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The use of composite materials is on the rise in different engineering fields, the main advantage of these materials for the aerospace industry is their low weight for excellent mechanical qualities. The analysis of failure modes, such as delamination, of these materials has received great attention from researchers. This paper proposes a method to evaluate the mode I Strain Energy Release Rate (SERR) of sandwich structures. This method associated a two-dimensional mixed finite element with virtual crack extension technique for the analysis of interfacial delamination of sandwich beams. A symmetrical Double Cantilever Beam (DCB) and asymmetrical Double Cantilever Beam (UDCB) have been analyzed in this study. The comparison of the results obtained by this method and those found in the literature shows efficiency and good precision for the calculation of Strain Energy Release Rate (SERR).

Growing use of recycled asphalt materials in asphalt pavement means the current volumetric-based Superpave mixture design may not address durability concerns arising from replacement of a proportion of virgin binder with recycled ones. To address this limitation, performance-based testing is introduced to supplement conventional volumetric mixture design in assessing cracking performance of asphalt mixtures. Louisiana Department of Transportation and Development’s Specifications for Roads and Bridges specify a criterion for the critical strain energy release rate, Jc, obtained from semi-circular bend (SCB) test as a complement of current practice to evaluate cracking resistance of asphalt mixtures. Quality control/assurance practices, however, require SCB samples to be long-term aged for five days at 85°C, which is a time-consuming process. Therefore, it is beneficial to be able to estimate SCB Jc for long-term aged asphalt mixtures based on SCB Jc measured from plant-produced asphalt mixtures. Asphalt mixture aging is complex, and various variables are involved in the aging process, including volumetric properties of asphalt mixture and chemical/rheological characteristics of asphalt binder. With the capability of artificial neural network (ANN) to address complex relationships between input and output variables, this study aims to predict the fracture parameter, SCB Jc, of asphalt mixtures using ANN. A total of 34 asphalt mixtures were selected for this study. SCB fracture test and asphalt binder tests for chemical and rheological characterization were conducted. Stepwise regression analysis was used to determine the significant parameters in the correlation with SCB Jc. With determined significant parameters, ANN using the gradient descent backpropagation approach was then applied to develop and validate the predictive model. It was shown that the developed ANN model was able to predict the fracture parameter, SCB Jc, of asphalt mixtures more accurately than linear and non-linear regression models.

We characterized the strain energy release rate and local crack-tip strain field for elastic hydrogels under several types of biaxial loading: planar, unequal biaxial, and equibiaxial extensions. The strain energy release rate (G) in each type of biaxial strain is characterized via two different approaches. One evaluates G from the change in strain energy with respect to the notch length (Xc) using single-edge notched specimens with various Xc values. The other estimates G from the difference in strain energy density between the two regions far behind and ahead of the crack tip. The excellent agreement between the G values obtained by the two methods demonstrated their reliability. We also revealed the features of the local crack-tip strain field in biaxial loading, including crack-tip opening displacement, strain field area, strain magnitude resulting from crack opening, and strain singularity exponent for strain growth near the crack tip. Importantly, these properties are governed exclusively by G, independent of the biaxial loading type. The results provide an important basis for a comprehensive understanding of the fracture behavior of elastic soft materials under complicated deformations.

Non-conventional fracture test geometries such as single cantilever bending, clamped beam bending and clamped wire bending have been developed over the years to suit the needs of micro- and nano-scale testing. The same geometries can also be used at the macro-scale if testing standards are well established. Development of length scale compatible geometries helps the materials engineer to seamlessly extract material properties across multiple length scales. This article proposes the crack driving force (or energy release rate G) criteria for the above three geometries. These geometries have found widespread use at the micro-scale and can be adapted to the macro-scale. Use of a global energy-based criterion instead of the local stress-based criteria (stress intensity factor K) has its own advantages, especially in multi-phase materials and interface-dominated structures which display an R-curve. Aspects of crack stability even under load control arising because of the geometric factors, especially the beam or wire aspect ratio, are discussed in this context. Validation of the compliance approach is carried out by comparing it to the J-integral extracted directly for a linear elastic material using extended finite element modeling and also using the analytical formulation for a double-cantilever beam specimen. Experimental evidence of the validity of the solutions in determining the fracture energy of a linear elastic brittle material, PMMA, as a homogeneous model system is shown.

