Generalized Maximum Tangential Stress Criterion Research Articles

Modified Generalized Maximum Tangential Stress Criterion for Simulation of Crack Propagation and Its Application in Discontinuous Deformation Analysis

This work modified the generalized maximum tangential stress (MTS) criterion by taking parallel and perpendicular nonsingular stresses, i.e., Tx and Ty, into account. When applied to the traditional discontinuous deformation analysis (DDA) procedure, the modified generalized MTS criterion was influential in simulating open crack propagation and modeling closed crack propagation. The generalized J integrals (J1 and J2 integrals) were used to calculate the stress intensity factors (SIFs) and the T-stresses, the basic parameters of the modified generalized MTS criterion. The open crack models, namely the center cracked circular disc (CCCD) model and the edge cracked semicircular bend (SCB) model, were simulated by the DDA method with the modified generalized MTS criterion. Moreover, the closed crack models dealing with the specimens with a center crack subjected to compression stress were simulated. The simulation results of the open and closed crack models were all in good agreement with the experimental data.

Geometry Effects on Mode I Brittle Fracture in VO-Notched PMMA Specimens.

This paper gathers experimental and theoretical investigations about both the geometry-dependent fracture initiation angle and the fracture strength in VO-notched polymethyl methacrylate (PMMA) specimens under mode I loading conditions. The numerical analyses revealed that despite the application of pure mode I loading on the geometrically symmetric VO-notched samples, the maximum tangential stress occurs at two points symmetrically placed on either side of the notch bisector line. The experimental tests performed on some specimens showed that a crack does not necessarily propagate along the notch bisector line. Stress-based theoretical studies were then carried out to justify the experimental findings. The conventional maximum tangential stress (MTS) criterion gave weak predictions of the fracture. Therefore, the predictions were checked with the generalized MTS (GMTS) criterion by taking into consideration the higher-order stress terms. It was demonstrated that the GMTS criterion predictions have satisfactory consistency with the experimental results of the crack initiation angle and the fracture strength.

Loading rate effect on mixed mode I/II brittle fracture behavior of PMMA using inclined cracked SBB specimen

This paper investigates the effect of loading rate on the mixed-mode I/II fracture behavior of PolymethylMethacrylate (PMMA). Experimental studies are performed using a novel fracture test specimen which has recently been developed, called short bend beam (SBB), in different loading rates of 1 mm/min, 20 mm/min, and 200 mm/min. Fracture test data are presented for pure mode I, pure mode II, and mixed-mode I/II conditions, thanks to the geometrical configuration offered by the specimen covering a full spectrum of mode mixities. Two fracture criteria including maximum tangential stress (MTS), and generalized maximum tangential stress (GMTS) are employed to predict the onset of fracture and the fracture initiation angle in different loading rates. The MTS criterion only considers the singular crack tip terms associated with the stress intensity factors (SIFs) in the solution while the GMTS includes the T-stress effect as well as the SIF-related terms. While enhanced predictions provided by the GMTS criterion, as compared to MTS results, reveals the significance of including the T-stress term in the theoretical calculations, the critical distance (rc) is also found as another major parameter playing an important role in the fracture behavior. It is shown that the size of rc decreases by increasing the loading rate. Therefore, for the first time, a variable and loading rate dependent rc value is utilized for employment of the GMTS criterion and it is demonstrated that considering variable critical distance can provide acceptable theoretical predictions for different loading rates.

Laboratory-scale mixed-mode I/II fracture tests on columnar saline ice

Laboratory-scale experiments on mixed-mode I/II (including pure modes I and II) fracture of non-oriented columnar saline ice were performed. In the experiments, obliquely notched, three-point bending specimens were used, with the load applied in the direction perpendicular to the columnar grains. Tests were performed on dry isothermal (−10 °C) specimens and specimens floating in water and having a temperature gradient (mean temperature: −2.5 °C). The fracture loads and crack initiation angles were analyzed. The apparent mode I, mode II and mixed-mode fracture toughness and the flexural strength of the floating and relatively warm specimens were only about thirty percent of those of the dry and cold specimens. The results showed that the T-stress significantly influenced the mixed-mode I/II fracture of ice; good agreement was found between the experimental results and those predicted using the generalized maximum tangential stress criterion. Both trans- and inter-granular crack growth were observed, regardless of the specimen type or mode of loading.

