Energy Release Rate Analysis Research Articles

Size-Dependent Analysis of Strain Energy Release Rate of Buckling Delamination Based on the Modified Couple Stress Theory

Size-Dependent Analysis of Strain Energy Release Rate of Buckling Delamination Based on the Modified Couple Stress Theory

Stress and energy release rate analysis of cross-ply carbon fiber-reinforced plastic laminate with transverse cracks subjected to ultrasonic vibration using a variational approach

Application of carbon fiber reinforced plastics (CFRP) to structures that are subjected to increasingly high numbers of cyclic loads is expected to expand, so evaluation of fatigue properties up to the very-high cycle regime is essential to prove their long-term reliability. Conventional fatigue testing is not practical for such conditions owing to the excessive time required; ultrasonic fatigue testing, which can be performed at a frequency of 20 kHz, is an effective alternative. Stress distribution in ultrasonic fatigue testing differs from that in conventional fatigue testing because the specimen is resonated. The stress distribution of cross-ply laminates with transverse cracks subjected to resonance was calculated using a variational approach. The energy release rate was calculated based on the results of a previous study on transverse crack initiation. The results of the stress analysis are in good agreement with those of finite-element analysis. Quantitative evaluation of transverse crack initiation was also conducted.

Analysis of energy release rate of laser-induced cohesive bonding of carbon fiber-reinforced polyetherketoneketone thermoplastic composites

In this study, laser joining of carbon fiber/polyetherketoneketone composites with several patterns was investigated to achieve weight reduction without any mechanical fasteners. The laser beam concentrated the energy, and heat conduction in the through-thickness direction of heterogeneous carbon fiber-reinforced thermoplastics caused molecular diffusion at the joining interface. According to the double-beam cantilever test results, the maximum energy release rate (ERR) was 2.01 J/mm2, which was 900 % higher than that of epoxy adhesive joining using laser power densities in the range of 1.05–1.34 W/mm2. A higher ERR was achieved because the optimized laser joining pattern secured repetitive cohesive joining at the interface. Thus, a complicated and step-wise crack opening was observed, which interfered with the propagation.

A chemo-mechanical coupling model of oxidation and interlayer cracking of copper nanowires

Copper nanowires have received extensive attention for their potential applications in optics, electricity and catalysis, while oxidation erosion has become the biggest obstacle to their widespread application. Here, we present a chemo-mechanical coupling model to investigate the interlayer cracking behaviors of nanowires during oxidation. In contrast to existing chemo-mechanical models, the present model emphasizes that the process of oxygen entry into copper nanowires is chemical reaction-mediated layer-by-layer replacement rather than vacancy-mediated diffusion, which means the oxygen ions in the outer layer would not cross over the oxygen atoms in the inner layer during their entry. These conclusions are validated by molecular dynamics simulations. We then discuss the effect of the chemical reaction-induced free energy on the stress state of the nanowire during the reaction. Finally, a self-developed finite difference procedure is used to solve the control equations and the fracture location is determined according to the energy release rate analysis. We find the fracture of nanowires is closely dependent on the size of nanowire, the reaction rate and the oxygen concentration. This work deepens our understanding of the mechanism of chemo-mechanical coupling and fracture behavior of metals due to oxidation, thus has implications in other areas involving chemo-mechanical coupling.

Statically undetermined multilayered beam of non-linear viscoelastic behaviour: a delamination study

Delamination of a twice statically undetermined multilayered beam structure which has non-linear viscoelastic behaviour is studied analytically. The beam is made of layers whose time-dependent behaviour is treated by a non-linear viscoelastic mechanical model having equal number of springs and dashpots. The strain energy release rate is derived by analyzing the balance of the energy. The curvatures and the coordinates of neutral axes of the beam portions needed for obtaining of the strain energy release rate are found by resolving the static indeterminacy. The delamination is studied also by the method of J-integral to verify the strain energy release rate. In order to evaluate the effect of the static indeterminacy, an analysis of the strain energy release rate is carried-out also assuming that the beam under consideration is statically determinate structure.

