Values Of T-stress Research Articles

Numerical elastic fracture analysis of SENT test specimen subjected to non-linear loading

Crack characterization of any component depends on specimen type and geometry, material properties, and loading pattern. The geometrical and material property dependency of crack description is well established in literature, but loading pattern influence is limited to classical Mode-I, II and III types. Here, an effort is made to relate the crack stress state for different load pattens and crack length to specimen width, (a/W) using 2D and 3D linear elastic fracture analysis. The crack stress state is characterized by KI and T-stress in the present analysis using ABAQUS software. The non-uniform load patterns were defined by a non-linear stress distribution term σ (x). The stress distributions applied on the crack faces and were classified as constant, linear, parabolic, and cubic. The a/W varied as 0.2, 0.4, 0.6, and 0.8 to account the in-plane dimension effect on crack driving parameters. The 3D normalized KI and T-stress magnitudes were directly proportional to a/W. The normalized KI magnitudes decreased in the stress distribution order of constant, linear, parabolic and cubic. 3D normalized KI and T-stress values represented the real stress state of the crack. To ease the complex computational simulations, simple equations were proposed to estimate the normalized KI and T-stress for the different load patterns and a/W. To avoid the conservatism in component design, an attempt is made to represent the real load patterns through constraint inclusiveness in the 3D fracture analysis.

A comprehensive study on ring shape specimens under compressive and tensile loadings for covering the full range of I+II fracture modes of gypsum material

Using ring-shape specimens containing two aligned cracks on the internal surface of the ring, two test configurations subjected to tensile or compressive loads namely (i) diametrically compressed ring (DCR) and (ii) diametrically tensile ring (DTR) specimens were suggested to investigate the full mixed-mode I/II fracture problem. The fracture parameters, including modes I and II stress intensity factors and T-stress, were determined numerically for these two test specimens with different crack lengths and crack angles. Also, the ability of the specimens was examined by conducting experimental fracture tests on gypsum material. In addition, the direction of fracture kinking was investigated both experimentally and theoretically. The experimental results were then compared and predicted using the mixed mode fracture criteria such as maximum tangential stress (MTS) and generalized maximum tangential stress (GMTS). The normalized fracture toughness (KIIc/KIc) ratios of the tested DCR and DTR specimens were about 0.72 and 0.95, respectively. Such difference was related to the considerable effect of T-stress values and it was shown that the GMTS criterion provides more accurate predictions for the test results of both DCR and DCT samples compared to the MTS criterion.

Development of maximum tangential strain (MTSN) criterion for prediction of mixed-mode I/III brittle fracture

A number of fracture criteria are available for predicting the cracking behavior under combined contribution of opening-tearing damage mechanism (i.e. mixed-mode I/III). But most of them have some limitations or discrepancies with the experimental results. In this research, a new form of maximum tangential strain criterion called 3D-MTSN is developed for predicting mixed-mode I/III fracture phenomenon. This criterion was used originally for analyzing the mixed-mode I/II fracture but we extended its ability for mixed mode I/III as well. Also, the influence of T-stress in addition to modes I and III stress intensity factors was also considered in driving the fracture toughness and fracture angle formulations of the 3D-MTSN criterion. According to this strain-based criterion it is shown that both sign and magnitude of T-stress can affect the fracture behavior of mixed mode I/III. In general, positive T-stress increases the mixed mode I/III fracture envelope and conversely negative sign of T-stress can decrease it. Meanwhile, the Poisson’s ratio (v) has noticeable influence on the mixed mode I/III fracture envelopes and by increasing v, the mixed mode fracture curve predicted by the generalized MTSN criterion shifts down except for those specimens having positive T-stress values and subjected to dominantly pure mode I loading conditions. The practical ability and validity of 3D-MTSN criterion is examined by predicting different sets of mixed mode I/III experimental results reported in the literature for different brittle and quasi-brittle materials tested with different test samples including edge-notch disc bend (ENDB), inclined single edge notch beam (ISENB) and semi-circular bend (SCB) specimens. A comprehensive comparison with the well-known 3D-MTS (stress-based) criterion was also performed. Compared to the other available energy-based fracture models, the presented 3D-MTSN criterion provided better estimations for the experimental results of different materials and specimens under dominantly mode III conditions.

