Elastic Strain Energy Release Rate Research Articles

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.

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.

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.

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.

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.

Obtaining the J-integral by diffraction-based crack-field strain mapping

The analysis by diffraction of polycrystalline materials can determine the full tensor of the elastic strains within them. Point-by-point maps of elastic strain can thus be obtained in fine-grained engineering alloys, typically using synchrotron X-rays or neutrons. In this paper, a novel approach is presented to calculate the elastic strain energy release rate of a loaded crack from two-dimensional strain maps that are obtained by diffraction. The method is based on a Finite Element approach, which uses diffraction data to obtain the parameters required to calculate the J-integral via the contour integral method. The J integral is robust to uncertainties in the crack tip position and to poor definition of the field in the crack vicinity, and does not rely on theoretical assumptions of the field shape. A validation of the technique is presented using a synthetic dataset from a finite element model. Its experimental application is demonstrated in an analysis of a synchrotron X-ray diffraction strain map for a loaded fatigue crack in a bainitic steel.

Variation in electromagnetic radiation during plastic deformation under tension and compression of metals

This paper presents some significant variations in the intermittent electromagnetic radiation (EMR) during plastic deformation under tension and compression of some metals with selected crystal structure, viz. zinc, hexagonal closed packed (hcp), copper, face-centred cubic (fcc: stacking fault energy 0.08 J/m2), aluminium (fcc: stacking fault energy 0.2 J/m2) and 0.18 % carbon steel, body-centred cubic (bcc). The intermittent EMR signals starting near yielding are either oscillatory or exponential under both modes of deformation except a very few intermediate signals, random in nature, in zinc under compression. The number and amplitude of EMR signals exhibit marked variations under tension and compression. The smooth correlation between elastic strain energy release rate and average EMR energy release rate suggests a novel technique to determine the fracture toughness of metals. The first EMR emission amplitude and EMR energy release rate occurring near the yield increase, but maximum EMR energy burst frequency decreases almost linearly with increase in Debye temperature of the metals under tension while all EMR parameters decrease nonlinearly under compression. These results can be developed into a new technique to evaluate dislocation velocity. The EMR amplitude and energy release rate of the first EMR emission vary parabolically showing a maxima with increase in electronic heat constant of the metals under tension while they first sharply decrease and then become asymptotic during compression. However, the variation in EMR maximum energy burst frequency is apparently similar under both modes of deformation. These results strongly suggest that the mechanism of EMR emission during plastic deformation of metals involves not only the interaction of conduction electrons with the lattice periodic potential as presented in the previous theoretical models but also the interaction of conduction electrons with phonons. However, during crack propagation and fracture, charge oscillations at fractured surfaces due to breaking of atomic bonds constitute an additional factor.

Multiscale analysis of stiffness and fracture of nanoparticle-reinforced composites using micromechanics and global–local finite element models

A combined micromechanics analysis and global–local finite element method is proposed to study the interaction of particles and matrix at the nano-scale near a crack tip. An analytical model is used to obtain the effective elastic modulus of nanoparticle-reinforced composites, then a global–local multi-scale finite element model with effective homogeneous material properties is used to study the fracture of a compact tension sample. For SiO 2 particle-reinforced epoxy composites with various volume fractions, the simulation results for effective elastic modulus, fracture toughness, and critical strain energy release rate show good agreement with previously published experimental data. It is demonstrated that the proposed parametric multi-scale model can be used to efficiently study the toughness mechanisms at both the macro and nano-scale.

Numerical simulation of growth pattern of a fluid-filled subsurface crack under moving hertzian loading

Cracking of a fluid-filled subsurface crack is studied by means of the distributed dislocation technique within the framework of two-dimensional linear elastic fracture mechanics. The Griffith crack was initially opened by the application of hydrostatic pressure of an incompressible fluid within the crack. A moving Hertz line contact load distribution is applied at the surface of the half-plane in the presence of friction. The stress intensity factors at the tips of the fluid-filled crack are analyzed with the restriction that due to the fluid incompressibility there is no change of the crack-opening volume. When the crack starts to propagate/kink, numerical results show that the internal fluid pressure will be relieved, and as the ratio of the branched crack length to main crack length increases, the elastic strain energy release rate decreases. The crack growth is assumed to be arrested when the energy release rate is below a certain value. Based on the energy criterion, predictions are attempted for determining the load position where the crack propagation/kink commences as well as the growth increment of the branch crack before it is arrested. A step-by-step crack path is constructed to simulate the growth pattern of the fluid-filled crack under moving Hertzian loading.

