Elastic Energy Release Rate Research Articles

Interrelation between mechanical and electromagnetic radiation emission parameters with variable notch-width ratios under tensile fracture in silicon steel

Abstract The research investigates the effect of variable notch-width ratios on mechanical and electromagnetic radiation (EMR) parameters during the tensile fracture of silicon steel. The primary purpose is to comprehend the plastic deformation and crack propagation at an atomic level. The mechanical and EMR parameters chosen for analysis were correlated. The EMR energy release rate correlated well with the elastic strain energy release rate. The good fit between the EMR parameters and the plastic zone radius is a novel method to determine the crack growth behaviour of metals. A theoretical model of dislocation predicted the nature of EMR signals at fracture. A reasonable agreement between cross-slip energy with maximum stress at crack instability, the elastic strain energy release rate, and the EMR energy release rate will help assess the dislocation dynamics of metals. The EMR amplitude was sensitive to varying strain rates.

Influence of an Engineered Notch on the Electromagnetic Radiation Performance of NiTi Shape Memory Alloy.

This work explores the influence of a pre-engineered notch on the electromagnetic radiation (EMR) parameters in NiTi shape memory alloy (SMA) during tensile tests. The test data showed that the EMR signal fluctuated between oscillatory and exponential, signifying that the specimen's viscosity damping coefficient changes during strain hardening. The EMR parameters, maximum EMR amplitude, and average EMR energy release rate remained constant initially but rose sharply with the plastic zone radius with progressive loading. It was postulated that new Frank-Read sources permit dislocation multiplication and increase the number of edge dislocations participating in EMR emissions, leading to a rise in the value of EMR parameters. The study of the correlation between EMR emission parameters and the plastic zone radius before the crack tip is a vital crack growth monitoring tool. An analysis of the interrelationship of the EMR energy release rate at fracture with the elastic strain energy release rate would help develop an innovative approach to assess fracture toughness, a critical parameter for the design and safety of metals. The microstructural analysis of tensile fractures and the interrelation between deformation behaviours concerning the EMR parameters offers a novel and real-time approach to improve the extant understanding of the behaviour of metallic materials.

Exploring the impact of varying notch-width ratios on electromagnetic radiation parameters at tensile fracture of C35000 brass

The paper discusses experimental research to analyze how the notch-width ratio (2a/w) impacts Electromagnetic Radiation (EMR) emission parameters at tensile fracture in C35000 brass. The EMR emission signals during tensile fracture were captured using a copper chip antenna and stored in an oscilloscope for further analysis. The EMR parameters and mechanical parameters at fracture showed a smooth correlation. Investigating the association between the EMR parameters and the plastic zone radius formed before the crack tip may help develop an innovative tool for crack growth monitoring. The interrelation between the EMR energy release rate and the Elastic strain energy release rate may help create an innovative method for assessing fracture toughness, a fundamental property of metallic materials. The EMR energy release rate exhibited a parabolic relationship with an analytical correlation of stacking fault energy. Field emission scanning electron microscopy (FESEM) examined the fractured specimen's microstructure. A thorough examination of the relationship between dislocations, EMR characteristics, and real-time applications could be a novel technique for understanding material behaviour in detail.

Design and Manufacturing of a Low-Cost Prosthetic Foot

Below-knee prosthetics are used to restore the functional activity and appearance of persons with lower limb amputation. This work attempted to design and manufacture a low-cost, novel, comfortable, lightweight, durable, and flexible smart below-knee foot prosthesis prototype. This prosthesis foot was designed according to the natural leg measurement of an adult male patient. The foot is composed of rigid PVC layers interspersed with elastic strips of PTFE, and the axis of the ankle joint is flexible and consists of metal layers and a composite of polymeric damping strips with different mechanical properties, making it flexible and allowing it to absorb shocks and store and release energy. The design, modeling, and simulation of the manufactured prosthetic foot were performed via the ANSYS 18.0 software and the finite element method (FEM), where a large number of parallel and oblique planes and sketches were created. This work included four adult patients weighing 50, 75, 90, and 120 kg with different walking cycles. The results show that the highest equivalent von Mises stress and total deformations for the prosthetic limb occur at the beginning of the walking step, while the highest equivalent elastic strains and strain energy release rates are observed at the end of the walking step, regardless of the weight. This prototype can satisfactorily perform the biomechanical functions of a natural human foot, and it can be produced in attractive sizes, models, and shapes to suit different levels of below-knee amputations for different ages and weights, especially for patients with limited income.

