Fracture Energy Release Rate Research Articles

Validation of a hybrid multi-phase field model for fracture of wood

Fracture mechanics simulations are crucial for understanding the failure of wood, where the microstructure strongly influences mechanical properties. In particular, complex crack topologies present a challenge for which not many modeling approaches are suited. Therefore, a hybrid multi-phase field model, supporting cohesive failure in orthotropic materials with favorable fracture planes, is used. We show that the model agrees well with the investigated experiments, with tensile strengths and fracture energy release rates in a reasonable range for wood. Those findings allow the application of this model to more complex situations like wooden boards with multiple knots and complex fiber courses and show that the model’s input parameters are not purely numerical values but rather material parameters.

Mechanical, fracture toughness, and Dynamic Mechanical properties of twill weaved bamboo fiber‐reinforced Artocarpus heterophyllus seed husk biochar epoxy composite

AbstractThis research aimed to find the effect of Artocarpus heterophyllus fruit seed husk biochar (ASB) and twill weaved bamboo fiber (TBF) in mechanical, DMA, and fracture toughness behavior of epoxy‐based composite. The surface of both weaved bamboo fiber and biochar was treated with amino silane before composite making. In this investigation, the laminates were fabricated by hand layup process and analyzed by appropriate ASTM standards. Results of this study revealed that the incorporation of 40 vol.% twill weaved bamboo fiber (EB) into the resin improved the mechanical properties. The load distribution was uniform with twilled weaving. For composite designation EBJ3, the maximum measured tensile strength was 168 MPa, the tensile modulus is 6.24 GPa, the flexural strength is 195 MPa, and the flexural modulus is 6.85 GPa, the izod impact is 6.24 J, and the hardness is 90 shore‐D. Similarly, the maximum storage modulus and lowest loss factor for the composite designation EBJ3 were measured to be 3.8 GPa and 0.4, respectively. Moreover, the maximum measured fracture toughness and energy release rate is 39.4 MPa.√m and 0.88 MJ/m2 for composite designation EBJ3 with 5.0% biochar and 40% bamboo fibers in volume. The SEM fractography revealed that the matrix molecules are adhered to the fiber, indicating enhanced bonding. These biomass waste converted fruit seed husk biochar and industrial crop bamboo fiber epoxy composites could be used as workable material in structural, defense, automotive, and domestic product‐making applications.

In-situ characterization on crack propagation behavior of SiCf/SiC composites during monotonic tensile loading

The microstructure and crack propagation path of 2.5D SiCf/SiC composites were observed by synchrotron radiation x-ray computed micro tomography (SR-μCT) equipped with in-situ tensile device. The results showed that the pore morphologies of the SiCf/SiC composites are mainly divided into three types in three-dimension space: interconnected pores, isolated pores and micro pores in fiber bundles. The crack initiation occurred at the root of the defects under in-situ tensile load and the crack was perpendicular, parallel to the stress axis or mixed mode to propagate. At the interface scale between fiber and matrix, the crack deflection will be controlled by physical parameters such as fracture energy release rate and the modulus of elasticity. At the fiber bundle scale, the crack is easy to shear propagate along the interface between weft and warp fiber bundles due to the existence of the mechanical bonding and residual tensile stress.

Characterization of anisotropic mode II fracture behaviors of a typical layered rock combining AE and DIC techniques

Shear-sliding mode fracture, i.e., mode II fracture, is a very common rupture mode of layered rocks. To achieve a better understanding of the anisotropy in the real mode II fracture, which propagates in a self-similar manner, a series of direct shear tests were conducted on single-notched specimens made of shale with three bedding angles, i.e., β = 0°, 45° and 90°. The ranking of the anisotropic mode II fracture toughness (KIIc) with different bedding angles is KIIc,45° >KIIc,90° >KIIc,0°, which is different from that of the anisotropic mode II fracture energy release rate (GIIc), i.e., GIIc,90° >GIIc,45° >GIIc,0°, suggesting that, unlike isotropic rocks, the crack propagation resistance of a layered rock cannot be completely characterized by its fracture toughness. From the acoustic emission monitoring results, it is found that the fracture process initiates and accelerates from the notch front once the applied mode II stress intensity factor (SIF) reaches its first and second thresholds, KII, FPI (approximately 50%∼70% of the fracture toughness) and KII, FPA (approximately 85%∼95% of the fracture toughness), respectively; generally, both KII, FPI and KII, FPA show noticeable anisotropies. The results of the b value indicate that more small-scale events occur in the specimen with β = 0°, and large-scale events account for a greater proportion in the specimen with β = 45°. A dominant high strain zone along the prefabricated crack direction and a secondary high strain zone along the bedding planes were discovered. Combining the acoustic emission and digital image correlation results, three typical fracture mechanisms were observed: (1) shear fracture along bedding planes when shearing along beddings; (2) shear fracture in matrix and along bedding planes for β = 45°; and (3) shear fracture in matrix and tensile fracture of bedding planes when shearing perpendicular to the beddings.