Some basic aspects of electromagnetic radiation emission during plastic deformation and crack propagation in Cu–Zn alloys

This paper presents some basic aspects of electromagnetic radiation (EMR) emission during plastic deformation and crack propagation in Cu–Zn alloys. Six parameters, viz. stress intensity factor, elastic strain energy release rate, EMR amplitude (maximum and rms), EMR frequency, and electromagnetic energy release rate, at different percent of zinc content have been analyzed. Results show that EMR parameters increase with increase in zinc up to 30% and then they decrease with higher zinc percentage. Investigations showed that the electromagnetic energy release rate has a direct correlation with the elastic strain energy release rate, which can prove to be a novel technique for the evaluation of fracture toughness. It was further observed that the electromagnetic energy release rate bears a parabolic relation with the ratio of stress at crack tip instability, σ, to the stacking fault energy, U f, where cross-slip energy is also known to be only a function of ( σ/ U f).

Effect of processing parameters on the electromagnetic radiation emission during plastic deformation and crack propagation in copper-zinc alloys

This paper presents some investigations on the effect of processing parameters on the emission of electromagnetic radiation (EMR) during plastic deformation and crack propagation in copper-zinc alloys. Timing of the EMR emissions, maximum stress during crack instability, stress-intensity factor, elastic strain energy release rate, maximum EMR amplitude, RMS value of EMR amplitude, EMR frequency and electromagnetic energy release rate were analysed for the effect of rolling directions at different percentage of zinc content in Cu-Zn alloy specimens. The same parameters were also analysed for 68-32 Cu-Zn alloy specimens at different annealing temperatures and at different angles ϑ, to the rolling direction. EMR emissions are observed to be highly anisotropic in nature. At ϑ=45° to 60°, marked changes in mechanical and electromagnetic parameters were observed. Specimens annealed at 500 °C, just above the recrystallization temperature, and at 700 °C, when grain-size growth is rapid, EMR responses have been found to have well-defined patterns.

Polymer/metal interfacial crack growth characterized by C*

This paper establishes a simple testing scheme to simultaneously measure the linear elastic strain energy release rate G, the non-linear J-integral, and the rate-dependent C*-integral for a growing crack at a polymer/metal interface. The test is applicable to fracture of adhesive bonds. A criterion governing C*-controlled fracturing is derived, analogous to the Hutchinson-Paris ω-criterion for J-controlled growth. The interfacial toughness of an adhesive commonly used for bonding metal plates is characterized at room temperature, and is shown to fracture in a C*-controlled manner. A relationship between C* and the crack growth rate is observed. The nature of this relationship warrants further exploration.

Dynamic ductile fracture of 7075-T6 – an experimental analysis

Dynamic moiré interferometry fringes surrounding a rapidly propagating crack in single edge notched, 7075-T6 aluminum specimen of 1.6 mm thickness were used to compare directly the T ∗ ε -integral values associated with a near-crack integration contour, the crack-tip opening angles and the elastic strain energy release rate, G. While T ∗ ε reached a steady state value and remained constant at the terminal crack velocity, G followed the well-known gamma curve and varied with the crack driving force at the terminal velocity. This limited result may be an indication of the inadequacy in linear elastic fracture mechanics characterization of dynamic ductile fracture.

The effect of environment on the fatigue of bonded composite joints. Part 2: fatigue threshold prediction

In Part 2 of this paper, the fatigue strength of adhesively bonded joints is analysed using stress analysis and fracture mechanics. Composite lap strap joints are considered for this study. Substrates made of unidirectional and multidirectional composite laminates are bonded together using epoxy film adhesive. Non-linear stress and fracture analyses are performed in order to predict the strength of the joints in different hostile environmental conditions. The use of several threshold criteria is investigated. Criteria based on the principal stress provide good threshold prediction for small plastic deformation. The maximum principal strain, von Mises strain, shear stress and von Mises stress predict with good accuracy the fatigue thresholds of the joints that undergo large plasticity. The plastic zone size does not show correlation at the fatigue threshold load in the different joint types. Furthermore, elastic and elasto-plastic fracture parameters are calculated for two different inherent cracks. The first one is initiated at the adhesive/adherend interface, while the second is in the centre of the adhesive layer. The J-integral that accounts for plasticity and the elastic strain energy release rate have been shown to correlate with the threshold load for the different joints.