Effect Of T-stress Research Articles

Ductile crack growth behaviors at different locations of a weld joint for an X80 pipeline steel: A numerical investigation using GTN models

The finite element method (FEM) based on the Gurson–Tvergaard–Needleman (GTN) model was used to investigate the ductile crack growth behaviors at different weld joint locations of X80 pipeline steel. As the result of the welding process, the X80 weld joints are inhomogeneous and can be divided into different zones (base metal, weld metal and heat affected zones), with different material properties and ductile crack growth resistance characteristics. By fitting the experimental results of uniaxial tension and single-edge notched bending (SENB) tests for specific zones, the GTN model parameters were calibrated in consideration of the inhomogeneity of the weld joint. The calibrated GTN models were then used to analyze the ductile crack growth behaviors in single-edge notched tension (SENT) tests at different locations of the weld joint. In addition, the effect of T-stress on the crack propagation at different locations was also studied using the small-scale yield model. It is demonstrated the calibrated GTN models are capable of predicting crack growth resistance curves at different weld joint locations, under different constraint conditions.

Effects of T-Stress on Fracture Behavior of Central-Cracked Stiffened Plate

Traditionally, the stress intensity factor (SIF) is solely focused on in the fracture analyses of stiffened plate, while the T-stress is usually ignored. However, the fracture toughness is influenced by T-stress and the effects need to be studied. By means of three-dimensional finite element method, the characteristics of mode I SIF and in-plane T-stress are investigated in the double symmetrical central stiffened plate (DSC-SP). Then the fracture toughness is corrected with in-plane T-stress based on the two-parameter model in the R6 assessment procedure. Lastly, the curves of corrected fracture toughness and crack arrest effect are obtained in the stiffened plate. The results show that the T-stress is dependent on the size and integrity of the stiffener, and has significant effects on the fracture toughness of stiffened plate. Compared with the traditional estimation of the crack arrest effect of the stiffener, the evaluation is more reasonable when the influences of in-plane T-stress are taken into account.

Experimental Study on Mixed Mode Fracture Behavior of Sandstone under Water–Rock Interactions

Water–rock interactions can significantly deteriorate the physical and mechanical properties of rocks, and it has been identified as one of the significant factors influencing the stability and safety of structures in rock–soil engineering. In this study, the fracture mechanical properties of sandstone under periodic water–rock interactions and long-term immersion have been studied with central cracked Brazilian disk specimens. The degradation mechanism of water–rock interactions was also studied using a scanning electron microscope (SEM). Finally, the generalized maximum tangential stress and generalized maximum tangential strain criteria were adopted to evaluate the experimental results. The results show that periodic water–rock interactions can remarkably affect the fracture resistance of sandstone. With the increase in the number of cycles, the pure mode I, pure mode II, and mixed mode fracture toughness decreases greatly, however, the values of KIf/KIC and KIIf/KIC decrease slightly. Furthermore, the fracture resistance of sandstone influenced by cyclic wetting–drying is more significant than long-term immersion. Moreover, the fracture criteria, which considers the effect of T-stress, can reproduce the test results very well.

Mixed mode I/II fracture criterion for arbitrary cracks in orthotropic materials considering T-stress effects

General and extended minimum strain energy density criterion for orthotropic materials with unidirectional fibers is employed to anticipate the onset of crack growth. It is postulated that the crack is embedded in the material in an arbitrary orientation with respect to fibers. As crack growth occurs in the isotropic matrix, isotropic stress state is used in the proposed criterion. Crack tip stress state of the isotropic matrix is related to composite one by definition of Reduced Stress (ReSt) coefficients. Since in the case of arbitrary crack-fiber angle, the effect of nonsingular term is significant on crack growth, T-stress term is considered in the calculations. Furthermore, a new concept of critical stress intensity factor is defined and formulated for arbitrary inclination cracks with respect to the fibers. Finally, a test procedure is presented to validate the proposed mixed mode I/II fracture criterion. Test results display excellent consistency with new criterion’s fracture limit curve.

Atomistic investigation of the T-stress effect on fracture toughness of copper and aluminum single crystals

The T-stress effect on the fracture toughness of Cu and Al single crystals with the (010)[001] crack system was investigated based on atomistic simulations. The interatomic potential function of the embedded-atom method was used to model the face-centered cubic structures. A molecular statics approach using the conjugate gradient algorithm was employed to simulate mode-I fracture testing, and a K-field displacement with various magnitudes of T-stress was applied to load the simulation system. The critical energy release rates were calculated based on the global energy balance to evaluate fracture toughness, and the results were compared with asymptotic solutions obtained from conventional linear elastic fracture mechanics. The obtained values of fracture toughness exhibit a strong T-stress dependence for both the Cu and Al single crystals. Furthermore, the crack growth behavior is explained from an atomistic view of fracturing to analyze the T-stress effect on crack growth resistance.