Longitudinal vertical crack analysis in beam with relaxation stresses

PurposeThis paper is concerned with analysis of the time-dependent strain energy release rate for a longitudinal crack in a beam subjected to linear relaxation. A viscoelastic model with an arbitrary number of parallel units is used for treating the relaxation. Each unit has one dashpot and two springs. A stress-strain-time relationship is derived for the case when the coefficient of viscosity in each unit of the viscoelastic model changes continuously with time. The beam exhibits continuous material inhomogeneity along the thickness. Thus, the moduli of elasticity and the coefficients of viscosity vary continuously in the thickness direction. The aim of the present paper is to obtain time-dependent solutions to the strain energy release rate that take into account the relaxation when the coefficient of viscosity changes with time.Design/methodology/approachTime-dependent solutions to the strain energy release rate are derived by considering the time-dependent strain energy and also by using the compliance method. The two solutions produce identical results.FindingsThe variation of the strain energy release rate with time due to the relaxation is analysed. The influence of material inhomogeneity and the crack location along the beam width on the strain energy release rate are evaluated. The effects of change of the coefficients of viscosity with time and the number of units in the viscoelastic model on the strain energy release rate are assessed by applying the solutions derived.Originality/valueThe time-dependent strain energy release rate for a longitudinal vertical crack in a beam under relaxation is analysed for the case when the coefficients of viscosity change with time.

Analysis of the Strain Energy Release Rate for a Delamination Crack in a Multilayered Beam with Material Non-Linearity

The strain energy release rate for a delamination crack in a multilayered cantilever beam which exhibits material non-linearity is derived by considering the energy balance. The material non-linearity is described by the Ramberg-Osgood stress-strain relation. A cantilever beam made of adhesively bonded lengthwise vertical layers is studied. Each layer has individual widths and material properties. Besides, the delamination is located arbitrary between layers. The strain energy release rate is derived also by differentiating the complementary strain energy with respect to the crack area for verification. It is shown that the solution derived is useful for parametric investigations of delamination in multilayered beams.

Non-linear fracture analysis of multilayered two-dimensional graded beams

PurposeThe purpose of this paper is to present an analytical study of the delamination fracture behaviour of a multilayered two-dimensional functionally graded cantilever beam configuration. A delamination crack is located arbitrary along the height of the beam cross-section. The layers have different thicknesses and material properties. Perfect adhesion is assumed between layers. The material is functionally graded in both thickness and width directions in each layer. Besides, the material of the beam exhibits non-linear-elastic behaviour.Design/methodology/approachThe delamination fracture behaviour is analysed in terms of the strain energy release rate. The J-integral approach is applied in order to verify the analysis of the strain energy release rate developed in the present paper.FindingsThe influence of material properties, the crack location along the height of the beam cross-section and the non-linear behaviour of the material on the delamination fracture is examined.Originality/valueA non-linear delamination fracture analysis of multilayered two-dimensional non-symmetric functionally graded beam configuration is developed.

Delamination in a Two-Dimensional Functionally Graded Beam

An analytical study of delamination in the crack lap shear beam is performed. It is assumed that the material is functionally graded along the width and height of the beam. Delamination is studied in terms of the total strain energy release rate by applying methods of linear-elastic fracture mechanics. An additional analysis of the total strain energy release rate is performed by considering the strain energies in the beam cross sections ahead of and behind the crack front for verification. The effects of the crack location and material gradient on delamination are evaluated.

Fracture analysis of a three-dimensional functionally graded beam

PurposeThe purpose of this paper is to carry out a delamination fracture analysis of the three-dimensional functionally graded split cantilever beam (SCB) configuration.Design/methodology/approachThe fracture behaviour was studied analytically in terms of the strain energy release rate by applying methods of linear elastic fracture mechanics. It was assumed that the material is functionally graded along the beam width, height and length. The strain energy release rate was derived by analysing the stress and strain state in the beam cross-sections ahead and behind the crack front. An additional analysis of the strain energy release rate was performed by considering the beam strain energy for verification.FindingsThe influence of material gradient along the beam width, height and length on the delamination fracture behaviour was investigated. The effect of crack length was analysed too. The analytical approach developed is very useful for parametric fracture investigations. The results obtained in the present study can be applied for optimisation of three-dimensional functionally graded beam systems in their design with respect to delamination fracture behaviour.Originality/valueAn analytical approach for studying the delamination fracture in the SCB configuration that is functionally graded along the beam width, height and length was developed.

