Irreversible Cohesive Zone Model Research Articles

Paintings crack initiation time caused by microclimate

The current paper aims to use an irreversible cohesive zone model to investigate the effects of temperature and relative humidity cycles on multilayer thin-film paintings. The homogenous one-dimensional paint layers composed of alkyd and acrylic gesso over a canvas foundation (support) with known constant thicknesses are considered as the mechanical model of painting. Experimental data was used for mathematical modeling of canvas as a linear elastic material and paint as a viscoelastic material with the Prony series. Growth of crack through the length of the paint layers under the low amplitude cyclic stresses are modeled by cyclic mechanical loadings. The three-dimensional system is modeled using a finite element method. Fatigue damage parameters such as crack initiation time and maximum loads are calculated by an irreversible cohesive zone model used to control the interface separation. In addition, the effects of initial crack length and layers thickness are studied. With the increase of the painting thickness and/or the initial crack length, the value of the maximum force increases. Moreover, by increasing the Relative Humidity (RH) and the temperature difference at loading by one cycle per day, the values of initiation time of delamination decrease. It is shown that the thickness of painting layers is the most important parameter in crack initiation times and crack growth rate in historical paintings in museums and conservation settings.

Crack propagation of a thin hard coating under cyclic loading: Irreversible cohesive zone model

The numerical study of the fatigue behaviour of steel and light alloy substrates when coated with thin hard coatings is limited. This paper aims to investigate the fatigue failure mechanism of the coating system by observing the initiation and propagation of cracks within the coating under the cyclic loading. The model coating system is composed of three layers: the TiN coating, a case-hardened diffusion zone and the H11 steel substrate. The cohesive elements were arranged evenly in the horizontal direction and vertically through the thickness of the coating layer in order to observe the crack initiation and propagation. The model coating system was indented by a spherical indenter of 300 μm radius. Both the coating and the substrate were characterised as being homogenous, with elastic properties followed by linearly-hardening plastic behaviour. The irreversible cohesive zone model, allowing for the local degradation of the material properties to be incorporated into the model, was employed to simulate the crack initiation and propagation under cyclic loading. It was observed that the crack was initiated at the edge of the contact area between the indenter and coated surface at early stage of loading cycles, then progressed rapidly through the thickness of the coating layer. The deepest crack was found at 1.4 μm below the top surface. The study has demonstrated that the irreversible cohesive zone model can be used to track the evolution of crack propagation with cyclic loading, therefore has the capability to predict the loading bearing capacity of the coating system under contact fatigue loading conditions.

A hysteresis cohesive approach for predicting mixed-mode delamination onset of composite laminates under cyclic loading: Part I, model development

A new approach is proposed to predict onset of fatigue-induced delamination in composite laminates under cyclic loading by progressive interface degradation. Based on the hysteresis cohesive zone approach, a new damage parameter is defined to construct an irreversible cohesive zone model. Residual displacement jump is introduced and used along with mixed-mode bilinear traction-separation law parameters for calculating the damage parameter. Fatigue-induced delamination onset is then predicted by proposing a damage criterion. 3-D Finite Element (FE) formulation is developed with proper elements for plies and also proper elements for the interface. Cyclic loading is also simulated mimicked by the MIN-MAX method. The current research is conducted in two parts as Part I and Part II. While this article focuses on the theoretical framework of the developed modeling, the numerical implementation of the modeling and also a comparison of the outputs with experimental observations will be presented in the companion paper as Part II.

The roles of yield strength mismatch, interface strength, and plastic strain gradients in fatigue crack growth across interfaces

An irreversible cohesive zone model was used to understand how plastic strain gradients and yield strength mismatches affect fatigue crack growth across bi-material and multilayer interfaces for a range of interface strengths. Parametric studies identified regimes of penetration through the interface, deflection into the interface, and a transition where cracks extend on both paths. Plastic strain gradients strongly influence the transition regime, and a yield strength mismatch is necessary to cause deflection. For crack growth across an interlayer, interactions between the interfaces occur when the crack-tip plastic zone spans the interlayer. Plastic strain gradients promote penetration through the interlayer.

Plastic strain gradients and transient fatigue crack growth: A computational study

Fatigue crack growth is analyzed for steady state and overload conditions. The model combines an elastic-plastic strain gradient hardening material and an irreversible cohesive zone model. Plastic strain gradients are found not to affect steady-state fatigue crack growth but play a key role in the overload response. Plastic strain gradient hardening lowers plastic strain magnitudes and alters the spatial distribution of plastic strain. This leads to reduced crack closure and higher crack growth rates during and after the overload. Using classical plasticity alone to describe fatigue crack growth following an overload is thus nonconservative.

