined as the average stress within the critical distance from notch root. The region from the notch root to the critical distance corresponds to the fatigue fracture process zone for crack initiation. It has been found that a good correlation exists between the critical distance stress and crack initiation life of small notched specimens if the critical distance is calibrated by the two notched fatigue failure curves of different notch root radii. The calibrated critical distances did not vary clearly over a wide range of fatigue failure cycles from medium-cycle low-cycle fatigue regime to high-cycle fatigue regime and have an almost constant value. This critical distance corresponds to the size of crystallographic facet at the fatigue crack initiation site for the wide range of fatigue cycles.     

An extended maximum tangential strain energy density criterion considering T‐stress for combined mode I–III brittle fracture

The maximum tangential strain energy density (MTSED) criterion was modified by taking the influences of stress intensity factors and T‐stress into consideration for combined mode I–III brittle fracture. Furthermore, the Poisson's ratio and T‐stress influencing the fracture characteristics of cracked components were discussed by using the extended MTSED criterion. Moreover, the predicted values of this extended MTSED criterion and some testing results were comparatively analysed. The results indicate that the Poisson's ratio and T‐stress have no impact on the out‐of‐plane initiation angle; however, their effects on fracture resistance ratios are significant especially for pure mode III. A positive T‐stress increases the fracture resistance ratio, and it is opposite for a negative T‐stress. The predicted values calculated by the extended MTSED criterion agree very well with the testing data obtained with edge‐notched disc bend samples especially for pure mode III case.     

A criterion for low-stress brittle fracture of notched specimens based on combined micro- and macro fracture mechanics—1

Based on the combined micro- and macro fracture mechanics, the two requisites necessary for the crack propagation, that is, the energy unstable requisite and the critical local stress requisite, are derived for the low-stress brittle fracture of notched specimens. Thus the fracture criterion was obtained. The criterion is compared with the experimental data, such as on the relationships between the fracture stress or the fracture toughness and the grain size diameter, the crack length, the notch tip radius or the yield stress. The good agreement is obtained.     

The fracture behaviour of notched specimens of polymethylmethacrylate

The fracture behaviour of notched specimens of polymethylmethacrylate has been examined for a wide range of geometries in Charpy impact tests, and in tensile and slow bend fracture tests. It was found that the failure of the very sharply notched specimens was consistent with linear elastic fracture mechanics and defined a constant fracture toughness K _IC for a constant notch tip radius, whereas the blunt notched specimens failed at a constant critical stress at the root of the notch.     

The role of first non‐singular stress terms in mixed mode brittle fracture of V‐notched components: an experimental study

This paper investigates the effects of the first non‐singular stress terms on the fracture assessment of sharp V‐notches under mixed mode loading. First, numerical studies have been performed on a fracture test configuration called single V‐notched ring (SVR) specimen. Then, the notch stress intensity factors as well as the coefficients of the first non‐singular stress terms, which are vital parameters in brittle fracture of V‐notched components, were calculated via a finite element over‐deterministic algorithm for a wide range of loading and geometry conditions. The obtained results demonstrate that the SVR specimen is able to provide a complete range of mode mixities from pure mode I to pure mode II loading conditions. The numerical results, next, have been converted to dimensionless parameters and are illustrated in several graphs. Indeed, these graphs can be easily employed by the engineers for rapid calculation of the corresponding notch stress intensity factors and the coefficients of the first non‐singular stress terms in the SVR specimen. The obtained fracture parameters are then submitted to the maximum tangential stress criterion to assess the effects of the first non‐singular terms on fracture behaviour of the specimen. Finally, an experimental study has been performed on the SVR specimen made of Nayriz Marble rock for two notch angles with a complete range of mode mixities. The obtained experimental data confirm the significant role of the first non‐singular stress terms. In fact, these results show that considering only the singular stress terms may induce an average error of 38% in the predicted fracture loads, which can be decreased to about 12% just by adding the contribution of the first non‐singular terms to the maximum tangential stress criterion.     

