Energy Release Rate Of Crack Research Articles

Effect of Printing Orientation on the Mechanical Properties of Low-Force Stereolithography-Manufactured Durable Resin

This study presents the results of fracture toughness tests conducted on specimens obtained by additive manufacturing techniques, specifically using low-force stereolithography. The samples were manufactured from a transparent 3D printing material for biocompatible applications, the so-called BioMed Durable Resin, which is a Formlabs-patented polymer material that simulates the strength and rigidity of polyethylene. The selected toughness tests in this context were performed following the ASTM D5045-99 guidelines. All tests were conducted under controlled laboratory conditions at 23 °C and 50% relative humidity, ensuring adherence to the standard and the replicability of the experimental results. To investigate the influence of printing plane orientation, specimens were produced at three printing orientation angles (0, 45, and 90 degrees). These angles were selected to provide a comprehensive evaluation of the anisotropy effects in the material. They cover both extreme orientations (0° and 90°) and include an intermediate value (45°), allowing us to assess variations in mechanical behavior across a representative range of printing orientations, consistent with prior research in the field. The experimental tests yielded data on the crack resistance and energy release rate for each angle of orientation. There are various implications of the findings, beyond materials engineering, for applications in biomedicine. Indeed, this same approach opens the door to new research methods for manufacturing certified biocompatible materials from such durable resins. Finally, complementary issues such as related medical applications have been slightly addressed for future work, since biomedicine innovation clusters can contribute to accelerating growth in this crucial field for productive sector activity and the local business environment.

Variational damage model: A novel consistent approach to fracture

The computational modeling of fractures in solids using damage mechanics faces challenge when dealing with complex crack topologies. One effective approach to address this challenge is by reformulating damage mechanics within a variational framework. In this paper, we present a novel variational damage model that incorporates a threshold value to prevent damage initiation at low energy levels. The proposed model defines fracture energy density (ϕ˜) and damage field (s) based on the energy density (ϕ), crack energy release rate (Gc), and crack length scale (ℓ). Specifically, if ϕ≤Gc2ℓ, then ϕ˜=ϕ and s=0; otherwise, ϕ˜=−Gc24ℓ21ϕ+Gcℓ and s=1−Gc2ℓ1ϕ. Furthermore, we extend the model with a threshold value to a higher-order version. Utilizing this functional, we derive the governing equation for fractures that evolve automatically with ease. The formulation can be seamlessly integrated into conventional finite element methods for elastic solids with minimal modifications. The proposed formulation offers sharper crack interfaces compared to phase field methods using the same mesh density. We demonstrate the capabilities of our approach through representative numerical examples in both 2D and 3D, including static fracture problems, cohesive fractures, and dynamic fractures. The open-source code is available on GitHub via the link https://github.com/hl-ren/vdm.

Cracking in semiconductor devices–effect of plasticity under triaxial constraint

A semiconductor device integrates dissimilar materials of small sizes and complex geometries. During fabrication, the materials are deposited at various temperatures. Both deposition and change in temperature cause stresses in the materials. Under the stresses, ductile materials may deform plastically, and brittle materials may crack. Here we focus on how plastic deformation in the ductile materials affects cracking in nearby brittle materials. We study a model structure in which a metal line is encased by a silicon substrate and a brittle oxide layer. In the triaxially constrained metal, the stresses readily exceed the yield strength of the metal. Such high stresses in the metal elevate the stresses in the oxide. The degree of triaxial constraint varies with the aspect ratio of the metal. We compute the stress in the oxide, as well as the energy release rate of an edge crack and a long channel crack. We discuss strategies to avert cracking in the oxide.

