On the dynamic crack propagation in an interphase with spatially varying elastic properties under inplane loading

This article provides a comprehensive theoretical investigation on a finite crack with constant length (Yoffe type crack) propagating in an interfacial layer with spatially varying elastic properties under inplane loading. The analytical formulations are developed using Fourier transforms and solving the resulting singular integral equations in terms of the opening and sliding displacements of the crack. The dynamic stress intensity factors and energy release rate are analyzed to study the dynamic fracture property of this inherent mixed mode crack problem. Numerical examples are provided to show the effects of the material properties, the thickness of the interfacial layer, the crack position and speed upon the dynamic fracture behaviour, and the singularity transition between the current crack and the corresponding interfacial crack for thin interphase.     

Sub critical crack advance vs. impact fracture on high impact polystyrene with different second phase volume contents and structures

Also for polymers, many fractures in service occurs after a period in which an existing crack has propagated in a sub-critical manner, while the laboratory tests are mainly concentrated on impact fractures. Aim of this paper is then to investigate the sub critical fracture in some high impact polystyrene (HIPS) materials with different second phase volume fraction and particle size and to compare it with the outcomes of impact Fracture Mechanics experiments. Large differences in the results of the two mechanical test procedures are evidenced: the materials behaviour is then examined from the structural point of view and an interesting case of interfacial failure, which disappears at high strain rate, is attested on some HIPSs by means of different techniques, i.e. electron microscopy, nuclear magnetic resonance spectroscopy and dynamic mechanical spectroscopy, indicating that the slow crack fracture behaviour can be influenced by parameters that do not affect ordinary mechanical tests.     

INTERFACIAL CRACK INITIATION UNDER QUASI-STATIC AND DYNAMIC LOADING CONDITIONS: AN EXPERIMENTAL STUDY

Abstract— Interfacial fracture parameters under quasi-static and dynamic loading are examined in a large elastic mismatch bimatenal system. A wide range of remote field loading ratios of shear and tension are considered. The crack tip fields are mapped using the optical method of coherent gradient sensing or CGS and fracture parameters are quantified. Distinctly different crack initiation responses are observed for positive and negative shear stresses acting on the interface. Also, low velocity impact loading experiments are conducted to study the influence of dynamic loading on crack initiation parameters. Dynamic interfacial crack tip fields are recorded using high speed photography and fracture parameters for dynamically loaded stationary cracks are obtained. Measurements suggest significant crack initiation toughness reduction under dynamic loading conditions.     

A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns

The numerical modeling of dynamic failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies and demands the formulation of additional branching criteria. This drawback can be overcome by a diffusive crack modeling, which is based on the introduction of a crack phase field. Following our recent works on quasi‐static modeling of phase‐field‐type brittle fracture, we propose in this paper a computational framework for diffusive fracture for dynamic problems that allows the simulation of complex evolving crack topologies. It is based on the introduction of a local history field that contains a maximum reference energy obtained in the deformation history, which may be considered as a measure of the maximum tensile strain in the history. This local variable drives the evolution of the crack phase field. Its introduction provides a very transparent representation of the balance equation that governs the diffusive crack topology. In particular, it allows for the construction of a very robust algorithmic treatment for elastodynamic problems of diffusive fracture. Here, we extend the recently proposed operator split scheme from quasi‐static to dynamic problems. In a typical time step, it successively updates the history field, the crack phase field, and finally the displacement field. We demonstrate the performance of the phase field formulation of fracture by means of representative numerical examples, which show the evolution of complex crack patterns under dynamic loading. Copyright © 2012 John Wiley & Sons, Ltd.     

