Measured Fracture Energy Research Articles

Analysis and Comparison of Three Bending Tests on Phosphogypsum-Based Material According to Peridynamic Theory

Phosphogypsum-based materials have gained much attention in the field of road infrastructure from the economic and sustainable perspectives. The Three-point bending test, the Four-point bending test and the Semi-circular bending test are three typical test methods applied for fracture energy measurement. However, the optimal test method for fracture energy evaluation has not been determined for phosphogypsum-based materials. To contribute to the gap, this study aims to analyze and compare the three test methods for fracture energy evaluation of phosphogypsum materials based on the peridynamic theory. For this purpose, the load–displacement, vertical displacement–Crack Mouth Opening Displacement (CMOD) and fracture energy of the phosphogypsum-based materials were measured and calculated from the three test methods. The simulated load–displacement and vertical displacement–CMOD by PD numerical models, with different fracture energy as inputs, were compared to the corresponding tested values according to simulation error results. The results showed that the Four-point bending test led to minimized errors lower than 0.189 and indicators lower than 0.124, demonstrating the most optimal test method for the fracture energy measurement of phosphogypsum-based material. The results of this study can provide new methodological references for the selection of material fracture energy measurement tests.

Risk of fracture in massive cultural objects made of lime wood: a case study of Veit Stoss’ altarpiece

Massive cultural objects made of wood are often situated in historic interiors in which they experience uncontrolled dynamic variations of relative humidity (RH). Although the objects usually have acclimatized to the natural climate variability, preventing risks related to any kind of modification of their environment requires an understanding of the object’s response to the expected changes. In the present study, an analysis of the risk of cracking related to continuous or intermittent heating, or the transfer to hypothetically ideal conditions in a conservation studio was performed for the case of elements of Veit Stoss’ altarpiece (1477–1489) preserved in St. Mary’s Basilica in Krakow, Poland. Massive sculptures carved in lime wood and approximately one meter in diameter were analysed. The study aimed at determining safe margins of environment modifications that would not cause propagation of cracks that are known to have accumulated in wood during centuries of the altarpiece’s existence. The mechanical properties of lime wood were determined experimentally to feed the numerical model. The energy release rates around the tips of cracks of various depths in a wooden sculpture were calculated using the finite element analysis and compared with the critical value of the parameter triggering the fracture propagation in the material, derived from the fracture energy measurement. It was shown that the church interior housing the altarpiece can be heated to 11 °C during the cold season to provide human comfort. The allowable duration of intermittent heating events to more comfortable 18 °C that would induce drops in RH of up to 40% was assessed as 12 h. The study demonstrated that moving the sculptures to the conservation studio would have to be done with extreme caution as it would be connected with risks depending on the depth of existing cracks and the duration of the RH change.

Novel, high throughput interface fracture testing method for thermal spray coatings: The modified cantilever bend technique

To measure the interfacial fracture toughness of ceramic/metal interfaces such as thermal spray coatings, a novel modified cantilever beam bending method is proposed. Finite element simulations are used to determine the energy release rate and phase angle for an interfacial crack in a bi-layered cantilever for varying modulus, thickness and beam aspect ratios. A high-throughput experimental procedure for the new test geometry is presented to extract a large number of measurements of interface fracture energy from the same sample, using digital image correlation. Interfacial fracture energies GC, determined using this method are compared for thermal spray coatings of Alumina and YSZ on steel substrates. GC of these coating-substrate combinations follow the same trend as measured from four-point bending or modified clamped beam bend techniques. Advantages and limitations of the technique in comparison to other methods in practice are discussed.

The Relationship Between Intra-articular Fracture Energy and a Patient's Inflammatory Response.