Experimental investigation of the effects of supercritical carbon dioxide on fracture toughness of bituminous coals

Effects of supercritical carbon dioxide (scCO2) on fracture toughness of bituminous coals are studied. The semi-circular specimens under three-point bending (SCB) were adopted for conducting experiments on the coal samples after being immersed in scCO2 for different soaking periods. To investigate the fracture toughness in different loading conditions, including pure mode I, pure mode II, and mixed mode I/II, the inclination angles of the prefabricated cracks in the coal SCB samples were set as 0°, 5°, 15°, 30°, 45° and 54°, respectively. The experimental results show that after being soaked in scCO2 for 7 days, 14 days and 21 days, the pure mode I fracture toughness of the coals reduced by up to 30.8%, 69.2% and 82.1%, respectively, and the mode II fracture toughness 29.1%, 66.7% and 79.9%, respectively. The fracture toughness in pure mode I loading is more sensitive to the effect of scCO2 than that in pure mode II loading. The values of the effective fracture toughness Keff in mixed mode I/II loading also declined due to the effect of scCO2, and the samples with different crack inclination angles exhibited no obvious differences in the degradation degrees of Keff. With increasing soaking time, the compaction stage extended, and the slope of the load–displacement curve in the elastic stage decreased significantly. The microcracks on the surface of the coal SCB specimens gradually increased with the soaking time increasing. In addition to causing the reduction of surface energy and swelling of coals, scCO2 mobilizes organic molecules from coals, leading to the modification of the physical structure of the coal matrix and the degradation of fracture toughness in various loading modes. Based on the modified maximum tangential stress (MMTS) criterion, which takes into account the effects of T-stress, the theoretical values are in better agreement with experimental results compared with the traditional maximum tangential stress (MTS) criterion.

Simulation of ductile fracture in pipeline steels under varying constraint conditions using cohesive zone modeling

In this study, the effect of non-singular T-stress (a measure of crack tip constraint) on crack growth resistance curves (R-curves) and crack tip opening angle (CTOA) was investigated. The investigation proceeded in two parts; first using a modified boundary layer (MBL) model to systematically assess the effect of T-stress on the R-curves and CTOA, and second comparing the CTOA under different loading modes, namely, bending and tension. Three steels were examined in this work; the first was a typical high strength steel referred to as TH, the second and third were pipeline steels referred to as X70 and X100. Surface-based cohesive zone models with four sets of bilinear traction-separation (TS) laws were used for TH steel. The models of X70 and X100 were computed using element-based cohesive zone modeling with a trapezoidal TS law. All simulations were conducted using the finite element (FE) program ABAQUS. It was assumed in these simulations that there was no effect of T-stress on the TS laws per se. With this assumption, it was found that the T-stress and loading mode have only a small effect (1–2°) on the CTOA for the materials studied.

Numerical simulation of the interaction between a crack and an inclusion

PurposeThe purpose of this paper is to propose the interaction integral method combing with a XFEM-based local mesh replacement method to evaluate both the stress intensity factors (SIFs) and T-stress at the crack tip near a circular inclusion.Design/methodology/approachSpecial attention is pay to the effect of T-stress on crack initiation angle in 2D composite medium. The generalized maximum tangential stress criterion is employed during the simulation which simultaneously involves the effects of the mixed-mode SIFs, the T-stress and a physical length scale rc (the size of the fracture process zone).FindingsIt is shown that T-stress could affect the crack initiation angle significantly for mixed-mode conditions. Varies types of material mismatch are also considered and their influences on T-stress are given quantitatively.Originality/valueThe proposed numerical method allows a considerable flexibility for such problems and provides a basic framework for quasi-static crack growth in materials containing complex interfaces.

