Stress Triaxiality Parameter Research Articles

Burst speed prediction and reliability assessment of turbine disks: Experiments and probabilistic aspects

Under harsh and stochastic environmental conditions, turbine disks may exceed their maximum allowable speed and then burst. Aeroengine certification requires demonstrating its integrity at higher rotation speeds than the designed steady-state speed. In particular, testing the burst speed of turbine disk is an essential part of this procedure. In this work, based on the average stress approach, a novel model for turbine disk burst speed assessment is proposed, in which the notch strength ratio and the stress triaxiality parameter are introduced to characterize the inhomogeneous stress field and multiaxial stress state, respectively. Disk overspeed test data are utilized for model validation and comparison, and results show that the proposed model matches the experimental evidences well. Furthermore, a probabilistic framework is built to characterize the influence of material property dispersion on burst speed, and the proposed model is extended to a probabilistic one. Finally, the relationship between the safety margin and the reliability index is established, which provides a reference for reliability-based design and evaluation of turbine disk.

Low cycle fatigue evaluation of welded structures with arbitrary stress-strain curve considering stress triaxiality effect

In this work, load-controlled low-cycle fatigue tests of butt and lap joints are conducted, and a structural strain range parameter is proposed to characterize the fatigue behavior of weldment. A new scheme to calculate the structural strain range is formulated, which can deal with arbitrary material elastic–plastic behavior. The method captures the lateral structural constraint effect through the stress triaxiality parameter. The new fatigue parameter shows superior data transferability, which correlates high and low-cycle fatigue data of steel, aluminum, titanium, and magnesium weldments into one master E-N curve.

Fracture locus characteristics of Al alloy 5083 processed by equal channel angular pressing using miniaturized specimens

After severe plastic deformation (SPD) processing, aluminum alloys show increased strength but low ductility. However, the ductility of the materials obtained during tensile tests does not reflect the full plastic deformation ability of the materials. This work presents the results of a more comprehensive plasticity analysis, which is applied first time to material after SPD processing. The current study considers an aluminum alloy 5083 before and after equal channel angular pressing (ECAP). The plasticity analysis was implemented based on the fracture locus, which was plotted in the space of the equivalent strain to fracture, the stress triaxiality parameter, and the Lode angle parameter using the Hosford–Coulomb (H–C) model. The parameters of the H–C model were determined using a combined experimental–numerical approach. It was found that the plasticity of the 5083 alloy strongly depended on a combination of the stress triaxiality and Lode angle parameter. However, the fracture locus of the material after ECAP processing showed slightly higher values of equivalent strain to fracture than that of the initial material. This approach makes it possible to estimate the ultimate plasticity of the materials after ECAP processing for a wide range of stress-strain states and can be used to predict fracture in plastic deformation processes.

Comparative analysis of stress-strain state of bars from aluminum alloys A2024 and A7075 processed by RSR based on FEM modeling

In this article the analysis of temperature conditions and stress–strain state during radial-shear rolling (RSR) of bars from industrial deformed aluminum alloys A2024 and A7075 was carried out. The RSR was made for four different variants of elongation ratio µ for each alloy: 1.2, 1.6, 2.0, 2.4. It is shown that for the alloy A2024 in the zone of maximum reduction, the growth of elongation ratio leads to the increase in the temperature difference, and for A7075, the temperature difference decreases. After rolling the temperature of bar increases due to the deformation heating in average by 5–30°C in dependence on reduction per pass. At deformation with µ <2.0 the axis zone of bars is characterized by the presence of positive average stresses. The analysis of stress triaxiality parameter showed that the alloy A2024 has a large margin of technological plasticity in comparison with the alloy A7075 when deformed by the RSR method with similar parameter.

Characteristics of selected measures of stress triaxiality near the crack tip for 145Cr6 steel - 3D issues for stationary cracks

Abstract In the paper the numerical analysis of the stress fields for 145Cr6 steel, near crack tip is presented, based on three-dimensional finite element method (FEM) analysis. The FEM analysis is focused on SEN(B) specimens with relative crack length a/W ≈ 0.30. In addition to the presentation of the normal components of the stress tensor, the paper presents selected measures of stress triaxiality parameters, measured for the value of the J-integral, corresponding to the experimentally determined fracture toughness, denoted as JIC , which is considered to be a material constant or material characteristic [1, 2]. Presented topic is a continuation of papers [3, 4],whichwere based on experimental analysis, presented in [5].

