Cohesive Zone Approach Research Articles

Numerical Modelling of Microcracking in PV Modules Induced by Thermo-mechanical Loads

Micro-cracking in polycrystalline Silicon is a serious concern for the durability of photovoltaic (PV) modules due to the resulting electrical power-loss. In this contribution, a thermo-mechanical cohesive zone model is proposed to predict the evolution of micro-cracks under the action of mechanical and thermal loads. The classical nonlinear cohesive zone approach, used in fracture mechanics to depict the phenomenon of cracking as a result of progressive breakage of atomic bonds, is extended to thermo-elastic fields. The additional thermal resistance of micro-cracks due to imperfect bonding is estimated according to an analogy with a contact mechanics formulation, where the dependency on the crack opening is suitably accounted for. A numerical example shows the applicability of the proposed approach to practical problems.

XFEM modeling of inelastic material behavior of composite

AbstractIn the present contribution the authors applied numerical homogenization techniques to predict the effective material behavior of composite based on the simulation of a representative volume element (RVE) [1]. An enriched displacement approximation (XFEM) is used to describe weak and strong discontinuities within the displacement field, independent from the underlying FE mesh. For the description of curved material interfaces a higher order XFEM formulation based on quadratic shape functions and consisting integration sub domains is developed. In order to incorporate microscopic damage effects, the XFEM approximation has been combined with a cohesive zone approach to model failure of the fiber‐matrix interface. The inelastic properties of the polymeric matrix material are described via constitutive relations of fractional viscoelasticity with process dependent viscous properties. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Numerical modeling of fluid‐driven fractures in cohesive poroelastoplastic continuum

SUMMARYIn this article, we investigate the main parameters that influence the propagation of a fluid‐driven fracture in a poroelastoplastic continuum. These parameters include the cohesive zone, the stress anisotropy, and the pore pressure field. The fracture is driven in a permeable porous domain that corresponds to weak formation by pumping of an incompressible viscous fluid at the fracture inlet under plane strain conditions. Rock deformation is modeled with the Mohr–Coulomb yield criterion with associative flow rule. Fluid flow in the fracture is modeled by the lubrication theory. The movement of the pore fluid in the surrounding medium is assumed to obey the Darcy law and is of the same nature as the fracturing fluid. The cohesive zone approach is used as the fracture propagation criterion. The problem is modeled numerically with the finite element method to obtain the solution for the fracture length, the fracture opening, and the propagation pressure as a function of the time and distance from the pumping inlet. It is demonstrated that the plastic yielding that is associated with the rock dilation in an elastoplastic saturated porous continuum is significantly affected by the cohesive zone characteristics, the stress anisotropy, and the pore pressure field. These influences result in larger fracture profiles and propagation pressures due to the larger plastic zones that are developing during the fracture propagation. Furthermore, it is also found that the diffusion process that is a major mechanism in hydraulic fracture operations influences further the obtained results on the fracture dimensions, plastic yielding, and fluid pressures. These findings may explain partially the discrepancies in net pressures between field measurements and conventional model predictions. Copyright © 2012 John Wiley & Sons, Ltd.

Studies on the reliability of power packages based on strength and fracture criteria

Thermal cycling induced failure in power packages has been studied comparing thermal cycling (TC) with thermal shock (TS) tests by thermo-mechanical analyses. The major question for the time reduction is if the failure mechanism changes and if it depends on loading type and duration. These questions were addressed by theoretical analyses including coupled transient thermal–mechanical analyses and interface fracture mechanics applying the cohesive zone approach. By the latter, critical states for delamination failures could be derived. Finally, critical interface fracture parameters of the package were compared with results from the button shear test.

Computational Analysis of Fatigue Crack Propagation at Elevated Temperature for IN718

Creep damage is an important failure factor of high-temperature alloy. The fatigue crack growth under elevated temperature of the material is investigated for life prediction. In this paper, the numerical simulation of the crack propagation in nickel-based super alloy, IN718, was presented. A modified creep damage model was employed to accumulate the creep damage under cyclic loading conditions. The numerical results exhibit a reasonable agreement in the comparison with the experimental data. The cohesive zone approach, combining with the extended finite element method, has the ability to simulate the creep-fatigue crack propagation even for more complex loading conditions and specimen geometries.