Prior studies have demonstrated elevated inflammatory cytokine concentrations in the synovial fluid of articular fracture patients postinjury. Similarly, CT-based fracture energy measurements have been correlated with posttraumatic osteoarthritis risk after pilon fracture. The purpose of this study was to determine the associations between synovial fluid cytokine levels, fracture energy, and overall trauma to the body in articular fracture patients. Acute tibial plateau, tibial plafond, and rotational ankle fracture patients were prospectively enrolled from December 2011 through January 1, 2019. Synovial fluid concentrations of interleukin-1 beta, interleukin-1 receptor antagonist, IL-6, IL-8, IL-10, matrix metallopeptidase-1, MMP-3, and MMP-13 were quantified. Patient CT scans were used to calculate fracture energy. The Injury Severity Score (ISS) was used to relate cytokine levels to whole-body injury severity. Spearman rho correlation coefficients were calculated to assess the relationship between injury severity metrics and synovial fluid cytokine, chemokine, and matrix metallopeptidase concentrations. Eighty-seven patients were enrolled with 42 had a tibial plateau fractures (OTA/AO 41B1-2, 41B2-14, 41B3-3, 41C1-3, 41C2-4, 41C3-16), 24 patients had a tibial plafond fracture (OTA/AO 43B1-2, 43B2-4, 43B3-5, 43C1-2, 43C2-3, 43C3-8), and 21 had a rotational ankle fracture (OTA/AO 44B1-3, 44B2-3, 44B3-6, 44C1-4, 44C2-5). Fracture energy significantly differed between fracture patterns, with ankle fractures involving substantially less fracture energy (median = 2.92 J) than plafond (10.85 J, P < 0.001) and plateau fractures (13.05 J, P < 0.001). After adjustment for multiple comparisons, MMP-3 was significantly correlated with transformed fracture energy (r = 0.41, 95% confidence interval [CI], 0.22-0.58, P < 0.001), while IL-1β was significantly correlated with the Injury Severity Score (Spearman ρ = 0.31, 95% CI, 0.08-0.49, P = 0.004). Synovial fluid MMP-3 concentration was significantly correlated with CT-quantified fracture energy in intra-articular fracture patients. Given that in clinical practice fracture energy tends to correlate with posttraumatic osteoarthritis risk, MMP-3 may warrant further investigation for its role in posttraumatic osteoarthritis development after articular fracture. Prognostic Level III. See Instructions for Authors for a complete description of levels of evidence.

An intrinsic ductility parameter derived from anisotropic linear elasticity theory

A new indicator of intrinsic ductility (κ) is introduced based on linear elasticity. In the limit of elastic isotropy this parameter is equal to the Pugh ratio (B/G) plus a constant; but unlike the Pugh ratio, κ incorporates anisotropy and crystallography to improve predictive value. We identify a single ductile-to-brittle transition setpoint for κ that predicts crack-tip plasticity in atomistic simulations, experimental elongation to failure of polycrystalline elemental metals pulled in tension, and fracture energy measurements of glasses, suggesting commonality in the relationship between plasticity and fracture across all three of these cases. Statistical analysis supports the superiority of κ over B/G at predicting crack-tip plasticity in atomistic simulations and elongation to failure of polycrystalline elemental metals.

Direct cohesive law measurement under mixed-mode loading using semi-circular bend (SCB) specimens

The present paper suggests a new method to obtain pure mode and mixed mode traction-separation laws of adhesives using semi-circular bend (SCB) specimen by employing the digital image correlation (DIC) technique. This specimen was recently proposed by the same authors for fracture energy assessment of adhesives. This test method doesn't require any special apparatus or loading jig for mixed mode fracture tests ranging from pure mode I to pure mode II. Lower cost and higher precision than conventional methods are the most advantages of using SCB fracture tests. The primary drawback of this test method lies in its data reduction process. To address this limitation, this paper introduces a direct approach for measuring fracture energy and cohesive law parameters of the adhesive. In this method, substrate strains at the interface are used to calculate the cohesive stress applied to the adhesive layer at each desired section. Shear and normal separation values are obtained directly from DIC displacement results. The proposed method was applied to the SCB specimen subjected to pure modes I and II and for mixed-mode I/II cohesive laws. Four different SCB specimens were manufactured and tested to cover different mode mixities between pure mode I and pure mode II. The experimentally obtained cohesive laws were evaluated using finite element analysis (FEA). Good agreement between the experimental and numerical results were observed.