Crack path stability in brittle fracture under pure mode I loading

The crack growth path is expected to be along the initial crack line when the pre-cracked components possess symmetric geometry and loading conditions relative to the crack line. However, it has been previously shown that in some mode I specimens the path of crack growth is not stable and deviates from its initial line after some stages of crack growth. The aim of this paper is to develop an energy-based theoretical model for predicting the instability in the path of crack growth. The theoretical model takes into account both the singular term of stress ahead of the crack tip and the first non-singular term known as the T-stress. The corresponding two-term stresses are replaced in the energy relation around the crack tip and a model is extracted for predicting instability of crack path under mode I loading. The results obtained from the energy-based criterion was then compared to the results obtained from the well-known Generalized Maximum Tangential Stress (GMTS) criterion, which is a two-parameter stress-based fracture criterion that considers the effect of T-stress. To validate the theoretical model, the experimental results published recently from fracture test on several mode I cracked specimens are used. Very good prediction is provided for the path of crack growth in these specimens. It is shown the crack path instability is significantly geometry dependent and can be prevented by modifying the specimen geometry or loading type. The results obtained in this research are important because an appropriate knowledge about the stability of crack path and fracture trajectory can play a key role on the extent of damage that occurs in a cracked structure when it experiences mode I brittle fracture.

T-stress effects on fatigue crack growth – Theory and experiment

The effects of specimen geometry on the fatigue crack growth rate and the number of elapsed cycles have been investigated experimentally and theoretically for Al 7075-T6 using four different cracked specimens with positive and negative T-stresses. All the specimens have been tested under high cycle fatigue loading. An energy-based method, namely the generalized strain energy density (GSED) criterion has been proposed to estimate the fatigue crack growth rate and the number of elapsed cycles by considering the T-stress effects. It is shown that the proposed criterion can provide significantly improved predictions for the fatigue crack growth behavior of the pre-cracked specimens.

Effect of T-stress on the initial fracture toughness of concrete under I/II mixed-mode loading

The mixed-mode stress intensity factors (SIFs) and T-stress for different geometries of four-point bending specimens were calculated by means of finite element analysis through a software suite Abaqus, where the influence of the crack length, loading point and crack location were considered. Thereafter, a series of four-point bending tests were re-interpreted to account for the consequences of the T-stress on the initial fracture of concrete, where a generalized maximum tangential stress (MTS) criterion was employed. The results indicate that the inclusion of T-stress is essential to predict a more realistic initial fracture toughness of concrete subjected to mixed-mode I/II loading.

Fracture prediction of rocks under mode I and mode II loading using the generalized maximum tangential strain criterion

The effects of specimen geometry on mode I and mode II fracture toughness (i.e., KIc and KIIc), and the ratio of KIIc to KIc for a given rock material were derived on the basis of a generalized maximum tangential strain (GMTSN) fracture criterion, in which the effects of T-stress and radial stress on rock fracturing can be taken into consideration. To verify these theoretical predictions, laboratory tests using semi-circular bend (SCB) and center-cracked circular disc (CCCD) specimens were conducted. Experimental results indicate that the GMTSN criterion is capable of estimating the geometry dependence of KIc and KIIc, the ratio of KIIc to KIc and the fracture initiation angle of rocks. Moreover, the GMTSN criterion can provide better estimates for the experimental results than some other frequently-used fracture criteria. In addition, our study reveals that the SCB fracture test using asymmetric bottom supports can be identified as a suitable testing method to estimate the upper bound of mode II fracture resistance.

Rock Fracture Toughness Under Mode II Loading: A Theoretical Model Based on Local Strain Energy Density

The values of mode II fracture toughness reported in the literature for several rocks are studied theoretically by using a modified criterion based on strain energy density averaged over a control volume around the crack tip. The modified criterion takes into account the effect of T-stress in addition to the singular terms of stresses/strains. The experimental results are related to mode II fracture tests performed on the semicircular bend and Brazilian disk specimens. There are good agreements between theoretical predictions using the generalized averaged strain energy density criterion and the experimental results. The theoretical results reveal that the value of mode II fracture toughness is affected by the size of control volume around the crack tip and also the magnitude and sign of T-stress.

Mixed mode fracture analysis using generalized averaged strain energy density criterion for linear elastic materials

A modified energy-based model called the generalized averaged strain energy density (ASED) criterion is proposed to predict the mixed mode I/II fracture resistance of brittle and quasi-brittle materials. The proposed criterion takes into account the effect of T-stress in addition to the stress intensity factors KI and KII when calculating the strain energy density averaged in a control volume around the crack tip. The effect of T-stress on the mixed mode fracture resistance of materials is investigated by using the generalized ASED criterion and the generalized SED criterion. The results predicted by these criteria are compared with the experimental results reported in the literature from fracture tests conducted on the Brazilian disc specimens and the semi-circular bend specimens made of Harsin marble and Guiting limestone. It is shown that the theoretical estimates of the generalized ASED criterion are consistent very well with the experimental results. The theoretical results also show that the specimens having a negative T-stress require higher loads in order their averaged strain energy density around the crack tip attains its critical value.