The single edge notch specimen (SEN) is commonly used to measure the fracture toughness, or critical energy release rate of soft elastic materials. To measure toughness, an expression for the energy release rate, J, the mechanical energy available for growing the crack per unit area, is needed. Since strains in these fracture experiments can easily exceed several hundred percent, large deformation analysis is needed to calculate J. An approximate formula for J in SEN samples subjected to moderately large deformation was given by Rivlin and Thomas in J Polym Sci 10:291–318. https://doi.org/10.1002/pol.1953.120100303 (1953) and Greensmith in J Appl Polymer Sci 7:993–1002. https://doi.org/10.1002/app.1963.070070316 (1963). However, this formula works only for small crack lengths, for stretch ratio up to two and does not match the linear elastic result in the limit of small strains. In this paper we carry out a series of finite element (FE) simulations to obtain accurate approximations that are valid for all practical crack lengths and strain levels. Our FE result shows that the small crack approximation of by Rivlin and Thomas in J Polym Sci 10:291–318. https://doi.org/10.1002/pol.1953.120100303 (1953) does not work well in the small strain regime, and in particular, result of Greensmith in J Appl Polymer Sci 7:993–1002. https://doi.org/10.1002/app.1963.070070316 (1963) underestimates the energy release rate for stretch ratios less than 1.5.

The goal of this paper is to derive closed form expressions for the energy release rate and mode partitioning offace/core debonds for the Single Cantilever Beam Sandwich Composite testing configuration, which is loaded with an applied shear force and/or bending moment. This is achieved by an elastic foundation approach, in which a finite length sandwich beam is treated as having a free “debonded” section and a “joined” section where a series of springs exists between the face and the substrate (core and bottom face). The elastic foundation analysis is done for a general asymmetric sandwich construction. A J-integral approach is subsequently used to derive a closed form expression for the energy release rate. It is also shown that the energy release rate is very close to the differential energy stored in the springs at the beginning of the elastic foundation, i.e. the energy released by the “broken” differential spring element as the debond propagates. In the context of this elastic foundation model, a mode partitioning measure is defined based on the transverse and axial displacements at the beginning of the elastic foundation. Since the normal springs account for the transverse compressibility of the core but not for the shear, a correction for the shear of the substrate is included by deriving the expression for the corresponding shear angle and accounting for the additional horizontal “tip” displacement. The results are compared with finite element results for a range of core materials and show very good agreement.

The purpose of this study is to explore the hyperelastic effect on the energy release rate of a crack extension at the nanoscale. A molecular statics computation has been carried out to characteris...

Models of Representative Volume Elements of cross-ply laminates with different geometric configurations and damage states are studied. Debond growth is characterized by the estimation of the Mode I and Mode II Energy Release Rate using the Virtual Crack Closure Technique. It is found that the presence of the [Formula: see text] interface and the thickness of the [Formula: see text] layer has no effect, apart from laminates with ultra-thin [Formula: see text] plies where it is however modest. The present analysis supports the claim that debond growth is not affected by the ply-thickness effect.

The former studies indicate that loading rates significantly affect dynamic behavior of brittle materials, for instance, the dynamic compressive and tensile strength increase with loading rates. However, there still are many unknown or partially unknown aspects. For example, whether loading rates have effect on crack dynamic propagating behavior (propagation toughness, velocity and arrest, etc). To further explore the effect of loading rates on crack dynamic responses, a large-size single-cleavage trapezoidal open (SCTO) specimen was proposed, and impacting tests using the SCTO specimen under drop plate impact were conducted. Crack propagation gauges (CPGs) were employed in measuring impact loads, crack propagation time and velocities. In order to verify the testing result, the corresponding numerical model was established using explicit dynamic software AUTODYN, and the simulation result is basically consistent with the experimental results. The ABAQUS software was used to calculate the dynamic SIFs. The universal function was calculated by fractal method. The experimental-numerical method was employed in determining initiation toughness and propagation toughness. The results indicate that crack propagating velocities, dynamic fracture toughness and energy release rates increase with loading rates; crack delayed initiation time decreases with loading rates.

