Nonlinear Fracture Mechanics Parameters Research Articles

An extensive investigations on fracture parameters of concretes based on quaternary binders (QBC) by means of the DIC technique

• Determination of the fracture toughness K Ic S and CTO D c in quaternary binder concretes (QBC). • Application of Digital Image Correlation (DIC) measurements to QBC. • Two measuring devices were used in the studies, i.e. MTS 810 press and DIC system. • Linear and nonlinear fracture mechanics parameters were analyzed. • There is a correlation between K Ic S and CTO D c obtained by using two measuring devices. The following article presents an extensive investigations of the fracture mechanics parameters of concretes made of quaternary binders (QBC). A composition of the two most commonly used mineral additives, i.e. fly ash (FA) and silica fume (SF) in combination with nanosilica (nS), has been proposed as a partial replacement of the ordinary Portland cement (OPC) binder. Four series of concretes were made, one of which was the reference concrete (REF) and the remaining three were QBC. During the studies K Ic S and CTOD c were investigated. In addition, digital image correlation (DIC) technique was used. Based on the conducted studies it was found that the QBC containing: 80% OPC, 5% FA, 10% SF, and 5% nS have shown the best results of K Ic and CTOD c, whereas the worst parameters were characterized by concrete with more content of FA additive in the concrete mix, i.e.,15%.

Proposal of analysis method of global-local finite element method for finite strain elastic-plastic fracture mechanics analysis

The purpose of this study is to make it possible to perform a large number of paratric analyzes on the position and shape of cracks under finite elasto-plastic deformation. In this report, we propose a one-way coupled analysis method using displacement interpolation between a global finite element method analysis model created without assuming cracks and a local finite element method analysis model assuming cracks. The proposed method is based on the superconvergent patch recovery, and uses the least-squares method to apply the nodal displacements of the global finite element model to the nodes of the local finite element model as displacement boundary conditions. In addition, we will create an merged finite element method analysis model assuming a crack directly in the global finite element method analysis model and identify the application conditions that can be applied to the problem without loss of accuracy through relative comparison by J-integral calculation at the crack tip which is nonlinear fracture mechanics parameter.

Characterization of plastic and creep behavior in thick aluminum wire for power modules

One of the common reliability concern on most of power modules is a failure of its bonding. Stress, strain, and displacement fields around those bonding in power modules are required for highly-reliable design based on physically/mechanically based failure model. They can be accurately obtained from CAE tools such as finite element computer codes for stress analysis with mechanical properties of materials not only in the elastic region but also in the inelastic region. In this paper, for the reliability study of an aluminum bonding wire, an experimental study was performed to acquire its plastic and creep characteristics. The temperature-dependent constitutive equations for plastic and creep behavior of an aluminum wire are presented based on the isothermal tensile test data. These constitutive equations can be used at the temperatures ranging from 20 °C to 250°C, and are useful for estimating fatigue life predictions of bonding wires, when we utilize the failure models based on the physical quantities such as the inelastic strain range, the inelastic strain energy density range, the nonlinear fracture mechanics parameter T* range and so on.

Review of Methodologies for Structural Integrity Evaluation of Power Modules

AbstractThis paper reviews the previous research on the methodologies for evaluating structural integrity of wire bonds and die-attachments in power modules. Under power module operation, these parts are subjected to repeated temperature variations which induce repeated thermal stress due to the mismatch in coefficients of thermal expansion (CTE) of the constituent materials. Thus, thermal fatigue phenomena are critical issues for the structural integrity of power modules. In the present paper, we also deal with the evaluation methodologies for thermal fatigue in the temperatures over 200 °C, which are expected operational temperatures for wide bandgap semiconductor power modules. The failure models based on the temperature range ΔT widely used in the power electronics community are critically reviewed from a mechanical engineering viewpoint. Detailed discussion is given concerning the superiority of failure models based on the physical quantities such as the inelastic strain range Δεin, the inelastic strain energy density range ΔWin, and the nonlinear fracture mechanics parameter range ΔT* over the conventional ΔT-based failure models. It is also pointed out that the distributed state concept (DSC) approaches based on the unified constitutive modeling and the unified mechanics theory are promising for evaluating the structural integrity of power modules. Two kinds of test methods, a power cycling test (PCT) and a thermal cycling test (TCT), are discussed in the relation to evaluating the lifetimes of wire-liftoff and die attach cracking.

