Generalized Maximum Tangential Stress Criterion Research Articles

Experimental and theoretical investigation of the influence of post-curing on mixed mode fracture properties of 3d-printed polymer samples

This study explores the mechanical properties and fracture characteristics of additively manufactured acrylonitrile butadiene styrene specimens, focusing on the impact of raster angle and post-process heat treatment. To this end, a large number of tensile and semi-circular bending samples with three distinct raster angles of 0/90°, 22/ − 68°, and 45/ − 45° were prepared and exposed to four types of heat treatments with different temperature and pressure conditions. Simultaneously, theoretical models of maximum tangential stress (MTS) and generalized MTS (GMTS) were developed to estimate the onset of specimen fracture under mixed-mode in-plane loading conditions. Recognizing the non-linear behavior within the stress–strain curve of tensile test samples, particularly in the annealed samples, an effort was undertaken to transform the original ductile material into a virtual brittle material through the application of the equivalent material concept (EMC). This approach serves the dual purpose of bypassing intricate and tedious elastoplastic analysis, while concurrently enhancing the precision of the GMTS criterion. The experimental findings have revealed that while the annealing process has a minimal effect on the yield strength, it considerably enhances energy absorption capacity, increases fracture toughness, and reduces the anisotropy. Additionally, the combined EMC-GMTS criterion has demonstrated its capability to predict the failure of the additively manufactured parts with an acceptable level of accuracy.

Influence of coupled water and thermal treatments on the fracture characteristics of a typical sandstone

Understanding the fracture behavior of rock after coupled water and thermal environment is important for many geotechnical projects. This study examines the influence of coupled water and thermal treatments on the fracture toughness and characteristics of a typical sandstone under mode I and mode II loading conditions. Notched deep beam (NDB) specimens were utilized and subjected to soaking treatments at various water temperatures (23 °C, 60 °C, and 99 °C). The experimental results indicate a significant reduction in both mode I and mode II fracture toughness values, with reductions ranging from 15.4% to 13.2% for mode I and 26.1% to 8.9% for mode II respectively. As the water temperatures increase, a slightly rising trend is observed in both mode I and mode II fracture toughness within the examined temperature range. Sandstone specimens displayed typical brittle fracture characteristics at lower soaking temperatures. For mode I specimens, an increase in ductility was evident with higher soaking temperatures, while the ductile behavior is less pronounced in the mode II specimens. Based on the Maximum Tangential Stress (MTS) criterion and the Generalized Maximum Tangential Stress (GMTS) criterion, the predicted values of mode II fracture toughness and the fracture process zone (FPZ) were discussed. The results show that both the GMTS and MTS criteria exhibit inaccuracies in predicting the mode II fracture toughness of sandstone treated at different soaking water temperatures. However, the GMTS criterion, which incorporates T-stress, demonstrates smaller errors compared to the MTS criterion. The study shows that the radius r0 of the fracture process zone is not a constant under both mode I and mode II loading conditions. The calculation of the fracture process zone radius r0 in the GMTS criterion requires further theoretical and experimental study.

Mixed mode I/II and I/III fracture toughness investigation for preplaced aggregate concrete mixtures: Experimental study and theoretical prediction

AbstractIn this paper, mixed mode I/II and I/III fracture toughness of preplaced aggregate concrete was studied using an edge‐notched disc bend specimen. The results showed the dependency of the fracture toughness value on the mode mixity. The values of modes I, II, and III fracture toughness were obtained to be equal to , , and , respectively. Several theoretical fracture criteria were examined for predicting the trends of experimental data in the tested preplaced aggregate concrete material. The 3D averaged strain energy density criteria provided the best predictions for the KIIIc/KIc ratio. Mixed mode I/III fracture toughness data were between the predicted envelopes of the maximum tensile stress and 3D maximum tangential strain theories. The generalized maximum tangential stress criterion provided accurate predictions for pure mode II and mixed mode I/II fracture data among the investigated mixed mode fracture criteria. By comparing the preplaced aggregate concrete fracture results with those of other types of concrete, it is observed that preplaced aggregate concrete has acceptable and in‐the‐range fracture resistance.

