Predefined Crack Path Research Articles

3D Finite‐Element Simulation of Wedge Splitting Test of Non‐Standard Ceramic Double Cantilever Beam with Chevron Notch

Small‐scaled non‐standard specimens with chevron notch (CN) from Zirconia ceramics are probed both numerically and experimentally by wedging. The original construction in the form of double cantilever beam (DCB) with CN is considered for the fracture toughness determination of ZrO2 specimens. The fracture toughness is determined in experiment on wedging of DCB with CN, with application of analytical formula derived by one of the authors and maximum force, bending the cantilever's arm. The 3D finite‐element simulations of wedge splitting test are performed using two approaches: cohesive zone modeling (CZM) approach and element elimination technique (EET). The specific fracture energy defined in experiments is taken as the input parameter for CZM simulations of crack propagation. The effect of parameters, namely, cohesive strength, and friction coefficient, between ceramic wedge and ceramic cantilever, is considered. Different traction–separation laws are implemented, and the resulting force–displacement curves are compared with experimentally obtained ones. In the CZM approach, considering the fracture energy and the predefined crack path, matching of experimental and numerical results is not achieved. In EET, in which the restrictions on the crack paths and the requirements for inputting the fracture energy are not imposed, a good match with the experimental results is achieved.

Modelling of environmentally assisted material degradation in the crack phase-field framework

The simulation of crack propagation was conducted with a diffusive crack model in a variational framework. More, the physically sound introduction of mass transport and coupling mechanisms due to environmentally assisted effects could be realised in this framework. The objective consists of the application of the phase-field approach towards the simulation of environmentally assisted material degradation with the advantage of a non-required predefined crack path and a mesh-independent non-local formulation that facilitates the damage evolution with respect to material softening. The sharp crack is regularised by the introduction of a phase-field order parameter leading to a diffusive crack formulation. Besides the equations originating from the linear momentum balance an additional evolution equation for the crack phase-field is introduced. Furthermore, mass transport is simulated by a diffusion equation. The description delivered by the variational phase-field framework is able to simulate crack propagation according to published numerical test cases. Additionally, the calculation of stress intensity factors is possible as well as crack resistance curves that describe stable crack propagation.

A phase‐field approach to fracture coupled with mass transport for the simulation of environmentally‐assisted damage

AbstractWith the introduction of a mass transport mechanism the entire problem is subjected to a time frame that dictates the time‐dependent action of soluted species on mechanical properties. A numerical framework within the phase‐field approach is presented with an embrittlement‐based coupling mechanism. The underlying functionals are expressed in terms of the displacement, mass concentration and crack phase‐field. Within the phase‐field approach the modelling of sharp crack discontinuities is replaced by a diffusive crack model facilitating crack initiation and complex crack topologies without the requirement of a predefined crack path. The isotropic hardening of the elasto‐plastic deformation model and the local fracture criterion are affected by the species concentration. This allows for embrittlement and leads to an accelerated crack propagation. An extended mass transport equation for hydrogen embrittlement, accounting for mechanical stresses and deformations, is implemented. For stabilisation purposes a staggered scheme is applied to solve the system of partial differential equations by a multi‐field finite‐element method. A thermodynamically consistent coupling relation that accommodates the required mechanisms is presented. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Characterization of Delamination Crack in Multidirectional E-glass/epoxy Composite under Mode I Loading

In this study, mode I critical strain energy release rate ( G Ic ) of unidirectional E-glass/epoxy was determined by double cantilever beam (DCB) test. Calculated G Ic was used to initiate delamination in numerical models. The effect of stacking sequence and fiber orientation of the sublaminates and the effect of thickness on mode I delamination crack length and G Ic distribution along the specimen width in 0 o //0 o interface have been studied using ANSYS ® . 3-D 8-node linear interface element INTER 205 is used to create a predefined crack path. To investigate the fiber orientation effect , composites with [+θ 2 , 90 2 , -θ 2 , 0 2 ] s stacking sequences were modeled. Interlaminar fracture analyses were performed by Virtual Crack Closure Technique (VCCT). Experimental and numerical critical loads ( P cr ) showed a good agreement. According to the results, while fiber orientation affects significantly the extended crack length and the G Ic distribution along the specimen width, stacking sequence only affects the G Ic distribution.