A 3D Peridynamic Model to Simulate Indirect Tensile Failure in Marble

Driven by the commitment of achieving peak carbon dioxide emissions before 2030 and carbon neutrality before 2060, China is promoting the optimization of its energy and industry structures. In the electricity supply industry, a large number of different types of sophisticated large and giant hydropower stations are planned or being constructed in western China. In future decades, hydropower may take the dominant position in China’s electricity supply. Rock fracturing behavior plays a vital role in geotechnical hazard prevention and geotechnical engineering design. With the construction of hydropower stations, rock mechanics investigation will be of great concern. This study presents a hybrid model that coupled the finite element method and peridynamic theory to simulate the indirect tensile strength of marble. Sensitivity analyses of the loading rate, mesh size, and fracture energy release rate are performed. The numerical results indicate that both the loading rate and mesh size significantly affect the numerical representation of rock properties. After the calibration of the fracture energy release rate, Brazilian tensile strength modeling is successfully conducted, and the numerical results are consistent with the experimental results.

Enabling lightweight polycarbonate-polycarbonate (PC-PC) photovoltaics module technology – Enhancing integration of silicon solar cells into aesthetic design for greener building and urban structures

Light weight photovoltaic (PV) modules have advantages both to reduce costs of PV installations as well as to enhance their further integration with building and other urban structures such as roofs of public parking areas and bus stations. Polycarbonate (PC) materials have been studied before as glass or front sheet replacement, but recently the PC-PC module design (where both front and back sheets are made of PC) has gained attractions both in industry as well as in research. It offers further additional benefits, such as improved reliability (in terms of silicon cell cracks) and enhanced ease of integration into not only flat surfaces, but also curved ones such as integrated PV in cars, trucks, and boats. These benefits may enable more aesthetic design that can increase the appeal of the PV technology. However, a few technological issues stand between the current forms of PC-PC PV module design and the increasing market demands for more aesthetically pleasing and contour-confirming PV integrations. Two of the most important ones are the silicon sensitivity against fracture (especially in bending mode) and interface delamination (especially between PC and the encapsulants). Both are driven by mechanical stresses in the silicon cells as well as in other materials in the PV module/package design. Having published widely our studies in stresses in silicon solar cells in PV module design, both experimentally as well as computationally as shown in the literature review of this manuscript, our research group has obtained unique insights in the primary driving forces of failures in the typical PV module design (glass-back sheet). In the present manuscript, we use the Width Tapered Cantilever Beam (WTCB) method to investigate the interfacial delamination issues systematically. We found that the energy release rate for delamination or fracture at the interfaces between PC and EVA (Ethylene Vinyl Acetate) was fairly low (i.e. low adhesion strength), but could be enhanced with process parameters during the PV lamination step or separate thermal treatment. Hence, this could be taken advantage for enabling unique and highly innovative PV modules based on PC, and for aesthetic purposes for the wider applications of PV technology.

How to obtain a more accurate maximum energy release rate for mixed mode fracture

Energy release rate (ERR) is considered one of the most widely employed fracture criteria. However, for mixed mode fracture situations, the exact computation of ERR for an infinitesimal branch crack is challenging. With some assumptions, Nuismer's theoretical expression (Int. J. Fracture. 11 (1975)) has been used to determine the ERR. In this work, we investigate its deviation. Based on St. Venant's theorem, it is first proved that the stress intensity factor (SIF) of a branch crack is almost independent of its length when the branch crack is small enough as compared to the main crack, which enables us to more accurately obtain the ERR and SIF of an infinitesimal branch crack by simulating a finitely short branch crack in finite element simulations. More accurate curves for the maximum ERR and the corresponding branch angle under any mixed mode are provided. From results of more accurate simulation, we find that Nuismer's model has the maximum difference of 11.2% in the maximum ERR and the 7.1% difference in the branch angle prediction. These are also the differences of predictions between the maximum circumferential stress criterion and the maximum energy release rate criterion.