Geometry effects on mode I brittle fracture in U‐notched specimens

AbstractThe effects of geometrical constraints on the fracture initiation location and the fracture strength are evaluated in U‐notched specimens using theoretical and experimental analyses. It is proven that high geometrical constraints in pure mode I loading of geometrically symmetric U‐notched specimens can result in occurrence of the maximum tangential stress (MTS) at two symmetric points on both sides of the notch bisector line. The experiments also indicated that the fracture takes place from a direction that is not along the notch bisector line. The experimental results are then examined theoretically through a stress‐based brittle fracture criterion. Because the conventional MTS criterion was poor to predict the onset of fracture properly, an attempt is made to use the generalized MTS (GMTS) criterion by considering the higher order terms in the fracture model. It is shown that the GMTS criterion gives very good predictions for experimentally obtained values of crack initiation angle and notch fracture resistance.

Failure prediction of multi-cracked ductile polymeric specimens under mixed mode I/II loading

Elastic-plastic failure of multi-cracked specimens made from epoxy material is studied theoretically and experimentally for the first time under mixed mode I/II loading conditions. Different cracks arrangements are considered for preparing the specimens. For providing different mixed mode I/II loading conditions in the fracture tests on epoxy specimens, different crack inclination angles are considered in the samples. Load-carrying capacities (LCCs) of the multi-cracked specimens are obtained experimentally by performing fracture tests. In order to avoid the complex and time-consuming elastic–plastic failure predictions, the Equivalent Material Concept (EMC) is used in conjunction of the dislocation method and generalized maximum tangential stress criterion to obtain experimental and theoretical fracture parameters. It is demonstrated that the proposed combined approach can provide reliable predictions of fracture toughness and fracture estimation under mixed mode I/II loading.

Fracture loads prediction of the modified 3D-printed ABS specimens under mixed-mode I/II loading

The fracture features of the 3D-printed samples are assessed employing Semi-Circular Bending (SCB) specimens. The critical failure loads are experimentally measured and have been predicted using both Maximum Tangential Stress (MTS) and Generalized Maximum Tangential Stress (GMTS) criteria. The 3D-printing process is improved with several approaches to decline the voids volume and escalate the weld lines strength of the 3D-printed specimens to boost their mechanical specifications. The Acrylonitrile Butadiene Styrene (ABS) SCB samples with numerous pre-crack angles ranged from pure mode I to pure mode II are produced utilizing a modified 3D-printing process. The results of the tensile tests confirmed that the properties of the specimens created by the modified 3D-printing process are independent of the raster of printing orientation. The predicted failure loads with the GMTS criterion had a better correlation with the experiment compared to the MTS criterion owing to the impact of the T-stress term in the 3D-printed SCB samples. Furthermore, the cross laminar fracture augmented fracture toughness and declined crack kinking behavior of the 3D- printed ABS specimens.

Evaluation of Critical Crack Orientations and Crack Growth Analysis in Compressor Blade Root Subjected to Fatigue

Abstract Aero-engine compressor blade and disk assemblies are subjected to radially outward centrifugal force due to blade rotation and the bending of the blade due to gas pressure. Static analysis is done initially to find the critical crack orientation at the root of the blade. With simulated initial cracks, the cracks are allowed to grow in low cycle fatigue (LCF) and isochromatics are captured at selected intervals. Using digital photoelasticity, isochromatic images are used along with an over-deterministic least-squares approach to find the fracture parameters. As the stress fields are very complex, a multiparameter solution with a higher number of parameters was needed to model the stress field. Crack growth angles are evaluated using maximum tangential stress (MTS), strain energy density (SED), and generalized MTS (GMTS) criteria. It is observed that the GMTS criterion predicted closer results to that of experimental values, which implied the significance of T-stress in predicting the crack growth angle.