Numerical analysis of plasticity induced crack closure based on an irreversible cohesive zone model

During the last years different numerical models based on node to node crack growth scheme have been employed to study the effect of plasticity induced crack closure (PICC). This paper presents a numerical analysis of PICC based on a cohesive zone model (CZM) ith with irreversible damage that employs a crack growth method coupled with cyclic plasticity at crack tip and phenomenological fracture. The CZM produces a plastic wake from volumetric plastic strain that is different than that generated in uncoupled methods. Thus, the proposed model generates a high deviatoric plastic strain, allowing the closure study without strain ratcheting at first node behind the crack tip. Results obtained from the proposed numerical analysis are compared with those obtained from experimental fatigue tests conducted on a 2024-T3 aluminum alloy compact-tension specimens (CT). Numerical results show an excellent correlation with those obtained experimentally highlighting the ability of the proposed CZM to capture the influence of crack tip plasticity in the evaluation of crack closure phenomenon.

Investigation of the initiation and propagation of cracks in the coated surface of spur gear: An application of irreversible cohesive zone model

Spur gears are the most common type of gears for industry, due to its simple structures and low costs of manufacture. Under the action of rolling contact fatigue, the main mode of the coated teeth failure is surface or subsurface originated micro-pitting, leading to the debonding of coating from substrate, fracture in the coating and even subsurface failure. Failure may originate from initiation of cracks, and its growth and propagation, however, basic failure mechanism is still not clear. In this paper, a comprehensive finite element modeling procedure including submodelling techniques and irreversible cohesive zone modelling techniques (CZM) is developed to investigate the failure mechanisms under the rolling contact fatigue loading. The details of the localized stresses distribution will be simulated using the submodelling technique. Irreversible CZM will be used to simulate the initiation and propagation of the cracks in the coated surface of the spur gears under the cyclic contact loading.

Cohesive zone modeling of fatigue crack growth in brazed joints

Fatigue crack growth in low carbon steel brazed joints with copper filler metal is modeled by an irreversible Cohesive Zone Model. Strain-controlled fatigue tests are performed on the brazed specimens, and the corresponding fatigue crack initiation and propagation lives are recorded. A cyclic damage evolution law is coupled to a bilinear Cohesive Zone Model to irreversibly account for the joint stiffness degradation over the number of cycles. The damage law parameters are calibrated based on Irwin’s analytical solution and the experimental fatigue crack growth data. Using the characterized irreversible Cohesive Zone Model, the fatigue crack growth is simulated and the corresponding fatigue crack growth rates are obtained. The agreement between the numerical results and the experimental data shows the applicability of the Cohesive Zone Model to fatigue crack growth analysis and life estimation of brazed joints.

Prediction of delamination in multilayer artist paints under low amplitude fatigue loading

The objective of this study is to model the effect of low amplitude cyclic stresses on multilayer paint systems found in works of art. Acrylic gesso grounds with superimposed alkyd paint layers on canvas were investigated. Data from uniaxial testing of free-standing paint films was used to determine the constitutive properties of the paint. Peel tests were performed to determine the cohesive zone properties of the paint interface. A finite element model of a coating on a primed canvas substrate was subjected to combined cyclic and static mechanical loadings typically experienced by fine art paintings. Interface separation was controlled by an irreversible cohesive zone model that includes damage accumulation due to cyclic loading. Fatigue crack initiation times in years were predicted for various conditions including ordinary and extreme histories that paintings may experience in museum and conservation settings.

Numerical analysis for effects of shot peening on fatigue crack growth

In the present work numerical analysis for effects of shot peening on fatigue crack growth are reported and discussed. Simulations reported in the present work use irreversible cohesive zone model and are based on experimental data for a Nickel-based superalloy. The capability of the cohesive zone model to catch the effects of short crack is investigated. The two-dimensional computations fit known experimental records in the CT specimen which confirms that the cohesive zone model has the potential for engineering application. The fatigue crack growth of shot-peened specimens are studied for different loading amplitudes and different shot peening intensities. The numerical results reveal that the crack initiation position and time depend not only on the shot peening intensity but also on the cyclic loading amplitude. Retardation of fatigue crack growth is more effective at lower loading amplitude for shot-peened specimens, and higher applied loading will eliminate the beneficial effects of shot peening.

