Search Results (11)

Understanding fracture mechanics in rock-like materials under compression-shear condition is critical for predicting failure mechanisms in various engineering applications, such as mining and civil infrastructure. This study conducted uniaxial compression tests on cubic gypsum specimens of varying sizes (side lengths of 75 mm, 100 mm, 125 mm, and 150 mm) and crack inclination angles (ranging from 0° to 90°) to assess the size effect on fracture behavior. The effects of specimen size and crack inclination on fracture characteristics, including strength, failure mode, and crack initiation angle, were analyzed based on the maximum tangential stress (MTS) criterion and the generalized maximum tangential stress (GMTS) criterion, with relative critical size (α) and relative openness (η). Results indicate that the crack initiation angle increases with crack inclination, while compressive strength decreases significantly with increasing specimen size. For example, at a 30° crack inclination, the peak compressive strength of 75 mm specimens was 2.53 MPa, whereas that of 150 mm specimens decreased to 1.05 MPa. Crack type and failure mode were found to be primarily influenced by crack inclination rather than specimen size. The experimental crack initiation angle aligned with the theoretical crack initiation angle at inclinations below 50° but diverged at higher inclinations. A linear relationship was established between r_c and specimen size (L) under compression-shear stress, expressed as $r_c=-0.01772L+3.54648$; larger specimens exhibited increased tangential stress at the crack tip, leading to earlier macroscopic crack formation, while r_c decreased as specimen size increased. These results underscore the significant influence of size on fracture behavior in quasi-brittle materials under compression-shear stress, providing essential insights for predicting material failure in rock-like structures. Full article

To investigate the influence of non-singular terms (T stress) in the stress field on the composite fractures of hard rock Type I–II, such as rock splitting failure and hydraulic fracture propagation, this study focused on hard rocks in metallic mines. Through splitting tests and hydraulic fracturing experiments, the impact of T stress on the characteristics of Type I–II composite fractures in hard rocks was analyzed. Utilizing the generalized maximum tangential (GMTS) stress criterion considering T stress, the stress intensity factors of hard rock Type I–II composite fractures with different pre-existing crack angles were predicted. The critical fracture pressure expression for hard rocks was derived based on the maximum tangential stress (MTS) criterion. The results indicate that the GMTS criterion, considering T stress, is more suitable for describing the characteristics of Type I–II composite fractures under rock-splitting loads. However, under hydraulic fracturing, T stress has a minor influence on the fracture characteristics of hard rock hydraulic fractures. Therefore, when predicting the critical fracture pressure of hydraulic fractures, T stress can be disregarded. This study provides a scientific basis and guidance for hard rock hydraulic fracturing engineering. Full article

In this study, a modified maximum tangential stress criterion by considering T-stress and uniaxial compression tests have been utilized to theoretically and experimentally reveal the fracture initiation mechanism of a center-symmetric closed crack in compacted clay. The results show that wing cracks occur in the linear elastic phase of the stress-strain curve. In the plastic phase of the stress-strain curve, the wing cracks extend gradually and the shear cracks occur. The crack initiation stress and peak stress of compacted clay first decrease with the rise in pre-crack inclination angle (β = 0°–40°), and then increase with the rise in pre-crack inclination angle (β = 50°–90°). When the pre-crack inclination angle is relatively small or large (β ≤ 10° or β ≥ 70°), the crack type is mainly tension cracks. Secondary shear cracks occur when the pre-crack inclination angle is 10°–80°. When the dimensionless crack length is larger than 0.35, the crack types include wing-type tension cracks and secondary shear cracks. The experimental results were compared with the theoretical values. It was found that the critical size r_c of compacted clay under compression-shear loading was 0.75 mm, smaller than the value calculated by the empirical formula (12 mm). The MTS criterion considering T-stress can be used to predict the compression-shear fracture behavior of compacted clay. Full article

This paper investigates the effects of support friction on mixed-mode I/II fracture behavior of compacted clay using notched deep beam (NDB) specimens under symmetric fixed support. Numerical models of 330 NDB specimens were established considering the crack inclination angle, crack length, support span, and support friction coefficient, and the normalized fracture parameters (Y_I, Y_II, and T*) of NDB specimens were calibrated. The numerical results showed that the values of Y_I, Y_II, and T* decreased at different degrees after considering the support friction. Notably, the support friction coefficient could significantly change the loading pattern at the crack tip. To verify this phenomenon, 12 compacted clay NDB specimens were prepared, and a mixed-mode I/II fracture test was performed under fixed support conditions; the phenomenon of asymmetric crack propagation was studied. The test data were processed using the numerical calibration results of Y_I, Y_II, and T* with and without consideration of friction. Afterward, the test data were compared and analyzed by combining the generalized maximum tangential stress (GMTS) and the maximum tangential stress (MTS) criteria. The analysis indicated that the real fracture characteristics of compacted clay NDB specimens could not be reflected when conducting mixed-mode I/II fracture tests under symmetric fixed support conditions if the test results were analyzed by Y_I, Y_II, and T* without considering support friction, as in previous studies. Full article