Multiscale study of enhancing the fracture properties of interfacial transition zone: Insights from molecular dynamics and finite element simulations

Cementitious composites are widely used in architecture and construction field, but usually show quasi-brittle failure at macroscale under tensile or bending loads. In contrast, the calcium silicate hydrates (C-S-H) exhibits noticeable ductile response at nanoscale. In this article, we focus on the interfacial transition zone between cement paste and aggregate, which consists of the C-S-H/quartz and the calcium hydroxide (CH)/quartz interface structures. To comprehend how a nanoscale design might improve concrete’s macro mechanical qualities, molecular dynamics and finite element simulations are performed at the nanoscale and macroscale, respectively. The elastic properties, modulus, fracture toughness and critical energy release rate of C-S-H/CH/graphene oxide (GO)/quartz composites are calculated using the molecular dynamics method at nanoscale. These parameters then are used in macro-simulation and calculating mechanical properties of macro concrete structures. The incorporation of GO sheets into the interface results in a 38.40% to 58.06% increase in the fracture toughness of interfacial transition zone (ITZ) systems and an 80% and 9.81% improvement in the tensile strength and tensile modulus of the concrete model, respectively. This fundamental insight into nanoscale interfaces notably allows for more accurate predictions of macroscopic mechanical behavior, paving the way for innovative and enhanced cement-based materials in the future.

Adaptive phase-field modeling of fracture propagation in bi-layered materials

We study fracture propagation in bi-layered materials using an adaptive phase-field method. The method combines a phase-field representation of fracture with spatial adaptivity to provide mesh refinement in the smeared zone of damage, where higher accuracy is needed to resolve the solution. We place a particular emphasis on studying the competition between crack arrest, deflection, and penetration at the interface of two dissimilar materials. To explore this competition, we perform tension tests on various models with different combinations of material and geometric properties. We begin by validating the adaptive phase-field model through a uniaxial tension test. The material mismatch and locations of the initial damage for this example are chosen such that the fracture propagation behavior is identical to that in a homogeneous material. Next, we independently vary the mismatches in elastic stiffness and critical energy release rate to study their influence on crack growth. Our observations show that both mismatches contribute to an effective toughening of the model, but in different ways. Critical energy release rate mismatch causes crack deflection along the interfaces, while elastic stiffness mismatch results in retardation of crack growth. We also note that for a specific combination of material mismatch and location of initial damage, crack nucleation in the adjacent material is preferred over propagation from the existing notch. Finally, through models with inclined interfaces, we demonstrate the effect of the relative orientation between the approaching crack and the material interface on crack penetration, deflection, and nucleation. The numerical results from this study provide valuable insight into the various failure mechanisms in bi-layered materials.

Energy evolution characteristics of engineered cementitious composites (ECC) under tensile and compressive loading

To more truly reflect the failure law of engineered cementitious composites (ECC), this research investigates the multiple cracking and failure process of ECC from the perspective of energy and reveals the energy evolution characteristics of this process. The mechanical properties and energy evolution characteristics of ECC under different water-binder ratios were studied by uniaxial compression test. The effects of water-binder ratios, fiber volume fractions, and fiber aspect ratio on the tensile properties, energy evolution characteristics, and fracture energy of ECC were systematically investigated. It was found that the increase in the water-binder ratios decreases the compressive strength and elastic strain energy release rate, but increases the dissipated energy. The increase of fiber volume fraction and fiber aspect ratio can effectively improve the tensile properties, elastic strain energy, dissipated energy, and fracture energy. The abrupt change in the elastic energy consumption ratio can be used as a criterion for ECC failure.

Obtaining The Fracture Resistance Curve Using The General Displacement

In this paper, the energy release energy corresponding to the unit crack propagation obtained from the displacement controlled load-displacement plot is equalized to the elastic energy release rate, and the variation of stiffness based on the crack length is obtained. For this purpose, instead of measuring the amount of crack mouth opening in the single edge-cracked tensile specimen, the extensiometer elongation amount was taken in the middle part of the specimen. Thanks to the equality of the stiffness to the crack length, the transformation of the load-displacement curve into the material resistance curve was realized.

HR-EBSD analysis of in situ stable crack growth at the micron scale

Understanding the local fracture resistance of microstructural features, such as brittle inclusions, coatings, and interfaces, at the microscale is critical for microstructure-informed design of materials. In this study, a novel approach has been formulated to decompose the J-integral evaluation of the elastic energy release rate to the three-dimensional stress intensity factors directly from experimental measurements of the elastic deformation gradient tensors of the crack field by in situ high (angular) resolution electron backscatter diffraction (HR-EBSD). An exemplar study is presented of a quasi-static crack, inclined to the observed surface, propagating on low index {hkl} planes in a (001) single crystal silicon wafer.