Investigating factors influencing interlaminar stresses and energy release rates of semi-elliptical cracks at free edges

Traditional approaches that rely on stress or energy-based criteria to predict delamination require the determination of stresses before crack onset or energy release rates after crack initiation, respectively. While a relatively new coupled criterion, Finite Fracture Mechanics, necessitates the computation of both stresses and energy release rates. This study discusses the numerical determination of the interlaminar stresses and energy release rates of interlaminar semi-elliptical cracks emanating at the free edge in carbon fibre-reinforced polymer materials. The method establishes a new semi-analytical framework, based on dimensional analysis, which permits obtaining a functional expression for the stresses and the energy release rates in function of material and geometrical parameters. This framework eliminates the need to re-solve the underlying boundary value problem for a different material, geometry, and load. The non-dimensional functions are obtained by performing careful interpolation from a set of finite element solutions, ensuring predictions are accurate and within acceptable numerical limits. The influence of material contrast and relative ply thickness on interlaminar stresses and energy release rates are investigated using the semi-analytical framework. Additionally, the fracture mechanics analysis is also conducted to investigate the influence of semi-axes of semi-elliptical crack on energy release rate distributions. Understanding the interlaminar stresses and energy release rates is essential for applying either stress, energy, or coupled criterion to predict the structural strength of a layered body.

Novel, high throughput interface fracture testing method for thermal spray coatings: The modified cantilever bend technique

To measure the interfacial fracture toughness of ceramic/metal interfaces such as thermal spray coatings, a novel modified cantilever beam bending method is proposed. Finite element simulations are used to determine the energy release rate and phase angle for an interfacial crack in a bi-layered cantilever for varying modulus, thickness and beam aspect ratios. A high-throughput experimental procedure for the new test geometry is presented to extract a large number of measurements of interface fracture energy from the same sample, using digital image correlation. Interfacial fracture energies GC, determined using this method are compared for thermal spray coatings of Alumina and YSZ on steel substrates. GC of these coating-substrate combinations follow the same trend as measured from four-point bending or modified clamped beam bend techniques. Advantages and limitations of the technique in comparison to other methods in practice are discussed.

Characteristics of crack growth in brittle solids with the effects of material heterogeneity and multi-crack interaction

AbstractDespite the extensive research on crack propagation in brittle solids, numerous unexplored problems still necessitate in-depth study. In this work, we focus on numerical modeling of multi-crack growth, aiming to explore the effect of material heterogeneity and multi-crack interaction on this process. To do this, an improved singular-finite element method (singular-FEM) is proposed with incorporation of heterogeneity and crack interaction. An efficient algorithm is proposed for simulating multi-crack propagation and interaction. Stress singularity near crack tip is reproduced by the singular elements. The singular-FEM is convenient and cost-effective, as the zone far away from crack tips is directly discretized using linear elements, in contrast to the quadratic or transition elements utilized in traditional FEM. Next, the proposed method is validated through benchmark study. Numerical results demonstrate that the superiority of the singular-FEM, which combines the merits of low cost and high accuracy. Then, the mechanics of crack growth are explored in more complex scenarios, accounting for the effects of crack interaction, loading condition and heterogeneity on crack trajectory, stress field and energy release rate. The findings reveal that the combined effect of heterogeneity and crack interaction plays a critical role in the phenomenon of crack growth, and the proposed method is capable of effectively modeling the process.

A four-point bending technique for characterizing the interface fracture toughness between soft thin films and stiff substrates

Interface fracture toughness, also called work of adhesion or adhesion energy, is a quantity characterizing the resistance of an interface between two adhered solids against interfacial delamination. Determining the interface fracture toughness should be of great value to the studies on the related adhesion and delamination problems. Four-point bending test is an experimental approach that was originally used to measure the flexural stiffness and fracture toughness of monolithic materials. It was also used to characterize the fracture toughness of the interface when a bi-layered notched composite beam specimen is adopted (Int. J. Frac. 1989; 40: 235). However, this method does not work very well when a thin and soft material is encountered because the interface delamination cannot be triggered easily. To address this problem, in this paper, we revise the configuration of the four-point bending specimen from bi-layer to tri-layer by imposing an additional stiffer layer on the top of the thin and soft layer. The analytical solution to the energy release rate of the preexisting interfacial crack is revisited. Finite element analysis is carried out to assess the applicability and limitations of the analytical solution. With the modified four-point bending specimen, the interface fracture toughness between an epoxy coating and a steel substrate is successfully measured from the critical load that leads to the delamination of the preexisting interfacial crack.

