Mixed-mode Fracture Toughness Research Articles

Fracture toughness of mixed-mode anticracks in highly porous materials

When porous materials are subjected to compressive loads, localized failure chains, commonly termed anticracks, can occur and cause large-scale structural failure. Similar to tensile and shear cracks, the resistance to anticrack growth is governed by fracture toughness. Yet, nothing is known about the mixed-mode fracture toughness for highly porous materials subjected to shear and compression. We present fracture mechanical field experiments tailored for weak layers in a natural snowpack. Using a mechanical model for interpretation, we calculate the fracture toughness for anticrack growth for the full range of mode interactions, from pure shear to pure collapse. The measurements show that fracture toughness values are significantly larger in shear than in collapse, and suggest a power-law interaction between the anticrack propagation modes. Our results offer insights into the fracture characteristics of anticracks in highly porous materials and provide important benchmarks for computational modeling.

Experimental and virtual testing of mode II and mixed mode crack propagation under dynamic loading

Under static loading, measuring experimentally the mode II and mixed mode fracture toughness of composite materials and adhesive joints is well standardised. However, under dynamic loading, no standard procedure has been defined yet. Therefore, this paper proposes an experimental methodology to measure the mode II and mixed mode interlaminar fracture toughness of composite materials and adhesive joints. The methodology is based on a modified split Hopkinson compression bar. Two different data reduction schemes are explored and compared, one based on measuring the crack length, and another based on measuring the force from the strains in the transmitted bar. The two data reduction methods provided considerably different results. By using the method based on measuring the force, the mode II and mixed mode fracture toughness for both interlaminar and adhesive joints decreased for higher strain rates, while the opposite was found with the other approach. The method based on the crack length measurement was deemed to be unreliable due to the difficulties in measuring it.

Fracture Performance Study of Carbon-Fiber-Reinforced Resin Matrix Composite Winding Layers under UV Aging Effect.

There is limited research on the fracture toughness of carbon-fiber-reinforced polymer (CFRP) materials under accelerated UV aging conditions. In this study, the primary focus was on investigating the influence of varying durations of ultraviolet (UV) irradiation at different temperatures on the Mode I, Mode II, and mixed-mode fracture toughness of CFRP laminates. The results indicate that with increasing UV aging duration, the material's Mode I fracture toughness increases, while Mode II fracture toughness significantly decreases. The mixed-mode fracture toughness exhibits an initial increase followed by a subsequent decrease. Furthermore, as the aging temperature increases, the change in the fracture toughness of the material is more obvious and the rate of change is faster. In addition, the crack expansion of the composite layer of crack-containing Type IV hydrogen storage cylinders was analyzed based on the extended finite element method in conjunction with the performance data after UV aging. The results reveal that cracks in the aged composite material winding layers become more sensitive, with lower initiation loads and longer crack propagation lengths under the same load. UV aging diminishes the overall load-bearing capacity and crack resistance of the hydrogen storage cylinder, posing increased safety risks during its operational service.

Designing a simple and suitable laboratory test specimen for investigating the general mixed mode I/II/III fracture problem

A novel test specimen was designed for experimental investigations of pure and mixed mode fracture. This novel test configuration is called “modified edge notched disc bend” (M-ENDB) specimen. The M-ENDB specimen has a circular disc shape with an edge crack along its diameter that is loaded using asymmetric three-point bending. Different fracture parameters including: stress intensity factors (SIFs), geometry factors, T-stress, biaxiality ratio (BR), and out-of-plane constraint factor (Tz) were determined for the suggested disc bend specimen using the extensive finite element (FE) analyses. According to the obtained results, the proposed specimen can present all combinations of mode mixities, including pure modes I, II, and III as well as mixed-mode I/II, I/III, and I/II/III deformations. Afterwards, a large number of pure and mixed-mode fracture toughness experiments were carried out on polyurethane (PUR) foam to examine the capabilities of the suggested M-ENDB specimen. Fracture path, fracture surface, fracture toughness, work of fracture, and critical T-stress of broken foams under general mixed mode conditions were investigated. Mixed mode I/II/III fracture toughness value was smaller than the pure mode I fracture toughness (KIc) value showing the weakness of brittle materials against multi-axial fracture compared to pure tensile type fracture.