Fracture energy and cohesive law analysis of adhesives using a recently developed SCB joint: The influence of joint geometry and mode mixity

In a prior study, the current authors proposed the utilization of semi-circular bend (SCB) specimens for analyzing the fracture energy of adhesive materials. However, similar to standard fracture test specimens, the geometry and size of the joint can impact the measured fracture energy when using SCB samples. Therefore, the objective of this research is to investigate the influence of adhesive layer thickness, substrate thickness, and disk radius of SCB specimens on cohesive law parameters and fracture energy of the adhesive. The study examines the fracture energy under different loading conditions, including pure mode I, pure mode II, and two mixed-mode conditions. By employing an inverse data reduction method, the cohesive law parameters of the tested adhesive are determined for various joint geometries. The results demonstrate that the disk radius does not affect the cohesive law of the joint. Furthermore, it is observed that bondline thicknesses of 0.2 mm and 0.4 mm lead to similar cohesive laws, whereas an adhesive thickness of 1 mm results in lower initial stiffness but higher fracture energy and damage initiation traction. Moreover, the study reveals that an increase in substrate thickness reduces the final fracture separation, indicating a more brittle fracture behavior. This can be attributed to a smaller fracture process zone caused by the plane strain load distribution in the adhesive layer.

An indirect method for measurement of rock dynamic tensile strength and fracture energy using blasting experiments

Many parameters in numerical simulation can be directly measured through experiments, yet specific parameters pose challenges for experimental testing. The quantification of dynamic tensile strength and fracture energy in rocks constitutes an indispensable requirement for accurately predicting crack initiation location and propagation velocity. It is imperative to acknowledge that these two parameters exhibit a profound dependence on the strain rate imposed on the rocks. Hence, it is essential to establish a reliable strategy for accurately measuring these parameters. In this paper, a novel blasting experimental measuring system was used to determine crucial dynamic fracture parameters. A single internal crack circular disc (SICCD) configuration was proposed and applied in the sandstone specimens testing. A series of numerical models were developed using a tensile crack softening failure criterion. The mechanical behavior and fracture mechanism of the rock under blasting were analyzed numerically. The relationships between dynamic tensile strength, fracture energy, crack initiation time, and propagation velocity have been thoroughly assessed. Through the utilization of statistical methods and the rapid drawing method, the dynamic tensile strength and fracture energy of rocks can be predicted with high precision by integrating experimental and numerical methods specifically designed. The combined approach enables a comprehensive understanding of the dynamic behavior of rock under extreme loading conditions. Furthermore, the validity of the predicted dynamic tensile strength can be rigorously verified through meticulous testing and evaluation procedures.

Characterizing the Adhesion Between Thin Films and Rigid Substrates Using Digital Image Correlation-Informed Inverse Finite Elements and the Blister Test

Abstract Characterizing the adhesion between thin films and rigid substrates is crucial in engineering applications. Still, existing standard methods suffer from issues such as poor reproducibility, difficulties in quantifying adhesion parameters, or overestimation of adhesion strength and fracture energy. Recent studies have shown that the blister test (BT) is a superior method for characterizing adhesion, as it provides a quantifiable measurement of mix-mode fracture energy, and it is highly reproducible. In this paper, we present a novel method to characterize mechanical mix-mode adhesion between thin films and rigid substrates using the BT. Our method combines the full triaxial displacement field obtained through digital image correlation with inverse finite element method simulations using cohesive zone elements. This approach eliminates the need for making any mechanistic or kinematic assumptions of the blister formation and allows the characterization of the full traction-separation law governing the adhesion between the film and the substrate. To demonstrate the efficacy of this methodology, we conducted a case study analyzing the adhesion mechanics of a polymeric pressure-sensitive adhesive on an aluminum substrate. Our results indicate that the proposed technique is a reliable and effective method for characterizing the mix-mode traction-separation law governing the mechanical behavior of the adhesive interface and could have broad applications in the field of materials science and engineering. Also, by providing a comprehensive understanding of the adhesion mechanics between thin films and rigid substrates, our method can aid in the design and optimization of adhesively bonded structures.