Fracture behavior of notched unidirectional Si-Ti-C-O/BMAS composite

Experimental and modeling studies on tensile fracture behavior of notched unidirectional Si-Ti-C-O (Tyranno fiber) reinforced BMAS (barium magnesium aluminosilicate) glass matrix composite were carried out. The longitudinal crack arose at the tip of the transverse notch before overall fracture. The critical energy release rate around at initiation of the longitudinal cracking was estimated to be nearly 100 J/m² by application of the present model to the experimentally observed relation between the stress of the composite in the very early stage of longitudinal cracking and the notch size. The notched strength was higher than that predicted by the fracture mechanical criterion due to the blunting arising from the premature longitudinal cracking, but it was lower than that predicted by the net stress criterion due to the constraint effect arising from the bridging of the fibers and the spalling of the segmented matrix into the longitudinal crack.     

Fracture behaviour of 8%Ni 980 MPa high strength steel at various temperatures Part 3 – Four-point notched bend tests

Abstract

Based on the results of four-point notched bend tests together with detailed microscopic observations of fracture surfaces and crack configurations below the unbroken notch roots of double notch specimens, the fracture mechanisms in notched specimens of 8%Ni high strength (980 MPa) steel have been observed to be as follows. A fibrous crack initiates in the bainitic matrix at the notch root and then develops into a cleavage crack at a critical length. The cleavage crack propagates in an unstable manner and causes the final fracture of specimen. The critical event controlling the cleavage fracture is the propagation of the bainitic packet-sized crack, and the local fracture stress is measured as around 1845–2200 MPa.     

Fracture analysis of functionally graded materials with U‐ and V‐notches under mode I loading using the averaged strain‐energy density criterion

One of the most powerful criteria to predict the critical fracture load in plates with notches is the strain‐energy density averaged over a well‐defined control volume ahead of the notch tip. Although the averaged strain‐energy density (ASED) criterion has been proposed for homogeneous materials, it has been shown in this paper that this criterion can also be applied for non‐homogeneous materials, especially for functionally graded materials (FGMs). A numerical method has been used to evaluate the control volume boundary, the averaged strain‐energy density over the control volume, and also the critical fracture load in FGMs under mode I loading. A new set of experimental results on fracture of blunt V‐notched samples made of austenitic–martensitic functionally graded steel under mode I loading have been provided.     

Effect of strength mis-match and dynamic loading on ductile fracture initiation

It has been well known that ductile fracture of steels is accelerated by triaxial stresses. The characteristics of ductile crack initiation in steels are evaluated quantitatively using a two-parameter criterion based on equivalent plastic strain and stress triaxiality.The present study focuses on the effects of geometrical discontinuity, strength mis-match, which can elevate plastic constraint due to heterogeneous plastic straining, and loading rate on the critical condition for ductile fracture initiation using a two-parameter criterion. Fracture initiation testing has been conducted under static and dynamic loading using circumferentially notched round-bar specimens. In order to evaluate the stress/strain state in the specimens, especially under dynamic loading, a thermal elastic-plastic dynamic finite element (FE) analysis considering the temperature rise due to plastic deformation has been carried out.The tensile tests on specimens with an undermatching interlayer showed that the relationship between the critical equivalent plastic strain to initiate ductile fracture and stress triaxiality was equivalent to that obtained on homogeneous specimens under static loading. Moreover, the two-parameter criterion for ductile fracture initiation is shown to be independent of the loading rate. It was demonstrated that the critical global strain to initiate ductile fracture in specimens with strength mis-match under various loading rate can be estimated based on the local criterion, that is two-parameter criterion obtained on homogeneous specimens under static tension, by mean of FE-analysis taken into account accurately both strength mis-match and dynamic loading effects on stress/strain behaviors.     

Brittle Mixed-Mode (I+II) Fracture: Application of the Equivalent Notch Stress Intensity Factor to Cracks Emanating from Notches

In the present paper, crack initiation in mixed-mode (I+II) fracture has been studied using notched circular ring specimens. A new criterion of brittle mixed-mode (I+II) fracture based on the notch tangential stress and the volumetric approach has been developed. The critical value of the equivalent notch stress-intensity factor has been considered as fracture toughness in mixed-mode (I+II) fracture.     