In order to measure the interfacial Strain Energy Release Rate (SERR) of adhesively bonded joints with metallic substrates, an alternative to the Tapered Double Cantilever Beam (TDCB) specimen is used here. In particular, the dimensions of one of the two substrates were reduced to create an Asymmetric Tapered Double Cantilever Beam (ATDCB) specimen. The ATDCB specimen has been introduced in the past by other research teams to study the mode I+II cohesive fracture properties of structural adhesives. It is shown the geometric dissymmetry of the ATDCB specimen affects the crack propagation path towards the interface with the smaller (less stiff) substrate. However, this substrate plasticises during the fracture test; hence, a strategy is also presented to evaluate the amount of potential energy spent for this phenomenon and subtract it from the total potential energy induced in the system during the fracture test. After this operation, the SERR of the adhesive under investigation was calculated by means of the Linear Elastic Fracture Mechanics (LEFM) theory before and after water ageing. The results showed a large decrease of the SERR with the increase of the ageing time.

The compressive behavior of composites after low velocity impact is one of the most important characteristics that should be taken into consideration when evaluating the damage tolerance of composite structures. In this paper, a novel experimental method combining infrared thermography and digital image correlation has been proposed to measure the energy release rate of composites under the compression-after-impact test. This method was chosen to avoid the error caused by the thermal stability assumption in the traditional methods that are used. First, a theoretical framework was developed and the formula for the energy release rate was established. Then, the calculation procedure has been described in detail with the combination of the temperature information from infrared thermography and the displacement information from the digital image correlation. Finally, an experimental case has been presented and by comparing the new method with the traditional methods, the accuracy of this proposed method has been validated.

In this paper, fracture behaviour of marine sandwich structured composite beams manufactured by vacuum-assisted resin infusion process with a PVC foam core, and different thicknesses of upper and lower glass fibre-reinforced polymer face sheets have been investigated. Fracture toughness in terms of strain energy release rate of sandwich composite beam is obtained using three end notched flexure test (3 ENF) by analytical method, finite element simulation using J integral and virtual crack closure technique (VCCT). Experimental testing has been applied with more accurate loading values for finite element modelling (FEM) simulations. The good agreement between experimental and numerical results shows that the finite element model is acceptable. A parametric study is carried out to observe the effects of core thickness, density of core, length of specimens, loading directions of the specimens on strain energy release rate (SERR) of sandwich composite beams under mode II loading. It is developed for the different core thicknesses with varying density combinations. The variations of maximum SERR value are presented graphically using numerical method and compared with analytical solution.

The behavior of fast straight-cracks in brittle, linear-elastic solids was described exactly nearly half-a-century ago by Freund. However, the subsequent attempts to describe analytically the velocity and the energy release rate of fast circular-cracks predicted behaviors which were inconsistent with the observed, experimental evidence. In this manuscript, a novel M−integral approach was used to determine exactly the dynamic energy release rate of axisymmetric-cracks in brittle materials. The proposed model adapted Freund’s mode I, two-dimensional, fast-crack solution to the geometric constraints imposed by circular-cracks. The relationship between the crack-tip’s velocity and the crack’s radial-extension predicted by the current model tracked closely the experimental results for soda-lime glasses obtained in this work and the ones for various brittle materials reported in the literature. A variation of the model for the energy release rate of moving circular-cracks, which is applicable to fractal fracture-surfaces, was also described.