Fracture Energy Measurement in Different Concrete Grades

Fracture energy is regarded as an intrinsic (material) properties that dominates crack mechanisms and associated crack growth in concrete damage under applied stress. In recent times, significant advancements in computing technology have driven the adoption of finite element analysis (FEA) methodologies that necessitate the integration of constitutive models, includingthe traction-separation relationship derived from cutting-edge fracture mechanics. A physically-based model requires fracture energy values; therefore, a properly measured fracture energy value is essential to exhibit better structure response within FEA models. There are large arrays of parameters involved during the concrete mixture, such as beam size effect, aggregate size, and concrete grade, that affect the flexural resistance of the concrete. The fracture and failure in concrete ahead of the crack tip are represented by fracture energy values where micro-damage events such as interfacial failure, fiber-bridging, and matrix cracking occurred.This study aims to determinethe fracture energy of concrete specimens with combination of notch depth aoat mid-span, design concrete strength as specified in the testing series. Independent compression strength, fcand measured load-displacement profiles underathree-point bendingtest were used to determine fracture energy by incorporating three available fracture energy expressions such as Bazant, Hillerborg,and CEB-FIP models.

Atomistic measurement and modeling of intrinsic fracture toughness of two-dimensional materials

Quantifying the intrinsic mechanical properties of two-dimensional (2D) materials is essential to predict the long-term reliability of materials and systems in emerging applications ranging from energy to health to next-generation sensors and electronics. Currently, measurements of fracture toughness and identification of associated atomistic mechanisms remain challenging. Herein, we report an integrated experimental-computational framework in which in-situ high-resolution transmission electron microscopy (HRTEM) measurements of the intrinsic fracture energy of monolayer MoS2 and MoSe2 are in good agreement with atomistic model predictions based on an accurately parameterized interatomic potential. Changes in crystalline structures at the crack tip and crack edges, as observed in in-situ HRTEM crack extension tests, are properly predicted. Such a good agreement is the result of including large deformation pathways and phase transitions in the parameterization of the inter-atomic potential. The established framework emerges as a robust approach to determine the predictive capabilities of molecular dynamics models employed in the screening of 2D materials, in the spirit of the materials genome initiative. Moreover, it enables device-level predictions with superior accuracy (e.g., fatigue lifetime predictions of electro- and opto-electronic nanodevices).

Effect of temperature on the fracture energy of adhesive layers of engineered wood

Adhesive layers in engineered wood are critical for shear stress transfer, particularly under load-bearing conditions. Though there is some data on the shear strength of the adhesive layers, there is limited data on their fracture energy and how it varies with temperature. Understanding the fracture energy could reduce the inconsistencies caused by stress singularity and crack nucleation in a shear strength testing methodology. Therefore, in this article, a 4-pointing bending test framework was used to investigate the fracture energy of the adhesive layers at different temperatures. It is found that the fracture energy of the adhesive layer bonding the 0o/90o (cross-laminated) oriented timber plies is ∼30% lesser than that of the layer bonding 0o/0o (parallel) plies. More importantly, irrespective of the arrangement/orientation of the plies, a steady decline in fracture energy is seen with increase in temperature. For instance, by ∼130oC, the fracture energy of the adhesive layer has reduced by ∼53% in a cross-laminated state and ∼39% for those plies bonded in 0o/0o orientation. Finite element analysis was also conducted based on the cohesive elements and cohesive zone model for validation of the experimentally measured fracture energy.