Mixed-Mode Crack Propagation in Presence of Vein Fracture in Shale Sample in SCB Test

Mixed-mode fracture toughness refers to the ability of a material to withstand loads and expand under multiple modes of loading. It is usually tested by a semi-circular bend (SCB) to investigate the shale fracture toughness under combined modes of loading, such as tension and shear. When shale samples contain vein fractures, the dimensionless parameters Y1 and Y2 used in the SCB test method can be affected. The finite element method (FEM) was used to conduct a study investigating the impact of the natural fracture angle on the dimensionless parameters Y1 and Y2. The research findings indicate that as the vein fracture angle increases, Y1 and Y2 gradually increase. A construction was made to simulate the propagation path of a mixed-mode crack and compare it under various experimental conditions, utilizing the cohesive zone method (CZM). The results indicate that as the thickness of the vein fracture increases, the propagation path of the fracture becomes more tortuous. When the fracture encounters a vein with lower fracture strength, it will extend the vein fracture propagation. On the other hand, when the fracture encounters a vein with higher fracture strength, it will cross the vein fracture. This research considers the magnitude of the dimensionless stress intensity factor under different vein angles, simulating the crack propagation for varying vein widths and strengths.

Mixed mode fracture toughness of epoxy molding compound/printed circuit board interface of semiconductor packages with respect to temperature and moisture

Interfacial delamination is a critical factor for dissimilar bi-material interfaces in terms of structural mechanical behavior and reliability. In this study, the mixed mode interfacial fracture toughness of a thin epoxy molding compound/printed circuit board bilayer with different mixities was measured via the asymmetric double cantilever beam test with a reinforced metal jig. Additionally, mode II fracture toughness properties were measured through the end notched flexure test. All tests were performed under various temperature and moisture absorption conditions below 100℃/85 %RH. Then, a finite element simulation was performed with the cohesive zone model technique to validate the experimentally measured fracture toughness values by comparing the load–displacement curves from the experiment and simulation. Additionally, the single leg beam test and its finite element simulation were conducted and compared for validation of the measured mixed mode fracture toughness values. It was demonstrated that the developed mixed mode fracture toughness measurement method could provide accurate fracture toughness, which could effectively predict the overall load–displacement curve and damage propagation behavior.

Damage prediction of sintered α‐SiC using thermo‐mechanical coupled fracture model

AbstractA three‐way coupled thermo‐mechanical fracture model is presented to predict the damage of brittle ceramics, in particular α‐SiC, over a wide range of temperatures (20–1400°C). Predicting damage over such a range of temperatures is crucial for thermal protection systems for many systems such as spacecraft. The model, which has been implemented in MOOSE, is divided into three modules: elasticity, damage phase field, and heat conduction. Analytical approaches for determining crack lengthscales are presented for both simple tension and simple shear. Validation tests are conducted for both flexural strength and fracture toughness over the specified range of temperatures. Flexural strength simulation results fall within the uncertainty region of the experimental data, and mode I fracture toughness simulation results are also in agreement with the experimental data. Mode II and mixed mode fracture toughness simulations results are presented with the modified G‐criterion. Finally, the parallel computing capabilities of the model are considered in various scalability tests.

A comprehensive experimental investigation of the rate-dependent interlaminar delamination behaviour of CFRP composites

The paper presents a systematic experimental study of the interlaminar delamination behaviour of a carbon composite subjected to Mode I, Mode II and Mixed-mode delamination at both quasi-static (QS) and high-rate (HR) conditions, which were conducted on a screw-driven test machine and in-house Hopkinson bar systems, respectively. A methodology integrating digital image correlation and the compliance-based beam theory was employed to circumvent the challenges in measuring the loads at HR tests and maintain good consistency during the data analysis of all delamination tests. The results demonstrated a positive rate-dependent delamination behaviour, with the HR Mode I, Mode II and Mixed-mode fracture toughness properties being 1.56, 1.66 and 1.60 times their QS counterparts, respectively. The cause of such a dependency was revealed following a detailed fractographic analysis, which highlighted that the observed dependency was associated with the transition of the predominant failure mechanisms in the QS and HR conditions.