Fracture of Titanium Alloys at High Strain Rates and under Stress Triaxiality

The present study investigates the effect of stress triaxiality on mechanical behavior and fracture of Ti-5Al-2.5Sn alloy in a practical relevant strain rate range from 0.1 to 1000 s−1. Tensile tests were carried out on flat smoothed and notched specimens using an Instron VHS 40/50-20 servo-hydraulic test machine. High-speed video registration was conducted by Phantom 711 Camera. Strain fields on the specimen gauge area were investigated by the digital image correlation method (DIC). The fracture surface relief was studied using digital microscope Keyence VHX-600D. Stress and strain fields during testing of the Ti-5Al-2.5Sn alloy were analyzed by the numerical simulation method. The evolution of strain fields at the investigated loading condition indicates that large plastic deformation occurs in localization bands. The alloy undergoes fracture governing by damage nucleation, growth, and coalescence in the localized plastic strain bands oriented along the maximum shear stresses. Results confirm that the fracture of near alpha titanium alloys has ductile behavior at strain rates from 0.1 to 1000 s−1, stress triaxiality parameter 0.33 &lt; η &lt; 0.6, and temperature close to 295 K.

Failure behavior of adhesively bonded joints with a rubber modified epoxy adhesive under tensile-shear combined cyclic loading

Rubber-modified epoxy adhesives are used widely as structural adhesive owing to their properties of high fracture toughness. In many cases, these adhesively bonded joints are exposed to cyclic loading. Generally, the rubber modification decreases the static and fatigue strength of bulk adhesive without flaw. Hence, it is necessary to investigate the effect of rubber-modification on the fatigue strength of adhesively bonded joints, where industrial adhesively bonded joints usually have combined stress condition of normal and shear stresses in the adhesive layer. Therefore, it is necessary to investigate the effect of rubber-modification on the fatigue strength under combined cyclic stress conditions. Adhesively bonded butt and scarf joints provide considerably uniform normal and shear stresses in the adhesive layer except in the vicinity of the free end, where normal to shear stress ratio of these joints can cover the stress combination ratio in the adhesive layers of most adhesively bonded joints in industrial applications.In this study, to investigate the effect of rubber modification on fatigue strength with various combined stress conditions in the adhesive layers, fatigue tests were conducted for adhesively bonded butt and scarf joints bonded with rubber modified and unmodified epoxy adhesives, wherein damage evolution in the adhesive layer was evaluated by monitoring strain the adhesive layer and the stress triaxiality parameter was used for evaluating combined stress conditions in the adhesive layer. The main experimental results are as follows: S–N characteristics of these joints showed that the maximum principal stress at the endurance limit indicated nearly constant values independent of combined stress conditions, furthermore the maximum principal stress at the endurance limit for the unmodified adhesive were nearly equal to that for the rubber modified adhesive. From the damage evolution behavior, it was observed that the initiation of the damage evolution shifted to early stage of the fatigue life with decreasing stress triaxiality in the adhesive layer, and the rubber modification accelerated the damage evolution under low stress triaxiality conditions in the adhesive layer.

Yield limit dependence of titanic alloy VТ14 from the stress state parameters

The stress state mode has influence on the yield limit of construction materials that causes the necessity of account of this phenomenon at determination of this material resource. A quantitative characterization of the stress state can be given by means of two parameters which describe, accordingly, by the volume constituent of tensor and stress deviator mode. Influence of the volume constituent of tensor is characterized by the stress triaxiality parameter, and stress deviator mode - by the Lode parameter, Lode corners or normalized third deviatoric stress invariant. In paper is proposed the yield limit dependences as second degree polynomials of the stress state parameters. These dependences are concreted for the titanic alloy VТ14 on the basis of experiments with the loading of tubular specimen by axial force and intrinsic pressure. Supposed, that the stress state in the wall of specimen corresponded to what exists in on his middle surface. At the calculation of the stress intensity not only axial and circuitous but also radial stresses token into account, that resulted in reduction of divergence of yield limits at the different stress state from 12,4 to 10,2 %. The results of calculations showed that the best from the polynomials is equation with contain members: the first degree from both stress state parameters, multiplicity of these parameters and second degree from the stress triaxiality parameter. From the point of view of statistical meaningfulness appeared the best equation that as stress deviator parameter contained the module of the normalized third deviatoric stress invariant. The level of meaningfulness of this equalization on the criterion of Fisher and constants on the criterion of Student exceeded a size 94 %. The application of the proposed regression equation for describing the dependence of the yield strength of a titanium alloy VT14 on parameters of the stress state type makes it possible to make fuller use of the resource capabilities of this material.