Towards modeling intergranular stress corrosion cracks on grain size scales

Abstract Development of advanced models at the grain size scales has so far been mostly limited to simulated geometry structures such as for example 3D Voronoi tessellations. The difficulty came from a lack of non-destructive techniques for measuring the microstructures. In this work a novel grain-size scale approach for modelling intergranular stress corrosion cracking based on as-measured 3D grain structure of a 400 μm stainless steel wire is presented. Grain topologies and crystallographic orientations are obtained using a diffraction contrast tomography, reconstructed within a detailed finite element model and coupled with advanced constitutive models for grains and grain boundaries. The wire is composed of 362 grains and over 1600 grain boundaries. Grain boundary damage initialization and early development is then explored for a number of cases, ranging from isotropic elasticity up to crystal plasticity constitutive laws for the bulk grain material. In all cases the grain boundaries are modeled using the cohesive zone approach. The feasibility of the approach is explored.

Modeling delamination growth in composites under fatigue loadings of varying amplitudes

A numerical model was developed to simulate the progressive delamination of a composite subjected to mode I fatigue loading regimes of varying amplitude. The model employs a cohesive zone approach, which combines damage mechanics and fracture mechanics, and requires only standard material data as input, namely the delamination toughness and the fatigue delamination growth curve. The proposed model was validated against delamination growth data obtained from a fatigue test conducted on a DCB specimen. The model predictions agree very well with the experimental results. This model is an initial step toward life prediction of composite structures subjected to complex fatigue regimes.

Role of modulus mismatch on crack propagation and toughness enhancement in bioinspired composites

Natural materials such as nacre exhibit a high resistance to crack propagation, inspiring the development of artificial composites imitating the structure of these biological composites. We use a phase field approach to study the role played by the elastic modulus mismatch between stiff and soft layers on crack propagation in such bioinspired composites. Our simulations show that the introduction of a thin layer of a soft phase in a stiff matrix can lead to arrest of a propagating crack and can also lead to crack branching. The crack branching observed in the phase field model is analyzed using a cohesive zone approach. Further, we show that the toughness of such a composite can be substantially higher than that of its constituents.

Cohesive zone modeling of intergranular fatigue damage in rolling contacts

Fatigue lives of rolling element bearings exhibit much scatter due to the statistical nature of the failure process. The localized character of contact stresses enhances the effects of microstructural features on fatigue life. In this paper, the growth of intergranular fatigue damage in rolling contacts is investigated. An explicit finite element model is developed which models the grain boundaries using an irreversible cohesive zone approach. The effects that the grain boundary properties play in fatigue life scatter and final spall patterns are presented and discussed. The predicted fatigue lives and spall patterns were found to be similar to experimental results.

Static and Fatigue Failures of Adhesively Bonded Laminate Joints in Moist Environments

Advanced structural adhesives are now an important joining technique in automobile and aerospace applications. The perceived uncertainty in the long-term structural performance of bonded members when subjected to static/fatigue loads in aggressive environments is probably restricting an even more widespread use of this joining technology. In this article, the effect of moisture on the static and fatigue resistances of adhesively bonded laminate joints was investigated. Experimental tests were performed on both aged and unaged adhesively bonded laminate joints for static and fatigue responses. Further, using a cohesive zone approach for the adhesive bondlines, a combined diffusion–stress analysis was developed to predict the progressive damage observed in the joints tested experimentally. The numerical predictions were found to be in good agreement with the experimental test results.

Modelling competitive delamination and debonding phenomena in composite T-Joints

Experimental studies on the failure mode of composite T-joint specimens, in the presence of adhesive interlaminar layers, are presented. Tests underline the role played by the interaction between delamination and debonding phenomena. Quasi static analyses of the tests are performed by means of explicit FE models. A modelling technique based on a cohesive zone approach is adopted to simulate damage propagation both in the adhesive interface and in the most critical interlaminar layers of laminates. All the numerical results are compared against the experimental evidences in terms of fracture patterns, of load vs. displacement responses and local strain levels.