Research on Pure Modes I and II and Mixed-Mode (I/II) Fracture Toughness of Geopolymer Fiber-Reinforced Concrete

The unsustainable use of resources and the rising demand for traditional concrete have disrupted ecological equilibrium, necessitating the adoption of a more appropriate and long-lasting alternative. One such substitute for cement in concrete production is geopolymer concrete, although this material is prone to cracking and fracturing due to its low tensile strength, leading to costly repairs or even structural collapse. Fiber-reinforced concrete has recently been widely adopted as a construction material to counteract these issues. This research examined the crack proliferation and fracture toughness of geopolymer concrete comprising different fibers using a cracked Brazilian disc. Four different fibers were used, such as polypropylene and steel fiber (short and long), at a dosage of 1.5% by volume. Fracture toughness was computed for various modes (I, II, and I/II) of fractures, and crack propagation from cracked specimens was studied. A different angle of inclination (0, 15, 28, 83, 60, 75, and 90 degrees) was used to conduct the Brazilian disc test on the specimens with respect to the preexisting crack direction. The findings indicate that the increasing loading angle increased the load-carrying capacity. The fracture toughness values of specimens under all three modes ranged from 0.26 to 1.75 MPa.m1/2. Additionally, long polypropylene and steel fibers exhibit higher fracture toughness than short fibers.

Effect of using available GGBFS, silica fume, quartz powder and steel fibres on the fracture behavior of sustainable reactive powder concrete

Reactive Powder Concrete (RPC) is a relatively new composite concrete material type. The development of RPC aims to achieve a microstructural improvement primarily through incorporating fine aggregates rather than coarse aggregates, more tightly packed particles, increased toughness, and supplementary cementing materials. Although the RPC has excellent engineering properties, its brittleness is the main drawback that can be mitigated by adding steel fibres. This research aims to assess the efficiency of fibrous RPC made from silica fume (SF), ground granulated blast furnace slag (GGBFS), and quartz powder (QZ). In this context, twelve mixtures comprising a combination of GGBFS (75, 85 and 100%), SF (0, 15 and 30%), QZ (20 and 30%) and steel fibres (1 and 2% by volume) were prepared and examined. The experimental program includes flow test, compressive strength, and fracture toughness test under various modes. Many cracked disc-shaped RPC specimens were subjected to pure (I and III) and mixed (I/III) modes to evaluate the fracture toughness. Besides, the microstructure properties were analyzed using X-ray diffraction analysis and scanning electron microscope images. The Findings unveiled that increasing QZ from 20 to 30% resulted in a marginal improvement in fracture toughness under all three loading modes. The addition of 15% and 30% SF to the RPC specimen with 1% fibre resulted in a 5.65% and 7.91% increase in fracture toughness under mode I, respectively; the addition of 2% fibre resulted in a 4.51% and 7.75% increment, compared to thereference specimen. The improved mixed mode fracture toughness ranged from 1.09 to 6.88% for a 20° loading angle and 1.35 to 4.33% for a 50° loading angle. Furthermore, increased fracture toughness was measured between 0.71 and 6.63% under pure mode III. It is worth highlighting that the contribution of fibre is remarkable in increasing the fracture toughness than the SF and QZ. Besides, the mode III fracture is more critical and recorded fewer values than the mode I and mixed mode.

