Bridging effects on Mixed Mode delamination: experiments and numerical simulation

Composite materials and, in particular, Carbon Fibre Reinforced Polymers (CFRP) have been well studied and developed in the past years due to their advanced mechanical characteristics. These materials are used in several different application fields, such as aerospace, automotive, energy production, bio-prosthesis and sport equipment. The combination of carbon fibers with epoxy resin allows obtaining materials characterized by high specific stiffness, low weight, and extremely high ultimate strength. Although the mechanical properties of the single carbon fiber are impressive, damage initiation often occurs at lower stresses. These materials are produced by stacking a sequence of several layers, which makes them prone to delamination. This process may lead to the creation of bridging fibers across the crack surfaces, which increases the total fracture toughness. Several efforts have been devoted in the past years to study the delamination process of composite materials under pure Mode I and pure Mode II. However, studies of delamination and bridging in Mixed Mode have not received adequate attention in the literature. The first goal of this project is to study the delamination process for unidirectional CFRP under Mixed Mode conditions. Experiments are performed over a wide range of different mode mixities, by using a Mixed Mode Bending (MMB) setting and monitoring the applied displacement, reaction force, crack propagation and internal strains. Axial strain values are measured in specific specimens by embedding optical fibers with Bragg grating sensors (FBGs) between the carbon layers. Delamination tests are performed at pure Mode I, Mixed Mode at 20%, 30%, 40%, 60% and pure Mode II, in order to obtain a complete set of experimental data. The results allowed characterizing both the energy release rate at crack initiation Gc and the corresponding bridging energy contribution Gb, as a function of the applied mode mixity. The second goal of this work is to create a numerical FE Model, based on cohesive elements, able to reproduce the correct delamination behavior and bridging contribution for each tested mode mixity, by using a unique cohesive law. Unfortunately, the cohesive law formulations for Mixed Mode delamination known so far show several limitations since they are not able to properly predict the delamination behavior in a MMB test when large scale bridging occurs. For this reason, an innovative mode-dependent cohesive formulation is implemented: it extends the constitutive laws of the previous models to incorporate the proper bridging contribution, by using an external customized routine. The bridging tractions are defined by three parameters: the corresponding energy contribution Gb, the maximum stress Ïmax and the crack opening displacement at failure ÎŽf . These bridging parameters are described by three different functions, dependent on the local mode mixity, by means of the coefficients ÎŸi =[ÎŸGb , ÎŸÏmax , ÎŸÎŽf ]. The coefficients ÎŸi are obtained by using an inverse method, where the strains measured by the FBGs and the ones computed by the Finite Element Model (FEM) are involved in an optimization process. In contrast to the standard Mixed Model models, this algorithm provides a unique mode-dependent cohesive law able to properly simulate all the different delamination tests, from pure Mode I up to pure Mode II, predicting the load, the crack propagation, the energy release rate (ERR) and the strains evolution.

Assessment of mechanical properties in unirradiated and irradiated zircaloys and steels with non-standard tests and finite element calculations