Theoretical and experimental study on mixed-mode I + II fracture characteristics of thermally treated granite under liquid nitrogen cooling

Liquid nitrogen fracturing technology is widely used in the exploitation of hot dry rock (HDR) geothermal resources. It is necessary to understand the fracture characteristics of hot dry rocks under liquid nitrogen cooling. In this study, the mixed-mode I + II fracture characteristics of the thermally treated granite under liquid nitrogen cooling were investigated. The results indicate that as the exposed temperature increases, the number of internal microcracks increases, while the fracture energy and fracture toughness of the granites decrease. From 25 ℃ to 600 ℃, mode I fracture toughness decreases from 1.286MP·m1/2 to 0.612MP·m1/2; mode Ⅱ fracture toughness decreases from 0.830MP·m1/2 to 0.413MP·m1/2; mixed-mode Ⅰ+Ⅱ fracture toughness decreases from 1.082 MP·m1/2 to 0.530MP·m1/2 at Me = 0.705 and from 0.914 MP·m1/2 to 0.445 MP·m1/2 at Me = 0.427, respectively. Additionally, the intergranular fracture behavior increases as temperature increases, resulting in an increase in irregularity of fracture surfaces. The generalized maximum tangential stress (GMTS) criterion is used for predicting the fracture characteristics (fracture initiation angle and fracture toughness) of thermal damaged granites. The accuracy of the GMTS criterion in predicting crack resistance when mode II loading dominates has been improved by considering the variation of critical damage radius.

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Experimental Study on Mixed-Mode (I–II) Fracture Toughness of Freshwater Ice

In recent years, the issue of aircraft icing has gained widespread recognition. The breaking and detachment of dynamic ice can pose a threat to flight safety. However, the shedding and fracture mechanisms of dynamic ice are unclear and cannot meet the engineering needs of ice-shedding hazard assessment. Therefore, studying the fracture toughness of ice bodies has extremely important practical significance. To address this issue, this article uses a centrally cracked Brazilian disk (CCBD) specimen to measure the pure mode I toughness and pure mode II fracture toughness of freshwater ice at different loading rates. The mixed-mode (I–II) fracture characteristics of ice are discussed, and the experimental results are compared and analyzed with the theoretical values of the generalized maximum tangential stress (GMTS) criterion considering the influence of T-stress. The results indicated that as the loading rate increases, the pure mode I toughness and pure mode II fracture toughness of freshwater ice decrease, and the fracture toughness of freshwater ice is more sensitive to the loading rate. In terms of fracture criteria, the theoretical value of the ratio of pure mode II fracture toughness to pure mode I fracture toughness based on the GMTS criterion is in good agreement with the experimental value, while the theoretical value based on the maximum tangential stress (MTS) criterion deviates significantly from the experimental value, indicating that the GMTS criterion considering the influence of T-stress can better predict the experimental results.

Fracture analysis of Brazilian circular hole disk under mixed mode loading

The paper presents an investigation into a Brazilian disk specimen featuring a concentric circular hole, accompanied by two internal edge radial cracks. By introducing rotations of the cracks relative to the vertical axis, a combination of fracture modes I and II is induced. Employing the finite element method, we compute stress intensity factors related to fracture modes I and II, alongside T-stresses, while varying geometric parameters such as inner and outer diameters, crack length-to-ring width ratio, and crack inclination angle. Experimental analyses of ebonite's fracture toughness in the mixed mode are conducted, subjecting samples to static loading until complete failure. Each test provides the angle at which crack initiation occurs and the corresponding critical load. Three distinct fracture criteria - the generalized maximum tangential stress criterion (GMTS), extended maximum tangential strain criterion (EMTSN), and generalized strain energy density (GSED) criterion - are employed to predict fracture direction and critical load. The outcomes exhibit good correspondence between experimental critical loads and theoretical predictions.