NUMERICAL TREATMENT OF DAMAGE PROPAGATION IN AXIALLY COMPRESSED COMPOSITE AIRFRAME PANELS

In the design phase of stringer-stiffened composite airframe panels, it is a key issue to exploit material reserves as far as possible to create lighter and safer aircraft. A recent approach is to apply postbuckling design — standard for metallic panels — also to composite parts. This work focusses on the development of a simulation procedure which accurately predicts the postbuckling response of composite panels while accounting for damage propagation. For this purpose we employ a robust shell element formulation which allows for arbitrary stacking sequences as well as a variable location of the reference plane. A ply discount model is incorporated to account for intralaminar damage growth. The cohesive zone approach is implemented in a so-called interface element to predict interlaminar damage growth, respective skin–stringer separation. The numerical model is validated via a numerical example with experimental evidence.

The influence of the cohesive process zone in hydraulic fracturing modelling

This paper studies the importance of the cohesive zone in the modelling of a fluid driven fracture under plain strain conditions. The fracture is driven by pumping of an incompressible viscous fluid at the fracture inlet. Rock deformation is modeled for linear elastic and poroelastic solids. Fluid flow in the fracture is modeled by lubrication theory. The cohesive zone approach is used as the fracture propagation criterion. Finite element analysis was used to compute the solution for the crack length, the fracture opening and propagation pressure as a function of the time and distance from the wellbore. It is demonstrated that the crack profiles and the propagation pressures are larger in the case of elastic-softening cohesive model compared to the results of the rigid-softening cohesive model for both elastic and poroelastic cohesive solids. It is found that the results are affected by the slope of the loading branch of the cohesive model and they are nearly unaffected from the exact form of the softening branch. Furthermore, the size of the process zone, the fracture geometry and the propagation pressure increase with increasing confining stresses. These results may explain partially the discrepancies in net-pressures between field measurements and conventional model predictions.

Finite-Element Model for Failure Study of Two-Dimensional Triaxially Braided Composite

A new three-dimensional finite element model of two-dimensional triaxially braided composites is presented in this paper. This meso-scale modeling technique is used to examine and predict the deformation and damage observed in tests of straight sided specimens. A unit cell based approach is used to take into account the braiding architecture as well as the mechanical properties of the fiber tows, the matrix and the fiber tow-matrix interface. A 0 deg / plus or minus 60 deg. braiding configuration has been investigated by conducting static finite element analyses. Failure initiation and progressive degradation has been simulated in the fiber tows by use of the Hashin failure criteria and a damage evolution law. The fiber tow-matrix interface was modeled by using a cohesive zone approach to capture any fiber-matrix debonding. By comparing the analytical results to those obtained experimentally, the applicability of the developed model was assessed and the failure process was investigated.

A generalised damage model for constant amplitude fatigue loading of adhesively bonded joints

The fatigue resistance of adhesively bonded joints is an important aspect of reliable structural design in many sectors. In this paper, the effect of load ratio on the fatigue behaviour of adhesively bonded joints was investigated using both experimental and numerical approaches. Single lap joints were tested under cyclic loading at different load ratios and load levels to characterise their response. A numerical model that accounts for the load ratio effect in constant amplitude fatigue loading was developed to predict the response of these bonded joints. The progressive damage of the adhesive material was modelled using a cohesive zone approach with a bi-linear traction-separation response. Damage initiation and propagation phases were monitored using the backface-strain and in-situ video-microscopy techniques. The load ratio effect on the fatigue behaviour of adhesively bonded joints was successfully predicted using a strain-based fatigue damage model. The numerical results were found to be in good agreement with the experimentally observed fatigue damage evolution and failure life.

Elastic response of a carbon nanotube fiber reinforced polymeric composite: A numerical and experimental study

Premature failure due to low mechanical properties in the transverse direction to the fiber constitutes a fundamental weakness of fiber reinforced polymeric composites. A solution to this problem is being addressed through the creation of nanoreinforced laminated composites where carbon nanotubes are grown on the surface of fiber filaments to improve the matrix-dominated composite properties. The carbon nanotubes increase the effective diameter of the fiber and provide a larger interface area for the polymeric matrix to wet the fiber. A study was conducted to numerically predict the elastic properties of the nanoreinforced composites. A multiscale modeling approach and the Finite Element Method were used to evaluate the effective mechanical properties of the nanoreinforced laminated composite. The cohesive zone approach was used to model the interface between the nanotubes and the polymer matrix. The elastic properties of the nanoreinforced laminated composites including the elastic moduli, the shear modulus, and the Poisson’s ratios were predicted and correlated with iso-strain and iso-stress models. An experimental program was also conducted to determine the elastic moduli of the nanoreinforced laminated composite and correlate them with the numerical values.