A Phase Field Approach to Fracture with Mass Transport Extension for the Simulation of Environmentally-Assisted Cracking

The fracture mechanics assessment of materials exposed to harmful environments requires the understanding of the interaction between the soluted species and the affected mechanical behaviour. With the introduction of a mass transport mechanism the entire problem is subjected to a time frame that dictates the time-dependent action of soluted species on mechanical properties. A numerical framework within the phase field approach is presented with an embrittlement-based coupling mechanism showing the influence on crack patterns and fracture toughness. Within the phase field approach the modeling of sharp crack discontinuities is replaced by a diffusive crack model facilitating crack initiation and complex crack topologies such as curvilinear crack patterns, without the requirement of a predefined crack path. The isotropic hardening of the elasto-plastic deformation model and the local fracture criterion are affected by the species concentration. This allows for embrittlement and leads to accelerated crack propagation. An extended mass transport equation for hydrogen embrittlement, accounting for mechanical stresses and deformations, is implemented. For stabilisation purposes a staggered scheme is applied to solve the system of partial differential equations. The simulation of showcases demonstrates crack initiation and crack propagation aiming for the determination of stress-intensity factors and crack-resistance curves.

Virtual hybrid test control of sinuous crack

The present study aims at proposing a new generation of experimental protocol for analysing crack propagation in quasi brittle materials. The boundary conditions are controlled in real-time to conform to a predefined crack path. Servo-control is achieved through a full-field measurement technique to determine the pre-set fracture path and a simple predictor model based on linear elastic fracture mechanics to prescribe the boundary conditions on the fly so that the actual crack path follows at best the predefined trajectory. The final goal is to identify, for instance, non-local damage models involving internal lengths. The validation of this novel procedure is performed via a virtual test-case based on an enriched damage model with an internal length scale, a prior chosen sinusoidal crack path and a concrete sample. Notwithstanding the fact that the predictor model selected for monitoring the test is a highly simplified picture of the targeted constitutive law, the proposed protocol exhibits a much improved sensitivity to the sought parameters such as internal lengths as assessed from the comparison with other available experimental tests.

Simulation of Environmentally-Assisted Material Degradation by a Thermodynamically Consistent Phase-Field Model

Environmentally-assisted material degradation involves mass transport and mechanical processes interacting in the material. A well-known example is hydrogen-induced stress-corrosion cracking. One major challenge within this scope is the quantification of the coupling mechanisms in question. The computational modeling of environmentally-assisted cracks is the key objective ofthis investigation and realised within the theory of gradient-extended dissipative continua with length-scales. The modeling of sharp crack discontinuities is replaced by a diffusive crack model based onthe introduction of a crack phase-field to maintain the evolution of complex crack topologies. Withina thermodynamical framework allowing for mechanical and mass transport processes the crack phase-field is capable to model crack initiation and propagation bythe finite element method. As complexcrack situations such as crack initiation, curvilinear crack patterns and crack branching are usuallyhard to realise with sharp crack models, they can be assessedwithout the requirement of a predefinedcrack path within this method. The numerical modeling of a showcase demonstrates a crack initiationas well as a crack propagation situation with respect to the determination of stress-intensity factors; acrack deviation situation with a curvilinear crack path is modeled by the introduction of a geometricalperturbation and a locally enhanced species concentration

Numerical Simulation of Fatigue Crack Growth Rate and Crack Retardation due to an Overload Using a Cohesive Zone Model

In this work, a numerical method is pursued based on a cohesive zone model (CZM). The method is aimed at simulating fatigue crack growth as well as crack growth retardation due to an overload. In this cohesive zone model, the degradation of the material strength is represented by a variation of the cohesive traction with respect to separation of the cohesive surfaces. Simulation of crack propagation under cyclic loads is implemented by introducing a damage mechanism into the cohesive zone. Crack propagation is represented in the process zone (cohesive zone in front of crack-tip) by deterioration of the cohesive strength due to damage development in the cohesive element. Damage accumulation during loading is based on the displacements in the cohesive zone. A finite element model of a compact tension (CT) specimen subjected to a constant amplitude loading with an overload is developed. The cohesive elements are placed in front of the crack-tip along a pre-defined crack path. The simulation is performed in the finite element code Abaqus. The cohesive elements behavior is described using the user element subroutine UEL. The new damage evolution function used in this work provides a good agreement between simulation results and experimental data.