On the decay of fracture toughness of sandstone subjected to freeze–thaw cycles

AbstractIn cold regions, progressive cracking, caused by freeze–thaw cycles, plays an important role in deteriorating engineering rock mass. Employing central cracked Brazilian disks (CCBDs) of sandstone, this paper aims at investigating the variations of falling rate among different modes of fracture toughness exposed to freeze–thaw cycles and the applicability of fracture criterion in predictions. Results revealed that different modes of fracture toughness exhibited comparable descending trends after varied freeze–thaw cycles. There was an agreement between the predictions via the generalized maximum tangential stress criterion (GMTS) and the test results. In specified conditions, the GMTS criterion incorporating fracture process zone of 0 freeze–thaw cycle can be applied to estimations for different freeze–thaw cycles. With increasing freeze–thaw cycles the fractal dimensions of mode I and mixed‐mode I–II fracture surfaces displayed a growing trend, indicating that the fracture surfaces became rougher and more complicated.

Investigation of Constraint Effect and Fracture Mode for Mixed Mode Inclination Surface Crack in Infinite Plate Under Compression

Abstract The stress field, constraint effect, and fracture mode transition at crack tip of mixed mode I-II-III inclination surface crack under compression have been investigated. The effects of geometrical configurations (relative crack depth and aspect ratio), friction coefficient, and biaxial scale factor on stress intensity factor (KII and KIII) and in-plane constraint parameter T-stress are quantitatively studied, the stress field at different crack inclination angles under tension and compression are compared, the failure mode at special locations along crack front of inclination surface crack is analyzed according to the generalized maximum tangential stress criterion (GMTS). The relative crack depth has slight effect on stress intensity factor and T-stress, and aspect ratio has a significant effect on stress intensity factor and T-stress. The friction coefficient decreases the magnitude of stress intensity factor and increases the magnitude of T-stress, the greater the crack inclination angle is, the more pronounced the effect is when crack inclination angle greater than 30 deg. The stress distribution around crack tip under tension and compression is completely different. At free surface, the crack will failure in-plane shear mode II sliding crack, and at the deepest part of crack, the crack will start as out-plane shear mode III tearing crack under compression.

Mixed mode I/II fracture behavior of CSTBD sandstone specimen under different loading angles

Cracks are often exposed to mixed mode I/II loading because of the random direction of crack relative to the external load, causing rock failure in rock engineering. However, many mixed mode I/II fracture properties of rock with different loading angles (β) are still poorly understood. To investigate the influence of β on mixed mode I/II fracture behavior, cracked straight through Brazilian disc tests were performed on sandstone under various β at the loading rate of 0.2 kN/s. The results show that the effect of β on the peak load and crack propagation velocity is slight. The mode I stress intensity factor (SIF) decreases from positive to negative with increasing β, while mode II SIF first increases and then decreases as β exceeds approximately 30°. The mixed mode I/II fracture toughness increases linearly with increasing β. When β exceeds 60°, the crack initiation location shifts from the center of the semi-circular notch tip to the surface of preset crack. For non-tip cracking, the crack propagates toward the loading point in a direction approximately perpendicular to the preset crack. The threshold β for it decreases with increasing internal friction coefficient and relative crack length. Moreover, the mixed-mode fracture surface becomes smoother as the mode I component contribution drops. There are remarkable differences in the prediction of fracture initiation angles and SIFs of various rock types applying the generalized maximum tangential stress criterion. The findings of this study could help understand the mixed mode I/II fracture observed in rock engineering.