Exceptional stress-director coupling at the crack tip of a liquid crystal elastomer

A liquid crystal elastomer (LCE) is a special elastomer containing rod-like liquid crystals, which align in a certain direction, called the director. The director of a LCE can rotate under stress, resulting in large spontaneous strain and soft elastic behavior. This study unravels how the strong stress-director coupling in a monodomain LCE induces unique crack-tip fields and fracture behavior. Through stretching edge-cracked LCEs with various initial directors, we characterize the displacement and director fields theoretically and experimentally. The results reveal that the directors undergo significant and inhomogeneous rotation at the crack tips, leading to very different stress/strain distributions from traditional elastomers. Particularly, when the initial director is tilted to the loading direction, the stress/strain distributions are asymmetrical about the crack plane. Notably, we discover a domain wall forms along a certain polar angle at the crack tip, with opposite director rotation, and thereby shear strain, on the two sides of the domain wall. Moreover, LCEs with a tilted initial director to the loading exhibit much smaller crack openings and energy release rates than those of neo-Hookean materials, while LCEs with a parallel director exhibit higher values. We attribute these findings to a combined effect of bulk softening at the remote region and the formation of domains of opposite director rotation near the crack tip. This study provides an understanding of how the stress-director coupling of LCEs triggers their unique crack-tip fields, and insights into strategies to enhance the fracture properties of LCEs for future applications.

Energy release rate of a mode-I crack in pure shear specimens subjected to large deformation

Energy release rate of a mode-I crack in pure shear specimens subjected to large deformation

Cracks in tensile-contracting and tensile-dilating poroelastic materials

Fibrous gels such as cartilage, blood clots, and carbon-nanotube-based sponges with absorbed oils suffer a reduction in volume by the expulsion of liquid under uniaxial tension, and this directly affects crack-tip fields and energy release rates. A continuum model is formulated for isotropic fibrous gels that exhibit a range of behaviors from volume increasing to volume decreasing in uniaxial tension by changing the ratio of two material parameters. The motion of liquid in the pores of such gels is modeled using poroelasticity. The direction of liquid fluxes around cracks is shown to depend on whether the gel locally increases or decreases in volume. The energy release rate for cracks is computed using a surface-independent integral and it is shown to have two contributions — one from the stresses in the solid network, and another from the flow of liquid. The contribution to the integral from liquid permeation tends to be negative when the gel exhibits volume decrease, which effectively is a crack shielding mechanism.

An Investigation on the Most Likely Failure Locations in the BEoL Stack of a 20 nm Chip Due to Chip Package Interaction with the Use of Novel Semi-Elliptical Cracks.

The era of 20 nm integrated circuits has arrived. There exist abundant heterogeneous micro/nano structures, with thicknesses ranging from hundreds of nanometers to sub-microns in the IC back end of the line stack, which put stringent demands on the reliability of the device. In this paper, the reliability issues of a 20 nm chip due to chip-package interaction during the reflow process is studied. A representative volume element of the detailed complex BEoL structure has been analyzed to obtain mechanical properties of the BEoL stack by adopting a sub-model analysis. For the first time, semi-elliptical cracks were used in conjunction with J-integral techniques to analyze the failure caused by Chip-to-Package Interaction for a 20 nm chip. The Energy Release Rate(ERR)for cracks at various interfaces and locations in the BEoL stack were calculated to predict the most likely mode and location of failure. We found that the ERR of interfacial cracks at the bottom surface of the interconnects are, on average, more than double those at the sidewalls, which are in turn more than double the number of cracks in the low-k inter-layer dielectric. A total of 500 cycles of thermal shock were conducted, which verified the predictions of the finite element simulations.

STRESS CONCENTRATIONS ASSOCIATED WITH RUBBER TO METAL BONDS

ABSTRACT Hot-bonded metal inserts, used to modify the stiffnesses of rubber components and to provide a means of attaching the rubber component to other parts of an overall system, can result in high local stresses. Detailed design is called for to reduce the tendency for initiation of failure in their vicinity. Results are presented for energy release rates for short cracks obtained by finite element analysis for a range of geometries, mostly near bond but also within fillets introduced to reduce the likelihood of failure initiation at bond edges.