A modified mixed mode fracture criterion, called generalized maximum energy release rate criterion, is proposed to predict the fracture initiation angles and estimate the fracture resistances in brittle and quasi-brittle materials under mixed mode loading. With this generalized maximum energy release rate criterion, the energy release rate around the crack tip is calculated by considering the contributions from both singular stress terms and T-stress. Experimental data, extracted from prior literatures for central cracked Brazilian disk, cracked semi-circular bend and edge-crack triangular specimens, are used to validate the modified criterion and evaluate the accuracy of the prediction obtained from this modified criterion. Results show that the T-stress plays a remarkable role in the mixed mode I/II fracture analysis when the energy-based criterion is employed. In addition, it is shown that the modified criterion can well predict the mixed mode I/II fracture behaviors of brittle and quasi-brittle materials.

Structure fabricated by welding identical steels or a fractured steel component repaired by steel weld filler of different strength leads to the presence of two interfaces with strength mismatch across them. Mode I crack in such a bi-material upon growing across the weld interlayer experiences the effect of the interfaces that manifests by way of change in crack tip energy release rate from the far field or remote value. The paper presents a strain based analytical model for estimation of the effect of interface over the crack tip. Crack tip energy release rate is determined at all the positions of the crack under SSY or K dominant conditions. The weld interlayer is assumed to be homogeneous and over-matched which possesses higher strength than that of the constituent steels. The modulus of elasticity is same throughout the domain. Edge crack of various discrete lengths is investigated in infinite body under uniform monotonic tension of 150 MPa in plane stress situation for demonstration of the model behavior.

Based on stress triaxiality analysis and SEM observations, the similarities and differences of fracture (damage) mechanisms for notched (both Mode I/II loading) and unnotched (uniaxial tension, uniaxial compression and spherical indentation tests) specimens were investigated. The investigations revealed that when the stress triaxiality was similar, the notched and unnotched specimens had a similar fracture (damage) mechanism. Thus, the damage in tensile tests was correlated with Mode I fractures, while the damage in uniaxial compression and spherical indentation tests were correlated with Mode II fractures. Taking the damage mechanism into consideration, a unified energy release rate based model to calculate the fracture toughness was proposed. Compared with previous studies, the energy release rate based model proposed in this study has a clear physical meaning and can be applied to different specimen configurations. Experiments on SA508, SA533, 15CrMoR, and S30408 revealed that the fracture toughness calculated from all three kinds of unnotched specimens using the new proposed energy release rate based model are as reliable as those from conventional compact tension tests.

The material with anisotropic properties are becoming widely essential due to the ease to manipulate their mechanical properties in order to obtain a particular quality, insure safety or a specific behavior. Those kind of materials are considered anisotropic because their characteristics and behavior are dependent to every direction of the material’s orientation. In this work, the virtual crack closure-integral technique is implemented to a mixed finite element, in addition with the stiffness derivative procedure, to evaluate the energy release rate of crack extension in anisotropic materials. A simulation of a cracked edge rectangular plat with anisotropic characteristics is taken for example. The results obtained are in good agreement with the analytical results, making the proposed technique a good model for fracture investigation and allow it to study more complicated cases in future works.

A method for evaluating the contributions from mode I and II components of loading to the energy release rate J in ductile asymmetric four-point bend (4-PB) specimens is proposed. The validity of the method is established by conducting elastic-plastic finite element analysis of several asymmetric 4-PB specimens exhibiting a range of mode mixities from pure mode I to II and having different crack length to width (a / W) ratios. Further, a definition of plastic mode mixity is introduced based on the near-tip opening and sliding displacements. This definition and the proposed method to evaluate J are easy to apply since the required crack opening and sliding displacements can be determined from in-situ optical imaging coupled with Digital Image Correlation (DIC) technique. The application of the proposed methodology is demonstrated by analyzing mixed-mode fracture experiments being conducted with a magnesium alloy. It is found that the critical value of J at crack initiation reduces as loading changes from mode I to II.