Multi-fidelity model using GRNN and ANFIS algorithms-based fracture criterion for predicting mixed-mode I-II of sugarcane leaves/epoxy composite

Artificial intelligence plays a huge role in solving engineering problems. In the fracture mechanics field, artificial intelligence is used to predict fracture behavior or parameters, based on testing data, which is a destructive type of testing, so it is difficult to get a large amount of data for the learning modeling process. Therefore, this study presents artificial intelligence modeling to predict the fracture toughness by reducing the use of the actual testing fracture toughness data, while replacing the data with a sufficient quantity of data by fracture toughness prediction from the fracture criterion, for which artificial intelligence was modeled by the concept called the “multi-fidelity model”. The concept of the modeling begins with calculating and predicting the difference between the actual data set and the criterion data set, then combining the data sets, which is the data from the criterion performed mathematically with the data from the above difference prediction to the actual data set to create a model based on the increased data volume of combining the two data sets. In this study, the mixed-mode I-II fracture toughness of sugarcane leaves/epoxy composite with different mixing conditions was performed on an inclined crack specimen via the three-point bending test configuration used as the actual data set, while the generalized maximum tangential stress criterion (GMTS), which is preliminary fracture toughness, was used as criterion data. The multi-fidelity model is proposed via different artificial intelligence algorithms, namely the general regression neural network (GRNN) and the adaptive neuro-fuzzy inference system (ANFIS). Once the modeling process was complete, the performance metrics showed a clear increase in the efficiency of multi-fidelity models compared to the original artificial intelligence models.

Numerical & experimental assessment of mixed-modes (I/II) fracture of PMMA/hydroxyapatite nanocomposite

Nowadays, polymer-based nanocomposites widely used in biocompatible restorative materials and medical equipment and polymer-based nanocomposites are the most important of them. One of the most useful biocompatible polymers in this field is polymethyl methacrylate (PMMA). In this research, the experimental and numerical analysis of the fracture behaviors of PMMA nanocomposites that are reinforced with hydroxyapatite (HA) nanoparticles are investigated under pure mode I, pure mode II and mixed-mode (I/II) loading. For this purpose, notched semi-circular bend (SCB) specimens containing various Wt. % of HA nanoparticles and different notch angles were fabricated. Then, the mechanical properties of the specimens and the fracture toughness of the notched specimens were investigated. To evaluate the accuracy of nanomaterial distribution, scanning electron microscopy (SEM) images are analyzed and it was observed that at Wt. % of more than 1.5%, specimens with more cumulative masses of hydroxyapatite nanoparticles have more strength reduction. Also, to investigate the fracture behaviors of the produced specimens, the failure criteria of maximum tangential stress (MTS) and generalized maximum tangential stress (GMTS) were evaluated and it was observed that the GMTS criterion is more in line with the experimental results. In addition, the results showed that by increasing the Wt. % of HA nanoparticles from zero to 1% mass, the KIC value increased compared to the pure PMMA, whereas, by increasing this value to 1.5% mass, the fracture toughness decreased. Finally, the fracture initiation and propagation are evaluated using FEM and XFEM numerical methods and the values of stress intensity factors and crack growth path are predicted and compared with experimental values. The obtained numerical results are in good agreement with the experimental results.

Mixed-mode fracture of compacted tailing soils. I: Fracture toughness

Mine tailings are man-made soils and leftovers from the mineral processing that share the similar geotechnical properties with natural soils. In areas with abundant mineral reserves and developed mining industries, tailings could be utilized as an alternative of natural soils for subgrade materials of pavement and adobes for building and construction constructions. The tailing soils are also the based materials for tailing dams. The compacted tailing soils might thus be subject to combined opening or shearing deformations that were unexplored in the current academic society. In this paper, a test configuration called asymmetric semi-circular bending (ASCB) was adopted to investigate the mixed I/II mode fracture properties of the compacted tailing soils. First, the load–displacement relationships of the SCB specimens for different notch depths and span ratios were presented. The mode I and II fracture toughness components were then calculated by referring to the theoretical solutions derived from classical fracture mechanics. The fracture envelope from mode I and II fracture toughness components were presented. Meanwhile, the mixity parameter was introduced to evaluate the mode mixity of the ASCB specimens. Finally, the crack initiation angles of the SCB specimens were measured through experimental tests and compared to the theoretical results obtained from generalized maximum tangential stress criterion (GMTS). Results show that the mode I fracture toughness component of the compacted tailing soils increased with the span ratio, while the mode II fracture toughness component increased with the decrease of span ratio. The mode mixity and crack initiation angles of the SCB specimens under mixed mode loading conditions increased with the decrease of span ratio.