The influence of natural and synthetic fibers on mixed mode I/II fracture behavior of cement concrete materials

This paper evaluated mixed mode I/II fracture toughness of fiber-reinforced concrete using cracked semi-circular bend (SCB) specimens subjected to three-point bending test. Additionally, a comparison was made between the experimental results and the estimations made by different theoretical criteria. Natural and synthetic fibers at various concentrations were used in this study. After producing cracks in SCB specimens at different inclination angles to induce different mixed mode loading conditions (from pure mode I to II), the fracture toughness of SCB specimens was determined. Furthermore, the compressive, splitting tensile, and flexural strength of natural and synthetic fiber-reinforced concrete were measured after 7 and 28 days of curing. While there is an increase in the aforementioned strengths with fiber content increase, 0.3% was found to be the optimum percentage regarding fracture toughness for both fibers. Also, the comparison between the experimental and theoretical results showed that generalized maximum tangential stress criterion estimated the experimental data satisfactorily.

Numerical Analysis of Crack Initiation Direction in Quasi-brittle Materials: Effect of T-Stress

A two-dimensional finite element analysis was adopted to assess the effect of T-stress on predicting crack initiation angle in a quasi-brittle material. Asymmetric semicircular PMMA specimen containing a vertical edge crack subjected to three-point bending was employed. The specimen was assumed as an isotropic and homogeneous material. Relative crack length ratios of 0.3, 0.4, 0.5, 0.6 and 0.7 were examined. Several relative bottom span ratios were included to develop a wide range of mixed-mode I/II loading conditions. The conventional maximum tangential stress (MTS) criterion could not precisely predict the crack initiation angle through the total range of pure mode I to pure mode II. The generalized maximum tangential stress (GMTS) criterion showed a significant effect of T-stress on the numerical prediction of the crack initiation angles in PMMA specimens. In the present study, neglecting the T-stress in the MTS criterion overestimates the crack initiation angle. The numerical predictions using the GMTS criterion showed a good agreement with the relevant experimental data found in the literature. The ability of GMTS in predicting the crack initiation angle is improved by considering the T-stress.

Using the generalized maximum tangential stress criterion to predict mode II fracture of hot mix asphalt in terms of mode I results – A statistical analysis

Low-temperature cracking of asphalt pavements is among the most important deteriorations in flexible pavements. Different modes of fracture may occur in a pavement depending on the vehicle wheel load position relative to the existing crack. Therefore, it is needed to test the fracture performance of asphaltic materials at different modes, which is time and cost consuming. Therefore, finding a statistical approach to correlate different modes of fracture of asphalt mixtures can be very beneficial. In this research, several semi-circular bending (SCB) specimens were tested under mode I and mode II fracture conditions. Then, the predictability of experimental mode II test results in terms of mode I fracture toughness data was investigated using the generalized maximum tangential stress (GMTS) theory. The Weibull distribution curves were also used for statistical analyses of the test data. It was found that the GMTS criterion successfully predicts the Weibull parameters of mode II results in terms of mode I fracture data.

Maximum tangential stress coupled with probabilistic aspect of fracture toughness of hybrid bio-composite

The statistical aspect of mode I, mode II and mixed mode I/II fracture toughness of epoxy based bio-composite reinforced with 20 wt% walnut shell particle and 10 wt% coconut fiber is studied. The bio-composite is fabricated by the squeeze casting method. A series of fracture tests are conducted on hybrid bio-composite using three point bend, four point bend and semicircular arc bend specimen. The statistical distribution of normalized geometry parameters, T stress, crack tip plastic zone size, particle and fiber size are studied. Generalized maximum tangential stress criterion is modified considering the stochastic nature of the geometry and strength parameters assuming them to follow two parameters Weibull probability distribution. The model developed is applied to the bio-composite and predicted results are compared with the experimental values. Very good agreement is found between the experimental results and predicted results. The variability in the fracture toughness values are correlated with the particle and fiber size determined from scanning electron microscopy.