Mode II brittle fracture assessment using an energy based criterion

In this paper the minimum strain energy density criterion is modified to predict the values of mode II fracture toughness reported in the literature for several brittle and quasi-brittle materials. The experimental results are all related to mode II fracture tests performed on the semicircular bend specimen. The modified mode II fracture criterion takes into account the effect of T-stress (in addition to the singular terms of stresses/strains) when calculating the strain energy density factor at a very small critical distance from the crack tip. It is shown that the proposed criterion provides significantly better predictions for mode II fracture toughness compared with the classical minimum strain energy density criterion.

The T-stress effect on the plastic zone size in a thin ductile material layer sandwiched between two elastic adherents

This paper investigates the crack tip plastic zone in a thin ductile layer sandwiched between two identical perfectly elastic adherents subjected to normal loading. The well-known Varias et al. model for calculation of the plastic zone length in a thin constrained elastic-plastic layer was extended by the second nonsingular term of the Williams expansion. A useful engineering formula for the length of the plastic zone has been deduced, where the mechanical properties of the substrates and the layer material as well as T-stress value are included. The proposed theoretical model was verified on the basis of numerical FEM calculations. The results obtained by the model are in good agreement with numerical data.

T -stress effects on crack deflection: Straight vs. curved crack advance

Abstract T-stress effects on crack deflection in notched brittle materials are investigated by means of an average stress approach. It is shown that the crack advance always reveals to be straight if the T contribution is negligible. On the contrary, if T is different from zero, the trajectory tends to curve: the higher is |T|, the larger is the curvature parameter, its value being either positive or negative depending on the sign of T. Analogies and differences with respect to straight crack propagation are quantified in terms of the fracture loci and of the critical kinking angle. The investigation on the stability of crack deflection under mode I loading conditions concludes the paper, together with a discussion on experimental observations.

Modified maximum tangential stress criterion for fracture behavior of zirconia/veneer interfaces

The veneering porcelain sintered on zirconia is widely used in dental prostheses, but repeated mechanical loadings may cause a fracture such as edge chipping or delamination. In order to predict the crack initiation angle and fracture toughness of zirconia/veneer bi-layered components subjected to mixed mode loadings, the accuracy of a new and traditional fracture criteria are investigated. A modified maximum tangential stress criterion considering the effect of T-stress and critical distance theory is introduced, and compared to three traditional fracture criteria. Comparisons to the recently published fracture test data show that the traditional fracture criteria are not able to properly predict the fracture initiation conditions in zirconia/veneer bi-material joints. The modified maximum tangential stress criterion provides more accurate predictions of the experimental results than the traditional fracture criteria.

Finite Fracture Mechanics: a deeper investigation on negative T-stress effects

In the present work, the coupled stress and energy criterion of Finite Fracture Mechanics (FFM) is applied to investigate negative T-stress effects related to mixed-mode brittle fracture of cracked elements. Only two material parameters are involved in the analysis, the tensile strength and the fracture toughness, which are independent of the mode-mixity. Below a critical T-value, the shear contribution to the strain energy release rate (ERR) starts to prevail in the mode II-dominated zone. This affects FFM results in terms of: (1) the fracture loci, with the critical mode II-stress intensity factor (SIF) never exceeding the fracture toughness; (2) the critical kinking angle and the actual crack advance (which results to be a structural parameter), both decreasing to infinitesimal quantities as mode II-loading conditions are approached. These predictions can be revised by considering a large amount of energy dissipated under mode II loading conditions and by assuming a mode-mixity dependent ERR. A discussion on experimental data for brittle and quasi-brittle materials available in the literature is included.

Effect of initial T-stress on stress intensity factor for a crack in a thin pre-stressed layer

Fracture of a pre-stressed thin elastic layer is studied and modelled as bending of double clamped beams with axial force. Using the beam theory, the strain energy in bending state of the beam with an axial force is derived. Explicit expressions for energy release rate and stress intensity factor (SIF) for a crack with initial transverse stress (T-stress) are obtained. Results show that tensile (compressive) initial T-stress decreases (increases) the SIF and impedes (promotes) crack growth. The influence of compressive initial stress is greater than that of tensile initial stress in the same magnitude.