Study of fracture parameters and complete fracture process of concrete at low temperatures using an energy approach

The fracture parameters and complete fracture process of concrete under low-temperature environment were studied by using an energy approach. The fracture parameters including the initial fracture energy release rate GIcini, unstable fracture energy release rate GIcun and critical cohesive energy release rate GIcc were determined, and the accuracy of the double-G fracture model was verified by the unstable fracture energy release rate GIcun∗. Furthermore, the equivalence of the double-G fracture model and double-K fracture model was verified by the effective double-K fracture toughness (KIcini¯ and KIcun¯). Finally, the complete fracture process of concrete was simulated by taking GIcini as the condition of each crack propagation. The availability of the numerical method was proved, and the effect of temperature on the crack extension resistance curve was investigated.

Effect of liquid nitrogen freeze–thaw cycle on fracture toughness and energy release rate of saturated sandstone

To enhance the ability of tight sandstone gas extraction, liquid nitrogen (LN2) freeze–thaw cycle method can be employed to improve the physical and mechanical properties of the sandstone. Rock fracture behaviors and mechanical properties after fracturing play an important role to successfully implement reservoir stimulation. Since tight sandstone gas reservoirs are usually characterized by high water content, the influences of LN2 freeze–thaw cycle on the fracture toughness and energy-release rate of the saturated sandstone are studied in this paper. The three-point bending experiment is carried out on the notched semicircular bending sandstone samples subjected to different LN2 freeze–thaw cycle times under three different modes, that is, mode I, mixed mode (I/II), and mode II. The structure damage and facture morphology analyses are performed to explain the differences in fracturing behaviors. The energy release rate of the saturated sandstone subjected to the LN2 freeze–thaw cycle is corrected by the P-wave velocity. The experimental results indicate that the LN2 freeze–thaw cycle can promote the weakening of cementation between mineral particles and produce microcracks inside the saturated sandstone, further resulting in an increase in the roughness of the crack surface after loading failure. For all three modes, the fracture toughness and the energy-release rate gradually decrease with the increase in the LN2 freeze–thaw cycle times. For all the LN2 freeze–thaw cycles, mode I requires the minimum applied energy for the fracture propagation, while mode II requires maximum applied energy. In the three modes, the energy-release rate in mode I is the largest. Compared with mixed mode and mode II, the fracture toughness and fracture energy of mode I are more sensitive to the LN2 freeze–thaw cycle. The fracture energy depends on both the microstructure characteristics inside rocks and the mechanism of the fracture propagation. The results are helpful to better understand the initiation and propagation of cracks during the sandstone gas extraction.

Steel plate cold commercial - carbon fiber reinforced plastics hybrid laminates for automotive applications: curing perspective with thermal residual effect

The curing effect on hybrid materials consisting of steel plate cold commercial - carbon fiber reinforced plastics (SPCC-CFRP) hybrid laminates that have potential applications in automobile structures were evaluated in the present study. Specimens with stacking sequences consists of one SPCC plate and six layers of CFRP ([SPCC/[0] 6 ]) under a double cantilever beam (DCB) test were investigated experimentally and analytically. The characterization was performed using a differential scanning calorimetry (DSC) and fourier transform infrared (FTIR) analysis. The specimens were exposed to two different curing times to observe the different strain energy release rates. The results show specimens with a curing time of three hours have stability in strain energy release rate value compared to one-hour curing time. However, in the early stage of fracture, the fracture toughness of 1-hour has a higher value than 3-hour. The critical crack length in this study occurred between 40 and 70 mm. Furthermore, the average strain energy release rate value of G I in 1-hour and 3-hour curing time from the crack length between 98 and 104 mm was 116.6687 J/m 2 based on compliance calibration (CC) method, 113.3966 J/m 2 based on correction factor, and 116.3831 J/m 2 from considering temperature effect theory compared to 1-hour curing time with 81.3232; 79.1026; and 81.0376 J/m 2 , respectively. Based on this study, the fracture toughness and energy release rate of hybrid laminate significantly affected by the curing conditions during the manufacturing process.