Theoretical-numerical Approaches to Simulate Fracture in Polymeric Materials

Fracture in structures is usually to be avoided or, if intended like for airbags or peel foils, it should occur along a predefined crack path. The integrity and usability of a part has to be ensured over the lifetime of the structure. In order to optimize a structure at the design stage, simulations allow to analyze and to predict the structural behavior for a development of the best layout. The contribution at hand presents appropriated material modeling strategies for polymers and introduces the so-called configurational force approach for inelasticity and finite strains as a method to analyze the energy release rate, the crack advancement and the crack growth direction. Certain numerical methods like cohesive elements, containing e.g. inelastic cohesive zone models and the node splitting approach combined with an r-adaptive discretization are shown as valuable simulation features.

Modeling flat to slant fracture transition using the computational cell methodology

Macroscopic mode I ductile crack propagation in metallic sheets or plates often starts in mode I as a flat triangle (coplanar with the precrack) whose normal corresponds to the loading direction. After some limited extension, the crack becomes slanted and propagates under local mixed mode I/III. Modeling and understanding this phenomenon is challenging. In this work, the “computational cell” methodology proposed in [1], which uses a predefined crack path, is used to study flat to slant fracture transition. The energy dissipation rate is studied as a function of the assumed crack tilt angle. It is shown that a minimum is always reached for an angle equal to 45°. This correlates well with the variation of the crack tip opening angle (CTOA) or the mean plastic deformation along the crack path. Stress and strain states in the stable tearing region hardly depend on the assumed tilt angle. A parametric study shows that flat to slant fracture transition is less likely to occur in materials having high work hardening and favored if additional damage is caused by the local stress/strain state (plane strain, low Lode parameter) in the stable tearing region.

Three-dimensional cohesive crack model prediction of the flexural capacity of concrete slabs on soil

A three-dimensional approach to discretely account for crack initiation, crack growth, and determination of the flexural load capacity of concrete slabs on an elastic foundation under mode I loading is proposed. The finite element model incorporated cohesive crack elements along a pre-defined crack path in the concrete slab. A bilinear softening model was used to describe the stress-crack opening relationship for plain concrete and was defined solely on measured strength and fracture properties. The proposed method predicted the slab’s flexural load capacity as compared to the large-scale experimental concrete slab results for several geometries and notch configurations. The model also provided insight into stress concentration areas and crack propagation positions at different load levels.

Micromechanical investigation of the fatigue crack growth behaviour of Al–SiC MMCs

A defect tolerant approach to fatigue modelling for constant amplitude loading was developed by Bruzzi and McHugh (Int. J. Fatigue 24 (2002) 1071). It was applied to two metal matrix composites (MMCs): (1) a forged 2124 Al reinforced with 17% SiC particles and (2) a cast 359 Al reinforced with 20% SiC particles MMC, in Bruzzi and McHugh (Int. J. Fatigue 25 (2003) 577). However, no explicit representation of the two-phased microstructure was considered. The material was assumed to be homogeneous and behave as a continuum. In this work, the extreme effects of the reinforcing particles on the growth behaviour of a small fatigue crack, using the modelling methodology of Bruzzi and McHugh, is investigated for the Al 2124 MMC. This is performed using micromechanical models, in which separate representations of the matrix and the reinforcing particles are included, in order to assess local stress fields within the matrix. Two extreme cases of idealised crack growth are examined: (1) a predefined crack path approaching a reinforcing particle and (2) a predefined crack path lying between two reinforcing particles. The predicted stress gradients along each of the predefined paths are then included in the fatigue modelling methodology described by Bruzzi and McHugh. Finally, the predicted results of the extreme cases of the short crack growth behaviour for the two-phase Al 2124 MMC are presented, discussed and compared to the short crack growth rate behaviour of the homogenised MMC model of Bruzzi and McHugh.