Predicting the influence of overload and loading mode on fatigue crack growth: A numerical approach using irreversible cohesive elements

This paper describes an irreversible cohesive zone model to simulate fatigue crack growth. The model includes a three-dimensional (3-D) cohesive law that follows a distinct loading/unloading path and a damage evolution mechanism that reflects a gradual degradation of cohesive properties of the material under the influence of cyclic loading. To overcome convergence difficulties arising from nonlinearity of the cohesive zone model, the stabilization technique and the viscous regularization of the constitutive law are employed. For high-cycle fatigue applications, a damage extrapolation scheme is adopted to reduce computational cost. The irreversible cohesive zone model is implemented in the finite element software ABAQUS through a user defined subroutine and is used to predict fatigue crack growth in a compact-tension-shear (CTS) specimen with an emphasis on the extrinsic influence of overload for different loading modes. The numerical results show good agreement with experimental records documented in the open literature and capture the essential features of fatigue crack growth for various loading conditions. This indicates that the irreversible cohesive zone model can serve both as an accurate and efficient tool for the prediction of fatigue crack growth.

Computational simulations of delamination wear in a coating system

Delamination wear constitutes one relevant wear process in many materials. In particular, wear failure through delamination is relevant for material systems where a coating is present on a substrate material. A computational modeling approach is presented that aims to describe the processes of formation and growth of wear delaminations. The model is based on the cohesive zone model approach. An irreversible cohesive zone model is used in a parametric numerical study of delamination wear in a coating system. The model predicts trends in agreement with the trends emerging from Archard's law. The proposed modeling approach has the advantage that details of the delamination wear process can numerically be studied, and that a unified framework from delamination initiation and propagation is provided.

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.

Computations of fatigue crack growth with strain gradient plasticity and an irreversible cohesive zone model

Computations of fatigue crack growth with a first-order strain gradient plasticity (SGP) model and an irreversible cohesive zone model are reported. SGP plays a significant role in the model predictions and leads to increased fatigue crack growth rates relative to predictions with classical plasticity. Increased magnitudes of tractions and material separation at the crack tip together with reduced crack closure appear as the cause for accelerated crack growth in SGP. Under plane strain conditions SGP appears as an essential feature of the development of the crack closure zone. Size effects are explored relative to changes in internal material length scale as well as to structural length scales.

Numerical simulation of constraint effects in fatigue crack growth

The computational analysis of constraint effects on fatigue crack growth is discussed. An irreversible cohesive zone model is used in the computations to describe the processes of material separation under cyclic loading. This approach is promising for the investigation of fatigue crack growth under constraint as the energy dissipation due to the formation of new crack surface and cyclic plastic deformation is accounted for independently. Fatigue crack growth in multi-layer structures under consideration of different levels of T-stress are conducted with a modified boundary layer model. Fatigue crack growth is computed as a function of layer thickness and T-stress for constant and variable amplitude loading cases.

A numerical analysis of constraint effects in fatigue crack growth by use of an irreversible cohesive zone model

The analysis of constraint effects in fatigue crack growth in multi-layer structures is discussed. The process of material separation under cyclic loading is described by a cohesive zone model (CZM) with an irreversible constitutive relationship. The traction–separation behavior does not follow a predefined path, but is dependent on the evolution of the damage dependent cohesive zone properties. A modified boundary layer model is used in simulations of fatigue crack growth along the centerline crack of the metal layer sandwiched between two elastic substrates. Fatigue crack growth is computed for a series of values of metal layer thickness under constant and variable amplitude loading conditions. The results of the computations demonstrate that certain combinations of load magnitude, layer thickness and material properties results in significant constrain effects in fatigue crack growth. The influence of these constraint effects on fatigue crack growth rates and on crack closure processes is determined. The evolutions of the traction–separation law, the accumulated and current plastic zones, as well as the stress fields during the crack propagation are discussed.

A numerical study of transient fatigue crack growth by use of an irreversible cohesive zone model

Transient fatigue crack growth is studied for a material system in which the crack tip is shielded due to crack bridging. The process of material separation during fatigue crack growth is described by the use of an irreversible cohesive zone model. In contrast to past developments of cohesive zone models, the traction–separation behavior does not follow a predefined path, but is dependent on the evolution of the damage dependent cohesive zone properties. The model definition is given and the basic uniaxial response of the model documented. The cohesive zone model is subsequently applied in a numerical study of transient fatigue crack growth. Single overload cases are computed to demonstrate the effects of variations in the cohesive zone properties. Block loading sequences with variations in the amplitude and the load ratio are computed. Model predictions qualitatively compare well to experimentally observed effects of fatigue crack growth transients in materials with crack bridging zones.