Computation of conventional fracture mechanics parameters via molecular dynamics simulations

The Williams series expansion is the fundamental solution of conventional continuum fracture mechanics for characterizing the stress fields around the crack tip in a homogeneous material in the linear elastic regime. Nowadays stress intensity factors, T-stresses and the higher-order coefficients of the Williams series expansion are proved to be important parameters describing the near crack-tip fields in isotropic linear elastic materials. The central aim of this study is to understand if one can obtain these fracture parameters of conventional fracture mechanics from atomistic simulations based on molecular dynamics simulations. The ability to describe fracture processes at atomic scale via stress intensity factors, T-stresses and higher-order coefficients will provide the opportunity to take into account many effects such as material microstructures, crystallographic orientation, chemical compositions and concentrations and others. In this research the values of stress intensity factors, T-stress and coefficients of the Williams series expansion are obtained using atomistic simulations based on molecular dynamics method with a classical molecular dynamics code Large-scale Atomic/Molecular Massively Parallel Simulator. The classical over-deterministic method is used to determine stress intensity factors, T-stresses and coefficients of higher-order terms of the Williams series expansion of the near crack-tip stress field from molecular dynamics modelling of a plate with a central crack. The accuracy of the proposed approach is tested for this rather simple cracked configuration. There is the theoretical analytical solution with all the coefficients of the higher-order terms in the Williams series expansion. The existing theoretical solution allows us to compare the angular distributions of the stress tensor components for a large plane with the central crack. It is shown that results obtained from molecular dynamics simulations and the theoretical analytical solutions are in good agreement.

Investigation of the interaction mechanism of two dynamic propagating cracks under blast loading

Crack interactions significantly influence the propagation behavior of cracks, and further alter the crack coalescence characteristic. Caustic experiments, combined with numerical simulations, are carried out to further investigate the interaction mechanism between cracks. The results show that the local stress field significantly superposed when the distance between the two opposite propagating cracks is within a critical distance, resulting in an increase in both the dynamic stress intensity factors and the crack velocities during the crack interactions, and further control the fracture behaviors between the two cracks. During the crack interactions, both the absolute values of dynamic stress intensity factor KIId and T-stress increased significantly, indicating that the cracks turned from tensile fracture to mixed tensile-shear fracture conditions, and deflected from its original direction. Moreover, it is found that before the two cracks overlap, the sign of KIId was negative, T-stress was positive, and leading the cracks propagated in an anticlockwise direction. Whereas after the two cracks overlap, the sign of KIId turned to positive, T-stress turned to negative, and further inducing the cracks propagated in an clockwise direction. In addition, the results also implies that the two opposite propagating cracks first exhibit repulsion effect, then turn to attraction effect, and finally form a clasping shape between the two cracks. However, both the repulsion effect and the attraction effect decrease with the increase of the vertical distance between cracks. And the interactions between cracks decreased significantly after the initial vertical distance between two cracks is beyond a critical value. Results may shed lights on the interaction behaviors between two opposite propagating cracks.

Atomistic Determination of Fracture Mechanics Parameters

Stress intensity factors, T-stresses and higher order coefficients in the Williams series expansion are the fundamental concepts of continuum fracture mechanics for characterizing the stress fields around the crack tip in a homogeneous material in the linear regime. It is well-known that critical values of stress intensity factors stipulate the of materials to growth a crack. Nowadays the modern multi-purpose computational tools such as Simulia Abaqus allow us to calculate T-stresses in cracked specimens and structures along with stress intensity factors. The aim of this study is to understand if one can obtain this fracture parameters of conventional fracture mechanics from atomistic simulations based on molecular dynamics method. The ability to describe fracture processes at atomic scale by means of stress intensity factors, T-stresses and higher-order coefficients will provide the opportunity to take into account many effects such as material microstructures, chemical compositions and concentrations and others. In this study the values of stress intensity factors, T-stress and coefficients of the Williams series expansion are determined using atomistic simulations based on molecular dynamics method with a classical molecular dynamics code Large-scale Atomic/Molecular Massively Parallel Simulator. The over-deterministic method is used to determine SIFs, T-stresses and coefficients of higher-order terms from molecular dynamics modelling of a plate with a central crack. The accuracy of the proposed approach is tested for this rather simple cracked configuration. There is the theoretical analytical solution with all the coefficients of the higher-order terms in the Williams series expansion. The existing theoretical solution allows us to compare the angular distributions of the stress tensor components for a large plane with the central crack. It is shown that results obtained from molecular dynamics simulations and the theoretical analytical solutions coincide qualitatively.