Constraint effects on the elastic–plastic fracture behaviour in strain gradient solids

ABSTRACT Crack‐tip constraint effects (or T‐stress effects) on the elastic–plastic fracture behaviour in strain gradient materials are analysed in the present study. The T‐stress effects on the stress distributions along the plane ahead of the stationary and growing crack tip, respectively, are analysed by using the Fleck and Hutchinson strain gradient plasticity formation. For a steadily growing crack, the T‐stress effects on the steady‐state fracture toughness are analysed by adopting the embedded fracture process zone model. In addition, the analysis for the growing crack is applied to an interfacial cracking experiment for a metal/ceramic system, and the material length‐scale parameter appearing in the strain gradient plasticity theory is predicted. In the present analyses, a new finite element method specially designed for strain gradient problems by Wei and Hutchinson is adopted.     

Fracturing behaviors of FRP-strengthened concrete structures

In this paper, we focus on the study of concrete cracking behavior and interfacial debonding fracture in fiber reinforced polymer (FRP)-strengthened concrete beams. An experimental program is systematically reviewed according to the observed failure modes, in which it is found that the interfacial debonding may propagate either within the adhesive layer or through concrete layer in the vicinity of bond interface. A finite element analysis is performed to investigate the different types of debonding propagation along FRP-concrete interface and crack distribution in concrete. For the numerical fracture models, interfacial debonding that initiates and propagates in adhesive layer is modeled by fictitious interfacial crack model. And concrete cracking, including the debonding fracture through interfacial concrete, is modeled by smeared crack model. Properties of the interfacial adhesive layer and concrete are considered to significantly influence the debonding propagation types and crack distribution. The interactions between interfacial bond strength, interfacial fracture energy of bond adhesive layer and tensile strength, fracture energy of concrete are discussed in detail through a parametric study. According to the results, the effects of these properties on different types of interfacial debonding, concrete cracking behavior and structural load-carrying capacity are clearly understood.     

Modelling dynamic crack propagation using the scaled boundary finite element method

This study presents a novel application of the scaled boundary finite element method (SBFEM) to model dynamic crack propagation problems. Accurate dynamic stress intensity factors are extracted directly from the semi‐analytical solutions of SBFEM. They are then used in the dynamic fracture criteria to determine the crack‐tip position, velocity and propagation direction. A simple, yet flexible remeshing algorithm is used to accommodate crack propagation. Three dynamic crack propagation problems that include mode‐I and mix‐mode fracture are modelled. The results show good agreement with experimental and numerical results available in the literature. It is found that the developed method offers some advantages over conventional FEM in terms of accuracy, efficiency and ease of implementation. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of in-plane transonically propagating interface crack with a finite contact zone

The report of Lambros and Rosakis [(1995) J Mech Phys Solids 43(2): 169–188] has focused attention on steady-state transonic interfacial crack growth accounting for the phenomenon of crack face contact in elastic/rigid bimaterial but could not handle issues relating to energy transmission across the interface. The present paper attempts to provide a complete explicit expression of the asymptotic fields induced by transonically propagating interfacial crack in elastic/elastic bimaterial for in-plane case. The energy distribution on the contact area, crack tip and two singular characteristic lines is analysed thoroughly and compared with the dynamic separated J-integrals. The length of the contact zone is also discussed briefly by establishing energy fracture criterion that satisfies contact condition. The two-dimensional in-plane asymptotic deformation field surrounding the contact area of a crack propagating transonically along an elastic/elastic bimaterial interface is observed and discussed thoroughly.     

Fracture Behaviour Investigation into a Polymer‐Bonded Explosive

Abstract: Polymer‐bonded explosive (PBX) is used widely in weapon systems. Failure of PBX caused by mechanical damage is one of the sources of accidental ignitions. A brittle crack of PBX produces local heating, creating a ‘hot spot’ finally. Investigation into the tensile fracture behaviour of PBX is one of the main works to determine the failure mechanism. Although many researchers have carried out the quasi‐static Brazilian test to understand the damage evolution of PBX, the fracture feature of PBX under dynamic impact is rarely reported. In this article, dynamic Brazilian tests were conducted. A single‐pulse loading apparatus was used to ensure that specimen was loaded only once during a dynamic Brazilian test. High‐speed camera, digital image correlation and micro‐observation techniques were adopted for strain measurement and microfracture observation. All the dynamic tensile crack exhibits transgranular fracture, which indicates more heat would released by the propagation of crack and more friction between fractured crystal surfaces. On the basis of the theories of interface debonding and transgranular fracture, larger crystals are more prone to crack, whereas smaller crystals simply debond with neighbouring binders. Discrete element method simulation results show that specimen with interface debonding microcracks was able to sustain additional load until transgranular fracture begins.     

