Calculation of adhesive and cohesive fracture toughness of a thin brittle coating on a polymer substrate

Determination of fracture parameters for brittle coatings with a sub-micron thickness is not a straightforward task. Since direct evaluation through testing with for instance a double cantilever beam or compact tension tests is hardly applicable due to the extreme thinness of the coating, methods such as the fragmentation test are used. When a structure with a brittle coating on a soft substrate is strained, the coating develops a crack pattern with parallel cracks perpendicular to the loading direction. The crack density (number of cracks per unit length) increases with strain up to a saturation value. Analytical formulas to model the fragmentation process exist but are limited to elastic materials. In this work finite element simulations are applied in order to deduce the adhesive and cohesive fracture properties of the interface and coating respectively from experimental data. The simulations include both the plastic behaviour of the substrate and debonding of the coating from the substrate, the latter achieved by application of a cohesive zone model. The main conclusion is that the plastic dissipation within the substrate must be correctly accounted for to get realistic interfacial and coating fracture toughness values.

Modeling of multiple cracking and decohesion of a thin film on a polymer substrate

Yves Leterrier, Jan-Anders Månson

Thin brittle films on polymer substrates are finding increasing use as gas barriers for example in the medical and food packaging industries and also for the next generation of ultra-light displays based on flexible polymer substrates. In order to determine the durability of the barrier under thermal and mechanical loads, test procedures and corresponding data reduction methods are needed to feed the analysis models. One of the tests frequently employed for this kind of multi-layer material systems is the fragmentation test, whose designation comes from the progressively denser pattern of parallel cracks developing when the specimen is loaded under uniaxial tension. From the crack-density versus strain data obtained, a critical strain for crack growth and an assessment of the adhesion of the coating to substrate can be obtained. However, no accepted data reduction methods exist to extract material properties from the test or inversely, successfully predict the crack density as a function of a set of material properties without fitting parameters. In an earlier paper, the authors presented a finite element based analysis methodology to determine the fracture toughness of both the coating and the interface from the fragmentation data. In the simulations, the plastic constitutive behavior of the substrate and the debonding of the coating from the substrate were explicitly included, the latter by use of a cohesive zone model. In this paper an extension of this methodology is presented that enables crack-density evolution with strain to be predicted. The results presented comprise comparisons with experiments to validate the methodology and the influence of (i) coating toughness, (ii) interface toughness and (iii) coating thickness on crack density versus strain.