Emiliano Campitelli

Nuclear materials have been successfully employed in commercial fission reactors for many decades. Research and material development for advanced fission system and future thermo-nuclear fusion reactors have acquired maturity while great challenges remain to be taken up. The goal of the material scientist is to understand the way neutron irradiation and aggressive reactor environment alter the original material properties and to safely manage the operation conditions for each particular reactor component. In the framework of surveillance programme, the need has arisen to design experimental methods to be used with a limited amount of material for Post Irradiation Examination (PIE) of reactor components to test the integrity of those on a regular time basis. Having to deal with radioactive material, it is particularly important to devise experimental testing procedures as simple as possible but from which reliable information can be drawn. Within materials development programme, irradiations have continuously been performed either in reactors or with particle accelerators. In both cases, the irradiation volumes are usually limited. The concern was to optimize the volume of the irradiated samples in order to increase their number to obtain a good statistical representation of their mechanical behavior after irradiation, and to have a very definite and homogeneous damage dose and irradiation temperature. The concerns explained above originated the development of small-scale specimen testing methods. Advantage is taken of the fact that, within size and geometry limitations, some mechanical properties of a sample are independent of its absolute size. In this way it is possible to perform mechanical tests on samples of reduced volume that represents big advantages to face the aforementioned challenges. Non-standard test on very small specimen have also been proposed to extract mechanical properties of the bulk. If these non-standard testing methods are to be employed for PIE, it becomes necessary to develop modeling tool to understand under what circumstances they can provide useful information and specially how to obtain it. Finite element modeling (FEM) of the non-standard tests has played a key role in this sense, providing a link between standard test analysis and that of the non-standard ones. The goal of this work was to implement finite element models for non-standard tests to ultimately study the mechanical properties of Zircaloy cladding tube and tempered martensitic steels in the unirradiated and irradiated condition. One model was developed for ring tensile tests. It was first validated with a quite ductile iron-chromium ferritic alloy, for which ring and uniaxial tensile test were performed at room temperature. Using the constitutive behavior determined from the uniaxial tensile tests, the load – displacement curves of the ring tensile tests were very well reproduced. Another model was developed for the so-called small ball punch test, which consists in deforming a 3 mm diameter disk clamped between two dies with a ball puncher and to record the load – displacement curve. In order to validate the model, a series of ball punch tests and of tensile tests were carried out on the austenitic steel 316L at room temperature. In this last case, the ball punch test curves were also well reconstructed with the model. Based upon a simple analysis and simulation results, we showed that it is possible to obtain, by ring tensile tests, a quick and accurate assessment of the constitutive behavior of an unknown material, simply by processing the experimental force-elongation data in the same way as for uniaxial tests, taking half the ring perimeter as initial length and twice the ring cross section as the sample cross section. The ring tensile test method was used to determine the hoop mechanical properties of Zircaloy tubes used in fission reactors. Tensile tests were also performed in the axial direction of the Zircaloy tubes. Differences between the yield stress as well as the post-yield behaviors in the axial direction and those in the circumferential direction of the tube could be measured reflecting some component of the anisotropy of the tube. Ball punch specimens were cut also out of the tube in the radial direction and tested. Using the FE model for punch test, in which the anisotropy of the mechanical properties are taken into account through the Hill's theory, the values of the Hill's yield function parameters were estimated. The irradiation hardening of neutron irradiated Zircaloy tube was finally determined. The ball punch test model was extensively used for numerical investigations, to determine how the constitutive behavior of the materials (uniaxial true stress – true strain) employed as input acts in combination with other experimental factors (specimen thickness, friction coefficient) in mediating the shape of the experimental curves. In the light of the results, we derived calibrations between parameters of the non-standard and standard tests. For instance we proposed a new approach to determine the yield stress from the ball punch test. We also showed how the slope of the punch tests scales with the average flow stress of the material. The calibrations proposed in the past by authors and published in the open literature have been revisited and critically reviewed. Based upon the findings of the numerical studies, we propose a given methodology to unambiguously evaluate the material constitutive behavior of a material in a case where the only available data comes from various non-standard tests. Experimental ball punch test results obtained on proton-irradiated specimen (0.5 dpa and Tirr = 523 K), of the tempered martensitic steel, EUROFER97, have been obtained. The irradiation hardening was found equal to about 150 MPa, consistently with previous data on similar steels and irradiation conditions. From the simulations of the ball punch test curves of the irradiated specimens, it was concluded that the irradiation does not affect the strain hardening at relatively low fluence.