One of the assumptions of Linear Elastic Fracture Mechanics is that the crack faces are traction-free or, at most, loaded by bounded tractions. The standard Irwin's crack closure integral, widely used for the computation of the Energy Release Rate, also relies upon this assumption. However, there are practical situations where the load acting on the crack boundaries is singular. This is the case, for instance, in hydraulic fracturing, where the fluid inside the crack exerts singular tangential tractions at its front. Another example of unbounded tractions is the case of a rigid line inclusion (anticrack) embedded into an elastic body. In such situations, the classical Irwin's crack closure integral fails to provide the correct value of the Energy Release Rate. In this paper, we address the effects occurring when square-root singular tractions act at the boundary of a line defect in an elastic solid and provide a generalisation of Irwin's crack closure integral. The latter yields the correct Energy Release Rate and allows broad applications, including, among others, hydraulic fracturing, soft materials containing stiff inclusions, rigid inclusions, shear bands and cracks characterized by the Gurtin-Murdoch surface stress elasticity. We present the results in the most general form, where six Stress Intensity Factors are present: three of them are classical SIFs corresponding to the modes I-II-III and computed under the assumption of homogeneous boundary conditions at the defect surfaces, while the other three SIFs are associated with singular admissible tractions (those that lead to a finite ERR value). It is demonstrated that this approach resolves an ambiguity in using the same SIF's terminology in the cases of open cracks and rigid inclusions, among other benefits., 22 pages 2 pictures

Silica-based and borate-based glass series, with increasing amounts of TiO2 incorporated, are characterized in terms of their mechanical properties relevant to their use as metallic coating materials. It is observed that borate-based glasses exhibit CTE (Coefficient of Thermal Expansion) closer to the substrate’s (Ti6Al4V) CTE, translating into higher mode I critical strain energy release rates of glasses and compressive residual stresses and strains at the coating/substrate interface, outperforming the silica-based glasses counterparts. An increase in the content of TiO2 in the glasses results in an increase in the mode I critical strain energy release rate for both the bulk glass and for the coating/substrate system, proving that the addition of TiO2 to the glass structure enhances its toughness, while decreasing its bulk hardness. Borate-based glass BRT3, with 15 mol % TiO2 incorporated, exhibits superior properties overall compared to the other proposed glasses in this work, as well as 45S5 Bioglass® and Pyrex.

A methodology of repair in pipes involving bonded joints, manufactured through the wrappage of a composite around the pipe, is becoming a common practice in the industry for a series of ass...

The interfacial crack in bimaterials is a very interesting problem for composite materials and which has received particular attention from several researchers. In this study, we will propose a numerical modeling of the interfacial crack between two orthotropic materials using a special mixed finite element. For the calculation of the energy release rate, a technique, based on the association of the present mixed finite element with the virtual crack extension method, was used. The numerical model proposed, in this work, was used to study a problem of interfacial crack in bimaterials. Two cases were treated: isotropic and orthotropic bimaterials. The results obtained, using the present element, were compared with the values of the analytical solution and other numerical models found in the literature.

Adhesion between coatings and substrates is an important parameter determining the integrity and reliability of film/substrate systems. In this paper, a new and more refined theory for characterizing adhesion between elastic coatings and rigid substrates is developed based on a previously proposed pressurized blister method. A compressed air driven by liquid potential energy is applied to the suspended circular coating film through a circular hole in the substrate, forcing the suspended film to bulge, and then to debond slowly from the edge of the hole as the air pressure intensifies, and finally to form a blister with a certain circular delamination area. The problem from the initially flat coating to the stable blistering film under a prescribed pressure is simplified as a problem of axisymmetric deformation of peripherally fixed and transversely uniformly loaded circular membranes. The adhesion strength depends on the delamination area and is quantified in terms of the energy released on per unit delamination area, the so-called energy release rate. In the present work, the problem of axisymmetric deformation is reformulated with out-of-plane and in-plane equilibrium equations and geometric equations, simultaneously improved, and a new closed-form solution is presented, resulting in the new and more refined adhesion characterization theory.

This paper summarizes the development of a technique of using miniature bulge test combined with three-dimensional digital image correlation (3D-DIC) for measuring energy release rate or fracture toughness of bimaterial interface of thin metal foils. The energy release rate associated with the HIPed aluminum/aluminum interfacial delamination is determined experimentally using the proposed technique. Detailed discussions of the schemes of preparing and conducting the bulge test, and computing various quantities required for the determination of the energy release rate are presented.