On the fracture behavior of cortical bone microstructure: The effects of morphology and material characteristics of bone structural components

Bone encompasses a complex arrangement of materials at different length scales, which endows it with a range of mechanical, chemical, and biological capabilities. Changes in the microstructure and characteristics of the material, as well as the accumulation of microcracks, affect the bone fracture properties. In this study, two-dimensional finite element models of the microstructure of cortical bone were considered. The eXtended Finite Element Method (XFEM) developed by Abaqus software was used for the analysis of the microcrack propagation in the model as well as for local sensitivity analysis. The stress–strain behavior obtained for the different introduced models was substantially different, confirming the importance of bone tissue microstructure for its failure behavior. Considering the role of interfaces, the results highlighted the effect of cement lines on the crack deflection path and global fracture behavior of the bone microstructure. Furthermore, bone micromorphology and areal fraction of cortical bone tissue components such as osteons, cement lines, and pores affected the bone fracture behavior; specifically, pores altered the crack propagation path since increasing porosity reduced the maximum stress needed to start crack propagation. Therefore, cement line structure, mineralization, and areal fraction are important parameters in bone fracture.The parameter-wise sensitivity analysis demonstrated that areal fraction and strain energy release rate had the greatest and the lowest effect on ultimate strength, respectively. Furthermore, the component-wise sensitivity analysis revealed that for the areal fraction parameter, pores had the greatest effect on ultimate strength, whereas for the other parameters such as elastic modulus and strain energy release rate, cement lines had the most important effect on the ultimate strength. In conclusion, the finding of the current study can help to predict the fracture mechanisms in bone by taking the morphological and material properties of its microstructure into account.

Combined evaluation of Young modulus and fracture toughness in small specimens of fine grained nuclear graphite using 3D image analysis

The fracture toughness of the fine-grained nuclear graphite SNG742 has been investigated by observation of stable crack propagation in double cleavage drilled compression specimens. The three-dimensional displacement fields were obtained by digital volume correlation (DVC) of in situ laboratory X-ray computed tomographs. The crack tip location and crack opening displacements were determined using an image edge detection algorithm based on the wavelet modulus maxima. The Young modulus was estimated by fitting a finite element model to DVC displacement field data measured before crack initiation. Using the 3D crack geometry and the surrounding full-field 3D displacement fields as boundary conditions, the elastic strain energy release rate J and the three-dimensional stress intensity factors KI to KIII were then evaluated via the contour integral method. Constant mode I critical stress intensity factor was obtained along the curved crack fronts, with negligible shearing modes. This method allows evaluation of the fracture toughness without prior knowledge of elastic properties, and has potential applications to assess the effects of high temperature, oxidation and irradiation in small specimens of nuclear graphite.

A critical elastic strain energy storage-based concept for characterizing crack propagation in elastic–plastic materials

This paper provides a new insight on the problem of crack propagation in elastic–plastic materials from the perspective of the critical elastic strain energy release rate Ge. Specifically, Ge is derived from the power balance during crack propagation with the elimination of plastic dissipation and is assumed available for new crack formation. To validate this assumption, a series of experiments are carried out. The results show that the critical elastic strain energy storage decreases linearly with the increase of crack length. Therefore, Ge is believed as a more intrinsic parameter to describe the crack propagation in elastic–plastic materials.

A quasi-monolithic phase-field description for orthotropic anisotropic fracture with adaptive mesh refinement and primal–dual active set method

In this work, thermodynamically consistent phase-field fracture frameworks for transversely isotropic and orthotropic settings are proposed. We formulate an anisotropic crack phase-field via a penalization approach for each family of fibers. The resulting model is augmented with thermodynamical arguments and then carefully analyzed from a mechanical perspective. The fracture dissipation inequality to prevent crack healing is imposed via a primal–dual active set strategy. Predictor–corrector mesh adaptivity allows to work with small length-scale parameters at a reasonable computational cost. Due to the importance of laminated structures for industrial applications, fracture responses for transversely isotropic and orthotropic materials are performed. Therein, several studies are conducted that include comparisons of anisotropic formulations with Griffith’s critical elastic energy release rate and with specific critical fracture energy formulations, as well as non-split and split approaches.