2006

Mixed-Mode Static and Fatigue Failure Criteria for Adhesively-Bonded FRP Joints

Moslem Shahverdi

Fiber-reinforced polymer (FRP) composites are increasingly used in many load-bearing structures. Joints are the most critical structural elements as they often become the weak links in engineering structures. Bonding and bolting are two of the main joining techniques used for composite elements but, although bolted and bonded joints have their advantages and disadvantages, adhesively-bonded joints are often preferred. This is thanks to their better performance in terms of cost-effective structures with uniformly distributed stresses without the need for cutting fastener holes that result in high stress concentrations in the FRP adherends at the edges of the holes. In addition, due to the absence of stress concentrations, adhesively-bonded joints exhibit better fatigue behavior. However, the efficient and reliable use of adhesively-bonded joints requires a thorough understanding of their failure mechanisms under mixed-mode quasi-static and fatigue loading conditions. In real structural applications, failure of adhesively-bonded joints occurs due to crack initiation and propagation under varying mixed-mode ratios. Since it is difficult to describe this progressive fracture in a structural joint, fracture joints with constant mode-mixity ratios are used to determine the strain energy release rates for crack initiation and propagation. Subsequently, mixed-mode failure criteria based on the determined strain energy release rates can be established and used to model/predict the fatigue and fracture behaviors of structural joints. The main objectives of this thesis were to understand the fracture and fatigue behaviors of adhesively-bonded FRP fracture joints under Mode I, Mode II, and mixed-Mode I/II loading conditions and, consequently, develop mixed-mode static and fatigue failure criteria applicable to structural joints. To fulfill these objectives a combined experimental-analytical-numerical study was undertaken. Double cantilever beam (DCB-Mode I), end-load split (ELS-Mode II), and mixed-mode bending (MMB-Mode I/II) specimens were examined under quasi-static and constant amplitude fatigue loading. Analytical approaches were used to determine the strain energy release rates under quasi-static and fatigue loading, whereas phenomenological models were developed to characterize the fatigue and fracture behaviors of the joints. A new approach designated the “extended global method” was established and applied for the analysis of the quasi-static and fatigue experimental data and the fracture mode partitioning in the mixed-mode experiments. In parallel, non-linear finite element models were developed to simulate the quasi-static fracture behavior and investigate the effects of both the existing asymmetry and the observed fiber bridging on the fracture behavior of the examined joints. The bridging zone was modeled by zero-thickness cohesive elements. An exponential traction-separation description of the cohesive zone model was shown to appropriately model the fiber bridging and calculate its contribution to the fracture energy under quasi-static loading. The FE models were successfully employed for the separation of the fracture parameters, i.e. strain energy released at the crack tip (Gtip) and the amount of energy released along the crack-bridging zone (Gbr), in the quasi-static mixed-mode failure criterion for crack propagation. In addition to the studies on the quasi-static fracture behavior of the joints, a new phenomenological fatigue crack growth formulation for the modeling and prediction of Rratio effects on the Mode I fatigue behavior of adhesively-bonded joints was also derived. The model was used for prediction of the fatigue behavior of the examined joints under different R-ratios. The results proved that the model could accurately simulate the fatigue behavior of the examined joints and was also capable of predicting behavior exhibited under unseen loading conditions, i.e. the R-ratios used for estimating the model parameters were different from those used for validating its prediction capability. The experimental results and numerical analyses combined with the phenomenological models were used to establish mixed-mode static and fatigue failure criteria for crack initiation and crack propagation for the adhesively-bonded joints. The derived mixed-mode failure criteria can be used for simulating/predicting the crack initiation and progressive crack propagation in structural joints comprising the same adhesive and adherends.

EPFL2013

Damage evolution in coated cemented carbides under compressive contact loads

Maria-Simona Moldovan

This work deals principally with two important issues and their interrelation: the evolution of damage in coated cemented carbide tools used for cold forming, and the assessment of mechanical behavior of cemented carbides under compressive contact loads. Damage evolution in ironing tools is qualitatively investigated by planar and cross-sectional microscopical observations. Several mechanisms of damage are identified by taking into account the circumferential distribution along the surface of the ironing tools: coating wear and/ fracture, plastic deformation and fracture of the substrate. In the context of damage location in the substrate, the emphasis is put on the study of damage following all processing steps in substrate and coating preparation. This analysis aims at determining whether the substrate is weakened or not by the mechanical and chemical pre-treatment prior to coating. Spherical indentation testing is used as an experimental procedure to reproduce the compression stress state during cold forming. Large indenter tips (300 microns) are employed for testing cemented carbides in an effort to minimize the effects of material structural inhomogeneities. The behavior of cemented carbides under compressive loads is governed by the reversibility of deformation induced by indentation. A unique feature revealed by analysis of experimental load-displacement indentation curves is the positive energy balance, in that a gain of energy is evidenced after a loading-unloading cycle. Two hypotheses are developed for interpreting such a behavior: the strain induced martensitic transformation of the cobalt ductile phase and the thermal residual stresses in the composite. Substrate weakening subsequent to mechanical and chemical pretreatment prior to coating is expected to have a particular role on the indentation behavior of cemented carbides. The impact of substrate damage on the indentation parameters is identified by a parametric study using finite element simulations in which the damage is considered uniform. In reality, the damage distribution over the surface is rather irregular. In this context, a statistical approach is used for assessment of the material indentation parameters. The failure of coating/substrate systems under compressive contact loads is investigated by finite element simulations. The first failure events are identified by considering that system failure occurs either by substrate plastic deformation or coating fracture. The response of coated systems to spherical indentation is synthesized in damage diagrams which can predict whether the coating or the substrate fails first. The possibility for using such diagrams for assessing the evolution of damage in coated cemented carbide tools is highlighted.