Higher order crack tip stresses, displacements, T-stress and energy release rate with a constant speed in anisotropic materials are studied. The dynamic stresses and displacements are derived from the displacement potentials and higher order complex functions. Using the dynamic stress and displacement components, the dynamic T-stress and energy release rate are derived. The effects of fiber direction and crack speed on the stresses, displacements, T-stress and energy release rate are examined. The maximum values of stresses σxx and σyy at crack tip around are greater when the direction of the stress component approaches to the fiber direction than when the direction of the stress component is dissimilar to the fiber direction. T-stress in anisotropic materials, unlike isotropic and orthotropic materials, appears in the stress term of mode II as well as mode I. Energy release rate GI for opening mode decreases as α increases and GII for shearing mode increases as α increases.

An energy method based on beam theory is proposed to determine the strain energy release rate of an existing crack in composite laminates. The developed analytical method was implemented in isotropic materials, and the obtained strain energy release rate of a crack was validated by reference results and finite element solutions. The general behavior of crack growth on the left or right crack tip was evaluated, and basic trends leading to crack propagation to one side of the crack were established. A correction factor was introduced to improve the accuracy of the strain energy release rate for small cracks. The singularity at the crack tip caused by dissimilar materials was investigated and was found that the inclusion of the singularity effect could increase the accuracy for small cracks. The calculated strain energy release rate of a crack in a composite beam has been verified by comparing with a finite element model.

This article presents an approach for modelling fracture and delamination, based on the partition of finite elements and on the energy release rate due to crack propagation in cross-ply laminates. The energy release rate is implemented within an Extended Finite Element Method (XFEM) framework. This approach is enabling the prediction of delamination propagation without pre-allocating damage zones. No element deletion techniques were used either. Mesh refinement was not needed for the propagation of cracks. Virtual testing of transverse cracks – eventually triggering delamination in cross-ply laminates – is presented to show the technique efficiency. Thus, a maximum energy release rate of 0.9kJ/m 2 is found for a transverse crack within [0 0 ,90 0 ] s laminate. When maximum energy release rate is reached, delamination in the {0 0 /90 0 } interface is triggered. Furthermore, delamination in a composite double cantilever beam is simulated and presented in some detail. The results were compared with experimental outputs and/or by other numerical means showing an excellent correlation.

The effect of a buffer-layer on the steady-state energy release rate of a tunneling crack in the adhesive layer of a wind turbine blade joint, loaded in tension, is investigated using a parametric 2D tri-material finite element model . The idea of embedding a buffer-layer in-between the adhesive and the basis glass fiber laminate to improve the existing joint design is novel, but the implications hereof need to be addressed. The results show that it is advantageous to embed a buffer-layer near the adhesive with controllable thickness- and stiffness properties in order to improve the joint design against propagation of tunneling cracks. However, for wind turbine blade relevant material combinations it is found more effective to reduce the thickness of the adhesive layer since the stiffness mismatch between the existing laminate and the adhesive is already high. The effect of material orthotropy was found to be relatively small for the blade relevant materials.

Topological derivatives provide the variation of a functional when an infinitesimal hole is introduced into the domain. In Silva et al. (J Mech Phys Solids 59(5):925–939, 2011), the authors developed a first-order approximation of the energy release rate associated with a small crack at any boundary location and at any orientation using a first-order topological derivative. This approach offers significant computational advantages over other methods because (i) it requires only a single analysis while other methods require an analysis for each crack size-location-direction combination, and (ii) it is performed on the non-cracked domain, removing the need to create very fine meshes in the vicinity of the crack. In the present study, higher-precision approximations of the energy release rate are developed using higher-order topological derivatives which allow the analyst to accurately treat longer cracks and determine the crack lengths for which the first-order approximation is accurate.