Mixed mode fracture toughness and mode mixity analysis of face/core debonds in a single-leg sandwich bending specimen

Mixed mode fracture, which often occurs during composite materials, can present a safety hazard to the structure. Analytical expressions for the energy release rate (ERR) and mode mixity phase angle are derived for an asymmetric single-leg sandwich bending (SLSB) fracture specimen. Meanwhile, the modified crack surface displacement extrapolation (MCSDE) method is proposed to obtain the numerical solution of ERR and mode mixity. The effects of loading characteristics, core and face sheet geometric parameters and material parameters on ERR and mode mixity are investigated. To solve the problem of excessive deformation of the thin plate specimen during the test, a reinforced single-leg sandwich bending specimen (RSLSB) is proposed, and the detailed derivation process of the RSLSB fracture specimen's analytical solution is given. The results show that loading magnitude greatly affects ERR and mode mixity. The core’s geometric and material parameters have little effect on ERR but have apparent effects on mode mixity. The face sheet's geometric and material parameters have apparent effects on the ERR and mode mixity. The existence of the reinforced layer will increase the mode I fracture component.

Effect of heat-treatment on the pure- and mixed-mode fracture properties of a homogeneous sandstone

Fracture-mechanical properties of the sedimentary rocks at elevated temperature strongly control hydraulic fracturing in rocks, geothermal energy extraction, deep tunnelling, and spent fuel disposal in geological medium. This paper investigates the relationship between the strength properties (e.g. tensile strength, brittleness index and Young’s modulus) and the pure-mode and mixed-mode fracture toughness of Dholpur sandstone at temperatures ranging from room temperature to 500 °C. A suitable brittleness index definition was identified to quantify the deformational changes. Additionally, evolution of the stress–strain behaviour, change in the degradation degree (DD), peak strain, and evolution in porosity values were closely studied to comment on the potential brittle–ductile transition of the rock. The fracture toughness remained unchanged between 25–150 °C, sharply increased 3%–28% between 150–200 °C, and followed by a 75%–80% decrease from 200–500 °C. All the pure- and mixed-mode fracture toughness were found to maintain an exponential relationship with the Young’s modulus, tensile strength, and brittleness index of the heat-treated rocks across all the temperatures. A potential brittle to quasi-brittle/semi-ductile transition temperature of 225 °C was identified for Dholpur sandstone. Additionally, mixed mode fracture behaviour of the heat-treated rock was investigated using generalized maximum tangential stress (GMTS) criterion. It was noticed that GMTS is far better at predicting the KII/KI ratio of mode-II fractures than the conventional maximum tangential stress (MTS) criterion. Statistical analysis of the test data indicate that a 3-parameter Weibull function can be successfully employed to predict the mode-II fracture toughness of heat-treated sandstone in terms of the mode-I data.

Study on the Accuracy of Fracture Criteria in Predicting Fracture Characteristics of Granite with Different Occurrence Depths

The fracture network of a deep geothermal reservoir forms the place for heat exchange between injected fluid and rock mass with high temperature. The fracture resistance ability of reservoir rocks will affect the formation of fracture-network structure, heat exchange and transmission characteristics, and reservoir mechanical stability. However, there are few reports on the fracture toughness and trajectory prediction of geothermal reservoirs with different depths. In this paper, the modified maximum tangential stress criterion (MMTS) is analyzed. The results show that the experimental data are significantly different from the theoretical estimate of MMTS under the influence of different occurrence depths. It is found that the fracture process zone (FPZ) seriously affects the accuracy of predicting fracture initiation angle and mixed-mode (I+II) fracture toughness by MMTS. The FPZ value, considering the influence of different occurrence depths, is modified, and the accuracy of MMTS in predicting the fracture mechanical characteristics of granite is improved. In addition, the mechanical test results show that the Brazilian splitting strength (σt) of granite fluctuates increase with the increase in temperature. With the increase in deviatoric stress, the Brazilian splitting strength and the Brazilian splitting modulus of rock show a trend of first increasing, then decreasing, and then increasing.

Improvement of Mixed-Mode I/II Fracture Toughness Modeling Prediction Performance by Using a Multi-Fidelity Surrogate Model Based on Fracture Criteria.