Effective toughness of disordered brittle solids: A homogenization framework

This paper addresses the question of the homogenization of fracture properties for three-dimensional disordered brittle solids. The effective toughness, identified as the minimum elastic energy release rate required to ensure crack growth, is predicted from a semi-analytical framework inspired by both micromechanics and statistical physics, that encompasses the decisive influences of both the material disorder and the mechanisms of interaction between a crack and heterogeneities. Theoretical predictions are compared to numerical values of the effective toughness that are computed with the fracture-mechanics-based semi-analytical method of Lebihain et al. (2020). Based on a perturbative approach of Linear Elastic Fracture Mechanics, this method allows for the efficient computation of crack propagation under tensile Mode I loading in composite materials containing several millions of inclusions, where the crack interacts with them through two mechanisms : crossing, wherein the crack penetrates the inclusion, and by-pass, wherein the crack wanders out-of-plane and follows the inclusion/matrix interface. We show that our homogenization procedure provides an accurate prediction of the homogenized fracture properties for a broad range of microstructural parameters such as the inclusion toughness, density or shape. This original theoretical framework constitutes a powerful mean to connect the microstructural parameters of materials to their crack growth resistance, beyond the particular cases considered in the simulations performed. As a result, it provides new strategies for the rational design of optimized brittle composites with tailored fracture properties.

Assessment of the fracture toughness of neutron-irradiated nuclear graphite by 3D analysis of the crack displacement field

Digital volume correlation of in situ synchrotron X-ray computed tomographs has been used to measure the three-dimensional displacement fields around quasi-static propagating cracks in neutron irradiated and unirradiated graphite in specimens of the double cleavage drilled compression geometry. The crack tip location and crack opening were extracted from the displacement fields using a phase congruency edge detection method as cracks were propagated over ∼5 mm. The cracks propagated in mode I, maintaining a constant crack opening angle that was ∼50% smaller for the irradiated graphite. 3D finite element simulations, using the measured full field displacements as boundary conditions, obtained the critical elastic strain energy release rate for crack propagation by calculation of the domain contour J-integral. When the non-linear properties of unirradiated graphite were considered, the strain energy release rate for propagation was constant (180 ± 22 Jm-2) with increasing crack length. The irradiated graphite (fluence of 19.7 × 1020 neutrons cm−2 or 2.6 dpa, 4% weight loss by radiolytic oxidation) had linear elastic properties, and the strain energy release rate for propagation increased linearly from 118 ± 12Jm-2 to 485 ± 75 Jm-2 with crack length.

Brittle Characteristic and Microstructure of Sandstone under Freezing‐Thawing Weathering

As an important property of rock material, brittleness plays a vital role in rock engineering. This paper raised the concept of elastic strain energy release rate and proposed an elastic strain energy release rate based brittleness index based on the most acceptable definition of brittleness. Mechanical and Nuclear Magnetic Resonance parameters of sandstone under various Freezing‐Thawing (F‐T) cycles are also acquired and analyzed. Then, the proposed brittleness index is used to compare with two recently proposed brittleness indices to verify its correctness and applicability. Finally, the brittleness index is applied to evaluate the brittle behavior of F‐T cycles treated sandstone under uniaxial compression. The results show that elastic modulus, value of the postpeak modulus, and peak stress decrease with F‐T cycles, and the porosity and microstructure develop with F‐T cycles. The proposed brittleness index is highly related to F‐T cycles, peak stress, porosity, and elastic modulus of sandstone that suffered recurrent F‐T cycles. It declines exponentially with F‐T cycles and porosity increase while growing exponentially with peak stress and elastic modulus increase.

A New Bursting Liability Evaluation Index for Coal –The Effective Elastic Strain Energy Release Rate

Because both faults and cleats exist in coal, sharp stress drops occur during loading when coal is deformed. These drops occur during the pre-peak stage and are accompanied by sudden energy releases. After a stress drop, the stress climbs slowly following a zigzag path and the energy accumulated during the pre-peak stage is unstable. A stress–strain curve is the basic tool used to evaluate the bursting liability of coal. Based on energy accumulation in an unsteady state, the pre-peak stress–strain curve is divided into three stages: pre-extreme, stress drop, and re-rising stage. The energy evolution of the specimen during each stage is analyzed. In this paper, an index called the effective elastic strain energy release rate (EESERR) index is proposed and used to evaluate the coal’s bursting liability. The paper shows that the propagation and coalescence of cracks is accompanied by energy release. The stress climb following a zigzag path prolongs the plastic deformation stage. This causes a significant difference between the work done by a hydraulic press during a laboratory uniaxial compression experiment and the elastic strain energy stored in the specimen during the experiment, so the evaluation result of the burst energy index would be too high. The determination of bursting liability is a comprehensive evaluation of the elastic strain energy accumulated in coal that is released when the specimen is damaged. The index proposed in this paper fully integrates the energy evolution of coal samples being damaged by loading, the amount of elastic strain energy released during the sample failure divided by the failure time is the energy release rate. The calculation method is simplified so that the uniaxial compressive strength and elastic modulus are included which makes the new index more universal and comprehensive. Theoretical analysis and physical compression experiments validate the reliability of the evaluation.