Comparison of fracture behavior between acrylic and epoxy adhesives

An experimental study was conducted on the strength of adhesively bonded steel joints, prepared epoxy and acrylic adhesives. At first, to obtain strength characteristics of these adhesives under uniform stress distributions in the adhesive layer, tensile tests for butt, scarf and torsional test for butt joints with thin-wall tube were conducted. Based on the above strength data, the fracture envelope in the normal stress-shear stress plane for the acrylic adhesive was compared with that for the epoxy adhesive. Furthermore, for the epoxy and acrylic adhesives, the effect of stress triaxiality parameter on the failure stress was also investigated. From those comparison, it was found that the effect of stress tri-axiality in the adhesive layer on the joint strength with the epoxy adhesive differed from that with the acrylic adhesive. Fracture toughness tests were then conducted under mode l loading using double cantilever beam (DCB) specimens with the epoxy and acrylic adhesives. The results of the fracture toughness tests revealed continuous crack propagation for the acrylic adhesive, whereas stick-slip type propagation for the epoxy one. Finally, lap shear tests were conducted using lap joints bonded by the epoxy and acrylic adhesives with several lap lengths. The results of the lap shear tests indicated that the shear strength with the epoxy adhesive rapidly decreases with increasing lap length, whereas the shear strength with the acrylic adhesive decreases gently with increasing the lap length.

Three-Dimensional Computational Analysis of Stress State Transition in Through-Cracked Plates

Stress state is a main parameter within fracture mechanics. It has a major influence on different phenomena, namely those involving diffusion, plastic deformation, and brittle fracture. As is well-known, in the near-surface regions of a crack front, the plane stress state dominates, while at interior positions the plane strain state prevails. The main objective here is to examine the extent of surface regions in through-cracked planar geometries subjected to cyclic loading. Two constitutive material models were developed to characterise the stress state along the crack front. A new criterion based on the h stress triaxiality parameter was proposed to define the transition between surface and near-surface regions. Finally, a linear relation between the stable value of the extent of surface region and the maximum stress intensity factor was established.

Fatigue Surface Crack Growth in Aluminum Alloys under Different Temperatures

The variation of crack growth behavior is studied under cyclic axial tension fatigue loading for the different temperatures conditions. The subject for studies is cylindrical hollow specimens of B95 and D16 aluminum alloys with semi-elliptical surface cracks. By experimental studies for considered temperature conditions the relations between the crack sizes on the free surface of specimen, crack opening displacements (COD), crack growth rate and aspect ratio were obtained. These relationships are useful for automation of experimental studies of surface crack growth. For the same specimen configuration and the different crack front position as a function of cyclic tension loading and temperatures conditions, the following constraint parameters were analyzed, namely, the non-singular T-stress, Tz -factor and the stress triaxiality parameter h in the 3D series of elastic-plastic computations. The governing parameter of the elastic-plastic stress fields In-factor distributions along various crack fronts was also determined from numerical calculations. The plastic stress intensity factor (SIF) approach was applied to the fatigue crack growth on the free surface of the hollow specimens as well as the deepest point of the semi-elliptical surface crack front. As result principal particularities of the fatigue surface crack growth rate as a function of temperature conditions are established.

Evaluation of ductile failure models in Sheet Metal Forming

Traditionally, combination of equivalent plastic strain and stress triaxiality parameters are taken into account when performing characterization of material ductility. Some well-established models like Lemaitre model, GTN based models and many others perform relatively well at high-triaxiality stress states but fail to give adequate answers to low-triaxiality states. In this work, three damage models are presented, applied and assessed to a cross-shaped component. Concerning material, AA5182-O, corresponding damage parameters are characterized by an inverse analysis procedure for each damage model.