Notched strength of satin-woven Si-Ti-C-O fiber-bonded ceramic composite

The fracture behavior of Si-Ti-C-O fiber-bonded ceramic composite produced by hot-pressing oxidized 8 harness-satin-woven Si-Ti-C-O fibers was investigated by using unnotched and double edge notched tensile test specimens with different width (8 and 40 mm). The main results are summarized as follows. (i) The tensile strength of unnotched specimens for 8 mm width was higher than that for 40 mm width. Such a width-dependence of the unnotched strength could be described fairly well from the viewpoint of effective volume by application of the experimentally estimated Weibull's shape parameter. (ii) The applicability of the fracture toughness criterion (fracture arises when the stress intensity factor reaches the critical value) and net section stress criterion (fracture arises when the strength of the ligament reaches the unnotched strength) to the present composite was examined. The fracture strength of a notched specimen for 8 mm width was described by the net stress criterion. On the other hand, the strength for 40 mm width obeyed the net stress criterion for a small notch length but it shifted toward the fracture toughness criterion for large one. The shift of the fracture criterion from net strength- to fracture toughness-criterion arose around at the relative notch length 0.2 (notch length 8 mm), corresponding to periodical spacing of fiber strands (8 harness). (iii) The fiber pull-out length (0.4 mm on an average) was nearly the same as the half length of the fiber strand whose deformation is not constricted by the other strands in the satin-weave. (iv) The present fiber-bonded ceramic composite is insensitive to notch under the condition where the width of specimen is narrow and the notch length is smaller than 8 mm. This composite could be therefore applicable to industrial objects safely when the objects are designed as to satisfy the notch-insensitive condition.     

The influence of manganese addition on mechanical properties of commercial Al‐4Mg casting alloys

The aim of this study was to investigate the mechanical properties of Al‐Mg‐Si alloys aged to peak hardness with different dispersoid volume fraction. It was found that the tensile strength increases with dispersoid content, for alloys having similar ductility. The effect of an increasingly triaxial stress state on a fracture strain above mentioned alloys were measured using a series of notched tensile specimens whose notch root radius of curvature was changed. The alloy ductility was found to increase with dispersoid content and root radius and to decrease with increased stress triaxiality. The fracture toughness of these alloys was determined as a function of dispersoid content and notch root radius of curvature. It was observed that the fracture toughness increased as the dispersoid content and the notch root radius increased. scanning electron microscope analysis of the fracture surfaces revealed that fracture mechanism was transgranular fracture with dimples formation. It is argued that optimum mechanical properties in these alloys can be achieved at about 0.5 % Mn content.     

Notch brittleness of ductile glassy polymers under plane strain

The brittle fracture behaviour of ductile glassy polycarbonate, poly(vinyl chloride) and poly(methyl methacrylate) notched bars subjected to plane strain tension has been studied at varying strain rates. Morphological observations of thin sections and fracture surfaces revealed that a disc-type craze was nucleated at the tip of the plastic zone which spread from the notch root. A slip-line theory modified so that the yield criterion is influenced by a hydrostatic stress component allows the calculation of the stress components at the elastic-plastic boundary, where the hydrostatic stress is highest, from the knowledge of the location of the fracture origin. An analysis of the data resulted in the conclusion that Orowan's analysis for notch brittleness is appropriate.     

Werkstoffmechanische Beanspruchungsanalyse gekerbter Strukturen bei synchronen Belastungskombinationen

Elastic‐Plastic analysis of notched structures under synchronous cyclic loading This paper focuses on analysing the elastic‐plastic stress‐strain behaviour at the failure‐critical location of notched components and structures under multiaxial synchronous cyclic loading. For this, various load configurations are investigated numerically consisting of constant and cyclic load components with constant and variable amplitudes. The von Mises yield criterion and the kinematic hardening rule of Prager and Ziegler describe the elastic‐plastic material property. The finite element software of ABAQUS is used to solve the boundary element problem. A parametrical study is carried out and numerical results are presented to show the effects of load amplitude, mean load and spectrum shape on the local stress‐strain paths.     

A notch critical plane approach of multiaxial fatigue life prediction for metallic notched specimens

An approach based on the local stress response is proposed to locate the fatigue critical point for metallic blunt notched specimens under multiaxial fatigue loading. According to the stress analysis, both stress gradient and gradient of loading nonproportionality exist at notch root. The plane in the vicinity of the notch that passes through the fatigue critical point and experiences the maximum shear stress amplitude is defined as the critical plane for notch specimens (CPN). Furthermore, the Susmel's fatigue damage parameter is modified to assess fatigue life of notched components by combining CPN and the theory of critical distance (TCD). The multiaxial fatigue test of the thin‐walled round tube specimens made of Ni‐base alloy GH4169 is carried out to verify the above approaches. In addition, test data of two kinds of materials are collected. The results show that the maximum absolute error of the fatigue critical point is 9.6° and the majority of the predicted life falls within the three‐time scatter band.