Analytical Study of Delamination in Multilayered Two-Dimensional Functionally Graded Non-Linear Elastic Beams

AbstractThe present paper is focused on the delamination fracture in a multilayered two-dimensional functionally graded beam configuration which exhibits non-linear behavior of the material. The beam is loaded by two longitudinal forces applied at the beam free ends. The beam contains a delamination crack which is located symmetrically with respect to the beam mid-span. The delamination is studied analytically in terms of the strain energy release rate. TheJ-integral approach is applied for verification of the analysis of the strain energy release rate. The solution derived is valid for a beam made of an arbitrary number of layers. It is assumed that each layer has individual thickness and material properties. Also, the material is two-dimensional functionally graded in the cross-section of each layer. The solution obtained can be applied for a delamination crack located arbitrary along the height of the beam cross-section. It is shown that the solution is very convenient for investigating the influences of material gradients and crack location on the delamination fracture behavior. The results obtained can be used for optimization of multilayered two-dimensional functionally graded structural members and components with respect to their delamination fracture performance.

A study of mode-I self-similar dynamic crack propagation using a lattice spring model

The spontaneous crack growth in an infinite domain is studied using the distinct lattice spring model (DLSM). The kinetic energy, strain energy, crack opening, and crack branching during the crack growth are investigated numerically using a simple spring model. The discrete simulation satisfactorily reproduces the experimental observations and the theoretical predictions of the fracture energy increase even without considering the crack tip damage zone and crack bifurcation. Moreover, from analysis of the intrinsic fracture energy release rate, it was concluded that the observed fracture energy increase should originate from the distribution of kinetic energy during self-similar crack growth.

Energy release rate analysis on the interface cracks of enamel-cement-bracket fracture using virtual crack closure technique

This paper presents the energy method to evaluate fracture behavior of enamel-cement-bracket system based on cement thickness. Finite element (FE) model of enamel-cement-bracket was constructed by using ANSYS Parametric Design Language (APDL). Three different thickness were used in this study, 0.05, 0.2, and 0.271 mm which assigned as thin, medium and thick for both enamel-cement and cement bracket interface cracks. Virtual crack closure technique (VCCT) was implemented as a simulation method to calculated energy release rate (ERR). Simulation results were obtained for each thickness are discussed by using Griffith’s energy balance approach. ERR for thin thickness are found to be the lowest compared to medium and thick. Peak value of ERR also showed a significant different between medium and thick thickness. Therefore, weakest bonding occurred at low cement thickness because less load required to produce enough energy to detach the bracket. For medium and thick thickness, both increased rapidly in energy value at about the mid-point of the enamel-cement interface. This behavior occurred because of the increasing in mechanical and surface energy when the cracks are increasing. However, result for thick thickness are higher at mid-point compared to thin thickness. In conclusion, fracture behavior of enamel cracking process for medium most likely the safest to avoid enamel fracture and withstand bracket debonding.

Non-linear elastic delamination of multilayered functionally graded beam

PurposeThe purpose of this paper is to perform an analytical study of non-linear elastic delamination fracture in the multilayered functionally graded split cantilever beam (SCB) configuration. The SCB studied may have an arbitrary number of vertical layers. The material in each layer is functionally graded along the layer thickness. Also, the material properties may be different in each layer. The analytical solution derived was applied for parametric investigations in order to evaluate the effects of material properties and delamination crack location on the non-linear fracture behaviour.Design/methodology/approachThe delamination fracture was studied in terms of the strain energy release rate. The SCB mechanical response was described by using a power-law stress-strain relation. A non-linear analytical solution for the strain energy release rate was derived by considering the SCB complementary strain energy. In order to verify the solution, an additional analysis of the strain energy release rate was developed by considering the complementary strain energy in the beam cross-sections ahead and behind the crack front.FindingsThe effects of material gradient, crack location along the beam width and non-linear material behaviour on the delamination fracture were evaluated. The analytical solution derived is useful for parametric studies of non-linear fracture in multilayered functionally graded beams.Originality/valueDelamination fracture in the multilayered functionally graded SCB configuration was analysed with considering the non-linear material behaviour.