Short fatigue crack behaviour of LZ50 railway axle steel under multi-axial loading in low-cycle fatigue

An experimental study was carried out on the low-cycle fatigue of LZ50 railway axle steel under multi-axial loading. The initiation and propagation behaviour of a short fatigue crack was observed and analysed as per the principles of effective short fatigue crack. Our results showed that in the microstructurally short crack (MSC) stage, the crack propagation was strongly influenced by the microstructural features of the material and did not satisfy the linear elastic fracture mechanics. At the physically short crack (PSC) stage, the crack was long enough to not be directly influenced by the microstructures; nevertheless, linear elastic fracture mechanics still could not explain the law of crack propagation properly owing to the large-scale yield range of the crack tip. Based on these observations, a crack growth rate model under multi-axial loading was presented to explain the short fatigue crack behaviour. The non-linear elastic-plastic fracture mechanics parameter, J-integral (cyclic), was adopted as the driving parameter in this model and the crack closure effect was also taken into account. In the MSC stage, the crack growth rate fluctuated significantly when the cyclic J-integral was used owing to the influence of the microstructure. However, at the PSC stage, the crack growth rate fluctuations were small. A linear correlation for the PSC was obtained with R = 0.934 and this model could be applied to describe the short fatigue crack behaviour in the PSC stage.

Application of Nonlinear Fracture Mechanics Parameter to Predicting Wire-Liftoff Lifetime of Power Module at Elevated Temperatures

Power modules are utilized for electric power control and play a key role in efficient energy conversion. A structural reliability problem of wire bonding, wire-liftoff, in power modules becomes important at high-temperature operation. Wire-liftoff is a thermal fatigue phenomenon caused by thermal stress due to mismatch of coefficients of thermal expansion between a wire and a chip material. According to experimental studies, a saturation phenomenon of wire-liftoff lifetime was observed in power modules above the maximum junction temperature of 200 °C. In this paper, we examine the failure models for predicting wire-liftoff lifetime proposed in the previous studies and also propose a new failure model based on the nonlinear fracture mechanics parameter $T^\ast $ -integral range $\Delta T^\ast $ . Among various failure models, the proposed model is the best to represent a saturation phenomenon of wire-liftoff lifetime. For practical use of the failure model based on $\Delta T^\ast $ -integral range, we propose a simple calculation method of $\Delta T^\ast $ -integral range that can be calculated by using the commercial finite element computer code such as Marc, Ansys, and so on.

Crack growth rate and lifetime prediction for aviation gas turbine engine compressor disk based on nonlinear fracture mechanics parameters

In this study, the fatigue crack growth and life-time prediction of aviation gas turbine engine compressor disks under operating conditions are analyzed. Different combinations of rotational speed, temperature, surface flaw forms and sizes, as well as elastic–plastic titanium alloy BT3-1 properties are considered. A crack growth rate equation, which included the fracture process zone size and nonlinear stress intensity factor, is derived. The assessments of the structural integrity of the rotating disk are compared for elastic and elastic-plastic solutions. It is indicated that the traditional elastic crack growth models overestimate the residual fatigue lifetime with respect to the nonlinear fracture mechanics approach.

Computational assessment of nonlinear fracture resistance parameters for cracked fuselage panel under biaxial loading

This study focused on the numerical analysis of a cracked fuselage panel of an airplane on the basis of new nonlinear fracture mechanics parameters and concepts. Through finite element analysis (FEA) of the fragment of the fuselage panel with central crack, the governing parameters of the elastic–plastic crack-tip stress field (i.e., In-integral and the plastic stress intensity factor) were determined as a function of the crack length and biaxial loading conditions. Elastic–plastic FEAs of the cracked fuselage panel were performed by considering the accumulated damages in the fracture process zone at the crack tip via special cohesive elements. The curvilinear crack path in the fuselage panel under biaxial loading was predicted on the basis of strain energy density and cohesive zone concepts.

Identification of elasto-plastic and nonlinear fracture mechanics parameters of silver-plated copper busbars for photovoltaics

Silver-plated copper busbars are screen printed onto silicon solar cells and have the key role to collect the electric current produced by the solar cell. Busbars of two adjacent solar cells are then connected by a soldered ribbon made of the same material. Due to mechanical and thermal loads, such a ribbon is subject to axial deformation that, often, causes plasticity and, in some cases, its breakage due to crack growth. A procedure based on the gradient-descent method and particle swarm optimization is herein proposed for the identification of elasto-plastic and nonlinear (cohesive zone model, CZM) fracture mechanics parameters of silver-plated copper busbars. The proposed method requires the experimental determination of the force-displacement curves from uniaxial tensile tests on busbar samples with and without initial notches. The inspection of in situ SEM images during the tests allows also the estimation of the crack opening, which is found to be an important local quantity to assess the reliability of different CZMs in simulating a crack growth process consistent with the real one.