Simulation of Buckling‐Induced Failure in Composite Laminates

AbstractThis contribution presents a simple model for the analysis of buckling–induced failure in thin–walled composite laminates in the framework of the finite element method. The plies are modeled with shear deformable geometrically non–linear four–node shell elements which are layered according to the classical laminate theory. Shear locking effects are reduced via the well–known assumed natural strains (ANS) approach. A ply discount model is applied for the successive failure of the plies. The cohesive zone approach which is implemented in so–called interface elements is employed for delamination. The failure processes are history dependent leading to non–recurring stiffness degradation in areas where damage is detected. A numerical example with experimental evidence highlights the performance and applicability of the proposed model. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A cohesive zone model for fatigue and creep–fatigue crack growth in single crystal superalloys

A numerical analysis using cohesive zone model under cyclic loading is proposed to develop a coupled predictive approach of crack growth in single crystal. The process of material damage during fatigue crack growth is described using an irreversible cohesive zone model, which governs the separation of the crack flanks and eventually leads to the formation of free surfaces. The cohesive zone element is modeled to accumulate fatigue damage during loadings and no damage during unloadings. This paper presents the damage model and its application in the study of the crack growth for precracked specimens. The use of cohesive zone approach is validated through a convergence study. Then, a general procedure of parameters calibration is presented in pure fatigue crack growth. In the last section, an extension of the cohesive zone model is presented in the case of creep–fatigue regime at high temperature. The model showed its capability to predict with a good agreement the crack growth in the case of complex loading and complex specimen geometries.

On the toughening of brittle materials by grain bridging: Promoting intergranular fracture through grain angle, strength, and toughness

The structural reliability of many brittle materials such as structural ceramics relies on the occurrence of intergranular, as opposed to transgranular, fracture in order to induce toughening by grain bridging. For a constant grain boundary strength and grain boundary toughness, the current work examines the role of grain strength, grain toughness, and grain angle in promoting intergranular fracture in order to maintain such toughening. Previous studies have illustrated that an intergranular path and the consequent grain bridging process can be partitioned into five distinct regimes, namely: propagate, kink, arrest, stall, and bridge. To determine the validity of the assumed intergranular path, the classical penetration/deflection problem of a crack impinging on an interface is re-examined within a cohesive zone framework for intergranular and transgranular fracture. Results considering both modes of propagation, i.e., a transgranular and intergranular path, reveal that crack-tip shielding is a natural outcome of the cohesive zone approach to fracture. Cohesive zone growth in one mode shields the opposing mode from the stresses required for cohesive zone initiation. Although stable propagation occurs when the required driving force is equivalent to the toughness for either transgranular or intergranular fracture, the mode of propagation depends on the normalized grain strength, normalized grain toughness, and grain angle. For each grain angle, the intersection of single path and multiple path solutions demarcates “strong” grains that increase the macroscopic toughness and “weak” grains that decrease it. The unstable transition to intergranular fracture reveals that an increasing grain toughness requires a growing region of the transgranular cohesive zone be near the cohesive strength. The inability of the body to provide the requisite stress field yields an overdriven and unstable configuration. The current results provide restrictions for the achievement of substantial toughening through intergranular fracture.

Steady-state tensile stresses during the growth of polycrystalline films

Tensile stresses that arise during the growth of polycrystalline films are described using a cohesive zone approach, along with a finite element model that accounts for different dihedral angles at grain boundary intersections with the growth surface. This combined approach predicts the maximum tensile stress as a function of the grain size and the grain boundary/surface energies. These relationships differ from those proposed previously. The model also indicates that grain boundary cusps can have a significant effect on the magnitude of tensile growth stresses, with sharper grain boundary cusps leading to lower steady-state tensile stresses in the film. Data from several materials with large tensile growth stresses are in reasonable agreement with the model. In particular, AlN films grown by metal organic chemical vapor deposition exhibit tensile stresses that are at or near the maximum predicted tensile values. The experimental results from these nitride films are also consistent with two other model predictions for growth at the tensile limit: the stresses are (i) independent of the growth rate and (ii) at (or close to) the fracture limit.