The quasi-static Mode I fracture behaviour of joints bonded with either a brittle or toughened epoxy adhesive or a ductile polyurethane adhesive has been investigated by means of digital image correlation (DIC). A novel method to measure the crack length using DIC analysis is proposed. By measuring the crack tip separation, beam rotation and crack length, the energy release rate G and the J-integral are obtained and are compared to analyse the validity of Linear Elastic Fracture Mechanics (LEFM) methods. Simultaneously the traction-separation laws (TSLs) for the adhesive joints were measured. The TSLs were then used as input data for FE modelling to evaluate their accuracy by comparing with experimental results. It is shown that LEFM is valid for the joints bonded with either the brittle or toughened epoxy adhesives but is invalid for joints bonded with the polyurethane adhesive. The procedure proposed here to measure the crack length via DIC shows great promise and can be automated readily in practice.

Fracture analysis of crack growth in between two material interfaces (different engineering materials) is one of the challenging tasks in the engineering field. In the present investigation, different properties of bi-material are considering to study the damage-tolerant design and analysis of fracture mechanics. A double cantilever beam (DCB) with a bi-material crack is considered for analysis. In FEM, specifically a post-processing command virtual crack closure technique (VCCT) is used for evaluation of mixed mode energy release rate of bi-material interface cracks. Validation of obtained results is done with a benchmark problem in the literature. Then parametric studies have been conducted on four different material combinations for a range of crack length and height of the beam. The results generated will be useful for assessing structural integrity.

The equilibrium, path-independent J-integral is commonly interpreted as the rate of decrease in the potential energy of an elastic body, containing a crack, per unit area of the new surface created by crack extension. Such an interpretation encounters difficulties. The correct, contradiction-free description of the energy-release rate is the approach based on the dynamic energy flow into the crack tip. As a corollary, it leads to the correct quasistatic criteria for brittle-fracture propagation.

When performing predictive durability analyses on tires using finite element methods, it is generally recognized that energy release rate (ERR) is the best measure by which to characterize the fatigue behavior of rubber. By addressing actual cracks in a simulation geometry, ERR provides a more appropriate durability criterion than the strain energy density (SED) of geometries without cracks. If determined as a function of crack length and loading history, and augmented with material crack growth properties, ERR allows for a quantitative prediction of fatigue life. Complications arise, however, from extra steps required to implement the calculation of ERR within the analysis process. This article presents an overview and some details of a method to perform such analyses. The method involves a preprocessing step that automates the creation of a ribbon crack within an axisymmetric-geometry finite element model at a predetermined location. After inflating and expanding to three dimensions to fully load the tire against a surface, full ribbon sections of the crack are then incrementally closed through multiple solution steps, finally achieving complete closure. A postprocessing step is developed to determine ERR as a function of crack length from this enforced crack closure technique. This includes an innovative approach to calculating ERR as the crack length approaches zero.

In this article, we determine experimentally the energy release rate (ERR) of gelatin hydrogels on a smooth glass surface in the direct shear mode using slide-hold-slide (SHS) experiments. The crack lengths and corresponding forces measured in SHS experiment are ultimately used to estimate ERR of the sliding surfaces. The ERR at static, dynamic and residual strengths are physically correlated in terms of work of rupture , work of steady sliding and work of adhesion respectively. Moreover, it is observed that and increase with pulling velocity, normal stress and gelatin concentrations. Although at the residual strength remains independent of pulling velocity, the same increases with the normal stress and gelatin concentrations. The novelty of the present study is that the frictional properties of gelatin hydrogels on glass surface is now correlated with fracture mechanics.

3D problems for plane cracks of arbitrary shape in anisotropic media are considered. The stress intensity factors are determined by the intensity factors of the crack displacement discontinuity field. Strong ellipticity of the constructed pseudodifferential operator is proved. The solution of the pseudodifferential operator of the crack theory is obtained by the specially constructed potentials with densities concentrated at the crack front. Irwin’s relation for the energy release rate is obtained for a plane crack of arbitrary shape in a medium with arbitrary elastic anisotropy.