Lengthwise Fracture Analysis of Inhomogeneous Viscoelastic Cantilever Beam Subjected to Sinusoidal Strains

This paper describes a research of lengthwise fracture in a viscoelastic inhomogeneous cantilever beam under strain that is a sinusoidal function of time. The beam mechanical behavior is investigated by a model having two linear springs and a linear dashpot. The beam material is continuously inhomogeneous along thickness. Therefore, the modules of elasticity of the springs and the coefficient of viscosity of the dashpot vary smoothly in the thickness direction. The compliance method is applied to derive the strain energy release rate (SERR) for the lengthwise crack in the beam structure. The integral J is applied for verification. The stress-strain-time dependence of the viscoelastic model is used for describing the behavior of the beam when obtaining solutions of the SERR and the J-integral. Solutions are derived for both positive and negative rotation angle of the lower crack arm end (when the angle is positive, the upper crack arm is load free, while at negative angle both crack arms are loaded). The effects of various factors including the sign of the angle of rotation on the SERR are analyzed.

A double-phase field method for mixed mode crack modelling in 3D elasto-plastic solids with crack-direction-based strain energy decomposition

Crack-direction-based decomposition of elastic strain energy could effectively control the propagation of tensile and shear cracks in a phase field modelling context. The objective of the proposed double-phase field model is to extend the crack-direction-based decomposition strategy from 2D brittle fracture to complex mixed-mode crack modelling in a 3D setting, with plastic deformation incorporated. Both effective (undamaged) stress and plastic strain are split in the crack-orientation-based coordinate system. The decomposed tensile/shear stress contribute to tensile/shear damage evolution, respectively. The plastic contribution is coupled by relating the decomposed tensile/shear plastic strain to the corresponding tensile/shear crack energy release rates. Crack surface normal direction, represented by two orientation variables in 3D spatial domains, is determined by the F-criterion. The proposed model is implemented via ABAQUS subroutines with a staggered scheme for two phase field variables and crack direction. The simulation of a single-edge notch specimen under shear loading demonstrates that the ratio between shear and tensile crack energy release rates plays a significant role in the crack mode and mechanical response. Numerical results of a group of uniaxial tension, simple shear and tension shear specimens show good agreement with the experimental data in terms of the force–displacement curve and crack path, exhibiting the validity of the proposed model for capturing different crack modes. This model has also been proven effective for complex 3D problems via the third Sandia Challenge example.

Comparison and correlation between polymer modified asphalt binders and mastics in high- and intermediate-temperature rheological behaviors

Traditional evaluation parameters for multiple stress creep recovery (MSCR) test and linear amplitude sweep (LAS) test are difficult to deeply and theoretically characterize the high- and intermediate-temperature rheological behaviors of polymer modified asphalt (PMA) binders and mastics. In this paper, one neat asphalt and four types of PMA binders and mastics are selected (i.e., the rubber modified ones, SBS modified ones, thermoplastic elastomer modified ones and SBS/Rubber modified ones). Two new analysis methods, i.e. Burgers model and damage mechanics-based crack growth model, are applied in analyzing the high- and intermediate-temperature rheological behaviors of PMA materials respectively. The Burgers model results indicate adding filler decreases the viscous deformation, and leads to lower non-recoverable compliance in the MSCR test. The polymer modification transfers the delayed elastic deformation to elastic deformation, thus causing more excellent rutting resistance. The damage mechanics-based crack growth model analysis reveals that adding filler enhances the crack growth rate and crack length, thus sacrificing the fatigue resistance. By contrast, the polymer modification enhances the fatigue resistance regardless of polymer types. Notably, a two-stage pattern based on crack growth rate and energy release rate was further proposed to identify the crack initiation and propagation of PMA materials. Specifically, 30% rubber modified asphalt binders and mastics perform best in both rutting and fatigue resistance. Moreover, PMA binders and mastics have strong correlation based on the recovery percentage and delayed elastic deformation. The correlation of fatigue life between PMA binders and mastics is very significant, however there was no obvious correlation in terms of crack length.