Mixed-mode fracture of synthesized nanocrystalline forsterite for biomedical applications

Nanocrystalline forsterite is an important biocompatible, nanostructured bioceramic. Various studies have examined essential properties of this biomaterial, including bioactivity, biocompatibility, typical mechanical features, etc. In this research nanocrystalline forsterite powder was produced by the sol–gel method and was characterized via XRD and SEM analysis. By pressurizing the nanopowder under 200 MPa and sintering at 1500 °C, semi-circular bending (SCB) samples were prepared with cracks of different angles. Fracture tests were then performed under mode-I, mode-II and mixed-mode loading in order to investigate the fracture resistance of forsterite. The specimens were all failed in a brittle manner. The results, then, were compared with two common mixed-mode fracture models called maximum tangential stress (MTS) and generalized maximum tangential stress (GMTS). The generalized MTS criterion provided very good estimations for the experimental results.

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.

Investigation on the correlation of mode II fracture toughness of sandstone with tensile strength

A series of tests with centrally cracked Brazilian disc and un-cracked Brazilian disc specimens were conducted to investigate the relation between the mode II fracture toughness KIIC and tensile strength σt of sandstone under different treatment conditions. The results indicated that there was a good linear relation between these two rock parameters. Further, this conclusion was also validated by theoretical analysis based on the generalized maximum tangential stress criterion. Moreover, an empirical formula KIIC=0.2159σt was obtained using linear regression analysis, which can be confidently used to estimate the mode II fracture toughness with tensile strength of rocks.

The stress intensity factor and propagation of an inclined crack in the central layer of a composite laminate under tension

Intra-laminar cracks are usually the initial damage of fibre-reinforced composite laminates. While transverse cracks that are perpendicular to the interfaces in composite laminates are extensively studied, inclined cracks, which may occur in these laminates, are less investigated. In this paper, the stress intensity factor of an inclined crack embedded in the central layer of an angle-ply laminate is solved by the Fourier transform method, and the propagation of the crack is examined based on the generalized maximum tangential stress criterion. It is shown that the ply angle of the outer constraining sublaminates and the crack inclination angle significantly influence the stress intensity factor. The propagation direction of the crack is primarily determined by the inclination angle. Due to the constraining effect, the crack perpendicular to the interfaces does not always correspond to the minimum critical propagation stress; instead, an inclined crack when its tips are close to the interfaces may correspond to a minimum propagation stress for graphite/epoxy laminates. For the glass/epoxy material system, the crack perpendicular to the interfaces is always in the most dangerous state. This work reveals some features of crack propagation in composite laminates that are different from those of a crack in a homogeneous material. The results provide an in-depth understanding and more accurate prediction of the damage process of composite laminates.

The tension-shear fracture behavior of polymeric bone cement modified with hydroxyapatite nano-particles

Polymethylmethacrylate (PMMA)-based bone cement is a well-known polymer in the medicine, especially orthopedic. However it has some drawbacks like lack of enough biocompatibility and poor mechanical properties. These problems can be addressed by incorporation of nano-materials. Hydroxyapatite has been proved to enhance biocompatibility of acrylic bone cements. This bioceramic can affect the mechanical properties of polymeric cements as well. In this study, a number of fracture tests were carried out to investigate the influence of nano-hydroxyapatite (HA) on the fracture behavior of acrylic bone cement under combined tension-shear (mixed mode) loading conditions. Semi-circular specimens were prepared by incorporating different amounts of HA powder into the cement matrix. It was found that adding up to 10wt% HA into the cement causes an increase in the fracture toughness of PMMA/HA nano-composite in all modes. However, pure cement exhibited the greatest fracture resistance among all samples. Moreover, the comparison between the experimental and theoretical results showed that the generalized maximum tangential stress criterion could estimate the experimental data satisfactorily.