Theory and experiment on true mode [formula omitted] fracturing of rocks

This paper discusses the use of the double-edge notched Brazilian disk test (DNBD) for measuring true mode II fracture toughness of rocks. The term true emphasises that in this test, not only is the crack tip loading shear-based, but also the material failure is shear-induced. Conventional mode II tests typically experience dominantly tensile failure. We introduce a fracture growth criterion that explains where and how a shear-based fracture extension occurs. Our theoretical analysis demonstrates that large values of compressive T-stress in the DNBD specimen significantly help inducing a true mode II fracturing. Crack tip parameters are computed by finite element analyses for various notch lengths and loading angles. These values are then employed to determine the geometry and loading condition for the optimal performance of the test. We also compare the DNBD with two other available tests for measuring true mode II fracture toughness, and show that the DNBD test typically has a lower contribution of mode I loading than the two alternative approaches and, therefore, better approximates the true mode II condition while at the same time being the experimentally simplest. Three types of rocks (limestone, marble and granite) were tested using the new approach and their true mode II fracture toughness is reported for two different crack lengths. The measured true mode II fracture toughness is compared with the mode I fracture toughness obtained from the semi-circular bending test.

Fracture path of cracks emigrating from two circular holes under blasting load

In rock excavating and mining, blasting a row of circular holes is a common practice. It is often observed that cracks emanating from two adjacent holes tend to avoid each other when closely approached and form a hooked or butterfly-shaped loops. Five crack models were designed in this paper to study the propensity of forming the hook pattern. The five models are to simulate geometric imperfection in the field or laboratory for the two borehole case. Using the T-stress at the crack tip, the incremental crack growth method is adopted to simulate the crack propagation paths. The results showed that: (1) the T-stress values calculated from the first two models are negative, indicating curving (or hooking) cannot occur, (2) the T-stress at the crack tip is positive in the third model, and therefore crack curving (or hooking) may occur, (3) unlike the first three models, the fourth and fifth models are mixed mode I/II crack geometries and the mode II stress intensity factor dictates the crack curving direction, (4) the hook pattern would indeed happen under certain conditions.

Evaluation of the SIF and T-stress values of the Brazilian disc with a central notch by hybrid method

The near-crack-tip displacement field of a Brazilian disc with a central notch (BDCN) under mixed mode I/II conditions was measured via digital image correlation (DIC) and the stress intensity factor (SIF) was estimated using a hybrid method that allowed the fitting of the experimental data into the Williams series expansion. The effects of higher-order terms in the Williams expansion (T-stress) were analysed for different sizes of the crack tip fitting region and the results were compared with analytical predictions as well as with results obtained based on the numerically calculated crack-tip displacement field.

T-Stress on a cruciform specimen: A preliminary study for a new crack propagation model

Mixed mode fatigue crack growth (FCG) can occur due to complex loading or specimen geometry. Fatigue crack paths can be determined using propagation criteria like the Maximum Tangential Stress (MTS) criterion, or the Maximum Shear Stress (MSS) criterion, for mode I and II dominated propagation respectively. These criteria only consider mode I and II Stress Intensity Factors (SIF), neglecting the T-Stress effects. In order to develop a new fatigue crack propagation model, that takes this fracture mechanics parameter into account, T-Stress values on a cruciform specimen were calculated for different loading conditions. Using a previously developed Finite Element Analysis (FEA) automatic propagation algorithm, cracks with two different initial orientations, were allowed to grow under different biaxial loading ratios and phases. Also, two holes were simulated on the specimen, in order to assess their influence on FCG. The resulting T-Stress values were determined as a function of the loading conditions and compared with the crack paths. It was possible to correlate the T-stress values with crack propagation direction stability and loading parameters, enabling the future development of a new crack propagation model, considering the influence of this fracture mechanics parameter.

The T-stress influence on the plastic zone size around the crack tip under the thermal load

A review of the fracture mechanics problems for estimating the safety of constructions with the crack-like defects is carried out. The need to develop a new methodology that combines the advantages of calculation and instrumental methods was revealed. The correlations between the most important fracture mechanics parameters and the characteristics of acoustic-emission signals proposed to use for estimating the parameters of stress-strain state. It is noted that considerable attention should be paid to the size and shape of the plastic zone in order to establish a theoretical relationship between the characteristics of acoustic signals and the fracture mechanics parameters. It is assumed that T-stresses are the cause of differences in the coefficients of the power dependence of the parameters of acoustic signals for the same values of the stress intensity factor. The task of finding the influence of T-stresses on the size of the plastic zone at the crack tip is set. A numerical modeling of thermal loading of a steel sheet with a central crack by the finite element method is carried out in order to determine the dependence of the crack tip plastic zone size on the stress intensity factor for several values of T-stress. Multiple calculations of the stress intensity factor and the T-stresses were performed for the several values of the cooling zone, using the parametric design language ANSYS APDL. By substituting the yield point of the material into the equations of linear elastic fracture mechanics, the specific volume and linear plastic zone size along the crack line were determined for the previously found values of the stress intensity factor and T-stress. A relationship between the fracture mechanics parameters and the plastic zone size at the crack tip was established using numerical methods. The assumptions that the T-stress influence to the plastic zone size are qualitatively confirmed. It is shown, that the negative values of T-stresses decrease the plastic zone size for a same value of the stress intensity factor.