Temperature, moisture and mode-mixity effects on copper leadframe/EMC interfacial fracture toughness

A systematic investigation and characterization of the interfacial fracture toughness of the bi-material copper leadframe/epoxy molding compound is presented. Experiments and finite element simulations were used to investigate delamination and interfacial fracture toughness of the bi-material. Two dimensional simulations using virtual crack closure technique, virtual crack extension and J-integral proved to be computationally cheap and accurate to investigate and characterize the interfacial fracture toughness of bi-material structures. The effects of temperature, moisture diffusion and mode-mixity on the interfacial fracture toughness of the bi-material were considered. Testing temperature and moisture exposure significantly reduce the interfacial fracture toughness, and should be avoided if possible.     

Study of mode I crack dynamic propagation behaviour and rock dynamic fracture toughness by using SCT specimens

To study crack dynamic propagation behaviour and rock dynamic fracture toughness, a single cleavage triangle (SCT) specimen was proposed in this paper. By using these specimens and a drop‐weight test system, impact experiments were conducted, and the crack propagation velocity and the fracture time were measured by using crack propagation gauges. To examine the effectiveness of the SCT specimen and to predict the test results, finite difference numerical models were established by using AUTODYN code, and the simulation results showed that the crack propagation path agrees with the test results, and crack arrest phenomena could happen. Meanwhile, by using these numerical models, the crack dynamic propagation mechanism was investigated. Finite element code ABAQUS was applied in the calculation of crack dynamic stress intensity factors (SIFs) based on specimen dimension and the loading curves measured, and the curves of crack dynamic SIFs versus time were obtained. The fracture toughness (including initiation toughness and propagation toughness) was determined according to the fracture time and crack speeds measured by crack propagation gauges. The results show that the SCT specimen is applicable to the study of crack dynamic propagation behaviour and fracture toughness, and in the process of crack propagation, the propagation toughness decreases with crack propagation velocity, and the crack arrest phenomena could happen. The critical SIF of an arrest crack (or arrest toughness) was higher than the crack propagation toughness but was lower than the initiation toughness.     

Modeling method for the crack problem of a functionally graded interfacial zone with arbitrary material properties

A new multi-layered model is developed for the fracture analysis of a functionally graded interfacial zone with arbitrary material properties. It is assumed that the interfacial zone is divided into sub-layers with the material properties of each sub-layer varying in a power-law function. The model is used to study the crack problem in the functionally graded interfacial zone between two homogeneous half-planes under a dynamic anti-plane load. Using Fourier–Laplace transforms and the transfer matrix method, the mixed boundary value problem is reduced to a Cauchy singular integral equation, which is solved numerically in the Laplace transform domain. Laplace numerical inversion transform is employed to obtain the stress intensity factors. The results show that the new model is general and effective for the crack problem of the functionally graded interfacial zone with arbitrary properties.     

Mechanisms of fatigue fracture in short glass fibre-reinforced polymers

Fatigue-crack profiles and fracture surfaces of several short glass fibre-reinforced polymers were examined to gain insight into the mechanisms of cyclic damage and fatigue-crack propagation in these materials. Several distinctly different features were noted between fracture surfaces generated by stable fatigue crack growth and those produced by monotonic or unstable fracture. Among the most significant differences were the higher degree of single and multiple fibre fracture generally observed on stable fatigue-crack growth fracture surfaces, and the variations in the interfacial failure site in well-bonded systems. While the former effect is attributed to the occurrence of crack closure and the build-up of compressive stresses in the crack-tip damage zone during unloading, the differences in the interfacial failure mode are related to the adverse effect of fatigue loading on the interfacial bond strength. No features could be identified that would allow a quantitative correlation between the applied stress intensity factor level or the crack growth rates and characteristic fracture surface details.     