Application of quantifier elimination to mixed-mode fracture criteria in crack problems

Several criteria for mixed-mode fracture in crack problems are based on the maximum of a quantity quite frequently related to stress components. This quantity should not reach a critical value. Computationally, this approach requires the use of the first and the second derivatives of the above quantity although frequently the use of the second derivative is omitted because of the necessary complicated computations. Therefore, mathematically, the determination of the maximum of the quantity of interest is not assured when the classical approach is used without the second derivative. Here a completely different and more rigorous approach is proposed. The present approach is based on symbolic computations and makes use of modern quantifier elimination algorithms implemented in the computer algebra system Mathematica. The maximum tangential stress criterion, the generalized maximum tangential stress criterion (with a T-stress term), the T-criterion and the modified maximum energy release rate criterion are used for the illustration of the present new approach in the mode I/II case. Beyond the conditions of fracture initiation, the determination of the fracture angle is also studied. The mode I/III case is also considered in brief. The present approach completely avoids differentiations, similarly the necessity of a distinction between maxima and minima, always leads to a global (absolute) and not to a local (relative) maximum and frequently to closed-form formulae and automatically makes a distinction of cases in the final formula whenever this is necessary. Moreover, its use is easy and direct and the maximum of the quantity of interest is always assured.

Mixed mode fracture analysis of CCBD specimens based on the extended maximum tangential strain criterion

AbstractThe maximum tangential strain (MTSN) criterion has been modified to include the effects of T‐stress and stress intensity factors in conditions of both plane stress and plane strain. Further, both the T‐stress and Poisson's ratio affecting the crack propagation are also discussed according to the extended MTSN (EMTSN) criterion, which is a modified MTSN criterion. Finally, the generalized maximum tangential stress (GMTS) criterion and the EMTSN criterion are used to predict the test results obtained with central cracked Brazilian disc (CCBD) specimens. The results indicate that the T‐stress and Poisson's ratio have a remarkable influence on the mixed mode fracture resistance based on the EMTSN criterion. Theoretical values of both the EMTSN and the GMTS criteria are in very good agreement with the test results. Moreover, the EMTSN criterion provides a better prediction for pure mode II.

Fracture Behavior Investigation of a Typical Sandstone Under Mixed-Mode I/II Loading Using the Notched Deep Beam Bending Method

The brittle fracture behavior of rocks under mixed-mode loading is important in rock engineering. First, a new configuration called the notched deep beam (NDB) specimen was introduced for the fracture testing of rock materials under mixed-mode I/II loading, and a series of finite element analyses were performed to calibrate the dimensionless fracture parameters (i.e., Y I, Y II and $$T^{*}$$ ). The results showed that an NDB specimen subjected to three-point bending is able to generate pure mode I loading, pure mode II loading, and any mixed-mode loading in between. Then, several NDB specimens made of sandstone were used to investigate the brittle fracture behavior of rock under mixed-mode I/II loading. The fracture surfaces were theoretically described using a statistical method, and the results indicated that all the fracture surfaces generated under different mixed-mode loading were statistically identical; to some extent, these results experimentally showed that only tensile fracture occurs under mixed-mode I/II loading. The obtained fracture strengths were then analyzed using several brittle fracture criteria. The empirical criterion, maximum energy release rate criterion, generalized maximum tangential stress (GMTS) criterion, and improved R-criterion accurately predicted the fracture strength envelope of the sandstone. Finally, based on the concepts of point stress and mean stress, the micro-crack zones (MCZs) under different mixed-mode loading were theoretically estimated based on the MTS and GMTS criteria. The critical radius of MCZ in the crack propagation direction was not a constant for all mixed-mode loading conditions regardless of whether the T-stress was considered. This result suggests that the size of the core region used to predict the crack initiation direction and fracture strength based on the GMTS criterion should be chosen more carefully.