Corrosion effect, constraint and path orientation estimated in cracked gas turbine blade

The severe damage of gas turbine is due to the failure of the blade, in which the occurrence of a serious pitting occurred on the blade surfaces was evidence of fatigue marks in the fracture surface. This paper deals with the effect of semi-elliptical crack propagation on the crack path using a basic approach in predicting crack paths, namely, incremental methods. The crack position was chosen at the node coordinate where we have the maximum principal stresses. In this node, we have created a semi-elliptical crack and we have compared the results with the Stress Intensity Factors and T-stress values. The local fracture criterion of the maximum average tangential stress in the vicinity of fracture process zone including two terms of the Williams series solution for the mixed mode I/II loading has been used for predicting the angle of surface crack growth. The volumetric method (VM) for the compression-sensitive materials is described by a linear combination of the effective stress and the effective stress intensity factor. The results of our finite element computations based on a two-parameter fracture mechanics formulation showed that the T-stress has significant effects on the crack path.

DETERMINATION OF THE WILLIAMS SERIES EXPANSION’S COEFFICIENTS USING DIGITAL PHOTOELASTICITY METHOD AND FINITE ELEMENT METHOD

In the present work, photoelastic and finite element methods have been employed to study the near crack tip fields in isotropic linear elastic cracked bodies under mixed mode loading. The investigated fracture results have been obtained for a series of cracked specimens by testing plates with two parallel cracks, two inclined parallel cracks, three-point bend specimens, four-point bend specimens, inclined edge crack triangular shape specimens subjected to symmetric three point bend loading. The multi-parameter Williams series expansion is used for the crack tip field characterization. Digital photoelasticity method is utilized for determination of the Williams series expansions coefficients. The unknown coefficients in the multi-parameter equation are determined using a linear least squares method in an over-deterministic manner. Together with the experimental determination of the fracture mechanics parameters finite element method is invoked to describe the crack tip stress field. Coefficients of higher order terms are either found numerically by finite element method. A good agreement is found between the numerical and experimental results. The significant advantages using multi-parameter equations in the analysis of the stress field are shown and the errors that a study with a limited number of terms produce is demonstrated. The comparison with finite element analysis highlighted the importance and precision of the photoelastic observation for the evaluation of the fracture mechanics parameters. The experimental SIF, T-stress values and coefficients of higher-order terms estimated using the digital photoelasticity method for the extensive series of cracked specimens are compared with finite element analysis (FEA) results, and are found to be in good agreement.

The dependence of the crack growth trajectory on the parameters of the crack tip stress field

The significant influence of non-singular terms of stress expansion (T-stress) on the stress-strain state at the crack tip is shown. Proposed to take into account the constant values of T-stress and other higher order members of stress expansion by representing as a single function of the angular distribution of T-stress. For a disk sample with a central crack, the crack growth direction was calculated for different parameters of mixed loading. The experimental results for predicting of crack growth direction, theoretical results on the well-known maximum tangential stress criterion, results using stress averaging in the pre-fracture zone, and the results of the proposed criterion are presented. It is shown that the results of theoretical calculations according to the proposed criterion are closest to the experimental results compared with the well-known tangential stress criterion.

The effect of low-cycle fatigue on evolution of fracture mechanics parameters in residual stress field caused by cold hole expansion

Localized displacement measurements based on electronic speckle-pattern interferometry are used to obtain crack mouth opening displacement (CMOD), stress intensity factor (SIF) and T-stress values during crack growth around cold-expanded holes. The specimens with a central open hole are made from 2024 aluminium alloy. The expansion level is 5% of nominal interference. The results are obtained for the same stress range   = 350 MPa, but different stress ratio R = –0.4 and R = –1.0. A sequence of narrow notches, inserted under the constant external load, serves for crack modelling at different stages of cyclic loading. Initial experimental data represent in-plane displacement component values measured in the vicinity of the crack tip. The transition from in-plane displacement components to SIF and T-stress values follows from the relationships of modified version of the crack compliance method. The crack length curves of CMOD, SIF and T-stress profiles are obtained for different stages of cyclic loading. These data provide the construction of dependencies of fracture mechanics parameters for cracks of fixed lengths from the loading cycle number.