Application of R6 failure assessment method to obtain fracture toughness

Determination of fracture toughness, J–R curve from experimental test results requires certain geometry factors. These expressions of geometry factors are available for standard geometries and loading configurations. However, these expressions are not available in open literature for complex geometries and loading configurations. R6 Failure Assessment Diagram (FAD) methodology is used for assessment of failure in the failure regime of cleavage fracture, ductile crack initiation and plastic collapse. In this paper, the use of this method is extended to estimate the entire J–R curve from the fracture test results. Under comprehensive test programme initiated at RSD (Reactor Safety Division), BARC (Bhabha Atomic Research Centre), large numbers of straight pipes with circumferential cracks have been tested. These experimental results have been used to calculate material J–R curves using R6 FAD, which are subsequently compared with conventionally calculated J–R curves using η factor approach. It can be observed that the J–R curves calculated using both approaches are in good agreements for three out of total six pipes studied. Further, the segregation of J–R curves based on the size of pipes has been studied in the light of prevalent crack tip constraints. Here, crack tip constraints are calculated in terms of stress triaxiality parameters ‘Q’ for all pipes. It can be noted that the J–R curves for 8in. pipes are ‘toughened’ because they have lower constraints than 16in. pipes. This establishes the theory that high/low crack tip constraint causes low/high material fracture toughness.

A Study on the Effect of the Stress State on Ductile Fracture

The main purpose of this paper is to demonstrate that besides the stress triaxiality parameter, the Lode angle, which can be related to the third invariant of the deviatoric stress tensor, also has an important effect on ductile fracture. This is achieved by conducting a series of micromechanics analyses of void-containing unit cells and experimental-numerical studies of carefully designed specimens experiencing a wide range of stress states. As a result, a fracture criterion is expressed in terms of the equivalent failure strain as a function of the stress triaxiality and the Lode angle (or the third invariant of the stress deviator) and this function is calibrated for a DH36 steel plate.

Fracture behaviour and cleavage initiation in hypoeutectoid pearlitic steel

The paper reports on an investigation of the micromechanism of cleavage fracture in hypoeutectoid pearlitic R7T steel, commonly used for producing railway wheels. The steel possesses extensive Luders deformation, which somewhat complicates finite element (FE) modelling and analyses of fracture behaviour. Standard Charpy V-notch specimens were used in order to analyse the fracture behaviour at quasistatic and impact loading. Finite element 3D calculations were performed and the elastic-plastic behaviour of notched bars up to the fracture was simulated. Detailed fractographic analysis was carried out on a number of Charpy V-notch specimens in order to investigate the origin site of cleavage fracture initiation and its distance from the notch root. The suitability of the three-criterion micromechanical model (Chen et al. Acta Materialia 51:1841–1855, 2003) for cleavage initiation was verified. The R7T steel under investigation exhibited a cleavage fracture stress of 1,837 MPa. Its independence on temperature evidenced the micromechanism of cleavage fracture to be microcrack propagation-controlled. For the investigated blunt-notched bend bars, an active volume exists ahead of the notch root in which pearlite colony-associated initiation sites are located. The cleavage fracture initiation of the steel is thus governed by the sites lying in the active volume. The active volume is determined by the values of three parameters. A plastic strain lying in interval from \({\varepsilon_{\rm pmin}}\) to \({\varepsilon_{\rm pmax}}\) (for the steel investigated from 0.033 to 0.108) is necessary to create a cleavage crack nucleus at any location within the active volume depending on the local pearlite properties. A stress triaxiality parameter ranging from hmin to hmax (from 0.93 to 1.39) is supposed to prevent the blunting process at the site of the cleavage nucleus. Once the main principal stress σ1 exceeds the local cleavage fracture stress σCFmin, an unstable global cleavage fracture occurs in a blunt-notched bar.

Modeling of ductile fracture: Significance of void coalescence

In this paper void coalescence is regarded as the result of localization of plastic flow between enlarged voids. We obtain the failure criterion for a representative material volume (RMV) in terms of the macroscopic equivalent strain ( E c) as a function of the stress triaxiality parameter ( T) and the Lode angle ( θ) by conducting systematic finite element analyses of the void-containing RMV subjected to different macroscopic stress states. A series of parameter studies are conducted to examine the effects of the initial shape and volume fraction of the primary void and nucleation, growth, and coalescence of secondary voids on the predicted failure surface E c( T, θ). As an application, a numerical approach is proposed to predict ductile crack growth in thin panels of a 2024-T3 aluminum alloy, where a porous plasticity model is used to describe the void growth process and the expression for E c is calibrated using experimental data. The calibrated computational model is applied to predict crack extension in fracture specimens having various initial crack configurations and the numerical predictions agree very well with experimental measurements.