Fatigue voids and their significance

ABSTRACT Fractures from tests on 2014‐T6511 and 2024‐T3 test coupons under specially designed programmed loading reveal voids with distinct fatigue markings. These ‘fatigue voids’ appear to form as a consequence of the separation of noncoherent secondary particulates from the matrix in early fatigue. The process of their formation is through the initiation, growth and coalescence of multiple interfacial cracks around the particulate. Such voids become visible on the fatigue fracture surface if and when the crack front advances through them. In vacuum, each fatigue void is the potential initiator of an embedded penny‐shaped crack. The one closest to the specimen surface is likely to become the dominant crack, indicating that fatigue voids appear to be the likely origins of the dominant crack in vacuum. In air, the dominant crack forms at the notch surface and grows much faster, giving less opportunity for multiple internal cracks to spawn off from the innumerable internal fatigue‐voids. Thus in air, fatigue voids do not appear to affect the fatigue process at low and intermediate growth rates. At high crack growth rates involving considerable crack tip shear, slip planes with particulate concentration offer the path of least resistance. This explains the increasing density of fatigue voids with growth rate. Very high growth rates signal the onset of a quasi‐static crack growth component that manifests itself through growing clusters of microvoid coalescence associated with static fracture. Fatigue voids are likely to form in other Al‐alloys with secondary noncoherent particulates. They have nothing in common with microvoids associated with ductile fracture.     

Study on Fracture Behaviour of a Polymer‐Bonded Explosive Simulant Subjected to Uniaxial Compression Using Digital Image Correlation Method

Abstract: Quasi‐static uniaxial compression experiments were conducted on a polymer‐bonded explosive (PBX) simulant. At macro‐scale, the deformation and fracture process of samples were recorded using a charge‐coupled‐device camera. Microscopic examination was conducted to in situ observe the deformation and fracture processes of samples using SEM equipped with a loading stage. Microscopic damage modes, including interfacial debonding and particle fracture, were observed. The digital image correlation (DIC) technique was used to calculate the recorded images, and the macro‐ and micro‐scale displacement and strain fields were determined. Crack initiation, crack propagation, fracture behaviour and failure mechanism of samples were studied. The effects of aspect ratios on fracture behaviour and failure mechanism of PBX simulant were analysed.     

Topology optimization of particle‐matrix composites for optimal fracture resistance taking into account interfacial damage

This paper presents a topology optimization framework for optimizing the fracture resistance of two‐phase composites considering interfacial damage interacting with crack propagation through a redistribution of the inclusions phase. A phase field method for fracture capable of describing interactions between bulk brittle fracture and interfacial damage is adopted within a diffuse approximation of discontinuities. This formulation avoids the burden of remeshing problem during crack propagation and is well adapted to topology optimization purpose. Efficient design sensitivity analysis is performed by using the adjoint method, and the optimization problem is solved by an extended bidirectional evolutionary structural optimization method. The sensitivity formulation accounts for the whole fracturing process involving crack nucleation, propagation, and interaction, either from the interfaces and then through the solid phases, or the opposite. The spatial distribution of material phases are optimally designed using the extended bidirectional evolutionary structural optimization method to improve the fractural resistance. We demonstrate through several examples that the fracture resistance of the composite can be significantly increased at constant volume fraction of inclusions by the topology optimization process.     