Block structured adaptive mesh refinement and strong form elasticity approach to phase field fracture with applications to delamination, crack branching and crack deflection

Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have emerged to model and predict crack failure. The phase field method for fracture uses a surrogate damage field to model crack propagation, eliminating the arduous need for explicit crack meshing. In this work a novel numerical framework is proposed for implementing hybrid phase field fracture in heterogeneous materials. The proposed method is based on the “reflux-free” method for solving, in strong form, the equations of linear elasticity on a block-structured adaptive mesh refinement (BSAMR) mesh. The use of BSAMR enables highly efficient and scalable regridding, facilitates the use of temporal subcycling for explicit time integration, and allows for ultra-high refinement at crack boundaries with minimal computational cost. The method is applied to a variety of simple heterogeneous structures: laminates, wavy interfaces, and circular inclusions. In each case a non-dimensionalized parameter study is performed to identify regions of behavior, varying both the geometry of the problem and the relative fracture energy release rate. In the laminate and wavy interface cases, regions of delamination and fracture correspond to simple analytical predictions. For the circular inclusions, the modulus ratio of the inclusion is varied as well as the delamination energy release rate and the problem geometry. In this case, a wide variety of behaviors was observed, including deflection, splitting, delamination, and pure fracture.

A computational framework for crack propagation in spatially heterogeneous materials.

This paper presents a mathematical formulation and numerical modelling framework for brittle crack propagation in heterogeneous elastic solids. Such materials are present in both natural and engineered scenarios. The formulation is developed in the framework of configurational mechanics and solved numerically using the finite-element method. We show the methodology previously established for homogeneous materials without the need for any further assumptions. The proposed model is based on the assumption of maximal dissipation of energy and uses the Griffith criterion; we show that this is sufficient to predict crack propagation in brittle heterogeneous materials, with spatially varying Young's modulus and fracture energy. Furthermore, we show that the crack path trajectory orientates itself such that it is always subject to Mode-I. The configurational forces and fracture energy release rate are both expressed exclusively in terms of nodal quantities, avoiding the need for post-processing and enabling a fully implicit formulation for modelling the evolving crack front and creation of new crack surfaces. The proposed formulation is verified and validated by comparing numerical results with both analytical solutions and experimental results. Both the predicted crack path and load-displacement response show very good agreement with experiments where the crack path was independent of material heterogeneity for those cases. Finally, the model is successfully used to consider the real and challenging scenario of fracture of an equine bone, with spatially varying material properties obtained from CT scanning. This article is part of a discussion meeting issue 'A cracking approach to inventing new tough materials: fracture stranger than friction'.

Experimental correlation of rheological relaxation and interface healing times in welding thermoplastic PEKK composites

The evolution of polymer welding time to join the interface of thermoplastic Polyetherketoneketone (PEKK) matrix composites was characterized. Using a creep-recovery test protocol to analyse the evolution of rheological behavior, it was shown that for temperatures above the melting point (T>360°C), the polymer visco-elastic relaxation time increases exponentially with time–indicating polymer crosslinking or branching. To confirm that relaxation time is proportional to interface healing time, the rheological results were compared to the fracture energy release rate (G1c) of samples prepared on a custom bench which is capable of isothermally weld composite samples for controlled time intervals. The welding time corresponds directly to the relaxation time. Furthermore, the thermal history that the polymer experienced results in cross linking and influences the welding time. The implication is that temperature exposure from prior processing steps (IR oven pre-heating or autoclave consolidation) can limit the ability to weld components in a predictable way.