Plane strain mixed mode crack-tip stress fields characterized by a triaxial stress parameter and a plastic deformation extent based characteristic length

Using physical observations from controlled crack growth experiments in ductile materials as a guide, a series of numerical and theoretical studies were performed. Results from these studies demonstrate that a self-similar family of mixed mode crack-tip stress fields exist in the crack-tip region that are characterized in terms of (a) a stress triaxiality parameter, A m, based on the ratio between the mean stress and effective stress, and (b) a characteristic length scale, L p, based on the spatial extent of crack-tip plastic deformation. Finite element models used to demonstrate this include; small-scale yielding with a modified boundary layer formulation (SSY); slant cracked tension bar (TB); and an asymmetric three point bend (TPB) bar. Since experimental evidence has shown that crack growth occurs along local directions that are predominantly either mode I or mode II, special emphasis is placed on radial variations in stress components along these directions. Results for all cases indicate that, for the full range of mode mixity and constraint conditions present in the SSY, TB and TPB models, the proposed, self-similar family of mixed mode crack-tip fields accurately represents the stress fields for both SSY and all fracture specimens considered. Specifically, the crack-tip stress fields are shown to belong to a family of solutions parameterized by A m and L p when the distance from crack tip, r, is measured in terms of its normalized value by the characteristic length scale, r/ L p.

Fracture and yield behavior of adhesively bonded joints under triaxial stress conditions

Most of adhesively bonded joints are under complicatedly distributed triaxial stress in the adhesive layer. For the estimating of the strength of adhesively bonded joints, it is crucial to clarify behavior of yield and failure of the adhesives layer under triaxial stress conditions. Two types of the adhesively bonded joints were used in this study: One is the scarf joint which is under considerably uniform normal and shear stresses in the adhesive layer, where their combination ratio can be varied with scarf angle. The other is the butt joint with thin wall tube in which considerably uniform pure shear can be realized in the adhesive layer under torsional load conditions. These joints can cover the stress triaxiality in adhesive layers of most joints in industrial application. The effect of stress triaxiality on the yield and fracture stresses in the adhesive layer were investigated using the joints bonded by three kinds of adhesives in heterogeneous and homogeneous systems. The results showed that both the yield and failure criterion depend on the stress triaxiality and that the fracture mechanism of the homogeneous adhesive is different from that of the heterogeneous one. From these experimental results, a method of estimating the yield and failure stresses was proposed in terms of a stress triaxiality parameter.

Analysis of the 3d fracture characteristics of CT specimens in the elastic-plastic state

In this paper, the void growth ratio parameter V g is applied to describe the 3D fracture characteristics of CT specimens in the elastic-plastic state by means of the finite element method. The effects of stress triaxiality and plastic deformation on V g are analysed in both the r, ϑ plane and the thickness direction z. It is found that the maximum V g always takes place in the midsection of the specimen in the thickness direction; there are two peak values of V g around ϑ = π 4 and ϑ = π − π 4 in the r, ϑ plane, where z equals a constant. This can explain the bluntness of a sharp crack. Generally speaking, the stress triaxiality parameter is the main factor deciding the magnitude of V g but V g strongly depends on the equivalent plastic strain at larger plastic deformation.

Two-parameter description of creep/high-cycle- fatigue behaviour of notched 9% Cr steel

A notch effect under creep/high-cycle-fatigue loading conditions was studied both theoretically and experimentally in notched specimens of an advanced 9%Cr steel of the type P91 at 600°C. Experiments were performed under condition of the constant maximum net stress. The stress ratio R, i.e., the cyclic stress component of creep/fatigue loading was varied. The dependence of time to fracture on R exhibits nonmonotonous behaviour with a pronounced maximum coinciding with the fracture mode transition from pure creep to fatigue. The notched specimens show increased rupture strength when compared with smooth bars. The strengthening due to the notch depends on the notch geometry. It is shown that the notch tip stress triaxiality parameter is not sufficient to describe this phenomenon.