Today, artificial intelligence plays a huge role in the mechanical engineering field for solving many complex problems and the problem with fracture mechanics is one of them. In fracture mechanics, artificial intelligence is used to predict crack behavior under various conditions such as mixed-mode loading. Many parameters are used for explaining the crack behavior under various conditions, but those parameters are obtained from destructive testing, in which usually, only one data point is obtained from each test. An artificial problem method requires a large amount of data to train the model to be able to learn crack behavior, which is a disadvantage of applying this method to fracture mechanics. To eliminate the disadvantage of the large amount of experiment data required for modeling, in this study, the small data obtained from the experiment along with data obtained from fracture criteria that were used for elementary prediction of mixed mode fracture toughness were used to create an artificial intelligence model. Data from the experiment was combined with fracture criteria data using the multi-fidelity surrogate model that is described in this study. The mixed mode I/II fracture toughness of the PMMA material was tested in order to primarily propose the data combination technique. After the modeling process, the prediction results indicated that the performance of a model in which the actual test data was combined with the data from the fracture criteria (multi-fidelity surrogate model) was more predictively effective compared to only actual data-based modeling.

Evaluation of the cracked lap shear test for mixed-mode fracture toughness estimation of adhesive joints

Cohesive zone models are a widely used method in adhesive joint strength predictions, but it requires the knowledge of fracture toughness of the adhesive in the different loading modes, together with the mixed-mode behaviour. The cracked lap shear test is a simple but seldom studied mixed-mode test and, as such, a deeper knowledge about its accuracy and of the available data reduction methods is required. This work consists of the experimental and numerical analysis of the cracked lap shear test to estimate the mixed-mode fracture toughness of two structural adhesives. The experimental work consisted of testing cracked lap shear specimens with the different adhesives. Numerically, cohesive zone model were used to predict the behaviour of bonded joints under mixed mode, while assessing the validity of the available data reduction methods to estimate fracture toughness. While the experimental analysis showed that the Brussat’s method led to offset results compared to the other methods, the cohesive zone model analysis confirmed the inadequacy of the Brussat's method, and the suitability of the Grady and Kinloch's models for mixed-mode fracture analysis.

Static and dynamic fracture behavior of rock-concrete bi-material disc with different interface crack inclinations

The fracture behavior of rock-concrete bi-material structures with interface crack is of great significance to the stability of construction projects in rock engineering. Dynamic testing of cracked straight-through Brazilian disc (CSTBD) samples was performed using a split-Hopkinson pressure bar (SHPB) system. The fracture development of rock-concrete bi-material was monitored by the digital image correlation (DIC) technique. A static fracture test using the MTS322 hydraulic servo-controlled testing system was also carried out for comparison. The results show that three typical fracture patterns can be identified for CSTBD samples under both static and dynamic loading. At a smaller interface inclination angle, the disk samples fracture along the interface, while at a larger interface inclination angle, the samples suffer tensile fracture along the loading direction. The increase of strain rate leads to an increase in the number of secondary cracks. As the inclination of interface increases from 0° to 75°, the dissipated energy increases gradually. When the inclination exceeds 75°, the dissipated energy turns to weaken. The difference in peak dissipated energy between different inclination angles weakens as the strain rate increases. The dimensionless stress intensity factors (SIFs) at the two crack tips are different, and increasing the crack length-diameter ratio will enlarge the difference. The interface inclination angle has a significant effect on both the static and dynamic fracture toughness of CSTBD samples. As the inclination of the interface increases, the difference between mixed-mode static and dynamic fracture toughness also increases. The dependence of dynamic fracture toughness on inclination is significantly higher than that of static fracture toughness, and the ratio between dynamic and static fracture toughnesses increases with increasing loading rate.

Mixed mode fracture parameters and fracture characteristics of diorite using cracked straight through Brazilian disc specimen