Peeling behavior of a film on inner surface of a tube

Adhesion behavior of elastic films is a common phenomenon in many biological processes and industrial applications. Current film peeling theories and adhesion property testing methods are mostly limited to flat peeling cases. In this paper, peeling behaviors of elastic films on tubular surfaces are studied through theoretical analysis and finite element simulation. Based on the theory of non-linear elasticity, mechanical behaviors of cylindrical films under finite deformation are investigated and the total strain energy is obtained through dimensional analysis. Furthermore, an analytical expression for energy release rate of an axisymmetric crack is derived. By balancing with the density of energy, the length of crack varies linearly with the axial stretch. Finite element method is adopted to simulate the peeling process of a film and the results agree well with theoretical predictions. Our peeling method, which decouples the influence of surface frictions that commonly cannot be ignored in conventional one degree of freedom peeling setups, represents a new, useful, and easy-to-implement strategy to study elastic film peeling behaviors. Beyond this, the model and the results are also useful for measuring adhesion properties of soft films.

A “parallel universe” scheme for crack nucleation in the phase field approach to fracture

Crack nucleation is crucial in many industrial applications. The phase field method for fracture transforms the crack nucleation problem into a minimization problem of the sum of the elastic potential energy and the crack surface energy. Due to the polyconvexity of the formulation, starting from a crackless solid, a standard Newton iteration may lead to a solution with no crack, even though a cracked solution has a lower total energy. As such, the critical load for cracking is highly overestimated. Here, we propose an algorithm termed “parallel universe” algorithm to capture the global minimum. This algorithm has two key ingredients: (a) a necessary condition for cracking solely based on the current crackless solution, and (b) beginning from when this condition is met, Newton iteration with two initial guesses, a crackles one and a cracked one, will both be performed and the converged candidate solution with lower energy is accepted as the solution at that load step. Once the cracked candidate solution is accepted, the crackless one is discarded, i.e., only one universe is retained. This cracked initial guess is obtained only once for all load steps by solving a series of similar minimization problems with a progressively reduced critical crack energy release rate. Numerical examples with isotropic and anisotropic critical crack energy release rates indicate that the proposed algorithm is more reliable (as there is no need to retrace) and more efficient than the standard Newton iteration and a well-known backtracking algorithm.

The energy release rate of crack growth in an irradiation-induced thermo-diffusion-mechanical (I-TDM) coupling system

The material cracking behavior in the reactor is generated under the irradiation effect accompanied by thermal expansion, fission product diffusion, and mechanical load. In this study, the energy release rate for crack growth under irradiation has been deduced synthetically according to the thermodynamically consistent method and numerically implemented by the finite element method (FEM). Variation in the total energy was obtained based on the principle of minimum potential energy in which the dissipative behavior can be characterized by fission energy, irreversible heat flow, and diffusion of fission products. Through calculating the variation in the total energy with respect to crack length, the energy release rate for crack propagation was analytically represented. Additionally, the total energy release rate for deflective cracks was also derived to predict the crack kinking. Furthermore, the numerical implementation of the presented model was performed by FEM and the equivalent domain integral method. Effects of irradiation on the physical fields and the energy release rate near the crack tip were investigated and analyzed in such a complex I-TDM coupling system. This study can be developed to investigate fracture problems, assess structural integrity, and evaluate material strength of irradiated materials.

An Approach in Analyzing Longitudinal Fracture of Inhomogeneous Beams with Using Generalized Viscoplastic Models

This paper introduces a generalized viscoplastic model and describes its application in treating the longitudinal fracture of inhomogeneous beam structures. The model is a combination of an arbitrary number of parallel units. Each unit is obtained by two springs and a dashpot. Besides, a frictional slider is placed parallel with one of the springs in each unit of the model in order to treat the plastic strains. The time-dependent constitutive law of the model obtained by considering strains, stresses and equilibrium of the model components is used in deriving solution of the strain energy release rate for the longitudinal crack in the viscoplastic beam.

Inhomogeneous Beam of Circular Cross-Section with Concentric Lengthwise Cracks: A Fracture Analysis with Considering Viscoplastic Behaviour

In this paper, a lengthwise fracture analysis of a viscoplastic inhomogeneous cantilever beam of circular cross-section acted upon by a torsion moment is presented. The beam is with an arbitrary number of concentric lengthwise cracks. The time-dependent mechanical behaviour of the beam is treated by a viscoplastic model representing a series of units which are combinations of springs, dashpots and frictional sliders. Due to the sliders, the model units start to deform one after another with increasing of the external load. Constitutive laws of the viscoplastic model are obtained and applied to treat the beam mechanical behaviour when deriving time-dependent strain energy release rates for the lengthwise cracks.