EPFL2005

Deformation and Damage in Lead-free Solder Joints

Milad Maleki

For environmental reasons, lead has been banned from microelectronic solder materials since the adoption of the RoHS legislation in 2006. A large number of investigations have lead to the development of new lead-free solder materials like the SnAgCu alloy which can satisfy most of the technological requirements. However, the long-time reliability of the lead-free candidates is still a crucial issue and in several cases, failure of electronic assemblies has been attributed to that of the solder joints. To overcome the present challenge in the soldering technology, the damage mechanisms occurring along the service life of lead-free solder joints like microstructure evolution, viscoplastic deformation as well as interfacial cracking must be better understood. The main scope of this thesis is to shed light on the complex interdependency of microstructures, deformation property and the interfacial fracture of solder joints in order to explain the change in the failure mode of solder joints from ductile to brittle interfacial fracture as well as the link between microstructural evolution and the change in the mechanical property of the solders. The first part of this research focused on characterization and macroscopic modeling of the fracture at the interface of SnAgCu solder and Cu substrate with a special attention on the viscoplastic nature of the bulk solder. For this purpose, the viscoplastic behavior of the solder joint was initially identified and the material parameters related to a unified constitutive viscoplastic model were determined. The interfacial fracture behavior of the joint was characterized by performing stable fracture tests at different strain rates. The results confirmed that the failure mode of the solder joint is a function of the loading rate. It was shown that an increase in the loading rate causes a decrease in the load-bearing capacity of the joint by enhancing the tendency to develop an interfacial failure. The interfacial crack propagation in the fracture tests were simulated by developing a detailed three-dimensional (3D) finite element (FE) model containing a cohesive interface and considering the viscoplastic behavior of the bulk solder. The influence of strain rate and viscoplasticity on the load-bearing capacity and failure behavior of the joint were pointed out by analyzing the simulation results. It was shown how the normal stress generated at the interface is limited by the significant viscoplastic relaxation developed in the bulk solder at low strain rates, while a large portion of the external work is transferred to the interface at higher rates which gives rise to interfacial fracture. The second part of this thesis focused on developing microstructure-based models in order to simulate the change in the macroscopic mechanical response of the SnAgCu solder caused by the microstructural evolution during thermal ageing. For this purpose, first, the 3D configurations of microstructures in different ageing conditions were visualized using a combination of synchrotron X-ray and FIB/SEM tomography techniques. Analyses showed that although the size and orientation of crystalline grains as well as morphology of dendrites in SnAgCu solder remain stable during ageing, two main morphological changes occur in the Ag3Sn and Cu6Sn5 intermetallic particles: spheroidizing of needle-shape intermetallics and coarsening due to bulk diffusion. The mechanical property of the solder and its phases at different ageing conditions were experimentally characterized. A significant decrease in the yield strength of the solder joint was identified because of thermal ageing and it was shown that the deformation behavior of the solder is governed by the morphometrics of the dispersed intermetallics. The link between the microstructures and the deformation behavior of solder was successfully simulated by developing a hybrid microstructure-based modeling approach. The average indirect strengthening of the intermetallics was modeled by incorporating the effects of geometrically necessary dislocation on the in-situ deformation behavior of the tin matrix. Subsequently, a micromechanical FE homogenization was considered to model the load-sharing behavior of the intermetallics. For this purpose, the tomographic images were directly used to generate 3D FE meshes of the actual microstructures and then the constitutive deformation behavior of the solder were determined by adopting two levels of numerical homogenization in the eutectic phase and over the whole joint. The decrease in the yield strength of solder due to ageing was explained through analyses of indicators in the models. It was demonstrated how the change in the morphometrics of intermetallics during ageing reduces the contribution of intermetallics in load-sharing as well as the in-situ strength of the matrix by causing a significant change in the strain distribution as well as particle size effects. The simulation results were experimentally verified and the capabilities as well as limitations of the developed approach were pointed out. Overall, the results of this research led to a proper understanding of the critical reliability issues in lead-free solders during isothermal ageing, i.e., microstructural coarsening and interfacial fracture. In addition, through this work, a set of methodologies for multi-scale modeling and experimental characterization of the damage and deformation in solder joints were developed and validated which can be extremely helpful for efficient use of the SnAgCu solders in electronic industry as well as designing new solder alloys with higher strength and better reliability for a safe transition to lead-free solders in critical applications.

EPFL2012

An experimental-numerical investigation of hydrothermal response in adhesively bonded composite structures

John Botsis, Luis Pablo Canal Casado, Hans Georg Limberger, Véronique Michaud, Roohollah Sarfaraz Khabbaz, Georgios Violakis

Water absorption and thermal response of adhesive composite joints were investigated by measurements and numerical simulations. Water diffusivity, saturation, swelling, and thermal expansion of the constituent materials and the joint were obtained from gravimetric experiments and strain measurements using embedded fiber Bragg grating (FBG) sensors. The mechanical response of these materials at different temperatures and water content was characterized by dynamic mechanical analysis. Thermal loading and water absorption in joint specimens were detected by monitoring the FBG wavelength shift caused by thermal expansion or water swelling. The measured parameters were used in finite element models to simulate the response of the embedded sensor. The good correlation of experimental data and simulations confirmed that the change in FBG wavelength could be accurately related to the thermal load or water absorption process. The suitability of the embedded FBG sensors for monitoring of water uptake in adhesive composite joints was demonstrated. (C) 2015 Elsevier Ltd. All rights reserved.