Ag–SiO2 - An optimized braze for robust joining of commercial coated stainless steel to ceramic solid oxide cells

In this study, Ag–SiO2 was successfully used to join Ce/Co coated AISI 441 stainless steels produced by Sandvik to Solid Oxide Cells. Defect-free and robust joints were obtained at 950 °C when brazing in air. The influence of the chemical composition of the braze and the brazing temperature on the microstructure and mechanical properties of joints was studied. An enhanced interfacial adherence was achieved through the reaction of the SiO2 in the braze and the Co coating of the steel during the air brazing process. The obtained joints possess excellent mechanical robustness with a fracture energy of 96.5 J/m2, and a superior gas tightness (leak rate of 5.4 × 10−4 sccm cm−1) compared to the existing brazing systems. Long-term aging in air or the exposure to reducing atmosphere only had minor effects on the measured fracture energy.

Fracture energy of high-Poisson's ratio oxide glasses

The apparent relationship between Poisson's ratio and fracture energy has been used to guide the discovery of ductile glasses with a brittle-to-ductile (BTD) transition at Poisson's ratio around 0.32. Most organic and metallic glasses possess Poisson's ratio above 0.32, and thus, feature fracture energy that is around three orders of magnitude higher than that of oxide glasses, which feature Poisson's ratio typically below 0.30. However, whether the BTD transition can also be observed in oxide glasses remains unknown due to the lack of fracture energy measurements on oxide glasses with high Poisson's ratio. In this work, we measure the fracture energy of six oxide glasses with high Poisson's ratio between 0.30 and 0.34. We find no clear relationship between the two parameters even in those that possess the same Poisson's ratio as ductile metallic glasses. This suggests that Poisson's ratio is not the main property to enhance the fracture energy of oxide glasses. To this end, we instead find a positive relation between fracture energy and Young's modulus of oxide glasses, and even for some metallic glasses, which could explain their absence of ductility.

A fracture mechanics analysis of the micromechanical events in finite thickness fibre push-out tests

Understanding the micromechanical events of interfacial failure in fibre reinforced composites is vital to accurately characterising micromechanical properties and, consequently, the macroscopic properties of the composite. A fracture mechanics model of the fibre push-out test is developed, with an emphasis on the effect of sample thickness and residual stresses on the mechanisms of interfacial crack advancement. The model is applied to both a SiCf-SiC ceramic matrix composite and a SiCf-Ti metal matrix composite. The model demonstrates that previous assumptions about the micromechanical events of interfacial cracking are consistent with the measured values of interfacial fracture energy for ceramic matrix composites. Moreover, the model can identify the range of geometries for which different micromechanical cracking mechanisms occur simultaneously in a given material system. Identifying this range is important in choosing the sample geometry for fibre push-out testing because the interaction of advancing cracks affects the measurement of interfacial fracture energy by classical models.

Thermally induced self-rupture of a constrained liquid crystal elastomer

Liquid crystal elastomer (LCE) is a promising soft material which exhibits large actuation and can respond to different external fields with proper modifications. In the case of thermally actuated LCEs, the fracture properties are crucial to ensure that LCEs can robustly function under different loading and heating conditions, without unexpected failure. In this work, we systematically characterize the fracture energy of LCE at different temperatures and loading rates. We found that LCE behaves like a tough elastomer at low temperatures and high loading rates, but the fracture energy dramatically drops once LCE is heated beyond the nematic to isotropic transition temperature (TNI). At high temperatures, a constrained precut LCE sample can undergo self-rupture due to the large actuation stress. We have also used the measured fracture energy to successfully predict the critical temperature of self-rupture for different sample geometries.

Needle-induced-fracking in soft solids with crack blunting

Fracking, also known as hydraulic fracture, has been intensively studied in hard and brittle materials such as shale rocks and ice. In contrast, little is known about fracking in soft solids, especially with significant crack blunting. Recently, it has been found that during the needle-induced-cavitation experiments on soft gels or elastomers, the materials can be ruptured by pressurized fluid. Due to the large elastofracture length, a short crack in a soft solid during the fracking often shows severely blunted tips, and therefore, the crack extension and large deformation in the material become nearly indistinguishable in the experiments. In this letter, we propose to adopt a simple model, considering both large deformation and crack blunting, to predict the change of the hydraulic pressure during the needle-induced-fracking in soft solids. We found that the theoretical predictions agree very well with experimental data reported in the literature. The studies presented in this letter may provide new insights into the understanding of the fracking in soft tissues and cells, and lead to a facile way to measure fracture energy of soft materials, which can be very challenging for conventional testing methods.