Effect of water and rock composition on re-strengthening of cohesive faults during the deceleration phase of seismic slip pulses

The elastic strain energy release rate and seismic waves emitted during earthquakes are controlled by the on-fault temporal evolution of the shear stress during rupture propagation. High velocity friction experiments highlighted that shear stress on the fault surface evolves rapidly during seismic slip pulses. This temporal evolution of shear stress is controlled by both fault weakening at seismic slip initiation and re-strengthening rate towards the end of slip. While numerous studies focused on fault weakening, less attention was given to co-seismic re-strengthening processes. Here we performed 53 friction experiments (normal stress ≤30 MPa, slip-rate ≤6.5 ms−1) imposing constant slip acceleration and deceleration (7.8 ms−2), on cohesive Carrara marble (99% calcite) and micro-gabbro (silicate-built rock) under dry, vacuum and water pressurized conditions. Microstructural observations showed that micro-gabbro accommodated seismic slip by bulk melting of the sliding surfaces, whereas Carrara marble by coupled decarbonation and grain-size dependent crystal plastic processes. Under room humidity conditions and low imposed power density (i.e., product of normal stress per slip rate), re-strengthening rate during the deceleration stage was up to ∼ 17 times faster in marble than in micrograbbro. In the latter, the re-strengthening rate increased slightly with the power density. The presence of water enhanced further this trend. On the contrary, in marbles the re-strengthening rate decreased drastically with power density and in the presence of water. Our experimental observations highlighted the first order importance of the mineralogy and rheology of the slip zone materials and, to a second order, of the presence of water in controlling co-seismic re-strengthening of faults during seismic slip deceleration.

Synthesis and properties of a high solids triethoxysilane-modified alkyd coatings

Alkoxysilane modified linseed oil alkyds (TESLOA) were prepared using 3-(triethoxysilyl)propyl isocyanate (TESPIC). TESLOA was formulated as a high solids coating substituting up to 40% of an unmodified long oil linseed oil alkyd in increments of 10%. All the resulting high solids alkyds had a viscosity below 5000 cP. Toxicity and volatile organic compounds (VOCs) were reduced using an iron based primary drier and VOC-exempt acetone, respectively. An increase in adhesion was observed when TESLOA was used in formulations. The chemical resistance, appearance, and flexibility were examined using standard coating tests. An increase in chemical resistance and hardness was observed, while maintaining the flexibility and appearance. The surface energy was measured using contact angle. The TESLOA surface energy exhibited a hydrophobic shift in terms of surface wetting. The additional crosslinking sites of the TESLOA alkyds were evident in a higher glass transition temperature and crosslink density. Tensile properties also exhibited an increase in modulus. Fracture toughness testing showed up to a 50% increase in stress intensity factor at fracture, KIC, and the elastic energy release rate, GIC, when 20 wt.% of TESLOA in the formulation. Corrosion protection was studied using electrochemical impedance spectroscopy (EIS). The EIS data suggested that some self-healing properties could be obtained when using TESLOA as an additive.

Synchrotron X-ray characterization of crack strain fields in polygranular graphite

The strain field of a crack in polygranular isotropic nuclear graphite, a quasi-brittle material, has been studied during stable fracture propagation. Synchrotron X-ray computed tomography and strain mapping by diffraction were combined with digital volume correlation and phase congruency image analysis to extract the full field displacements and elastic crystal strains. The measured displacement fields have been analysed using a Finite Element method to extract the elastic strain energy release rate as a J-integral. Non-linear properties described the effect of microcracking on the elastic modulus in the fracture process zone. The analysis was verified by the good agreement of the predicted and measured elastic strain fields when using the non-linear model. The intrinsic critical elastic strain energy release rate for mode I crack propagation is approximately 200 J m−2.