In this research, the fracture behavior of brittle specimens weakened by V-shaped notches with end holes (VO-notches) is studied. First, an experimental investigation is conducted to evaluate the effect of VO-notches on fracture behavior. To this end, VO-notched samples of PMMA are made and exposed to pure opening mode loading, pure tearing mode loading, and some combinations of these two loading types. As part of this study, samples with end-hole radii of 1, 2, and 4 mm are prepared to determine the effect of the notch end-hole size on the fracture resistance. Second, two well-known stress-based criteria, namely the maximum tangential stress (MTS) criterion and the mean stress (MS) criterion, are developed for VO-shaped notches subjected to mixed-mode I/III loading, also determining the associated fracture limit curves. A comparison between the theoretical and the experimental critical conditions indicates that the resulting VO-MTS and VO-MS criteria predict the fracture resistance of VO-notched samples with about 92% and 90% accuracy, respectively, confirming their capacity to estimate fracture conditions. Full article

The purpose of this study is to predict the load-bearing capacity (LBC) of fracture specimens containing V-notched friction-stir welded (FSWed) joints of AA7075-Cu and AA7075-AA6061 materials and subjected to mode I loading conditions. Due to the resulting elastic-plastic behavior and the corresponding development of significant plastic deformations, the fracture analysis of the FSWed alloys requires elastic-plastic fracture criteria, which are complex and time-consuming. Thus, in this study, the equivalent material concept (EMC) is applied, equating the actual AA7075-AA6061 and AA7075-Cu materials to equivalent virtual brittle materials. Then, two brittle fracture criteria, the maximum tangential stress (MTS) and mean stress (MS), are utilized to estimate the LBC of the V-notched FSWed parts. The comparison between the experimental results and the theoretical predictions reveals that both fracture criteria, in combination with EMC, can accurately predict the LBC in the analyzed components. Full article

This work aims to assess both experimentally and analytically the fracture behavior of rock specimens containing sharp V-notches (SV-notches) subjected to mixed mode I/II loading. To this end, firstly, several mixed mode fracture tests were conducted on Brazilian disk specimens weakened by an SV-notch (SVNBD sample), performed in their corresponding center and with various notch opening angles. Secondly, the fracture resistance of the tested samples was predicted using a criterion named MTS-FEM. This approach is based on the maximum tangential stress (MTS) criterion, in which the tangential stress is determined from the finite element method (FEM). Additionally, in the present research, the required critical distance is calculated directly from finite element analyses performed on cracked samples. Comparing the experimental results and the analytical predictions, it is shown that the fracture curves obtained from the MTS-FEM criterion are in agreement with the experimental results. These results are achieved without the need for the calculation of stress series expansion coefficients, as an additional advantage of the proposed approach. Full article

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. Full article

This work analyzes, both theoretically and experimentally, the fracture process of square specimens weakened by keyhole notches and subjected to compressive stresses. Two materials are covered: general-purpose polystyrene (GPPS) and poly(methyl methacrylate) (PMMA). Firstly, the load-carrying capacity (LCC) of the specimens is determined experimentally. Then, by using the equivalent material concept (EMC) for compressive conditions coupled with the maximum tangential stress (MTS) and the mean stress (MS) criteria, the LCC of the notched specimens is predicted. The results show that by using the approach proposed in the present investigation, not only can the critical loads in the keyhole notched polymeric specimens be precisely predicted, but also the corresponding compressive critical stress of the two mentioned polymers can be successfully estimated. Full article

In this paper, the fracture of notched polymeric specimens under compressive stresses was investigated both experimentally and theoretically. In the experimental section, to determine the load-carrying capacity (LCC) of U-notched specimens made of general-purpose polystyrene (GPPS) and polymethyl-methacrylate (PMMA) polymers, tests were performed on notched square samples under compression, i.e., negative mode I loading. In the observation of the nonlinear behavior of the two polymers in the standard compressive tests, for the first time, the equivalent material concept (EMC) was used under compressive loading to theoretically estimate the critical stresses of the two polymers, which were shown to be significantly different from the ultimate strengths obtained from the standard compression tests. By linking the EMC to the maximum tangential stress (MTS) and mean stress (MS) criteria, the LCC of the notched specimens was predicted. The outcomes are twofold: First, MTS, MS, EMC–MTS, and EMC–MS criteria provide accurate predictions of the experimental critical loads observed in the U-notched polymeric specimens; second, the combination of the EMC with the MTS and MS criteria, allow such predictions to be obtained without any need for experimental calibration. Full article

This paper analyzes the notch effect on the fracture behavior of two biomaterials (a brittle bone cement and a ductile dental material) under mode I loading. U-notched Brazilian disk (UNBD) specimens of both materials were tested under remote compression, determining the corresponding fracture loads and load-displacement curves. Additionally, cracked rectangular and semicircular bend (SCB) specimens were tested under symmetric three-point bending in order to determine the fracture toughness of the two materials. Then, fracture loads were derived theoretically by applying the maximum tangential stress (MTS) and the mean stress (MS) criteria. Due to the brittle linear elastic behavior of the bone cement material, the MTS and MS criteria were directly applied to this material; however, given the significant nonlinear behavior of the dental material, the two fracture criteria were combined with the Equivalent Material Concept (EMC) for the fracture analyses of the dental material specimens. The results reveal a very good accuracy of both the MTS and the MS criteria for the fracture analysis of bone cement notched specimens. In the case of the dental material, very good results are also obtained when combining the MTS and the MS criteria with the EMC. The proposed approach can be useful for the fracture analysis of a wide range of biopolymers, from brittle to ductile behavior. Full article