Delamination fracture in a functionally graded multilayered beam with material nonlinearity

The present paper describes a theoretical study of delamination fracture in the functionally graded multilayered Crack Lap Shear (CLS) beam configuration with taking into account the nonlinear material behaviour. The fracture was analysed in terms of the strain energy release rate. The analytical solution derived is applicable for CLS with an arbitrary number of layers. Also, the delamination crack may be located arbitrary along the beam height. The mechanical behaviour of beam layers was modelled by a power-law stress–strain relation. It was assumed that the material in each layer is functionally graded along the thickness. Also, the material properties may be different in each layer. An analytical solution of the J-integral was derived in order to verify the nonlinear strain energy release rate analysis. The effects were evaluated of material gradient, crack location along the beam height and material nonlinearity on the strain energy release rate. It was shown that the analysis developed is a useful tool for the understanding of delamination fracture behaviour of functionally graded multilayered CLS beam configurations with material nonlinearity.

Mode II Fracture of Functionally Graded Beams Exhibiting Material Non-Lynearity

A non-linear analysis of the mode II fracture in functionally graded materials was developed by using a beam configuration with two longitudinal cracks located symmetrically with respect to the centroid. The beam mechanical behaviour was described by a non-linear stress-strain relation. The non-linear fracture was studied by the J-integral approach. An analysis of the strain energy release rate was conducted with considering the material non-linearity in order to verify the J-integral non-linear analytical solution derived. The solution obtained is very convenient for parametric studies of mode II fracture in functionally graded beams exhibiting material non-linearity. The effects of material properties and crack location along the beam height on the non-linear fracture were evaluated. The results can be used for optimization of the beam structures with respect to the fracture performance.

Analysis of elasto-plastic postbuckling and energy release rate for delaminated fiber metal laminated beams in thermal environment

The elasto-plastic postbuckling of fiber metal laminated beams with delamination and the energy release rate along the delamination front are discussed in this paper. Considering geometrical nonlinearity, thermal environment and geometrical initial imperfection, the incremental nonlinear equilibrium equations of delaminated fiber metal laminated beams are established, which are solved using the differential quadrature method and iterative method. Based on these, according to the J-integral theory, the elasto-plastic energy release rate is studied. The effects of some important parameters on the elasto-plastic postbuckling behavior and energy release rate of the aramid reinforced aluminum laminated beams are discussed in details.

Dynamic fracture analysis of aged glassy polycarbonate by the method of caustics

The purpose of this work is to investigate the dynamic fracture properties of glassy polycarbonate (PC) with different aging times. The optical method of caustics is adopted in which the shadow spot patterns are recorded by a high speed camera during the dynamic fracture process. Then, the dynamic crack propagation, the stress intensity factor (SIF) and the dynamic fracture toughness of aged PC are obtained through an analysis of the characteristic size of caustic pattern. Moreover, by combining with the investigation of the fracture surface and the energy release rate analysis, the influence of aging time on the dynamic fracture behavior is discussed. Results show that the dynamic fracture toughness and critical energy release rate of PC decreases with aging time for short aging times, whereas they have little change or even increase for longer aging times. Therefore, aging modifies the mechanical properties especially the dynamic fracture properties of PC nonlinearly, not linearly as generally thought of.

Analysis of Mixed Mode II/III Crack in Bilayered Composite Beam

Abstract Mixed mode II/III crack investigation in cantilever bilayered unidirectional fiber reinforced composite beam is reported. The crack is situated between the layers. The two crack arms have different widths. Formula for the strain energy release rate is obtained by the linear elastic fracture mechanics methods using the magnitude of the applied forces, geometrical characteristics of the cross-section, and the elastic moduli of the layers. An equivalent shear modulus of the un-cracked beam portion is used. Several diagrams illustrating the results of parametrical analysis of the strain energy release rate are presented. The paper is a part of a research in the field of fracture behaviour of composite beams.

An analytical analysis of energy release rate in bonded composite joints in a mode I condition

A complete analytical solution of mode I strain energy release rate, GI, was derived for bonded composite joints based on an augmented double cantilever beam (DCB) model. Good agreement was obtained between current and existing comparable theoretical solutions for this joint with a long adhesive bond. For a short bond length joint, the current solution can greatly reduce the degree of the mathematical singularity encountered in analyses of thick, short beams and avoid it entirely for thin, long beams. A correlation between the current theoretical and associated ASTM solutions was established. A bonded DCB laminate test case was conducted, and good agreement was obtained between the experimental and current theoretical results. Commentary was included regarding the tested critical strain energy release rate and the deduced critical adhesive peel stress.