Energy Requirement for Rock Breakage in Laboratory Experiments and Engineering Operations: A Review

Based on the review of a wide range of literature, this paper finds that: (1) the average specific surface energy of various single crystals is only 0.8 J/m2. (2) The average specific fracture energy of the rocks with a pre-crack under static cleavage tests is 4.6 J/m2. (3) The average specific fracture energy of the rocks with a pre-cut notch but with no pre-crack under static tensile fracture (mode I) tests is 4.6 J/m2. (4) The average specific fracture energies of regular rock specimens with neither pre-made crack nor pre-cut notch are 26.6, 13.9 and 25.7 J/m2 under uniaxial compression, tension and shear tests, respectively. (5) The average specific fracture energy of irregular single quartz particles under uniaxial compression is 13.8 J/m2. (6) The average specific fracture energy of particle beds under drop weight tests is 74.0 J/m2. (7) The average specific fracture energy of multi-particles in milling tests is 72.5 J/m2. (8) The average specific energy of rocks in percussive drilling is 399 J/m3, that in full-scale cutting is 131 J/m3, and that in rotary drilling is 157 J/m3. (9) The average energy efficiency of milling is only 1.10%. (10) The accurate measurements of specific fracture energy in blasting are too few to draw reliable conclusions. In the last part of the paper, the effects of inter-granular displacement, loading rate, confining pressure, surface area measurement, premade crack, attrition and thermal energy on the specific fracture energy of rock are discussed.

The effects of main toughening mechanisms and functionally interphase properties on fracture energy and fatigue characteristics of nanocomposites containing various fillers

Nowadays, novel technologies like nanofillers-based nanocomposites constitute one of the most active research fields in the extremely high performance materials, caused by the fact that this nanomaterial enhances the properties of different polymers in a significant way. Using these materials in polymer structure could enhance the mechanical properties such as fracture energy and fatigue behavior, which caused by variable or cyclic loadings. In the present study, by using the hierarchical multi-scale modeling procedure the fracture toughness (resistance to cracking), fracture energy and fatigue behavior of nanofillers/epoxy nanocomposites with consideration the contributions of the toughening mechanisms of interfacial debonding and plastic void growth in dissipation energy were investigated and discussed. Afterwards, the effect of CNT/matrix interphase on the fracture toughness, fracture energy and fatigue behavior was evaluated by varying the parameters of Young’s modulus and thickness of interphase. Furthermore, analysis of multi-scale modeling strategy was utilized in order to assess the influences of interphase properties and interfacial fracture energy on major parameters such as the critical stress debonding stress and radial component of the stress concentration tensor. In addition, different micromechanical models such as Halpin-Tsai and Maxwell and models were utilized to determine the Young’s modulus of nanocomposite as functionally graded (FG) interphase properties. Fracture energy and fatigue behavior measurements indicated that the properties of interphase region have a crucial importance on the fracture toughness of CNTs/epoxy nanocomposites. In order to verify the model, comparisons were carried out between the results of model with those predicted by experiments. The consistency between results for most fillers show the good performance of the procedure which has been utilized in this study.

Using digital image correlation to automate the measurement of crack length and fracture energy in the mode I testing of structural adhesive joints

In this study, the crack lengths in adhesively bonded double cantilever beam (DCB) test specimens have been determined using the digital image correlation technique in combination with an elastic foundation model. This method facilitates the continuous measurement of the crack length and offers significant advantages over conventional visual observation including improved accuracy and the potential for automation. This method has been applied to three joints bonded with different structural adhesives, and fracture energy Gc values calculated with the effective crack lengths determined by this method have been shown to be accurate by comparison to Jc values. Finally, a new method is proposed to correct the crack lengths that are visually measured and the Gc values determined using the standard analysis. This scheme is shown to improve the accuracy of the Gc values appreciably.