Comparison among estimation methods of C* parameter for axially oriented external surface crack in cylinders

C* is usually used to describe the creep crack growth. ASTM E1457 allows C* to be calculated from creep load line displacement rate. However in components it is difficult or impossible to measure load line displacement rate. Therefore for the components C* must be determined by finite element methods or reference stress concepts. Estimates of C* obtained by reference stress methods will depend on the collapse mechanism adopted and therefore several estimations are proposed. This paper presents a numerical study of non-linear fracture mechanics parameter predictions under elevated temperature for axially oriented external surface crack in cylinder. Comparison of C* calculated from FE analysis and different reference methods is conducted. The values of C* obtained from the API579 net section solution are also found to be slightly conservative and give the closest agreement to the F.E. contour integral C*. In addition, the comparison between C* of homogeneous material and TYPE IV cracking is conducted. The difference between homogeneous material and TYPE IV cracking is almost negligible and therefore the reference stress solutions for homogenous material could be applied to estimate C* for TYPE IV cracking.

Elastoplastic Fracture Resistance Analysis of NPP Primary Circuit Equipment Elements

Nurrent calculation analysis approaches to the fracture resistance assessment for main equipment elements of the WWER NPP primary circuit are considered. It is noted that the solution of the problems of justifying safe operation, assessment of the integrity and extension of the lifetime of the reactor pressure vessel is essentially dependent on the results of calculations of the kinetics of the stress strain state, a proper consideration of the residual welding stress and strain fields, reliable evaluation of non-linear fracture mechanics parameters. A general methodology is developed for a calculated analysis of the fracture resistance of WWER reactor pressure vessels in the simulation of emergency cooling conditions. The main statements in the elastoplastic calculation of the kinetics of the stress strain state for reactor pressure vessels are formulated with consideration of the residual welding stress and strain fields, and the calculation procedure for determining the fracture parameters of the postulated crack is presented. Using the calculation methods and software product developed, a significant influence of such factors as consideration of the thermomechanical loading history and elastoplastic deformation of the metal in the vicinity of the postulated crack front, different ways of taking into consideration the residual welding stress level, the regularity and density of the finite element mesh in the vicinity of the calculated crack front, the procedure for calculating the elastoplastic fracture parameters in discrete finite element method models on the calculated fracture resistance assessment of WWER-1000 reactor pressure vessels is shown. It is found that the neglect of the loading history and residual stress level after heat treatment results in a non-conservative assessment of the fracture resistance for the collector-to-nozzle welded joint in the PGV-1000 steam generator in the simulation of the operating cycle of loading.

Hydrogen diffusion analyses of a cracked steel pipe under internal pressure

In hydrogen diffusion in metals, we have to consider not only the hydrogen flux driven by the gradient of hydrogen concentration but also the hydrogen flux driven by the gradient of hydrostatic stress. Such hydrogen diffusion is a multi-physics problem coupled hydrogen diffusion with a stress field. We performed such hydrogen diffusion analyses for a steel pipe with a crack on an inner surface under internal pressure. On the inner surface of the pipe, the hydrogen concentration calculated using the fugacity of the hydrogen molecules was used as a boundary condition for a hydrogen diffusion equation. The finite element method was employed both for a hydrogen diffusion analysis and for a stress analysis. We obtained the hydrogen concentration around a crack tip by varying the magnitude of internal pressure and the crack length, and examined the relationship between the maximum hydrogen concentration and a nonlinear fracture mechanics parameter CTOD ( Crack Tip Opening Displacement). Good correlation is found between the maximum hydrogen concentration and CTOD.

Non-Linear Fracture Mechanics Analyses of Vibrating Screen Arthropleure

The dynamic properties of the model of vibrating screen are obtained using the software Pro/ MECHANICA. The natural frequencies and mode shapes of the screen are calculated, and the distribution law of dynamic stress is found out. It shows that the structure design of the screen is reasonable. Under the working conditions designed, its dynamic strength is satisfied. This paper provides engineering estimates of non-linear fracture mechanics parameters for vibrating screen arthropleure cracks, subject to alternate stress and Vibrating. Solutions are given in the form of two different approaches.

압력과 모멘트의 복합하중을 받는 곡관에 대한 유한요소 한계하중 해석

In the present paper, approximate plastic limit load solutions for pipe bends under combined internal pressure and bending are obtained from detailed three-dimensional (3-D) FE limit analyses based on elastic-perfectly plastic materials with the small geometry change option. The present FE results show that existing limit load solutions for pipe bends are lower bounds but can be very different from the present FE results in some cases, particularly for bending. Accordingly closed-form approximations are proposed for pipe bends under combined pressure and in-plane bending based on the present FE results. The proposed limit load solutions would be a basis of defective pipe bends and be useful to estimate non-linear fracture mechanics parameters based on the reference stress approach.