Interfacial delamination and delamination mechanism maps for 3D printed flexible electrical interconnects

Flexible electronic systems integrate heterogeneous materials such as ceramics, metals, and elastomers, which results in interfaces prone to delamination under stress. In this research, we show that delamination can be initiated in a polyimide-based flexible interconnect system directly printed on a polydimethylsiloxane substrate where the metallic interconnect acts as the crack initiation site. This problem is experimentally and analytically evaluated to identify the controlling parameters and propose pathways to prevent delamination. The driving force for delamination is shown to be the vapor pressure of the absorbed moisture in the polymer. Based on the dimensions of the cracks in our system (20–60 μm) and the thickness of the delaminated polymer films (2–6 μm), nonlinear von-Kármán plate theory is utilized to capture both membrane stretching and thin plate bending behavior in the polymer films. The model yields ‘delamination mechanism maps’ that relate the energy release rate to the geometric dimensions of the flexible interconnects/circuits. For thin polymer films, a ‘vapor starved’ regime is shown where insufficient moisture reduces the driving force for delamination. For thicker films, a higher resistance to fracture is observed due to an increased rigidity of the polymer layer which behaves as a ‘plate’ rather than a ‘membrane’. Under these conditions, however, the higher retained moisture in the thicker films sustains the driving force for fracture capable of reaching the critical energy release rate. The mechanism maps also reveal the width of the metallic conductor (i.e., the initial crack size) as an important factor controlling fracture. For example, it is shown that the energy release rate for fracture is reduced from 20.5 to 4.6 J/m2 when the conductor width is reduced from 50 μm to 30 μm for a polymer film thickness of 6 μm. These predictions are shown to be in reasonable agreement with our experimental observations. A finite element model is also developed and used to further validate the analytical model. The work presented in this paper provides highly important and practical design guidelines for improved reliability of flexible electronic systems.

Effects of span-depth ratios on the energy release rate for three-point bending beams

The effects of span-depth ratios on the energy release rate for three-point bending beams were examined. Expressions for the energy release rate for three-point bending specimens with various span-depth ratios were developed using linear interpolation method. The double-G fracture parameters were calculated through tests of three-point bending beams with the same span (800 mm) but various depths (100 mm, 150 mm, 200 mm, 250 mm and 300 mm) and the findings in literature. Results indicate that (1) with increasing the span-depth ratio, an almost constant initial fracture energy release rate was obtained, and slight decrease tendency of the unstable energy release rate was observed; (2) The empirical relationship between the initial fracture energy and total fracture energy suggested in size effect model was conformed using the unstable fracture energy release rate which was the same as the initial fracture energy; (3) Equivalence between double-G and double-K fracture model was verified; (4) Moreover, the analytical results of unstable fracture energy release rate exhibited a good consistency with the experimental ones, which were insensitive to the softening function.

A refined thermo-mechanical fully coupled peridynamics with application to concrete cracking

The accurate numerical prediction of concrete cracking under thermal or thermo-mechanical loads is essential and urgent due to the requirement of structure reliability and durability. In the present paper, a refined bond-based peridynamic approach for thermo-mechanical coupling problems is developed and applied to the thermal diffusion, thermal-induced deformation, and fracture of mesoscale concrete structures. Specifically, the classical differential thermo-mechanical equations are reformulated by applying the peridynamic differential operator on and thus converted to a novel nonlocal integral formulation, which is called a refined thermo-mechanical fully coupled peridynamics. It gets rid of the micro-conductivity and does not require any calibration procedure, and the temperature-deformation term is expressed in terms of the integral of displacement difference directly. Besides, A multi-rate explicit time integration scheme is applied to overcome different time-scale problems in multi-physical systems as well. Meanwhile, a new micro-conduction model is developed for the broken bonds, and the cracks are not assumed to be adiabatical herein. And, the fracture energy release rate is considered to be temperature-dependent. Moreover, three benchmark examples for thermal diffusion and fully coupled thermo-mechanical problems are analyzed to illustrate the correctness and accuracy of the proposed peridynamic approach. At last, the simulations of a thick-walled heterogeneous concrete cylinder geometrically modeled in two- and three-dimension suffering heating load are performed, whose cracking results agree well with corresponding experimental results.