Evolution of fracture mechanics parameters for cracks in residual stress fields

The paper is devoted to determination of crack mouth opening displacements (CMOD), stress intensity factors (SIF) and T-stresses for cracks emanating from cold expanded holes and welds at different stages of cyclic loading. Rectangular plates made from aluminum alloys are the objects of present investigation. A sequence of narrow notches, which are performed under the constant external load, is used for crack modelling. The experimental approach employs optical interferometric measurements of local deformation response to small notch length increment. Initial experimental data represent in-plane displacement component values measured by electronic speckle-pattern interferometry in the vicinity of the crack tip. Thus, the CMOD values are derived directly. The transition from measured in-plane displacement components to required SIF and T-stress values follows from the relationships of modified version of the crack compliance method. Experimental results are obtained for uniaxial tension-compression loading of specimens with the force direction is perpendicular to the crack line. Experimental data provide constructing the dependencies of fracture mechanics parameters for cracks of fixed lengths from a loading cycle number, which are of great interest to estimate residual stress effect on fatigue crack growth.

Growth of 3D edge cracks in mode I and T-stress on the atomistic level

We present results of 3D molecular dynamic (MD) simulations accompanied by stress calculations on the atomistic level in 3D bcc iron crystals with edge cracks (1¯10)[110]. Two different crack lengths in samples of SEN type loaded uniaxially in mode I were treated with negative and positive values of T-stress according to the continuum prediction by Fett for constant stress boundary condition. Atomistic results are compared with continuum predictions, including influence of T-stress on the ductile-brittle behavior of cracks.

Combining the crack compliance method and speckle interferometry data for determination of stress intensity factors and T-stresses

An advanced experimental technique for determination of the stress intensity factor (SIF) and the T-stress is developed and carefully verified. The approach employs optical interferometric measurements of local deformation response to small crack length increment. Narrow notches are used for crack modeling. Initial experimental data represent in-plane displacement component values measured by electronic speckle-pattern interferometry in the vicinity of the crack tip. Determination of the first four coefficients of Williams’ series is the main feature of the developed technique. Relationships for transition from measured in-plane displacement components to required fracture mechanics parameters are presented. Availability of high-quality interference fringe patterns, which are free from rigid-body motion, serves as a reliable indicator of real strain state near the crack tip. Experimental verification of the proposed method is performed for non-symmetrical and symmetrical crack in thin rectangular plates subjected to uniaxial tension. The distributions of SIF and T-stress values for cracks of different length in residual stress fields near electronically welded joints of thin plates are presented as an example of practical implementing.

The Influence of Specimen Type on Tensile Fracture Toughness of Rock Materials

Up to now, several methods have been proposed to determine the mode I fracture toughness of rocks. In this research, different cylindrical and disc shape samples, namely: chevron bend (CB), short rod (SR), cracked chevron notched Brazilian disc (CCNBD), and semi-circular bend (SCB) specimens were considered for investigating mode I fracture behavior of a marble rock. It is shown experimentally that the fracture toughness values of the tested rock material obtained from different test specimens are not consistent. Indeed, depending on the geometry and loading type of the specimen, noticeable discrepancies can be observed for the fracture toughness of a same rock material. The difference between the experimental mode I fracture resistance results is related to the magnitude and sign of T-stress that is dependent on the geometry and loading configuration of the specimen. For the chevron-notched samples, the critical value of T-stress corresponding to the critical crack length was determined using the finite element method. The CCNBD and SR specimens had the most negative and positive T-stress values, respectively. The dependency of mode I fracture resistance to the T-stress was shown using the extended maximum tangential strain (EMTSN) criterion and the obtained experimental rock fracture toughness data were predicted successfully with this criterion.

Sample Geometry and the Brittle-Ductile Behavior of Edge Cracks in 3D Atomistic Simulations by Molecular Dynamics

We present new results of molecular dynamic (MD) simulations in 3D bcc iron crystals with edge cracks (001)[010] and (-110)[110] loaded in mode I. Different sample geometries of SEN type were tested with negative and positive values of T-stress according to continuum prediction by Fett.