In this study, the cracked straight through Brazilian disc (CSTBD) specimen was applied to study the I/II mixed mode static fracture of diorite. The fracture load and fracture toughness for different prefabricated crack angles β were determined. The fracture and morphological characteristics were analyzed using digital image correlation (DIC), scanning electron microscope (SEM) and 3D topography scanning techniques. In addition, the key fracture parameters such as fracture energy, crack mouth opening displacement (CMOD) and fracture process zone (FPZ) were characterized, and a fracture energy calculation method considering the primary crack growth was proposed. The results show that the fracture mechanical behavior and fracture trajectories are controlled by the crack angle. At the millimeter measurement scale, the fractal dimensions of fracture surfaces do not vary with crack angle. Further SEM observation shows that intergranular fracture and transgranular fracture are the dominate micro fracture modes of fracture surfaces under mode I and mode II loading, respectively. With the increase of crack angle, the fracture energy first increases and then decreases, while the allowable CMOD decreases monotonically and even appears negative when β ≥ 45°. Based on the displacement gradient method, the calculated width of FPZ for the mode I fracture specimen at peak load is 0.5–1.4 mm and the length is 2.66 mm. Finally, the stress-based and strain-based fracture criteria were modified. It is found that the proposed EEMTSN criterion has the best prediction effect on the mixed mode fracture toughness of diorite.

Pure and mixed-mode (I/III) fracture toughness of preplaced aggregate fibrous concrete and slurry infiltrated fibre concrete and hybrid combination comprising nano carbon tubes

Concrete is the most widely used and inexpensive material in the construction sector. However, due to its weakness in tension, the cracking and brittle fracturing of concrete is considered a major deficiency. Advancements in fibrous concretes have recently been emerged to mitigate this issue. Preplaced Aggregate Fibrous Concrete (PAFC) and Slurry Infiltrated Fibrous Concrete (SIFCON) are unique cement composites made of fibres with surpassing mechanical properties and exceptional toughness values. The production of PAFC and SIFCON involves packing of aggregates and fibres in the mould and filling the gaps between the aggregates with the high flowability injected cement grout. Nevertheless, the mono and hybrid layered effect of PAFC and SIFCON on fracture toughness is still unexplored and needs special attention to bridge this research gap. This research examined the pure (I and III) and mixed (I/III) modes of fracture toughness of PAFC, SIFCON and hybrid two-layered PAFC-SIFCON samples. For this purpose, many notched specimens of circular disc shapes were prepared using single and double-layer concepts. To investigate the effect of fibres, three different fibre types were used; hooked-end steel fibre, macro polypropylene fibre and hybrid shape of crimped-hooked end steel fibre with dosages of 2.4% and 8% by volume to produce PAFC and SIFCON, respectively. Additionally, multi-walled nano-carbon tubes (MWCNT) were added to the composites with a dosage of 0.1% by cement weight. The compressive strength, stress intensity factors, effective stress intensity factors, mixity parameter, failure pattern, range of fracture toughness and scanning electron microscope were examined, discussed, and compared. Results indicated that pure mode III has a greater cracking risk than both mode I and mixed-mode I/III. The mixed-mode fracture toughness of PAFC specimens improved by 33.07 to 67.94%. Similarly, this improvement ranged from 59.77 to 210.70% for SIFCON and from 51.0 to 131.55% for PAFC-SIFCON. In addition, the fracture toughness of SIFCON is considerably higher than the PAFC and hybrid combination. In all three composite types, the hybrid shape steel fibre outperformed the hooked-end steel and polypropylene fibre under all three modes.

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.

Experimental and theoretical investigation of mixed-mode I/II and I/III fracture behavior of PUR foams using a novel strain-based criterion

Brittle fracture in Polyurethane (PUR) foam is experimentally and theoretically investigated under mixed-mode I/II and I/III loading conditions. Original test data are generated to examine different criteria in prediction of the mixed-mode fracture behavior of PUR foam. To this end, edge notched disc bend (ENDB) specimen which has been proven to be a suitable test configuration for such loading conditions is used, and subsequently, fracture angles and fracture toughness values are obtained experimentally. Three different fracture criteria, including minimum strain energy density (SED), maximum principal stress (MPS), and the recently introduced strain-based criterion called ECD-SN – which is established based on considering an effective critical distance – are considered to theoretically estimate the fracture behavior of PUR foam. A comparison between the experimental and theoretical results revealed that the ECD-SN criterion gives a better prediction both for the fracture angles and the mixed-mode fracture toughness of PUR foam. The results indicated that considering effective critical distance instead of the traditional approach, which assumes the critical distance is constant as a material property and independent of the loading mode, can considerably increase the accuracy of the theoretical estimation.