An electrical field based non-linear model in the fracture of piezoelectric ceramics

An analytical model based upon electric field saturation concept along the crack front is proposed in an attempt to predict the fracture of piezoelectric materials containing conducting cracks. Firstly, linear piezoelectroelasticity solution is obtained to show the singularity of the electric field near the crack tips. Then an electrically yielding strip near the crack front is proposed. Expressions for the stress intensity factor K and the energy release rate G are obtained in closed-form. Fracture criteria based on the non-linear fracture mechanics parameters K and G are established, which are shown to be equivalent for some special situations. Theoretically predicated fracture loads agree qualitatively with existing experimental observations.

Development of Flaw Evaluation System for Creep-Fatigue Crack Propagation of High-Temperature

Central Research Institute of Electric Power Industry (CRIEPI) has been conducting a research project on the verification of evaluation method for structural integrity of high-temperature components. As a part of the framework, we developed a flaw evaluation system on PC to predict creep-fatigue crack propagation, which was considered to be an essential crack driving force at high temperature especially in case where stresses caused by thermal loading were significant. The system is featured by easy and dialogical operation with graphical user interface. Fatigue and creep crack propagation behavior can be predicted using fatigue J-integral range and creep J-integral, respectively, which are the variations of the non-linear fracture mechanics parameter, J-integral. Both fatigue J-integral range and creep J-integral are calculated by the reference stress method with revised solutions developed by detailed finite element analysis.

巨視的非弾性挙動を考慮した多孔板の熱疲労き裂伝ぱ評価

Crack propagation behavior of a perforated plate of normalized and tempered 2 1/4Cr-1Mo steel modeling ligament regions of boiler headers was examined under out-of-phase thermal fatigue at a maximum temperature of 600°C in the air. Inelastic analysis of the perforated plate under the thermal fatigue was carried out, and the nonlinear fracture mechanics parameters such as the J and C* integral were obtained by the line integral method for observed crack distributions. A prediction method for these parameters was proposed, which is applicable to the displacement-controlled condition such as thermal fatigue. In this method, the change of the macroscopic stress-strain relation of the perforated plate with propagating cracks was combined with the reference stress concept under the displacement-controlled condition. The predicted fracture mechanics parameters from this method coincided well with those from the inelastic analysis. The prediction of the crack propagation life on the basis of the proposed method provided a good correspondence with the test results of the perforated plate under thermal fatigue.

3차원 유한요소해석을 통해 도출한 균열배관의 소성한계압력식

Based on detailed FE limit analyses, the present paper provides tractable approximations for plastic limit pressure solutions for axially through-wall-cracked pipe; axially (inner) surface-cracked pipe; circumferentially through-wall-cracked pipe; and circumferentially (inner) surface-cracked pipe. In particular, for surface crack problems, the effect of the crack shape, the semi-elliptical shape or the rectangular shape, on the limit pressure is quantified. Comparisons with existing analytical and empirical solutions show a large discrepancy in circumferential short through-wall cracks and in surface cracks (both axial and circumferential). Being based on detailed 3-D FE limit analysis, the present solutions are believed to be the most accurate, and thus to be valuable information not only for plastic collapse analysis of pressurised piping but also for estimating non-linear fracture mechanics parameters based on the reference stress approach.

Plastic limit pressures for cracked pipes using finite element limit analyses

Based on detailed finite element (FE) limit analyses, the present paper provides approximations for plastic limit pressure solutions for plane strain pipes with extended inner axial cracks; axi-symmetric (inner) circumferential cracks; axial through-wall cracks; axial (inner) surface cracks; circumferential through-wall cracks; and circumferential (inner) surface cracks. In particular, for surface crack problems, the effect of the crack shape, semi-elliptical or rectangular, on the limit pressure is quantified. Comparisons with existing analytical and empirical solutions show a large discrepancy for short circumferential through-wall cracks and for surface cracks (both axial and circumferential). Being based on detailed 3D FE limit analysis, the present solutions are believed to be accurate, and thus to be valuable information not only for plastic collapse analysis of pressurised piping but also for estimating non-linear fracture mechanics parameters based on the reference stress approach.

Non-linear fracture mechanics analyses of part circumferential surface cracked pipes

This paper provides engineering estimates of non-linear fracture mechanics parameters for pipes with part circumferential inner surface cracks, subject to internal pressure and global bending. Solutions are given in the form of two different approaches, the GE/EPRI approach and the reference stress approach. For the GE/EPRI approach, the plastic influence functions for fully plastic J solutions are tabulated based on extensive 3-D FE calculations using deformation plasticity, covering a wide range of pipe and crack geometries. The developed GE/EPRI-type fully plastic J estimation equations are then re-formulated using the concept of the reference stress approach for wider applications. The proposed reference stress based estimates are validated against detailed 3-D elastic-plastic and elastic-creep FE results. For a total of 26 cases considered in this paper, agreement between the proposed reference stress based J and C* estimates and the FE results is excellent. An important aspect of the proposed estimates is that they not only are simple and accurate but also can be used to estimate J and C* at an arbitrary point along the crack front.