Effect of coarse aggregate volume fraction on mode II fracture toughness of concrete

Mesostructure, cement, and interfacial transition zone (ITZ) play a vital role in the fracture process of concrete. This paper focuses on the effect of coarse aggregate volume fraction on the mode II fracture behaviors of concrete by the laboratory experiments. The tests of sixty concrete specimens were performed under different volume fractions of coarse aggregate of 19%, 25%, 31%, 37%, 43%, and 50%. The mode II fracture toughness and energy release rate were determined by the compression on half part of the non-notched specimens. The experimental results show that the mode II fracture toughness KIIC and the critical energy release rate GIIC increase with increasing the volume fraction of coarse aggregate from 19% to 37%, and then both decrease with increasing the volume fraction of coarse aggregate from 37% to 50%. The technique of digital image correlation (DIC) was also used to track the fracture evolution during the tests and it was found that the shape of fracture process zone (FPZ) of concrete with mode II fracture is a curved band around the potential shear ligament.

Characteristics of Stress Drop and Energy Budget from Extended Slip-Weakening Model and Scaling Relationships

The extended slip-weakening model was investigated by using a compiled set of source-spectrum-related parameters, i.e. seismic moment Mo, S-wave velocity Vs, corner-frequency fc, and source-controlled high-cut frequency fmax, for 113 shallow crustal earthquakes (focal depth less than 25 km, MW 3.0~7.5) that occurred in Japan from 1987 to 2016. The investigation was focused on the characteristics of stress drop, radiation energy-to-seismic moment ratio, radiation efficiency, and fracture energy release rate, Gc. The scaling relationships of those source parameters were also investigated and compared with those in previous studies, which were based on generally used singular models with the dimensionless numbers corresponding to fc given by Brune and Madariaga. The results showed that the stress drop from the singular model with Madariaga’s dimensionless number was equivalent to the breakdown stress drop, as well as Brune’s effective stress, rather than to static stress drop as has been usually assumed. The scale dependence of stress drop showed a different tendency in accordance with the size category of the earthquakes, which may be divided into small-moderate earthquakes and moderate-large earthquakes by comparing to Mo = 1017~1018 Nm. The scale dependence was quite similar to that shown by Kanamori and Rivera. The scale dependence was not because of a poor dynamic range of recorded signals or missing data as asserted by Ide and Beroza, but rather it was because of the scale dependent Vr-induced local similarity of spectrum as shown in a previous study by the authors. The energy release rate Gc with respect to breakdown distance Dc from the extended slip-weakening model coincided with that given by Ellsworth and Beroza in a study on the rupture nucleation phase; and the empirical relationship given by Abercrombie and Rice can represent the results from the extended slip-weakening model, the results from laboratory stick-slip experiments by Ohnaka, and the results given by Ellsworth and Beroza simultaneously. Also the energy flux into the breakdown zone was well correlated with the breakdown stress drop,   and peak slip velocity of the fault faces. Consequently, the investigation results indicate the appropriateness of the extended slip-weakening model.

A local-domain based phase field method for crack propagation

The phase field method transfers the crack surface area into a domain integral through a smeared damage parameter. As a result, the fracture energy release rate can be directly incorporated into the energy form without tracking of crack surface, and a minimization approach to optimize the crack shape becomes possible. This nonlocal damage approach requires a fine mesh discretization to capture the damage gradient in the smeared crack zone, which produces a significant degree of freedom problem to optimize over the entire domain. In this research, a local-domain based phase field method is proposed. This method considers only elements in critical regions for energy minimization, whose internal energy are dominant, thus significantly reducing the degree of freedom to be solved. A numerical verification is carried out to demonstrate the feasibility of this approach, and simulations are presented to verify the accuracy of the new method.

Experimental study on fracture properties of CFRP-to-concrete interface subject to salt water

The mechanical property degradation of bonding interface between FRP (fiber reinforced polymer) and concrete has an adverse effect on the performance of FRP strengthened concrete structures. In order to increase the durability database and have a better understanding of the degradation mechanism, the effect of NaCl solution on CFRP (carbon fiber reinforced polymer)-to-concrete interface under mode I and mode II loading is studied by using pulling test and wedge driving test method, respectively. The relationship between salt water content and fracture energy release rate of CFRP-to-concrete interface is studied. Because the interfacial salt water content cannot be measured directly, a finite element simulation is established based on salt water uptake tests of component materials. The results show that both mode I and mode II fracture energy release rate of CFRP-to-concrete interface decrease nonlinearly with salt water content, and the change of failure mode from debonding within the concrete layer to cohesive failure along the interface is also observed.