Mesh refinement strategies without mapping of nonlinear solutions for the generalized and standard FEM analysis of 3‐D cohesive fractures

A robust and efficient strategy is proposed to simulate mechanical problems involving cohesive fractures. This class of problems is characterized by a global structural behavior that is strongly affected by localized nonlinearities at relatively small‐sized critical regions. The proposed approach is based on the division of a simulation into a suitable number of sub‐simulations where adaptive mesh refinement is performed only once based on refinement window(s) around crack front process zone(s). The initialization of Newton‐Raphson nonlinear iterations at the start of each sub‐simulation is accomplished by solving a linear problem based on a secant stiffness, rather than a volume mapping of nonlinear solutions between meshes. The secant stiffness is evaluated using material state information stored/read on crack surface facets which are employed to explicitly represent the geometry of the discontinuity surface independently of the volume mesh within the generalized finite element method framework. Moreover, a simplified version of the algorithm is proposed for its straightforward implementation into existing commercial software. Data transfer between sub‐simulations is not required in the simplified strategy. The computational efficiency, accuracy, and robustness of the proposed strategies are demonstrated by an application to cohesive fracture simulations in 3‐D. Copyright © 2016 John Wiley & Sons, Ltd.     

Multiscale dynamic fracture analysis of composite materials using adaptive microstructure modeling

In this study, a computational framework is proposed to investigate multiscale dynamic fracture phenomena in materials with microstructures. The micro- and macro-scales of a composite material are integrated by introducing an adaptive microstructure representation. Then, the far and local fields are simultaneously computed using the equation of motion, which satisfies the boundary conditions between the two fields. Cohesive surface elements are dynamically inserted where and when needed, and the Park-Paulino-Roesler cohesive model is employed to approximate nonlinear fracture processes in a local field. A topology-based data structure is utilized to efficiently handle adjacency information during mesh modification events. The efficiency and validity of the proposed computational framework are demonstrated by checking the energy balances and comparing the results of the proposed computation with direct computations. Furthermore, the effects of microstructural properties, such as interfacial bonding strength and unit cell arrangement, on the dynamic fracture behavior are investigated. The computational results demonstrate that local crack patterns depend on the combination of microstructural properties such as unit cell arrangement and interfacial bonding strength; therefore, the microstructure of a material should be carefully considered for dynamic cohesive fracture investigations.     

On a moving dielectric crack in a piezoelectric interface with spatially varying properties

This paper provides a comprehensive theoretical analysis of a finite crack propagating with constant speed along an interface between two dissimilar piezoelectric media under inplane electromechanical loading. The interface is modeled as a graded piezoelectric layer with spatially varying properties (functionally graded piezoelectric materials, i.e., FGPMs). The analytical formulations are developed using Fourier transforms and the resulting singular integral equations are solved with Chebyshev polynomials. Using a dielectric crack model with deformation-dependent electric boundary condition, the dynamic stress intensity factors, electric displacement intensity factor, crack opening displacement (COD) intensity factor, and energy release rate are derived to fully understand this inherent mixed mode dynamic fracture problem. Numerical simulations are made to show the effects of the material mismatch, the thickness of the interfacial layer, the crack position, and the crack speed upon the dynamic fracture behavior. A critical state for the electromechanical loading applied to the medium is identified, which determines whether the traditional impermeable (or permeable) crack model serves as the upper or lower bound for the dielectric model considering the effect of dielectric medium crack filling.     

Fracture analysis and improved design for a symmetrically bonded smart structure with linearly non-homogeneous magnetoelectroelastic properties

The mechanical model was established for the anti-plane interfacial fracture problem of a symmetrically bonded smart structure with linearly non-homogeneous magnetoelectroelastic properties. The system of Cauchy singular integral equations for the interfacial crack was derived by Fourier integral transform. The numerical solutions of the Cauchy singular integral equations were obtained by the Lobatto-Chebyshev collocation method put up by Erdogan and Gupta. The mechanical strain energy release rate and the total energy release rate were chosen as fracture parameters to discuss the effect of the non-homogeneity parameter on the extension force of the crack. A conclusion was drawn that, to reduce the weak-discontinuity of the interface in the magnetoelectroelastic structure would be beneficial to decrease the extension force of the interfacial crack. Based on this conclusion, a new improved design was suggested for the symmetrically bonded linearly non-homogeneous magnetoelectroelastic composite. The enhancement of the capability of the improved structure to resist interfacial fracture was validated by comparison between the improved and unimproved structures for their fracture responses.