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.

Investigation on the mixed mode fracture toughness of freshwater ice using the semi-circular bend method

The fracture toughness of ice is of great importance to understand the fracture behaviour of ice impact and blasting. In this study, the mixed mode (I + II) fracture toughness and mode II fracture toughness of granular freshwater ice were first investigated using the semi-circular bend method. A series of fracture tests were carried out to investigate the effects of the grain size (0.8 mm to 4.5 mm) and notch inclination angle (0° to 75°) on the fracture toughness under mixed mode loading conditions. The experimental results indicate that the mode II and mixed mode fracture toughness values slowly decrease in general as the grain size increases. The fracture initiation angles and critical stress intensity factors of the SCB ice specimens were predicted using the generalized maximum tangential stress (GMTS) criteria and conventional maximum tangential Stress (MTS). The GMTS criterion provides a better understanding for mixed mode fracture toughness of ice specimens with various grain sizes, particularly for mode II dominated loading conditions. The grain size of ice directly affects the size of the fracture process zone, which in turn affects the variation law of mixed mode fracture toughness. The strain field and displacement field were initially analysed based on digital image correlation. The results indicate that the variation in the mixed mode crack was complex, eventually exhibiting an asymmetrical distribution of the displacement field.

Investigation on the Feasibility of Different Semicircular Bend Methods for Asphalt Concrete

Cracking of asphalt pavement is mostly caused by the mixed fracture of asphalt concrete. Determining a simple, repeatable, and accurate method is necessary for evaluating the fracture resistance of asphalt concrete. To explore the mixed fracture performance of asphalt concrete and determine the feasibility of different semicircular bend methods, the mixed fracture performances of asphalt concrete at medium and low temperatures were measured. The mixed fracture modes were realized through changing the position of the support and notch or changing the notch angle. After that, the crack propagating characteristics, crack initiation angle, and fracture toughness were analyzed. Results show that temperature has a significant impact on the fracture path, and crack initiation angle at low temperature follows the generalized maximum tangential stress (GMTS) theory. The measured fracture toughness ratios are lower than the theoretical value of GMTS criterion, but the established empirical model has higher accuracy. In the semicircular bend method, changing the positions of the support and notch is stable and repeatable. Therefore, this method may be preferred to evaluate the mixed fracture performance of asphalt concrete in the future.

Investigation of the deleterious effects of low-temperature and hygrothermal aging conditions on the mixed-mode fracture resistance of epoxy resin using a short-beam bend specimen

The effect of different environmental aging conditions on the mixed-mode fracture behavior of epoxy resins was investigated using a sub-size specimen. The short-beam bend (SBB) specimens with different crack inclination angles were manufactured and subjected to low-temperature (-71 °C), hygrothermal (immersion in deionized water at 60 °C) and room-temperature conditions. The deleterious effect of low-temperature and hygrothermal aging conditions on the mode-I, mode-II and mixed-mode I/II fracture responses of the epoxy resin was studied by testing the aged and unaged SBB specimens under three-point bend loading. The experimental results indicated that the hygrothermal aging condition, with a reduction of 49% in the effective fracture toughness, imposed a more severe deleterious effect on the fracture response of the specimens in comparison with the low-temperature condition with a decrease of 35% in the effective fracture toughness. The generalized maximum tangential stress criterion was used to predict the fracture loads of the aged and unaged specimens. Moreover, optical microscopy and scanning electron microscopy techniques were employed to assess the fracture surfaces of the specimens aged under different conditions.

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.